Finite Group Databasebeta

← C2×#23776883 #35195224

Subgroups — C2×#23776883 #35195224

Order 20224.

12314 conjugacy classes of subgroups.

The subgroup lattice has 1556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11929624C211yesmaximal, characteristic, complemented
2C22×#41×D79C211yesmaximal, characteristic, complemented
3#23776883C2132yesmaximal, direct product factor
4C2×#19099231C211yesmaximal, characteristic, complemented
5C2×#19099226C211yesmaximal, characteristic, complemented
6C2×#19099223C211yesmaximal, characteristic, complemented
7C2×#19099219C211yesmaximal, characteristic, complemented
8C2×#19099215C211yesmaximal, characteristic, complemented
9C2×#19099211C212yesmaximal, complemented
10C2×#19099210C211yesmaximal, characteristic, complemented
11C2×#19099205C212yesmaximal, complemented
12C2×#19099204C211yesmaximal, characteristic, complemented
13C2×#19099200C212yesmaximal, complemented
14C2×#19099197C211yesmaximal, characteristic, complemented
15C2×#19099195C212yesmaximal, complemented
16C2×#19099110C212yesmaximal, complemented
17C2×#19099109C211yesmaximal, characteristic, complemented
18C2×#19099075C211yesmaximal, characteristic, complemented
19C2×#19099072C212yesmaximal, complemented
20C2×#19099072C212yesmaximal, complemented
21C2×#19099031C211yesmaximal, characteristic, complemented
22C22×C4×C22⋊D79C211yesmaximal, characteristic, complemented
23C2×C4×D4×D79C212yesmaximal, complemented
24C2×#525×C79C211yesmaximal, characteristic, complemented
25C22×#11929625C2211yescharacteristic, complemented
26C22×#11929624—216no—
27C22×#11929624C2211yescharacteristic
28C22×#11929624C2212yescomplemented
29C22×#11929624C2211yescharacteristic, complemented
30C22×#11929624C2211yescharacteristic, complemented
31C22×#11929624C2212yescomplemented
32C22×#11929624C2212yescomplemented
33C22×#11929624C2211yescharacteristic, complemented
34C22×#11929624C22116yescomplemented
35C22×#11929623C2212yescomplemented
36C22×#11929623C2211yescharacteristic, complemented
37C2×#41×D79—216no—
38C2×#41×D79C22116yescomplemented
39C23×Dic158C2211yescharacteristic, complemented
40C22×Q8×D79C2211yescharacteristic, complemented
41C23×D316C2211yescharacteristic, complemented
42C23×C22⋊D79C2211yescharacteristic
43C23×C22⋊D79C2212yescomplemented
44C22×D4×D79C2212yes—
45C22×D4×D79C2212yescomplemented
46C22×D4×D79C2211yescharacteristic, complemented
47C23×C4×D79C2212yescomplemented
48C23×C4×D79C2212yescomplemented
49C23×C4×D79C2211yescharacteristic, complemented
50#19099231C22116yescomplemented
51#19099226C22116yescomplemented
52#19099223C22116yescomplemented
53#19099219C22116yescomplemented
54#19099215C22116yescomplemented
55#19099211C22132yescomplemented
56#19099210C22116yescomplemented
57#19099205C22132yescomplemented
58#19099204C22116yescomplemented
59#19099200C22132yescomplemented
60#19099197C22116yescomplemented
61#19099195C22132yescomplemented
62#19099110C22132yescomplemented
63#19099109C22116yescomplemented
64C2×#14579160C2212yescomplemented
65C2×#14579159C2211yescharacteristic, complemented
66C2×#14579157C2212yescomplemented
67C2×#14579157C2211yescharacteristic, complemented
68C2×#14579150C2211yescharacteristic, complemented
69C2×#14579148C2211yescharacteristic, complemented
70C2×#14579147C2212yescomplemented
71C2×#14579147C2212yescomplemented
72#19099075C22116yescomplemented
73#19099072C22132yescomplemented
74#19099072C22132yescomplemented
75C2×#14579146C2212yescomplemented
76C2×#14579146C2212yescomplemented
77C2×#14579145C2212yescomplemented
78C2×#14579143C2212yescomplemented
79C2×#14579143C2212yescomplemented
80C2×#14579141C2211yescharacteristic, complemented
81C2×#14579141C2211yescharacteristic, complemented
82C2×#14579139C2212yescomplemented
83C2×#14579139C2212yescomplemented
84C2×#14579138C2212yescomplemented
85C2×#14579138C2212yescomplemented
86C2×#14579136C2211yescharacteristic, complemented
87C2×#14579136C2212yescomplemented
88C2×#14579136C2211yescharacteristic, complemented
89C2×#14579134C2212yescomplemented
90C2×#14579134C2212yescomplemented
91C2×#14579134C2212yescomplemented
92C2×#14579134C2212yescomplemented
93C2×#14579133C2212yescomplemented
94C2×#14579133C2212yescomplemented
95C2×#14579133C2212yescomplemented
96C2×#14579133C2212yescomplemented
97C2×#14579132C2212yescomplemented
98C2×#14579131C2212yescomplemented
99C2×#14579131C2212yescomplemented
100C2×#14579131C2212yescomplemented
101C2×#14579129C2212yescomplemented
102C2×#14579129C2212yescomplemented
103#19099031C22116yescomplemented
104C2×#14579126C2211yescharacteristic, complemented
105C2×#14579126C2211yescharacteristic, complemented
106C2×C4×D316C2212yescomplemented
107C2×C4×D316C2212yescomplemented
108C2×D4×Dic79C2212yescomplemented
109C2×#14579123C2212yescomplemented
110C2×#14579123C2211yescharacteristic, complemented
111C2×#14579123C2211yescharacteristic, complemented
112C2×C4×C22⋊D79C2211yescharacteristic
113C2×C4×C22⋊D79C2211yescharacteristic
114C2×C4×C22⋊D79C2212yescomplemented
115C2×C4×C22⋊D79C2211yescharacteristic, complemented
116C2×C4×C22⋊D79C2211yescharacteristic, complemented
117C2×C4×C22⋊D79C2211yescharacteristic, complemented
118C2×C4×C22⋊D79C2211yescharacteristic, complemented
119C2×C4×C22⋊D79C2211yescharacteristic, complemented
120C2×C4×C22⋊D79C2211yescharacteristic, complemented
121C2×C4×C22⋊D79C2212yescomplemented
122C2×C4×C22⋊D79C22116yescomplemented
123C2×(C22⋊D79)⋊C4C2212yes—
124C2×(C22⋊D79)⋊C4C2212yescomplemented
125C2×(C22⋊D79)⋊C4C2212yescomplemented
126C2×(C22⋊D79)⋊C4C2212yescomplemented
127C4×D4×D79C22132yescomplemented
128C2×#14579118C2212yescomplemented
129C22×Dic79⋊C4C2211yescharacteristic, complemented
130C2×C4⋊C4×D79C2212yescomplemented
131C22×C22⋊Dic79C2211yescharacteristic, complemented
132C22×(C2×D79)⋊C4C2211yescharacteristic, complemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C22⋊C4×D79C2212yescomplemented
135C22×C4×Dic79C2211yescharacteristic, complemented
136C2×C42×D79C2212yescomplemented
137C22×#41×C79C2211yescharacteristic, complemented
138C24×C4×C79C2211yescharacteristic, complemented
139#525×C79C22116yescomplemented
140C2×#123×C79C2212yescomplemented
141C2×C22⋊Q8×C79C2211yescharacteristic, complemented
142C2×C22⋊Q8×C79C2211yescharacteristic, complemented
143C2×#121×C79C2211yescharacteristic, complemented
144C2×#121×C79C2211yescharacteristic, complemented
145C2×#120×C79C2212yescomplemented
146C2×C4×D4×C79C2212yescomplemented
147C2×C4×D4×C79C2212yescomplemented
148C2×#117×C79C2211yescharacteristic, complemented
149C24×D79C2312yes—
150C24×D79C2312yes—
151C24×D79C2311yescharacteristic
152C2×#11929625—28no—
153C2×#11929625C2318yescomplemented
154C2×#11929624—28no—
155C2×#11929624—2128no—
156C2×#11929624—28no—
157C2×#11929624—28no—
158C2×#11929624—216no—
159C2×#11929624—216no—
160C2×#11929624—216no—
161C2×#11929624D4116yescomplemented
162C2×#11929624C2318yes—
163C2×#11929624C23116yescomplemented
164C2×#11929624C2318yescomplemented
165C2×#11929624C2318yescomplemented
166C2×#11929624C23116yescomplemented
167C2×#11929624C23116yescomplemented
168C2×#11929624C2318yescomplemented
169C2×#11929623—28no—
170C2×#11929623—216no—
171C2×#11929623C23116yescomplemented
172C2×#11929623C2318yescomplemented
173#41×D79—2128no—
174C22×Dic158—28no—
175C22×Dic158C2312yes—
176C22×Dic158C2312yes—
177C22×Dic158C2311yescharacteristic
178C22×Dic158C2311yescharacteristic
179C22×Dic158C2318yescomplemented
180C2×Q8×D79—28no—
181C2×Q8×D79C2318yescomplemented
182C22×D316—28no—
183C22×D316C2312yes—
184C22×D316C2312yes—
185C22×D316C2312yes—
186C22×D316C2311yescharacteristic
187C22×D316C2312yes—
188C22×D316C2311yescharacteristic
189C22×D316C2318yescomplemented
190C22×C22⋊D79—216no—
191C22×C22⋊D79—28no—
192C22×C22⋊D79C2318yes—
193C22×C22⋊D79C2312yes—
194C22×C22⋊D79C2311yescharacteristic
195C22×C22⋊D79C2311yescharacteristic
196C22×C22⋊D79C2311yescharacteristic
197C22×C22⋊D79C2312yes—
198C22×C22⋊D79C2312yes—
199C22×C22⋊D79C2312yes—
200C22×C22⋊D79C2312yes—
201C22×C22⋊D79C2312yes—
202C22×C22⋊D79C2312yes—
203C22×C22⋊D79C2312yes—
204C22×C22⋊D79C2311yescharacteristic
205C22×C22⋊D79C23116yescomplemented
206C2×D4×D79—28no—
207C2×D4×D79—216no—
208C2×D4×D79—216no—
209C2×D4×D79C23116yes—
210C2×D4×D79C23116yescomplemented
211C2×D4×D79C2318yescomplemented
212C23×Dic79C2311yescharacteristic
213C23×Dic79C2311yescharacteristic
214C23×Dic79C2312yes—
215C23×Dic79C2312yes—
216C23×Dic79C2311yescharacteristic
217C22×C4×D79—28no—
218C22×C4×D79—216no—
219C22×C4×D79—216no—
220C22×C4×D79C2312yes—
221C22×C4×D79C2312yes—
222C22×C4×D79C2312yes—
223C22×C4×D79C2312yes—
224C22×C4×D79C2312yes—
225C22×C4×D79C2311yescharacteristic
226C22×C4×D79C2311yescharacteristic
227C22×C4×D79C2312yes—
228C22×C4×D79C2311yescharacteristic
229C22×C4×D79C2311yescharacteristic
230C22×C4×D79C2312yes—
231C22×C4×D79C2312yes—
232C22×C4×D79C23116yescomplemented
233C22×C4×D79C23116yescomplemented
234C22×C4×D79C2318yescomplemented
235#14579160C23116yescomplemented
236#14579159C2318yescomplemented
237#14579157C23116yescomplemented
238#14579157C2318yescomplemented
239#14579150C2318yescomplemented
240#14579148C2318yescomplemented
241#14579147C23116yescomplemented
242#14579147C23116yescomplemented
243#14579146C23116yescomplemented
244#14579146C23116yescomplemented
245#14579145C23116yescomplemented
246#14579143C23116yescomplemented
247#14579143C23116yescomplemented
248#14579141C2318yescomplemented
249#14579141C2318yescomplemented
250#14579139C23116yescomplemented
251#14579139C23116yescomplemented
252#14579138C23116yescomplemented
253#14579138C23116yescomplemented
254#14579136C2318yescomplemented
255#14579136C23116yescomplemented
256#14579136C2318yescomplemented
257#14579134C23116yescomplemented
258#14579134C23116yescomplemented
259#14579134C23116yescomplemented
260#14579134C23116yescomplemented
261#14579133C23116yescomplemented
262#14579133C23116yescomplemented
263#14579133C23116yescomplemented
264#14579133C23116yescomplemented
265#14579132C23116yescomplemented
266#14579131C23116yescomplemented
267#14579131C23116yescomplemented
268#14579131C23116yescomplemented
269#14579129C23116yescomplemented
270#14579129C23116yescomplemented
271#14579126C2318yescomplemented
272#14579126C2318yescomplemented
273C4×D316C23116yescomplemented
274C4×D316C23116yescomplemented
275D4×Dic79C23116yescomplemented
276#14579123C2318yescomplemented
277#14579123C2318yescomplemented
278#14579123C23116yescomplemented
279C4×C22⋊D79C2318yes—
280C4×C22⋊D79C2318yes—
281C4×C22⋊D79C2318yescomplemented
282C4×C22⋊D79C2318yescomplemented
283C4×C22⋊D79C2318yescomplemented
284C4×C22⋊D79C23116yescomplemented
285C4×C22⋊D79C2318yescomplemented
286C4×C22⋊D79C2318yescomplemented
287C4×C22⋊D79C2318yescomplemented
288C4×C22⋊D79C23116yescomplemented
289(C22⋊D79)⋊C4C23116yes—
290(C22⋊D79)⋊C4C23116yescomplemented
291(C22⋊D79)⋊C4C23116yescomplemented
292(C22⋊D79)⋊C4C23116yescomplemented
293#14579118C23116yescomplemented
294C2×C4⋊Dic79C2312yes—
295C2×C4⋊Dic79C2312yes—
296C2×Dic79⋊C4C2311yescharacteristic
297C2×Dic79⋊C4C2312yes—
298C2×Dic79⋊C4C2311yescharacteristic
299C2×Dic79⋊C4C2311yescharacteristic
300C2×Dic79⋊C4C2311yescharacteristic
301C2×Dic79⋊C4C2312yes—
302C2×Dic79⋊C4C2312yes—
303C2×Dic79⋊C4C2312yes—
304C2×Dic79⋊C4C2318yescomplemented
305C4⋊C4×D79C23116yescomplemented
306C2×C22⋊Dic79C2311yescharacteristic
307C2×C22⋊Dic79C2312yes—
308C2×C22⋊Dic79C2311yescharacteristic
309C2×C22⋊Dic79C2311yescharacteristic
310C2×C22⋊Dic79C2311yescharacteristic
311C2×C22⋊Dic79C2312yes—
312C2×C22⋊Dic79C2318yescomplemented
313C2×(C2×D79)⋊C4C2311yescharacteristic
314C2×(C2×D79)⋊C4C2312yes—
315C2×(C2×D79)⋊C4C2312yes—
316C2×(C2×D79)⋊C4C2312yes—
317C2×(C2×D79)⋊C4C2311yescharacteristic
318C2×(C2×D79)⋊C4C2311yescharacteristic
319C2×(C2×D79)⋊C4C2311yescharacteristic
320C2×(C2×D79)⋊C4C2312yes—
321C2×(C2×D79)⋊C4C2312yes—
322C2×(C2×D79)⋊C4C2312yes—
323C2×(C2×D79)⋊C4C2312yes—
324C2×(C2×D79)⋊C4C2312yes—
325C2×(C2×D79)⋊C4C2318yescomplemented
326C22⋊C4×D79C23116yescomplemented
327C22⋊C4×D79C23116yescomplemented
328C2×C4×Dic79C2311yescharacteristic
329C2×C4×Dic79C2312yes—
330C2×C4×Dic79C2312yes—
331C2×C4×Dic79C2311yescharacteristic
332C2×C4×Dic79C2311yescharacteristic
333C2×C4×Dic79C2311yescharacteristic
334C2×C4×Dic79C2318yescomplemented
335C42×D79C23116yescomplemented
336C25×C79C2311yescharacteristic
337C2×#41×C79—28no—
338C2×#41×C79C2318yescomplemented
339C22×Q8×C79C2311yescharacteristic
340C22×D4×C79C2312yes—
341C22×D4×C79C2312yes—
342C22×D4×C79C2311yescharacteristic
343C22×D4×C79C2312yes—
344C23×C4×C79—28no—
345C23×C4×C79C2311yescharacteristic
346C23×C4×C79C2311yescharacteristic
347C23×C4×C79C2312yes—
348C23×C4×C79C2311yescharacteristic
349C23×C4×C79C2311yescharacteristic
350C23×C4×C79C2311yescharacteristic
351C23×C4×C79C2311yescharacteristic
352C23×C4×C79C2318yescomplemented
353#123×C79C23116yescomplemented
354C22⋊Q8×C79C2318yescomplemented
355C22⋊Q8×C79C2318yescomplemented
356#121×C79C2318yescomplemented
357#121×C79C2318yescomplemented
358#120×C79C23116yescomplemented
359C4×D4×C79C23116yescomplemented
360C4×D4×C79C23116yescomplemented
361#117×C79C2318yescomplemented
362C2×C4⋊C4×C79C2311yescharacteristic
363C2×C4⋊C4×C79C2311yescharacteristic
364C2×C4⋊C4×C79C2312yes—
365C2×C4⋊C4×C79C2312yes—
366C2×C22⋊C4×C79C2312yes—
367C2×C22⋊C4×C79C2312yes—
368C2×C22⋊C4×C79C2312yes—
369C2×C22⋊C4×C79C2312yes—
370C2×C22⋊C4×C79C2312yes—
371C2×C42×C79C2312yes—
372C23×D79—24no—
373C23×D79—28no—
374C23×D79—28no—
375C23×D79—28no—
376C23×D79—28no—
377C23×D79—24no—
378C23×D79—44no—
379C23×D79—44no—
380C23×D79—42no—
381C23×D79C2411yescharacteristic
382C23×D79C2412yes—
383C23×D79C2418yes—
384C23×D79C2418yes—
385C23×D79C2414yes—
386C23×D79C2412yes—
387C23×D79C2411yescharacteristic
388#11929625—232no—
389#11929624—232no—
390#11929624—264no—
391#11929624—264no—
392#11929624—232no—
393#11929624—232no—
394#11929624—264no—
395#11929624C2×D4164yescomplemented
396#11929623—232no—
397#11929623—264no—
398C2×Dic158—28no—
399C2×Dic158—28no—
400C2×Dic158—232no—
401C2×Dic158—24no—
402C2×Dic158C2×D418yescomplemented
403C2×Dic158C2418yes—
404C2×Dic158C2418yes—
405C2×Dic158C2414yes—
406C2×Dic158C2414yes—
407Q8×D79—232no—
408C2×D316—232no—
409C2×D316—28no—
410C2×D316—28no—
411C2×D316—28no—
412C2×D316—24no—
413C2×D316—44no—
414C2×D316C2×D418yescomplemented
415C2×D316C2418yes—
416C2×D316C2414yes—
417C2×D316C2418yes—
418C2×D316C2418yes—
419C2×D316C2418yes—
420C2×D316C2414yes—
421C2×C22⋊D79—28no—
422C2×C22⋊D79—28no—
423C2×C22⋊D79—28no—
424C2×C22⋊D79—24no—
425C2×C22⋊D79—28no—
426C2×C22⋊D79—24no—
427C2×C22⋊D79—28no—
428C2×C22⋊D79—28no—
429C2×C22⋊D79—24no—
430C2×C22⋊D79—264no—
431C2×C22⋊D79—232no—
432C2×C22⋊D79—44no—
433C2×C22⋊D79C2×D4116yescomplemented
434C2×C22⋊D79#4118yescomplemented
435C2×C22⋊D79C2418yes—
436C2×C22⋊D79C2418yes—
437C2×C22⋊D79C2418yes—
438C2×C22⋊D79C2418yes—
439C2×C22⋊D79C2418yes—
440C2×C22⋊D79C2418yes—
441C2×C22⋊D79C2414yes—
442C2×C22⋊D79C2414yes—
443C2×C22⋊D79C2414yes—
444C2×C22⋊D79C2418yes—
445C2×C22⋊D79C2418yes—
446C2×C22⋊D79C2414yes—
447D4×D79—232no—
448D4×D79—264no—
449D4×D79—264no—
450C22×Dic79—28no—
451C22×Dic79—28no—
452C22×Dic79—24no—
453C22×Dic79—24no—
454C22×Dic79—42no—
455C22×Dic79C2411yescharacteristic
456C22×Dic79C2412yes—
457C22×Dic79C2418yes—
458C22×Dic79C2414yes—
459C22×Dic79C2418yes—
460C22×Dic79C2411yescharacteristic
461C22×Dic79C2411yescharacteristic
462C22×Dic79C2411yescharacteristic
463C22×Dic79C2414yes—
464C22×Dic79C2411yescharacteristic
465C22×Dic79C2414yes—
466C22×Dic79C2412yes—
467C22×Dic79C2411yescharacteristic
468C2×C4×D79—28no—
469C2×C4×D79—28no—
470C2×C4×D79—28no—
471C2×C4×D79—264no—
472C2×C4×D79—264no—
473C2×C4×D79—28no—
474C2×C4×D79—28no—
475C2×C4×D79—24no—
476C2×C4×D79—24no—
477C2×C4×D79—28no—
478C2×C4×D79—24no—
479C2×C4×D79—24no—
480C2×C4×D79—232no—
481C2×C4×D79—44no—
482C2×C4×D79C2×D4116yescomplemented
483C2×C4×D79C2418yes—
484C2×C4×D79C2414yes—
485C2×C4×D79C2418yes—
486C2×C4×D79C2414yes—
487C2×C4×D79C2418yes—
488C2×C4×D79C2418yes—
489C2×C4×D79C2414yes—
490C2×C4×D79C2418yes—
491C2×C4×D79C2418yes—
492C2×C4×D79C2414yes—
493C2×C4×D79C2418yes—
494C2×C4×D79C2418yes—
495C4⋊Dic79C2418yes—
496C4⋊Dic79C2418yes—
497Dic79⋊C4C2414yes—
498Dic79⋊C4C2418yes—
499Dic79⋊C4C2414yes—
500Dic79⋊C4C2414yes—
501Dic79⋊C4C2414yes—
502Dic79⋊C4C2418yes—
503Dic79⋊C4C2418yes—
504Dic79⋊C4C2418yes—
505C22⋊Dic79C2414yes—
506C22⋊Dic79C2418yes—
507C22⋊Dic79C2414yes—
508C22⋊Dic79C2414yes—
509C22⋊Dic79C2414yes—
510C22⋊Dic79C2418yes—
511(C2×D79)⋊C4C2414yes—
512(C2×D79)⋊C4C2418yes—
513(C2×D79)⋊C4C2418yes—
514(C2×D79)⋊C4C2418yes—
515(C2×D79)⋊C4C2414yes—
516(C2×D79)⋊C4C2414yes—
517(C2×D79)⋊C4C2414yes—
518(C2×D79)⋊C4C2418yes—
519(C2×D79)⋊C4C2418yes—
520(C2×D79)⋊C4C2418yes—
521(C2×D79)⋊C4C2418yes—
522(C2×D79)⋊C4C2418yes—
523C4×Dic79C2414yes—
524C4×Dic79C2418yes—
525C4×Dic79C2418yes—
526C4×Dic79C2414yes—
527C4×Dic79C2414yes—
528C4×Dic79C2414yes—
529C24×C79—24no—
530C24×C79—24no—
531C24×C79—42no—
532C24×C79C2412yes—
533C24×C79C2411yescharacteristic
534C24×C79C2414yes—
535C24×C79C2411yescharacteristic
536C24×C79C2411yescharacteristic
537#41×C79—232no—
538C2×Q8×C79—24no—
539C2×Q8×C79C2414yes—
540C2×D4×C79—28no—
541C2×D4×C79—28no—
542C2×D4×C79—24no—
543C2×D4×C79—44no—
544C2×D4×C79C2418yes—
545C2×D4×C79C2414yes—
546C2×D4×C79C2418yes—
547C2×D4×C79C2418yes—
548C22×C4×C79—24no—
549C22×C4×C79—24no—
550C22×C4×C79—24no—
551C22×C4×C79—24no—
552C22×C4×C79—28no—
553C22×C4×C79—24no—
554C22×C4×C79—232no—
555C22×C4×C79C2×D418yescomplemented
556C22×C4×C79C2411yescharacteristic
557C22×C4×C79C2412yes—
558C22×C4×C79C2414yes—
559C22×C4×C79C2414yes—
560C22×C4×C79C2414yes—
561C22×C4×C79C2414yes—
562C22×C4×C79C2418yes—
563C22×C4×C79C2412yes—
564C22×C4×C79C2412yes—
565C22×C4×C79C2411yescharacteristic
566C22×C4×C79C2414yes—
567C22×C4×C79C2411yescharacteristic
568C22×C4×C79C2411yescharacteristic
569C22×C4×C79C2414yes—
570C4⋊C4×C79C2414yes—
571C4⋊C4×C79C2414yes—
572C4⋊C4×C79C2418yes—
573C4⋊C4×C79C2418yes—
574C22⋊C4×C79C2418yes—
575C22⋊C4×C79C2418yes—
576C22⋊C4×C79C2418yes—
577C22⋊C4×C79C2418yes—
578C22⋊C4×C79C2418yes—
579C42×C79C2418yes—
580C23×C79—22no—
581C23×C79—22no—
582C23×C79—22no—
583C23×C79—22no—
584C23×C79—24no—
585C23×C79—28no—
586C23×C79—22no—
587C23×C79—22no—
588C23×C79—24no—
589C23×C79—28no—
590C23×C79—24no—
591C23×C79—22no—
592C23×C79—44no—
593C23×C79—416no—
594C23×C79C22×D414yes—
595C23×C79C2×#4114yescomplemented
596C23×C79C2514yes—
597C23×C79C2512yes—
598C23×C79C2512yes—
599C23×C79C2512yes—
600C23×C79C2511yescharacteristic
601C22×D79—22no—
602C22×D79—24no—
603C22×D79—24no—
604C22×D79—22no—
605C22×D79—28no—
606C22×D79—24no—
607C22×D79—22no—
608C22×D79—22no—
609C22×D79—24no—
610C22×D79—216no—
611C22×D79—24no—
612C22×D79—22no—
613C22×D79—216no—
614C22×D79—216no—
615C22×D79—216no—
616C22×D79—28no—
617C22×D79—48no—
618C22×D79—44no—
619C22×D79—48no—
620C22×D79—432no—
621C22×D79—416no—
622C22×D79—432no—
623C22×D79C22×D418yes—
624C22×D79C2×#4114yescomplemented
625C22×D79C2512yes—
626C22×D79C2514yes—
627C22×D79C2514yes—
628C22×D79C2512yes—
629Q8×C79—28no—
630D4×C79—216no—
631D4×C79—216no—
632D4×C79—28no—
633D4×C79—48no—
634C2×C4×C79—22no—
635C2×C4×C79—24no—
636C2×C4×C79—22no—
637C2×C4×C79—28no—
638C2×C4×C79—24no—
639C2×C4×C79—24no—
640C2×C4×C79—28no—
641C2×C4×C79—216no—
642C2×C4×C79—28no—
643C2×C4×C79—28no—
644C2×C4×C79—28no—
645C2×C4×C79C22×D414yes—
646C2×C4×C79C22×D414yes—
647C2×C4×C79C22×D4116yescomplemented
648C2×C4×C79C2514yes—
649C2×C4×C79C2514yes—
650C2×C4×C79C2512yes—
651C2×C4×C79C2514yes—
652C2×C4×C79C2512yes—
653C2×C4×C79C2512yes—
654C2×C4×C79C2512yes—
655C22⋊D79—216no—
656C22⋊D79—28no—
657C22⋊D79—216no—
658C22⋊D79—216no—
659C22⋊D79—28no—
660C22⋊D79—216no—
661C22⋊D79—216no—
662C22⋊D79—216no—
663C22⋊D79—28no—
664C22⋊D79—48no—
665C22⋊D79C22×D4132yescomplemented
666C22⋊D79C2×#41116yescomplemented
667C2×Dic79—22no—
668C2×Dic79—24no—
669C2×Dic79—22no—
670C2×Dic79—28no—
671C2×Dic79—22no—
672C2×Dic79—22no—
673C2×Dic79—22no—
674C2×Dic79—216no—
675C2×Dic79—216no—
676C2×Dic79—28no—
677C2×Dic79—44no—
678C2×Dic79C22×D418yes—
679C2×Dic79C2×#4114yescomplemented
680C2×Dic79C2512yes—
681C2×Dic79C2512yes—
682C2×Dic79C2512yes—
683C2×Dic79C2512yes—
684C2×Dic79C2514yes—
685C2×Dic79C2512yes—
686C2×Dic79C2514yes—
687C2×Dic79C2512yes—
688D316—216no—
689D316—216no—
690D316—216no—
691D316—28no—
692D316—48no—
693D316C22×D4116yescomplemented
694C4×D79—216no—
695C4×D79—216no—
696C4×D79—28no—
697C4×D79—28no—
698C4×D79—28no—
699C4×D79—216no—
700C4×D79—28no—
701C4×D79—216no—
702C4×D79—216no—
703C4×D79—216no—
704C4×D79—48no—
705C4×D79C22×D4132yescomplemented
706Dic158—28no—
707Dic158—216no—
708Dic158—216no—
709Dic158C22×D4116yescomplemented
710C22×C79—22no—
711C22×C79—22no—
712C22×C79—22no—
713C22×C79—22no—
714C22×C79—28no—
715C22×C79—28no—
716C22×C79—22no—
717C22×C79—24no—
718C22×C79—22no—
719C22×C79—24no—
720C22×C79—24no—
721C22×C79—22no—
722C22×C79—416no—
723C22×C79—48no—
724C22×C79—44no—
725C22×C79C23×D414yes—
726C22×C79C23×D412yes—
727C22×C79C22×#4112yes—
728C22×C79C22×#4114yescomplemented
729C22×C79#58512yes—
730C22×C79C2611yescharacteristic
731C2×D79—22no—
732C2×D79—24no—
733C2×D79—22no—
734C2×D79—24no—
735C2×D79—28no—
736C2×D79—216no—
737C2×D79—24no—
738C2×D79—22no—
739C2×D79—22no—
740C2×D79—24no—
741C2×D79—24no—
742C2×D79—22no—
743C2×D79—432no—
744C2×D79—416no—
745C2×D79—432no—
746C2×D79—44no—
747C2×D79—48no—
748C2×D79C23×D418yes—
749C2×D79C22×#4114yescomplemented
750C4×C79—22no—
751C4×C79—22no—
752C4×C79—24no—
753C4×C79—24no—
754C4×C79—24no—
755C4×C79C23×D414yes—
756C4×C79C23×D414yes—
757Dic79—24no—
758Dic79—22no—
759Dic79—22no—
760Dic79—22no—
761Dic79—22no—
762Dic79—22no—
763Dic79C23×D418yes—
764Dic79C22×#4114yescomplemented
765C2×D4×#41—791nomaximal, Sylow
766C2×C79—24no—
767C2×C79—24no—
768C2×C79—44no—
769C2×C79—42no—
770C2×C79D4×#4114yescomplemented
771C2×C79C24×D411yescharacteristic
772C2×C79C23×#4111yescharacteristic
773C2×C79C2×#58511yescharacteristic
774D79—24no—
775D79—28no—
776D79—42no—
777D79—44no—
778C23×#41—791no—
779C23×#41—791no—
780D4×#41—7932no—
781C2×#550—791no—
782C2×D4×Q8—791no—
783C2×#548—791no—
784C2×#548—791no—
785C2×#547—792no—
786C2×#547—791no—
787C2×#546—792no—
788C2×#546—791no—
789C2×#546—791no—
790C2×#546—792no—
791C2×D42—791no—
792C2×D42—792no—
793C2×#532—791no—
794C2×#532—792no—
795C2×#525—792no—
796C2×#525—792no—
797C2×#525—791no—
798C2×#525D7911yescharacteristic, complemented
799C2×C4×#41—791no—
800C22×C4×D4—791no—
801C22×C4×D4—792no—
802C79C2×D4×#4111yescharacteristic, complemented, Sylow
803C22×#41—7916no—
804C22×#41—791no—
805C22×#41—792no—
806C22×#41—791no—
807C22×#41—791no—
808C22×#41—792no—
809C22×#41—792no—
810C22×#41—791no—
811C22×#41—791no—
812C22×#41—792no—
813C22×#41—791no—
814C22×#41—7916no—
815C22×#41—15816no—
816C22×#41—15816no—
817C22×#41C2×D7911yescharacteristic, complemented
818C23×Q8—791no—
819C23×Q8—791no—
820C23×D4—792no—
821C23×D4—791no—
822C23×D4—792no—
823C23×D4—791no—
824C23×D4—792no—
825C23×D4—791no—
826C24×C4—792no—
827C24×C4—792no—
828C24×C4—791no—
829C24×C4C2×D7911yescharacteristic, complemented
830#550—7916no—
831D4×Q8—7916no—
832#548—7916no—
833#548—7916no—
834#547—7932no—
835#547—7916no—
836#546—7932no—
837#546—7916no—
838#546—7916no—
839#546—7932no—
840D42—7916no—
841D42—7932no—
842#532—7916no—
843#532—7932no—
844C2×C4⋊Q8—791no—
845C2×C4⋊Q8—792no—
846C2×#127—791no—
847C2×#127—792no—
848C2×#124—791no—
849C2×#124—791no—
850C2×#124—792no—
851C2×#124—792no—
852#525—7932no—
853#525—7932no—
854#525—7916no—
855#525C2×D79116yescomplemented
856C2×#123—792no—
857C2×#123—792no—
858C2×#123—792no—
859C2×#123—792no—
860C2×#123—792no—
861C2×#123C2×D7912yescomplemented
862C2×C22⋊Q8—792no—
863C2×C22⋊Q8—791no—
864C2×C22⋊Q8—792no—
865C2×C22⋊Q8—791no—
866C2×C22⋊Q8—792no—
867C2×C22⋊Q8—792no—
868C2×C22⋊Q8C2×D7911yescharacteristic, complemented
869C2×C22⋊Q8C2×D7911yescharacteristic, complemented
870C2×#121—792no—
871C2×#121—792no—
872C2×#121—792no—
873C2×#121—792no—
874C2×#121—792no—
875C2×#121—791no—
876C2×#121—791no—
877C2×#121—792no—
878C2×#121—792no—
879C2×#121—792no—
880C2×#121—792no—
881C2×#121—792no—
882C2×#121C2×D7911yescharacteristic, complemented
883C2×#121C2×D7911yescharacteristic, complemented
884C2×#120—792no—
885C2×#120—792no—
886C2×#120—792no—
887C2×#120—792no—
888C2×#120—792no—
889C2×#120C2×D7912yescomplemented
890C4×#41—7916no—
891C2×C4×Q8—791no—
892C2×C4×Q8—791no—
893C2×C4×D4—792no—
894C2×C4×D4—791no—
895C2×C4×D4—791no—
896C2×C4×D4—791no—
897C2×C4×D4—792no—
898C2×C4×D4—791no—
899C2×C4×D4—791no—
900C2×C4×D4—791no—
901C2×C4×D4—791no—
902C2×C4×D4—791no—
903C2×C4×D4—792no—
904C2×C4×D4—7916no—
905C2×C4×D4—7932no—
906C2×C4×D4—792no—
907C2×C4×D4—791no—
908C2×C4×D4—791no—
909C2×C4×D4—792no—
910C2×C4×D4—792no—
911C2×C4×D4—792no—
912C2×C4×D4—792no—
913C2×C4×D4—792no—
914C2×C4×D4—792no—
915C2×C4×D4C2×D7912yescomplemented
916C2×C4×D4C2×D7912yescomplemented
917C2×#117—792no—
918C2×#117C2×D7911yescharacteristic, complemented
919C22×C4⋊C4—791no—
920C22×C4⋊C4—792no—
921C22×C22⋊C4—791no—
922C22×C22⋊C4—791no—
923C22×C22⋊C4—792no—
924C22×C22⋊C4—792no—
925C22×C42—791no—
926C22×C42—792no—
927C25—792no—
928C25—791no—
929C25—792no—
930C25C22×D7911yescharacteristic
931C2×#41—28no—
932C2×#41—798no—
933C2×#41—7916no—
934C2×#41—798no—
935C2×#41—7916no—
936C2×#41—798no—
937C2×#41—7916no—
938C2×#41—7916no—
939C2×#41—798no—
940C2×#41—798no—
941C2×#41—7916no—
942C2×#41—798no—
943C2×#41—15816no—
944C2×#41—15816no—
945C2×#41—15816no—
946C2×#41—1588no—
947C2×#41—1588no—
948C2×#41—158128no—
949C2×#41—15816no—
950C2×#41—1588no—
951C2×#41—1588no—
952C2×#41—158128no—
953C2×#41—1588no—
954C2×#41C22×D7918yescomplemented
955C22×Q8—798no—
956C22×Q8—791no—
957C22×Q8—792no—
958C22×Q8—792no—
959C22×Q8—791no—
960C22×Q8—798no—
961C22×Q8—1588no—
962C22×Q8—1588no—
963C22×Q8C22×D7911yescharacteristic
964C22×D4—792no—
965C22×D4—791no—
966C22×D4—792no—
967C22×D4—791no—
968C22×D4—791no—
969C22×D4—792no—
970C22×D4—791no—
971C22×D4—798no—
972C22×D4—792no—
973C22×D4—792no—
974C22×D4—792no—
975C22×D4—792no—
976C22×D4—792no—
977C22×D4—7916no—
978C22×D4—7916no—
979C22×D4—7916no—
980C22×D4—798no—
981C22×D4—792no—
982C22×D4—791no—
983C22×D4—792no—
984C22×D4—792no—
985C22×D4—792no—
986C22×D4—791no—
987C22×D4—798no—
988C22×D4—1588no—
989C22×D4—15816no—
990C22×D4—1588no—
991C22×D4—15816no—
992C22×D4—15816no—
993C22×D4—1588no—
994C22×D4C22×D7912yes—
995C22×D4C22×D7912yes—
996C22×D4C22×D7911yescharacteristic
997C22×D4C22×D7912yes—
998C23×C4—28no—
999C23×C4—791no—
1000C23×C4—792no—
1001C23×C4—792no—
1002C23×C4—791no—
1003C23×C4—791no—
1004C23×C4—792no—
1005C23×C4—792no—
1006C23×C4—792no—
1007C23×C4—792no—
1008C23×C4—792no—
1009C23×C4—792no—
1010C23×C4—791no—
1011C23×C4—792no—
1012C23×C4—791no—
1013C23×C4—7916no—
1014C23×C4—7916no—
1015C23×C4—798no—
1016C23×C4—791no—
1017C23×C4—791no—
1018C23×C4—792no—
1019C23×C4—15816no—
1020C23×C4—15816no—
1021C23×C4—1588no—
1022C23×C4C22×D7911yescharacteristic
1023C23×C4C22×D7911yescharacteristic
1024C23×C4C22×D7911yescharacteristic
1025C23×C4C22×D7911yescharacteristic
1026C23×C4C22×D7912yes—
1027C23×C4C22×D7911yescharacteristic
1028C23×C4C22×D7911yescharacteristic
1029C23×C4C22×D7918yescomplemented
1030C4⋊Q8—798no—
1031C4⋊Q8—7916no—
1032#127—798no—
1033#127—7916no—
1034#124—798no—
1035#124—798no—
1036#124—7916no—
1037#124—7916no—
1038#123—7916no—
1039#123—7916no—
1040#123—7916no—
1041#123—7916no—
1042#123—7916no—
1043#123C22×D79116yescomplemented
1044C22⋊Q8—7916no—
1045C22⋊Q8—798no—
1046C22⋊Q8—7916no—
1047C22⋊Q8—798no—
1048C22⋊Q8—7916no—
1049C22⋊Q8—7916no—
1050C22⋊Q8C22×D7918yescomplemented
1051C22⋊Q8C22×D7918yescomplemented
1052#121—7916no—
1053#121—7916no—
1054#121—7916no—
1055#121—7916no—
1056#121—7916no—
1057#121—798no—
1058#121—798no—
1059#121—7916no—
1060#121—7916no—
1061#121—7916no—
1062#121—7916no—
1063#121—7916no—
1064#121C22×D7918yescomplemented
1065#121C22×D7918yescomplemented
1066#120—7916no—
1067#120—7916no—
1068#120—7916no—
1069#120—7916no—
1070#120—7916no—
1071#120C22×D79116yescomplemented
1072C4×Q8—798no—
1073C4×Q8—798no—
1074C4×D4—7916no—
1075C4×D4—798no—
1076C4×D4—798no—
1077C4×D4—798no—
1078C4×D4—7916no—
1079C4×D4—798no—
1080C4×D4—798no—
1081C4×D4—798no—
1082C4×D4—798no—
1083C4×D4—798no—
1084C4×D4—7916no—
1085C4×D4—7916no—
1086C4×D4—798no—
1087C4×D4—798no—
1088C4×D4—7916no—
1089C4×D4—7916no—
1090C4×D4—7916no—
1091C4×D4—7916no—
1092C4×D4—7916no—
1093C4×D4—7916no—
1094C4×D4C22×D79116yescomplemented
1095C4×D4C22×D79116yescomplemented
1096#117—7916no—
1097#117C22×D7918yescomplemented
1098C2×C4⋊C4—791no—
1099C2×C4⋊C4—792no—
1100C2×C4⋊C4—791no—
1101C2×C4⋊C4—791no—
1102C2×C4⋊C4—791no—
1103C2×C4⋊C4—792no—
1104C2×C4⋊C4—798no—
1105C2×C4⋊C4—792no—
1106C2×C4⋊C4—792no—
1107C2×C4⋊C4—792no—
1108C2×C4⋊C4—792no—
1109C2×C4⋊C4—7916no—
1110C2×C4⋊C4C22×D7912yes—
1111C2×C4⋊C4C22×D7911yescharacteristic
1112C2×C4⋊C4C22×D7911yescharacteristic
1113C2×C4⋊C4C22×D7912yes—
1114C2×C22⋊C4—791no—
1115C2×C22⋊C4—791no—
1116C2×C22⋊C4—791no—
1117C2×C22⋊C4—792no—
1118C2×C22⋊C4—791no—
1119C2×C22⋊C4—798no—
1120C2×C22⋊C4—792no—
1121C2×C22⋊C4—791no—
1122C2×C22⋊C4—791no—
1123C2×C22⋊C4—792no—
1124C2×C22⋊C4—791no—
1125C2×C22⋊C4—792no—
1126C2×C22⋊C4—792no—
1127C2×C22⋊C4—791no—
1128C2×C22⋊C4—798no—
1129C2×C22⋊C4—792no—
1130C2×C22⋊C4—792no—
1131C2×C22⋊C4—792no—
1132C2×C22⋊C4—792no—
1133C2×C22⋊C4—792no—
1134C2×C22⋊C4—7916no—
1135C2×C22⋊C4—7916no—
1136C2×C22⋊C4C22×D7912yes—
1137C2×C22⋊C4C22×D7912yes—
1138C2×C22⋊C4C22×D7912yes—
1139C2×C22⋊C4C22×D7912yes—
1140C2×C22⋊C4C22×D7912yes—
1141C2×C42—792no—
1142C2×C42—791no—
1143C2×C42—792no—
1144C2×C42—791no—
1145C2×C42—798no—
1146C2×C42—791no—
1147C2×C42—791no—
1148C2×C42—7916no—
1149C2×C42C22×D7912yes—
1150C24—24no—
1151C24—24no—
1152C24—42no—
1153C24—3162no—
1154C24—3164no—
1155C24—3164no—
1156C24—798no—
1157C24—794no—
1158C24—798no—
1159C24—791no—
1160C24—792no—
1161C24—792no—
1162C24—791no—
1163C24—1588no—
1164C24—1588no—
1165C24—1584no—
1166C24—1588no—
1167C24—1588no—
1168C24—1584no—
1169C24C23×D7912yes—
1170C24C23×D7911yescharacteristic
1171C24C23×D7914yes—
1172C24C23×D7911yescharacteristic
1173C24C23×D7911yescharacteristic
1174#41—232no—
1175#41—7964no—
1176#41—15864no—
1177#41—15864no—
1178#41—15864no—
1179#41—15832no—
1180#41—15832no—
1181#41—15864no—
1182#41—15832no—
1183#41—15832no—
1184#41—15832no—
1185C2×Q8—24no—
1186C2×Q8—794no—
1187C2×Q8—798no—
1188C2×Q8—798no—
1189C2×Q8—794no—
1190C2×Q8—798no—
1191C2×Q8—1588no—
1192C2×Q8—1588no—
1193C2×Q8—15832no—
1194C2×Q8—15832no—
1195C2×Q8—1584no—
1196C2×Q8C23×D7914yes—
1197C2×D4—28no—
1198C2×D4—28no—
1199C2×D4—24no—
1200C2×D4—44no—
1201C2×D4—3164no—
1202C2×D4—3164no—
1203C2×D4—798no—
1204C2×D4—798no—
1205C2×D4—794no—
1206C2×D4—798no—
1207C2×D4—7916no—
1208C2×D4—794no—
1209C2×D4—794no—
1210C2×D4—798no—
1211C2×D4—794no—
1212C2×D4—798no—
1213C2×D4—798no—
1214C2×D4—798no—
1215C2×D4—798no—
1216C2×D4—798no—
1217C2×D4—798no—
1218C2×D4—794no—
1219C2×D4—798no—
1220C2×D4—798no—
1221C2×D4—798no—
1222C2×D4—794no—
1223C2×D4—798no—
1224C2×D4—15832no—
1225C2×D4—1588no—
1226C2×D4—1588no—
1227C2×D4—1588no—
1228C2×D4—1588no—
1229C2×D4—1584no—
1230C2×D4—1588no—
1231C2×D4—1588no—
1232C2×D4—15864no—
1233C2×D4—15864no—
1234C2×D4—15832no—
1235C2×D4—15832no—
1236C2×D4—15864no—
1237C2×D4—1584no—
1238C2×D4—1588no—
1239C2×D4—1588no—
1240C2×D4—1584no—
1241C2×D4—1588no—
1242C2×D4—1584no—
1243C2×D4C23×D7918yes—
1244C2×D4C23×D7918yes—
1245C2×D4C23×D7914yes—
1246C2×D4C23×D7918yes—
1247C22×C4—24no—
1248C22×C4—24no—
1249C22×C4—24no—
1250C22×C4—24no—
1251C22×C4—24no—
1252C22×C4—28no—
1253C22×C4—232no—
1254C22×C4—3164no—
1255C22×C4—3162no—
1256C22×C4—794no—
1257C22×C4—798no—
1258C22×C4—791no—
1259C22×C4—792no—
1260C22×C4—798no—
1261C22×C4—7916no—
1262C22×C4—791no—
1263C22×C4—791no—
1264C22×C4—791no—
1265C22×C4—794no—
1266C22×C4—791no—
1267C22×C4—791no—
1268C22×C4—792no—
1269C22×C4—794no—
1270C22×C4—798no—
1271C22×C4—798no—
1272C22×C4—798no—
1273C22×C4—798no—
1274C22×C4—798no—
1275C22×C4—794no—
1276C22×C4—794no—
1277C22×C4—798no—
1278C22×C4—798no—
1279C22×C4—794no—
1280C22×C4—798no—
1281C22×C4—794no—
1282C22×C4—1588no—
1283C22×C4—1588no—
1284C22×C4—15864no—
1285C22×C4—15864no—
1286C22×C4—1588no—
1287C22×C4—1588no—
1288C22×C4—1588no—
1289C22×C4—1588no—
1290C22×C4—1588no—
1291C22×C4—1584no—
1292C22×C4—1584no—
1293C22×C4—1584no—
1294C22×C4—1584no—
1295C22×C4—1584no—
1296C22×C4—1588no—
1297C22×C4—1584no—
1298C22×C4—15832no—
1299C22×C4D4×D7918yescomplemented
1300C22×C4C23×D7912yes—
1301C22×C4C23×D7912yes—
1302C22×C4C23×D7911yescharacteristic
1303C22×C4C23×D7912yes—
1304C22×C4C23×D7911yescharacteristic
1305C22×C4C23×D7914yes—
1306C22×C4C23×D7914yes—
1307C22×C4C23×D7918yes—
1308C22×C4C23×D7914yes—
1309C22×C4C23×D7914yes—
1310C22×C4C23×D7914yes—
1311C22×C4C23×D7911yescharacteristic
1312C22×C4C23×D7914yes—
1313C22×C4C23×D7911yescharacteristic
1314C4⋊C4—794no—
1315C4⋊C4—798no—
1316C4⋊C4—794no—
1317C4⋊C4—794no—
1318C4⋊C4—794no—
1319C4⋊C4—798no—
1320C4⋊C4—798no—
1321C4⋊C4—798no—
1322C4⋊C4—798no—
1323C4⋊C4—798no—
1324C4⋊C4C23×D7918yes—
1325C4⋊C4C23×D7914yes—
1326C4⋊C4C23×D7914yes—
1327C4⋊C4C23×D7918yes—
1328C22⋊C4—794no—
1329C22⋊C4—794no—
1330C22⋊C4—794no—
1331C22⋊C4—798no—
1332C22⋊C4—794no—
1333C22⋊C4—798no—
1334C22⋊C4—794no—
1335C22⋊C4—794no—
1336C22⋊C4—798no—
1337C22⋊C4—794no—
1338C22⋊C4—798no—
1339C22⋊C4—798no—
1340C22⋊C4—794no—
1341C22⋊C4—798no—
1342C22⋊C4—798no—
1343C22⋊C4—798no—
1344C22⋊C4—798no—
1345C22⋊C4—798no—
1346C22⋊C4C23×D7918yes—
1347C22⋊C4C23×D7918yes—
1348C22⋊C4C23×D7918yes—
1349C22⋊C4C23×D7918yes—
1350C22⋊C4C23×D7918yes—
1351C42—794no—
1352C42—794no—
1353C42—798no—
1354C42—794no—
1355C42—798no—
1356C42—794no—
1357C42C23×D7918yes—
1358C23—22no—
1359C23—22no—
1360C23—22no—
1361C23—22no—
1362C23—22no—
1363C23—24no—
1364C23—28no—
1365C23—22no—
1366C23—24no—
1367C23—24no—
1368C23—22no—
1369C23—28no—
1370C23—44no—
1371C23—416no—
1372C23—31632no—
1373C23—31616no—
1374C23—3164no—
1375C23—3168no—
1376C23—3168no—
1377C23—31632no—
1378C23—792no—
1379C23—794no—
1380C23—798no—
1381C23—794no—
1382C23—794no—
1383C23—792no—
1384C23—15816no—
1385C23—15816no—
1386C23—1588no—
1387C23—15816no—
1388C23—1584no—
1389C23—1582no—
1390C23—1588no—
1391C23—1584no—
1392C23—1582no—
1393C23—1582no—
1394C23—1584no—
1395C23—15816no—
1396C23—1584no—
1397C23—1582no—
1398C23—1582no—
1399C23—1584no—
1400C23C2×D4×D7914yes—
1401C23#41×D7914yescomplemented
1402C23C24×D7914yes—
1403C23C24×D7912yes—
1404C23C24×D7912yes—
1405C23C24×D7912yes—
1406C23C24×D7911yescharacteristic
1407Q8—28no—
1408Q8—7916no—
1409Q8—15816no—
1410Q8—15816no—
1411Q8—1588no—
1412D4—216no—
1413D4—216no—
1414D4—28no—
1415D4—48no—
1416D4—3168no—
1417D4—3168no—
1418D4—7932no—
1419D4—7916no—
1420D4—7916no—
1421D4—15816no—
1422D4—15816no—
1423D4—15816no—
1424D4—15816no—
1425D4—1588no—
1426D4—15816no—
1427D4—15816no—
1428D4—1588no—
1429D4—15816no—
1430D4—15816no—
1431D4—15816no—
1432D4—1588no—
1433D4—1588no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—28no—
1438C2×C4—24no—
1439C2×C4—24no—
1440C2×C4—28no—
1441C2×C4—28no—
1442C2×C4—28no—
1443C2×C4—28no—
1444C2×C4—216no—
1445C2×C4—3168no—
1446C2×C4—3164no—
1447C2×C4—792no—
1448C2×C4—794no—
1449C2×C4—798no—
1450C2×C4—794no—
1451C2×C4—7932no—
1452C2×C4—792no—
1453C2×C4—792no—
1454C2×C4—792no—
1455C2×C4—792no—
1456C2×C4—792no—
1457C2×C4—794no—
1458C2×C4—15816no—
1459C2×C4—15816no—
1460C2×C4—15816no—
1461C2×C4—15816no—
1462C2×C4—15816no—
1463C2×C4—15816no—
1464C2×C4—15816no—
1465C2×C4—1588no—
1466C2×C4—1582no—
1467C2×C4—1582no—
1468C2×C4—1582no—
1469C2×C4—1584no—
1470C2×C4—1582no—
1471C2×C4—1588no—
1472C2×C4—1582no—
1473C2×C4—1588no—
1474C2×C4—1588no—
1475C2×C4—1588no—
1476C2×C4—15816no—
1477C2×C4—1588no—
1478C2×C4C2×D4×D7914yes—
1479C2×C4C2×D4×D7914yes—
1480C2×C4C2×D4×D79116yescomplemented
1481C2×C4C24×D7914yes—
1482C2×C4C24×D7914yes—
1483C2×C4C24×D7912yes—
1484C2×C4C24×D7914yes—
1485C2×C4C24×D7912yes—
1486C2×C4C24×D7912yes—
1487C2×C4C24×D7912yes—
1488C22—28no—
1489C22—28no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—24no—
1496C22—24no—
1497C22—22no—
1498C22—22no—
1499C22—24no—
1500C22—416no—
1501C22—44no—
1502C22—48no—
1503C22—31632no—
1504C22—31616no—
1505C22—31632no—
1506C22—3168no—
1507C22—3164no—
1508C22—798no—
1509C22—794no—
1510C22—1584no—
1511C22—1582no—
1512C22—1584no—
1513C22—1582no—
1514C22—1582no—
1515C22—1584no—
1516C22—1588no—
1517C22—15816no—
1518C22—1582no—
1519C22—1584no—
1520C22—1584no—
1521C22—1582no—
1522C22C22×D4×D7914yes—
1523C22C22×D4×D7912yes—
1524C22C2×#41×D7912yes—
1525C22C2×#41×D7914yescomplemented
1526C22#1909939912yes—
1527C22C25×D7911yescharacteristic
1528C4—22no—
1529C4—22no—
1530C4—24no—
1531C4—24no—
1532C4—24no—
1533C4—798no—
1534C4—794no—
1535C4—1582no—
1536C4—1584no—
1537C4—1582no—
1538C4—1582no—
1539C4—1582no—
1540C4—1582no—
1541C4C22×D4×D7914yes—
1542C4C22×D4×D7914yes—
1543C2—24no—
1544C2—24no—
1545C2—42no—
1546C2—44no—
1547C2—3164no—
1548C2—3162no—
1549C2—1584no—
1550C2—1588no—
1551C2#2377688314yesdirect product factor
1552C2C23×D4×D7911yescharacteristic
1553C2C22×#41×D7911yescharacteristic
1554C2C2×#1909939911yescharacteristic
subgroupG/H
centerC22×C4C23×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#525×C79C2
socleC23×C79C25
hypercenterC2×#525D79
hypocenterC79C2×D4×#41
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×#11929624C2semidirect
2. C22×#41×D79C2semidirect
3. #23776883C2direct (N × H)
4. C2×#19099231C2semidirect
5. C2×#19099226C2semidirect
6. C2×#19099223C2semidirect
7. C2×#19099219C2semidirect
8. C2×#19099215C2semidirect
9. C2×#19099211C2semidirect
10. C2×#19099210C2semidirect
11. C2×#19099205C2semidirect
12. C2×#19099204C2semidirect
13. C2×#19099200C2semidirect
14. C2×#19099197C2semidirect
15. C2×#19099195C2semidirect
16. C2×#19099110C2semidirect
17. C2×#19099109C2semidirect
18. C2×#19099075C2semidirect
19. C2×#19099072C2semidirect
20. C2×#19099072C2semidirect
21. C2×#19099031C2semidirect
22. C22×C4×C22⋊D79C2semidirect
23. C2×C4×D4×D79C2semidirect
24. C2×#525×C79C2semidirect
25. C22×#11929625C22semidirect
28. C22×#11929624C22semidirect
29. C22×#11929624C22semidirect
30. C22×#11929624C22semidirect
31. C22×#11929624C22semidirect
32. C22×#11929624C22semidirect
33. C22×#11929624C22semidirect
34. C22×#11929624C22semidirect
35. C22×#11929623C22semidirect
36. C22×#11929623C22semidirect
38. C2×#41×D79C22semidirect
39. C23×Dic158C22semidirect
40. C22×Q8×D79C22semidirect
41. C23×D316C22semidirect
43. C23×C22⋊D79C22semidirect
45. C22×D4×D79C22semidirect
46. C22×D4×D79C22semidirect
47. C23×C4×D79C22semidirect
48. C23×C4×D79C22semidirect
49. C23×C4×D79C22semidirect
50. #19099231C22semidirect
51. #19099226C22semidirect
52. #19099223C22semidirect
53. #19099219C22semidirect
54. #19099215C22semidirect
55. #19099211C22semidirect
56. #19099210C22semidirect
57. #19099205C22semidirect
58. #19099204C22semidirect
59. #19099200C22semidirect
60. #19099197C22semidirect
61. #19099195C22semidirect
62. #19099110C22semidirect
63. #19099109C22semidirect
64. C2×#14579160C22semidirect
65. C2×#14579159C22semidirect
66. C2×#14579157C22semidirect
67. C2×#14579157C22semidirect
68. C2×#14579150C22semidirect
69. C2×#14579148C22semidirect
70. C2×#14579147C22semidirect
71. C2×#14579147C22semidirect
72. #19099075C22semidirect
73. #19099072C22semidirect
74. #19099072C22semidirect
75. C2×#14579146C22semidirect
76. C2×#14579146C22semidirect
77. C2×#14579145C22semidirect
78. C2×#14579143C22semidirect
79. C2×#14579143C22semidirect
80. C2×#14579141C22semidirect
81. C2×#14579141C22semidirect
82. C2×#14579139C22semidirect
83. C2×#14579139C22semidirect
84. C2×#14579138C22semidirect
85. C2×#14579138C22semidirect
86. C2×#14579136C22semidirect
87. C2×#14579136C22semidirect
88. C2×#14579136C22semidirect
89. C2×#14579134C22semidirect
90. C2×#14579134C22semidirect
91. C2×#14579134C22semidirect
92. C2×#14579134C22semidirect
93. C2×#14579133C22semidirect
94. C2×#14579133C22semidirect
95. C2×#14579133C22semidirect
96. C2×#14579133C22semidirect
97. C2×#14579132C22semidirect
98. C2×#14579131C22semidirect
99. C2×#14579131C22semidirect
100. C2×#14579131C22semidirect
101. C2×#14579129C22semidirect
102. C2×#14579129C22semidirect
103. #19099031C22semidirect
104. C2×#14579126C22semidirect
105. C2×#14579126C22semidirect
106. C2×C4×D316C22semidirect
107. C2×C4×D316C22semidirect
108. C2×D4×Dic79C22semidirect
109. C2×#14579123C22semidirect
110. C2×#14579123C22semidirect
111. C2×#14579123C22semidirect
114. C2×C4×C22⋊D79C22semidirect
115. C2×C4×C22⋊D79C22semidirect
116. C2×C4×C22⋊D79C22semidirect
117. C2×C4×C22⋊D79C22semidirect
118. C2×C4×C22⋊D79C22semidirect
119. C2×C4×C22⋊D79C22semidirect
120. C2×C4×C22⋊D79C22semidirect
121. C2×C4×C22⋊D79C22semidirect
122. C2×C4×C22⋊D79C22semidirect
124. C2×(C22⋊D79)⋊C4C22semidirect
125. C2×(C22⋊D79)⋊C4C22semidirect
126. C2×(C22⋊D79)⋊C4C22semidirect
127. C4×D4×D79C22semidirect
128. C2×#14579118C22semidirect
129. C22×Dic79⋊C4C22semidirect
130. C2×C4⋊C4×D79C22semidirect
131. C22×C22⋊Dic79C22semidirect
132. C22×(C2×D79)⋊C4C22semidirect
133. C2×C22⋊C4×D79C22semidirect
134. C2×C22⋊C4×D79C22semidirect
135. C22×C4×Dic79C22semidirect
136. C2×C42×D79C22semidirect
137. C22×#41×C79C22semidirect
138. C24×C4×C79C22semidirect
139. #525×C79C22semidirect
140. C2×#123×C79C22semidirect
141. C2×C22⋊Q8×C79C22semidirect
142. C2×C22⋊Q8×C79C22semidirect
143. C2×#121×C79C22semidirect
144. C2×#121×C79C22semidirect
145. C2×#120×C79C22semidirect
146. C2×C4×D4×C79C22semidirect
147. C2×C4×D4×C79C22semidirect
148. C2×#117×C79C22semidirect
153. C2×#11929625C23semidirect
161. C2×#11929624D4semidirect
163. C2×#11929624C23semidirect
164. C2×#11929624C23semidirect
165. C2×#11929624C23semidirect
166. C2×#11929624C23semidirect
167. C2×#11929624C23semidirect
168. C2×#11929624C23semidirect
171. C2×#11929623C23semidirect
172. C2×#11929623C23semidirect
179. C22×Dic158C23semidirect
181. C2×Q8×D79C23semidirect
189. C22×D316C23semidirect
205. C22×C22⋊D79C23semidirect
210. C2×D4×D79C23semidirect
211. C2×D4×D79C23semidirect
232. C22×C4×D79C23semidirect
233. C22×C4×D79C23semidirect
234. C22×C4×D79C23semidirect
235. #14579160C23semidirect
236. #14579159C23semidirect
237. #14579157C23semidirect
238. #14579157C23semidirect
239. #14579150C23semidirect
240. #14579148C23semidirect
241. #14579147C23semidirect
242. #14579147C23semidirect
243. #14579146C23semidirect
244. #14579146C23semidirect
245. #14579145C23semidirect
246. #14579143C23semidirect
247. #14579143C23semidirect
248. #14579141C23semidirect
249. #14579141C23semidirect
250. #14579139C23semidirect
251. #14579139C23semidirect
252. #14579138C23semidirect
253. #14579138C23semidirect
254. #14579136C23semidirect
255. #14579136C23semidirect
256. #14579136C23semidirect
257. #14579134C23semidirect
258. #14579134C23semidirect
259. #14579134C23semidirect
260. #14579134C23semidirect
261. #14579133C23semidirect
262. #14579133C23semidirect
263. #14579133C23semidirect
264. #14579133C23semidirect
265. #14579132C23semidirect
266. #14579131C23semidirect
267. #14579131C23semidirect
268. #14579131C23semidirect
269. #14579129C23semidirect
270. #14579129C23semidirect
271. #14579126C23semidirect
272. #14579126C23semidirect
273. C4×D316C23semidirect
274. C4×D316C23semidirect
275. D4×Dic79C23semidirect
276. #14579123C23semidirect
277. #14579123C23semidirect
278. #14579123C23semidirect
281. C4×C22⋊D79C23semidirect
282. C4×C22⋊D79C23semidirect
283. C4×C22⋊D79C23semidirect
284. C4×C22⋊D79C23semidirect
285. C4×C22⋊D79C23semidirect
286. C4×C22⋊D79C23semidirect
287. C4×C22⋊D79C23semidirect
288. C4×C22⋊D79C23semidirect
290. (C22⋊D79)⋊C4C23semidirect
291. (C22⋊D79)⋊C4C23semidirect
292. (C22⋊D79)⋊C4C23semidirect
293. #14579118C23semidirect
304. C2×Dic79⋊C4C23semidirect
305. C4⋊C4×D79C23semidirect
312. C2×C22⋊Dic79C23semidirect
325. C2×(C2×D79)⋊C4C23semidirect
326. C22⋊C4×D79C23semidirect
327. C22⋊C4×D79C23semidirect
334. C2×C4×Dic79C23semidirect
335. C42×D79C23semidirect
338. C2×#41×C79C23semidirect
352. C23×C4×C79C23semidirect
353. #123×C79C23semidirect
354. C22⋊Q8×C79C23semidirect
355. C22⋊Q8×C79C23semidirect
356. #121×C79C23semidirect
357. #121×C79C23semidirect
358. #120×C79C23semidirect
359. C4×D4×C79C23semidirect
360. C4×D4×C79C23semidirect
361. #117×C79C23semidirect
395. #11929624C2×D4semidirect
402. C2×Dic158C2×D4semidirect
414. C2×D316C2×D4semidirect
433. C2×C22⋊D79C2×D4semidirect
434. C2×C22⋊D79#41semidirect
482. C2×C4×D79C2×D4semidirect
555. C22×C4×C79C2×D4semidirect
595. C23×C79C2×#41semidirect
624. C22×D79C2×#41semidirect
647. C2×C4×C79C22×D4semidirect
665. C22⋊D79C22×D4semidirect
666. C22⋊D79C2×#41semidirect
679. C2×Dic79C2×#41semidirect
693. D316C22×D4semidirect
705. C4×D79C22×D4semidirect
709. Dic158C22×D4semidirect
728. C22×C79C22×#41semidirect
749. C2×D79C22×#41semidirect
764. Dic79C22×#41semidirect
770. C2×C79D4×#41semidirect
798. C2×#525D79semidirect
802. C79C2×D4×#41semidirect
817. C22×#41C2×D79semidirect
829. C24×C4C2×D79semidirect
855. #525C2×D79semidirect
861. C2×#123C2×D79semidirect
868. C2×C22⋊Q8C2×D79semidirect
869. C2×C22⋊Q8C2×D79semidirect
882. C2×#121C2×D79semidirect
883. C2×#121C2×D79semidirect
889. C2×#120C2×D79semidirect
915. C2×C4×D4C2×D79semidirect
916. C2×C4×D4C2×D79semidirect
918. C2×#117C2×D79semidirect
954. C2×#41C22×D79semidirect
1029. C23×C4C22×D79semidirect
1043. #123C22×D79semidirect
1050. C22⋊Q8C22×D79semidirect
1051. C22⋊Q8C22×D79semidirect
1064. #121C22×D79semidirect
1065. #121C22×D79semidirect
1071. #120C22×D79semidirect
1094. C4×D4C22×D79semidirect
1095. C4×D4C22×D79semidirect
1097. #117C22×D79semidirect
1299. C22×C4D4×D79semidirect
1401. C23#41×D79semidirect
1480. C2×C4C2×D4×D79semidirect
1525. C22C2×#41×D79semidirect
1551. C2#23776883direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#119296242
C22×#41×D792
#237768832
C2×#190992312
C2×#190992262
C2×#190992232
C2×#190992192
C2×#190992152
C2×#190992112
C2×#190992102
C2×#190992052
C2×#190992042
C2×#190992002
C2×#190991972
C2×#190991952
C2×#190991102
C2×#190991092
C2×#190990752
C2×#190990722
C2×#190990312
C22×C4×C22⋊D792
C2×C4×D4×D792
C2×#525×C792
C2×D4×#4179