Finite Group Databasebeta

← C2×#23777263 #35196346

Subgroups — C2×#23777263 #35196346

Order 20224.

7130 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777263C2132yesmaximal, direct product factor
2C2×#19099296C212yesmaximal, complemented
3C2×#19099290C212yesmaximal, complemented
4C2×#19099286C211yesmaximal, characteristic, complemented
5C2×#19099284C214yesmaximal, complemented
6C2×#19099283C211yesmaximal, characteristic, complemented
7C2×#19099274C211yesmaximal, characteristic, complemented
8C2×#19099248C212yesmaximal, complemented
9C2×#19099247C212yesmaximal, complemented
10C2×#19099159C214yesmaximal, complemented
11C2×#19099136C212yesmaximal, complemented
12C2×#19099118C211yesmaximal, characteristic, complemented
13C2×#19099110C211yesmaximal, characteristic
14C2×#19099098C212yesmaximal, complemented
15C2×#19099095C212yesmaximal, complemented
16C2×#19099044C212yesmaximal, complemented
17C2×C4×Q8×D79C211yesmaximal, characteristic, complemented
18C2×#554×C79C211yesmaximal, characteristic, complemented
19C22×#11929624C2212yes—
20C22×Q8×D79C2211yescharacteristic
21#19099296C22132yescomplemented
22#19099290C22132yescomplemented
23#19099286C22116yescomplemented
24#19099284C22164yescomplemented
25#19099283C22116yescomplemented
26#19099274C22116yescomplemented
27#19099248C22132yescomplemented
28#19099247C22132yescomplemented
29#19099159C22164yescomplemented
30#19099136C22132yescomplemented
31#19099118C22116yescomplemented
32#19099110C22116yes—
33C2×#14579161C2211yescharacteristic
34C2×#14579160C2211yescharacteristic
35C2×#14579160C2214yes—
36C2×#14579157C2211yescharacteristic
37#19099098C22132yescomplemented
38#19099095C22132yescomplemented
39C2×#14579156C2214yes—
40C2×#14579156C2214yes—
41C2×#14579154C2214yes—
42C2×#14579154C2214yes—
43C2×#14579152C2212yes—
44C2×#14579152C2212yes—
45C2×#14579151C2214yes—
46C2×#14579151C2214yes—
47C2×#14579149C2212yes—
48C2×#14579148C2212yes—
49C2×#14579147C2212yes—
50C2×#14579147C2214yes—
51C2×#14579146C2214yes—
52C2×#14579144C2214yes—
53C2×#14579143C2214yes—
54C2×#14579143C2214yes—
55C2×#14579141C2212yes—
56C2×#14579141C2212yes—
57C2×#14579140C2212yes—
58C2×#14579137C2212yes—
59C2×#14579137C2214yes—
60C2×#14579137C2212yes—
61C2×#14579136C2211yescharacteristic
62C2×#14579134C2212yes—
63C2×#14579132C2211yescharacteristic
64#19099044C22132yescomplemented
65C2×Q8×Dic79C2211yescharacteristic
66C2×Q8×Dic79C2212yes—
67C2×C4×Dic158C2211yescharacteristic
68C2×C4×Dic158C2212yes—
69C2×C4×Dic158C2212yes—
70C2×#14579126C2211yescharacteristic
71C2×#14579126C2212yes—
72C2×#14579126C2214yes—
73C2×#14579126C2212yes—
74C2×#14579126C2212yes—
75C4×Q8×D79C22116yescomplemented
76C2×C4×D316C2211yescharacteristic
77C2×#14579123C2214yes—
78C2×#14579123C2212yes—
79C2×C4×C22⋊D79C2214yes—
80C2×C4×C22⋊D79C2214yes—
81C2×C4×C22⋊D79C2212yes—
82C2×#14579120C2212yes—
83C2×#14579120C2214yes—
84C2×#14579119C2212yes—
85C2×#14579119C2212yes—
86C2×#14579119C2214yes—
87C2×C4⋊C4×D79C2211yescharacteristic
88C2×C4⋊C4×D79C2212yes—
89C2×C4⋊C4×D79C2212yes—
90C2×C42×D79C2212yes—
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—
101C2×#11929624—216no—
102C2×#11929624C23116yes—
103C22×Dic158C2312yes—
104C22×Dic158C2312yes—
105C22×Dic158C2311yescharacteristic
106C22×Dic158C2312yes—
107C2×Q8×D79—28no—
108C2×Q8×D79C2318yes—
109C22×D316C2311yescharacteristic
110C22×D316C2312yes—
111C22×C22⋊D79C2312yes—
112C22×C22⋊D79C2312yes—
113C22×C22⋊D79C2312yes—
114C22×C4×D79C2311yescharacteristic
115C22×C4×D79C2312yes—
116C22×C4×D79C2312yes—
117C22×C4×D79C2312yes—
118C22×C4×D79C2311yescharacteristic
119C22×C4×D79C2314yes—
120C22×C4×D79C2311yescharacteristic
121#14579161C2318yes—
122#14579160C23132yes—
123#14579160C2318yes—
124#14579157C2318yes—
125#14579156C23132yes—
126#14579156C23132yes—
127#14579154C23132yes—
128#14579154C23132yes—
129#14579152C23116yes—
130#14579152C23116yes—
131#14579151C23132yes—
132#14579151C23132yes—
133#14579149C23116yes—
134#14579148C23116yes—
135#14579147C23132yes—
136#14579147C23116yes—
137#14579146C23132yes—
138#14579144C23132yes—
139#14579143C23132yes—
140#14579143C23132yes—
141#14579141C23116yes—
142#14579141C23116yes—
143#14579140C23116yes—
144#14579137C23116yes—
145#14579137C23116yes—
146#14579137C23132yes—
147#14579136C2318yes—
148#14579134C23116yes—
149#14579132C2318yes—
150Q8×Dic79C2318yes—
151Q8×Dic79C23116yes—
152C4×Dic158C2318yes—
153C4×Dic158C23116yes—
154C4×Dic158C23116yes—
155#14579126C2318yes—
156#14579126C23116yes—
157#14579126C23116yes—
158#14579126C23132yes—
159#14579126C23116yes—
160C4×D316C2318yes—
161#14579123C23132yes—
162#14579123C23116yes—
163C4×C22⋊D79C23132yes—
164C4×C22⋊D79C23116yes—
165C4×C22⋊D79C23132yes—
166#14579120C23116yes—
167#14579120C23132yes—
168#14579119C23116yes—
169#14579119C23132yes—
170#14579119C23116yes—
171C2×C4⋊Dic79C2311yescharacteristic
172C2×C4⋊Dic79C2312yes—
173C2×C4⋊Dic79C2312yes—
174C2×C4⋊Dic79C2314yes—
175C2×C4⋊Dic79C2314yes—
176C2×C4⋊Dic79C2311yescharacteristic
177C2×C4⋊Dic79C2312yes—
178C2×Dic79⋊C4C2312yes—
179C2×Dic79⋊C4C2314yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2312yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2314yes—
184C2×Dic79⋊C4C2314yes—
185C2×Dic79⋊C4C2314yes—
186C4⋊C4×D79C23116yes—
187C4⋊C4×D79C23116yes—
188C4⋊C4×D79C2318yes—
189C2×C22⋊Dic79C2312yes—
190C2×C22⋊Dic79C2314yes—
191C2×C22⋊Dic79C2314yes—
192C2×(C2×D79)⋊C4C2312yes—
193C2×(C2×D79)⋊C4C2314yes—
194C2×(C2×D79)⋊C4C2314yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2314yes—
197C2×(C2×D79)⋊C4C2312yes—
198C2×C4×Dic79C2312yes—
199C2×C4×Dic79C2312yes—
200C2×C4×Dic79C2311yescharacteristic
201C2×C4×Dic79C2312yes—
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2314yes—
205C2×C4×Dic79C2314yes—
206C2×C4×Dic79C2314yes—
207C42×D79C23116yes—
208C42×D79C2318yes—
209C22×Q8×C79C2311yescharacteristic
210C22×Q8×C79C2312yes—
211C22×D4×C79C2311yescharacteristic
212C23×C4×C79C2312yes—
213C23×C4×C79C2314yes—
214C4⋊Q8×C79C2318yes—
215#125×C79C23116yes—
216C22⋊Q8×C79C23116yes—
217C22⋊Q8×C79C23132yes—
218C4×Q8×C79C2318yes—
219C4×D4×C79C2318yes—
220C4×D4×C79C23116yes—
221C2×C4⋊C4×C79C2311yescharacteristic
222C2×C4⋊C4×C79C2314yes—
223C2×C4⋊C4×C79C2312yes—
224C2×C4⋊C4×C79C23116yes—
225C2×C4⋊C4×C79C2311yescharacteristic
226C2×C4⋊C4×C79C2312yes—
227C2×C4⋊C4×C79C2312yes—
228C2×C4⋊C4×C79C2314yes—
229C2×C22⋊C4×C79C2312yes—
230C2×C22⋊C4×C79C2314yes—
231C2×C42×C79C2312yes—
232C2×C42×C79C2311yescharacteristic
233C23×D79C2412yes—
234C23×D79C2411yescharacteristic
235#11929624—264no—
236C2×Dic158—28no—
237C2×Dic158—28no—
238C2×Dic158—24no—
239C2×Dic158—28no—
240C2×Dic158C2414yes—
241C2×Dic158C2418yes—
242C2×Dic158C2418yes—
243C2×Dic158C2418yes—
244Q8×D79—232no—
245C2×D316—28no—
246C2×D316—24no—
247C2×D316C2418yes—
248C2×D316C2414yes—
249C2×C22⋊D79—28no—
250C2×C22⋊D79—28no—
251C2×C22⋊D79—44no—
252C2×C22⋊D79C2418yes—
253C2×C22⋊D79C2418yes—
254C2×C22⋊D79C2418yes—
255C22×Dic79C2412yes—
256C22×Dic79C2414yes—
257C22×Dic79C2412yes—
258C22×Dic79C2411yescharacteristic
259C22×Dic79C2412yes—
260C22×Dic79C2411yescharacteristic
261C22×Dic79C2411yescharacteristic
262C2×C4×D79—28no—
263C2×C4×D79—28no—
264C2×C4×D79—24no—
265C2×C4×D79—44no—
266C2×C4×D79—48no—
267C2×C4×D79—42no—
268C2×C4×D79#4118yes—
269C2×C4×D79C2418yes—
270C2×C4×D79C2418yes—
271C2×C4×D79C2414yes—
272C2×C4×D79C2418yes—
273C2×C4×D79C2414yes—
274C2×C4×D79C24116yes—
275C2×C4×D79C2414yes—
276C4⋊Dic79C2414yes—
277C4⋊Dic79C2418yes—
278C4⋊Dic79C2418yes—
279C4⋊Dic79C24116yes—
280C4⋊Dic79C24116yes—
281C4⋊Dic79C2414yes—
282C4⋊Dic79C2418yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C2418yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C2418yes—
288Dic79⋊C4C24116yes—
289Dic79⋊C4C24116yes—
290Dic79⋊C4C24116yes—
291C22⋊Dic79C2418yes—
292C22⋊Dic79C24116yes—
293C22⋊Dic79C24116yes—
294(C2×D79)⋊C4C2418yes—
295(C2×D79)⋊C4C24116yes—
296(C2×D79)⋊C4C24116yes—
297(C2×D79)⋊C4C24116yes—
298(C2×D79)⋊C4C24116yes—
299(C2×D79)⋊C4C2418yes—
300C4×Dic79C2418yes—
301C4×Dic79C2418yes—
302C4×Dic79C2414yes—
303C4×Dic79C2418yes—
304C4×Dic79C2414yes—
305C4×Dic79C2414yes—
306C4×Dic79C24116yes—
307C4×Dic79C24116yes—
308C4×Dic79C24116yes—
309C24×C79C2412yes—
310C2×Q8×C79—24no—
311C2×Q8×C79—44no—
312C2×Q8×C79C2414yes—
313C2×Q8×C79C2418yes—
314C2×D4×C79—24no—
315C2×D4×C79C2414yes—
316C22×C4×C79—28no—
317C22×C4×C79—48no—
318C22×C4×C79C2412yes—
319C22×C4×C79C2412yes—
320C22×C4×C79C2418yes—
321C22×C4×C79C2411yescharacteristic
322C22×C4×C79C2412yes—
323C22×C4×C79C2414yes—
324C22×C4×C79C24116yes—
325C22×C4×C79C2411yescharacteristic
326C22×C4×C79C2411yescharacteristic
327C4⋊C4×C79C2414yes—
328C4⋊C4×C79C24116yes—
329C4⋊C4×C79C2418yes—
330C4⋊C4×C79C2414yes—
331C4⋊C4×C79C2418yes—
332C4⋊C4×C79C2418yes—
333C4⋊C4×C79C24116yes—
334C22⋊C4×C79C2418yes—
335C22⋊C4×C79C24116yes—
336C42×C79C2418yes—
337C42×C79C2414yes—
338C23×C79—24no—
339C23×C79—24no—
340C23×C79—24no—
341C23×C79C2514yes—
342C23×C79C2511yescharacteristic
343C22×D79—22no—
344C22×D79—22no—
345C22×D79—24no—
346C22×D79—24no—
347C22×D79—24no—
348C22×D79C2×#4114yes—
349C22×D79C2514yes—
350C22×D79C2512yes—
351Q8×C79—28no—
352Q8×C79—48no—
353D4×C79—28no—
354C2×C4×C79—24no—
355C2×C4×C79—24no—
356C2×C4×C79—24no—
357C2×C4×C79—28no—
358C2×C4×C79—22no—
359C2×C4×C79—216no—
360C2×C4×C79—416no—
361C2×C4×C79C2×#4114yes—
362C2×C4×C792−1+414yes—
363C2×C4×C79C2514yes—
364C2×C4×C79C2514yes—
365C2×C4×C79C2512yes—
366C2×C4×C79C2518yes—
367C2×C4×C79C2514yes—
368C2×C4×C79C2512yes—
369C2×C4×C79C2512yes—
370C22⋊D79—216no—
371C22⋊D79—216no—
372C22⋊D79—48no—
373C2×Dic79—24no—
374C2×Dic79—24no—
375C2×Dic79—22no—
376C2×Dic79—28no—
377C2×Dic79—24no—
378C2×Dic79—22no—
379C2×Dic79C2×#4114yes—
380C2×Dic79C2512yes—
381C2×Dic79C2514yes—
382C2×Dic79C2518yes—
383C2×Dic79C2514yes—
384C2×Dic79C2514yes—
385C2×Dic79C2512yes—
386C2×Dic79C2512yes—
387D316—216no—
388D316—28no—
389C4×D79—216no—
390C4×D79—216no—
391C4×D79—28no—
392C4×D79—44no—
393C4×D79—48no—
394C4×D79—416no—
395C4×D79C2×#41116yes—
396Dic158—28no—
397Dic158—216no—
398Dic158—216no—
399Dic158—216no—
400C22×C79—24no—
401C22×C79—24no—
402C22×C79—24no—
403C22×C79—48no—
404C22×C79C22×#4112yes—
405C22×C79C2×2−1+412yes—
406C22×C79#58512yes—
407C22×C79C2611yescharacteristic
408C2×D79—22no—
409C2×D79—22no—
410C2×D79—28no—
411C2×D79—24no—
412C2×D79—24no—
413C2×D79—24no—
414C2×D79—48no—
415C2×D79C22×#4114yes—
416C4×C79—24no—
417C4×C79—24no—
418C4×C79—24no—
419C4×C79—28no—
420C4×C79—22no—
421C4×C79C22×#4114yes—
422C4×C79C2×2−1+414yes—
423Dic79—24no—
424Dic79—24no—
425Dic79—28no—
426Dic79—22no—
427Dic79—22no—
428Dic79—24no—
429Dic79C22×#4114yes—
430C2×#3507—791nomaximal, Sylow
431C2×C79—44no—
432C2×C79#350714yescomplemented
433C2×C79C23×#4111yescharacteristic
434C2×C79C22×2−1+411yescharacteristic
435C2×C79C2×#58511yescharacteristic
436D79—24no—
437D79—44no—
438#3507—7932no—
439C2×#559—792no—
440C2×#557—792no—
441C2×#556—794no—
442C2×#556—791no—
443C2×#556—791no—
444C2×#554—791no—
445C2×#554D7911yescharacteristic, complemented
446C2×#552—792no—
447C2×#552—792no—
448C2×#539—794no—
449C2×#536—792no—
450C2×#533—791no—
451C2×#532—791no—
452C2×#529—792no—
453C2×#529—792no—
454C2×#520—792no—
455C22×C4×Q8—791no—
456C79C2×#350711yescharacteristic, complemented, Sylow
457C22×#41—792no—
458C23×Q8—791no—
459#559—7932no—
460#557—7932no—
461#556—7964no—
462#556—7916no—
463#556—7916no—
464#554—7916no—
465#554C2×D79116yescomplemented
466#552—7932no—
467#552—7932no—
468#539—7964no—
469#536—7932no—
470#533—7916no—
471#532—7916no—
472C2×C4⋊Q8—791no—
473C2×C4⋊Q8—794no—
474C2×C4⋊Q8—791no—
475C2×C4⋊Q8C2×D7911yescharacteristic
476C2×#127—791no—
477#529—7932no—
478#529—7932no—
479C2×#126—794no—
480C2×#126—794no—
481C2×#126—794no—
482C2×#126—794no—
483C2×#125—792no—
484C2×#125—792no—
485C2×#125—794no—
486C2×#125—794no—
487C2×#125C2×D7912yes—
488C2×#124—792no—
489C2×#124—792no—
490C2×#124—794no—
491C2×#124—792no—
492C2×#123—794no—
493C2×#123—794no—
494C2×#123—794no—
495C2×#123—794no—
496C2×C22⋊Q8—792no—
497C2×C22⋊Q8—792no—
498C2×C22⋊Q8—794no—
499C2×C22⋊Q8—792no—
500C2×C22⋊Q8—792no—
501C2×C22⋊Q8—792no—
502C2×C22⋊Q8C2×D7912yes—
503C2×C22⋊Q8C2×D7914yes—
504C2×#121—791no—
505C2×#121—791no—
506C2×#121—792no—
507#520—7932no—
508C2×C4×Q8—791no—
509C2×C4×Q8—792no—
510C2×C4×Q8—7916no—
511C2×C4×Q8—791no—
512C2×C4×Q8—792no—
513C2×C4×Q8—794no—
514C2×C4×Q8—792no—
515C2×C4×Q8—792no—
516C2×C4×Q8—791no—
517C2×C4×Q8—792no—
518C2×C4×Q8—792no—
519C2×C4×Q8C2×D7911yescharacteristic
520C2×C4×D4—794no—
521C2×C4×D4—794no—
522C2×C4×D4—792no—
523C2×C4×D4—794no—
524C2×C4×D4—792no—
525C2×C4×D4—791no—
526C2×C4×D4C2×D7912yes—
527C2×C4×D4C2×D7911yescharacteristic
528C2×#117—792no—
529C2×#117—794no—
530C2×#117—792no—
531C2×#117—792no—
532C2×#117—794no—
533C22×C4⋊C4—791no—
534C22×C4⋊C4—792no—
535C22×C4⋊C4—792no—
536C22×C4⋊C4C2×D7912yes—
537C22×C42—792no—
538C22×C42—791no—
539C2×#41—7916no—
540C2×#41—15816no—
541C22×Q8—798no—
542C22×Q8—792no—
543C22×Q8—791no—
544C22×Q8—792no—
545C22×Q8—792no—
546C22×Q8—1588no—
547C22×Q8C22×D7911yescharacteristic
548C22×Q8C22×D7912yes—
549C22×D4—792no—
550C22×D4—792no—
551C22×D4—792no—
552C22×D4—791no—
553C22×D4—792no—
554C22×D4C22×D7911yescharacteristic
555C23×C4—792no—
556C23×C4—791no—
557C23×C4—794no—
558C23×C4—791no—
559C23×C4—792no—
560C23×C4—792no—
561C23×C4—791no—
562C23×C4C22×D7912yes—
563C23×C4C22×D7914yes—
564C4⋊Q8—798no—
565C4⋊Q8—7932no—
566C4⋊Q8—798no—
567C4⋊Q8C22×D7918yes—
568#127—798no—
569#126—7932no—
570#126—7932no—
571#126—7932no—
572#126—7932no—
573#125—7916no—
574#125—7916no—
575#125—7932no—
576#125—7932no—
577#125C22×D79116yes—
578#124—7916no—
579#124—7916no—
580#124—7932no—
581#124—7916no—
582#123—7932no—
583#123—7932no—
584#123—7932no—
585#123—7932no—
586C22⋊Q8—7916no—
587C22⋊Q8—7916no—
588C22⋊Q8—7932no—
589C22⋊Q8—7916no—
590C22⋊Q8—7916no—
591C22⋊Q8—7916no—
592C22⋊Q8C22×D79116yes—
593C22⋊Q8C22×D79132yes—
594#121—798no—
595#121—798no—
596#121—7916no—
597C4×Q8—798no—
598C4×Q8—7916no—
599C4×Q8—798no—
600C4×Q8—7916no—
601C4×Q8—7932no—
602C4×Q8—7916no—
603C4×Q8—7916no—
604C4×Q8—798no—
605C4×Q8—7916no—
606C4×Q8—7916no—
607C4×Q8C22×D7918yes—
608C4×D4—7932no—
609C4×D4—7932no—
610C4×D4—7916no—
611C4×D4—7932no—
612C4×D4—7916no—
613C4×D4—798no—
614C4×D4C22×D79116yes—
615C4×D4C22×D7918yes—
616#117—7916no—
617#117—7932no—
618#117—7916no—
619#117—7916no—
620#117—7932no—
621C2×C4⋊C4—791no—
622C2×C4⋊C4—792no—
623C2×C4⋊C4—794no—
624C2×C4⋊C4—792no—
625C2×C4⋊C4—792no—
626C2×C4⋊C4—792no—
627C2×C4⋊C4—792no—
628C2×C4⋊C4—794no—
629C2×C4⋊C4—794no—
630C2×C4⋊C4—791no—
631C2×C4⋊C4—792no—
632C2×C4⋊C4—794no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—794no—
635C2×C4⋊C4—792no—
636C2×C4⋊C4—798no—
637C2×C4⋊C4—7916no—
638C2×C4⋊C4—7916no—
639C2×C4⋊C4C22×D7911yescharacteristic
640C2×C4⋊C4C22×D7912yes—
641C2×C4⋊C4C22×D7912yes—
642C2×C4⋊C4C22×D7914yes—
643C2×C4⋊C4C22×D79116yes—
644C2×C4⋊C4C22×D7914yes—
645C2×C4⋊C4C22×D7912yes—
646C2×C4⋊C4C22×D7911yescharacteristic
647C2×C22⋊C4—792no—
648C2×C22⋊C4—794no—
649C2×C22⋊C4—794no—
650C2×C22⋊C4—792no—
651C2×C22⋊C4—794no—
652C2×C22⋊C4—794no—
653C2×C22⋊C4—794no—
654C2×C22⋊C4—792no—
655C2×C22⋊C4—794no—
656C2×C22⋊C4C22×D7912yes—
657C2×C22⋊C4C22×D7914yes—
658C2×C42—794no—
659C2×C42—794no—
660C2×C42—792no—
661C2×C42—792no—
662C2×C42—794no—
663C2×C42—791no—
664C2×C42—792no—
665C2×C42—791no—
666C2×C42—791no—
667C2×C42—7916no—
668C2×C42—798no—
669C2×C42C22×D7911yescharacteristic
670C2×C42C22×D7912yes—
671C24—791no—
672C24—792no—
673C24C23×D7912yes—
674#41—15864no—
675C2×Q8—24no—
676C2×Q8—44no—
677C2×Q8—798no—
678C2×Q8—794no—
679C2×Q8—798no—
680C2×Q8—798no—
681C2×Q8—1588no—
682C2×Q8—1588no—
683C2×Q8—15832no—
684C2×Q8—1584no—
685C2×Q8—1588no—
686C2×Q8C23×D7914yes—
687C2×Q8C23×D7918yes—
688C2×D4—24no—
689C2×D4—3164no—
690C2×D4—798no—
691C2×D4—798no—
692C2×D4—798no—
693C2×D4—794no—
694C2×D4—798no—
695C2×D4—1588no—
696C2×D4—1588no—
697C2×D4—1588no—
698C2×D4—1584no—
699C2×D4C23×D7914yes—
700C22×C4—28no—
701C22×C4—48no—
702C22×C4—3164no—
703C22×C4—3168no—
704C22×C4—3162no—
705C22×C4—798no—
706C22×C4—794no—
707C22×C4—7916no—
708C22×C4—791no—
709C22×C4—798no—
710C22×C4—794no—
711C22×C4—791no—
712C22×C4—792no—
713C22×C4—794no—
714C22×C4—792no—
715C22×C4—792no—
716C22×C4—791no—
717C22×C4—794no—
718C22×C4—798no—
719C22×C4—798no—
720C22×C4—1588no—
721C22×C4—1588no—
722C22×C4—1584no—
723C22×C4C23×D7918yes—
724C22×C4C23×D7912yes—
725C22×C4C23×D7912yes—
726C22×C4C23×D7911yescharacteristic
727C22×C4C23×D7912yes—
728C22×C4C23×D7914yes—
729C22×C4C23×D79116yes—
730C22×C4C23×D7911yescharacteristic
731C22×C4C23×D7911yescharacteristic
732C4⋊C4—798no—
733C4⋊C4—7916no—
734C4⋊C4—798no—
735C4⋊C4—798no—
736C4⋊C4—798no—
737C4⋊C4—7916no—
738C4⋊C4—7916no—
739C4⋊C4—7916no—
740C4⋊C4—794no—
741C4⋊C4—798no—
742C4⋊C4—798no—
743C4⋊C4—7916no—
744C4⋊C4—7916no—
745C4⋊C4—794no—
746C4⋊C4—798no—
747C4⋊C4C23×D7914yes—
748C4⋊C4C23×D7918yes—
749C4⋊C4C23×D7918yes—
750C4⋊C4C23×D79116yes—
751C4⋊C4C23×D79116yes—
752C4⋊C4C23×D7918yes—
753C4⋊C4C23×D7914yes—
754C22⋊C4—798no—
755C22⋊C4—7916no—
756C22⋊C4—7916no—
757C22⋊C4—798no—
758C22⋊C4—7916no—
759C22⋊C4—7916no—
760C22⋊C4—7916no—
761C22⋊C4—798no—
762C22⋊C4—7916no—
763C22⋊C4C23×D7918yes—
764C22⋊C4C23×D79116yes—
765C42—798no—
766C42—798no—
767C42—794no—
768C42—798no—
769C42—794no—
770C42—794no—
771C42—7916no—
772C42—7916no—
773C42—7916no—
774C42C23×D7914yes—
775C42C23×D7918yes—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—792no—
780C23—794no—
781C23—794no—
782C23—1584no—
783C23—1584no—
784C23—1584no—
785C23—1582no—
786C23—1582no—
787C23C24×D7914yes—
788C23C24×D7911yescharacteristic
789Q8—28no—
790Q8—48no—
791Q8—15816no—
792Q8—15816no—
793Q8—15816no—
794Q8—1588no—
795D4—28no—
796D4—3168no—
797D4—15816no—
798D4—15816no—
799D4—15816no—
800D4—1588no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—216no—
807C2×C4—416no—
808C2×C4—3168no—
809C2×C4—31616no—
810C2×C4—3164no—
811C2×C4—792no—
812C2×C4—794no—
813C2×C4—7916no—
814C2×C4—792no—
815C2×C4—794no—
816C2×C4—798no—
817C2×C4—794no—
818C2×C4—794no—
819C2×C4—792no—
820C2×C4—15816no—
821C2×C4—1582no—
822C2×C4—1588no—
823C2×C4—1584no—
824C2×C4—1582no—
825C2×C4—1584no—
826C2×C4—1584no—
827C2×C4—1588no—
828C2×C4—15816no—
829C2×C4#41×D7914yes—
830C2×C4#1457920914yes—
831C2×C4C24×D7914yes—
832C2×C4C24×D7914yes—
833C2×C4C24×D7912yes—
834C2×C4C24×D7914yes—
835C2×C4C24×D7918yes—
836C2×C4C24×D7912yes—
837C2×C4C24×D7912yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—48no—
842C22—3168no—
843C22—794no—
844C22—1584no—
845C22—1584no—
846C22—1584no—
847C22—1582no—
848C22—1582no—
849C22—1588no—
850C22C2×#41×D7912yes—
851C22C2×#1457920912yes—
852C22#1909939812yes—
853C22C25×D7911yescharacteristic
854C4—24no—
855C4—24no—
856C4—24no—
857C4—28no—
858C4—22no—
859C4—794no—
860C4—1584no—
861C4—1584no—
862C4—1582no—
863C4—1588no—
864C4—1584no—
865C4—1582no—
866C4C2×#41×D7914yes—
867C4C2×#1457920914yes—
868C2—44no—
869C2—3164no—
870C2—1584no—
871C2#2377726314yesdirect product factor
872C2C22×#41×D7911yescharacteristic
873C2C22×#1457920911yescharacteristic
874C2C2×#1909939811yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×#554×C79C2
socleC23×C79C25
prime radicalC2×#19099110C2
hypercenterC2×#554D79
hypocenterC79C2×#3507
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #23777263C2direct (N × H)
2. C2×#19099296C2semidirect
3. C2×#19099290C2semidirect
4. C2×#19099286C2semidirect
5. C2×#19099284C2semidirect
6. C2×#19099283C2semidirect
7. C2×#19099274C2semidirect
8. C2×#19099248C2semidirect
9. C2×#19099247C2semidirect
10. C2×#19099159C2semidirect
11. C2×#19099136C2semidirect
12. C2×#19099118C2semidirect
14. C2×#19099098C2semidirect
15. C2×#19099095C2semidirect
16. C2×#19099044C2semidirect
17. C2×C4×Q8×D79C2semidirect
18. C2×#554×C79C2semidirect
21. #19099296C22semidirect
22. #19099290C22semidirect
23. #19099286C22semidirect
24. #19099284C22semidirect
25. #19099283C22semidirect
26. #19099274C22semidirect
27. #19099248C22semidirect
28. #19099247C22semidirect
29. #19099159C22semidirect
30. #19099136C22semidirect
31. #19099118C22semidirect
37. #19099098C22semidirect
38. #19099095C22semidirect
64. #19099044C22semidirect
75. C4×Q8×D79C22semidirect
92. #554×C79C22semidirect
432. C2×C79#3507semidirect
445. C2×#554D79semidirect
456. C79C2×#3507semidirect
465. #554C2×D79semidirect
871. C2#23777263direct (N × H)

Maximal subgroups

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

subgroupindex
#237772632
C2×#190992962
C2×#190992902
C2×#190992862
C2×#190992842
C2×#190992832
C2×#190992742
C2×#190992482
C2×#190992472
C2×#190991592
C2×#190991362
C2×#190991182
C2×#190991102
C2×#190990982
C2×#190990952
C2×#190990442
C2×C4×Q8×D792
C2×#554×C792
C2×#350779