Finite Group Databasebeta

← C2×#23775520 #35164981

Subgroups — C2×#23775520 #35164981

Order 20224.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099234C211yesmaximal, characteristic
2#23775520C2116yesmaximal, direct product factor
3C2×#19098929C211yesmaximal, characteristic, complemented
4C2×#19098881C211yesmaximal, characteristic, complemented
5C2×#19098887C211yesmaximal, characteristic, complemented
6C2×#19098867C211yesmaximal, characteristic, complemented
7C2×#19098811C211yesmaximal, characteristic, complemented
8C2×#19098794C211yesmaximal, characteristic, complemented
9C2×#19098763C211yesmaximal, characteristic, complemented
10C2×#19098723C211yesmaximal, characteristic, complemented
11C2×#19098723C211yesmaximal, characteristic, complemented
12C2×#19098668C211yesmaximal, characteristic, complemented
13C2×#19098635C211yesmaximal, characteristic, complemented
14C2×#19098562C211yesmaximal, characteristic, complemented
15C2×#19098557C211yesmaximal, characteristic, complemented
16C2×#552×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929624C2211yescharacteristic
19C22×#11929614C2211yescharacteristic
20C22×#11929611C2211yescharacteristic
21C22×#11929611C2211yescharacteristic
22C22×#11929608C2211yescharacteristic
23C23×C79⋊C8C2211yescharacteristic
24#19099234—24no—
25#19099234C2218yes—
26C2×#14579158C2211yescharacteristic
27C2×#14579157—21no—
28C2×#14579135C2211yescharacteristic
29C2×#14579135C2211yescharacteristic
30C2×#14579134—21no—
31C2×#14579134—21no—
32C2×C4×Dic158C2211yescharacteristic
33C2×#14579123—21no—
34#19098929C2218yescomplemented
35#19098887C2218yescomplemented
36#19098881C2218yescomplemented
37#19098867C2218yescomplemented
38#19098811C2218yescomplemented
39#19098794C2218yescomplemented
40#19098763C2218yescomplemented
41#19098723C2218yescomplemented
42#19098723C2218yescomplemented
43#19098668C2218yescomplemented
44#19098635C2218yescomplemented
45C2×#14579094C2211yescharacteristic
46C2×#14579092C2211yescharacteristic
47C2×#14579092C2211yescharacteristic
48C2×C4⋊(C79⋊C8)C2211yescharacteristic
49#19098562C2218yescomplemented
50#19098557C2218yescomplemented
51C2×#14579085C2211yescharacteristic
52C2×#14579084C2211yescharacteristic
53C2×#14579084C2211yescharacteristic
54C2×#14579084C2211yescharacteristic
55C2×#14579081C2211yescharacteristic
56C2×#14579081C2211yescharacteristic
57C2×#14579081C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×#14579081C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×C22⋊(C79⋊C8)C2211yescharacteristic
63C2×#14579072C2211yescharacteristic
64#552×C79—24no—
65#552×C79C2218yescomplemented
66C2×#126×C79—21no—
67C2×#125×C79—21no—
68C2×#125×C79C2211yescharacteristic
69C2×#123×C79—21no—
70C2×C22⋊Q8×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×C4×Q8×C79C2211yescharacteristic
73C2×C4×D4×C79C2211yescharacteristic
74C2×#117×C79—21no—
75C2×#117×C79C2211yescharacteristic
76C22×C4⋊C4×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—22no—
79C2×#11929624—24no—
80C2×#11929624—24no—
81C2×#11929624—42no—
82C2×#11929624—42no—
83C2×#11929624C2314yes—
84C2×#11929624C2314yes—
85C22×Dic158C2311yescharacteristic
86C22×D316—21no—
87C22×D316—21no—
88C22×D316C2311yescharacteristic
89C22×D316C2311yescharacteristic
90C22×C22⋊D79—21no—
91C22×C22⋊D79—21no—
92C22×C22⋊D79—21no—
93C22×C22⋊D79—21no—
94C22×C4×D79—21no—
95C22×C4×D79—21no—
96C2×#11929614—24no—
97C2×#11929614C2314yes—
98C2×#11929611—42no—
99C2×#11929611—42no—
100C2×#11929611C2314yes—
101C2×#11929611C2314yes—
102C2×#11929608—42no—
103C2×#11929608C2314yes—
104C22×C79⋊C8—42no—
105C22×C79⋊C8C2311yescharacteristic
106C22×C79⋊C8C2311yescharacteristic
107C22×C79⋊C8C2311yescharacteristic
108C22×C79⋊C8C2311yescharacteristic
109C22×C79⋊C8C2314yes—
110#14579158—22no—
111#14579158C2314yes—
112#14579157—28no—
113#14579135—22no—
114#14579135—22no—
115#14579135C2314yes—
116#14579135C2314yes—
117#14579134—28no—
118#14579134—28no—
119C4×Dic158—22no—
120C4×Dic158C2314yes—
121#14579123—28no—
122C2×C4⋊Dic79C2311yescharacteristic
123C2×Dic79⋊C4—21no—
124C2×(C2×D79)⋊C4—21no—
125C2×(C2×D79)⋊C4—21no—
126C2×C4×Dic79—21no—
127#14579094C2314yes—
128#14579092C2314yes—
129#14579092C2314yes—
130C4⋊(C79⋊C8)C2314yes—
131#14579085C2314yes—
132#14579084C2314yes—
133#14579084C2314yes—
134#14579084C2314yes—
135#14579081C2314yes—
136#14579081C2314yes—
137#14579081C2314yes—
138#14579081C2314yes—
139#14579081C2314yes—
140#14579081C2314yes—
141C22⋊(C79⋊C8)C2314yes—
142C22⋊(C79⋊C8)C2314yes—
143#14579072C2314yes—
144C22×Q8×C79C2311yescharacteristic
145C22×D4×C79D411yescharacteristic
146C23×C4×C79—21no—
147C23×C4×C79C2311yescharacteristic
148C23×C4×C79C2311yescharacteristic
149#126×C79—28no—
150#125×C79—28no—
151#125×C79—22no—
152#125×C79C2314yes—
153#123×C79—28no—
154C22⋊Q8×C79—22no—
155C22⋊Q8×C79—22no—
156C22⋊Q8×C79C2314yes—
157C22⋊Q8×C79C2314yes—
158C4×Q8×C79—22no—
159C4×Q8×C79C2314yes—
160C4×D4×C79D414yes—
161C4×D4×C79C2314yes—
162#117×C79—22no—
163#117×C79—28no—
164#117×C79C2314yes—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79—21no—
172C2×C4⋊C4×C79D411yescharacteristic
173C2×C4⋊C4×C79C2314yes—
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C4⋊C4×C79C2311yescharacteristic
176C2×C4⋊C4×C79C2311yescharacteristic
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180C2×C22⋊C4×C79D411yescharacteristic
181C2×C22⋊C4×C79D411yescharacteristic
182C2×C42×C79—21no—
183C2×C42×C79—21no—
184C2×C42×C79C2311yescharacteristic
185C23×D79—21no—
186C23×D79—21no—
187#11929624—28no—
188#11929624—28no—
189#11929624—44no—
190#11929624—44no—
191#11929624—48no—
192#11929624—48no—
193C2×Dic158—21no—
194C2×Dic158—22no—
195C2×Dic158#4114yes—
196C2×Dic158C2412yes—
197C2×D316—21no—
198C2×D316—21no—
199C2×D316—24no—
200C2×D316—24no—
201C2×D316—22no—
202C2×D316—22no—
203C2×D316—22no—
204C2×D316—22no—
205C2×D316—44no—
206C2×D316—82no—
207C2×D316C2412yes—
208C2×D316C2412yes—
209C2×C22⋊D79—24no—
210C2×C22⋊D79—24no—
211C2×C22⋊D79—24no—
212C2×C22⋊D79—24no—
213C2×C22⋊D79—44no—
214C2×C22⋊D79—44no—
215C2×C22⋊D79—82no—
216C2×C22⋊D79—82no—
217C22×Dic79—21no—
218C22×Dic79—21no—
219C2×C4×D79—24no—
220C2×C4×D79—24no—
221C2×C4×D79—44no—
222C2×C4×D79—44no—
223#11929614—28no—
224#11929611—44no—
225#11929611—44no—
226#11929608—44no—
227C2×C79⋊C8—22no—
228C2×C79⋊C8—22no—
229C2×C79⋊C8—22no—
230C2×C79⋊C8—22no—
231C2×C79⋊C8—44no—
232C2×C79⋊C8C2412yes—
233C2×C79⋊C8C2412yes—
234C2×C79⋊C8C2412yes—
235C2×C79⋊C8C2412yes—
236C4⋊Dic79—21no—
237C4⋊Dic79C2412yes—
238Dic79⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4—24no—
241C4×Dic79—24no—
242C24×C79C2×D411yescharacteristic
243C24×C79C2×D411yescharacteristic
244C2×Q8×C79—21no—
245C2×Q8×C79—22no—
246C2×Q8×C79—22no—
247C2×Q8×C79C2412yes—
248C2×D4×C79—42no—
249C2×D4×C79C2×D414yes—
250C22×C4×C79—22no—
251C22×C4×C79—22no—
252C22×C4×C79—22no—
253C22×C4×C79—22no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—24no—
259C22×C4×C79—44no—
260C22×C4×C79C2×D412yes—
261C22×C4×C79C2×D412yes—
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79C2×D411yescharacteristic
265C22×C4×C79C2×D411yescharacteristic
266C22×C4×C79C2412yes—
267C22×C4×C79C2412yes—
268C22×C4×C79C2411yescharacteristic
269C4⋊C4×C79—21no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79—24no—
272C4⋊C4×C79—24no—
273C4⋊C4×C79—24no—
274C4⋊C4×C79—24no—
275C4⋊C4×C79—24no—
276C4⋊C4×C79—24no—
277C4⋊C4×C79—21no—
278C4⋊C4×C79C2×D414yes—
279C4⋊C4×C79C2412yes—
280C4⋊C4×C79C2412yes—
281C4⋊C4×C79C2412yes—
282C22⋊C4×C79—24no—
283C22⋊C4×C79—24no—
284C22⋊C4×C79—24no—
285C22⋊C4×C79C2×D414yes—
286C22⋊C4×C79C2×D414yes—
287C42×C79—24no—
288C42×C79—24no—
289C42×C79C2×D412yes—
290C42×C79C2412yes—
291C23×C79—22no—
292C23×C79—22no—
293C23×C79—22no—
294C23×C79—22no—
295C23×C79—22no—
296C23×C79—22no—
297C23×C79C22×D412yes—
298C23×C79C22×D412yes—
299C23×C79C22×D411yescharacteristic
300C22×D79—22no—
301C22×D79—22no—
302C22×D79—42no—
303C22×D79—42no—
304C22×D79—42no—
305C22×D79—42no—
306C22×D79—42no—
307C22×D79—42no—
308Q8×C79—22no—
309Q8×C79—22no—
310Q8×C79—42no—
311D4×C79—44no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—22no—
316C2×C4×C79—24no—
317C2×C4×C79—24no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—22no—
325C2×C4×C79—22no—
326C2×C4×C79—48no—
327C2×C4×C79—42no—
328C2×C4×C79—42no—
329C2×C4×C79—42no—
330C2×C4×C79—42no—
331C2×C4×C79C22×D412yes—
332C2×C4×C79C22×D412yes—
333C2×C4×C79C22×D412yes—
334C2×C4×C79C22×D412yes—
335C2×C4×C79C22×D411yescharacteristic
336C2×C4×C79C2×#4112yes—
337C2×C4×C79H(5,𝔽2)12yes—
338C2×C4×C79C2511yescharacteristic
339C22⋊D79—48no—
340C22⋊D79—48no—
341C22⋊D79—84no—
342C22⋊D79—84no—
343C2×Dic79—24no—
344C2×Dic79—22no—
345C2×Dic79—22no—
346C2×Dic79—42no—
347D316—22no—
348D316—22no—
349D316—22no—
350D316—22no—
351D316—48no—
352D316—42no—
353D316—42no—
354D316—84no—
355C4×D79—48no—
356C4×D79—48no—
357Dic158—24no—
358Dic158—22no—
359Dic158C2×#4114yes—
360C79⋊C8—22no—
361C79⋊C8—22no—
362C79⋊C8—22no—
363C79⋊C8—22no—
364C22×C79—22no—
365C22×C79—22no—
366C22×C79—22no—
367C22×C79—22no—
368C22×C79—22no—
369C22×C79—22no—
370C22×C79—44no—
371C22×C79—44no—
372C22×C79#54612yes—
373C22×C79#57512yes—
374C22×C79#57712yes—
375C22×C79C23×D411yescharacteristic
376C2×D79—42no—
377C2×D79—42no—
378C2×D79—42no—
379C2×D79—42no—
380C2×D79—42no—
381C2×D79—42no—
382C2×D79—84no—
383C2×D79—84no—
384C4×C79—22no—
385C4×C79—22no—
386C4×C79—22no—
387C4×C79—22no—
388C4×C79—42no—
389C4×C79—42no—
390C4×C79—42no—
391C4×C79—42no—
392C4×C79#54612yes—
393C4×C79C22×#4111yescharacteristic
394C4×C79C2×H(5,𝔽2)11yescharacteristic
395Dic79—24no—
396Dic79—42no—
397C2×#3317—791nomaximal, Sylow
398C2×C79—42no—
399C2×C79—42no—
400C2×C79#331714yescomplemented
401C2×C79C2×#54611yescharacteristic
402C2×C79C2×#57511yescharacteristic
403C2×C79C2×#57711yescharacteristic
404D79—82no—
405D79—82no—
406C2×#552D7911yescharacteristic, complemented
407C2×#550—791no—
408#3317—7916no—
409C2×#490—791no—
410C2×#481—791no—
411C2×#482—791no—
412C2×#479—791no—
413C2×#468—791no—
414C2×#465—791no—
415C2×#460—791no—
416C2×#452—791no—
417C2×#452—791no—
418C2×#441—791no—
419C2×#435—791no—
420C2×#417—791no—
421C2×#416—791no—
422C79C2×#331711yescharacteristic, complemented, Sylow
423C22×#41—791no—
424C22×#41—791no—
425C22×Q16—791no—
426C22×SD16—791no—
427C22×SD16—791no—
428C22×M16—791no—
429C23×C8—791no—
430#552—24no—
431#552C2×D7918yescomplemented
432#550—798no—
433#550—1584no—
434C2×#127—791no—
435C2×#127—1581no—
436C2×#126—21no—
437C2×#125—21no—
438C2×#125C2×D7911yescharacteristic
439C2×#123—21no—
440C2×C22⋊Q8C2×D7911yescharacteristic
441C2×C22⋊Q8C2×D7911yescharacteristic
442C2×#121—791no—
443C2×#121—791no—
444C2×#121—1581no—
445C2×#121—1581no—
446C2×C4×Q8—791no—
447C2×C4×Q8C2×D7911yescharacteristic
448C2×C4×D4—1581no—
449C2×C4×D4C2×D7911yescharacteristic
450C2×#117—21no—
451C2×#117C2×D7911yescharacteristic
452C22×C4⋊C4C2×D7911yescharacteristic
453#490—798no—
454#482—798no—
455#481—798no—
456#479—798no—
457#468—798no—
458#465—798no—
459#460—798no—
460#452—798no—
461#452—798no—
462#441—798no—
463#435—798no—
464C2×#107—791no—
465C2×#106—791no—
466C2×#106—791no—
467C2×C4⋊C8—791no—
468#417—798no—
469#416—798no—
470C2×#103—791no—
471C2×#103—791no—
472C2×#103—791no—
473C2×#103—791no—
474C2×#102—791no—
475C2×#102—791no—
476C2×#102—791no—
477C2×#102—791no—
478C2×#102—791no—
479C2×#102—791no—
480C2×C22⋊C8—791no—
481C2×C22⋊C8—791no—
482C2×#97—791no—
483C2×#41—3162no—
484C2×#41—3162no—
485C2×#41—794no—
486C2×#41—794no—
487C2×#41—1584no—
488C2×#41—1584no—
489C2×#41—1582no—
490C2×#41—1582no—
491C22×Q8—791no—
492C22×Q8C22×D7911yescharacteristic
493C22×D4—791no—
494C22×D4—791no—
495C22×D4—1581no—
496C22×D4—1581no—
497C22×D4—1581no—
498C22×D4—1581no—
499C22×D4—1581no—
500C22×D4—1581no—
501C22×D4C22⋊D7911yescharacteristic
502C23×C4—21no—
503C23×C4—1581no—
504C23×C4—1581no—
505C23×C4C22×D7911yescharacteristic
506C23×C4C22×D7911yescharacteristic
507C2×Q16—794no—
508C2×Q16—1584no—
509C2×SD16—3162no—
510C2×SD16—3162no—
511C2×SD16—794no—
512C2×SD16—794no—
513C2×M16—3162no—
514C2×M16—794no—
515C22×C8—3162no—
516C22×C8—794no—
517C22×C8—791no—
518C22×C8—791no—
519C22×C8—791no—
520C22×C8—791no—
521#127—794no—
522#127—1588no—
523#127—1582no—
524#126—28no—
525#125—28no—
526#125—22no—
527#125C22×D7914yes—
528#123—28no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8C22×D7914yes—
532C22⋊Q8C22×D7914yes—
533#121—794no—
534#121—794no—
535#121—1582no—
536#121—1582no—
537#121—1588no—
538#121—1588no—
539C4×Q8—22no—
540C4×Q8—794no—
541C4×Q8—1582no—
542C4×Q8C22×D7914yes—
543C4×D4—1588no—
544C4×D4C22⋊D7914yes—
545C4×D4C22×D7914yes—
546#117—22no—
547#117—28no—
548#117C22×D7914yes—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—791no—
557C2×C4⋊C4—1581no—
558C2×C4⋊C4C22⋊D7911yescharacteristic
559C2×C4⋊C4C22×D7911yescharacteristic
560C2×C4⋊C4C22×D7911yescharacteristic
561C2×C4⋊C4C22×D7914yes—
562C2×C4⋊C4C22×D7911yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—1581no—
567C2×C22⋊C4—1581no—
568C2×C22⋊C4C22⋊D7911yescharacteristic
569C2×C22⋊C4C22⋊D7911yescharacteristic
570C2×C42—21no—
571C2×C42—21no—
572C2×C42—1581no—
573C2×C42C22×D7911yescharacteristic
574#107—794no—
575#106—794no—
576#106—794no—
577C4⋊C8—794no—
578#103—794no—
579#103—794no—
580#103—794no—
581#103—794no—
582#102—794no—
583#102—794no—
584#102—794no—
585#102—794no—
586#102—794no—
587#102—794no—
588C22⋊C8—794no—
589C22⋊C8—794no—
590#97—794no—
591C24—1581no—
592C24—1581no—
593C24C2×C22⋊D7911yescharacteristic
594C24C2×C22⋊D7911yescharacteristic
595#41—3168no—
596#41—3168no—
597#41—3164no—
598#41—3164no—
599#41—1588no—
600#41—1588no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—794no—
605C2×Q8—792no—
606C2×Q8—1582no—
607C2×Q8—1581no—
608C2×Q8C23×D7912yes—
609C2×D4—42no—
610C2×D4—3164no—
611C2×D4—3164no—
612C2×D4—3164no—
613C2×D4—792no—
614C2×D4—792no—
615C2×D4—6322no—
616C2×D4—6322no—
617C2×D4—6322no—
618C2×D4—1584no—
619C2×D4—1584no—
620C2×D4—1584no—
621C2×D4—1584no—
622C2×D4—1582no—
623C2×D4—1582no—
624C2×D4—1582no—
625C2×D4—1582no—
626C2×D4—1584no—
627C2×D4—1581no—
628C2×D4—1581no—
629C2×D4—1584no—
630C2×D4C2×C22⋊D7914yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—44no—
641C22×C4—3164no—
642C22×C4—3164no—
643C22×C4—1581no—
644C22×C4—1584no—
645C22×C4—1584no—
646C22×C4—1581no—
647C22×C4C2×C22⋊D7912yes—
648C22×C4C2×C22⋊D7912yes—
649C22×C4C2×C22⋊D7911yescharacteristic
650C22×C4C2×C22⋊D7911yescharacteristic
651C22×C4C2×C22⋊D7911yescharacteristic
652C22×C4C2×C22⋊D7911yescharacteristic
653C22×C4C23×D7912yes—
654C22×C4C23×D7912yes—
655C22×C4C23×D7911yescharacteristic
656Q16—1588no—
657SD16—3164no—
658SD16—3164no—
659M16—3164no—
660C2×C8—3164no—
661C2×C8—792no—
662C2×C8—792no—
663C2×C8—792no—
664C2×C8—792no—
665C2×C8—1582no—
666C2×C8—1582no—
667C2×C8—1582no—
668C2×C8—1582no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—21no—
678C4⋊C4—792no—
679C4⋊C4—1584no—
680C4⋊C4—1581no—
681C4⋊C4C2×C22⋊D7914yes—
682C4⋊C4C23×D7912yes—
683C4⋊C4C23×D7912yes—
684C4⋊C4C23×D7912yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1584no—
689C22⋊C4—1584no—
690C22⋊C4C2×C22⋊D7914yes—
691C22⋊C4C2×C22⋊D7914yes—
692C42—24no—
693C42—24no—
694C42—1584no—
695C42C2×C22⋊D7912yes—
696C42C23×D7912yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—3162no—
704C23—3162no—
705C23—3162no—
706C23—3162no—
707C23—3162no—
708C23—3162no—
709C23—1582no—
710C23—1582no—
711C23C22×C22⋊D7912yes—
712C23C22×C22⋊D7912yes—
713C23C22×C22⋊D7911yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—794no—
718Q8—1582no—
719Q8—1584no—
720D4—44no—
721D4—3168no—
722D4—3168no—
723D4—3168no—
724D4—3162no—
725D4—3162no—
726D4—6324no—
727D4—6324no—
728D4—6324no—
729D4—1582no—
730D4—1582no—
731D4—1582no—
732D4—1582no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—3168no—
753C2×C4—3168no—
754C2×C4—3162no—
755C2×C4—1582no—
756C2×C4—1584no—
757C2×C4—1582no—
758C2×C4C22×C22⋊D7912yes—
759C2×C4C22×C22⋊D7912yes—
760C2×C4C22×C22⋊D7912yes—
761C2×C4C22×C22⋊D7912yes—
762C2×C4C22×C22⋊D7911yescharacteristic
763C2×C4#41×D7912yes—
764C2×C4#1457920712yes—
765C2×C4C24×D7911yescharacteristic
766C8—1582no—
767C8—1582no—
768C8—1582no—
769C8—1582no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—3162no—
779C22—3162no—
780C22—3162no—
781C22—3162no—
782C22—3162no—
783C22—3162no—
784C22—6324no—
785C22—6324no—
786C22#1909920112yes—
787C22#1909936112yes—
788C22#1909937112yes—
789C22C23×C22⋊D7911yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—3162no—
799C4—1584no—
800C4#1909920112yes—
801C4C2×#41×D7911yescharacteristic
802C4C2×#1457920711yescharacteristic
803C2—42no—
804C2—42no—
805C2—6322no—
806C2—6322no—
807C2#2377552014yesdirect product factor
808C2C2×#1909920111yescharacteristic
809C2C2×#1909936111yescharacteristic
810C2C2×#1909937111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#552×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099234C2
hypercenterC2×#552D79
hypocenterC79C2×#3317
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #23775520C2direct (N × H)
3. C2×#19098929C2semidirect
4. C2×#19098881C2semidirect
5. C2×#19098887C2semidirect
6. C2×#19098867C2semidirect
7. C2×#19098811C2semidirect
8. C2×#19098794C2semidirect
9. C2×#19098763C2semidirect
10. C2×#19098723C2semidirect
11. C2×#19098723C2semidirect
12. C2×#19098668C2semidirect
13. C2×#19098635C2semidirect
14. C2×#19098562C2semidirect
15. C2×#19098557C2semidirect
16. C2×#552×C79C2semidirect
34. #19098929C22semidirect
35. #19098887C22semidirect
36. #19098881C22semidirect
37. #19098867C22semidirect
38. #19098811C22semidirect
39. #19098794C22semidirect
40. #19098763C22semidirect
41. #19098723C22semidirect
42. #19098723C22semidirect
43. #19098668C22semidirect
44. #19098635C22semidirect
49. #19098562C22semidirect
50. #19098557C22semidirect
65. #552×C79C22semidirect
400. C2×C79#3317semidirect
406. C2×#552D79semidirect
422. C79C2×#3317semidirect
431. #552C2×D79semidirect
807. C2#23775520direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992342
#237755202
C2×#190989292
C2×#190988812
C2×#190988872
C2×#190988672
C2×#190988112
C2×#190987942
C2×#190987632
C2×#190987232
C2×#190986682
C2×#190986352
C2×#190985622
C2×#190985572
C2×#552×C792
C2×#331779