Finite Group Databasebeta

← C2×#23777186 #35196734

Subgroups — C2×#23777186 #35196734

Order 20224.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579208C211yesmaximal, characteristic, complemented
2C22×#14579206C211yesmaximal, characteristic, complemented
3#23777186C2132yesmaximal, direct product factor
4C2×#19099223C211yesmaximal, characteristic, complemented
5C2×#19099222C211yesmaximal, characteristic, complemented
6C2×#19099221C211yesmaximal, characteristic, complemented
7C2×#19099219C211yesmaximal, characteristic, complemented
8C2×#19099208C211yesmaximal, characteristic, complemented
9C2×#19099207C211yesmaximal, characteristic, complemented
10C2×#19099205C212yesmaximal, complemented
11C2×#19099203C212yesmaximal, complemented
12C2×#19099202C212yesmaximal, complemented
13C2×#19099201C211yesmaximal, characteristic, complemented
14C2×#19099200C212yesmaximal, complemented
15C2×#19099136C211yesmaximal, characteristic, complemented
16C2×#19099135C212yesmaximal, complemented
17C2×#19099129C211yesmaximal, characteristic, complemented
18C2×#19099128C212yesmaximal, complemented
19C2×#19099110C211yesmaximal, characteristic, complemented
20C2×#19099108C212yesmaximal, complemented
21C22×#14579147C212yesmaximal, complemented
22C2×#124×D79C211yesmaximal, characteristic, complemented
23C2×C4×#11929623C211yesmaximal, characteristic, complemented
24C2×#546×C79C211yesmaximal, characteristic, complemented
25C2×#14579208—216no—
26C2×#14579208C22116yescomplemented
27C2×#14579206—216no—
28C2×#14579206C22116yescomplemented
29C22×#11929624C2211yescharacteristic
30C22×#11929624C2211yescharacteristic
31C22×#11929624C2212yescomplemented
32C22×#11929624C2211yescharacteristic, complemented
33C22×#11929623C2211yescharacteristic
34C22×#11929623C2212yes—
35C22×#11929623C2211yescharacteristic
36C22×#11929623C2212yescomplemented
37C22×#11929623C2211yescharacteristic, complemented
38C22×#11929623C2212yescomplemented
39C23×Dic158C2211yescharacteristic, complemented
40C23×Dic158C2212yescomplemented
41C22×Q8×D79C2211yescharacteristic, complemented
42C22×Q8×D79C2211yescharacteristic, complemented
43C23×C22⋊D79C2212yes—
44C23×C22⋊D79C2212yes—
45C22×D4×D79C2211yescharacteristic
46C22×D4×D79C2212yes—
47C22×D4×D79C2211yescharacteristic
48#19099223C22116yescomplemented
49#19099222C22116yescomplemented
50#19099221C22116yescomplemented
51#19099219C22116yescomplemented
52#19099208C22116yescomplemented
53#19099207C22116yescomplemented
54#19099205C22132yescomplemented
55#19099203C22132yescomplemented
56#19099202C22132yescomplemented
57#19099201C22116yescomplemented
58#19099200C22132yescomplemented
59#19099136C22116yescomplemented
60#19099135C22132yescomplemented
61#19099129C22116yescomplemented
62#19099128C22132yescomplemented
63#19099110C22116yescomplemented
64#19099108C22132yescomplemented
65C2×#14579160C2212yescomplemented
66C2×#14579160C2211yescharacteristic, complemented
67C2×#14579157C2212yescomplemented
68C2×#14579157C2211yescharacteristic, complemented
69C2×#14579150C2211yescharacteristic, complemented
70C2×#14579149C2211yescharacteristic, complemented
71C2×#14579148C2211yescharacteristic, complemented
72C2×#14579147C2212yescomplemented
73C2×#14579147C2212yescomplemented
74C2×#14579147C2212yescomplemented
75C2×#14579147C2212yescomplemented
76C2×#14579147C2212yescomplemented
77C2×#14579147C2212yescomplemented
78C2×#14579147C2211yescharacteristic, complemented
79C2×#14579147C2212yescomplemented
80C2×#14579147C2212yescomplemented
81C2×#14579147C2211yescharacteristic, complemented
82C2×#14579147C22132yescomplemented
83#124×D79C22116yescomplemented
84C2×#14579146C2212yescomplemented
85C2×#14579145C2212yescomplemented
86C2×#14579144C2212yescomplemented
87C2×#14579143C2212yescomplemented
88C2×#14579142C2212yescomplemented
89C2×#14579141C2211yescharacteristic, complemented
90C2×#14579140C2211yescharacteristic, complemented
91C2×#14579139C2212yescomplemented
92C2×#14579139C2212yescomplemented
93C2×#14579138C2212yescomplemented
94C2×#14579138C2212yescomplemented
95C2×#14579137C2211yescharacteristic, complemented
96C2×#14579136C2211yescharacteristic, complemented
97C2×#14579136C2211yescharacteristic, complemented
98C2×#14579135C2211yescharacteristic, complemented
99C2×#14579135C2212yescomplemented
100C2×#14579134C2211yescharacteristic, complemented
101C2×#14579134C2211yescharacteristic, complemented
102C2×#14579134C2212yescomplemented
103C2×#14579134C2212yescomplemented
104C2×#14579133C2212yescomplemented
105C2×#14579133C2212yescomplemented
106C2×#14579133C2212yescomplemented
107C2×#14579133C2212yescomplemented
108C2×#14579132C2211yescharacteristic, complemented
109C2×#14579132C2211yescharacteristic, complemented
110C2×#14579131C2212yescomplemented
111C2×#14579131C2212yescomplemented
112C2×#14579130C2212yescomplemented
113C2×#14579129C2212yescomplemented
114C2×#14579129C2212yescomplemented
115C4×#11929623C22116yescomplemented
116C2×C4×Dic158C2211yescharacteristic, complemented
117C2×#14579126C2211yescharacteristic, complemented
118C2×C4×D316C2211yescharacteristic, complemented
119C2×D4×Dic79C2211yescharacteristic, complemented
120C2×D4×Dic79C2212yescomplemented
121C2×#14579123C2212yescomplemented
122C2×C4×C22⋊D79C2212yescomplemented
123C2×C4×C22⋊D79C2211yescharacteristic, complemented
124C2×C4×C22⋊D79C2211yescharacteristic, complemented
125C2×(C22⋊D79)⋊C4C2212yescomplemented
126C2×(C22⋊D79)⋊C4C2212yescomplemented
127C2×(C22⋊D79)⋊C4C2212yescomplemented
128C2×#14579119C2211yescharacteristic, complemented
129C2×#14579117C2212yescomplemented
130C22×C22⋊Dic79C2212yescomplemented
131C22×(C2×D79)⋊C4C2212yescomplemented
132C22×(C2×D79)⋊C4C2212yescomplemented
133C2×C22⋊C4×D79C2212yescomplemented
134C2×C22⋊C4×D79C2212yescomplemented
135C22×C4×Dic79C2212yescomplemented
136C2×C42×D79C2211yescharacteristic, complemented
137C22×#41×C79C2211yescharacteristic, complemented
138C23×D4×C79C2211yescharacteristic
139#546×C79C22116yescomplemented
140C2×#124×C79C2211yescharacteristic, complemented
141C2×#123×C79C2212yescomplemented
142C2×C22⋊Q8×C79C2211yescharacteristic, complemented
143C2×#121×C79C2212yescomplemented
144C2×#121×C79C2211yescharacteristic, complemented
145C2×#120×C79C2212yescomplemented
146C2×C4×D4×C79C2211yescharacteristic, complemented
147C2×C4×D4×C79C2211yescharacteristic, complemented
148C22×C22⋊C4×C79C2212yescomplemented
149C24×D79C2312yes—
150C24×D79C2312yes—
151#14579208—2128no—
152#14579206—2128no—
153C2×#11929624—28no—
154C2×#11929624—216no—
155C2×#11929624—28no—
156C2×#11929624—28no—
157C2×#11929624C2318yes—
158C2×#11929624C2318yes—
159C2×#11929624C23116yescomplemented
160C2×#11929624C2318yescomplemented
161C2×#11929623—28no—
162C2×#11929623—28no—
163C2×#11929623—216no—
164C2×#11929623—216no—
165C2×#11929623—216no—
166C2×#11929623D4116yescomplemented
167C2×#11929623C2318yes—
168C2×#11929623C23116yes—
169C2×#11929623C2318yes—
170C2×#11929623C23116yescomplemented
171C2×#11929623C2318yescomplemented
172C2×#11929623C23116yescomplemented
173C22×Dic158—28no—
174C22×Dic158—216no—
175C22×Dic158C2312yes—
176C22×Dic158C2312yes—
177C22×Dic158C2311yescharacteristic
178C22×Dic158C2312yes—
179C22×Dic158C2311yescharacteristic
180C22×Dic158C2311yescharacteristic
181C22×Dic158C2311yescharacteristic
182C22×Dic158C2318yescomplemented
183C22×Dic158C23116yescomplemented
184C2×Q8×D79—28no—
185C2×Q8×D79—28no—
186C2×Q8×D79C2318yescomplemented
187C2×Q8×D79C2318yescomplemented
188C22×D316C2311yescharacteristic
189C22×D316C2311yescharacteristic
190C22×D316C2311yescharacteristic
191C22×D316C2312yes—
192C22×D316C2311yescharacteristic
193C22×C22⋊D79—216no—
194C22×C22⋊D79—216no—
195C22×C22⋊D79C23116yes—
196C22×C22⋊D79C23116yes—
197C22×C22⋊D79C2311yescharacteristic
198C22×C22⋊D79C2312yes—
199C22×C22⋊D79C2311yescharacteristic
200C22×C22⋊D79C2312yes—
201C22×C22⋊D79C2312yes—
202C22×C22⋊D79C2312yes—
203C22×C22⋊D79C2312yes—
204C22×C22⋊D79C2311yescharacteristic
205C22×C22⋊D79C2311yescharacteristic
206C22×C22⋊D79C2312yes—
207C22×C22⋊D79C2312yes—
208C22×C22⋊D79C2311yescharacteristic
209C22×C22⋊D79C2311yescharacteristic
210C22×C22⋊D79C2312yes—
211C2×D4×D79—28no—
212C2×D4×D79—216no—
213C2×D4×D79—28no—
214C2×D4×D79C2318yes—
215C2×D4×D79C23116yes—
216C2×D4×D79C2318yes—
217C23×Dic79C2312yes—
218C23×Dic79C2312yes—
219C23×Dic79C2312yes—
220C23×Dic79C2312yes—
221C23×Dic79C2312yes—
222C22×C4×D79C2312yes—
223C22×C4×D79C2312yes—
224C22×C4×D79C2312yes—
225C22×C4×D79C2311yescharacteristic
226C22×C4×D79C2311yescharacteristic
227C22×C4×D79C2311yescharacteristic
228C22×C4×D79C2311yescharacteristic
229C22×C4×D79C2311yescharacteristic
230#14579160C23116yescomplemented
231#14579160C2318yescomplemented
232#14579157C23116yescomplemented
233#14579157C2318yescomplemented
234#14579150C2318yescomplemented
235#14579149C2318yescomplemented
236#14579148C2318yescomplemented
237#14579147C23116yescomplemented
238#14579147C23116yescomplemented
239#14579147C23116yescomplemented
240#14579147C23116yescomplemented
241#14579147C23116yescomplemented
242#14579147C23116yescomplemented
243#14579147C23116yescomplemented
244#14579147C2318yescomplemented
245#14579147C23116yescomplemented
246#14579147C2318yescomplemented
247#14579146C23116yescomplemented
248#14579145C23116yescomplemented
249#14579144C23116yescomplemented
250#14579143C23116yescomplemented
251#14579142C23116yescomplemented
252#14579141C2318yescomplemented
253#14579140C2318yescomplemented
254#14579139C23116yescomplemented
255#14579139C23116yescomplemented
256#14579138C23116yescomplemented
257#14579138C23116yescomplemented
258#14579137C2318yescomplemented
259#14579136C2318yescomplemented
260#14579136C2318yescomplemented
261#14579135C2318yescomplemented
262#14579135C23116yescomplemented
263#14579134C2318yescomplemented
264#14579134C2318yescomplemented
265#14579134C23116yescomplemented
266#14579134C23116yescomplemented
267#14579133C23116yescomplemented
268#14579133C23116yescomplemented
269#14579133C23116yescomplemented
270#14579133C23116yescomplemented
271#14579132C2318yescomplemented
272#14579132C2318yescomplemented
273#14579131C23116yescomplemented
274#14579131C23116yescomplemented
275#14579130C23116yescomplemented
276#14579129C23116yescomplemented
277#14579129C23116yescomplemented
278C4×Dic158C2318yescomplemented
279#14579126C2318yescomplemented
280C4×D316C2318yescomplemented
281D4×Dic79C23116yescomplemented
282D4×Dic79C2318yescomplemented
283#14579123C23116yescomplemented
284C4×C22⋊D79C2318yescomplemented
285C4×C22⋊D79C23116yescomplemented
286C4×C22⋊D79C2318yescomplemented
287(C22⋊D79)⋊C4C23116yescomplemented
288(C22⋊D79)⋊C4C23116yescomplemented
289(C22⋊D79)⋊C4C23116yescomplemented
290#14579119C2318yescomplemented
291#14579117C23116yescomplemented
292C2×C4⋊Dic79C2311yescharacteristic
293C2×C4⋊Dic79C2312yes—
294C2×C4⋊Dic79C2311yescharacteristic
295C2×Dic79⋊C4C2312yes—
296C2×Dic79⋊C4C2312yes—
297C2×Dic79⋊C4C2312yes—
298C2×Dic79⋊C4C2312yes—
299C2×Dic79⋊C4C2311yescharacteristic
300C2×Dic79⋊C4C2311yescharacteristic
301C2×C22⋊Dic79C2312yes—
302C2×C22⋊Dic79C2312yes—
303C2×C22⋊Dic79C2311yescharacteristic
304C2×C22⋊Dic79C2312yes—
305C2×C22⋊Dic79C2312yes—
306C2×C22⋊Dic79C2312yes—
307C2×C22⋊Dic79C2311yescharacteristic
308C2×C22⋊Dic79C23116yescomplemented
309C2×(C2×D79)⋊C4C2312yes—
310C2×(C2×D79)⋊C4C2312yes—
311C2×(C2×D79)⋊C4C2312yes—
312C2×(C2×D79)⋊C4C2312yes—
313C2×(C2×D79)⋊C4C2311yescharacteristic
314C2×(C2×D79)⋊C4C2311yescharacteristic
315C2×(C2×D79)⋊C4C2312yes—
316C2×(C2×D79)⋊C4C2312yes—
317C2×(C2×D79)⋊C4C2312yes—
318C2×(C2×D79)⋊C4C2312yes—
319C2×(C2×D79)⋊C4C2312yes—
320C2×(C2×D79)⋊C4C2311yescharacteristic
321C2×(C2×D79)⋊C4C2311yescharacteristic
322C2×(C2×D79)⋊C4C23116yescomplemented
323C2×(C2×D79)⋊C4C23116yescomplemented
324C22⋊C4×D79C23116yescomplemented
325C22⋊C4×D79C23116yescomplemented
326C2×C4×Dic79C2311yescharacteristic
327C2×C4×Dic79C2311yescharacteristic
328C2×C4×Dic79C2311yescharacteristic
329C2×C4×Dic79C2312yes—
330C2×C4×Dic79C2312yes—
331C2×C4×Dic79C2312yes—
332C2×C4×Dic79C23116yescomplemented
333C42×D79C2318yescomplemented
334C25×C79C2312yes—
335C2×#41×C79—28no—
336C2×#41×C79C2318yescomplemented
337C22×Q8×C79C2311yescharacteristic
338C22×D4×C79—28no—
339C22×D4×C79C2318yes—
340C22×D4×C79C2312yes—
341C22×D4×C79C2312yes—
342C22×D4×C79C2311yescharacteristic
343C22×D4×C79C2311yescharacteristic
344C22×D4×C79C2312yes—
345C22×D4×C79C2311yescharacteristic
346C23×C4×C79C2312yes—
347C23×C4×C79C2311yescharacteristic
348C23×C4×C79C2311yescharacteristic
349C23×C4×C79C2312yes—
350#124×C79C2318yescomplemented
351#123×C79C23116yescomplemented
352C22⋊Q8×C79C2318yescomplemented
353#121×C79C23116yescomplemented
354#121×C79C2318yescomplemented
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—28no—
371C23×D79—28no—
372C23×D79—44no—
373C23×D79—44no—
374C23×D79—44no—
375C23×D79—44no—
376C23×D79C2412yes—
377C23×D79C2411yescharacteristic
378C23×D79C2411yescharacteristic
379C23×D79C2411yescharacteristic
380C23×D79C2418yes—
381C23×D79C2418yes—
382#11929624—232no—
383#11929624—232no—
384#11929624—232no—
385#11929624—264no—
386#11929623—264no—
387#11929623—264no—
388#11929623—232no—
389#11929623—232no—
390#11929623—264no—
391#11929623C2×D4164yescomplemented
392C2×Dic158—28no—
393C2×Dic158—28no—
394C2×Dic158—28no—
395C2×Dic158—24no—
396C2×Dic158—264no—
397C2×Dic158—24no—
398C2×Dic158—232no—
399C2×Dic158—24no—
400C2×Dic158C2×D418yes—
401C2×Dic158C2418yes—
402C2×Dic158C2414yes—
403C2×Dic158C2418yes—
404C2×Dic158C2418yes—
405C2×Dic158C2414yes—
406C2×Dic158C2414yes—
407C2×Dic158C2414yes—
408Q8×D79—232no—
409Q8×D79—232no—
410C2×D316—24no—
411C2×D316—24no—
412C2×D316—24no—
413C2×D316—42no—
414C2×D316—44no—
415C2×D316C2414yes—
416C2×D316C2414yes—
417C2×D316C2414yes—
418C2×D316C2418yes—
419C2×D316C2414yes—
420C2×C22⋊D79—24no—
421C2×C22⋊D79—28no—
422C2×C22⋊D79—28no—
423C2×C22⋊D79—28no—
424C2×C22⋊D79—24no—
425C2×C22⋊D79—264no—
426C2×C22⋊D79—28no—
427C2×C22⋊D79—28no—
428C2×C22⋊D79—24no—
429C2×C22⋊D79—24no—
430C2×C22⋊D79—264no—
431C2×C22⋊D79—44no—
432C2×C22⋊D79—42no—
433C2×C22⋊D79—44no—
434C2×C22⋊D79—42no—
435C2×C22⋊D79C2×D4116yes—
436C2×C22⋊D79C2418yes—
437C2×C22⋊D79C2418yes—
438C2×C22⋊D79C2418yes—
439C2×C22⋊D79C2414yes—
440C2×C22⋊D79C2418yes—
441C2×C22⋊D79C2414yes—
442C2×C22⋊D79C2414yes—
443C2×C22⋊D79C2418yes—
444C2×C22⋊D79C2414yes—
445C2×C22⋊D79C2418yes—
446C2×C22⋊D79C2418yes—
447C2×C22⋊D79C2414yes—
448C2×C22⋊D79C2414yes—
449C2×C22⋊D79C2418yes—
450D4×D79—232no—
451D4×D79—232no—
452D4×D79—264no—
453C22×Dic79—28no—
454C22×Dic79—28no—
455C22×Dic79—28no—
456C22×Dic79—44no—
457C22×Dic79C2×D4116yes—
458C22×Dic79C2411yescharacteristic
459C22×Dic79C2412yes—
460C22×Dic79C2411yescharacteristic
461C22×Dic79C2418yes—
462C22×Dic79C2418yes—
463C22×Dic79C2418yes—
464C22×Dic79C2411yescharacteristic
465C22×Dic79C2412yes—
466C22×Dic79C2411yescharacteristic
467C22×Dic79C2418yes—
468C22×Dic79C2411yescharacteristic
469C22×Dic79C2412yes—
470C22×Dic79C2418yes—
471C2×C4×D79—28no—
472C2×C4×D79—28no—
473C2×C4×D79—28no—
474C2×C4×D79—24no—
475C2×C4×D79—24no—
476C2×C4×D79—42no—
477C2×C4×D79—42no—
478C2×C4×D79C2×D418yes—
479C2×C4×D79C2418yes—
480C2×C4×D79C2418yes—
481C2×C4×D79C2414yes—
482C2×C4×D79C2418yes—
483C2×C4×D79C2414yes—
484C2×C4×D79C2414yes—
485C2×C4×D79C2414yes—
486C2×C4×D79C2414yes—
487C4⋊Dic79C2414yes—
488C4⋊Dic79C2418yes—
489C4⋊Dic79C2414yes—
490Dic79⋊C4C2418yes—
491Dic79⋊C4C2418yes—
492Dic79⋊C4C2418yes—
493Dic79⋊C4C2418yes—
494Dic79⋊C4C2414yes—
495Dic79⋊C4C2414yes—
496C22⋊Dic79C2418yes—
497C22⋊Dic79C2418yes—
498C22⋊Dic79C2414yes—
499C22⋊Dic79C2418yes—
500C22⋊Dic79C2418yes—
501C22⋊Dic79C2418yes—
502C22⋊Dic79C2414yes—
503(C2×D79)⋊C4C2418yes—
504(C2×D79)⋊C4C2418yes—
505(C2×D79)⋊C4C2418yes—
506(C2×D79)⋊C4C2418yes—
507(C2×D79)⋊C4C2414yes—
508(C2×D79)⋊C4C2414yes—
509(C2×D79)⋊C4C2418yes—
510(C2×D79)⋊C4C2418yes—
511(C2×D79)⋊C4C2418yes—
512(C2×D79)⋊C4C2418yes—
513(C2×D79)⋊C4C2418yes—
514(C2×D79)⋊C4C2414yes—
515(C2×D79)⋊C4C2414yes—
516C4×Dic79C2414yes—
517C4×Dic79C2414yes—
518C4×Dic79C2414yes—
519C4×Dic79C2418yes—
520C4×Dic79C2418yes—
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×C79C2418yes—
541C2×D4×C79C2414yes—
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×C79C2411yescharacteristic
551C22×C4×C79C2412yes—
552C22×C4×C79C2411yescharacteristic
553C22×C4×C79C2418yes—
554C22×C4×C79C2414yes—
555C22×C4×C79C2414yes—
556C22×C4×C79C2411yescharacteristic
557C22×C4×C79C2411yescharacteristic
558C22×C4×C79C2412yes—
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—22no—
594C22×D79—22no—
595C22×D79—22no—
596C22×D79—24no—
597C22×D79—22no—
598C22×D79—22no—
599C22×D79—22no—
600C22×D79—22no—
601C22×D79—24no—
602C22×D79—24no—
603C22×D79—22no—
604C22×D79—216no—
605C22×D79—216no—
606C22×D79—48no—
607C22×D79—48no—
608C22×D79—48no—
609C22×D79—48no—
610C22×D79—816no—
611C22×D79—816no—
612C22×D79C22×D414yes—
613C22×D79C2514yes—
614C22×D79C2512yes—
615C22×D79C2512yes—
616C22×D79C2512yes—
617Q8×C79—28no—
618D4×C79—216no—
619D4×C79—216no—
620D4×C79—28no—
621D4×C79—48no—
622D4×C79—44no—
623D4×C79C22×D4116yes—
624C2×C4×C79—22no—
625C2×C4×C79—24no—
626C2×C4×C79—22no—
627C2×C4×C79—216no—
628C2×C4×C79—22no—
629C2×C4×C79—22no—
630C2×C4×C79—24no—
631C2×C4×C79—28no—
632C2×C4×C79—28no—
633C2×C4×C79—48no—
634C2×C4×C79C22×D414yes—
635C2×C4×C79C2512yes—
636C2×C4×C79C2514yes—
637C2×C4×C79C2512yes—
638C2×C4×C79C2514yes—
639C2×C4×C79C2512yes—
640C2×C4×C79C2512yes—
641C2×C4×C79C2512yes—
642C22⋊D79—216no—
643C22⋊D79—216no—
644C22⋊D79—28no—
645C22⋊D79—28no—
646C22⋊D79—216no—
647C22⋊D79—216no—
648C22⋊D79—28no—
649C22⋊D79—216no—
650C22⋊D79—28no—
651C22⋊D79—44no—
652C22⋊D79—44no—
653C22⋊D79—48no—
654C22⋊D79—48no—
655C22⋊D79C22×D4132yes—
656C2×Dic79—22no—
657C2×Dic79—24no—
658C2×Dic79—22no—
659C2×Dic79—216no—
660C2×Dic79—22no—
661C2×Dic79—22no—
662C2×Dic79—24no—
663C2×Dic79—216no—
664C2×Dic79—216no—
665C2×Dic79—48no—
666C2×Dic79C22×D418yes—
667C2×Dic79C22×D414yes—
668C2×Dic79C22×D4132yes—
669C2×Dic79C2512yes—
670C2×Dic79C2514yes—
671C2×Dic79C2512yes—
672C2×Dic79C2514yes—
673C2×Dic79C2512yes—
674C2×Dic79C2512yes—
675C2×Dic79C2512yes—
676C2×Dic79C2514yes—
677D316—28no—
678D316—28no—
679D316—28no—
680D316—48no—
681D316—44no—
682C4×D79—216no—
683C4×D79—28no—
684C4×D79—28no—
685C4×D79—216no—
686C4×D79—216no—
687C4×D79—44no—
688C4×D79—44no—
689C4×D79C22×D4116yes—
690Dic158—28no—
691Dic158—216no—
692Dic158—216no—
693Dic158—28no—
694Dic158—216no—
695Dic158—28no—
696Dic158C22×D4116yes—
697C22×C79—24no—
698C22×C79—24no—
699C22×C79—216no—
700C22×C79—22no—
701C22×C79—22no—
702C22×C79—24no—
703C22×C79—22no—
704C22×C79—22no—
705C22×C79—24no—
706C22×C79—22no—
707C22×C79—24no—
708C22×C79—22no—
709C22×C79—48no—
710C22×C79—44no—
711C22×C79—44no—
712C22×C79—816no—
713C22×C79C23×D418yes—
714C22×C79C23×D412yes—
715C22×C79#58512yes—
716C22×C79#58512yes—
717C22×C79C2611yescharacteristic
718C2×D79—22no—
719C2×D79—22no—
720C2×D79—28no—
721C2×D79—24no—
722C2×D79—22no—
723C2×D79—22no—
724C2×D79—22no—
725C2×D79—22no—
726C2×D79—24no—
727C2×D79—22no—
728C2×D79—24no—
729C2×D79—22no—
730C2×D79—44no—
731C2×D79—48no—
732C2×D79—44no—
733C2×D79—816no—
734C2×D79—816no—
735C2×D79C23×D414yes—
736C4×C79—22no—
737C4×C79—22no—
738C4×C79—24no—
739C4×C79—22no—
740C4×C79—24no—
741C4×C79—22no—
742C4×C79C23×D414yes—
743Dic79—22no—
744Dic79—24no—
745Dic79—22no—
746Dic79—22no—
747Dic79—24no—
748Dic79—22no—
749Dic79C23×D414yes—
750Dic79C23×D418yes—
751C2×#3500—791nomaximal, Sylow
752C2×C79—28no—
753C2×C79—44no—
754C2×C79—42no—
755C2×C79—42no—
756C2×C79#350014yescomplemented
757C2×C79C24×D411yescharacteristic
758C2×C79C2×#58511yescharacteristic
759C2×C79C2×#58511yescharacteristic
760D79—24no—
761D79—42no—
762D79—44no—
763D79—42no—
764C22×2−1+4—791no—
765C22×H(5,𝔽2)—791no—
766#3500—7932no—
767C2×#548—791no—
768C2×#548—791no—
769C2×#548—791no—
770C2×#548—791no—
771C2×#546—791no—
772C2×#546—791no—
773C2×#546—792no—
774C2×#546—792no—
775C2×#546—792no—
776C2×#546—791no—
777C2×#546—792no—
778C2×#546D7911yescharacteristic, complemented
779C2×#536—792no—
780C2×#536—791no—
781C2×#535—791no—
782C2×#535—792no—
783C2×#532—792no—
784C2×#532—791no—
785C22×#124—791no—
786C22×#124—792no—
787C2×C4×#41—791no—
788C79C2×#350011yescharacteristic, complemented, Sylow
789C2×2−1+4—7916no—
790C2×2−1+4—15816no—
791C2×H(5,𝔽2)—7916no—
792C2×H(5,𝔽2)—15816no—
793C22×#41—791no—
794C22×#41—792no—
795C22×#41—791no—
796C22×#41—792no—
797C22×#41—791no—
798C22×#41—792no—
799C22×#41—791no—
800C22×#41—791no—
801C22×#41—791no—
802C22×#41—792no—
803C22×#41C2×D7911yescharacteristic, complemented
804C23×Q8—791no—
805C23×Q8—791no—
806C23×Q8—792no—
807C23×Q8—791no—
808C23×D4—792no—
809C23×D4—792no—
810C23×D4—791no—
811C23×D4—792no—
812C23×D4—791no—
813C23×D4C2×D7911yescharacteristic
814#548—7916no—
815#548—7916no—
816#548—7916no—
817#548—7916no—
818#546—7916no—
819#546—7916no—
820#546—7932no—
821#546—7932no—
822#546—7932no—
823#546—7916no—
824#546—7932no—
825#546C2×D79116yescomplemented
826#536—7932no—
827#536—7916no—
828#535—7916no—
829#535—7932no—
830#532—7932no—
831#532—7916no—
832C2×C4⋊Q8—792no—
833C2×C4⋊Q8—791no—
834C2×#127—792no—
835C2×#127—791no—
836C2×#124—791no—
837C2×#124—791no—
838C2×#124—7916no—
839C2×#124—792no—
840C2×#124—791no—
841C2×#124—792no—
842C2×#124—792no—
843C2×#124—792no—
844C2×#124—792no—
845C2×#124—792no—
846C2×#124—792no—
847C2×#124—792no—
848C2×#124—791no—
849C2×#124—7932no—
850C2×#124—791no—
851C2×#124C2×D7911yescharacteristic, complemented
852C2×#123—792no—
853C2×#123—792no—
854C2×#123—792no—
855C2×#123—792no—
856C2×#123—792no—
857C2×#123C2×D7912yescomplemented
858C2×C22⋊Q8—791no—
859C2×C22⋊Q8—791no—
860C2×C22⋊Q8—792no—
861C2×C22⋊Q8—792no—
862C2×C22⋊Q8—791no—
863C2×C22⋊Q8—792no—
864C2×C22⋊Q8—792no—
865C2×C22⋊Q8C2×D7911yescharacteristic, complemented
866C2×#121—791no—
867C2×#121—792no—
868C2×#121—792no—
869C2×#121—791no—
870C2×#121—792no—
871C2×#121—792no—
872C2×#121—792no—
873C2×#121—791no—
874C2×#121—791no—
875C2×#121—791no—
876C2×#121—791no—
877C2×#121—791no—
878C2×#121—792no—
879C2×#121—792no—
880C2×#121C2×D7912yescomplemented
881C2×#121C2×D7911yescharacteristic, complemented
882C2×#120—792no—
883C2×#120—792no—
884C2×#120—792no—
885C2×#120—792no—
886C2×#120—792no—
887C2×#120C2×D7912yescomplemented
888C4×#41—7916no—
889C2×C4×Q8—791no—
890C2×C4×Q8—791no—
891C2×C4×D4—791no—
892C2×C4×D4—792no—
893C2×C4×D4—792no—
894C2×C4×D4—791no—
895C2×C4×D4—791no—
896C2×C4×D4—792no—
897C2×C4×D4—792no—
898C2×C4×D4—792no—
899C2×C4×D4—792no—
900C2×C4×D4—791no—
901C2×C4×D4C2×D7911yescharacteristic, complemented
902C2×C4×D4C2×D7911yescharacteristic, complemented
903C2×#117—791no—
904C2×#117—792no—
905C22×C22⋊C4—792no—
906C22×C22⋊C4—792no—
907C22×C22⋊C4—792no—
908C22×C22⋊C4—792no—
909C22×C22⋊C4—792no—
910C22×C22⋊C4C2×D7912yescomplemented
911C22×C42—792no—
912C22×C42—791no—
913C25—792no—
914C25—792no—
915C25C22×D7912yes—
9162−1+4—158128no—
917H(5,𝔽2)—158128no—
918C2×#41—28no—
919C2×#41—7916no—
920C2×#41—798no—
921C2×#41—7916no—
922C2×#41—798no—
923C2×#41—7916no—
924C2×#41—798no—
925C2×#41—7916no—
926C2×#41—798no—
927C2×#41—798no—
928C2×#41—798no—
929C2×#41—7916no—
930C2×#41—1588no—
931C2×#41—1588no—
932C2×#41—15816no—
933C2×#41—1588no—
934C2×#41—15816no—
935C2×#41—15816no—
936C2×#41—15816no—
937C2×#41—1588no—
938C2×#41—1588no—
939C2×#41C22×D7918yescomplemented
940C22×Q8—798no—
941C22×Q8—798no—
942C22×Q8—791no—
943C22×Q8—792no—
944C22×Q8—792no—
945C22×Q8—791no—
946C22×Q8—792no—
947C22×Q8—791no—
948C22×Q8—791no—
949C22×Q8—7916no—
950C22×Q8—798no—
951C22×Q8—15816no—
952C22×Q8—1588no—
953C22×Q8—1588no—
954C22×Q8—1588no—
955C22×Q8C22×D7911yescharacteristic
956C22×D4—28no—
957C22×D4—791no—
958C22×D4—792no—
959C22×D4—792no—
960C22×D4—791no—
961C22×D4—792no—
962C22×D4—791no—
963C22×D4—792no—
964C22×D4—791no—
965C22×D4—792no—
966C22×D4—792no—
967C22×D4—792no—
968C22×D4—792no—
969C22×D4—791no—
970C22×D4—7916no—
971C22×D4—791no—
972C22×D4—7916no—
973C22×D4—798no—
974C22×D4—7916no—
975C22×D4—798no—
976C22×D4—792no—
977C22×D4—791no—
978C22×D4—791no—
979C22×D4—791no—
980C22×D4—791no—
981C22×D4—1588no—
982C22×D4—15816no—
983C22×D4—15816no—
984C22×D4—15816no—
985C22×D4—1588no—
986C22×D4C22×D7912yes—
987C22×D4C22×D7912yes—
988C22×D4C22×D7911yescharacteristic
989C22×D4C22×D7918yes—
990C22×D4C22×D7912yes—
991C22×D4C22×D7911yescharacteristic
992C22×D4C22×D7911yescharacteristic
993C23×C4—792no—
994C23×C4—791no—
995C23×C4—791no—
996C23×C4—792no—
997C23×C4—791no—
998C23×C4—792no—
999C23×C4—792no—
1000C23×C4—792no—
1001C23×C4—792no—
1002C23×C4—792no—
1003C23×C4—791no—
1004C23×C4—792no—
1005C23×C4—791no—
1006C23×C4C22×D7912yes—
1007C23×C4C22×D7911yescharacteristic
1008C23×C4C22×D7911yescharacteristic
1009C23×C4C22×D7912yes—
1010C4⋊Q8—7916no—
1011C4⋊Q8—798no—
1012#127—7916no—
1013#127—798no—
1014#124—798no—
1015#124—798no—
1016#124—7916no—
1017#124—798no—
1018#124—7916no—
1019#124—7916no—
1020#124—7916no—
1021#124—7916no—
1022#124—7916no—
1023#124—7916no—
1024#124—7916no—
1025#124—798no—
1026#124—798no—
1027#124C22×D7918yescomplemented
1028#123—7916no—
1029#123—7916no—
1030#123—7916no—
1031#123—7916no—
1032#123—7916no—
1033#123C22×D79116yescomplemented
1034C22⋊Q8—798no—
1035C22⋊Q8—798no—
1036C22⋊Q8—7916no—
1037C22⋊Q8—7916no—
1038C22⋊Q8—798no—
1039C22⋊Q8—7916no—
1040C22⋊Q8—7916no—
1041C22⋊Q8C22×D7918yescomplemented
1042#121—798no—
1043#121—7916no—
1044#121—7916no—
1045#121—798no—
1046#121—7916no—
1047#121—7916no—
1048#121—7916no—
1049#121—798no—
1050#121—798no—
1051#121—798no—
1052#121—798no—
1053#121—798no—
1054#121—7916no—
1055#121—7916no—
1056#121C22×D79116yescomplemented
1057#121C22×D7918yescomplemented
1058#120—7916no—
1059#120—7916no—
1060#120—7916no—
1061#120—7916no—
1062#120—7916no—
1063#120C22×D79116yescomplemented
1064C4×Q8—798no—
1065C4×Q8—798no—
1066C4×D4—798no—
1067C4×D4—7916no—
1068C4×D4—7916no—
1069C4×D4—798no—
1070C4×D4—798no—
1071C4×D4—7916no—
1072C4×D4—7916no—
1073C4×D4—7916no—
1074C4×D4—7916no—
1075C4×D4—798no—
1076C4×D4C22×D7918yescomplemented
1077C4×D4C22×D7918yescomplemented
1078#117—798no—
1079#117—7916no—
1080C2×C4⋊C4—792no—
1081C2×C4⋊C4—792no—
1082C2×C4⋊C4—791no—
1083C2×C4⋊C4—791no—
1084C2×C4⋊C4—792no—
1085C2×C4⋊C4—792no—
1086C2×C4⋊C4—791no—
1087C2×C4⋊C4—792no—
1088C2×C4⋊C4—791no—
1089C2×C4⋊C4C22×D7911yescharacteristic
1090C2×C4⋊C4C22×D7912yes—
1091C2×C4⋊C4C22×D7911yescharacteristic
1092C2×C22⋊C4—792no—
1093C2×C22⋊C4—791no—
1094C2×C22⋊C4—792no—
1095C2×C22⋊C4—792no—
1096C2×C22⋊C4—792no—
1097C2×C22⋊C4—7916no—
1098C2×C22⋊C4—792no—
1099C2×C22⋊C4—791no—
1100C2×C22⋊C4—792no—
1101C2×C22⋊C4—791no—
1102C2×C22⋊C4—791no—
1103C2×C22⋊C4—792no—
1104C2×C22⋊C4—792no—
1105C2×C22⋊C4—792no—
1106C2×C22⋊C4—792no—
1107C2×C22⋊C4—792no—
1108C2×C22⋊C4—792no—
1109C2×C22⋊C4—792no—
1110C2×C22⋊C4—7916no—
1111C2×C22⋊C4—7916no—
1112C2×C22⋊C4—792no—
1113C2×C22⋊C4—791no—
1114C2×C22⋊C4—791no—
1115C2×C22⋊C4—7916no—
1116C2×C22⋊C4—7916no—
1117C2×C22⋊C4C22×D7912yes—
1118C2×C22⋊C4C22×D7912yes—
1119C2×C22⋊C4C22×D7911yescharacteristic
1120C2×C22⋊C4C22×D7912yes—
1121C2×C22⋊C4C22×D7912yes—
1122C2×C22⋊C4C22×D7912yes—
1123C2×C22⋊C4C22×D7911yescharacteristic
1124C2×C22⋊C4C22×D79116yescomplemented
1125C2×C42—792no—
1126C2×C42—791no—
1127C2×C42—792no—
1128C2×C42—792no—
1129C2×C42—791no—
1130C2×C42—7916no—
1131C2×C42—791no—
1132C2×C42—798no—
1133C2×C42C22×D7911yescharacteristic
1134C24—28no—
1135C24—44no—
1136C24—44no—
1137C24—3164no—
1138C24—3164no—
1139C24—3164no—
1140C24—3164no—
1141C24—798no—
1142C24—798no—
1143C24—791no—
1144C24—792no—
1145C24—791no—
1146C24—791no—
1147C24—1588no—
1148C24—1588no—
1149C24C23×D7912yes—
1150C24C23×D7911yescharacteristic
1151C24C23×D7911yescharacteristic
1152C24C23×D7912yes—
1153C24C23×D7918yes—
1154#41—232no—
1155#41—7964no—
1156#41—15832no—
1157#41—15832no—
1158#41—15864no—
1159#41—15832no—
1160#41—15864no—
1161#41—15864no—
1162#41—15864no—
1163#41—15832no—
1164#41—15832no—
1165C2×Q8—24no—
1166C2×Q8—794no—
1167C2×Q8—798no—
1168C2×Q8—798no—
1169C2×Q8—794no—
1170C2×Q8—798no—
1171C2×Q8—794no—
1172C2×Q8—794no—
1173C2×Q8—798no—
1174C2×Q8—1584no—
1175C2×Q8—1588no—
1176C2×Q8—1588no—
1177C2×Q8—1588no—
1178C2×Q8—15864no—
1179C2×Q8—1584no—
1180C2×Q8—15832no—
1181C2×Q8—15832no—
1182C2×Q8—15832no—
1183C2×Q8—1584no—
1184C2×Q8C23×D7914yes—
1185C2×D4—28no—
1186C2×D4—28no—
1187C2×D4—232no—
1188C2×D4—24no—
1189C2×D4—44no—
1190C2×D4—42no—
1191C2×D4—3164no—
1192C2×D4—3162no—
1193C2×D4—3162no—
1194C2×D4—3162no—
1195C2×D4—3164no—
1196C2×D4—3164no—
1197C2×D4—798no—
1198C2×D4—794no—
1199C2×D4—798no—
1200C2×D4—794no—
1201C2×D4—798no—
1202C2×D4—7916no—
1203C2×D4—794no—
1204C2×D4—798no—
1205C2×D4—794no—
1206C2×D4—798no—
1207C2×D4—798no—
1208C2×D4—798no—
1209C2×D4—798no—
1210C2×D4—794no—
1211C2×D4—794no—
1212C2×D4—798no—
1213C2×D4—794no—
1214C2×D4—794no—
1215C2×D4—794no—
1216C2×D4—794no—
1217C2×D4—1584no—
1218C2×D4—1584no—
1219C2×D4—15832no—
1220C2×D4—1584no—
1221C2×D4—1588no—
1222C2×D4—1588no—
1223C2×D4—1588no—
1224C2×D4—15864no—
1225C2×D4—1584no—
1226C2×D4—15864no—
1227C2×D4—15864no—
1228C2×D4—1584no—
1229C2×D4—1584no—
1230C2×D4—1588no—
1231C2×D4—1588no—
1232C2×D4—15832no—
1233C2×D4—1584no—
1234C2×D4D4×D7918yes—
1235C2×D4C23×D7918yes—
1236C2×D4C23×D7918yes—
1237C2×D4C23×D7914yes—
1238C2×D4C23×D7918yes—
1239C2×D4C23×D7914yes—
1240C2×D4C23×D7914yes—
1241C22×C4—28no—
1242C22×C4—24no—
1243C22×C4—24no—
1244C22×C4—44no—
1245C22×C4—3162no—
1246C22×C4—3162no—
1247C22×C4—3164no—
1248C22×C4—798no—
1249C22×C4—794no—
1250C22×C4—794no—
1251C22×C4—798no—
1252C22×C4—791no—
1253C22×C4—792no—
1254C22×C4—7916no—
1255C22×C4—794no—
1256C22×C4—798no—
1257C22×C4—798no—
1258C22×C4—798no—
1259C22×C4—798no—
1260C22×C4—791no—
1261C22×C4—791no—
1262C22×C4—792no—
1263C22×C4—791no—
1264C22×C4—792no—
1265C22×C4—791no—
1266C22×C4—798no—
1267C22×C4—798no—
1268C22×C4—794no—
1269C22×C4—798no—
1270C22×C4—794no—
1271C22×C4—1588no—
1272C22×C4—1588no—
1273C22×C4—1588no—
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×D7911yescharacteristic
1283C22×C4C23×D7912yes—
1284C22×C4C23×D7911yescharacteristic
1285C22×C4C23×D7912yes—
1286C22×C4C23×D7911yescharacteristic
1287C22×C4C23×D7911yescharacteristic
1288C22×C4C23×D7918yes—
1289C22×C4C23×D7911yescharacteristic
1290C4⋊C4—798no—
1291C4⋊C4—798no—
1292C4⋊C4—798no—
1293C4⋊C4—794no—
1294C4⋊C4—798no—
1295C4⋊C4—794no—
1296C4⋊C4—794no—
1297C4⋊C4—798no—
1298C4⋊C4—794no—
1299C4⋊C4C23×D7914yes—
1300C4⋊C4C23×D7918yes—
1301C4⋊C4C23×D7914yes—
1302C22⋊C4—798no—
1303C22⋊C4—794no—
1304C22⋊C4—798no—
1305C22⋊C4—798no—
1306C22⋊C4—798no—
1307C22⋊C4—798no—
1308C22⋊C4—794no—
1309C22⋊C4—798no—
1310C22⋊C4—794no—
1311C22⋊C4—798no—
1312C22⋊C4—794no—
1313C22⋊C4—798no—
1314C22⋊C4—798no—
1315C22⋊C4—798no—
1316C22⋊C4—798no—
1317C22⋊C4—798no—
1318C22⋊C4—798no—
1319C22⋊C4—798no—
1320C22⋊C4—794no—
1321C22⋊C4—794no—
1322C22⋊C4C23×D7918yes—
1323C22⋊C4C23×D7918yes—
1324C22⋊C4C23×D7914yes—
1325C22⋊C4C23×D7918yes—
1326C22⋊C4C23×D7918yes—
1327C22⋊C4C23×D7918yes—
1328C22⋊C4C23×D7914yes—
1329C42—794no—
1330C42—798no—
1331C42—794no—
1332C42—798no—
1333C42—798no—
1334C42—794no—
1335C42C23×D7914yes—
1336C23—24no—
1337C23—24no—
1338C23—22no—
1339C23—24no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—24no—
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—216no—
1348C23—48no—
1349C23—48no—
1350C23—816no—
1351C23—3168no—
1352C23—3168no—
1353C23—3168no—
1354C23—3168no—
1355C23—792no—
1356C23—794no—
1357C23—794no—
1358C23—792no—
1359C23—792no—
1360C23—63216no—
1361C23—63216no—
1362C23—15816no—
1363C23—1582no—
1364C23—1582no—
1365C23—1584no—
1366C23—1582no—
1367C23—1584no—
1368C23—1582no—
1369C23—1582no—
1370C23—1584no—
1371C23—1582no—
1372C23—15816no—
1373C23—1582no—
1374C23—1582no—
1375C23C2×D4×D7918yes—
1376C23C24×D7914yes—
1377C23C24×D7912yes—
1378C23C24×D7912yes—
1379C23C24×D7914yes—
1380C23C24×D7911yescharacteristic
1381Q8—28no—
1382Q8—7916no—
1383Q8—1588no—
1384Q8—15816no—
1385Q8—15816no—
1386Q8—15816no—
1387Q8—1588no—
1388Q8—1588no—
1389D4—216no—
1390D4—216no—
1391D4—28no—
1392D4—48no—
1393D4—44no—
1394D4—3168no—
1395D4—3164no—
1396D4—3164no—
1397D4—3164no—
1398D4—3168no—
1399D4—3168no—
1400D4—7932no—
1401D4—1588no—
1402D4—1588no—
1403D4—1588no—
1404D4—15816no—
1405D4—15816no—
1406D4—15816no—
1407D4—1588no—
1408D4—1588no—
1409D4—1588no—
1410D4—15816no—
1411D4—15816no—
1412D4—1588no—
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—3164no—
1425C2×C4—3164no—
1426C2×C4—3168no—
1427C2×C4—792no—
1428C2×C4—794no—
1429C2×C4—794no—
1430C2×C4—798no—
1431C2×C4—7932no—
1432C2×C4—7916no—
1433C2×C4—792no—
1434C2×C4—792no—
1435C2×C4—794no—
1436C2×C4—792no—
1437C2×C4—794no—
1438C2×C4—792no—
1439C2×C4—15816no—
1440C2×C4—15816no—
1441C2×C4—15816no—
1442C2×C4—15816no—
1443C2×C4—15816no—
1444C2×C4—1582no—
1445C2×C4—1582no—
1446C2×C4—1584no—
1447C2×C4—1582no—
1448C2×C4—1584no—
1449C2×C4—1582no—
1450C2×C4—15816no—
1451C2×C4—1588no—
1452C2×C4—1588no—
1453C2×C4C2×D4×D7914yes—
1454C2×C4C24×D7912yes—
1455C2×C4C24×D7914yes—
1456C2×C4C24×D7912yes—
1457C2×C4C24×D7914yes—
1458C2×C4C24×D7912yes—
1459C2×C4C24×D7912yes—
1460C2×C4C24×D7912yes—
1461C22—24no—
1462C22—24no—
1463C22—216no—
1464C22—22no—
1465C22—22no—
1466C22—24no—
1467C22—22no—
1468C22—24no—
1469C22—22no—
1470C22—22no—
1471C22—22no—
1472C22—24no—
1473C22—44no—
1474C22—48no—
1475C22—44no—
1476C22—816no—
1477C22—3164no—
1478C22—3168no—
1479C22—3164no—
1480C22—794no—
1481C22—63216no—
1482C22—63216no—
1483C22—1582no—
1484C22—1584no—
1485C22—1582no—
1486C22—1582no—
1487C22—1584no—
1488C22—1582no—
1489C22—1582no—
1490C22—1582no—
1491C22—1584no—
1492C22—1582no—
1493C22—1582no—
1494C22—1588no—
1495C22C22×D4×D7918yes—
1496C22C22×D4×D7912yes—
1497C22#1909939812yes—
1498C22#1909939912yes—
1499C22C25×D7911yescharacteristic
1500C4—22no—
1501C4—22no—
1502C4—24no—
1503C4—22no—
1504C4—24no—
1505C4—22no—
1506C4—794no—
1507C4—798no—
1508C4—1582no—
1509C4—1584no—
1510C4—1582no—
1511C4—1582no—
1512C4—1582no—
1513C4—1584no—
1514C4C22×D4×D7914yes—
1515C2—28no—
1516C2—42no—
1517C2—44no—
1518C2—42no—
1519C2—3162no—
1520C2—3164no—
1521C2—3162no—
1522C2—1584no—
1523C2#2377718614yesdirect product factor
1524C2C23×D4×D7911yescharacteristic
1525C2C2×#1909939811yescharacteristic
1526C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#546×C79C2
socleC23×C79C25
hypercenterC2×#546D79
hypocenterC79C2×#3500
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C22×#14579208C2semidirect
2. C22×#14579206C2semidirect
3. #23777186C2direct (N × H)
4. C2×#19099223C2semidirect
5. C2×#19099222C2semidirect
6. C2×#19099221C2semidirect
7. C2×#19099219C2semidirect
8. C2×#19099208C2semidirect
9. C2×#19099207C2semidirect
10. C2×#19099205C2semidirect
11. C2×#19099203C2semidirect
12. C2×#19099202C2semidirect
13. C2×#19099201C2semidirect
14. C2×#19099200C2semidirect
15. C2×#19099136C2semidirect
16. C2×#19099135C2semidirect
17. C2×#19099129C2semidirect
18. C2×#19099128C2semidirect
19. C2×#19099110C2semidirect
20. C2×#19099108C2semidirect
21. C22×#14579147C2semidirect
22. C2×#124×D79C2semidirect
23. C2×C4×#11929623C2semidirect
24. C2×#546×C79C2semidirect
26. C2×#14579208C22semidirect
28. C2×#14579206C22semidirect
31. C22×#11929624C22semidirect
32. C22×#11929624C22semidirect
36. C22×#11929623C22semidirect
37. C22×#11929623C22semidirect
38. C22×#11929623C22semidirect
39. C23×Dic158C22semidirect
40. C23×Dic158C22semidirect
41. C22×Q8×D79C22semidirect
42. C22×Q8×D79C22semidirect
48. #19099223C22semidirect
49. #19099222C22semidirect
50. #19099221C22semidirect
51. #19099219C22semidirect
52. #19099208C22semidirect
53. #19099207C22semidirect
54. #19099205C22semidirect
55. #19099203C22semidirect
56. #19099202C22semidirect
57. #19099201C22semidirect
58. #19099200C22semidirect
59. #19099136C22semidirect
60. #19099135C22semidirect
61. #19099129C22semidirect
62. #19099128C22semidirect
63. #19099110C22semidirect
64. #19099108C22semidirect
65. C2×#14579160C22semidirect
66. C2×#14579160C22semidirect
67. C2×#14579157C22semidirect
68. C2×#14579157C22semidirect
69. C2×#14579150C22semidirect
70. C2×#14579149C22semidirect
71. C2×#14579148C22semidirect
72. C2×#14579147C22semidirect
73. C2×#14579147C22semidirect
74. C2×#14579147C22semidirect
75. C2×#14579147C22semidirect
76. C2×#14579147C22semidirect
77. C2×#14579147C22semidirect
78. C2×#14579147C22semidirect
79. C2×#14579147C22semidirect
80. C2×#14579147C22semidirect
81. C2×#14579147C22semidirect
82. C2×#14579147C22semidirect
83. #124×D79C22semidirect
84. C2×#14579146C22semidirect
85. C2×#14579145C22semidirect
86. C2×#14579144C22semidirect
87. C2×#14579143C22semidirect
88. C2×#14579142C22semidirect
89. C2×#14579141C22semidirect
90. C2×#14579140C22semidirect
91. C2×#14579139C22semidirect
92. C2×#14579139C22semidirect
93. C2×#14579138C22semidirect
94. C2×#14579138C22semidirect
95. C2×#14579137C22semidirect
96. C2×#14579136C22semidirect
97. C2×#14579136C22semidirect
98. C2×#14579135C22semidirect
99. C2×#14579135C22semidirect
100. C2×#14579134C22semidirect
101. C2×#14579134C22semidirect
102. C2×#14579134C22semidirect
103. C2×#14579134C22semidirect
104. C2×#14579133C22semidirect
105. C2×#14579133C22semidirect
106. C2×#14579133C22semidirect
107. C2×#14579133C22semidirect
108. C2×#14579132C22semidirect
109. C2×#14579132C22semidirect
110. C2×#14579131C22semidirect
111. C2×#14579131C22semidirect
112. C2×#14579130C22semidirect
113. C2×#14579129C22semidirect
114. C2×#14579129C22semidirect
115. C4×#11929623C22semidirect
116. C2×C4×Dic158C22semidirect
117. C2×#14579126C22semidirect
118. C2×C4×D316C22semidirect
119. C2×D4×Dic79C22semidirect
120. C2×D4×Dic79C22semidirect
121. C2×#14579123C22semidirect
122. C2×C4×C22⋊D79C22semidirect
123. C2×C4×C22⋊D79C22semidirect
124. C2×C4×C22⋊D79C22semidirect
125. C2×(C22⋊D79)⋊C4C22semidirect
126. C2×(C22⋊D79)⋊C4C22semidirect
127. C2×(C22⋊D79)⋊C4C22semidirect
128. C2×#14579119C22semidirect
129. C2×#14579117C22semidirect
130. C22×C22⋊Dic79C22semidirect
131. C22×(C2×D79)⋊C4C22semidirect
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
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
159. C2×#11929624C23semidirect
160. C2×#11929624C23semidirect
166. C2×#11929623D4semidirect
170. C2×#11929623C23semidirect
171. C2×#11929623C23semidirect
172. C2×#11929623C23semidirect
182. C22×Dic158C23semidirect
183. C22×Dic158C23semidirect
186. C2×Q8×D79C23semidirect
187. C2×Q8×D79C23semidirect
230. #14579160C23semidirect
231. #14579160C23semidirect
232. #14579157C23semidirect
233. #14579157C23semidirect
234. #14579150C23semidirect
235. #14579149C23semidirect
236. #14579148C23semidirect
237. #14579147C23semidirect
238. #14579147C23semidirect
239. #14579147C23semidirect
240. #14579147C23semidirect
241. #14579147C23semidirect
242. #14579147C23semidirect
243. #14579147C23semidirect
244. #14579147C23semidirect
245. #14579147C23semidirect
246. #14579147C23semidirect
247. #14579146C23semidirect
248. #14579145C23semidirect
249. #14579144C23semidirect
250. #14579143C23semidirect
251. #14579142C23semidirect
252. #14579141C23semidirect
253. #14579140C23semidirect
254. #14579139C23semidirect
255. #14579139C23semidirect
256. #14579138C23semidirect
257. #14579138C23semidirect
258. #14579137C23semidirect
259. #14579136C23semidirect
260. #14579136C23semidirect
261. #14579135C23semidirect
262. #14579135C23semidirect
263. #14579134C23semidirect
264. #14579134C23semidirect
265. #14579134C23semidirect
266. #14579134C23semidirect
267. #14579133C23semidirect
268. #14579133C23semidirect
269. #14579133C23semidirect
270. #14579133C23semidirect
271. #14579132C23semidirect
272. #14579132C23semidirect
273. #14579131C23semidirect
274. #14579131C23semidirect
275. #14579130C23semidirect
276. #14579129C23semidirect
277. #14579129C23semidirect
278. C4×Dic158C23semidirect
279. #14579126C23semidirect
280. C4×D316C23semidirect
281. D4×Dic79C23semidirect
282. D4×Dic79C23semidirect
283. #14579123C23semidirect
284. C4×C22⋊D79C23semidirect
285. C4×C22⋊D79C23semidirect
286. C4×C22⋊D79C23semidirect
287. (C22⋊D79)⋊C4C23semidirect
288. (C22⋊D79)⋊C4C23semidirect
289. (C22⋊D79)⋊C4C23semidirect
290. #14579119C23semidirect
291. #14579117C23semidirect
308. C2×C22⋊Dic79C23semidirect
322. C2×(C2×D79)⋊C4C23semidirect
323. C2×(C2×D79)⋊C4C23semidirect
324. C22⋊C4×D79C23semidirect
325. C22⋊C4×D79C23semidirect
332. C2×C4×Dic79C23semidirect
333. C42×D79C23semidirect
336. C2×#41×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
391. #11929623C2×D4semidirect
756. C2×C79#3500semidirect
778. C2×#546D79semidirect
788. C79C2×#3500semidirect
803. C22×#41C2×D79semidirect
825. #546C2×D79semidirect
851. C2×#124C2×D79semidirect
857. C2×#123C2×D79semidirect
865. C2×C22⋊Q8C2×D79semidirect
880. C2×#121C2×D79semidirect
881. C2×#121C2×D79semidirect
887. C2×#120C2×D79semidirect
901. C2×C4×D4C2×D79semidirect
902. C2×C4×D4C2×D79semidirect
910. C22×C22⋊C4C2×D79semidirect
939. C2×#41C22×D79semidirect
1027. #124C22×D79semidirect
1033. #123C22×D79semidirect
1041. C22⋊Q8C22×D79semidirect
1056. #121C22×D79semidirect
1057. #121C22×D79semidirect
1063. #120C22×D79semidirect
1076. C4×D4C22×D79semidirect
1077. C4×D4C22×D79semidirect
1124. C2×C22⋊C4C22×D79semidirect
1523. C2#23777186direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145792082
C22×#145792062
#237771862
C2×#190992232
C2×#190992222
C2×#190992212
C2×#190992192
C2×#190992082
C2×#190992072
C2×#190992052
C2×#190992032
C2×#190992022
C2×#190992012
C2×#190992002
C2×#190991362
C2×#190991352
C2×#190991292
C2×#190991282
C2×#190991102
C2×#190991082
C22×#145791472
C2×#124×D792
C2×C4×#119296232
C2×#546×C792
C2×#350079