Finite Group Databasebeta

← C2×#23775834 #35166794

Subgroups — C2×#23775834 #35166794

Order 20224.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099253C211yesmaximal, characteristic, complemented
2#23775834C2116yesmaximal, direct product factor
3C2×#19098969C211yesmaximal, characteristic, complemented
4C2×#19098898C211yesmaximal, characteristic, complemented
5C2×#19098884C211yesmaximal, characteristic, complemented
6C2×#19098893C211yesmaximal, characteristic, complemented
7C2×#19098874C211yesmaximal, characteristic, complemented
8C2×#19098855C211yesmaximal, characteristic, complemented
9C2×#19098863C211yesmaximal, characteristic, complemented
10C2×#19098807C211yesmaximal, characteristic, complemented
11C2×#19098790C211yesmaximal, characteristic, complemented
12C2×#19098663C211yesmaximal, characteristic, complemented
13C2×#19098635C211yesmaximal, characteristic, complemented
14C2×#19098603C211yesmaximal, characteristic, complemented
15C22×#14579094C211yesmaximal, characteristic, complemented
16C2×#547×C79C211yesmaximal, characteristic
17C22×#11929612C2211yescharacteristic
18C22×#11929608C2211yescharacteristic
19C23×C79⋊C8C2211yescharacteristic
20#19099253—24no—
21#19099253C2218yescomplemented
22C2×#14579154—21no—
23C2×#14579153C2211yescharacteristic
24C2×#14579151—21no—
25C2×#14579142—21no—
26C2×#14579140C2211yescharacteristic
27C2×#14579140C2211yescharacteristic
28C2×C4×Dic158C2211yescharacteristic
29C2×#14579120C2211yescharacteristic
30C2×#14579117—21no—
31C22×C4⋊Dic79C2211yescharacteristic
32#19098969C2218yescomplemented
33#19098898C2218yescomplemented
34#19098893C2218yescomplemented
35#19098884C2218yescomplemented
36#19098874C2218yescomplemented
37#19098863C2218yescomplemented
38#19098855C2218yescomplemented
39#19098807C2218yescomplemented
40#19098790C2218yescomplemented
41#19098663C2218yescomplemented
42#19098635C2218yescomplemented
43#19098603C2218yescomplemented
44C2×#14579094C2211yescharacteristic
45C2×#14579094C2211yescharacteristic
46C2×#14579094C2211yescharacteristic
47C2×#14579094C2211yescharacteristic
48C2×#14579094C2211yescharacteristic
49C2×#14579094C2211yescharacteristic
50C2×#14579094C2218yescomplemented
51C2×#14579092C2211yescharacteristic
52C2×#14579092C2211yescharacteristic
53C2×#14579092C2211yescharacteristic
54C2×C4⋊(C79⋊C8)C2211yescharacteristic
55C2×#14579084C2211yescharacteristic
56C2×#14579084C2211yescharacteristic
57C2×#14579084C2211yescharacteristic
58C2×#14579082C2211yescharacteristic
59C2×#14579082C2211yescharacteristic
60C2×#14579082C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×C22⋊(C79⋊C8)C2211yescharacteristic
63C2×#14579072C2211yescharacteristic
64C22×#41×C79—21no—
65#547×C79—24no—
66#547×C79C2218yes—
67C2×C4⋊Q8×C79C2211yescharacteristic
68C2×#123×C79—21no—
69C2×#123×C79—21no—
70C2×C22⋊Q8×C79—21no—
71C2×#121×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73C2×C4×D4×C79C2211yescharacteristic
74C2×C4×D4×C79C2211yescharacteristic
75C22×C4⋊C4×C79C2211yescharacteristic
76C22×C4⋊C4×C79C2211yescharacteristic
77C22×Dic158C2311yescharacteristic
78C23×Dic79—21no—
79C2×#11929612—24no—
80C2×#11929612C2314yes—
81C2×#11929608—24no—
82C2×#11929608C2314yes—
83C22×C79⋊C8—24no—
84C22×C79⋊C8C2314yes—
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89#14579154—28no—
90#14579153—22no—
91#14579153C2314yes—
92#14579151—28no—
93#14579142—28no—
94#14579140—22no—
95#14579140—22no—
96#14579140C2314yes—
97#14579140C2314yes—
98C4×Dic158—22no—
99C4×Dic158C2314yes—
100#14579120—22no—
101#14579120C2314yes—
102#14579117—28no—
103C2×C4⋊Dic79—22no—
104C2×C4⋊Dic79—21no—
105C2×C4⋊Dic79C2314yes—
106C2×C4⋊Dic79C2311yescharacteristic
107C2×C4⋊Dic79C2311yescharacteristic
108C2×C4⋊Dic79C2311yescharacteristic
109C2×Dic79⋊C4—21no—
110C2×Dic79⋊C4—21no—
111C2×Dic79⋊C4—21no—
112C2×Dic79⋊C4—21no—
113C2×Dic79⋊C4—21no—
114C2×C22⋊Dic79—21no—
115C2×C22⋊Dic79—21no—
116C2×C22⋊Dic79—21no—
117C2×C4×Dic79—21no—
118C2×C4×Dic79—21no—
119#14579094C2314yes—
120#14579094C2314yes—
121#14579094C2314yes—
122#14579094C2314yes—
123#14579094C2314yes—
124#14579094C2314yes—
125#14579092C2314yes—
126#14579092C2314yes—
127#14579092C2314yes—
128C4⋊(C79⋊C8)C2314yes—
129#14579084C2314yes—
130#14579084C2314yes—
131#14579084C2314yes—
132#14579082C2314yes—
133#14579082C2314yes—
134#14579082C2314yes—
135C22⋊(C79⋊C8)C2314yes—
136C22⋊(C79⋊C8)C2314yes—
137#14579072C2314yes—
138C2×#41×C79—28no—
139C2×#41×C79—48no—
140C22×Q8×C79—21no—
141C22×D4×C79—21no—
142C22×D4×C79—21no—
143C22×D4×C79D411yescharacteristic
144C22×D4×C79C2311yescharacteristic
145C23×C4×C79—21no—
146C23×C4×C79—21no—
147C23×C4×C79—21no—
148C23×C4×C79C2311yescharacteristic
149C23×C4×C79C2311yescharacteristic
150C4⋊Q8×C79—22no—
151C4⋊Q8×C79C2314yes—
152#123×C79—28no—
153#123×C79—28no—
154C22⋊Q8×C79—28no—
155#121×C79—22no—
156#121×C79—22no—
157#121×C79C2314yes—
158#121×C79C2314yes—
159C4×D4×C79—22no—
160C4×D4×C79D414yes—
161C4×D4×C79C2314yes—
162C4×D4×C79C2314yes—
163C2×C4⋊C4×C79—21no—
164C2×C4⋊C4×C79—21no—
165C2×C4⋊C4×C79—22no—
166C2×C4⋊C4×C79—22no—
167C2×C4⋊C4×C79—21no—
168C2×C4⋊C4×C79D411yescharacteristic
169C2×C4⋊C4×C79C2314yes—
170C2×C4⋊C4×C79C2314yes—
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
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×C79C2311yescharacteristic
180C2×Dic158—21no—
181C2×Dic158—22no—
182C2×Dic158—22no—
183C2×Dic158C2412yes—
184C22×Dic79—21no—
185C22×Dic79—21no—
186C22×Dic79—21no—
187C22×Dic79—21no—
188C22×Dic79—24no—
189C22×Dic79—44no—
190#11929612—28no—
191#11929608—28no—
192C2×C79⋊C8—28no—
193C2×C79⋊C8—22no—
194C2×C79⋊C8—22no—
195C2×C79⋊C8—22no—
196C2×C79⋊C8#4114yescomplemented
197C2×C79⋊C8C2412yes—
198C2×C79⋊C8C2412yes—
199C2×C79⋊C8C2412yes—
200C2×C79⋊C8C2412yes—
201C4⋊Dic79—21no—
202C4⋊Dic79—21no—
203C4⋊Dic79—24no—
204C4⋊Dic79—21no—
205C4⋊Dic79C2412yes—
206C4⋊Dic79C2412yes—
207C4⋊Dic79C2412yes—
208Dic79⋊C4—24no—
209Dic79⋊C4—24no—
210Dic79⋊C4—24no—
211Dic79⋊C4—24no—
212Dic79⋊C4—24no—
213C22⋊Dic79—24no—
214C22⋊Dic79—24no—
215C22⋊Dic79—24no—
216C4×Dic79—24no—
217C4×Dic79—24no—
218C24×C79—21no—
219C24×C79C2×D411yescharacteristic
220C24×C79C2×D411yescharacteristic
221#41×C79—432no—
222C2×Q8×C79—24no—
223C2×Q8×C79—44no—
224C2×D4×C79—24no—
225C2×D4×C79—24no—
226C2×D4×C79—24no—
227C2×D4×C79—21no—
228C2×D4×C79—22no—
229C2×D4×C79—22no—
230C2×D4×C79—44no—
231C2×D4×C79—44no—
232C2×D4×C79C2×D414yes—
233C2×D4×C79C2412yes—
234C22×C4×C79—22no—
235C22×C4×C79—22no—
236C22×C4×C79—22no—
237C22×C4×C79—22no—
238C22×C4×C79—21no—
239C22×C4×C79—21no—
240C22×C4×C79—21no—
241C22×C4×C79—24no—
242C22×C4×C79—24no—
243C22×C4×C79—24no—
244C22×C4×C79—44no—
245C22×C4×C79—44no—
246C22×C4×C79—44no—
247C22×C4×C79C2×D411yescharacteristic
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D412yes—
252C22×C4×C79C2×D412yes—
253C22×C4×C79C2412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2411yescharacteristic
256C4⋊C4×C79—21no—
257C4⋊C4×C79—21no—
258C4⋊C4×C79—21no—
259C4⋊C4×C79—24no—
260C4⋊C4×C79—24no—
261C4⋊C4×C79—24no—
262C4⋊C4×C79C2×D414yes—
263C4⋊C4×C79C2412yes—
264C4⋊C4×C79C2412yes—
265C4⋊C4×C79C2412yes—
266C22⋊C4×C79—24no—
267C22⋊C4×C79—24no—
268C22⋊C4×C79—24no—
269C22⋊C4×C79C2×D414yes—
270C22⋊C4×C79C2×D414yes—
271C42×C79C2×D412yes—
272C42×C79C2412yes—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—42no—
280C23×C79—42no—
281C23×C79—42no—
282C23×C79AGL(1,ℤ/8)14yes—
283C23×C79C22×D412yes—
284C23×C79C22×D412yes—
285C23×C79C22×D411yescharacteristic
286Q8×C79—48no—
287D4×C79—28no—
288D4×C79—22no—
289D4×C79—22no—
290D4×C79—48no—
291D4×C79—48no—
292D4×C79—42no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—24no—
298C2×C4×C79—24no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—48no—
307C2×C4×C79—48no—
308C2×C4×C79—42no—
309C2×C4×C79—42no—
310C2×C4×C79—42no—
311C2×C4×C79—48no—
312C2×C4×C79C22×D412yes—
313C2×C4×C79C22×D412yes—
314C2×C4×C79C22×D412yes—
315C2×C4×C79C22×D412yes—
316C2×C4×C79C22×D411yescharacteristic
317C2×C4×C79C2×#4112yes—
318C2×C4×C792−1+412yes—
319C2×C4×C79C2511yescharacteristic
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—42no—
325C2×Dic79—48no—
326C2×Dic79—42no—
327C2×Dic79—42no—
328C2×Dic79—42no—
329Dic158—22no—
330Dic158—22no—
331Dic158—42no—
332C79⋊C8—22no—
333C79⋊C8—22no—
334C79⋊C8—22no—
335C79⋊C8C2×#4114yescomplemented
336C22×C79—28no—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—22no—
342C22×C79—44no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79—84no—
347C22×C79#54712yes—
348C22×C79C2×AGL(1,ℤ/8)14yes—
349C22×C79C2×AGL(1,ℤ/8)12yes—
350C22×C79#57812yes—
351C22×C79C23×D411yescharacteristic
352C4×C79—22no—
353C4×C79—22no—
354C4×C79—22no—
355C4×C79—22no—
356C4×C79—42no—
357C4×C79—42no—
358C4×C79—42no—
359C4×C79#54712yes—
360C4×C79C22×#4111yescharacteristic
361C4×C79C2×2−1+411yescharacteristic
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365Dic79—42no—
366C2×#3343—791nomaximal, Sylow
367C2×C79—24no—
368C2×C79—42no—
369C2×C79—82no—
370C2×C79#334314yescomplemented
371C2×C79C2×#54711yescharacteristic
372C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
373C2×C79C2×#57811yescharacteristic
374C2×#552—791no—
375C2×#547D7911yescharacteristic
376#3343—7916no—
377C2×#501—791no—
378C2×#484—791no—
379C2×#482—791no—
380C2×#483—791no—
381C2×#480—791no—
382C2×#477—791no—
383C2×#478—791no—
384C2×#468—791no—
385C2×#465—791no—
386C2×#440—791no—
387C2×#435—791no—
388C2×#428—791no—
389C22×#107—791no—
390C79C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—21no—
392C22×SD16—791no—
393C22×M16—791no—
394C23×C8—791no—
395#552—798no—
396#552—1584no—
397#547—24no—
398#547C2×D7918yes—
399C2×C4⋊Q8C2×D7911yescharacteristic
400C2×#126—1581no—
401C2×#125—791no—
402C2×#125—1581no—
403C2×#123—21no—
404C2×#123—21no—
405C2×#123—1581no—
406C2×C22⋊Q8—21no—
407C2×C22⋊Q8—791no—
408C2×C22⋊Q8—791no—
409C2×#121C2×D7911yescharacteristic
410C2×#121C2×D7911yescharacteristic
411C2×C4×Q8—791no—
412C2×C4×D4C2×D7911yescharacteristic
413C2×C4×D4C2×D7911yescharacteristic
414C2×#117—791no—
415C2×#117—1581no—
416C22×C4⋊C4—791no—
417C22×C4⋊C4C2×D7911yescharacteristic
418C22×C4⋊C4C2×D7911yescharacteristic
419#501—798no—
420#484—798no—
421#483—798no—
422#482—798no—
423#480—798no—
424#478—798no—
425#477—798no—
426#468—798no—
427#465—798no—
428#440—798no—
429#435—798no—
430#428—798no—
431C2×#107—791no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#107—791no—
435C2×#107—798no—
436C2×#107—791no—
437C2×#107—791no—
438C2×#106—791no—
439C2×#106—791no—
440C2×#106—791no—
441C2×C4⋊C8—791no—
442C2×#103—791no—
443C2×#103—791no—
444C2×#103—791no—
445C2×#102—791no—
446C2×#102—791no—
447C2×#102—791no—
448C2×C22⋊C8—791no—
449C2×C22⋊C8—791no—
450C2×#97—791no—
451C2×#41—28no—
452C2×#41—48no—
453C22×Q8—21no—
454C22×Q8—791no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C22⋊D7911yescharacteristic
458C22×D4C22×D7911yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—1581no—
463C23×C4C22×D7911yescharacteristic
464C23×C4C22×D7911yescharacteristic
465C2×SD16—794no—
466C2×SD16—1584no—
467C2×M16—794no—
468C2×M16—1584no—
469C22×C8—791no—
470C22×C8—791no—
471C22×C8—794no—
472C22×C8—791no—
473C22×C8—791no—
474C22×C8—1584no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D7914yes—
477#126—1588no—
478#125—794no—
479#125—1588no—
480#125—1582no—
481#123—28no—
482#123—28no—
483#123—1588no—
484C22⋊Q8—28no—
485C22⋊Q8—794no—
486C22⋊Q8—794no—
487C22⋊Q8—1582no—
488C22⋊Q8—1582no—
489#121—22no—
490#121—22no—
491#121C22×D7914yes—
492#121C22×D7914yes—
493C4×Q8—794no—
494C4×Q8—1582no—
495C4×D4—22no—
496C4×D4C22⋊D7914yes—
497C4×D4C22×D7914yes—
498C4×D4C22×D7914yes—
499#117—794no—
500#117—1582no—
501#117—1588no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—791no—
509C2×C4⋊C4—794no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—1581no—
512C2×C4⋊C4—1582no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4C22⋊D7911yescharacteristic
519C2×C4⋊C4C22×D7911yescharacteristic
520C2×C4⋊C4C22×D7911yescharacteristic
521C2×C4⋊C4C22×D7911yescharacteristic
522C2×C4⋊C4C22×D7914yes—
523C2×C4⋊C4C22×D7914yes—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4C22⋊D7911yescharacteristic
531C2×C22⋊C4C22⋊D7911yescharacteristic
532C2×C42—1581no—
533C2×C42—1581no—
534C2×C42C22×D7911yescharacteristic
535#107—794no—
536#107—794no—
537#107—794no—
538#107—794no—
539#107—794no—
540#107—794no—
541#106—794no—
542#106—794no—
543#106—794no—
544C4⋊C8—794no—
545#103—794no—
546#103—794no—
547#103—794no—
548#102—794no—
549#102—794no—
550#102—794no—
551C22⋊C8—794no—
552C22⋊C8—794no—
553#97—794no—
554C24—21no—
555C24C2×C22⋊D7911yescharacteristic
556C24C2×C22⋊D7911yescharacteristic
557#41—432no—
558C2×Q8—24no—
559C2×Q8—44no—
560C2×Q8—792no—
561C2×Q8—1582no—
562C2×Q8—1582no—
563C2×Q8—1581no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4C2×C22⋊D7914yes—
573C2×D4C23×D7912yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—3164no—
588C22×C4—1584no—
589C22×C4—1581no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1581no—
593C22×C4C2×C22⋊D7912yes—
594C22×C4C2×C22⋊D7912yes—
595C22×C4C2×C22⋊D7911yescharacteristic
596C22×C4C2×C22⋊D7911yescharacteristic
597C22×C4C2×C22⋊D7911yescharacteristic
598C22×C4C2×C22⋊D7911yescharacteristic
599C22×C4C23×D7912yes—
600C22×C4C23×D7912yes—
601C22×C4C23×D7911yescharacteristic
602SD16—1588no—
603M16—1588no—
604C2×C8—794no—
605C2×C8—792no—
606C2×C8—792no—
607C2×C8—792no—
608C2×C8—792no—
609C2×C8—1588no—
610C2×C8—1582no—
611C2×C8—1582no—
612C2×C8—1582no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—792no—
620C4⋊C4—792no—
621C4⋊C4—792no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1581no—
628C4⋊C4—1581no—
629C4⋊C4—1584no—
630C4⋊C4—1581no—
631C4⋊C4C2×C22⋊D7914yes—
632C4⋊C4C23×D7912yes—
633C4⋊C4C23×D7912yes—
634C4⋊C4C23×D7912yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1584no—
639C22⋊C4—1584no—
640C22⋊C4—1584no—
641C22⋊C4C2×C22⋊D7914yes—
642C22⋊C4C2×C22⋊D7914yes—
643C42—1584no—
644C42—1584no—
645C42C2×C22⋊D7912yes—
646C42C23×D7912yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#1457918714yes—
657C23C22×C22⋊D7912yes—
658C23C22×C22⋊D7912yes—
659C23C22×C22⋊D7911yescharacteristic
660Q8—48no—
661Q8—3162no—
662Q8—1582no—
663Q8—1582no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—48no—
689C2×C4—3162no—
690C2×C4—3168no—
691C2×C4—3162no—
692C2×C4—3162no—
693C2×C4—3162no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4C22×C22⋊D7912yes—
699C2×C4C22×C22⋊D7912yes—
700C2×C4C22×C22⋊D7912yes—
701C2×C4C22×C22⋊D7912yes—
702C2×C4C22×C22⋊D7911yescharacteristic
703C2×C4#41×D7912yes—
704C2×C4#1457920812yes—
705C2×C4C24×D7911yescharacteristic
706C8—794no—
707C8—1582no—
708C8—1582no—
709C8—1582no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22#1909921212yes—
722C22C2×#1457918714yes—
723C22C2×#1457918712yes—
724C22#1909937812yes—
725C22C23×C22⋊D7911yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—3162no—
734C4—3162no—
735C4—3162no—
736C4—3162no—
737C4#1909921212yes—
738C4C2×#41×D7911yescharacteristic
739C4C2×#1457920811yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2#2377583414yesdirect product factor
744C2C2×#1909921211yescharacteristic
745C2C22×#1457918711yescharacteristic
746C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
Fitting, prime radicalC2×#547×C79C2
socleC23×C79C22×D4
hypercenterC2×#547D79
hypocenterC79C2×#3343
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#19099253C2semidirect
2. #23775834C2direct (N × H)
3. C2×#19098969C2semidirect
4. C2×#19098898C2semidirect
5. C2×#19098884C2semidirect
6. C2×#19098893C2semidirect
7. C2×#19098874C2semidirect
8. C2×#19098855C2semidirect
9. C2×#19098863C2semidirect
10. C2×#19098807C2semidirect
11. C2×#19098790C2semidirect
12. C2×#19098663C2semidirect
13. C2×#19098635C2semidirect
14. C2×#19098603C2semidirect
15. C22×#14579094C2semidirect
21. #19099253C22semidirect
32. #19098969C22semidirect
33. #19098898C22semidirect
34. #19098893C22semidirect
35. #19098884C22semidirect
36. #19098874C22semidirect
37. #19098863C22semidirect
38. #19098855C22semidirect
39. #19098807C22semidirect
40. #19098790C22semidirect
41. #19098663C22semidirect
42. #19098635C22semidirect
43. #19098603C22semidirect
50. C2×#14579094C22semidirect
196. C2×C79⋊C8#41semidirect
335. C79⋊C8C2×#41semidirect
370. C2×C79#3343semidirect
390. C79C2×#3343semidirect
743. C2#23775834direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992532
#237758342
C2×#190989692
C2×#190988982
C2×#190988842
C2×#190988932
C2×#190988742
C2×#190988552
C2×#190988632
C2×#190988072
C2×#190987902
C2×#190986632
C2×#190986352
C2×#190986032
C22×#145790942
C2×#547×C792
C2×#334379