Finite Group Databasebeta

← C2×#23777872 #35195893

Subgroups — C2×#23777872 #35195893

Order 20224.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777872C2132yesmaximal, direct product factor
2C2×#19099309C214yesmaximal, complemented
3C2×#19099298C211yesmaximal, characteristic, complemented
4C2×#19099296C212yesmaximal, complemented
5C2×#19099288C211yesmaximal, characteristic, complemented
6C2×#19099274C212yesmaximal, complemented
7C2×#19099234C211yesmaximal, characteristic, complemented
8C2×#19099224C212yesmaximal, complemented
9C2×#19099215C212yesmaximal, complemented
10C2×#19099187C212yesmaximal, complemented
11C2×#19099186C212yesmaximal, complemented
12C2×#19099164C212yesmaximal, complemented
13C2×#19099159C214yesmaximal, complemented
14C2×#19099137C212yesmaximal, complemented
15C2×#19099117C211yesmaximal, characteristic, complemented
16C2×#19099114C211yesmaximal, characteristic, complemented
17C2×#19099095C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C79C211yesmaximal, characteristic, complemented
19C22×#11929625C2212yes—
20C22×#11929624C2212yes—
21#19099309C22164yescomplemented
22#19099298C22116yescomplemented
23#19099296C22132yescomplemented
24#19099288C22116yescomplemented
25#19099274C22132yescomplemented
26#19099234C22116yescomplemented
27#19099224C22132yescomplemented
28#19099215C22132yescomplemented
29#19099187C22132yescomplemented
30#19099186C22132yescomplemented
31#19099164C22132yescomplemented
32#19099159C22164yescomplemented
33#19099137C22132yescomplemented
34#19099117C22116yescomplemented
35#19099114C22116yescomplemented
36C2×#14579160C2211yescharacteristic
37C2×#14579159C2212yes—
38C2×#14579159C2211yescharacteristic
39C2×#14579158C2211yescharacteristic
40C2×#14579157C2212yes—
41#19099095C22116yescomplemented
42C2×#14579156C2214yes—
43C2×#14579154C2212yes—
44C2×#14579152C2211yescharacteristic
45C2×#14579152C2212yes—
46C2×#14579151C2212yes—
47C2×#14579151C2214yes—
48C2×#14579150C2212yes—
49C2×#14579150C2214yes—
50C2×#14579150C2212yes—
51C2×#14579149C2212yes—
52C2×#14579148C2211yescharacteristic
53C2×#14579147C2214yes—
54C2×#14579146C2214yes—
55C2×#14579146C2214yes—
56C2×#14579144C2214yes—
57C2×#14579144C2214yes—
58C2×#14579143C2214yes—
59C2×#14579143C2214yes—
60C2×#14579143C2212yes—
61C2×#14579141C2214yes—
62C2×#14579141C2211yescharacteristic
63C2×#14579141C2211yescharacteristic
64C2×#14579139C2212yes—
65C2×#14579137C2214yes—
66C2×#14579137C2211yescharacteristic
67C2×#14579137C2214yes—
68C2×#14579137C2214yes—
69C2×#14579136C2212yes—
70C2×#14579136C2212yes—
71C2×#14579135C2212yes—
72C2×#14579135C2214yes—
73C2×#14579134C2214yes—
74C2×#14579134C2214yes—
75C2×#14579132C2211yescharacteristic
76C2×Q8×Dic79C2212yes—
77C2×C4×Dic158C2211yescharacteristic
78C2×C4×Dic158C2211yescharacteristic
79C2×C4×Dic158C2212yes—
80C2×#14579126C2212yes—
81C2×C4×D316C2212yes—
82C2×#14579123C2212yes—
83C2×#14579123C2212yes—
84C2×#14579123C2212yes—
85C2×#14579123C2212yes—
86C2×C4×C22⋊D79C2212yes—
87C2×C4×C22⋊D79C2214yes—
88C2×#14579120C2212yes—
89C2×#14579118C2212yes—
90C2×C4⋊C4×D79C2214yes—
91C2×C42×D79C2211yescharacteristic
92C23×Q8×C79C2212yes—
93D4×Q8×C79C22116yescomplemented
94C2×C4⋊Q8×C79C2212yes—
95C2×C4⋊Q8×C79C2211yescharacteristic
96C2×C22⋊Q8×C79C2212yes—
97C2×C22⋊Q8×C79C2214yes—
98C2×C4×Q8×C79C2211yescharacteristic
99C2×C4×D4×C79C2211yescharacteristic
100C2×C4×D4×C79C2212yes—
101C2×#11929625—48no—
102C2×#11929625C23116yes—
103C2×#11929624—48no—
104C2×#11929624C23116yes—
105C22×Dic158C2311yescharacteristic
106C22×Dic158C2311yescharacteristic
107C22×Dic158C2312yes—
108C22×D316C2312yes—
109C22×D316C2312yes—
110C22×D316C2312yes—
111C22×D316C2314yes—
112C22×C22⋊D79C2312yes—
113C22×C22⋊D79C2314yes—
114C22×C22⋊D79C2314yes—
115C22×C4×D79C2311yescharacteristic
116C22×C4×D79C2311yescharacteristic
117C22×C4×D79C2311yescharacteristic
118C22×C4×D79C2314yes—
119C22×C4×D79C2314yes—
120C22×C4×D79C2314yes—
121#14579160C2318yes—
122#14579159C2318yes—
123#14579159C23116yes—
124#14579158C2318yes—
125#14579157C23116yes—
126#14579156C23132yes—
127#14579154C23116yes—
128#14579152C23116yes—
129#14579152C2318yes—
130#14579151C23116yes—
131#14579151C23132yes—
132#14579150C23116yes—
133#14579150C23116yes—
134#14579150C23132yes—
135#14579149C23116yes—
136#14579148C2318yes—
137#14579147C23132yes—
138#14579146C23132yes—
139#14579146C23132yes—
140#14579144C23132yes—
141#14579144C23132yes—
142#14579143C23132yes—
143#14579143C23132yes—
144#14579143C23116yes—
145#14579141C23132yes—
146#14579141C2318yes—
147#14579141C2318yes—
148#14579139C23116yes—
149#14579137C23132yes—
150#14579137C23132yes—
151#14579137C23132yes—
152#14579137C2318yes—
153#14579136C23116yes—
154#14579136C23116yes—
155#14579135C23132yes—
156#14579135C23116yes—
157#14579134C23132yes—
158#14579134C23132yes—
159#14579132C2318yes—
160Q8×Dic79C23116yes—
161C4×Dic158C2318yes—
162C4×Dic158C23116yes—
163C4×Dic158C2318yes—
164#14579126C23116yes—
165C4×D316C23116yes—
166#14579123C23116yes—
167#14579123C23116yes—
168#14579123C23116yes—
169#14579123C23116yes—
170C4×C22⋊D79C23132yes—
171C4×C22⋊D79C23116yes—
172#14579120C23116yes—
173#14579118C23116yes—
174C2×C4⋊Dic79C2312yes—
175C2×C4⋊Dic79C2312yes—
176C2×C4⋊Dic79C2312yes—
177C2×C4⋊Dic79C2311yescharacteristic
178C2×C4⋊Dic79C2311yescharacteristic
179C2×C4⋊Dic79C2314yes—
180C2×Dic79⋊C4C2312yes—
181C2×Dic79⋊C4C2314yes—
182C2×Dic79⋊C4C2312yes—
183C2×Dic79⋊C4C2312yes—
184C2×Dic79⋊C4C2312yes—
185C2×Dic79⋊C4C2314yes—
186C2×Dic79⋊C4C2312yes—
187C2×Dic79⋊C4C2312yes—
188C2×Dic79⋊C4C2312yes—
189C4⋊C4×D79C23132yes—
190C2×C22⋊Dic79C2312yes—
191C2×C22⋊Dic79C2312yes—
192C2×C22⋊Dic79C2312yes—
193C2×(C2×D79)⋊C4C2312yes—
194C2×(C2×D79)⋊C4C2312yes—
195C2×(C2×D79)⋊C4C2314yes—
196C2×(C2×D79)⋊C4C2312yes—
197C2×(C2×D79)⋊C4C2314yes—
198C2×(C2×D79)⋊C4C2314yes—
199C2×(C2×D79)⋊C4C2314yes—
200C2×(C2×D79)⋊C4C2314yes—
201C2×(C2×D79)⋊C4C2314yes—
202C2×C4×Dic79C2311yescharacteristic
203C2×C4×Dic79C2311yescharacteristic
204C2×C4×Dic79C2311yescharacteristic
205C2×C4×Dic79C2312yes—
206C2×C4×Dic79C2312yes—
207C2×C4×Dic79C2314yes—
208C42×D79C2318yes—
209C22×Q8×C79—48no—
210C22×Q8×C79C2311yescharacteristic
211C22×Q8×C79C2312yes—
212C22×Q8×C79C23116yes—
213C22×Q8×C79C2314yes—
214C22×D4×C79C2311yescharacteristic
215C23×C4×C79C2312yes—
216C23×C4×C79C2314yes—
217C4⋊Q8×C79C23116yes—
218C4⋊Q8×C79C2318yes—
219C22⋊Q8×C79C23132yes—
220C22⋊Q8×C79C23116yes—
221C4×Q8×C79C2318yes—
222C4×D4×C79C23116yes—
223C4×D4×C79C2318yes—
224C2×C4⋊C4×C79C2311yescharacteristic
225C2×C4⋊C4×C79C2312yes—
226C2×C4⋊C4×C79C2311yescharacteristic
227C2×C4⋊C4×C79C2312yes—
228C2×C4⋊C4×C79C2314yes—
229C2×C4⋊C4×C79C2312yes—
230C2×C22⋊C4×C79C2312yes—
231C2×C22⋊C4×C79C2314yes—
232C2×C42×C79C2311yescharacteristic
233C2×C42×C79C2312yes—
234C23×D79C2411yescharacteristic
235C23×D79C2414yes—
236#11929625—432no—
237#11929624—432no—
238C2×Dic158—24no—
239C2×Dic158—24no—
240C2×Dic158—44no—
241C2×Dic158C2414yes—
242C2×Dic158C2414yes—
243C2×Dic158C2418yes—
244C2×D316—28no—
245C2×D316—28no—
246C2×D316—48no—
247C2×D316—44no—
248C2×D316C2418yes—
249C2×D316C2418yes—
250C2×D316C24116yes—
251C2×D316C2418yes—
252C2×C22⋊D79—48no—
253C2×C22⋊D79—44no—
254C2×C22⋊D79—48no—
255C2×C22⋊D79C24116yes—
256C2×C22⋊D79C2418yes—
257C2×C22⋊D79C24116yes—
258C22×Dic79C2411yescharacteristic
259C22×Dic79C2412yes—
260C22×Dic79C2412yes—
261C22×Dic79C2412yes—
262C22×Dic79C2411yescharacteristic
263C22×Dic79C2411yescharacteristic
264C22×Dic79C2412yes—
265C2×C4×D79—24no—
266C2×C4×D79—24no—
267C2×C4×D79—48no—
268C2×C4×D79—48no—
269C2×C4×D79—48no—
270C2×C4×D79—42no—
271C2×C4×D79C2414yes—
272C2×C4×D79C2414yes—
273C2×C4×D79C24116yes—
274C2×C4×D79C24116yes—
275C2×C4×D79C2414yes—
276C2×C4×D79C24116yes—
277C4⋊Dic79C2418yes—
278C4⋊Dic79C2418yes—
279C4⋊Dic79C2418yes—
280C4⋊Dic79C2414yes—
281C4⋊Dic79C2414yes—
282C4⋊Dic79C24116yes—
283Dic79⋊C4C2418yes—
284Dic79⋊C4C24116yes—
285Dic79⋊C4C2418yes—
286Dic79⋊C4C2418yes—
287Dic79⋊C4C2418yes—
288Dic79⋊C4C24116yes—
289Dic79⋊C4C2418yes—
290Dic79⋊C4C2418yes—
291Dic79⋊C4C2418yes—
292C22⋊Dic79C2418yes—
293C22⋊Dic79C2418yes—
294C22⋊Dic79C2418yes—
295(C2×D79)⋊C4C2418yes—
296(C2×D79)⋊C4C2418yes—
297(C2×D79)⋊C4C24116yes—
298(C2×D79)⋊C4C2418yes—
299(C2×D79)⋊C4C24116yes—
300(C2×D79)⋊C4C24116yes—
301(C2×D79)⋊C4C24116yes—
302(C2×D79)⋊C4C24116yes—
303(C2×D79)⋊C4C24116yes—
304C4×Dic79C2414yes—
305C4×Dic79C2414yes—
306C4×Dic79C2414yes—
307C4×Dic79C2418yes—
308C4×Dic79C2418yes—
309C4×Dic79C24116yes—
310C24×C79C2412yes—
311C2×Q8×C79—28no—
312C2×Q8×C79—24no—
313C2×Q8×C79—48no—
314C2×Q8×C79—432no—
315C2×Q8×C79C2418yes—
316C2×Q8×C79C2414yes—
317C2×Q8×C79C24116yes—
318C2×D4×C79—24no—
319C2×D4×C79C2414yes—
320C22×C4×C79—28no—
321C22×C4×C79—48no—
322C22×C4×C79C2412yes—
323C22×C4×C79C2418yes—
324C22×C4×C79C2411yescharacteristic
325C22×C4×C79C2412yes—
326C22×C4×C79C2414yes—
327C22×C4×C79C2412yes—
328C22×C4×C79C24116yes—
329C22×C4×C79C2411yescharacteristic
330C22×C4×C79C2411yescharacteristic
331C4⋊C4×C79C2414yes—
332C4⋊C4×C79C2418yes—
333C4⋊C4×C79C2414yes—
334C4⋊C4×C79C2418yes—
335C4⋊C4×C79C24116yes—
336C4⋊C4×C79C2418yes—
337C22⋊C4×C79C2418yes—
338C22⋊C4×C79C24116yes—
339C42×C79C2414yes—
340C42×C79C2418yes—
341C23×C79—24no—
342C23×C79—24no—
343C23×C79—24no—
344C23×C79C2514yes—
345C23×C79C2511yescharacteristic
346C22×D79—22no—
347C22×D79—28no—
348C22×D79—22no—
349C22×D79—28no—
350C22×D79—22no—
351C22×D79—28no—
352C22×D79C2518yes—
353C22×D79C2512yes—
354Q8×C79—216no—
355Q8×C79—28no—
356Q8×C79—416no—
357D4×C79—28no—
358C2×C4×C79—24no—
359C2×C4×C79—28no—
360C2×C4×C79—24no—
361C2×C4×C79—24no—
362C2×C4×C79—22no—
363C2×C4×C79—216no—
364C2×C4×C79—416no—
365C2×C4×C79H(5,𝔽2)14yes—
366C2×C4×C792−1+414yes—
367C2×C4×C79C2518yes—
368C2×C4×C79C2512yes—
369C2×C4×C79C2514yes—
370C2×C4×C79C2514yes—
371C2×C4×C79C2514yes—
372C2×C4×C79C2512yes—
373C2×C4×C79C2512yes—
374C22⋊D79—416no—
375C22⋊D79—48no—
376C22⋊D79—416no—
377C2×Dic79—22no—
378C2×Dic79—24no—
379C2×Dic79—22no—
380C2×Dic79—24no—
381C2×Dic79—24no—
382C2×Dic79—22no—
383C2×Dic79—24no—
384C2×Dic79C2514yes—
385C2×Dic79C2514yes—
386C2×Dic79C2512yes—
387C2×Dic79C2512yes—
388C2×Dic79C2512yes—
389C2×Dic79C2514yes—
390C2×Dic79C2514yes—
391D316—216no—
392D316—216no—
393D316—48no—
394D316—416no—
395C4×D79—28no—
396C4×D79—28no—
397C4×D79—416no—
398C4×D79—44no—
399C4×D79—416no—
400C4×D79—416no—
401Dic158—28no—
402Dic158—28no—
403Dic158—48no—
404C22×C79—24no—
405C22×C79—24no—
406C22×C79—24no—
407C22×C79—48no—
408C22×C79C2×H(5,𝔽2)12yes—
409C22×C79C2×2−1+412yes—
410C22×C79#58512yes—
411C22×C79C2611yescharacteristic
412C2×D79—28no—
413C2×D79—22no—
414C2×D79—22no—
415C2×D79—28no—
416C2×D79—22no—
417C2×D79—28no—
418C2×D79—44no—
419C2×D79—416no—
420C4×C79—24no—
421C4×C79—24no—
422C4×C79—28no—
423C4×C79—24no—
424C4×C79—22no—
425C4×C79C2×H(5,𝔽2)14yes—
426C4×C79C2×2−1+414yes—
427Dic79—24no—
428Dic79—22no—
429Dic79—24no—
430Dic79—22no—
431Dic79—24no—
432Dic79—24no—
433Dic79—22no—
434C2×#3554—791nomaximal, Sylow
435C2×C79—44no—
436C2×C79#355414yescomplemented
437C2×C79C22×H(5,𝔽2)11yescharacteristic
438C2×C79C22×2−1+411yescharacteristic
439C2×C79C2×#58511yescharacteristic
440D79—48no—
441D79—42no—
442#3554—7932no—
443C2×#562—794no—
444C2×#559—791no—
445C2×#559—792no—
446C2×#557—791no—
447C2×#554—792no—
448C2×#550—791no—
449C2×D4×Q8D7911yescharacteristic, complemented
450C2×#548—792no—
451C2×#547—792no—
452C2×#542—792no—
453C2×#542—792no—
454C2×#540—792no—
455C2×#539—794no—
456C2×#536—792no—
457C2×#533—791no—
458C2×#532—791no—
459C2×#529—791no—
460C79C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—792no—
462C22×#41—792no—
463C23×Q8C2×D7912yes—
464#562—7964no—
465#559—7916no—
466#559—7932no—
467#557—7916no—
468#554—7932no—
469#550—7916no—
470D4×Q8C2×D79116yescomplemented
471#548—7932no—
472#547—7932no—
473#542—7932no—
474#542—7932no—
475#540—7932no—
476#539—7964no—
477#536—7932no—
478#533—7916no—
479#532—7916no—
480C2×C4⋊Q8—791no—
481C2×C4⋊Q8—792no—
482C2×C4⋊Q8—791no—
483C2×C4⋊Q8C2×D7911yescharacteristic
484C2×C4⋊Q8C2×D7912yes—
485C2×#127—792no—
486C2×#127—791no—
487#529—7916no—
488C2×#126—794no—
489C2×#126—792no—
490C2×#125—791no—
491C2×#125—792no—
492C2×#125—794no—
493C2×#125—792no—
494C2×#124—792no—
495C2×#124—792no—
496C2×#124—794no—
497C2×#124—791no—
498C2×#124—794no—
499C2×#124—792no—
500C2×#123—794no—
501C2×#123—794no—
502C2×#123—794no—
503C2×#123—794no—
504C2×#123—792no—
505C2×#123—794no—
506C2×#123—794no—
507C2×C22⋊Q8—791no—
508C2×C22⋊Q8—794no—
509C2×C22⋊Q8—794no—
510C2×C22⋊Q8—794no—
511C2×C22⋊Q8—791no—
512C2×C22⋊Q8—791no—
513C2×C22⋊Q8—792no—
514C2×C22⋊Q8—794no—
515C2×C22⋊Q8C2×D7914yes—
516C2×C22⋊Q8C2×D7912yes—
517C2×#121—791no—
518C2×#121—794no—
519C2×#121—792no—
520C2×#121—792no—
521C2×#121—792no—
522C2×#121—794no—
523C2×#121—794no—
524C2×C4×Q8—792no—
525C2×C4×Q8—792no—
526C2×C4×Q8—791no—
527C2×C4×Q8—791no—
528C2×C4×Q8—792no—
529C2×C4×Q8C2×D7911yescharacteristic
530C2×C4×D4—792no—
531C2×C4×D4—794no—
532C2×C4×D4—792no—
533C2×C4×D4—792no—
534C2×C4×D4—792no—
535C2×C4×D4—792no—
536C2×C4×D4—792no—
537C2×C4×D4C2×D7911yescharacteristic
538C2×C4×D4C2×D7912yes—
539C2×#117—792no—
540C2×#117—792no—
541C22×C4⋊C4—794no—
542C22×C42—791no—
543C2×#41—3168no—
544C2×#41—3168no—
545C2×#41—7916no—
546C2×#41—7916no—
547C22×Q8—48no—
548C22×Q8—792no—
549C22×Q8—791no—
550C22×Q8—791no—
551C22×Q8C22×D7912yes—
552C22×Q8C22×D7911yescharacteristic
553C22×Q8C22×D7914yes—
554C22×Q8C22×D79116yes—
555C22×D4—792no—
556C22×D4—794no—
557C22×D4—794no—
558C22×D4—792no—
559C22×D4—794no—
560C22×D4—792no—
561C22×D4—792no—
562C22×D4C22×D7911yescharacteristic
563C23×C4—794no—
564C23×C4—794no—
565C23×C4—794no—
566C23×C4—791no—
567C23×C4—791no—
568C23×C4—791no—
569C23×C4C22×D7912yes—
570C23×C4C22×D7914yes—
571C4⋊Q8—798no—
572C4⋊Q8—7916no—
573C4⋊Q8—798no—
574C4⋊Q8C22×D7918yes—
575C4⋊Q8C22×D79116yes—
576#127—7916no—
577#127—798no—
578#126—7932no—
579#126—7916no—
580#125—798no—
581#125—7916no—
582#125—7932no—
583#125—7916no—
584#124—7916no—
585#124—7916no—
586#124—7932no—
587#124—798no—
588#124—7932no—
589#124—7916no—
590#123—7932no—
591#123—7932no—
592#123—7932no—
593#123—7932no—
594#123—7916no—
595#123—7932no—
596#123—7932no—
597C22⋊Q8—798no—
598C22⋊Q8—7932no—
599C22⋊Q8—7932no—
600C22⋊Q8—7932no—
601C22⋊Q8—798no—
602C22⋊Q8—798no—
603C22⋊Q8—7916no—
604C22⋊Q8—7932no—
605C22⋊Q8C22×D79132yes—
606C22⋊Q8C22×D79116yes—
607#121—798no—
608#121—7932no—
609#121—7916no—
610#121—7916no—
611#121—7916no—
612#121—7932no—
613#121—7932no—
614C4×Q8—7916no—
615C4×Q8—7916no—
616C4×Q8—798no—
617C4×Q8—798no—
618C4×Q8—7916no—
619C4×Q8C22×D7918yes—
620C4×D4—7916no—
621C4×D4—7932no—
622C4×D4—7916no—
623C4×D4—7916no—
624C4×D4—7916no—
625C4×D4—7916no—
626C4×D4—7916no—
627C4×D4C22×D7918yes—
628C4×D4C22×D79116yes—
629#117—7916no—
630#117—7916no—
631C2×C4⋊C4—792no—
632C2×C4⋊C4—792no—
633C2×C4⋊C4—794no—
634C2×C4⋊C4—792no—
635C2×C4⋊C4—792no—
636C2×C4⋊C4—792no—
637C2×C4⋊C4—792no—
638C2×C4⋊C4—791no—
639C2×C4⋊C4—792no—
640C2×C4⋊C4—791no—
641C2×C4⋊C4—792no—
642C2×C4⋊C4—794no—
643C2×C4⋊C4—792no—
644C2×C4⋊C4—794no—
645C2×C4⋊C4—792no—
646C2×C4⋊C4—7932no—
647C2×C4⋊C4C22×D7914yes—
648C2×C4⋊C4C22×D7911yescharacteristic
649C2×C4⋊C4C22×D7911yescharacteristic
650C2×C4⋊C4C22×D7912yes—
651C2×C4⋊C4C22×D7912yes—
652C2×C4⋊C4C22×D7912yes—
653C2×C22⋊C4—792no—
654C2×C22⋊C4—792no—
655C2×C22⋊C4—792no—
656C2×C22⋊C4—792no—
657C2×C22⋊C4—792no—
658C2×C22⋊C4—794no—
659C2×C22⋊C4—794no—
660C2×C22⋊C4—794no—
661C2×C22⋊C4—794no—
662C2×C22⋊C4—792no—
663C2×C22⋊C4—794no—
664C2×C22⋊C4—794no—
665C2×C22⋊C4C22×D7912yes—
666C2×C22⋊C4C22×D7914yes—
667C2×C42—791no—
668C2×C42—792no—
669C2×C42—792no—
670C2×C42—791no—
671C2×C42—791no—
672C2×C42—794no—
673C2×C42—798no—
674C2×C42C22×D7912yes—
675C2×C42C22×D7911yescharacteristic
676C24—794no—
677C24—791no—
678C24C23×D7912yes—
679#41—31632no—
680#41—31632no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—48no—
684C2×Q8—432no—
685C2×Q8—3164no—
686C2×Q8—798no—
687C2×Q8—794no—
688C2×Q8—794no—
689C2×Q8—1584no—
690C2×Q8—1584no—
691C2×Q8C23×D7918yes—
692C2×Q8C23×D7914yes—
693C2×Q8C23×D79116yes—
694C2×D4—24no—
695C2×D4—3164no—
696C2×D4—3168no—
697C2×D4—3164no—
698C2×D4—3168no—
699C2×D4—3168no—
700C2×D4—798no—
701C2×D4—7916no—
702C2×D4—7916no—
703C2×D4—798no—
704C2×D4—7916no—
705C2×D4—798no—
706C2×D4—798no—
707C2×D4—1588no—
708C2×D4—1588no—
709C2×D4C23×D7914yes—
710C22×C4—28no—
711C22×C4—48no—
712C22×C4—3168no—
713C22×C4—3162no—
714C22×C4—3168no—
715C22×C4—3168no—
716C22×C4—794no—
717C22×C4—7916no—
718C22×C4—7916no—
719C22×C4—7916no—
720C22×C4—792no—
721C22×C4—792no—
722C22×C4—791no—
723C22×C4—791no—
724C22×C4—791no—
725C22×C4—792no—
726C22×C4—792no—
727C22×C4—794no—
728C22×C4—794no—
729C22×C4—1584no—
730C22×C4—1584no—
731C22×C4C23×D7918yes—
732C22×C4C23×D7911yescharacteristic
733C22×C4C23×D7914yes—
734C22×C4C23×D7912yes—
735C22×C4C23×D7912yes—
736C22×C4C23×D7912yes—
737C22×C4C23×D79116yes—
738C22×C4C23×D7911yescharacteristic
739C22×C4C23×D7911yescharacteristic
740C4⋊C4—798no—
741C4⋊C4—7916no—
742C4⋊C4—798no—
743C4⋊C4—798no—
744C4⋊C4—798no—
745C4⋊C4—798no—
746C4⋊C4—798no—
747C4⋊C4—7916no—
748C4⋊C4—798no—
749C4⋊C4—798no—
750C4⋊C4—798no—
751C4⋊C4—798no—
752C4⋊C4—794no—
753C4⋊C4—794no—
754C4⋊C4—7916no—
755C4⋊C4C23×D79116yes—
756C4⋊C4C23×D7914yes—
757C4⋊C4C23×D7914yes—
758C4⋊C4C23×D7918yes—
759C4⋊C4C23×D7918yes—
760C4⋊C4C23×D7918yes—
761C22⋊C4—798no—
762C22⋊C4—798no—
763C22⋊C4—798no—
764C22⋊C4—798no—
765C22⋊C4—798no—
766C22⋊C4—7916no—
767C22⋊C4—7916no—
768C22⋊C4—7916no—
769C22⋊C4—7916no—
770C22⋊C4—798no—
771C22⋊C4—7916no—
772C22⋊C4—7916no—
773C22⋊C4C23×D7918yes—
774C22⋊C4C23×D79116yes—
775C42—794no—
776C42—794no—
777C42—794no—
778C42—798no—
779C42—798no—
780C42—7916no—
781C42C23×D7914yes—
782C42C23×D7918yes—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—798no—
787C23—792no—
788C23—1588no—
789C23—1582no—
790C23—1582no—
791C23—1588no—
792C23—1582no—
793C23—1588no—
794C23C24×D7914yes—
795C23C24×D7911yescharacteristic
796Q8—28no—
797Q8—216no—
798Q8—416no—
799Q8—3168no—
800Q8—1588no—
801Q8—1588no—
802D4—28no—
803D4—31616no—
804D4—3168no—
805D4—3168no—
806D4—31616no—
807D4—31616no—
808D4—15816no—
809D4—15816no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—216no—
816C2×C4—416no—
817C2×C4—31616no—
818C2×C4—31616no—
819C2×C4—31616no—
820C2×C4—3164no—
821C2×C4—794no—
822C2×C4—794no—
823C2×C4—792no—
824C2×C4—792no—
825C2×C4—792no—
826C2×C4—794no—
827C2×C4—794no—
828C2×C4—1582no—
829C2×C4—1584no—
830C2×C4—1582no—
831C2×C4—1584no—
832C2×C4—1584no—
833C2×C4—1582no—
834C2×C4—1584no—
835C2×C4—1588no—
836C2×C4—1588no—
837C2×C4#1457920614yes—
838C2×C4#1457920914yes—
839C2×C4C24×D7912yes—
840C2×C4C24×D7918yes—
841C2×C4C24×D7914yes—
842C2×C4C24×D7914yes—
843C2×C4C24×D7914yes—
844C2×C4C24×D7912yes—
845C2×C4C24×D7912yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—31616no—
851C22—3164no—
852C22—1588no—
853C22—1582no—
854C22—1582no—
855C22—1588no—
856C22—1588no—
857C22—1582no—
858C22C2×#1457920612yes—
859C22C2×#1457920912yes—
860C22#1909940012yes—
861C22C25×D7911yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—1582no—
868C4—1584no—
869C4—1582no—
870C4—1584no—
871C4—1584no—
872C4—1582no—
873C4—1584no—
874C4C2×#1457920614yes—
875C4C2×#1457920914yes—
876C2—44no—
877C2—3168no—
878C2—3162no—
879C2#2377787214yesdirect product factor
880C2C22×#1457920611yescharacteristic
881C2C22×#1457920911yescharacteristic
882C2C2×#1909940011yescharacteristic
subgroupG/H
centerC23C24×D79
commutator, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×D4×Q8×C79C2
socleC23×C79C25
hypercenterC2×D4×Q8D79
hypocenterC79C2×#3554
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #23777872C2direct (N × H)
2. C2×#19099309C2semidirect
3. C2×#19099298C2semidirect
4. C2×#19099296C2semidirect
5. C2×#19099288C2semidirect
6. C2×#19099274C2semidirect
7. C2×#19099234C2semidirect
8. C2×#19099224C2semidirect
9. C2×#19099215C2semidirect
10. C2×#19099187C2semidirect
11. C2×#19099186C2semidirect
12. C2×#19099164C2semidirect
13. C2×#19099159C2semidirect
14. C2×#19099137C2semidirect
15. C2×#19099117C2semidirect
16. C2×#19099114C2semidirect
17. C2×#19099095C2semidirect
18. C2×D4×Q8×C79C2semidirect
21. #19099309C22semidirect
22. #19099298C22semidirect
23. #19099296C22semidirect
24. #19099288C22semidirect
25. #19099274C22semidirect
26. #19099234C22semidirect
27. #19099224C22semidirect
28. #19099215C22semidirect
29. #19099187C22semidirect
30. #19099186C22semidirect
31. #19099164C22semidirect
32. #19099159C22semidirect
33. #19099137C22semidirect
34. #19099117C22semidirect
35. #19099114C22semidirect
41. #19099095C22semidirect
93. D4×Q8×C79C22semidirect
436. C2×C79#3554semidirect
449. C2×D4×Q8D79semidirect
460. C79C2×#3554semidirect
470. D4×Q8C2×D79semidirect
879. C2#23777872direct (N × H)

Maximal subgroups

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

subgroupindex
#237778722
C2×#190993092
C2×#190992982
C2×#190992962
C2×#190992882
C2×#190992742
C2×#190992342
C2×#190992242
C2×#190992152
C2×#190991872
C2×#190991862
C2×#190991642
C2×#190991592
C2×#190991372
C2×#190991172
C2×#190991142
C2×#190990952
C2×D4×Q8×C792
C2×#355479