Finite Group Databasebeta

← C2×#23774077 #35158147

Subgroups — C2×#23774077 #35158147

Order 20224.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099168C211yesmaximal, characteristic, complemented
2#23774077C2116yesmaximal, direct product factor
3C2×#19098969C211yesmaximal, characteristic, complemented
4C2×#19098953C211yesmaximal, characteristic, complemented
5C2×#19098917C211yesmaximal, characteristic, complemented
6C2×#19098911C211yesmaximal, characteristic, complemented
7C2×#19098814C211yesmaximal, characteristic, complemented
8C2×#19098811C211yesmaximal, characteristic, complemented
9C2×#19098797C211yesmaximal, characteristic, complemented
10C2×#19098794C211yesmaximal, characteristic, complemented
11C2×#19098673C211yesmaximal, characteristic, complemented
12C2×#19098661C211yesmaximal, characteristic, complemented
13C2×C4×#11929611C211yesmaximal, characteristic, complemented
14C2×C4×#11929609C211yesmaximal, characteristic, complemented
15C2×#19098519C211yesmaximal, characteristic, complemented
16C2×#542×C79C211yesmaximal, characteristic, complemented
17C22×#11929611C2211yescharacteristic
18C22×#11929611C2211yescharacteristic
19C22×#11929609C2211yescharacteristic
20C22×#11929609C2211yescharacteristic
21C22×#11929608C2211yescharacteristic
22C23×C79⋊C8C2211yescharacteristic
23#19099168—24no—
24#19099168C2218yescomplemented
25C2×#14579158C2211yescharacteristic
26C2×#14579153C2211yescharacteristic
27C2×#14579146—21no—
28C2×#14579146—21no—
29C2×#14579135C2211yescharacteristic
30C2×#14579135C2211yescharacteristic
31C2×#14579134—21no—
32C2×#14579134—21no—
33C2×C4×D316C2211yescharacteristic
34C2×C4×D316C2211yescharacteristic
35#19098969C2218yescomplemented
36#19098953C2218yescomplemented
37#19098917C2218yescomplemented
38#19098911C2218yescomplemented
39#19098814C2218yescomplemented
40#19098811C2218yescomplemented
41#19098797C2218yescomplemented
42#19098794C2218yescomplemented
43#19098673C2218yescomplemented
44#19098661C2218yescomplemented
45C4×#11929611C2218yescomplemented
46C4×#11929609C2218yescomplemented
47C2×#14579094C2211yescharacteristic
48C2×#14579094C2211yescharacteristic
49C2×#14579092C2211yescharacteristic
50C2×#14579092C2211yescharacteristic
51C2×#14579085C2211yescharacteristic
52C2×#14579085C2211yescharacteristic
53C2×#14579082C2211yescharacteristic
54C2×#14579082C2211yescharacteristic
55C2×#14579081C2211yescharacteristic
56C2×#14579081C2211yescharacteristic
57C2×#14579081C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59#19098519C2218yescomplemented
60C2×#14579072C2211yescharacteristic
61C2×#14579072C2211yescharacteristic
62C2×C4×C79⋊C8C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#542×C79—24no—
65#542×C79C2218yescomplemented
66C2×C4⋊Q8×C79C2211yescharacteristic
67C2×#126×C79—21no—
68C2×#124×C79—21no—
69C2×#124×C79C2211yescharacteristic
70C2×#123×C79—21no—
71C2×C22⋊Q8×C79—21no—
72C2×C22⋊Q8×C79C2211yescharacteristic
73C2×#121×C79C2211yescharacteristic
74C2×C4×Q8×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C2×#117×C79C2211yescharacteristic
77C22×D316—21no—
78C22×D316—21no—
79C22×D316C2311yescharacteristic
80C22×D316C2311yescharacteristic
81C22×C22⋊D79—21no—
82C22×C22⋊D79—21no—
83C22×C4×D79—21no—
84C22×C4×D79—21no—
85C2×#11929611—24no—
86C2×#11929611—24no—
87C2×#11929611C2314yes—
88C2×#11929611C2314yes—
89C2×#11929609—24no—
90C2×#11929609—24no—
91C2×#11929609C2314yes—
92C2×#11929609C2314yes—
93C2×#11929608—24no—
94C2×#11929608C2314yes—
95C22×C79⋊C8—24no—
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98C22×C79⋊C8C2314yes—
99C22×C79⋊C8C2311yescharacteristic
100C22×C79⋊C8C2311yescharacteristic
101#14579158—22no—
102#14579158C2314yes—
103#14579153—22no—
104#14579153C2314yes—
105#14579146—28no—
106#14579146—28no—
107#14579135—22no—
108#14579135—22no—
109#14579135C2314yes—
110#14579135C2314yes—
111#14579134—28no—
112#14579134—28no—
113C4×D316—22no—
114C4×D316—22no—
115C4×D316C2314yes—
116C4×D316C2314yes—
117C2×C4⋊Dic79C2311yescharacteristic
118C2×C4⋊Dic79C2311yescharacteristic
119C2×Dic79⋊C4—21no—
120C2×Dic79⋊C4—21no—
121C2×(C2×D79)⋊C4—21no—
122C2×(C2×D79)⋊C4—21no—
123C2×(C2×D79)⋊C4—21no—
124C2×(C2×D79)⋊C4—21no—
125#14579094C2314yes—
126#14579094C2314yes—
127#14579092C2314yes—
128#14579092C2314yes—
129#14579085C2314yes—
130#14579085C2314yes—
131#14579082C2314yes—
132#14579082C2314yes—
133#14579081C2314yes—
134#14579081C2314yes—
135#14579081C2314yes—
136#14579081C2314yes—
137#14579072C2314yes—
138#14579072C2314yes—
139C4×C79⋊C8C2314yes—
140C4×C79⋊C8C2314yes—
141C22×Q8×C79—21no—
142C22×Q8×C79C2311yescharacteristic
143C22×D4×C79—21no—
144C22×D4×C79C2311yescharacteristic
145C23×C4×C79—21no—
146C23×C4×C79C2311yescharacteristic
147C4⋊Q8×C79—22no—
148C4⋊Q8×C79C2314yes—
149#126×C79—28no—
150#124×C79—28no—
151#124×C79—22no—
152#124×C79C2314yes—
153#123×C79—28no—
154C22⋊Q8×C79—22no—
155C22⋊Q8×C79—28no—
156C22⋊Q8×C79C2314yes—
157#121×C79—22no—
158#121×C79C2314yes—
159C4×Q8×C79—22no—
160C4×Q8×C79C2314yes—
161C4×D4×C79—22no—
162C4×D4×C79C2314yes—
163#117×C79D414yes—
164#117×C79C2314yes—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79D411yescharacteristic
169C2×C4⋊C4×C79D411yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C22⋊C4×C79—21no—
173C2×C22⋊C4×C79—21no—
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177C2×C22⋊C4×C79D411yescharacteristic
178C2×C22⋊C4×C79D411yescharacteristic
179C2×C42×C79—21no—
180C2×C42×C79C2311yescharacteristic
181C2×C42×C79C2311yescharacteristic
182C23×D79—21no—
183C23×D79—21no—
184C2×D316—21no—
185C2×D316—21no—
186C2×D316—24no—
187C2×D316—24no—
188C2×D316—22no—
189C2×D316—22no—
190C2×D316—22no—
191C2×D316—22no—
192C2×D316—82no—
193C2×D316—82no—
194C2×D316C2412yes—
195C2×D316C2412yes—
196C2×C22⋊D79—24no—
197C2×C22⋊D79—24no—
198C2×C22⋊D79—82no—
199C2×C22⋊D79—82no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C2×C4×D79—24no—
203C2×C4×D79—24no—
204C2×C4×D79—82no—
205C2×C4×D79—82no—
206#11929611—28no—
207#11929611—28no—
208#11929609—28no—
209#11929609—28no—
210#11929608—28no—
211C2×C79⋊C8—28no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8—22no—
214C2×C79⋊C8#4114yes—
215C2×C79⋊C8#4114yes—
216C2×C79⋊C8C2412yes—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C2×C79⋊C8C2412yes—
220C4⋊Dic79—21no—
221C4⋊Dic79—21no—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228(C2×D79)⋊C4—24no—
229(C2×D79)⋊C4—24no—
230C24×C79—21no—
231C24×C79C2×D411yescharacteristic
232C2×Q8×C79—21no—
233C2×Q8×C79—24no—
234C2×Q8×C79—22no—
235C2×Q8×C79—22no—
236C2×Q8×C79—82no—
237C2×Q8×C79C2412yes—
238C2×D4×C79—24no—
239C2×D4×C79—21no—
240C2×D4×C79—22no—
241C2×D4×C79—22no—
242C2×D4×C79—82no—
243C2×D4×C79C2412yes—
244C22×C4×C79—22no—
245C22×C4×C79—22no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79—21no—
249C22×C4×C79—24no—
250C22×C4×C79—82no—
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D412yes—
257C22×C4×C79C2412yes—
258C22×C4×C79C2411yescharacteristic
259C4⋊C4×C79—24no—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79C2×D414yes—
265C4⋊C4×C79C2×D414yes—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C22⋊C4×C79—24no—
269C22⋊C4×C79—24no—
270C22⋊C4×C79—24no—
271C22⋊C4×C79—24no—
272C22⋊C4×C79—24no—
273C22⋊C4×C79C2×D414yes—
274C22⋊C4×C79C2×D414yes—
275C42×C79—24no—
276C42×C79C2×D412yes—
277C42×C79C2×D412yes—
278C42×C79C2412yes—
279C42×C79C2412yes—
280C23×C79—22no—
281C23×C79—22no—
282C23×C79—22no—
283C23×C79—22no—
284C23×C79—42no—
285C23×C79—42no—
286C23×C79—42no—
287C23×C79C22×D412yes—
288C23×C79C22×D411yescharacteristic
289C22×D79—22no—
290C22×D79—22no—
291C22×D79—42no—
292C22×D79—42no—
293C22×D79—42no—
294C22×D79—42no—
295C22×D79—42no—
296C22×D79—42no—
297Q8×C79—22no—
298Q8×C79—22no—
299Q8×C79—42no—
300Q8×C79—84no—
301D4×C79—22no—
302D4×C79—22no—
303D4×C79—42no—
304D4×C79—84no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—24no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—22no—
316C2×C4×C79—42no—
317C2×C4×C79—42no—
318C2×C4×C79—42no—
319C2×C4×C79—84no—
320C2×C4×C79C22×D412yes—
321C2×C4×C79C22×D412yes—
322C2×C4×C79C22×D412yes—
323C2×C4×C79C22×D412yes—
324C2×C4×C79C22×D412yes—
325C2×C4×C79C22×D411yescharacteristic
326C2×C4×C79C2×#4112yes—
327C2×C4×C79C2×#4112yes—
328C2×C4×C79C2511yescharacteristic
329C22⋊D79—84no—
330C22⋊D79—84no—
331C2×Dic79—22no—
332C2×Dic79—22no—
333C2×Dic79—42no—
334C2×Dic79—42no—
335D316—22no—
336D316—22no—
337D316—22no—
338D316—22no—
339D316—42no—
340D316—42no—
341D316—84no—
342D316—84no—
343C4×D79—84no—
344C4×D79—84no—
345C79⋊C8—22no—
346C79⋊C8—22no—
347C79⋊C8C2×#4114yes—
348C79⋊C8C2×#4114yes—
349C22×C79—22no—
350C22×C79—22no—
351C22×C79—22no—
352C22×C79—44no—
353C22×C79—42no—
354C22×C79—42no—
355C22×C79—42no—
356C22×C79—84no—
357C22×C79#53212yes—
358C22×C79#57612yes—
359C22×C79#57712yes—
360C22×C79C23×D411yescharacteristic
361C2×D79—42no—
362C2×D79—42no—
363C2×D79—42no—
364C2×D79—42no—
365C2×D79—42no—
366C2×D79—42no—
367C2×D79—84no—
368C2×D79—84no—
369C4×C79—22no—
370C4×C79—22no—
371C4×C79—22no—
372C4×C79—22no—
373C4×C79—22no—
374C4×C79—42no—
375C4×C79—42no—
376C4×C79—42no—
377C4×C79#53212yes—
378C4×C79C22×#4111yescharacteristic
379C4×C79C22×#4111yescharacteristic
380Dic79—42no—
381Dic79—42no—
382C2×#3179—791nomaximal, Sylow
383C2×C79—42no—
384C2×C79—82no—
385C2×C79#317914yescomplemented
386C2×C79C2×#53211yescharacteristic
387C2×C79C2×#57611yescharacteristic
388C2×C79C2×#57711yescharacteristic
389D79—82no—
390D79—82no—
391C2×#542D7911yescharacteristic, complemented
392C2×#540—791no—
393#3179—7916no—
394C2×#501—791no—
395C2×#496—791no—
396C2×#488—791no—
397C2×#486—791no—
398C2×#469—791no—
399C2×#468—791no—
400C2×#466—791no—
401C2×#465—791no—
402C2×#442—791no—
403C2×#440—791no—
404C2×C4×SD16—791no—
405C2×C4×D8—791no—
406C2×#405—791no—
407C79C2×#317911yescharacteristic, complemented, Sylow
408C22×SD16—791no—
409C22×SD16—791no—
410C22×D8—791no—
411C22×D8—791no—
412C22×M16—791no—
413C23×C8—791no—
414#542—24no—
415#542C2×D7918yescomplemented
416#540—798no—
417#540—1584no—
418C2×C4⋊Q8C2×D7911yescharacteristic
419C2×#127—791no—
420C2×#126—21no—
421C2×#125—791no—
422C2×#124—21no—
423C2×#124C2×D7911yescharacteristic
424C2×#123—21no—
425C2×#123—1581no—
426C2×#123—1581no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8C2×D7911yescharacteristic
429C2×#121—791no—
430C2×#121—791no—
431C2×#121—1581no—
432C2×#121—1581no—
433C2×#121C2×D7911yescharacteristic
434C2×C4×Q8C2×D7911yescharacteristic
435C2×C4×D4—791no—
436C2×C4×D4—791no—
437C2×C4×D4C2×D7911yescharacteristic
438C2×#117C2×D7911yescharacteristic
439#501—798no—
440#496—798no—
441#488—798no—
442#486—798no—
443#469—798no—
444#468—798no—
445#466—798no—
446#465—798no—
447#442—798no—
448#440—798no—
449C4×SD16—798no—
450C4×D8—798no—
451C2×#107—791no—
452C2×#107—791no—
453C2×#106—791no—
454C2×#106—791no—
455C2×#103—791no—
456C2×#103—791no—
457C2×#102—791no—
458C2×#102—791no—
459C2×#102—791no—
460C2×#102—791no—
461C2×#102—791no—
462C2×#102—791no—
463#405—798no—
464C2×#97—791no—
465C2×#97—791no—
466C2×C4×C8—791no—
467C2×C4×C8—791no—
468C22×Q8—21no—
469C22×Q8C22×D7911yescharacteristic
470C22×D4—21no—
471C22×D4—791no—
472C22×D4—791no—
473C22×D4—1581no—
474C22×D4—1581no—
475C22×D4—1581no—
476C22×D4—1581no—
477C22×D4C22×D7911yescharacteristic
478C23×C4—21no—
479C23×C4—1581no—
480C23×C4—1581no—
481C23×C4C22×D7911yescharacteristic
482C2×SD16—794no—
483C2×SD16—794no—
484C2×SD16—1584no—
485C2×SD16—1584no—
486C2×D8—794no—
487C2×D8—794no—
488C2×D8—1584no—
489C2×D8—1584no—
490C2×M16—794no—
491C2×M16—1584no—
492C22×C8—791no—
493C22×C8—791no—
494C22×C8—791no—
495C22×C8—794no—
496C22×C8—791no—
497C22×C8—1584no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D7914yes—
500#127—794no—
501#127—1582no—
502#126—28no—
503#125—794no—
504#125—1582no—
505#124—28no—
506#124—22no—
507#124C22×D7914yes—
508#123—28no—
509#123—1588no—
510#123—1588no—
511C22⋊Q8—22no—
512C22⋊Q8—28no—
513C22⋊Q8C22×D7914yes—
514#121—22no—
515#121—794no—
516#121—794no—
517#121—1582no—
518#121—1582no—
519#121—1588no—
520#121—1588no—
521#121C22×D7914yes—
522C4×Q8—22no—
523C4×Q8C22×D7914yes—
524C4×D4—22no—
525C4×D4—794no—
526C4×D4—794no—
527C4×D4—1582no—
528C4×D4—1582no—
529C4×D4C22×D7914yes—
530#117C22⋊D7914yes—
531#117C22×D7914yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—791no—
536C2×C4⋊C4—791no—
537C2×C4⋊C4—1581no—
538C2×C4⋊C4—1581no—
539C2×C4⋊C4C22⋊D7911yescharacteristic
540C2×C4⋊C4C22⋊D7911yescharacteristic
541C2×C4⋊C4C22×D7911yescharacteristic
542C2×C4⋊C4C22×D7911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1581no—
549C2×C22⋊C4—1581no—
550C2×C22⋊C4—1581no—
551C2×C22⋊C4—1581no—
552C2×C22⋊C4C22⋊D7911yescharacteristic
553C2×C22⋊C4C22⋊D7911yescharacteristic
554C2×C42—21no—
555C2×C42C22×D7911yescharacteristic
556C2×C42C22×D7911yescharacteristic
557#107—794no—
558#107—794no—
559#106—794no—
560#106—794no—
561#103—794no—
562#103—794no—
563#102—794no—
564#102—794no—
565#102—794no—
566#102—794no—
567#102—794no—
568#102—794no—
569#97—794no—
570#97—794no—
571C4×C8—794no—
572C4×C8—794no—
573C24—21no—
574C24—1581no—
575C24—1581no—
576C24C2×C22⋊D7911yescharacteristic
577C2×Q8—21no—
578C2×Q8—24no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—82no—
582C2×Q8C23×D7912yes—
583C2×D4—24no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—82no—
588C2×D4—792no—
589C2×D4—792no—
590C2×D4—6322no—
591C2×D4—6322no—
592C2×D4—6322no—
593C2×D4—6322no—
594C2×D4—1584no—
595C2×D4—1584no—
596C2×D4—1582no—
597C2×D4—1582no—
598C2×D4—1582no—
599C2×D4—1582no—
600C2×D4—1581no—
601C2×D4—1581no—
602C2×D4—1584no—
603C2×D4—1584no—
604C2×D4C23×D7912yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—6322no—
613C22×C4—6322no—
614C22×C4—1581no—
615C22×C4—1581no—
616C22×C4—1584no—
617C22×C4—1584no—
618C22×C4C2×C22⋊D7912yes—
619C22×C4C2×C22⋊D7911yescharacteristic
620C22×C4C2×C22⋊D7911yescharacteristic
621C22×C4C2×C22⋊D7911yescharacteristic
622C22×C4C2×C22⋊D7911yescharacteristic
623C22×C4C2×C22⋊D7911yescharacteristic
624C22×C4C23×D7912yes—
625C22×C4C23×D7911yescharacteristic
626SD16—1588no—
627SD16—1588no—
628D8—1588no—
629D8—1588no—
630M16—1588no—
631C2×C8—794no—
632C2×C8—794no—
633C2×C8—792no—
634C2×C8—792no—
635C2×C8—792no—
636C2×C8—792no—
637C2×C8—1588no—
638C2×C8—1582no—
639C2×C8—1582no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—792no—
646C4⋊C4—792no—
647C4⋊C4—1584no—
648C4⋊C4—1584no—
649C4⋊C4—1581no—
650C4⋊C4—1581no—
651C4⋊C4C2×C22⋊D7914yes—
652C4⋊C4C2×C22⋊D7914yes—
653C4⋊C4C23×D7912yes—
654C4⋊C4C23×D7912yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1584no—
661C22⋊C4—1584no—
662C22⋊C4—1584no—
663C22⋊C4—1584no—
664C22⋊C4C2×C22⋊D7914yes—
665C22⋊C4C2×C22⋊D7914yes—
666C42—24no—
667C42C2×C22⋊D7912yes—
668C42C2×C22⋊D7912yes—
669C42C23×D7912yes—
670C42C23×D7912yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—3162no—
679C23—3162no—
680C23—3162no—
681C23—3162no—
682C23—3162no—
683C23—3162no—
684C23—1582no—
685C23—1582no—
686C23C22×C22⋊D7912yes—
687C23C22×C22⋊D7911yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—84no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—3162no—
697D4—3162no—
698D4—6324no—
699D4—6324no—
700D4—6324no—
701D4—6324no—
702D4—1582no—
703D4—1582no—
704D4—1582no—
705D4—1582no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—3162no—
722C2×C4—3162no—
723C2×C4—6324no—
724C2×C4—6324no—
725C2×C4—1582no—
726C2×C4—1582no—
727C2×C4C22×C22⋊D7912yes—
728C2×C4C22×C22⋊D7912yes—
729C2×C4C22×C22⋊D7912yes—
730C2×C4C22×C22⋊D7912yes—
731C2×C4C22×C22⋊D7912yes—
732C2×C4C22×C22⋊D7911yescharacteristic
733C2×C4#41×D7912yes—
734C2×C4#41×D7912yes—
735C2×C4C24×D7911yescharacteristic
736C8—794no—
737C8—794no—
738C8—1582no—
739C8—1582no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—3162no—
749C22—3162no—
750C22—3162no—
751C22—3162no—
752C22—3162no—
753C22—3162no—
754C22—6324no—
755C22—6324no—
756C22#1909910912yes—
757C22#1909936612yes—
758C22#1909937112yes—
759C22C23×C22⋊D7911yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—3162no—
769C4—3162no—
770C4#1909910912yes—
771C4C2×#41×D7911yescharacteristic
772C4C2×#41×D7911yescharacteristic
773C2—42no—
774C2—82no—
775C2—6322no—
776C2—6322no—
777C2#2377407714yesdirect product factor
778C2C2×#1909910911yescharacteristic
779C2C2×#1909936611yescharacteristic
780C2C2×#1909937111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#542×C79C2
socleC23×C79C22×D4
hypercenterC2×#542D79
hypocenterC79C2×#3179
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#19099168C2semidirect
2. #23774077C2direct (N × H)
3. C2×#19098969C2semidirect
4. C2×#19098953C2semidirect
5. C2×#19098917C2semidirect
6. C2×#19098911C2semidirect
7. C2×#19098814C2semidirect
8. C2×#19098811C2semidirect
9. C2×#19098797C2semidirect
10. C2×#19098794C2semidirect
11. C2×#19098673C2semidirect
12. C2×#19098661C2semidirect
13. C2×C4×#11929611C2semidirect
14. C2×C4×#11929609C2semidirect
15. C2×#19098519C2semidirect
16. C2×#542×C79C2semidirect
24. #19099168C22semidirect
35. #19098969C22semidirect
36. #19098953C22semidirect
37. #19098917C22semidirect
38. #19098911C22semidirect
39. #19098814C22semidirect
40. #19098811C22semidirect
41. #19098797C22semidirect
42. #19098794C22semidirect
43. #19098673C22semidirect
44. #19098661C22semidirect
45. C4×#11929611C22semidirect
46. C4×#11929609C22semidirect
59. #19098519C22semidirect
65. #542×C79C22semidirect
385. C2×C79#3179semidirect
391. C2×#542D79semidirect
407. C79C2×#3179semidirect
415. #542C2×D79semidirect
777. C2#23774077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991682
#237740772
C2×#190989692
C2×#190989532
C2×#190989172
C2×#190989112
C2×#190988142
C2×#190988112
C2×#190987972
C2×#190987942
C2×#190986732
C2×#190986612
C2×C4×#119296112
C2×C4×#119296092
C2×#190985192
C2×#542×C792
C2×#317979