Finite Group Databasebeta

← C2×#23777891 #35195980

Subgroups — C2×#23777891 #35195980

Order 20224.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777891C2132yesmaximal, direct product factor
2C2×#19099314C214yesmaximal, complemented
3C2×#19099293C211yesmaximal, characteristic, complemented
4C2×#19099292C211yesmaximal, characteristic, complemented
5C2×#19099290C212yesmaximal, complemented
6C2×#19099284C212yesmaximal, complemented
7C2×#19099283C212yesmaximal, complemented
8C2×#19099283C211yesmaximal, characteristic, complemented
9C2×#19099248C212yesmaximal, complemented
10C2×#19099194C212yesmaximal, complemented
11C2×#19099178C212yesmaximal
12C2×#19099176C212yesmaximal, complemented
13C2×#19099173C212yesmaximal, complemented
14C2×#19099173C214yesmaximal, complemented
15C2×#19099118C211yesmaximal, characteristic, complemented
16C2×#19099117C211yesmaximal, characteristic, complemented
17C2×#19099095C211yesmaximal, characteristic
18C2×#554×C79C211yesmaximal, characteristic, complemented
19#19099314C22164yescomplemented
20#19099293C22116yescomplemented
21#19099292C22116yescomplemented
22#19099290C22132yescomplemented
23#19099284C22132yescomplemented
24#19099283C22132yescomplemented
25#19099283C22116yescomplemented
26#19099248C22132yescomplemented
27#19099194C22132yescomplemented
28#19099178C22132yes—
29#19099176C22132yescomplemented
30#19099173C22132yescomplemented
31#19099173C22164yescomplemented
32#19099118C22116yescomplemented
33#19099117C22116yescomplemented
34C2×#14579161C2212yes—
35C2×#14579161C2211yescharacteristic
36C2×#14579160C2212yes—
37C2×#14579160C2211yescharacteristic
38C2×#14579160C2212yes—
39C2×#14579160C2214yes—
40C2×#14579159C2211yescharacteristic
41C2×#14579159C2214yes—
42#19099095C22116yes—
43C2×#14579156C2214yes—
44C2×#14579156C2214yes—
45C2×#14579154C2214yes—
46C2×#14579154C2212yes—
47C2×#14579154C2214yes—
48C2×#14579154C2214yes—
49C2×#14579154C2214yes—
50C2×#14579152C2214yes—
51C2×#14579152C2214yes—
52C2×#14579152C2212yes—
53C2×#14579152C2212yes—
54C2×#14579152C2211yescharacteristic
55C2×#14579152C2214yes—
56C2×#14579151C2214yes—
57C2×#14579151C2212yes—
58C2×#14579151C2214yes—
59C2×#14579148C2212yes—
60C2×#14579148C2211yescharacteristic
61C2×#14579147C2214yes—
62C2×#14579144C2214yes—
63C2×#14579143C2212yes—
64C2×#14579141C2211yescharacteristic
65C2×#14579141C2212yes—
66C2×#14579141C2211yescharacteristic
67C2×#14579140C2214yes—
68C2×#14579140C2214yes—
69C2×#14579140C2212yes—
70C2×#14579139C2212yes—
71C2×#14579137C2211yescharacteristic
72C2×#14579137C2212yes—
73C2×#14579132C2211yescharacteristic
74C2×Q8×Dic79C2212yes—
75C2×Q8×Dic79C2212yes—
76C2×C4×Dic158C2212yes—
77C2×C4×Dic158C2211yescharacteristic
78C2×C4×Dic158C2212yes—
79C2×C4×Dic158C2211yescharacteristic
80C2×#14579126C2212yes—
81C2×#14579126C2212yes—
82C2×#14579126C2212yes—
83C2×#14579126C2212yes—
84C2×#14579126C2214yes—
85C2×C4×C22⋊D79C2212yes—
86C2×#14579120C2212yes—
87C2×#14579120C2212yes—
88C2×#14579120C2214yes—
89C2×#14579119C2212yes—
90C2×#14579118C2212yes—
91C2×C42×D79C2211yescharacteristic
92#554×C79C22116yescomplemented
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#125×C79C2212yes—
95C2×C22⋊Q8×C79C2212yes—
96C2×C22⋊Q8×C79C2214yes—
97C2×C4×Q8×C79C2211yescharacteristic
98C2×C4×D4×C79C2212yes—
99C2×C4×D4×C79C2211yescharacteristic
100C22×C4⋊C4×C79C2212yes—
101C22×Dic158C2311yescharacteristic
102C22×Dic158C2312yes—
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2314yes—
105C22×Dic158C2312yes—
106C22×C22⋊D79C2312yes—
107C22×C4×D79C2311yescharacteristic
108C22×C4×D79C2311yescharacteristic
109C22×C4×D79C2311yescharacteristic
110#14579161C23116yes—
111#14579161C2318yes—
112#14579160C23116yes—
113#14579160C2318yes—
114#14579160C23116yes—
115#14579160C23132yes—
116#14579159C2318yes—
117#14579159C23132yes—
118#14579156C23132yes—
119#14579156C23132yes—
120#14579154C23132yes—
121#14579154C23116yes—
122#14579154C23132yes—
123#14579154C23132yes—
124#14579154C23132yes—
125#14579152C23132yes—
126#14579152C23132yes—
127#14579152C23116yes—
128#14579152C23132yes—
129#14579152C23116yes—
130#14579152C2318yes—
131#14579151C23116yes—
132#14579151C23132yes—
133#14579151C23132yes—
134#14579148C23116yes—
135#14579148C2318yes—
136#14579147C23132yes—
137#14579144C23132yes—
138#14579143C23116yes—
139#14579141C2318yes—
140#14579141C23116yes—
141#14579141C2318yes—
142#14579140C23132yes—
143#14579140C23116yes—
144#14579140C23132yes—
145#14579139C23116yes—
146#14579137C2318yes—
147#14579137C23116yes—
148#14579132C2318yes—
149Q8×Dic79C23116yes—
150Q8×Dic79C23116yes—
151C4×Dic158C23116yes—
152C4×Dic158C23116yes—
153C4×Dic158C2318yes—
154C4×Dic158C2318yes—
155#14579126C23116yes—
156#14579126C23132yes—
157#14579126C23116yes—
158#14579126C23116yes—
159#14579126C23116yes—
160C4×C22⋊D79C23116yes—
161#14579120C23116yes—
162#14579120C23132yes—
163#14579120C23116yes—
164#14579119C23116yes—
165#14579118C23116yes—
166C2×C4⋊Dic79C2312yes—
167C2×C4⋊Dic79C2311yescharacteristic
168C2×C4⋊Dic79C2312yes—
169C2×C4⋊Dic79C2314yes—
170C2×C4⋊Dic79C2312yes—
171C2×C4⋊Dic79C2312yes—
172C2×C4⋊Dic79C2311yescharacteristic
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2314yes—
175C2×C4⋊Dic79C2314yes—
176C2×Dic79⋊C4C2312yes—
177C2×Dic79⋊C4C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2314yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2314yes—
187C2×Dic79⋊C4C2312yes—
188C2×C22⋊Dic79C2312yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2312yes—
191C2×C22⋊Dic79C2314yes—
192C2×C22⋊Dic79C2314yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×C4×Dic79C2311yescharacteristic
198C2×C4×Dic79C2311yescharacteristic
199C2×C4×Dic79C2311yescharacteristic
200C2×C4×Dic79C2312yes—
201C2×C4×Dic79C2314yes—
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2314yes—
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2314yes—
206C42×D79C2318yes—
207C22×Q8×C79C2311yescharacteristic
208C22×Q8×C79C2312yes—
209C22×D4×C79C2311yescharacteristic
210C23×C4×C79C2312yes—
211C23×C4×C79C2314yes—
212C4⋊Q8×C79C2318yes—
213#125×C79C23116yes—
214C22⋊Q8×C79C23116yes—
215C22⋊Q8×C79C23132yes—
216C4×Q8×C79C2318yes—
217C4×D4×C79C23116yes—
218C4×D4×C79C2318yes—
219C2×C4⋊C4×C79C23116yes—
220C2×C4⋊C4×C79C2311yescharacteristic
221C2×C4⋊C4×C79C2314yes—
222C2×C4⋊C4×C79C2312yes—
223C2×C4⋊C4×C79C2311yescharacteristic
224C2×C4⋊C4×C79C2312yes—
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2314yes—
227C2×C22⋊C4×C79C2312yes—
228C2×C22⋊C4×C79C2314yes—
229C2×C42×C79C2312yes—
230C2×C42×C79C2311yescharacteristic
231C23×D79C2411yescharacteristic
232C2×Dic158—24no—
233C2×Dic158—28no—
234C2×Dic158—24no—
235C2×Dic158—44no—
236C2×Dic158—48no—
237C2×Dic158C2414yes—
238C2×Dic158C2418yes—
239C2×Dic158C2414yes—
240C2×Dic158C24116yes—
241C2×Dic158C2418yes—
242C2×C22⋊D79—44no—
243C2×C22⋊D79C2418yes—
244C22×Dic79C2412yes—
245C22×Dic79C2412yes—
246C22×Dic79C2411yescharacteristic
247C22×Dic79C2412yes—
248C22×Dic79C2414yes—
249C22×Dic79C2412yes—
250C22×Dic79C2411yescharacteristic
251C22×Dic79C2411yescharacteristic
252C2×C4×D79—24no—
253C2×C4×D79—24no—
254C2×C4×D79—42no—
255C2×C4×D79C2414yes—
256C2×C4×D79C2414yes—
257C2×C4×D79C2414yes—
258C4⋊Dic79C2418yes—
259C4⋊Dic79C2414yes—
260C4⋊Dic79C2418yes—
261C4⋊Dic79C24116yes—
262C4⋊Dic79C2418yes—
263C4⋊Dic79C2418yes—
264C4⋊Dic79C2414yes—
265C4⋊Dic79C2418yes—
266C4⋊Dic79C24116yes—
267C4⋊Dic79C24116yes—
268Dic79⋊C4C2418yes—
269Dic79⋊C4C2418yes—
270Dic79⋊C4C2418yes—
271Dic79⋊C4C2418yes—
272Dic79⋊C4C24116yes—
273Dic79⋊C4C24116yes—
274Dic79⋊C4C24116yes—
275Dic79⋊C4C24116yes—
276Dic79⋊C4C2418yes—
277Dic79⋊C4C2418yes—
278Dic79⋊C4C24116yes—
279Dic79⋊C4C2418yes—
280C22⋊Dic79C2418yes—
281C22⋊Dic79C2418yes—
282C22⋊Dic79C2418yes—
283C22⋊Dic79C24116yes—
284C22⋊Dic79C24116yes—
285(C2×D79)⋊C4C2418yes—
286(C2×D79)⋊C4C2418yes—
287(C2×D79)⋊C4C24116yes—
288(C2×D79)⋊C4C2418yes—
289C4×Dic79C2414yes—
290C4×Dic79C2414yes—
291C4×Dic79C2414yes—
292C4×Dic79C2418yes—
293C4×Dic79C24116yes—
294C4×Dic79C2418yes—
295C4×Dic79C24116yes—
296C4×Dic79C24116yes—
297C4×Dic79C24116yes—
298C24×C79C2412yes—
299C2×Q8×C79—24no—
300C2×Q8×C79—44no—
301C2×Q8×C79C2414yes—
302C2×Q8×C79C2418yes—
303C2×D4×C79—24no—
304C2×D4×C79C2414yes—
305C22×C4×C79—28no—
306C22×C4×C79—48no—
307C22×C4×C79C2412yes—
308C22×C4×C79C2414yes—
309C22×C4×C79C2412yes—
310C22×C4×C79C2411yescharacteristic
311C22×C4×C79C2412yes—
312C22×C4×C79C2418yes—
313C22×C4×C79C24116yes—
314C22×C4×C79C2411yescharacteristic
315C22×C4×C79C2411yescharacteristic
316C4⋊C4×C79C2414yes—
317C4⋊C4×C79C24116yes—
318C4⋊C4×C79C2418yes—
319C4⋊C4×C79C2414yes—
320C4⋊C4×C79C2418yes—
321C4⋊C4×C79C2418yes—
322C4⋊C4×C79C24116yes—
323C22⋊C4×C79C2418yes—
324C22⋊C4×C79C24116yes—
325C42×C79C2418yes—
326C42×C79C2414yes—
327C23×C79—24no—
328C23×C79—24no—
329C23×C79—24no—
330C23×C79C2514yes—
331C23×C79C2511yescharacteristic
332C22×D79—22no—
333C22×D79—22no—
334C22×D79—22no—
335C22×D79C2512yes—
336Q8×C79—28no—
337Q8×C79—48no—
338D4×C79—28no—
339C2×C4×C79—24no—
340C2×C4×C79—24no—
341C2×C4×C79—22no—
342C2×C4×C79—24no—
343C2×C4×C79—28no—
344C2×C4×C79—216no—
345C2×C4×C79—416no—
346C2×C4×C792−1+414yes—
347C2×C4×C792−1+414yes—
348C2×C4×C79C2514yes—
349C2×C4×C79C2514yes—
350C2×C4×C79C2518yes—
351C2×C4×C79C2512yes—
352C2×C4×C79C2514yes—
353C2×C4×C79C2512yes—
354C2×C4×C79C2512yes—
355C22⋊D79—48no—
356C2×Dic79—22no—
357C2×Dic79—22no—
358C2×Dic79—24no—
359C2×Dic79—28no—
360C2×Dic79—24no—
361C2×Dic79—22no—
362C2×Dic79—24no—
363C2×Dic79—24no—
364C2×Dic79C2512yes—
365C2×Dic79C2514yes—
366C2×Dic79C2514yes—
367C2×Dic79C2518yes—
368C2×Dic79C2514yes—
369C2×Dic79C2514yes—
370C2×Dic79C2512yes—
371C2×Dic79C2512yes—
372C4×D79—28no—
373C4×D79—28no—
374C4×D79—44no—
375Dic158—28no—
376Dic158—216no—
377Dic158—28no—
378Dic158—416no—
379Dic158—48no—
380C22×C79—24no—
381C22×C79—24no—
382C22×C79—24no—
383C22×C79—48no—
384C22×C79C2×2−1+412yes—
385C22×C79C2×2−1+412yes—
386C22×C79#58512yes—
387C22×C79C2611yescharacteristic
388C2×D79—22no—
389C2×D79—22no—
390C2×D79—22no—
391C2×D79—44no—
392C4×C79—24no—
393C4×C79—24no—
394C4×C79—24no—
395C4×C79—28no—
396C4×C79—22no—
397C4×C79C2×2−1+414yes—
398C4×C79C2×2−1+414yes—
399Dic79—24no—
400Dic79—28no—
401Dic79—24no—
402Dic79—22no—
403Dic79—22no—
404Dic79—24no—
405Dic79—24no—
406Dic79—22no—
407C2×#3555—791nomaximal, Sylow
408C2×C79—44no—
409C2×C79#355514yescomplemented
410C2×C79C22×2−1+411yescharacteristic
411C2×C79C22×2−1+411yescharacteristic
412C2×C79C2×#58511yescharacteristic
413D79—42no—
414#3555—7932no—
415C2×#563—794no—
416C2×Q82—791no—
417C2×#557—792no—
418C2×#557—791no—
419C2×#556—792no—
420C2×#556—792no—
421C2×#556—791no—
422C2×#554D7911yescharacteristic, complemented
423C2×#552—792no—
424C2×#544—792no—
425C2×#542—792no—
426C2×#541—792no—
427C2×#541—792no—
428C2×#541—794no—
429C2×#533—791no—
430C2×#533—791no—
431C2×#529—791no—
432C79C2×#355511yescharacteristic, complemented, Sylow
433#563—7964no—
434Q82—7916no—
435#557—7932no—
436#557—7916no—
437#556—7932no—
438#556—7932no—
439#556—7916no—
440#554C2×D79116yescomplemented
441#552—7932no—
442#544—7932no—
443#542—7932no—
444#541—7932no—
445#541—7932no—
446#541—7964no—
447#533—7916no—
448#533—7916no—
449C2×C4⋊Q8—791no—
450C2×C4⋊Q8—794no—
451C2×C4⋊Q8—791no—
452C2×C4⋊Q8—792no—
453C2×C4⋊Q8—792no—
454C2×C4⋊Q8—794no—
455C2×C4⋊Q8—791no—
456C2×C4⋊Q8—792no—
457C2×C4⋊Q8C2×D7911yescharacteristic
458#529—7916no—
459C2×#126—794no—
460C2×#126—794no—
461C2×#126—792no—
462C2×#126—794no—
463C2×#126—794no—
464C2×#126—794no—
465C2×#126—794no—
466C2×#125—791no—
467C2×#125—792no—
468C2×#125—792no—
469C2×#125—794no—
470C2×#125—794no—
471C2×#125—794no—
472C2×#125—794no—
473C2×#125—794no—
474C2×#125—792no—
475C2×#125C2×D7912yes—
476C2×#124—791no—
477C2×#124—792no—
478C2×#124—794no—
479C2×#123—794no—
480C2×#123—792no—
481C2×C22⋊Q8—791no—
482C2×C22⋊Q8—792no—
483C2×C22⋊Q8—794no—
484C2×C22⋊Q8—792no—
485C2×C22⋊Q8—794no—
486C2×C22⋊Q8—791no—
487C2×C22⋊Q8—792no—
488C2×C22⋊Q8—791no—
489C2×C22⋊Q8—792no—
490C2×C22⋊Q8C2×D7912yes—
491C2×C22⋊Q8C2×D7914yes—
492C2×#121—791no—
493C2×C4×Q8—792no—
494C2×C4×Q8—792no—
495C2×C4×Q8—792no—
496C2×C4×Q8—792no—
497C2×C4×Q8—794no—
498C2×C4×Q8—792no—
499C2×C4×Q8—792no—
500C2×C4×Q8—791no—
501C2×C4×Q8—792no—
502C2×C4×Q8—791no—
503C2×C4×Q8—792no—
504C2×C4×Q8C2×D7911yescharacteristic
505C2×C4×D4—792no—
506C2×C4×D4C2×D7911yescharacteristic
507C2×C4×D4C2×D7912yes—
508C2×#117—792no—
509C2×#117—794no—
510C2×#117—792no—
511C2×#117—792no—
512C2×#117—792no—
513C22×C4⋊C4C2×D7912yes—
514C22×C42—791no—
515C22×Q8—792no—
516C22×Q8—794no—
517C22×Q8—791no—
518C22×Q8—792no—
519C22×Q8—791no—
520C22×Q8C22×D7911yescharacteristic
521C22×Q8C22×D7912yes—
522C22×D4—792no—
523C22×D4C22×D7911yescharacteristic
524C23×C4—791no—
525C23×C4—791no—
526C23×C4—791no—
527C23×C4C22×D7912yes—
528C23×C4C22×D7914yes—
529C4⋊Q8—798no—
530C4⋊Q8—7932no—
531C4⋊Q8—798no—
532C4⋊Q8—7916no—
533C4⋊Q8—7916no—
534C4⋊Q8—7932no—
535C4⋊Q8—798no—
536C4⋊Q8—7916no—
537C4⋊Q8C22×D7918yes—
538#126—7932no—
539#126—7932no—
540#126—7916no—
541#126—7932no—
542#126—7932no—
543#126—7932no—
544#126—7932no—
545#125—798no—
546#125—7916no—
547#125—7916no—
548#125—7932no—
549#125—7932no—
550#125—7932no—
551#125—7932no—
552#125—7932no—
553#125—7916no—
554#125C22×D79116yes—
555#124—798no—
556#124—7916no—
557#124—7932no—
558#123—7932no—
559#123—7916no—
560C22⋊Q8—798no—
561C22⋊Q8—7916no—
562C22⋊Q8—7932no—
563C22⋊Q8—7916no—
564C22⋊Q8—7932no—
565C22⋊Q8—798no—
566C22⋊Q8—7916no—
567C22⋊Q8—798no—
568C22⋊Q8—7916no—
569C22⋊Q8C22×D79116yes—
570C22⋊Q8C22×D79132yes—
571#121—798no—
572C4×Q8—7916no—
573C4×Q8—7916no—
574C4×Q8—7916no—
575C4×Q8—7916no—
576C4×Q8—7932no—
577C4×Q8—7916no—
578C4×Q8—7916no—
579C4×Q8—798no—
580C4×Q8—7916no—
581C4×Q8—798no—
582C4×Q8—7916no—
583C4×Q8C22×D7918yes—
584C4×D4—7916no—
585C4×D4C22×D7918yes—
586C4×D4C22×D79116yes—
587#117—7916no—
588#117—7932no—
589#117—7916no—
590#117—7916no—
591#117—7916no—
592C2×C4⋊C4—792no—
593C2×C4⋊C4—792no—
594C2×C4⋊C4—791no—
595C2×C4⋊C4—792no—
596C2×C4⋊C4—792no—
597C2×C4⋊C4—794no—
598C2×C4⋊C4—792no—
599C2×C4⋊C4—792no—
600C2×C4⋊C4—792no—
601C2×C4⋊C4—791no—
602C2×C4⋊C4—792no—
603C2×C4⋊C4—794no—
604C2×C4⋊C4—794no—
605C2×C4⋊C4—794no—
606C2×C4⋊C4—794no—
607C2×C4⋊C4—792no—
608C2×C4⋊C4—792no—
609C2×C4⋊C4—794no—
610C2×C4⋊C4—792no—
611C2×C4⋊C4—794no—
612C2×C4⋊C4—792no—
613C2×C4⋊C4—794no—
614C2×C4⋊C4C22×D7911yescharacteristic
615C2×C4⋊C4C22×D7912yes—
616C2×C4⋊C4C22×D7914yes—
617C2×C4⋊C4C22×D79116yes—
618C2×C4⋊C4C22×D7911yescharacteristic
619C2×C4⋊C4C22×D7912yes—
620C2×C4⋊C4C22×D7914yes—
621C2×C4⋊C4C22×D7912yes—
622C2×C22⋊C4—792no—
623C2×C22⋊C4—792no—
624C2×C22⋊C4—792no—
625C2×C22⋊C4—794no—
626C2×C22⋊C4—794no—
627C2×C22⋊C4—792no—
628C2×C22⋊C4—794no—
629C2×C22⋊C4—792no—
630C2×C22⋊C4—792no—
631C2×C22⋊C4C22×D7912yes—
632C2×C22⋊C4C22×D7914yes—
633C2×C42—794no—
634C2×C42—791no—
635C2×C42—792no—
636C2×C42—792no—
637C2×C42—794no—
638C2×C42—794no—
639C2×C42—791no—
640C2×C42—794no—
641C2×C42—791no—
642C2×C42—798no—
643C2×C42C22×D7912yes—
644C2×C42C22×D7911yescharacteristic
645C24—791no—
646C24C23×D7912yes—
647C2×Q8—24no—
648C2×Q8—44no—
649C2×Q8—3164no—
650C2×Q8—3168no—
651C2×Q8—798no—
652C2×Q8—7916no—
653C2×Q8—794no—
654C2×Q8—798no—
655C2×Q8—794no—
656C2×Q8—1584no—
657C2×Q8—1588no—
658C2×Q8—1584no—
659C2×Q8C23×D7914yes—
660C2×Q8C23×D7918yes—
661C2×D4—24no—
662C2×D4—3164no—
663C2×D4—798no—
664C2×D4C23×D7914yes—
665C22×C4—28no—
666C22×C4—48no—
667C22×C4—3162no—
668C22×C4—794no—
669C22×C4—791no—
670C22×C4—792no—
671C22×C4—794no—
672C22×C4—792no—
673C22×C4—792no—
674C22×C4—792no—
675C22×C4—791no—
676C22×C4—791no—
677C22×C4—794no—
678C22×C4—794no—
679C22×C4—1584no—
680C22×C4—1584no—
681C22×C4C23×D7918yes—
682C22×C4C23×D7912yes—
683C22×C4C23×D7912yes—
684C22×C4C23×D7914yes—
685C22×C4C23×D7911yescharacteristic
686C22×C4C23×D7912yes—
687C22×C4C23×D79116yes—
688C22×C4C23×D7911yescharacteristic
689C22×C4C23×D7911yescharacteristic
690C4⋊C4—798no—
691C4⋊C4—798no—
692C4⋊C4—798no—
693C4⋊C4—798no—
694C4⋊C4—7916no—
695C4⋊C4—7916no—
696C4⋊C4—7916no—
697C4⋊C4—798no—
698C4⋊C4—7916no—
699C4⋊C4—798no—
700C4⋊C4—7916no—
701C4⋊C4—798no—
702C4⋊C4—798no—
703C4⋊C4—798no—
704C4⋊C4—794no—
705C4⋊C4—798no—
706C4⋊C4—7916no—
707C4⋊C4—798no—
708C4⋊C4—794no—
709C4⋊C4—7916no—
710C4⋊C4—798no—
711C4⋊C4—7916no—
712C4⋊C4C23×D7914yes—
713C4⋊C4C23×D7918yes—
714C4⋊C4C23×D79116yes—
715C4⋊C4C23×D7914yes—
716C4⋊C4C23×D7918yes—
717C4⋊C4C23×D79116yes—
718C4⋊C4C23×D7918yes—
719C22⋊C4—798no—
720C22⋊C4—798no—
721C22⋊C4—798no—
722C22⋊C4—7916no—
723C22⋊C4—7916no—
724C22⋊C4—798no—
725C22⋊C4—7916no—
726C22⋊C4—798no—
727C22⋊C4—798no—
728C22⋊C4C23×D7918yes—
729C22⋊C4C23×D79116yes—
730C42—794no—
731C42—794no—
732C42—794no—
733C42—7916no—
734C42—798no—
735C42—798no—
736C42—7916no—
737C42—7916no—
738C42—7916no—
739C42C23×D7914yes—
740C42C23×D7918yes—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—792no—
745C23—1582no—
746C23—1582no—
747C23—1582no—
748C23C24×D7914yes—
749C23C24×D7911yescharacteristic
750Q8—28no—
751Q8—48no—
752Q8—3168no—
753Q8—31616no—
754Q8—1588no—
755Q8—15816no—
756Q8—1588no—
757D4—28no—
758D4—3168no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—216no—
765C2×C4—416no—
766C2×C4—3164no—
767C2×C4—792no—
768C2×C4—794no—
769C2×C4—798no—
770C2×C4—794no—
771C2×C4—794no—
772C2×C4—794no—
773C2×C4—792no—
774C2×C4—792no—
775C2×C4—1582no—
776C2×C4—1584no—
777C2×C4—1582no—
778C2×C4—1588no—
779C2×C4—1584no—
780C2×C4—1582no—
781C2×C4—1584no—
782C2×C4—1584no—
783C2×C4—1588no—
784C2×C4—1588no—
785C2×C4#1457920814yes—
786C2×C4#1457920914yes—
787C2×C4C24×D7914yes—
788C2×C4C24×D7914yes—
789C2×C4C24×D7918yes—
790C2×C4C24×D7912yes—
791C2×C4C24×D7914yes—
792C2×C4C24×D7912yes—
793C2×C4C24×D7912yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—48no—
798C22—3164no—
799C22—1582no—
800C22—1582no—
801C22—1582no—
802C22C2×#1457920812yes—
803C22C2×#1457920912yes—
804C22#1909939812yes—
805C22C25×D7911yescharacteristic
806C4—24no—
807C4—24no—
808C4—24no—
809C4—28no—
810C4—22no—
811C4—1582no—
812C4—1584no—
813C4—1582no—
814C4—1588no—
815C4—1584no—
816C4—1582no—
817C4—1584no—
818C4—1584no—
819C4C2×#1457920814yes—
820C4C2×#1457920914yes—
821C2—44no—
822C2—3162no—
823C2#2377789114yesdirect product factor
824C2C22×#1457920811yescharacteristic
825C2C22×#1457920911yescharacteristic
826C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#554×C79C2
socleC23×C79C25
prime radicalC2×#14579132C22
hypercenterC2×#554D79
hypocenterC79C2×#3555
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #23777891C2direct (N × H)
2. C2×#19099314C2semidirect
3. C2×#19099293C2semidirect
4. C2×#19099292C2semidirect
5. C2×#19099290C2semidirect
6. C2×#19099284C2semidirect
7. C2×#19099283C2semidirect
8. C2×#19099283C2semidirect
9. C2×#19099248C2semidirect
10. C2×#19099194C2semidirect
12. C2×#19099176C2semidirect
13. C2×#19099173C2semidirect
14. C2×#19099173C2semidirect
15. C2×#19099118C2semidirect
16. C2×#19099117C2semidirect
18. C2×#554×C79C2semidirect
19. #19099314C22semidirect
20. #19099293C22semidirect
21. #19099292C22semidirect
22. #19099290C22semidirect
23. #19099284C22semidirect
24. #19099283C22semidirect
25. #19099283C22semidirect
26. #19099248C22semidirect
27. #19099194C22semidirect
29. #19099176C22semidirect
30. #19099173C22semidirect
31. #19099173C22semidirect
32. #19099118C22semidirect
33. #19099117C22semidirect
92. #554×C79C22semidirect
409. C2×C79#3555semidirect
422. C2×#554D79semidirect
432. C79C2×#3555semidirect
440. #554C2×D79semidirect
823. C2#23777891direct (N × H)

Maximal subgroups

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

subgroupindex
#237778912
C2×#190993142
C2×#190992932
C2×#190992922
C2×#190992902
C2×#190992842
C2×#190992832
C2×#190992482
C2×#190991942
C2×#190991782
C2×#190991762
C2×#190991732
C2×#190991182
C2×#190991172
C2×#190990952
C2×#554×C792
C2×#355579