Finite Group Databasebeta

← C2×#23768645 #34458663

Subgroups — C2×#23768645 #34458663

Order 20224.

2614 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23768645C2116yesmaximal, direct product factor
2C2×#19098505C211yesmaximal, characteristic, complemented
3C2×#19098479C211yesmaximal, characteristic
4C2×#19098474C211yesmaximal, characteristic, complemented
5C2×#19098470C211yesmaximal, characteristic, complemented
6C2×#19098457C211yesmaximal, characteristic, complemented
7C2×#19098452C211yesmaximal, characteristic, complemented
8C2×#19098440C211yesmaximal, characteristic
9C2×#19098439C211yesmaximal, characteristic
10C2×#19098430C211yesmaximal, characteristic, complemented
11C2×#19098430C211yesmaximal, characteristic, complemented
12C2×#19098425C211yesmaximal, characteristic, complemented
13C2×#19098424C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
15C2×#19098410C211yesmaximal, characteristic, complemented
16C2×#393×C79C211yesmaximal, characteristic, complemented
17C23×C22⋊D79C2211yescharacteristic
18C24×Dic79C2211yescharacteristic
19C23×C4×D79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×C22⋊Dic79C2211yescharacteristic
23C22×C22⋊Dic79C2211yescharacteristic
24C22×(C2×D79)⋊C4C2211yescharacteristic
25C22×(C2×D79)⋊C4C2211yescharacteristic
26C22×(C2×D79)⋊C4C2211yescharacteristic
27C22×(C2×D79)⋊C4C2211yescharacteristic
28C22×(C2×D79)⋊C4C2211yescharacteristic
29C22×C4×Dic79C2211yescharacteristic
30C22×C4×Dic79C2211yescharacteristic
31C22×C4×Dic79C2211yescharacteristic
32#19098505C2218yescomplemented
33#19098479C2218yes—
34#19098474C2218yescomplemented
35#19098470C2218yescomplemented
36#19098457C2218yescomplemented
37#19098452C2218yescomplemented
38#19098440C2218yes—
39#19098439C2218yes—
40#19098430C2218yescomplemented
41#19098430C2218yescomplemented
42#19098425C2218yescomplemented
43#19098424C2218yescomplemented
44C22⋊C4×Dic79C2218yescomplemented
45#19098410C2218yescomplemented
46C2×C79⋊#95C2211yescharacteristic
47C2×C79⋊#95C2211yescharacteristic
48C2×C79⋊#95C2211yescharacteristic
49C2×C79⋊#95C2211yescharacteristic
50C2×C79⋊#95C2211yescharacteristic
51C2×C79⋊#95C2211yescharacteristic
52C2×C79⋊#95C2211yescharacteristic
53C2×C79⋊#95C2211yescharacteristic
54C2×C79⋊#95C2211yescharacteristic
55C2×C79⋊#95C2211yescharacteristic
56C2×C79⋊#95C2211yescharacteristic
57C2×C79⋊#95C2211yescharacteristic
58C2×C79⋊#95C2211yescharacteristic
59C23×Q8×C79C2211yescharacteristic
60C22×C22⋊C4×C79C2211yescharacteristic
61C22×C22⋊C4×C79C2211yescharacteristic
62C22×C22⋊C4×C79C2211yescharacteristic
63#393×C79C2218yescomplemented
64C2×#95×C79C2211yescharacteristic
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C24×D79C2311yescharacteristic
68C22×C22⋊D79—24no—
69C22×C22⋊D79—24no—
70C22×C22⋊D79—42no—
71C22×C22⋊D79C2314yes—
72C23×Dic79—24no—
73C23×Dic79—24no—
74C23×Dic79—42no—
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2314yes—
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2311yescharacteristic
83C22×C4×D79—24no—
84C22×C4×D79—24no—
85C22×C4×D79—42no—
86C22×C4×D79C2314yes—
87C2×C4⋊Dic79—42no—
88C2×C4⋊Dic79C2314yes—
89C2×Dic79⋊C4—42no—
90C2×Dic79⋊C4C2314yes—
91C2×C22⋊Dic79—24no—
92C2×C22⋊Dic79—24no—
93C2×C22⋊Dic79C2314yes—
94C2×C22⋊Dic79C2314yes—
95C2×(C2×D79)⋊C4—24no—
96C2×(C2×D79)⋊C4—24no—
97C2×(C2×D79)⋊C4—24no—
98C2×(C2×D79)⋊C4—42no—
99C2×(C2×D79)⋊C4—42no—
100C2×(C2×D79)⋊C4C2314yes—
101C2×(C2×D79)⋊C4C2314yes—
102C2×(C2×D79)⋊C4C2314yes—
103C2×(C2×D79)⋊C4C2314yes—
104C2×(C2×D79)⋊C4C2314yes—
105C2×C4×Dic79—24no—
106C2×C4×Dic79—24no—
107C2×C4×Dic79—42no—
108C2×C4×Dic79C2314yes—
109C2×C4×Dic79C2314yes—
110C2×C4×Dic79C2314yes—
111C79⋊#95C2314yes—
112C79⋊#95C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123C79⋊#95C2314yes—
124C25×C79C2311yescharacteristic
125C22×Q8×C79—24no—
126C22×Q8×C79—42no—
127C22×Q8×C79—42no—
128C22×Q8×C79C2314yes—
129C23×C4×C79C2311yescharacteristic
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2311yescharacteristic
135C2×C22⋊C4×C79—24no—
136C2×C22⋊C4×C79—42no—
137C2×C22⋊C4×C79—42no—
138C2×C22⋊C4×C79C2314yes—
139C2×C22⋊C4×C79C2314yes—
140C2×C22⋊C4×C79C2314yes—
141#95×C79C2314yes—
142#95×C79C2314yes—
143#95×C79C2314yes—
144C23×D79—22no—
145C23×D79—22no—
146C23×D79—22no—
147C23×D79—22no—
148C23×D79—22no—
149C23×D79—22no—
150C23×D79#4114yes—
151C23×D79C2412yes—
152C2×C22⋊D79—28no—
153C2×C22⋊D79—28no—
154C2×C22⋊D79—44no—
155C2×C22⋊D79—416no—
156C22×Dic79—28no—
157C22×Dic79—22no—
158C22×Dic79—22no—
159C22×Dic79—22no—
160C22×Dic79—22no—
161C22×Dic79—22no—
162C22×Dic79—22no—
163C22×Dic79—22no—
164C22×Dic79—22no—
165C22×Dic79—22no—
166C22×Dic79—22no—
167C22×Dic79—28no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—22no—
171C22×Dic79—22no—
172C22×Dic79—22no—
173C22×Dic79—22no—
174C22×Dic79—22no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—44no—
178C22×Dic79—416no—
179C22×Dic79#4114yes—
180C22×Dic79#4114yes—
181C22×Dic79C2412yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C22×Dic79C2412yes—
185C22×Dic79C2412yes—
186C22×Dic79C2412yes—
187C22×Dic79C2412yes—
188C2×C4×D79—28no—
189C2×C4×D79—28no—
190C2×C4×D79—44no—
191C2×C4×D79—416no—
192C4⋊Dic79—44no—
193Dic79⋊C4—44no—
194C22⋊Dic79—28no—
195C22⋊Dic79—28no—
196(C2×D79)⋊C4—28no—
197(C2×D79)⋊C4—28no—
198(C2×D79)⋊C4—28no—
199(C2×D79)⋊C4—44no—
200(C2×D79)⋊C4—44no—
201C4×Dic79—28no—
202C4×Dic79—28no—
203C4×Dic79—44no—
204C24×C79—22no—
205C24×C79—22no—
206C24×C79—22no—
207C24×C79—22no—
208C24×C79—22no—
209C24×C79—22no—
210C24×C79#4114yes—
211C24×C79C2412yes—
212C24×C79C2411yescharacteristic
213C2×Q8×C79—28no—
214C2×Q8×C79—44no—
215C2×Q8×C79—44no—
216C2×Q8×C79—416no—
217C22×C4×C79—22no—
218C22×C4×C79—22no—
219C22×C4×C79—22no—
220C22×C4×C79—22no—
221C22×C4×C79—22no—
222C22×C4×C79—22no—
223C22×C4×C79—22no—
224C22×C4×C79—22no—
225C22×C4×C79—22no—
226C22×C4×C79—22no—
227C22×C4×C79—22no—
228C22×C4×C79—22no—
229C22×C4×C79—22no—
230C22×C4×C79—22no—
231C22×C4×C79—22no—
232C22×C4×C79—22no—
233C22×C4×C79—22no—
234C22×C4×C79#4114yes—
235C22×C4×C79C2412yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C22×C4×C79C2412yes—
241C22⋊C4×C79—28no—
242C22⋊C4×C79—44no—
243C22⋊C4×C79—44no—
244C23×C79—28no—
245C23×C79—28no—
246C23×C79—28no—
247C23×C79—22no—
248C23×C79—22no—
249C23×C79—22no—
250C23×C79—22no—
251C23×C79—22no—
252C23×C79—22no—
253C23×C79—44no—
254C23×C79—44no—
255C23×C79—44no—
256C23×C79—44no—
257C23×C79C2×#4112yes—
258C23×C79C2×#4112yes—
259C23×C79C2×#4112yes—
260C23×C79C2×#4112yes—
261C23×C79C2×#4114yes—
262C23×C79C2×#4112yes—
263C23×C79H(5,𝔽2)12yes—
264C23×C79H(5,𝔽2)12yes—
265C23×C79C2511yescharacteristic
266C22×D79—28no—
267C22×D79—28no—
268C22×D79—28no—
269C22×D79—22no—
270C22×D79—22no—
271C22×D79—22no—
272C22×D79—22no—
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—44no—
276C22×D79—44no—
277C22×D79—44no—
278C22×D79—44no—
279C22×D79C2×#4114yes—
280Q8×C79—416no—
281C2×C4×C79—28no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—22no—
285C2×C4×C79—22no—
286C2×C4×C79—22no—
287C2×C4×C79—22no—
288C2×C4×C79—22no—
289C2×C4×C79—22no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—22no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—44no—
300C2×C4×C79—44no—
301C2×C4×C79—44no—
302C2×C4×C79—44no—
303C2×C4×C79—44no—
304C2×C4×C79C2×#4114yes—
305C22⋊D79—416no—
306C2×Dic79—28no—
307C2×Dic79—28no—
308C2×Dic79—22no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—416no—
328C2×Dic79—44no—
329C2×Dic79—44no—
330C2×Dic79—44no—
331C2×Dic79—44no—
332C2×Dic79—44no—
333C2×Dic79C2×#4114yes—
334C2×Dic79C2×#4114yes—
335C4×D79—416no—
336C22×C79—24no—
337C22×C79—24no—
338C22×C79—24no—
339C22×C79—416no—
340C22×C79—42no—
341C22×C79—42no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79#52914yes—
345C22×C79#52914yes—
346C22×C79#53814yes—
347C22×C79#55114yes—
348C22×C79#55114yes—
349C22×C79#55114yes—
350C22×C79#55514yes—
351C22×C79C22×#4111yescharacteristic
352C22×C79C22×#4111yescharacteristic
353C22×C79C22×#4111yescharacteristic
354C22×C79C22×#4111yescharacteristic
355C22×C79C22×#4111yescharacteristic
356C22×C79C2×H(5,𝔽2)11yescharacteristic
357C22×C79C2×H(5,𝔽2)11yescharacteristic
358C2×D79—24no—
359C2×D79—24no—
360C2×D79—24no—
361C2×D79—416no—
362C2×D79—42no—
363C2×D79—42no—
364C2×D79—42no—
365C2×D79—42no—
366C4×C79—24no—
367C4×C79—42no—
368C4×C79—42no—
369C4×C79—42no—
370C4×C79—42no—
371C4×C79—42no—
372Dic79—24no—
373Dic79—24no—
374Dic79—42no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378Dic79—42no—
379C2×#2572—791nomaximal, Sylow
380C2×C79—44no—
381C2×C79#257218yescomplemented
382C2×C79C2×#52911yescharacteristic
383C2×C79C2×#52911yescharacteristic
384C2×C79C2×#53811yescharacteristic
385C2×C79C2×#55111yescharacteristic
386C2×C79C2×#55111yescharacteristic
387C2×C79C2×#55111yescharacteristic
388C2×C79C2×#55511yescharacteristic
389D79—44no—
390#2572—7916no—
391C2×#400—791no—
392C2×#394—791no—
393C2×#393—791no—
394C2×#393D7911yescharacteristic, complemented
395C2×#391—791no—
396C2×#388—791no—
397C2×#388—791no—
398C2×#386—791no—
399C2×#386—791no—
400C2×#383—791no—
401C2×#383—791no—
402C2×#381—791no—
403C2×#381—791no—
404C2×C4×C22⋊C4—791no—
405C2×C4×C22⋊C4—791no—
406C79C2×#257211yescharacteristic, complemented, Sylow
407C23×Q8C2×D7911yescharacteristic
408C23×D4—791no—
409C24×C4—791no—
410C24×C4—791no—
411C22×C4⋊C4—791no—
412C22×C4⋊C4—791no—
413C22×C22⋊C4—791no—
414C22×C22⋊C4—791no—
415C22×C22⋊C4—791no—
416C22×C22⋊C4—791no—
417C22×C22⋊C4—791no—
418C22×C22⋊C4—791no—
419C22×C22⋊C4—791no—
420C22×C22⋊C4C2×D7911yescharacteristic
421C22×C22⋊C4C2×D7911yescharacteristic
422C22×C22⋊C4C2×D7911yescharacteristic
423C22×C42—791no—
424C22×C42—791no—
425C22×C42—791no—
426#400—798no—
427#394—798no—
428#393—798no—
429#393C2×D7918yescomplemented
430#391—798no—
431#388—798no—
432#388—798no—
433#386—798no—
434#386—798no—
435#383—798no—
436#383—798no—
437#381—798no—
438#381—798no—
439C4×C22⋊C4—798no—
440C4×C22⋊C4—798no—
441C2×#95—791no—
442C2×#95—791no—
443C2×#95—791no—
444C2×#95—791no—
445C2×#95—791no—
446C2×#95—791no—
447C2×#95—791no—
448C2×#95—791no—
449C2×#95—791no—
450C2×#95—791no—
451C2×#95—791no—
452C2×#95—791no—
453C2×#95—791no—
454C2×#95C2×D7911yescharacteristic
455C2×#95C2×D7911yescharacteristic
456C2×#95C2×D7911yescharacteristic
457C25—791no—
458C25C22×D7911yescharacteristic
459C22×Q8—24no—
460C22×Q8—42no—
461C22×Q8—42no—
462C22×Q8C22×D7914yes—
463C22×D4—3162no—
464C22×D4—794no—
465C22×D4—1584no—
466C22×D4—1584no—
467C23×C4—3162no—
468C23×C4—3162no—
469C23×C4—794no—
470C23×C4—794no—
471C23×C4—791no—
472C23×C4—791no—
473C23×C4—791no—
474C23×C4—791no—
475C23×C4—791no—
476C23×C4—791no—
477C23×C4—791no—
478C23×C4—1584no—
479C23×C4—1584no—
480C23×C4—1584no—
481C23×C4—1584no—
482C23×C4C22×D7911yescharacteristic
483C23×C4C22×D7911yescharacteristic
484C23×C4C22×D7911yescharacteristic
485C23×C4C22×D7911yescharacteristic
486C23×C4C22×D7911yescharacteristic
487C23×C4C22×D7911yescharacteristic
488C2×C4⋊C4—3162no—
489C2×C4⋊C4—3162no—
490C2×C4⋊C4—794no—
491C2×C4⋊C4—794no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—3162no—
496C2×C22⋊C4—3162no—
497C2×C22⋊C4—794no—
498C2×C22⋊C4—794no—
499C2×C22⋊C4—794no—
500C2×C22⋊C4—794no—
501C2×C22⋊C4—794no—
502C2×C22⋊C4—794no—
503C2×C22⋊C4—794no—
504C2×C22⋊C4—1584no—
505C2×C22⋊C4—1584no—
506C2×C22⋊C4—1584no—
507C2×C22⋊C4—1584no—
508C2×C22⋊C4—1584no—
509C2×C22⋊C4C22×D7914yes—
510C2×C22⋊C4C22×D7914yes—
511C2×C22⋊C4C22×D7914yes—
512C2×C42—3162no—
513C2×C42—794no—
514C2×C42—794no—
515C2×C42—794no—
516C2×C42—1584no—
517C2×C42—1584no—
518#95—794no—
519#95—794no—
520#95—794no—
521#95—794no—
522#95—794no—
523#95—794no—
524#95—794no—
525#95—794no—
526#95—794no—
527#95—794no—
528#95—794no—
529#95—794no—
530#95—794no—
531#95C22×D7914yes—
532#95C22×D7914yes—
533#95C22×D7914yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—794no—
541C24—792no—
542C24—1582no—
543C24—1582no—
544C24—1582no—
545C24—1582no—
546C24—1582no—
547C24—1582no—
548C24#1192962514yes—
549C24C23×D7912yes—
550C24C23×D7911yescharacteristic
551C2×Q8—28no—
552C2×Q8—44no—
553C2×Q8—44no—
554C2×Q8—416no—
555C2×D4—31616no—
556C2×D4—3164no—
557C2×D4—1588no—
558C2×D4—1588no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—3164no—
577C22×C4—31616no—
578C22×C4—31616no—
579C22×C4—3164no—
580C22×C4—794no—
581C22×C4—794no—
582C22×C4—792no—
583C22×C4—792no—
584C22×C4—792no—
585C22×C4—792no—
586C22×C4—792no—
587C22×C4—792no—
588C22×C4—792no—
589C22×C4—1588no—
590C22×C4—1588no—
591C22×C4—1588no—
592C22×C4—1582no—
593C22×C4—1582no—
594C22×C4—1582no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4—1582no—
599C22×C4—1582no—
600C22×C4—1582no—
601C22×C4—1582no—
602C22×C4—1588no—
603C22×C4—1582no—
604C22×C4—1582no—
605C22×C4—1582no—
606C22×C4—1582no—
607C22×C4—1582no—
608C22×C4—1582no—
609C22×C4—1582no—
610C22×C4—1582no—
611C22×C4—1582no—
612C22×C4#1192962314yes—
613C22×C4C23×D7912yes—
614C22×C4C23×D7912yes—
615C22×C4C23×D7912yes—
616C22×C4C23×D7912yes—
617C22×C4C23×D7912yes—
618C22×C4C23×D7912yes—
619C4⋊C4—3164no—
620C4⋊C4—3164no—
621C22⋊C4—28no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—3164no—
625C22⋊C4—3164no—
626C22⋊C4—1588no—
627C22⋊C4—1588no—
628C22⋊C4—1588no—
629C22⋊C4—1588no—
630C22⋊C4—1588no—
631C42—3164no—
632C42—1588no—
633C42—1588no—
634C23—22no—
635C23—22no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—3164no—
648C23—3164no—
649C23—3164no—
650C23—3164no—
651C23—794no—
652C23—1582no—
653C23—1582no—
654C23—1588no—
655C23—1588no—
656C23—1588no—
657C23—1582no—
658C23—1582no—
659C23—1582no—
660C23—1582no—
661C23#41×D7912yes—
662C23#41×D7912yes—
663C23#41×D7912yes—
664C23C2×#1192962312yes—
665C23C2×#1192962514yes—
666C23C2×#1192962512yes—
667C23#1457920612yes—
668C23#1457920612yes—
669C23C24×D7911yescharacteristic
670Q8—416no—
671D4—31616no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—31616no—
696C2×C4—3164no—
697C2×C4—3164no—
698C2×C4—3164no—
699C2×C4—3164no—
700C2×C4—3164no—
701C2×C4—31616no—
702C2×C4—794no—
703C2×C4—794no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1582no—
708C2×C4—1582no—
709C2×C4—1582no—
710C2×C4—1582no—
711C2×C4—1582no—
712C2×C4—1582no—
713C2×C4—1582no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1582no—
717C2×C4—1582no—
718C2×C4—1582no—
719C2×C4—1582no—
720C2×C4—1582no—
721C2×C4—1588no—
722C2×C4—1588no—
723C2×C4—1582no—
724C2×C4—1582no—
725C2×C4C2×#1192962314yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—31616no—
735C22—3162no—
736C22—3162no—
737C22—3162no—
738C22—3162no—
739C22—1584no—
740C22—1584no—
741C22—1584no—
742C22#1909909214yes—
743C22#1909909914yes—
744C22#1909914814yes—
745C22#1909924014yes—
746C22#1909924014yes—
747C22#1909924314yes—
748C22#1909927514yes—
749C22C2×#41×D7911yescharacteristic
750C22C2×#41×D7911yescharacteristic
751C22C2×#41×D7911yescharacteristic
752C22C22×#1192962311yescharacteristic
753C22C22×#1192962511yescharacteristic
754C22C2×#1457920611yescharacteristic
755C22C2×#1457920611yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—3162no—
763C4—3162no—
764C4—3162no—
765C4—3162no—
766C4—3162no—
767C4—1584no—
768C4—1584no—
769C2—44no—
770C2—3164no—
771C2#2376864518yesdirect product factor
772C2C2×#1909909211yescharacteristic
773C2C2×#1909909911yescharacteristic
774C2C2×#1909914811yescharacteristic
775C2C2×#1909924011yescharacteristic
776C2C2×#1909924011yescharacteristic
777C2C2×#1909924311yescharacteristic
778C2C2×#1909927511yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#393×C79C2
socleC24×C79C24
prime radicalC23×C22⋊D79C22
hypercenterC2×#393D79
hypocenterC79C2×#2572
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. #23768645C2direct (N × H)
2. C2×#19098505C2semidirect
4. C2×#19098474C2semidirect
5. C2×#19098470C2semidirect
6. C2×#19098457C2semidirect
7. C2×#19098452C2semidirect
10. C2×#19098430C2semidirect
11. C2×#19098430C2semidirect
12. C2×#19098425C2semidirect
13. C2×#19098424C2semidirect
14. C2×C22⋊C4×Dic79C2semidirect
15. C2×#19098410C2semidirect
16. C2×#393×C79C2semidirect
32. #19098505C22semidirect
34. #19098474C22semidirect
35. #19098470C22semidirect
36. #19098457C22semidirect
37. #19098452C22semidirect
40. #19098430C22semidirect
41. #19098430C22semidirect
42. #19098425C22semidirect
43. #19098424C22semidirect
44. C22⋊C4×Dic79C22semidirect
45. #19098410C22semidirect
63. #393×C79C22semidirect
381. C2×C79#2572semidirect
394. C2×#393D79semidirect
406. C79C2×#2572semidirect
429. #393C2×D79semidirect
771. C2#23768645direct (N × H)

Maximal subgroups

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

subgroupindex
#237686452
C2×#190985052
C2×#190984792
C2×#190984742
C2×#190984702
C2×#190984572
C2×#190984522
C2×#190984402
C2×#190984392
C2×#190984302
C2×#190984252
C2×#190984242
C2×C22⋊C4×Dic792
C2×#190984102
C2×#393×C792
C2×#257279