Finite Group Databasebeta

← C2×#23777037 #35196306

Subgroups — C2×#23777037 #35196306

Order 20224.

11686 conjugacy classes of subgroups.

The subgroup lattice has 1532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579206C211yesmaximal, characteristic, complemented
2C22×#41×D79C211yesmaximal, characteristic, complemented
3#23777037C2132yesmaximal, direct product factor
4C2×#19099218C211yesmaximal, characteristic, complemented
5C2×#19099217C211yesmaximal, characteristic, complemented
6C2×#19099215C211yesmaximal, characteristic, complemented
7C2×#19099213C212yesmaximal, complemented
8C2×#19099212C211yesmaximal, characteristic, complemented
9C2×#19099211C212yesmaximal, complemented
10C2×#19099210C211yesmaximal, characteristic, complemented
11C2×#19099207C211yesmaximal, characteristic, complemented
12C2×#19099206C211yesmaximal, characteristic, complemented
13C2×#19099203C212yesmaximal, complemented
14C2×#19099200C212yesmaximal, complemented
15C2×#19099136C211yesmaximal, characteristic, complemented
16C2×#19099133C211yesmaximal, characteristic, complemented
17C2×#19099123C212yesmaximal, complemented
18C2×#19099121C212yesmaximal, complemented
19C2×#19099073C211yesmaximal, characteristic, complemented
20C2×#19099072C211yesmaximal, characteristic, complemented
21C22×#14579143C212yesmaximal, complemented
22C2×#123×D79C212yesmaximal, complemented
23C2×#19099035C211yesmaximal, characteristic, complemented
24C2×#546×C79C211yesmaximal, characteristic, complemented
25C2×#14579206—216no—
26C2×#14579206C22116yescomplemented
27C22×#11929625C2211yescharacteristic, complemented
28C22×#11929624C2211yescharacteristic
29C22×#11929624C2212yescomplemented
30C22×#11929624C2211yescharacteristic, complemented
31C22×#11929624C2211yescharacteristic, complemented
32C22×#11929623C2211yescharacteristic
33C22×#11929623C2212yescomplemented
34C22×#11929623C2211yescharacteristic, complemented
35C22×#11929623C2212yescomplemented
36C22×#11929623C2211yescharacteristic, complemented
37C2×#41×D79—216no—
38C2×#41×D79C22116yescomplemented
39C22×Q8×D79C2211yescharacteristic, complemented
40C23×C22⋊D79C2212yes—
41C23×C22⋊D79C2212yescomplemented
42C22×D4×D79C2212yes—
43C22×D4×D79C2211yescharacteristic
44C22×D4×D79C2211yescharacteristic, complemented
45C22×D4×D79C2212yescomplemented
46C23×C4×D79C2212yescomplemented
47C23×C4×D79C2211yescharacteristic, complemented
48#19099218C22116yescomplemented
49#19099217C22116yescomplemented
50#19099215C22116yescomplemented
51#19099213C22132yescomplemented
52#19099212C22116yescomplemented
53#19099211C22132yescomplemented
54#19099210C22116yescomplemented
55#19099207C22116yescomplemented
56#19099206C22116yescomplemented
57#19099203C22132yescomplemented
58#19099200C22132yescomplemented
59#19099136C22116yescomplemented
60#19099133C22116yescomplemented
61#19099123C22132yescomplemented
62#19099121C22132yescomplemented
63C2×#14579161C2211yescharacteristic, complemented
64C2×#14579160C2212yescomplemented
65C2×#14579159C2211yescharacteristic, complemented
66C2×#14579148C2211yescharacteristic, complemented
67C2×#14579147C2212yescomplemented
68#19099073C22116yescomplemented
69#19099072C22116yescomplemented
70C2×#14579146C2212yescomplemented
71C2×#14579146C2211yescharacteristic, complemented
72C2×#14579146C2212yescomplemented
73C2×#14579145C2212yescomplemented
74C2×#14579145C2212yescomplemented
75C2×#14579144C2212yescomplemented
76C2×#14579143C2212yescomplemented
77C2×#14579143C2212yescomplemented
78C2×#14579143C2212yescomplemented
79C2×#14579143C2212yescomplemented
80C2×#14579143C2212yescomplemented
81C2×#14579143C2212yescomplemented
82C2×#14579143C2212yescomplemented
83C2×#14579143C2211yescharacteristic, complemented
84C2×#14579143C2212yescomplemented
85C2×#14579143C2212yescomplemented
86C2×#14579143C22132yescomplemented
87C2×#14579142C2212yescomplemented
88C2×#14579142C2212yescomplemented
89#123×D79C22132yescomplemented
90C2×#14579141C2211yescharacteristic, complemented
91C2×#14579141C2211yescharacteristic, complemented
92C2×#14579140C2211yescharacteristic, complemented
93C2×#14579140C2211yescharacteristic, complemented
94C2×#14579139C2211yescharacteristic, complemented
95C2×#14579138C2212yescomplemented
96C2×#14579138C2212yescomplemented
97C2×#14579138C2211yescharacteristic, complemented
98C2×#14579137C2211yescharacteristic, complemented
99C2×#14579135C2212yescomplemented
100C2×#14579134C2211yescharacteristic, complemented
101C2×#14579134C2212yescomplemented
102C2×#14579134C2212yescomplemented
103C2×#14579133C2211yescharacteristic, complemented
104C2×#14579133C2212yescomplemented
105C2×#14579133C2212yescomplemented
106C2×#14579132C2212yescomplemented
107C2×#14579132C2211yescharacteristic, complemented
108C2×#14579132C2212yescomplemented
109C2×#14579131C2212yescomplemented
110C2×#14579131C2211yescharacteristic, complemented
111C2×#14579130C2212yescomplemented
112C2×#14579129C2212yescomplemented
113C2×#14579129C2211yescharacteristic, complemented
114C2×#14579129C2212yescomplemented
115#19099035C22116yescomplemented
116C2×C4×D316C2211yescharacteristic, complemented
117C2×C4×D316C2211yescharacteristic, complemented
118C2×D4×Dic79C2211yescharacteristic, complemented
119C2×D4×Dic79C2212yescomplemented
120C2×#14579123C2211yescharacteristic, complemented
121C2×C4×C22⋊D79C2212yescomplemented
122C2×C4×C22⋊D79C2211yescharacteristic, complemented
123C2×C4×C22⋊D79C2211yescharacteristic, complemented
124C2×(C22⋊D79)⋊C4C2212yescomplemented
125C2×(C22⋊D79)⋊C4C2212yescomplemented
126C2×#14579119C2211yescharacteristic, complemented
127C2×#14579118C2211yescharacteristic, complemented
128C22×C4⋊Dic79C2212yescomplemented
129C22×Dic79⋊C4C2212yescomplemented
130C2×C4⋊C4×D79C2212yescomplemented
131C2×C4⋊C4×D79C2212yescomplemented
132C22×C22⋊Dic79C2212yescomplemented
133C22×(C2×D79)⋊C4C2212yescomplemented
134C2×C22⋊C4×D79C2212yescomplemented
135C2×C22⋊C4×D79C2212yescomplemented
136C2×C22⋊C4×D79C2212yescomplemented
137C22×#41×C79C2211yescharacteristic, complemented
138C23×D4×C79C2211yescharacteristic, complemented
139#546×C79C22116yescomplemented
140C2×#124×C79C2211yescharacteristic, complemented
141C2×#123×C79C2212yescomplemented
142C2×C22⋊Q8×C79C2211yescharacteristic, complemented
143C2×#121×C79C2211yescharacteristic, complemented
144C2×#121×C79C2212yescomplemented
145C2×#120×C79C2212yescomplemented
146C2×C4×D4×C79C2211yescharacteristic, complemented
147C2×C4×D4×C79C2211yescharacteristic, complemented
148C22×C22⋊C4×C79C2212yescomplemented
149C24×D79C2312yes—
150C24×D79C2311yescharacteristic
151C24×D79C2312yes—
152#14579206—2128no—
153C2×#11929625—28no—
154C2×#11929625C2318yescomplemented
155C2×#11929624—28no—
156C2×#11929624—28no—
157C2×#11929624—216no—
158C2×#11929624—28no—
159C2×#11929624C2318yes—
160C2×#11929624C2318yescomplemented
161C2×#11929624C23116yescomplemented
162C2×#11929624C2318yescomplemented
163C2×#11929623—28no—
164C2×#11929623—28no—
165C2×#11929623—216no—
166C2×#11929623—216no—
167C2×#11929623—28no—
168C2×#11929623C2318yes—
169C2×#11929623C23116yescomplemented
170C2×#11929623C2318yescomplemented
171C2×#11929623C23116yescomplemented
172C2×#11929623C2318yescomplemented
173#41×D79—2128no—
174C22×Dic158C2312yes—
175C22×Dic158C2311yescharacteristic
176C22×Dic158C2311yescharacteristic
177C22×Dic158C2311yescharacteristic
178C2×Q8×D79—28no—
179C2×Q8×D79C2318yescomplemented
180C22×D316C2312yes—
181C22×D316C2311yescharacteristic
182C22×D316C2311yescharacteristic
183C22×D316C2311yescharacteristic
184C22×C22⋊D79—216no—
185C22×C22⋊D79—216no—
186C22×C22⋊D79C23116yes—
187C22×C22⋊D79C2312yes—
188C22×C22⋊D79C2312yes—
189C22×C22⋊D79C2311yescharacteristic
190C22×C22⋊D79C2312yes—
191C22×C22⋊D79C2312yes—
192C22×C22⋊D79C2312yes—
193C22×C22⋊D79C2311yescharacteristic
194C22×C22⋊D79C2312yes—
195C22×C22⋊D79C2312yes—
196C22×C22⋊D79C2311yescharacteristic
197C22×C22⋊D79C2311yescharacteristic
198C22×C22⋊D79C2312yes—
199C22×C22⋊D79C23116yescomplemented
200C2×D4×D79—216no—
201C2×D4×D79—216no—
202C2×D4×D79—28no—
203C2×D4×D79D4116yescomplemented
204C2×D4×D79C23116yes—
205C2×D4×D79C2318yes—
206C2×D4×D79C2318yescomplemented
207C2×D4×D79C23116yescomplemented
208C23×Dic79C2312yes—
209C23×Dic79C2312yes—
210C23×Dic79C2312yes—
211C23×Dic79C2311yescharacteristic
212C23×Dic79C2312yes—
213C22×C4×D79—216no—
214C22×C4×D79—28no—
215C22×C4×D79C2312yes—
216C22×C4×D79C2312yes—
217C22×C4×D79C2312yes—
218C22×C4×D79C2311yescharacteristic
219C22×C4×D79C2311yescharacteristic
220C22×C4×D79C2311yescharacteristic
221C22×C4×D79C2311yescharacteristic
222C22×C4×D79C2312yes—
223C22×C4×D79C2312yes—
224C22×C4×D79C2312yes—
225C22×C4×D79C2311yescharacteristic
226C22×C4×D79C23116yescomplemented
227C22×C4×D79C2318yescomplemented
228#14579161C2318yescomplemented
229#14579160C23116yescomplemented
230#14579159C2318yescomplemented
231#14579148C2318yescomplemented
232#14579147C23116yescomplemented
233#14579146C23116yescomplemented
234#14579146C23116yescomplemented
235#14579146C2318yescomplemented
236#14579145C23116yescomplemented
237#14579145C23116yescomplemented
238#14579144C23116yescomplemented
239#14579143C23116yescomplemented
240#14579143C23116yescomplemented
241#14579143C23116yescomplemented
242#14579143C23116yescomplemented
243#14579143C23116yescomplemented
244#14579143C23116yescomplemented
245#14579143C23116yescomplemented
246#14579143C23116yescomplemented
247#14579143C2318yescomplemented
248#14579143C23116yescomplemented
249#14579142C23116yescomplemented
250#14579142C23116yescomplemented
251#14579141C2318yescomplemented
252#14579141C2318yescomplemented
253#14579140C2318yescomplemented
254#14579140C2318yescomplemented
255#14579139C2318yescomplemented
256#14579138C23116yescomplemented
257#14579138C23116yescomplemented
258#14579138C2318yescomplemented
259#14579137C2318yescomplemented
260#14579135C23116yescomplemented
261#14579134C2318yescomplemented
262#14579134C23116yescomplemented
263#14579134C23116yescomplemented
264#14579133C2318yescomplemented
265#14579133C23116yescomplemented
266#14579133C23116yescomplemented
267#14579132C23116yescomplemented
268#14579132C2318yescomplemented
269#14579132C23116yescomplemented
270#14579131C23116yescomplemented
271#14579131C2318yescomplemented
272#14579130C23116yescomplemented
273#14579129C23116yescomplemented
274#14579129C2318yescomplemented
275#14579129C23116yescomplemented
276C4×D316C2318yescomplemented
277C4×D316C2318yescomplemented
278D4×Dic79C23116yescomplemented
279D4×Dic79C2318yescomplemented
280#14579123C2318yescomplemented
281C4×C22⋊D79C23116yescomplemented
282C4×C22⋊D79C2318yescomplemented
283C4×C22⋊D79C2318yescomplemented
284(C22⋊D79)⋊C4C23116yescomplemented
285(C22⋊D79)⋊C4C23116yescomplemented
286#14579119C2318yescomplemented
287#14579118C2318yescomplemented
288C2×C4⋊Dic79C2312yes—
289C2×C4⋊Dic79C2312yes—
290C2×C4⋊Dic79C2311yescharacteristic
291C2×C4⋊Dic79C2312yes—
292C2×C4⋊Dic79C2312yes—
293C2×C4⋊Dic79C2311yescharacteristic
294C2×C4⋊Dic79C23116yescomplemented
295C2×Dic79⋊C4C2311yescharacteristic
296C2×Dic79⋊C4C2312yes—
297C2×Dic79⋊C4C2312yes—
298C2×Dic79⋊C4C2312yes—
299C2×Dic79⋊C4C2311yescharacteristic
300C2×Dic79⋊C4C2312yes—
301C2×Dic79⋊C4C2312yes—
302C2×Dic79⋊C4C2311yescharacteristic
303C2×Dic79⋊C4C2311yescharacteristic
304C2×Dic79⋊C4C23116yescomplemented
305C4⋊C4×D79C23116yescomplemented
306C4⋊C4×D79C23116yescomplemented
307C2×C22⋊Dic79C2312yes—
308C2×C22⋊Dic79C2312yes—
309C2×C22⋊Dic79C2312yes—
310C2×C22⋊Dic79C2311yescharacteristic
311C2×C22⋊Dic79C2312yes—
312C2×C22⋊Dic79C2312yes—
313C2×C22⋊Dic79C2311yescharacteristic
314C2×C22⋊Dic79C2312yes—
315C2×C22⋊Dic79C23116yescomplemented
316C2×(C2×D79)⋊C4C2311yescharacteristic
317C2×(C2×D79)⋊C4C2311yescharacteristic
318C2×(C2×D79)⋊C4C2311yescharacteristic
319C2×(C2×D79)⋊C4C2312yes—
320C2×(C2×D79)⋊C4C2312yes—
321C2×(C2×D79)⋊C4C2312yes—
322C2×(C2×D79)⋊C4C2311yescharacteristic
323C2×(C2×D79)⋊C4C2312yes—
324C2×(C2×D79)⋊C4C2312yes—
325C2×(C2×D79)⋊C4C2312yes—
326C2×(C2×D79)⋊C4C2311yescharacteristic
327C2×(C2×D79)⋊C4C2311yescharacteristic
328C2×(C2×D79)⋊C4C23116yescomplemented
329C22⋊C4×D79C23116yescomplemented
330C22⋊C4×D79C23116yescomplemented
331C22⋊C4×D79C23116yescomplemented
332C2×C4×Dic79C2311yescharacteristic
333C2×C4×Dic79C2312yes—
334C25×C79C2312yes—
335C2×#41×C79—28no—
336C2×#41×C79C2318yescomplemented
337C22×Q8×C79C2311yescharacteristic
338C22×D4×C79—28no—
339C22×D4×C79C2312yes—
340C22×D4×C79C2312yes—
341C22×D4×C79C2311yescharacteristic
342C22×D4×C79C2311yescharacteristic
343C22×D4×C79C2312yes—
344C22×D4×C79C2311yescharacteristic
345C22×D4×C79C2318yescomplemented
346C23×C4×C79C2312yes—
347C23×C4×C79C2311yescharacteristic
348C23×C4×C79C2311yescharacteristic
349C23×C4×C79C2312yes—
350#124×C79C2318yescomplemented
351#123×C79C23116yescomplemented
352C22⋊Q8×C79C2318yescomplemented
353#121×C79C2318yescomplemented
354#121×C79C23116yescomplemented
355#120×C79C23116yescomplemented
356C4×D4×C79C2318yescomplemented
357C4×D4×C79C2318yescomplemented
358C2×C4⋊C4×C79C2311yescharacteristic
359C2×C4⋊C4×C79C2311yescharacteristic
360C2×C4⋊C4×C79C2312yes—
361C2×C22⋊C4×C79C2311yescharacteristic
362C2×C22⋊C4×C79C2312yes—
363C2×C22⋊C4×C79C2312yes—
364C2×C22⋊C4×C79C2312yes—
365C2×C22⋊C4×C79C2312yes—
366C2×C22⋊C4×C79C2311yescharacteristic
367C2×C22⋊C4×C79C2312yes—
368C2×C22⋊C4×C79C23116yescomplemented
369C2×C42×C79C2311yescharacteristic
370C23×D79—24no—
371C23×D79—28no—
372C23×D79—44no—
373C23×D79—44no—
374C23×D79—42no—
375C23×D79—42no—
376C23×D79—44no—
377C23×D79—44no—
378C23×D79C2×D4116yes—
379C23×D79C2411yescharacteristic
380C23×D79C2411yescharacteristic
381C23×D79C2411yescharacteristic
382C23×D79C2412yes—
383C23×D79C2418yes—
384C23×D79C2414yes—
385C23×D79C2418yes—
386#11929625—232no—
387#11929624—232no—
388#11929624—232no—
389#11929624—232no—
390#11929624—264no—
391#11929623—232no—
392#11929623—232no—
393#11929623—232no—
394#11929623—264no—
395#11929623—264no—
396C2×Dic158—28no—
397C2×Dic158—24no—
398C2×Dic158—24no—
399C2×Dic158—24no—
400C2×Dic158C2418yes—
401C2×Dic158C2414yes—
402C2×Dic158C2414yes—
403C2×Dic158C2414yes—
404Q8×D79—232no—
405C2×D316—28no—
406C2×D316—24no—
407C2×D316—42no—
408C2×D316C2×D418yes—
409C2×D316C2414yes—
410C2×D316C2418yes—
411C2×D316C2414yes—
412C2×D316C2414yes—
413C2×C22⋊D79—24no—
414C2×C22⋊D79—28no—
415C2×C22⋊D79—28no—
416C2×C22⋊D79—28no—
417C2×C22⋊D79—28no—
418C2×C22⋊D79—28no—
419C2×C22⋊D79—24no—
420C2×C22⋊D79—28no—
421C2×C22⋊D79—264no—
422C2×C22⋊D79—264no—
423C2×C22⋊D79—44no—
424C2×C22⋊D79—42no—
425C2×C22⋊D79—42no—
426C2×C22⋊D79C2×D4116yes—
427C2×C22⋊D79C2418yes—
428C2×C22⋊D79C2418yes—
429C2×C22⋊D79C2418yes—
430C2×C22⋊D79C2418yes—
431C2×C22⋊D79C2418yes—
432C2×C22⋊D79C2414yes—
433C2×C22⋊D79C2414yes—
434C2×C22⋊D79C2418yes—
435C2×C22⋊D79C2418yes—
436C2×C22⋊D79C2414yes—
437C2×C22⋊D79C2414yes—
438C2×C22⋊D79C2418yes—
439D4×D79—232no—
440D4×D79—264no—
441D4×D79—264no—
442D4×D79C2×D4164yescomplemented
443C22×Dic79—24no—
444C22×Dic79—28no—
445C22×Dic79—28no—
446C22×Dic79—28no—
447C22×Dic79—44no—
448C22×Dic79C2412yes—
449C22×Dic79C2411yescharacteristic
450C22×Dic79C2412yes—
451C22×Dic79C2418yes—
452C22×Dic79C2418yes—
453C22×Dic79C2418yes—
454C22×Dic79C2414yes—
455C22×Dic79C2411yescharacteristic
456C22×Dic79C2412yes—
457C22×Dic79C2411yescharacteristic
458C22×Dic79C2411yescharacteristic
459C22×Dic79C2418yes—
460C22×Dic79C2411yescharacteristic
461C2×C4×D79—24no—
462C2×C4×D79—232no—
463C2×C4×D79—28no—
464C2×C4×D79—264no—
465C2×C4×D79—28no—
466C2×C4×D79—28no—
467C2×C4×D79—28no—
468C2×C4×D79—24no—
469C2×C4×D79—24no—
470C2×C4×D79—24no—
471C2×C4×D79—44no—
472C2×C4×D79—44no—
473C2×C4×D79C2×D418yes—
474C2×C4×D79C2418yes—
475C2×C4×D79C2414yes—
476C2×C4×D79C2418yes—
477C2×C4×D79C2418yes—
478C2×C4×D79C2414yes—
479C2×C4×D79C2418yes—
480C2×C4×D79C2414yes—
481C2×C4×D79C2414yes—
482C2×C4×D79C2418yes—
483C2×C4×D79C2418yes—
484C2×C4×D79C2414yes—
485C4⋊Dic79C2418yes—
486C4⋊Dic79C2418yes—
487C4⋊Dic79C2414yes—
488C4⋊Dic79C2418yes—
489C4⋊Dic79C2418yes—
490C4⋊Dic79C2414yes—
491Dic79⋊C4C2414yes—
492Dic79⋊C4C2418yes—
493Dic79⋊C4C2418yes—
494Dic79⋊C4C2418yes—
495Dic79⋊C4C2414yes—
496Dic79⋊C4C2418yes—
497Dic79⋊C4C2418yes—
498Dic79⋊C4C2414yes—
499Dic79⋊C4C2414yes—
500C22⋊Dic79C2418yes—
501C22⋊Dic79C2418yes—
502C22⋊Dic79C2418yes—
503C22⋊Dic79C2414yes—
504C22⋊Dic79C2418yes—
505C22⋊Dic79C2418yes—
506C22⋊Dic79C2414yes—
507C22⋊Dic79C2418yes—
508(C2×D79)⋊C4C2414yes—
509(C2×D79)⋊C4C2414yes—
510(C2×D79)⋊C4C2414yes—
511(C2×D79)⋊C4C2418yes—
512(C2×D79)⋊C4C2418yes—
513(C2×D79)⋊C4C2418yes—
514(C2×D79)⋊C4C2414yes—
515(C2×D79)⋊C4C2418yes—
516(C2×D79)⋊C4C2418yes—
517(C2×D79)⋊C4C2418yes—
518(C2×D79)⋊C4C2414yes—
519(C2×D79)⋊C4C2414yes—
520C4×Dic79C2414yes—
521C4×Dic79C2418yes—
522C24×C79—28no—
523C24×C79—44no—
524C24×C79—44no—
525C24×C79C2412yes—
526C24×C79C2411yescharacteristic
527C24×C79C2411yescharacteristic
528C24×C79C2412yes—
529C24×C79C2418yes—
530#41×C79—232no—
531C2×Q8×C79—24no—
532C2×Q8×C79C2414yes—
533C2×D4×C79—28no—
534C2×D4×C79—28no—
535C2×D4×C79—232no—
536C2×D4×C79—24no—
537C2×D4×C79—42no—
538C2×D4×C79—44no—
539C2×D4×C79C2×D418yes—
540C2×D4×C79C2414yes—
541C2×D4×C79C2418yes—
542C2×D4×C79C2418yes—
543C2×D4×C79C2414yes—
544C2×D4×C79C2418yes—
545C2×D4×C79C2414yes—
546C22×C4×C79—28no—
547C22×C4×C79—24no—
548C22×C4×C79—24no—
549C22×C4×C79—44no—
550C22×C4×C79C2412yes—
551C22×C4×C79C2411yescharacteristic
552C22×C4×C79C2414yes—
553C22×C4×C79C2418yes—
554C22×C4×C79C2414yes—
555C22×C4×C79C2411yescharacteristic
556C22×C4×C79C2411yescharacteristic
557C22×C4×C79C2412yes—
558C22×C4×C79C2411yescharacteristic
559C22×C4×C79C2418yes—
560C22×C4×C79C2411yescharacteristic
561C4⋊C4×C79C2414yes—
562C4⋊C4×C79C2414yes—
563C4⋊C4×C79C2418yes—
564C22⋊C4×C79C2414yes—
565C22⋊C4×C79C2418yes—
566C22⋊C4×C79C2418yes—
567C22⋊C4×C79C2418yes—
568C22⋊C4×C79C2418yes—
569C22⋊C4×C79C2414yes—
570C22⋊C4×C79C2418yes—
571C42×C79C2414yes—
572C23×C79—24no—
573C23×C79—24no—
574C23×C79—22no—
575C23×C79—24no—
576C23×C79—22no—
577C23×C79—22no—
578C23×C79—24no—
579C23×C79—22no—
580C23×C79—22no—
581C23×C79—24no—
582C23×C79—22no—
583C23×C79—216no—
584C23×C79—48no—
585C23×C79—48no—
586C23×C79—816no—
587C23×C79C22×D418yes—
588C23×C79C2514yes—
589C23×C79C2512yes—
590C23×C79C2512yes—
591C23×C79C2514yes—
592C23×C79C2511yescharacteristic
593C22×D79—24no—
594C22×D79—24no—
595C22×D79—22no—
596C22×D79—22no—
597C22×D79—22no—
598C22×D79—22no—
599C22×D79—22no—
600C22×D79—22no—
601C22×D79—22no—
602C22×D79—22no—
603C22×D79—28no—
604C22×D79—216no—
605C22×D79—432no—
606C22×D79—48no—
607C22×D79—48no—
608C22×D79—44no—
609C22×D79—44no—
610C22×D79—48no—
611C22×D79—48no—
612C22×D79—416no—
613C22×D79—816no—
614C22×D79C22×D414yes—
615C22×D79C22×D418yes—
616C22×D79C22×D4132yes—
617C22×D79C2512yes—
618C22×D79C2512yes—
619C22×D79C2512yes—
620C22×D79C2514yes—
621Q8×C79—28no—
622D4×C79—216no—
623D4×C79—216no—
624D4×C79—28no—
625D4×C79—48no—
626D4×C79—44no—
627D4×C79C22×D4116yes—
628C2×C4×C79—22no—
629C2×C4×C79—22no—
630C2×C4×C79—24no—
631C2×C4×C79—216no—
632C2×C4×C79—22no—
633C2×C4×C79—24no—
634C2×C4×C79—22no—
635C2×C4×C79—28no—
636C2×C4×C79—28no—
637C2×C4×C79—48no—
638C2×C4×C79C22×D414yes—
639C2×C4×C79C2514yes—
640C2×C4×C79C2512yes—
641C2×C4×C79C2512yes—
642C2×C4×C79C2512yes—
643C2×C4×C79C2514yes—
644C2×C4×C79C2512yes—
645C2×C4×C79C2512yes—
646C22⋊D79—216no—
647C22⋊D79—216no—
648C22⋊D79—216no—
649C22⋊D79—216no—
650C22⋊D79—216no—
651C22⋊D79—216no—
652C22⋊D79—28no—
653C22⋊D79—28no—
654C22⋊D79—44no—
655C22⋊D79—48no—
656C22⋊D79—44no—
657C22⋊D79C22×D4132yes—
658C2×Dic79—22no—
659C2×Dic79—24no—
660C2×Dic79—216no—
661C2×Dic79—24no—
662C2×Dic79—22no—
663C2×Dic79—216no—
664C2×Dic79—22no—
665C2×Dic79—24no—
666C2×Dic79—22no—
667C2×Dic79—28no—
668C2×Dic79—216no—
669C2×Dic79—48no—
670C2×Dic79C22×D414yes—
671C2×Dic79C2512yes—
672C2×Dic79C2514yes—
673C2×Dic79C2512yes—
674C2×Dic79C2512yes—
675C2×Dic79C2514yes—
676C2×Dic79C2514yes—
677C2×Dic79C2512yes—
678C2×Dic79C2512yes—
679D316—28no—
680D316—216no—
681D316—44no—
682D316C22×D4116yes—
683C4×D79—28no—
684C4×D79—216no—
685C4×D79—216no—
686C4×D79—216no—
687C4×D79—216no—
688C4×D79—28no—
689C4×D79—28no—
690C4×D79—28no—
691C4×D79—48no—
692C4×D79—48no—
693C4×D79C22×D4116yes—
694Dic158—28no—
695Dic158—28no—
696Dic158—216no—
697Dic158—28no—
698C22×C79—24no—
699C22×C79—24no—
700C22×C79—216no—
701C22×C79—22no—
702C22×C79—22no—
703C22×C79—24no—
704C22×C79—22no—
705C22×C79—24no—
706C22×C79—22no—
707C22×C79—22no—
708C22×C79—24no—
709C22×C79—22no—
710C22×C79—44no—
711C22×C79—48no—
712C22×C79—44no—
713C22×C79—816no—
714C22×C79C23×D418yes—
715C22×C79C23×D412yes—
716C22×C79#58512yes—
717C22×C79#58512yes—
718C22×C79C2611yescharacteristic
719C2×D79—22no—
720C2×D79—22no—
721C2×D79—24no—
722C2×D79—24no—
723C2×D79—28no—
724C2×D79—216no—
725C2×D79—22no—
726C2×D79—22no—
727C2×D79—22no—
728C2×D79—22no—
729C2×D79—22no—
730C2×D79—22no—
731C2×D79—432no—
732C2×D79—416no—
733C2×D79—44no—
734C2×D79—44no—
735C2×D79—816no—
736C2×D79C23×D418yes—
737C2×D79C23×D414yes—
738C4×C79—22no—
739C4×C79—22no—
740C4×C79—24no—
741C4×C79—22no—
742C4×C79—24no—
743C4×C79—22no—
744C4×C79C23×D414yes—
745Dic79—24no—
746Dic79—22no—
747Dic79—24no—
748Dic79—22no—
749Dic79—22no—
750Dic79—24no—
751Dic79—22no—
752Dic79C23×D414yes—
753C2×#3485—791nomaximal, Sylow
754C2×C79—28no—
755C2×C79—42no—
756C2×C79—44no—
757C2×C79—42no—
758C2×C79#348514yescomplemented
759C2×C79C24×D411yescharacteristic
760C2×C79C2×#58511yescharacteristic
761C2×C79C2×#58511yescharacteristic
762D79—24no—
763D79—28no—
764D79—42no—
765D79—42no—
766C22×H(5,𝔽2)—791no—
767C23×#41—791no—
768#3485—7932no—
769C2×#547—791no—
770C2×#547—792no—
771C2×#547—791no—
772C2×#547—792no—
773C2×#547—791no—
774C2×#547—791no—
775C2×#546—791no—
776C2×#546—791no—
777C2×#546—791no—
778C2×#546—792no—
779C2×#546—792no—
780C2×#546D7911yescharacteristic, complemented
781C2×#536—791no—
782C2×#536—791no—
783C2×#534—792no—
784C2×#534—792no—
785C2×#525—791no—
786C2×#525—791no—
787C22×#123—792no—
788C22×#123—792no—
789C2×#518—791no—
790C79C2×#348511yescharacteristic, complemented, Sylow
791C2×H(5,𝔽2)—7916no—
792C2×H(5,𝔽2)—15816no—
793C22×#41—7916no—
794C22×#41—791no—
795C22×#41—791no—
796C22×#41—792no—
797C22×#41—791no—
798C22×#41—791no—
799C22×#41—792no—
800C22×#41—791no—
801C22×#41—792no—
802C22×#41—791no—
803C22×#41—791no—
804C22×#41—15816no—
805C22×#41C2×D7911yescharacteristic, complemented
806C23×Q8—791no—
807C23×D4—791no—
808C23×D4—792no—
809C23×D4—792no—
810C23×D4—792no—
811C23×D4—792no—
812C23×D4—791no—
813C23×D4C2×D7911yescharacteristic, complemented
814C24×C4—792no—
815C24×C4—791no—
816#547—7916no—
817#547—7932no—
818#547—7916no—
819#547—7932no—
820#547—7916no—
821#547—7916no—
822#546—7916no—
823#546—7916no—
824#546—7916no—
825#546—7932no—
826#546—7932no—
827#546C2×D79116yescomplemented
828#536—7916no—
829#536—7916no—
830#534—7932no—
831#534—7932no—
832C2×C4⋊Q8—791no—
833C2×C4⋊Q8—792no—
834C2×C4⋊Q8—791no—
835C2×#124—791no—
836C2×#124—792no—
837C2×#124C2×D7911yescharacteristic, complemented
838#525—7916no—
839#525—7916no—
840C2×#123—792no—
841C2×#123—792no—
842C2×#123—792no—
843C2×#123—7932no—
844C2×#123—791no—
845C2×#123—792no—
846C2×#123—792no—
847C2×#123—792no—
848C2×#123—791no—
849C2×#123—792no—
850C2×#123—792no—
851C2×#123—792no—
852C2×#123—792no—
853C2×#123—792no—
854C2×#123—792no—
855C2×#123—792no—
856C2×#123—792no—
857C2×#123—792no—
858C2×#123—792no—
859C2×#123—7932no—
860C2×#123C2×D7912yescomplemented
861C2×C22⋊Q8—791no—
862C2×C22⋊Q8—791no—
863C2×C22⋊Q8—791no—
864C2×C22⋊Q8—791no—
865C2×C22⋊Q8—791no—
866C2×C22⋊Q8—791no—
867C2×C22⋊Q8—791no—
868C2×C22⋊Q8—792no—
869C2×C22⋊Q8—792no—
870C2×C22⋊Q8C2×D7911yescharacteristic, complemented
871C2×#121—791no—
872C2×#121—791no—
873C2×#121—792no—
874C2×#121—792no—
875C2×#121—792no—
876C2×#121—792no—
877C2×#121—792no—
878C2×#121—791no—
879C2×#121—792no—
880C2×#121—792no—
881C2×#121C2×D7911yescharacteristic, complemented
882C2×#121C2×D7912yescomplemented
883C2×#120—792no—
884C2×#120—792no—
885C2×#120—791no—
886C2×#120—792no—
887C2×#120—791no—
888C2×#120—792no—
889C2×#120C2×D7912yescomplemented
890#518—7916no—
891C2×C4×D4—791no—
892C2×C4×D4—792no—
893C2×C4×D4—792no—
894C2×C4×D4—791no—
895C2×C4×D4—791no—
896C2×C4×D4—791no—
897C2×C4×D4—792no—
898C2×C4×D4—792no—
899C2×C4×D4—791no—
900C2×C4×D4—791no—
901C2×C4×D4C2×D7911yescharacteristic, complemented
902C2×C4×D4C2×D7911yescharacteristic, complemented
903C2×#117—791no—
904C2×#117—791no—
905C22×C4⋊C4—792no—
906C22×C4⋊C4—792no—
907C22×C4⋊C4—792no—
908C22×C4⋊C4—792no—
909C22×C22⋊C4—792no—
910C22×C22⋊C4—792no—
911C22×C22⋊C4—792no—
912C22×C22⋊C4—792no—
913C22×C22⋊C4—792no—
914C22×C22⋊C4C2×D7912yescomplemented
915C25—792no—
916C25—792no—
917C25—791no—
918C25C22×D7912yes—
919H(5,𝔽2)—158128no—
920C2×#41—28no—
921C2×#41—798no—
922C2×#41—798no—
923C2×#41—798no—
924C2×#41—7916no—
925C2×#41—798no—
926C2×#41—7916no—
927C2×#41—798no—
928C2×#41—798no—
929C2×#41—7916no—
930C2×#41—798no—
931C2×#41—1588no—
932C2×#41—15816no—
933C2×#41—1588no—
934C2×#41—1588no—
935C2×#41—1588no—
936C2×#41—15816no—
937C2×#41—15816no—
938C2×#41—1588no—
939C2×#41—158128no—
940C2×#41—1588no—
941C2×#41—1588no—
942C2×#41C22×D7918yescomplemented
943C22×Q8—798no—
944C22×Q8—792no—
945C22×Q8—791no—
946C22×Q8—791no—
947C22×Q8—791no—
948C22×Q8—1588no—
949C22×Q8C22×D7911yescharacteristic
950C22×D4—28no—
951C22×D4—791no—
952C22×D4—792no—
953C22×D4—791no—
954C22×D4—792no—
955C22×D4—7916no—
956C22×D4—798no—
957C22×D4—792no—
958C22×D4—792no—
959C22×D4—792no—
960C22×D4—791no—
961C22×D4—792no—
962C22×D4—792no—
963C22×D4—792no—
964C22×D4—791no—
965C22×D4—7916no—
966C22×D4—7916no—
967C22×D4—7916no—
968C22×D4—7916no—
969C22×D4—798no—
970C22×D4—791no—
971C22×D4—791no—
972C22×D4—792no—
973C22×D4—791no—
974C22×D4—1588no—
975C22×D4—15816no—
976C22×D4—15816no—
977C22×D4—15816no—
978C22×D4—15816no—
979C22×D4C22×D7912yes—
980C22×D4C22×D7912yes—
981C22×D4C22×D7911yescharacteristic
982C22×D4C22×D7912yes—
983C22×D4C22×D7911yescharacteristic
984C22×D4C22×D7911yescharacteristic
985C22×D4C22×D7918yescomplemented
986C23×C4—792no—
987C23×C4—792no—
988C23×C4—792no—
989C23×C4—791no—
990C23×C4—792no—
991C23×C4—792no—
992C23×C4—791no—
993C23×C4—792no—
994C23×C4—792no—
995C23×C4—792no—
996C23×C4—792no—
997C23×C4—791no—
998C23×C4—791no—
999C23×C4—791no—
1000C23×C4—791no—
1001C23×C4—792no—
1002C23×C4—7916no—
1003C23×C4—798no—
1004C23×C4—1588no—
1005C23×C4—15816no—
1006C23×C4C22×D7912yes—
1007C23×C4C22×D7911yescharacteristic
1008C23×C4C22×D7911yescharacteristic
1009C23×C4C22×D7912yes—
1010C4⋊Q8—798no—
1011C4⋊Q8—7916no—
1012C4⋊Q8—798no—
1013#124—798no—
1014#124—7916no—
1015#124C22×D7918yescomplemented
1016#123—7916no—
1017#123—7916no—
1018#123—7916no—
1019#123—798no—
1020#123—7916no—
1021#123—7916no—
1022#123—7916no—
1023#123—798no—
1024#123—7916no—
1025#123—7916no—
1026#123—7916no—
1027#123—7916no—
1028#123—7916no—
1029#123—7916no—
1030#123—7916no—
1031#123—7916no—
1032#123—7916no—
1033#123—7916no—
1034#123C22×D79116yescomplemented
1035C22⋊Q8—798no—
1036C22⋊Q8—798no—
1037C22⋊Q8—798no—
1038C22⋊Q8—798no—
1039C22⋊Q8—798no—
1040C22⋊Q8—798no—
1041C22⋊Q8—798no—
1042C22⋊Q8—7916no—
1043C22⋊Q8—7916no—
1044C22⋊Q8C22×D7918yescomplemented
1045#121—798no—
1046#121—798no—
1047#121—7916no—
1048#121—7916no—
1049#121—7916no—
1050#121—7916no—
1051#121—7916no—
1052#121—798no—
1053#121—7916no—
1054#121—7916no—
1055#121C22×D7918yescomplemented
1056#121C22×D79116yescomplemented
1057#120—7916no—
1058#120—7916no—
1059#120—798no—
1060#120—7916no—
1061#120—798no—
1062#120—7916no—
1063#120C22×D79116yescomplemented
1064C4×D4—798no—
1065C4×D4—7916no—
1066C4×D4—7916no—
1067C4×D4—798no—
1068C4×D4—798no—
1069C4×D4—798no—
1070C4×D4—7916no—
1071C4×D4—7916no—
1072C4×D4—798no—
1073C4×D4—798no—
1074C4×D4C22×D7918yescomplemented
1075C4×D4C22×D7918yescomplemented
1076#117—798no—
1077#117—798no—
1078C2×C4⋊C4—791no—
1079C2×C4⋊C4—791no—
1080C2×C4⋊C4—792no—
1081C2×C4⋊C4—792no—
1082C2×C4⋊C4—791no—
1083C2×C4⋊C4—792no—
1084C2×C4⋊C4—792no—
1085C2×C4⋊C4—792no—
1086C2×C4⋊C4—792no—
1087C2×C4⋊C4—792no—
1088C2×C4⋊C4—792no—
1089C2×C4⋊C4—792no—
1090C2×C4⋊C4—7916no—
1091C2×C4⋊C4—7916no—
1092C2×C4⋊C4—791no—
1093C2×C4⋊C4—791no—
1094C2×C4⋊C4—791no—
1095C2×C4⋊C4—7916no—
1096C2×C4⋊C4—7916no—
1097C2×C4⋊C4C22×D7911yescharacteristic
1098C2×C4⋊C4C22×D7912yes—
1099C2×C4⋊C4C22×D7911yescharacteristic
1100C2×C22⋊C4—792no—
1101C2×C22⋊C4—791no—
1102C2×C22⋊C4—792no—
1103C2×C22⋊C4—792no—
1104C2×C22⋊C4—792no—
1105C2×C22⋊C4—792no—
1106C2×C22⋊C4—7916no—
1107C2×C22⋊C4—792no—
1108C2×C22⋊C4—791no—
1109C2×C22⋊C4—792no—
1110C2×C22⋊C4—791no—
1111C2×C22⋊C4—791no—
1112C2×C22⋊C4—791no—
1113C2×C22⋊C4—791no—
1114C2×C22⋊C4—792no—
1115C2×C22⋊C4—792no—
1116C2×C22⋊C4—7916no—
1117C2×C22⋊C4—792no—
1118C2×C22⋊C4—792no—
1119C2×C22⋊C4—791no—
1120C2×C22⋊C4—792no—
1121C2×C22⋊C4—791no—
1122C2×C22⋊C4—7916no—
1123C2×C22⋊C4—7916no—
1124C2×C22⋊C4—7916no—
1125C2×C22⋊C4C22×D7912yes—
1126C2×C22⋊C4C22×D7912yes—
1127C2×C22⋊C4C22×D7912yes—
1128C2×C22⋊C4C22×D7911yescharacteristic
1129C2×C22⋊C4C22×D7912yes—
1130C2×C22⋊C4C22×D7912yes—
1131C2×C22⋊C4C22×D7911yescharacteristic
1132C2×C22⋊C4C22×D79116yescomplemented
1133C2×C42—792no—
1134C2×C42—791no—
1135C2×C42C22×D7911yescharacteristic
1136C24—28no—
1137C24—44no—
1138C24—44no—
1139C24—3164no—
1140C24—3164no—
1141C24—3162no—
1142C24—3162no—
1143C24—3164no—
1144C24—3164no—
1145C24—798no—
1146C24—7916no—
1147C24—798no—
1148C24—794no—
1149C24—791no—
1150C24—792no—
1151C24—791no—
1152C24—791no—
1153C24—1584no—
1154C24—1588no—
1155C24C23×D7912yes—
1156C24C23×D7911yescharacteristic
1157C24C23×D7911yescharacteristic
1158C24C23×D7912yes—
1159C24C23×D7918yes—
1160#41—232no—
1161#41—15832no—
1162#41—15864no—
1163#41—15832no—
1164#41—15832no—
1165#41—15832no—
1166#41—15864no—
1167#41—15864no—
1168#41—15832no—
1169#41—15832no—
1170#41—15832no—
1171C2×Q8—24no—
1172C2×Q8—798no—
1173C2×Q8—794no—
1174C2×Q8—794no—
1175C2×Q8—794no—
1176C2×Q8—1588no—
1177C2×Q8—1584no—
1178C2×Q8—15832no—
1179C2×Q8—1584no—
1180C2×Q8—1584no—
1181C2×Q8C23×D7914yes—
1182C2×D4—28no—
1183C2×D4—28no—
1184C2×D4—232no—
1185C2×D4—24no—
1186C2×D4—44no—
1187C2×D4—42no—
1188C2×D4—3162no—
1189C2×D4—3162no—
1190C2×D4—3162no—
1191C2×D4—3164no—
1192C2×D4—794no—
1193C2×D4—798no—
1194C2×D4—794no—
1195C2×D4—798no—
1196C2×D4—7916no—
1197C2×D4—7964no—
1198C2×D4—798no—
1199C2×D4—798no—
1200C2×D4—798no—
1201C2×D4—794no—
1202C2×D4—798no—
1203C2×D4—798no—
1204C2×D4—798no—
1205C2×D4—794no—
1206C2×D4—794no—
1207C2×D4—794no—
1208C2×D4—798no—
1209C2×D4—794no—
1210C2×D4—798no—
1211C2×D4—1584no—
1212C2×D4—1588no—
1213C2×D4—1584no—
1214C2×D4—15832no—
1215C2×D4—15864no—
1216C2×D4—15864no—
1217C2×D4—15864no—
1218C2×D4—1584no—
1219C2×D4—1588no—
1220C2×D4—1588no—
1221C2×D4—1588no—
1222C2×D4—1588no—
1223C2×D4—15864no—
1224C2×D4—1588no—
1225C2×D4—1588no—
1226C2×D4D4×D7918yes—
1227C2×D4C23×D7918yes—
1228C2×D4C23×D7918yes—
1229C2×D4C23×D7914yes—
1230C2×D4C23×D7918yes—
1231C2×D4C23×D7914yes—
1232C2×D4C23×D7914yes—
1233C22×C4—28no—
1234C22×C4—24no—
1235C22×C4—24no—
1236C22×C4—44no—
1237C22×C4—3164no—
1238C22×C4—3164no—
1239C22×C4—3164no—
1240C22×C4—798no—
1241C22×C4—798no—
1242C22×C4—798no—
1243C22×C4—791no—
1244C22×C4—794no—
1245C22×C4—798no—
1246C22×C4—798no—
1247C22×C4—798no—
1248C22×C4—794no—
1249C22×C4—798no—
1250C22×C4—791no—
1251C22×C4—791no—
1252C22×C4—792no—
1253C22×C4—791no—
1254C22×C4—792no—
1255C22×C4—791no—
1256C22×C4—792no—
1257C22×C4—798no—
1258C22×C4—798no—
1259C22×C4—798no—
1260C22×C4—794no—
1261C22×C4—794no—
1262C22×C4—794no—
1263C22×C4—794no—
1264C22×C4—798no—
1265C22×C4—1584no—
1266C22×C4—15832no—
1267C22×C4—1584no—
1268C22×C4—1588no—
1269C22×C4—1588no—
1270C22×C4—1588no—
1271C22×C4—15864no—
1272C22×C4—1588no—
1273C22×C4—1584no—
1274C22×C4—1588no—
1275C22×C4—1588no—
1276C22×C4—1588no—
1277C22×C4—1584no—
1278C22×C4—1584no—
1279C22×C4C23×D7918yes—
1280C22×C4C23×D7914yes—
1281C22×C4C23×D7914yes—
1282C22×C4C23×D7912yes—
1283C22×C4C23×D7911yescharacteristic
1284C22×C4C23×D7911yescharacteristic
1285C22×C4C23×D7911yescharacteristic
1286C22×C4C23×D7912yes—
1287C22×C4C23×D7911yescharacteristic
1288C22×C4C23×D7918yes—
1289C22×C4C23×D7911yescharacteristic
1290C4⋊C4—794no—
1291C4⋊C4—798no—
1292C4⋊C4—794no—
1293C4⋊C4—798no—
1294C4⋊C4—798no—
1295C4⋊C4—798no—
1296C4⋊C4—798no—
1297C4⋊C4—794no—
1298C4⋊C4—794no—
1299C4⋊C4—798no—
1300C4⋊C4—794no—
1301C4⋊C4—798no—
1302C4⋊C4—798no—
1303C4⋊C4—798no—
1304C4⋊C4—794no—
1305C4⋊C4C23×D7914yes—
1306C4⋊C4C23×D7918yes—
1307C4⋊C4C23×D7914yes—
1308C22⋊C4—798no—
1309C22⋊C4—794no—
1310C22⋊C4—798no—
1311C22⋊C4—798no—
1312C22⋊C4—798no—
1313C22⋊C4—798no—
1314C22⋊C4—794no—
1315C22⋊C4—798no—
1316C22⋊C4—798no—
1317C22⋊C4—794no—
1318C22⋊C4—794no—
1319C22⋊C4—794no—
1320C22⋊C4—794no—
1321C22⋊C4—798no—
1322C22⋊C4—798no—
1323C22⋊C4—798no—
1324C22⋊C4—798no—
1325C22⋊C4—794no—
1326C22⋊C4—798no—
1327C22⋊C4—794no—
1328C22⋊C4C23×D7918yes—
1329C22⋊C4C23×D7918yes—
1330C22⋊C4C23×D7918yes—
1331C22⋊C4C23×D7914yes—
1332C22⋊C4C23×D7918yes—
1333C22⋊C4C23×D7918yes—
1334C22⋊C4C23×D7914yes—
1335C42—798no—
1336C42—794no—
1337C42C23×D7914yes—
1338C23—24no—
1339C23—24no—
1340C23—22no—
1341C23—24no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—24no—
1346C23—22no—
1347C23—22no—
1348C23—24no—
1349C23—216no—
1350C23—48no—
1351C23—48no—
1352C23—816no—
1353C23—31632no—
1354C23—3168no—
1355C23—3168no—
1356C23—3164no—
1357C23—3164no—
1358C23—3168no—
1359C23—3168no—
1360C23—31616no—
1361C23—7932no—
1362C23—792no—
1363C23—794no—
1364C23—794no—
1365C23—798no—
1366C23—792no—
1367C23—792no—
1368C23—63216no—
1369C23—1588no—
1370C23—15816no—
1371C23—1582no—
1372C23—1582no—
1373C23—1582no—
1374C23—1582no—
1375C23—1582no—
1376C23—1582no—
1377C23—1584no—
1378C23—1582no—
1379C23—1584no—
1380C23—1582no—
1381C23C2×D4×D7918yes—
1382C23C24×D7914yes—
1383C23C24×D7912yes—
1384C23C24×D7912yes—
1385C23C24×D7914yes—
1386C23C24×D7911yescharacteristic
1387Q8—28no—
1388Q8—15816no—
1389Q8—1588no—
1390Q8—1588no—
1391Q8—1588no—
1392D4—216no—
1393D4—216no—
1394D4—28no—
1395D4—48no—
1396D4—44no—
1397D4—3164no—
1398D4—3164no—
1399D4—3164no—
1400D4—3168no—
1401D4—7932no—
1402D4—7916no—
1403D4—1588no—
1404D4—15816no—
1405D4—1588no—
1406D4—1588no—
1407D4—15816no—
1408D4—15816no—
1409D4—15816no—
1410D4—15816no—
1411D4—15816no—
1412D4—15816no—
1413D4C2×D4×D79116yes—
1414C2×C4—22no—
1415C2×C4—24no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—216no—
1421C2×C4—28no—
1422C2×C4—28no—
1423C2×C4—48no—
1424C2×C4—3168no—
1425C2×C4—3168no—
1426C2×C4—3168no—
1427C2×C4—792no—
1428C2×C4—794no—
1429C2×C4—7916no—
1430C2×C4—792no—
1431C2×C4—794no—
1432C2×C4—792no—
1433C2×C4—792no—
1434C2×C4—794no—
1435C2×C4—792no—
1436C2×C4—794no—
1437C2×C4—1588no—
1438C2×C4—1588no—
1439C2×C4—15816no—
1440C2×C4—15816no—
1441C2×C4—15816no—
1442C2×C4—15816no—
1443C2×C4—1588no—
1444C2×C4—15816no—
1445C2×C4—1582no—
1446C2×C4—1584no—
1447C2×C4—1582no—
1448C2×C4—1582no—
1449C2×C4—1584no—
1450C2×C4—1582no—
1451C2×C4—1584no—
1452C2×C4—15816no—
1453C2×C4—15816no—
1454C2×C4—1588no—
1455C2×C4—1588no—
1456C2×C4C2×D4×D7914yes—
1457C2×C4C24×D7914yes—
1458C2×C4C24×D7912yes—
1459C2×C4C24×D7912yes—
1460C2×C4C24×D7912yes—
1461C2×C4C24×D7914yes—
1462C2×C4C24×D7912yes—
1463C2×C4C24×D7912yes—
1464C22—216no—
1465C22—24no—
1466C22—24no—
1467C22—22no—
1468C22—22no—
1469C22—24no—
1470C22—22no—
1471C22—24no—
1472C22—22no—
1473C22—22no—
1474C22—22no—
1475C22—24no—
1476C22—44no—
1477C22—48no—
1478C22—44no—
1479C22—816no—
1480C22—31632no—
1481C22—31616no—
1482C22—3164no—
1483C22—3164no—
1484C22—794no—
1485C22—798no—
1486C22—63216no—
1487C22—1582no—
1488C22—1582no—
1489C22—1582no—
1490C22—1582no—
1491C22—1582no—
1492C22—1582no—
1493C22—1588no—
1494C22—15816no—
1495C22—1584no—
1496C22—1582no—
1497C22—1584no—
1498C22—1582no—
1499C22C22×D4×D7918yes—
1500C22C22×D4×D7912yes—
1501C22#1909939812yes—
1502C22#1909939912yes—
1503C22C25×D7911yescharacteristic
1504C4—22no—
1505C4—22no—
1506C4—24no—
1507C4—22no—
1508C4—24no—
1509C4—22no—
1510C4—794no—
1511C4—1582no—
1512C4—1584no—
1513C4—1582no—
1514C4—1584no—
1515C4—1582no—
1516C4—1584no—
1517C4—1582no—
1518C4C22×D4×D7914yes—
1519C2—28no—
1520C2—42no—
1521C2—44no—
1522C2—42no—
1523C2—3162no—
1524C2—3162no—
1525C2—1584no—
1526C2—1588no—
1527C2#2377703714yesdirect product factor
1528C2C23×D4×D7911yescharacteristic
1529C2C2×#1909939811yescharacteristic
1530C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#546×C79C2
socleC23×C79C25
hypercenterC2×#546D79
hypocenterC79C2×#3485
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C22×#14579206C2semidirect
2. C22×#41×D79C2semidirect
3. #23777037C2direct (N × H)
4. C2×#19099218C2semidirect
5. C2×#19099217C2semidirect
6. C2×#19099215C2semidirect
7. C2×#19099213C2semidirect
8. C2×#19099212C2semidirect
9. C2×#19099211C2semidirect
10. C2×#19099210C2semidirect
11. C2×#19099207C2semidirect
12. C2×#19099206C2semidirect
13. C2×#19099203C2semidirect
14. C2×#19099200C2semidirect
15. C2×#19099136C2semidirect
16. C2×#19099133C2semidirect
17. C2×#19099123C2semidirect
18. C2×#19099121C2semidirect
19. C2×#19099073C2semidirect
20. C2×#19099072C2semidirect
21. C22×#14579143C2semidirect
22. C2×#123×D79C2semidirect
23. C2×#19099035C2semidirect
24. C2×#546×C79C2semidirect
26. C2×#14579206C22semidirect
27. C22×#11929625C22semidirect
29. C22×#11929624C22semidirect
30. C22×#11929624C22semidirect
31. C22×#11929624C22semidirect
33. C22×#11929623C22semidirect
34. C22×#11929623C22semidirect
35. C22×#11929623C22semidirect
36. C22×#11929623C22semidirect
38. C2×#41×D79C22semidirect
39. C22×Q8×D79C22semidirect
41. C23×C22⋊D79C22semidirect
44. C22×D4×D79C22semidirect
45. C22×D4×D79C22semidirect
46. C23×C4×D79C22semidirect
47. C23×C4×D79C22semidirect
48. #19099218C22semidirect
49. #19099217C22semidirect
50. #19099215C22semidirect
51. #19099213C22semidirect
52. #19099212C22semidirect
53. #19099211C22semidirect
54. #19099210C22semidirect
55. #19099207C22semidirect
56. #19099206C22semidirect
57. #19099203C22semidirect
58. #19099200C22semidirect
59. #19099136C22semidirect
60. #19099133C22semidirect
61. #19099123C22semidirect
62. #19099121C22semidirect
63. C2×#14579161C22semidirect
64. C2×#14579160C22semidirect
65. C2×#14579159C22semidirect
66. C2×#14579148C22semidirect
67. C2×#14579147C22semidirect
68. #19099073C22semidirect
69. #19099072C22semidirect
70. C2×#14579146C22semidirect
71. C2×#14579146C22semidirect
72. C2×#14579146C22semidirect
73. C2×#14579145C22semidirect
74. C2×#14579145C22semidirect
75. C2×#14579144C22semidirect
76. C2×#14579143C22semidirect
77. C2×#14579143C22semidirect
78. C2×#14579143C22semidirect
79. C2×#14579143C22semidirect
80. C2×#14579143C22semidirect
81. C2×#14579143C22semidirect
82. C2×#14579143C22semidirect
83. C2×#14579143C22semidirect
84. C2×#14579143C22semidirect
85. C2×#14579143C22semidirect
86. C2×#14579143C22semidirect
87. C2×#14579142C22semidirect
88. C2×#14579142C22semidirect
89. #123×D79C22semidirect
90. C2×#14579141C22semidirect
91. C2×#14579141C22semidirect
92. C2×#14579140C22semidirect
93. C2×#14579140C22semidirect
94. C2×#14579139C22semidirect
95. C2×#14579138C22semidirect
96. C2×#14579138C22semidirect
97. C2×#14579138C22semidirect
98. C2×#14579137C22semidirect
99. C2×#14579135C22semidirect
100. C2×#14579134C22semidirect
101. C2×#14579134C22semidirect
102. C2×#14579134C22semidirect
103. C2×#14579133C22semidirect
104. C2×#14579133C22semidirect
105. C2×#14579133C22semidirect
106. C2×#14579132C22semidirect
107. C2×#14579132C22semidirect
108. C2×#14579132C22semidirect
109. C2×#14579131C22semidirect
110. C2×#14579131C22semidirect
111. C2×#14579130C22semidirect
112. C2×#14579129C22semidirect
113. C2×#14579129C22semidirect
114. C2×#14579129C22semidirect
115. #19099035C22semidirect
116. C2×C4×D316C22semidirect
117. C2×C4×D316C22semidirect
118. C2×D4×Dic79C22semidirect
119. C2×D4×Dic79C22semidirect
120. C2×#14579123C22semidirect
121. C2×C4×C22⋊D79C22semidirect
122. C2×C4×C22⋊D79C22semidirect
123. C2×C4×C22⋊D79C22semidirect
124. C2×(C22⋊D79)⋊C4C22semidirect
125. C2×(C22⋊D79)⋊C4C22semidirect
126. C2×#14579119C22semidirect
127. C2×#14579118C22semidirect
128. C22×C4⋊Dic79C22semidirect
129. C22×Dic79⋊C4C22semidirect
130. C2×C4⋊C4×D79C22semidirect
131. C2×C4⋊C4×D79C22semidirect
132. C22×C22⋊Dic79C22semidirect
133. C22×(C2×D79)⋊C4C22semidirect
134. C2×C22⋊C4×D79C22semidirect
135. C2×C22⋊C4×D79C22semidirect
136. C2×C22⋊C4×D79C22semidirect
137. C22×#41×C79C22semidirect
138. C23×D4×C79C22semidirect
139. #546×C79C22semidirect
140. C2×#124×C79C22semidirect
141. C2×#123×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. C22×C22⋊C4×C79C22semidirect
154. C2×#11929625C23semidirect
160. C2×#11929624C23semidirect
161. C2×#11929624C23semidirect
162. C2×#11929624C23semidirect
169. C2×#11929623C23semidirect
170. C2×#11929623C23semidirect
171. C2×#11929623C23semidirect
172. C2×#11929623C23semidirect
179. C2×Q8×D79C23semidirect
199. C22×C22⋊D79C23semidirect
203. C2×D4×D79D4semidirect
206. C2×D4×D79C23semidirect
207. C2×D4×D79C23semidirect
226. C22×C4×D79C23semidirect
227. C22×C4×D79C23semidirect
228. #14579161C23semidirect
229. #14579160C23semidirect
230. #14579159C23semidirect
231. #14579148C23semidirect
232. #14579147C23semidirect
233. #14579146C23semidirect
234. #14579146C23semidirect
235. #14579146C23semidirect
236. #14579145C23semidirect
237. #14579145C23semidirect
238. #14579144C23semidirect
239. #14579143C23semidirect
240. #14579143C23semidirect
241. #14579143C23semidirect
242. #14579143C23semidirect
243. #14579143C23semidirect
244. #14579143C23semidirect
245. #14579143C23semidirect
246. #14579143C23semidirect
247. #14579143C23semidirect
248. #14579143C23semidirect
249. #14579142C23semidirect
250. #14579142C23semidirect
251. #14579141C23semidirect
252. #14579141C23semidirect
253. #14579140C23semidirect
254. #14579140C23semidirect
255. #14579139C23semidirect
256. #14579138C23semidirect
257. #14579138C23semidirect
258. #14579138C23semidirect
259. #14579137C23semidirect
260. #14579135C23semidirect
261. #14579134C23semidirect
262. #14579134C23semidirect
263. #14579134C23semidirect
264. #14579133C23semidirect
265. #14579133C23semidirect
266. #14579133C23semidirect
267. #14579132C23semidirect
268. #14579132C23semidirect
269. #14579132C23semidirect
270. #14579131C23semidirect
271. #14579131C23semidirect
272. #14579130C23semidirect
273. #14579129C23semidirect
274. #14579129C23semidirect
275. #14579129C23semidirect
276. C4×D316C23semidirect
277. C4×D316C23semidirect
278. D4×Dic79C23semidirect
279. D4×Dic79C23semidirect
280. #14579123C23semidirect
281. C4×C22⋊D79C23semidirect
282. C4×C22⋊D79C23semidirect
283. C4×C22⋊D79C23semidirect
284. (C22⋊D79)⋊C4C23semidirect
285. (C22⋊D79)⋊C4C23semidirect
286. #14579119C23semidirect
287. #14579118C23semidirect
294. C2×C4⋊Dic79C23semidirect
304. C2×Dic79⋊C4C23semidirect
305. C4⋊C4×D79C23semidirect
306. C4⋊C4×D79C23semidirect
315. C2×C22⋊Dic79C23semidirect
328. C2×(C2×D79)⋊C4C23semidirect
329. C22⋊C4×D79C23semidirect
330. C22⋊C4×D79C23semidirect
331. C22⋊C4×D79C23semidirect
336. C2×#41×C79C23semidirect
345. C22×D4×C79C23semidirect
350. #124×C79C23semidirect
351. #123×C79C23semidirect
352. C22⋊Q8×C79C23semidirect
353. #121×C79C23semidirect
354. #121×C79C23semidirect
355. #120×C79C23semidirect
356. C4×D4×C79C23semidirect
357. C4×D4×C79C23semidirect
368. C2×C22⋊C4×C79C23semidirect
442. D4×D79C2×D4semidirect
758. C2×C79#3485semidirect
780. C2×#546D79semidirect
790. C79C2×#3485semidirect
805. C22×#41C2×D79semidirect
813. C23×D4C2×D79semidirect
827. #546C2×D79semidirect
837. C2×#124C2×D79semidirect
860. C2×#123C2×D79semidirect
870. C2×C22⋊Q8C2×D79semidirect
881. C2×#121C2×D79semidirect
882. C2×#121C2×D79semidirect
889. C2×#120C2×D79semidirect
901. C2×C4×D4C2×D79semidirect
902. C2×C4×D4C2×D79semidirect
914. C22×C22⋊C4C2×D79semidirect
942. C2×#41C22×D79semidirect
985. C22×D4C22×D79semidirect
1015. #124C22×D79semidirect
1034. #123C22×D79semidirect
1044. C22⋊Q8C22×D79semidirect
1055. #121C22×D79semidirect
1056. #121C22×D79semidirect
1063. #120C22×D79semidirect
1074. C4×D4C22×D79semidirect
1075. C4×D4C22×D79semidirect
1132. C2×C22⋊C4C22×D79semidirect
1527. C2#23777037direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792062
C22×#41×D792
#237770372
C2×#190992182
C2×#190992172
C2×#190992152
C2×#190992132
C2×#190992122
C2×#190992112
C2×#190992102
C2×#190992072
C2×#190992062
C2×#190992032
C2×#190992002
C2×#190991362
C2×#190991332
C2×#190991232
C2×#190991212
C2×#190990732
C2×#190990722
C22×#145791432
C2×#123×D792
C2×#190990352
C2×#546×C792
C2×#348579