Finite Group Databasebeta

← C2×#23777882 #35195985

Subgroups — C2×#23777882 #35195985

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#23777882C2132yesmaximal, direct product factor
2C2×#19099314C214yesmaximal, complemented
3C2×#19099293C211yesmaximal, characteristic, complemented
4C2×#19099289C212yesmaximal, complemented
5C2×#19099288C211yesmaximal, characteristic, complemented
6C2×#19099287C211yesmaximal, characteristic, complemented
7C2×#19099285C212yesmaximal, complemented
8C2×#19099281C212yesmaximal, complemented
9C2×#19099274C211yesmaximal, characteristic, complemented
10C2×#19099252C212yesmaximal, complemented
11C2×#19099193C212yesmaximal, complemented
12C2×#19099186C212yesmaximal
13C2×#19099176C212yesmaximal, complemented
14C2×#19099173C212yesmaximal, complemented
15C2×#19099171C214yesmaximal, complemented
16C2×#19099120C211yesmaximal, characteristic, complemented
17C2×#19099097C211yesmaximal, characteristic
18C2×#533×C79C211yesmaximal, characteristic, complemented
19#19099314C22164yescomplemented
20#19099293C22116yescomplemented
21#19099289C22132yescomplemented
22#19099288C22116yescomplemented
23#19099287C22116yescomplemented
24#19099285C22132yescomplemented
25#19099281C22132yescomplemented
26#19099274C22116yescomplemented
27#19099252C22132yescomplemented
28#19099193C22132yescomplemented
29#19099186C22132yes—
30#19099176C22132yescomplemented
31#19099173C22132yescomplemented
32#19099171C22164yescomplemented
33#19099120C22116yescomplemented
34C2×#14579161C2211yescharacteristic
35C2×#14579161C2211yescharacteristic
36C2×#14579160C2212yes—
37C2×#14579160C2212yes—
38C2×#14579160C2214yes—
39C2×#14579159C2212yes—
40C2×#14579159C2214yes—
41#19099097C22116yes—
42C2×#14579156C2214yes—
43C2×#14579156C2214yes—
44C2×#14579156C2214yes—
45C2×#14579155C2212yes—
46C2×#14579155C2214yes—
47C2×#14579154C2214yes—
48C2×#14579154C2214yes—
49C2×#14579153C2214yes—
50C2×#14579153C2211yescharacteristic
51C2×#14579153C2212yes—
52C2×#14579152C2214yes—
53C2×#14579152C2214yes—
54C2×#14579152C2212yes—
55C2×#14579152C2212yes—
56C2×#14579151C2214yes—
57C2×#14579151C2214yes—
58C2×#14579150C2212yes—
59C2×#14579149C2211yescharacteristic
60C2×#14579147C2214yes—
61C2×#14579144C2212yes—
62C2×#14579143C2214yes—
63C2×#14579141C2212yes—
64C2×#14579141C2212yes—
65C2×#14579141C2214yes—
66C2×#14579140C2211yescharacteristic
67C2×#14579140C2211yescharacteristic
68C2×#14579140C2211yescharacteristic
69C2×#14579140C2212yes—
70C2×#14579139C2214yes—
71C2×#14579137C2214yes—
72C2×#14579135C2211yescharacteristic
73C2×Q8×Dic79C2212yes—
74C2×Q8×Dic79C2212yes—
75C2×C4×Dic158C2211yescharacteristic
76C2×C4×Dic158C2211yescharacteristic
77C2×C4×Dic158C2214yes—
78C2×C4×Dic158C2212yes—
79C2×C4×Dic158C2211yescharacteristic
80C2×#14579126C2212yes—
81C2×#14579126C2212yes—
82C2×#14579126C2212yes—
83C2×C4×D316C2211yescharacteristic
84C2×#14579123C2212yes—
85C2×C4×C22⋊D79C2212yes—
86C2×#14579120C2212yes—
87C2×#14579119C2212yes—
88C2×#14579118C2212yes—
89C2×#14579118C2214yes—
90C2×C4⋊C4×D79C2212yes—
91#533×C79C22116yescomplemented
92C2×C4⋊Q8×C79C2211yescharacteristic
93C2×C4⋊Q8×C79C2211yescharacteristic
94C2×#125×C79C2212yes—
95C2×C22⋊Q8×C79C2212yes—
96C2×C22⋊Q8×C79C2212yes—
97C2×C4×Q8×C79C2212yes—
98C2×C4×Q8×C79C2212yes—
99C2×#117×C79C2212yes—
100C22×C42×C79C2211yescharacteristic
101C22×Dic158C2311yescharacteristic
102C22×Dic158C2311yescharacteristic
103C22×Dic158C2311yescharacteristic
104C22×Dic158C2312yes—
105C22×Dic158C2314yes—
106C22×D316C2311yescharacteristic
107C22×C22⋊D79C2312yes—
108C22×C4×D79C2312yes—
109C22×C4×D79C2314yes—
110#14579161C2318yes—
111#14579161C2318yes—
112#14579160C23116yes—
113#14579160C23116yes—
114#14579160C23132yes—
115#14579159C23132yes—
116#14579159C23116yes—
117#14579156C23132yes—
118#14579156C23132yes—
119#14579156C23132yes—
120#14579155C23116yes—
121#14579155C23132yes—
122#14579154C23132yes—
123#14579154C23132yes—
124#14579153C23116yes—
125#14579153C23132yes—
126#14579153C2318yes—
127#14579152C23132yes—
128#14579152C23116yes—
129#14579152C23132yes—
130#14579152C23116yes—
131#14579151C23132yes—
132#14579151C23132yes—
133#14579150C23116yes—
134#14579149C2318yes—
135#14579147C23132yes—
136#14579144C23116yes—
137#14579143C23132yes—
138#14579141C23132yes—
139#14579141C23116yes—
140#14579141C23116yes—
141#14579140C2318yes—
142#14579140C2318yes—
143#14579140C2318yes—
144#14579140C23116yes—
145#14579139C23132yes—
146#14579137C23132yes—
147#14579135C2318yes—
148Q8×Dic79C23116yes—
149Q8×Dic79C23116yes—
150C4×Dic158C23132yes—
151C4×Dic158C2318yes—
152C4×Dic158C23116yes—
153C4×Dic158C2318yes—
154C4×Dic158C2318yes—
155#14579126C23116yes—
156#14579126C23116yes—
157#14579126C23116yes—
158C4×D316C2318yes—
159#14579123C23116yes—
160C4×C22⋊D79C23116yes—
161#14579120C23116yes—
162#14579119C23116yes—
163#14579118C23132yes—
164#14579118C23116yes—
165C2×C4⋊Dic79C2311yescharacteristic
166C2×C4⋊Dic79C2311yescharacteristic
167C2×C4⋊Dic79C2312yes—
168C2×C4⋊Dic79C2312yes—
169C2×C4⋊Dic79C2311yescharacteristic
170C2×C4⋊Dic79C2311yescharacteristic
171C2×C4⋊Dic79C2314yes—
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2314yes—
174C2×C4⋊Dic79C2314yes—
175C2×Dic79⋊C4C2314yes—
176C2×Dic79⋊C4C2312yes—
177C2×Dic79⋊C4C2314yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2312yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2314yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2312yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C4⋊C4×D79C23116yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2312yes—
191C2×C22⋊Dic79C2312yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2312yes—
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2314yes—
201C2×C4×Dic79C2314yes—
202C2×C4×Dic79C2312yes—
203C2×C4×Dic79C2312yes—
204C2×C4×Dic79C2314yes—
205C22×Q8×C79C2312yes—
206C22×Q8×C79C2312yes—
207C23×C4×C79C2311yescharacteristic
208C23×C4×C79C2311yescharacteristic
209C23×C4×C79C2311yescharacteristic
210C4⋊Q8×C79C2318yes—
211C4⋊Q8×C79C2318yes—
212#125×C79C23116yes—
213C22⋊Q8×C79C23116yes—
214C22⋊Q8×C79C23116yes—
215C4×Q8×C79C23116yes—
216C4×Q8×C79C23116yes—
217#117×C79C23116yes—
218C2×C4⋊C4×C79C2312yes—
219C2×C4⋊C4×C79C2312yes—
220C2×C4⋊C4×C79C2314yes—
221C2×C4⋊C4×C79C2314yes—
222C2×C4⋊C4×C79C2312yes—
223C2×C4⋊C4×C79C2312yes—
224C2×C22⋊C4×C79C2314yes—
225C2×C42×C79C2311yescharacteristic
226C2×C42×C79C2311yescharacteristic
227C2×C42×C79C2311yescharacteristic
228C2×C42×C79C2311yescharacteristic
229C2×C42×C79C2318yes—
230C2×C42×C79C2314yes—
231C23×D79C2412yes—
232C2×Dic158—24no—
233C2×Dic158—24no—
234C2×Dic158—24no—
235C2×Dic158—48no—
236C2×Dic158—44no—
237C2×Dic158C2414yes—
238C2×Dic158C2414yes—
239C2×Dic158C2414yes—
240C2×Dic158C2418yes—
241C2×Dic158C24116yes—
242C2×D316—24no—
243C2×D316C2414yes—
244C2×C22⋊D79—44no—
245C2×C22⋊D79C2418yes—
246C22×Dic79C2412yes—
247C22×Dic79C2412yes—
248C22×Dic79C2412yes—
249C22×Dic79C2412yes—
250C22×Dic79C2412yes—
251C22×Dic79C2412yes—
252C22×Dic79C2412yes—
253C2×C4×D79—28no—
254C2×C4×D79—48no—
255C2×C4×D79C2418yes—
256C2×C4×D79C24116yes—
257C4⋊Dic79C2414yes—
258C4⋊Dic79C2414yes—
259C4⋊Dic79C2418yes—
260C4⋊Dic79C2418yes—
261C4⋊Dic79C2414yes—
262C4⋊Dic79C2414yes—
263C4⋊Dic79C24116yes—
264C4⋊Dic79C2418yes—
265C4⋊Dic79C24116yes—
266C4⋊Dic79C24116yes—
267Dic79⋊C4C24116yes—
268Dic79⋊C4C2418yes—
269Dic79⋊C4C24116yes—
270Dic79⋊C4C2418yes—
271Dic79⋊C4C2418yes—
272Dic79⋊C4C2418yes—
273Dic79⋊C4C24116yes—
274Dic79⋊C4C24116yes—
275Dic79⋊C4C24116yes—
276Dic79⋊C4C2418yes—
277Dic79⋊C4C2418yes—
278Dic79⋊C4C2418yes—
279Dic79⋊C4C2418yes—
280C22⋊Dic79C2418yes—
281C22⋊Dic79C2418yes—
282C22⋊Dic79C2418yes—
283(C2×D79)⋊C4C2418yes—
284(C2×D79)⋊C4C2418yes—
285(C2×D79)⋊C4C2418yes—
286(C2×D79)⋊C4C24116yes—
287(C2×D79)⋊C4C24116yes—
288(C2×D79)⋊C4C24116yes—
289(C2×D79)⋊C4C2418yes—
290C4×Dic79C2418yes—
291C4×Dic79C24116yes—
292C4×Dic79C24116yes—
293C4×Dic79C2418yes—
294C4×Dic79C2418yes—
295C4×Dic79C24116yes—
296C24×C79C2411yescharacteristic
297C2×Q8×C79—28no—
298C2×Q8×C79—44no—
299C2×Q8×C79C2418yes—
300C2×Q8×C79C2418yes—
301C22×C4×C79—24no—
302C22×C4×C79—24no—
303C22×C4×C79—42no—
304C22×C4×C79C2411yescharacteristic
305C22×C4×C79C2414yes—
306C22×C4×C79C2411yescharacteristic
307C22×C4×C79C2411yescharacteristic
308C22×C4×C79C2411yescharacteristic
309C22×C4×C79C2414yes—
310C22×C4×C79C2414yes—
311C22×C4×C79C2414yes—
312C22×C4×C79C2414yes—
313C22×C4×C79C2411yescharacteristic
314C22×C4×C79C2411yescharacteristic
315C4⋊C4×C79C2418yes—
316C4⋊C4×C79C2418yes—
317C4⋊C4×C79C24116yes—
318C4⋊C4×C79C24116yes—
319C4⋊C4×C79C2418yes—
320C4⋊C4×C79C2418yes—
321C22⋊C4×C79C24116yes—
322C42×C79C2414yes—
323C42×C79C2414yes—
324C42×C79C2414yes—
325C42×C79C2414yes—
326C42×C79C24116yes—
327C23×C79—22no—
328C23×C79—22no—
329C23×C79—22no—
330C23×C79C2512yes—
331C23×C79C2511yescharacteristic
332C22×D79—24no—
333C22×D79—24no—
334C22×D79—24no—
335C22×D79C2514yes—
336Q8×C79—216no—
337Q8×C79—48no—
338C2×C4×C79—22no—
339C2×C4×C79—22no—
340C2×C4×C79—28no—
341C2×C4×C79—28no—
342C2×C4×C79—22no—
343C2×C4×C79—22no—
344C2×C4×C79—28no—
345C2×C4×C79—28no—
346C2×C4×C79—44no—
347C2×C4×C792−1+414yes—
348C2×C4×C792−1+414yes—
349C2×C4×C79C2518yes—
350C2×C4×C79C2518yes—
351C2×C4×C79C2512yes—
352C2×C4×C79C2512yes—
353C2×C4×C79C2512yes—
354C2×C4×C79C2512yes—
355C2×C4×C79C2512yes—
356C2×C4×C79C2512yes—
357C22⋊D79—48no—
358C2×Dic79—24no—
359C2×Dic79—24no—
360C2×Dic79—24no—
361C2×Dic79—24no—
362C2×Dic79—24no—
363C2×Dic79—24no—
364C2×Dic79—24no—
365C2×Dic79C2514yes—
366C2×Dic79C2514yes—
367C2×Dic79C2514yes—
368C2×Dic79C2514yes—
369C2×Dic79C2514yes—
370C2×Dic79C2514yes—
371C2×Dic79C2514yes—
372D316—28no—
373C4×D79—216no—
374C4×D79—416no—
375Dic158—28no—
376Dic158—28no—
377Dic158—28no—
378Dic158—416no—
379Dic158—48no—
380C22×C79—22no—
381C22×C79—22no—
382C22×C79—22no—
383C22×C79—44no—
384C22×C79C2×2−1+412yes—
385C22×C79C2×2−1+412yes—
386C22×C79#58512yes—
387C22×C79C2611yescharacteristic
388C2×D79—24no—
389C2×D79—24no—
390C2×D79—24no—
391C2×D79—48no—
392C4×C79—22no—
393C4×C79—22no—
394C4×C79—28no—
395C4×C79—22no—
396C4×C79—22no—
397C4×C79—28no—
398C4×C79C2×2−1+414yes—
399C4×C79C2×2−1+414yes—
400Dic79—24no—
401Dic79—24no—
402Dic79—24no—
403Dic79—24no—
404Dic79—24no—
405Dic79—24no—
406Dic79—24no—
407C2×#3555—791nomaximal, Sylow
408C2×C79—42no—
409C2×C79#355514yescomplemented
410C2×C79C22×2−1+411yescharacteristic
411C2×C79C22×2−1+411yescharacteristic
412C2×C79C2×#58511yescharacteristic
413D79—44no—
414#3555—7932no—
415C2×#563—794no—
416C2×Q82—791no—
417C2×#557—791no—
418C2×#557—792no—
419C2×#556—791no—
420C2×#556—792no—
421C2×#556—792no—
422C2×#554—791no—
423C2×#552—792no—
424C2×#544—792no—
425C2×#542—792no—
426C2×#541—792no—
427C2×#541—792no—
428C2×#541—794no—
429C2×#533—791no—
430C2×#533D7911yescharacteristic, complemented
431C2×#529—791no—
432C79C2×#355511yescharacteristic, complemented, Sylow
433#563—7964no—
434Q82—7916no—
435#557—7916no—
436#557—7932no—
437#556—7916no—
438#556—7932no—
439#556—7932no—
440#554—7916no—
441#552—7932no—
442#544—7932no—
443#542—7932no—
444#541—7932no—
445#541—7932no—
446#541—7964no—
447#533—7916no—
448#533C2×D79116yescomplemented
449C2×C4⋊Q8—792no—
450C2×C4⋊Q8—794no—
451C2×C4⋊Q8—792no—
452C2×C4⋊Q8—792no—
453C2×C4⋊Q8—794no—
454C2×C4⋊Q8—791no—
455C2×C4⋊Q8—791no—
456C2×C4⋊Q8C2×D7911yescharacteristic
457C2×C4⋊Q8C2×D7911yescharacteristic
458#529—7916no—
459C2×#126—794no—
460C2×#126—794no—
461C2×#126—794no—
462C2×#126—794no—
463C2×#126—794no—
464C2×#126—792no—
465C2×#126—794no—
466C2×#125—794no—
467C2×#125—794no—
468C2×#125—792no—
469C2×#125—794no—
470C2×#125—794no—
471C2×#125—792no—
472C2×#125—791no—
473C2×#125—792no—
474C2×#125—794no—
475C2×#125C2×D7912yes—
476C2×#124—792no—
477C2×#124—794no—
478C2×#124—791no—
479C2×#123—792no—
480C2×#123—794no—
481C2×C22⋊Q8—794no—
482C2×C22⋊Q8—791no—
483C2×C22⋊Q8—791no—
484C2×C22⋊Q8—791no—
485C2×C22⋊Q8—792no—
486C2×C22⋊Q8—794no—
487C2×C22⋊Q8—792no—
488C2×C22⋊Q8—792no—
489C2×C22⋊Q8—794no—
490C2×C22⋊Q8C2×D7912yes—
491C2×C22⋊Q8C2×D7912yes—
492C2×#121—791no—
493C2×C4×Q8—792no—
494C2×C4×Q8—792no—
495C2×C4×Q8—792no—
496C2×C4×Q8—792no—
497C2×C4×Q8—792no—
498C2×C4×Q8—791no—
499C2×C4×Q8—791no—
500C2×C4×Q8—792no—
501C2×C4×Q8—791no—
502C2×C4×Q8—794no—
503C2×C4×Q8C2×D7912yes—
504C2×C4×Q8C2×D7912yes—
505C2×C4×D4—792no—
506C2×C4×D4—792no—
507C2×C4×D4—791no—
508C2×#117—792no—
509C2×#117—792no—
510C2×#117—792no—
511C2×#117—794no—
512C2×#117C2×D7912yes—
513C22×C4⋊C4—792no—
514C22×C42C2×D7911yescharacteristic
515C22×Q8—792no—
516C22×Q8—794no—
517C22×Q8—791no—
518C22×Q8—791no—
519C22×Q8—791no—
520C22×Q8C22×D7912yes—
521C22×Q8C22×D7912yes—
522C22×D4—792no—
523C22×D4—791no—
524C23×C4—794no—
525C23×C4—792no—
526C23×C4C22×D7911yescharacteristic
527C23×C4C22×D7911yescharacteristic
528C23×C4C22×D7911yescharacteristic
529C4⋊Q8—7916no—
530C4⋊Q8—7932no—
531C4⋊Q8—7916no—
532C4⋊Q8—7916no—
533C4⋊Q8—7932no—
534C4⋊Q8—798no—
535C4⋊Q8—798no—
536C4⋊Q8C22×D7918yes—
537C4⋊Q8C22×D7918yes—
538#126—7932no—
539#126—7932no—
540#126—7932no—
541#126—7932no—
542#126—7932no—
543#126—7916no—
544#126—7932no—
545#125—7932no—
546#125—7932no—
547#125—7916no—
548#125—7932no—
549#125—7932no—
550#125—7916no—
551#125—798no—
552#125—7916no—
553#125—7932no—
554#125C22×D79116yes—
555#124—7916no—
556#124—7932no—
557#124—798no—
558#123—7916no—
559#123—7932no—
560C22⋊Q8—7932no—
561C22⋊Q8—798no—
562C22⋊Q8—798no—
563C22⋊Q8—798no—
564C22⋊Q8—7916no—
565C22⋊Q8—7932no—
566C22⋊Q8—7916no—
567C22⋊Q8—7916no—
568C22⋊Q8—7932no—
569C22⋊Q8C22×D79116yes—
570C22⋊Q8C22×D79116yes—
571#121—798no—
572C4×Q8—7916no—
573C4×Q8—7916no—
574C4×Q8—7916no—
575C4×Q8—7916no—
576C4×Q8—7916no—
577C4×Q8—798no—
578C4×Q8—798no—
579C4×Q8—7916no—
580C4×Q8—798no—
581C4×Q8—7932no—
582C4×Q8C22×D79116yes—
583C4×Q8C22×D79116yes—
584C4×D4—7916no—
585C4×D4—7916no—
586C4×D4—798no—
587#117—7916no—
588#117—7916no—
589#117—7916no—
590#117—7932no—
591#117C22×D79116yes—
592C2×C4⋊C4—791no—
593C2×C4⋊C4—794no—
594C2×C4⋊C4—792no—
595C2×C4⋊C4—791no—
596C2×C4⋊C4—792no—
597C2×C4⋊C4—792no—
598C2×C4⋊C4—794no—
599C2×C4⋊C4—792no—
600C2×C4⋊C4—792no—
601C2×C4⋊C4—791no—
602C2×C4⋊C4—792no—
603C2×C4⋊C4—791no—
604C2×C4⋊C4—792no—
605C2×C4⋊C4—792no—
606C2×C4⋊C4—794no—
607C2×C4⋊C4—794no—
608C2×C4⋊C4—794no—
609C2×C4⋊C4—792no—
610C2×C4⋊C4—794no—
611C2×C4⋊C4—792no—
612C2×C4⋊C4—794no—
613C2×C4⋊C4—792no—
614C2×C4⋊C4—794no—
615C2×C4⋊C4—7916no—
616C2×C4⋊C4C22×D7912yes—
617C2×C4⋊C4C22×D7912yes—
618C2×C4⋊C4C22×D7912yes—
619C2×C4⋊C4C22×D7914yes—
620C2×C4⋊C4C22×D7914yes—
621C2×C4⋊C4C22×D7912yes—
622C2×C22⋊C4—792no—
623C2×C22⋊C4—792no—
624C2×C22⋊C4—792no—
625C2×C22⋊C4—792no—
626C2×C22⋊C4—792no—
627C2×C22⋊C4—792no—
628C2×C22⋊C4—794no—
629C2×C22⋊C4—794no—
630C2×C22⋊C4—792no—
631C2×C22⋊C4—794no—
632C2×C22⋊C4C22×D7914yes—
633C2×C42—792no—
634C2×C42—792no—
635C2×C42—792no—
636C2×C42—794no—
637C2×C42—794no—
638C2×C42—794no—
639C2×C42C22×D7911yescharacteristic
640C2×C42C22×D7914yes—
641C2×C42C22×D7911yescharacteristic
642C2×C42C22×D7911yescharacteristic
643C2×C42C22×D7911yescharacteristic
644C2×C42C22×D7918yes—
645C24—792no—
646C24C23×D7911yescharacteristic
647C2×Q8—28no—
648C2×Q8—44no—
649C2×Q8—3164no—
650C2×Q8—3168no—
651C2×Q8—798no—
652C2×Q8—7916no—
653C2×Q8—794no—
654C2×Q8—794no—
655C2×Q8—794no—
656C2×Q8—1584no—
657C2×Q8—1584no—
658C2×Q8—1584no—
659C2×Q8C23×D7918yes—
660C2×Q8C23×D7918yes—
661C2×D4—3164no—
662C2×D4—798no—
663C2×D4—794no—
664C2×D4—1584no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—3168no—
669C22×C4—7916no—
670C22×C4—792no—
671C22×C4—792no—
672C22×C4—792no—
673C22×C4—792no—
674C22×C4—792no—
675C22×C4—792no—
676C22×C4—792no—
677C22×C4—798no—
678C22×C4—1588no—
679C22×C4C23×D7914yes—
680C22×C4C23×D7914yes—
681C22×C4C23×D7914yes—
682C22×C4C23×D7914yes—
683C22×C4C23×D7911yescharacteristic
684C22×C4C23×D7911yescharacteristic
685C22×C4C23×D7911yescharacteristic
686C22×C4C23×D7911yescharacteristic
687C22×C4C23×D7914yes—
688C22×C4C23×D7911yescharacteristic
689C22×C4C23×D7911yescharacteristic
690C4⋊C4—7916no—
691C4⋊C4—798no—
692C4⋊C4—798no—
693C4⋊C4—7916no—
694C4⋊C4—798no—
695C4⋊C4—798no—
696C4⋊C4—798no—
697C4⋊C4—798no—
698C4⋊C4—7916no—
699C4⋊C4—798no—
700C4⋊C4—7916no—
701C4⋊C4—798no—
702C4⋊C4—7916no—
703C4⋊C4—794no—
704C4⋊C4—794no—
705C4⋊C4—798no—
706C4⋊C4—798no—
707C4⋊C4—794no—
708C4⋊C4—794no—
709C4⋊C4—7916no—
710C4⋊C4—7916no—
711C4⋊C4—7916no—
712C4⋊C4—798no—
713C4⋊C4C23×D7918yes—
714C4⋊C4C23×D7918yes—
715C4⋊C4C23×D7918yes—
716C4⋊C4C23×D79116yes—
717C4⋊C4C23×D79116yes—
718C4⋊C4C23×D7918yes—
719C22⋊C4—798no—
720C22⋊C4—798no—
721C22⋊C4—798no—
722C22⋊C4—798no—
723C22⋊C4—798no—
724C22⋊C4—798no—
725C22⋊C4—7916no—
726C22⋊C4—7916no—
727C22⋊C4—798no—
728C22⋊C4—7916no—
729C22⋊C4C23×D79116yes—
730C42—798no—
731C42—798no—
732C42—798no—
733C42—7916no—
734C42—7916no—
735C42—7916no—
736C42C23×D7914yes—
737C42C23×D7914yes—
738C42C23×D7914yes—
739C42C23×D7914yes—
740C42C23×D79116yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—794no—
745C23—1584no—
746C23—1584no—
747C23—1584no—
748C23C24×D7912yes—
749C23C24×D7911yescharacteristic
750Q8—216no—
751Q8—48no—
752Q8—3168no—
753Q8—31616no—
754Q8—1588no—
755Q8—1588no—
756Q8—1588no—
757D4—3168no—
758D4—1588no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—44no—
768C2×C4—31616no—
769C2×C4—794no—
770C2×C4—794no—
771C2×C4—794no—
772C2×C4—794no—
773C2×C4—794no—
774C2×C4—794no—
775C2×C4—794no—
776C2×C4—1584no—
777C2×C4—1584no—
778C2×C4—1584no—
779C2×C4—1584no—
780C2×C4—1584no—
781C2×C4—1584no—
782C2×C4—1584no—
783C2×C4—15816no—
784C2×C4#1457920814yes—
785C2×C4#1457920914yes—
786C2×C4C24×D7918yes—
787C2×C4C24×D7918yes—
788C2×C4C24×D7912yes—
789C2×C4C24×D7912yes—
790C2×C4C24×D7912yes—
791C2×C4C24×D7912yes—
792C2×C4C24×D7912yes—
793C2×C4C24×D7912yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—3168no—
799C22—1584no—
800C22—1584no—
801C22—1584no—
802C22C2×#1457920812yes—
803C22C2×#1457920912yes—
804C22#1909939912yes—
805C22C25×D7911yescharacteristic
806C4—22no—
807C4—28no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—28no—
812C4—1584no—
813C4—1584no—
814C4—1584no—
815C4—1584no—
816C4—1584no—
817C4—1584no—
818C4—1584no—
819C4C2×#1457920814yes—
820C4C2×#1457920914yes—
821C2—42no—
822C2—3164no—
823C2#2377788214yesdirect product factor
824C2C22×#1457920811yescharacteristic
825C2C22×#1457920911yescharacteristic
826C2C2×#1909939911yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#533×C79C2
socleC23×C79C25
prime radicalC2×#14579135C22
hypercenterC2×#533D79
hypocenterC79C2×#3555
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #23777882C2direct (N × H)
2. C2×#19099314C2semidirect
3. C2×#19099293C2semidirect
4. C2×#19099289C2semidirect
5. C2×#19099288C2semidirect
6. C2×#19099287C2semidirect
7. C2×#19099285C2semidirect
8. C2×#19099281C2semidirect
9. C2×#19099274C2semidirect
10. C2×#19099252C2semidirect
11. C2×#19099193C2semidirect
13. C2×#19099176C2semidirect
14. C2×#19099173C2semidirect
15. C2×#19099171C2semidirect
16. C2×#19099120C2semidirect
18. C2×#533×C79C2semidirect
19. #19099314C22semidirect
20. #19099293C22semidirect
21. #19099289C22semidirect
22. #19099288C22semidirect
23. #19099287C22semidirect
24. #19099285C22semidirect
25. #19099281C22semidirect
26. #19099274C22semidirect
27. #19099252C22semidirect
28. #19099193C22semidirect
30. #19099176C22semidirect
31. #19099173C22semidirect
32. #19099171C22semidirect
33. #19099120C22semidirect
91. #533×C79C22semidirect
409. C2×C79#3555semidirect
430. C2×#533D79semidirect
432. C79C2×#3555semidirect
448. #533C2×D79semidirect
823. C2#23777882direct (N × H)

Maximal subgroups

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

subgroupindex
#237778822
C2×#190993142
C2×#190992932
C2×#190992892
C2×#190992882
C2×#190992872
C2×#190992852
C2×#190992812
C2×#190992742
C2×#190992522
C2×#190991932
C2×#190991862
C2×#190991762
C2×#190991732
C2×#190991712
C2×#190991202
C2×#190990972
C2×#533×C792
C2×#355579