Finite Group Databasebeta

← C2×#23767964 #34457249

Subgroups — C2×#23767964 #34457249

Order 20224.

2658 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#23767964C2116yesmaximal, direct product factor
2C2×C79⋊#401C211yesmaximal, characteristic, complemented
3C2×#19098505C211yesmaximal, characteristic, complemented
4C2×#19098491C211yesmaximal, characteristic, complemented
5C2×#19098488C211yesmaximal, characteristic, complemented
6C2×#19098457C211yesmaximal, characteristic, complemented
7C2×#19098456C211yesmaximal, characteristic, complemented
8C2×#19098448C211yesmaximal, characteristic, complemented
9C2×#19098443C211yesmaximal, characteristic
10C2×#19098443C211yesmaximal, characteristic
11C2×#19098435C211yesmaximal, characteristic, complemented
12C2×#19098430C211yesmaximal, characteristic, complemented
13C2×#19098423C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic79C211yesmaximal, characteristic, complemented
15C22×C79⋊#95C211yesmaximal, characteristic, complemented
16C2×#386×C79C211yesmaximal, characteristic
17C24×Dic79C2211yescharacteristic
18C24×Dic79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×Dic79⋊C4C2211yescharacteristic
22C22×Dic79⋊C4C2211yescharacteristic
23C22×C22⋊Dic79C2211yescharacteristic
24C22×C22⋊Dic79C2211yescharacteristic
25C22×C22⋊Dic79C2211yescharacteristic
26C22×C22⋊Dic79C2211yescharacteristic
27C22×C22⋊Dic79C2211yescharacteristic
28C22×C22⋊Dic79C2211yescharacteristic
29C22×C4×Dic79C2211yescharacteristic
30C22×C4×Dic79C2211yescharacteristic
31C79⋊#401C2218yescomplemented
32#19098505C2218yescomplemented
33#19098491C2218yescomplemented
34#19098488C2218yescomplemented
35#19098457C2218yescomplemented
36#19098456C2218yescomplemented
37#19098448C2218yescomplemented
38#19098443C2218yes—
39#19098443C2218yes—
40#19098435C2218yescomplemented
41#19098430C2218yescomplemented
42#19098423C2218yescomplemented
43C22⋊C4×Dic79C2218yescomplemented
44C2×C79⋊#95C2211yescharacteristic
45C2×C79⋊#95C2211yescharacteristic
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⋊#95C2218yescomplemented
59C23×D4×C79C2211yescharacteristic
60C24×C4×C79C2211yescharacteristic
61C22×C22⋊C4×C79C2211yescharacteristic
62C22×C22⋊C4×C79C2211yescharacteristic
63C22×C22⋊C4×C79C2211yescharacteristic
64#386×C79C2218yes—
65C2×#95×C79C2211yescharacteristic
66C2×#95×C79C2211yescharacteristic
67C23×Dic79—24no—
68C23×Dic79—24no—
69C23×Dic79—24no—
70C23×Dic79—42no—
71C23×Dic79—42no—
72C23×Dic79—42no—
73C23×Dic79C2311yescharacteristic
74C23×Dic79C2311yescharacteristic
75C23×Dic79C2311yescharacteristic
76C23×Dic79C2311yescharacteristic
77C23×Dic79C2311yescharacteristic
78C23×Dic79C2311yescharacteristic
79C23×Dic79C2311yescharacteristic
80C23×Dic79C2314yes—
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2314yes—
83C2×C4⋊Dic79—24no—
84C2×C4⋊Dic79—42no—
85C2×C4⋊Dic79C2314yes—
86C2×C4⋊Dic79C2314yes—
87C2×Dic79⋊C4—42no—
88C2×Dic79⋊C4—42no—
89C2×Dic79⋊C4C2314yes—
90C2×Dic79⋊C4C2314yes—
91C2×C22⋊Dic79—24no—
92C2×C22⋊Dic79—24no—
93C2×C22⋊Dic79—24no—
94C2×C22⋊Dic79—42no—
95C2×C22⋊Dic79—42no—
96C2×C22⋊Dic79—42no—
97C2×C22⋊Dic79C2314yes—
98C2×C22⋊Dic79C2314yes—
99C2×C22⋊Dic79C2314yes—
100C2×C22⋊Dic79C2314yes—
101C2×C22⋊Dic79C2314yes—
102C2×C22⋊Dic79C2314yes—
103C2×C4×Dic79—24no—
104C2×C4×Dic79—42no—
105C2×C4×Dic79C2314yes—
106C2×C4×Dic79C2314yes—
107C79⋊#95C2314yes—
108C79⋊#95C2314yes—
109C79⋊#95C2314yes—
110C79⋊#95C2314yes—
111C79⋊#95C2314yes—
112C79⋊#95C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C25×C79C2311yescharacteristic
122C25×C79C2311yescharacteristic
123C22×D4×C79—24no—
124C22×D4×C79—24no—
125C22×D4×C79—24no—
126C22×D4×C79C2314yes—
127C23×C4×C79—24no—
128C23×C4×C79—24no—
129C23×C4×C79—42no—
130C23×C4×C79C2311yescharacteristic
131C23×C4×C79C2311yescharacteristic
132C23×C4×C79C2311yescharacteristic
133C23×C4×C79C2311yescharacteristic
134C23×C4×C79C2314yes—
135C23×C4×C79C2311yescharacteristic
136C2×C22⋊C4×C79—24no—
137C2×C22⋊C4×C79—24no—
138C2×C22⋊C4×C79—42no—
139C2×C22⋊C4×C79C2314yes—
140C2×C22⋊C4×C79C2314yes—
141C2×C22⋊C4×C79C2314yes—
142#95×C79C2314yes—
143#95×C79C2314yes—
144C22×Dic79—28no—
145C22×Dic79—22no—
146C22×Dic79—22no—
147C22×Dic79—22no—
148C22×Dic79—22no—
149C22×Dic79—22no—
150C22×Dic79—22no—
151C22×Dic79—22no—
152C22×Dic79—22no—
153C22×Dic79—22no—
154C22×Dic79—22no—
155C22×Dic79—28no—
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—22no—
168C22×Dic79—22no—
169C22×Dic79—22no—
170C22×Dic79—44no—
171C22×Dic79—44no—
172C22×Dic79—44no—
173C22×Dic79—416no—
174C22×Dic79—416no—
175C22×Dic79#4114yes—
176C22×Dic79C2412yes—
177C22×Dic79C2412yes—
178C22×Dic79C2412yes—
179C22×Dic79C2412yes—
180C22×Dic79C2412yes—
181C22×Dic79C2412yes—
182C22×Dic79C2412yes—
183C22×Dic79C2412yes—
184C4⋊Dic79—28no—
185C4⋊Dic79—44no—
186Dic79⋊C4—44no—
187Dic79⋊C4—44no—
188C22⋊Dic79—28no—
189C22⋊Dic79—28no—
190C22⋊Dic79—28no—
191C22⋊Dic79—44no—
192C22⋊Dic79—44no—
193C22⋊Dic79—44no—
194C4×Dic79—28no—
195C4×Dic79—44no—
196C24×C79—22no—
197C24×C79—22no—
198C24×C79—22no—
199C24×C79—22no—
200C24×C79—22no—
201C24×C79—22no—
202C24×C79—22no—
203C24×C79—22no—
204C24×C79—22no—
205C24×C79—22no—
206C24×C79—22no—
207C24×C79#4114yes—
208C24×C79#4114yes—
209C24×C79#4114yes—
210C24×C79C2412yes—
211C24×C79C2412yes—
212C24×C79C2411yescharacteristic
213C2×D4×C79—28no—
214C2×D4×C79—28no—
215C2×D4×C79—28no—
216C2×D4×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—28no—
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—28no—
233C22×C4×C79—44no—
234C22×C4×C79—416no—
235C22×C4×C79#4114yes—
236C22×C4×C79C2412yes—
237C22×C4×C79C2412yes—
238C22×C4×C79C2412yes—
239C22×C4×C79C2412yes—
240C22×C4×C79C2412yes—
241C22⋊C4×C79—28no—
242C22⋊C4×C79—28no—
243C22⋊C4×C79—44no—
244C23×C79—28no—
245C23×C79—28no—
246C23×C79—28no—
247C23×C79—28no—
248C23×C79—28no—
249C23×C79—28no—
250C23×C79—22no—
251C23×C79—22no—
252C23×C79—22no—
253C23×C79—22no—
254C23×C79—22no—
255C23×C79—22no—
256C23×C79—22no—
257C23×C79—22no—
258C23×C79—22no—
259C23×C79—22no—
260C23×C79—22no—
261C23×C79—44no—
262C23×C79—44no—
263C23×C79—44no—
264C23×C79—44no—
265C23×C79—44no—
266C23×C79—44no—
267C23×C79—44no—
268C23×C79#126116yes—
269C23×C79C2×#4112yes—
270C23×C79C2×#4114yes—
271C23×C79C2×#4114yes—
272C23×C79C2×#4112yes—
273C23×C79C2×#4112yes—
274C23×C79C2×#4112yes—
275C23×C79C2×#4114yes—
276C23×C79C2×#4112yes—
277C23×C79H(5,𝔽2)12yes—
278C23×C79H(5,𝔽2)12yes—
279C23×C79C2511yescharacteristic
280D4×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—416no—
297C2×C4×C79—44no—
298C2×C4×C79—44no—
299C2×C4×C79—44no—
300C2×C4×C79—44no—
301C2×C4×C79C2×#4114yes—
302C2×Dic79—28no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—22no—
307C2×Dic79—22no—
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—416no—
327C2×Dic79—416no—
328C2×Dic79—44no—
329C2×Dic79—44no—
330C2×Dic79—44no—
331C2×Dic79—44no—
332C2×Dic79—44no—
333C2×Dic79—44no—
334C2×Dic79—44no—
335C2×Dic79C2×#4114yes—
336C22×C79—24no—
337C22×C79—24no—
338C22×C79—24no—
339C22×C79—24no—
340C22×C79—24no—
341C22×C79—24no—
342C22×C79—232no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79—42no—
347C22×C79—42no—
348C22×C79—42no—
349C22×C79—42no—
350C22×C79—88no—
351C22×C79C2×#12618yes—
352C22×C79C2×#12614yes—
353C22×C79#52914yes—
354C22×C79#53814yes—
355C22×C79#55114yes—
356C22×C79#55114yes—
357C22×C79#55314yes—
358C22×C79#55314yes—
359C22×C79C22×#4111yescharacteristic
360C22×C79C22×#4111yescharacteristic
361C22×C79C22×#4111yescharacteristic
362C22×C79C22×#4111yescharacteristic
363C22×C79C22×#4111yescharacteristic
364C22×C79C2×H(5,𝔽2)11yescharacteristic
365C22×C79C2×H(5,𝔽2)11yescharacteristic
366C4×C79—24no—
367C4×C79—42no—
368C4×C79—42no—
369C4×C79—42no—
370C4×C79—42no—
371Dic79—24no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376Dic79—42no—
377Dic79—42no—
378Dic79—42no—
379C2×#2510—791nomaximal, Sylow
380C2×C79—28no—
381C2×C79—82no—
382C2×C79#251018yescomplemented
383C2×C79C22×#12611yescharacteristic
384C2×C79C2×#52911yescharacteristic
385C2×C79C2×#53811yescharacteristic
386C2×C79C2×#55111yescharacteristic
387C2×C79C2×#55111yescharacteristic
388C2×C79C2×#55311yescharacteristic
389C2×C79C2×#55311yescharacteristic
390#2510—7916no—
391C2×#401—791no—
392C2×#400—791no—
393C2×#397—791no—
394C2×#397—791no—
395C2×#388—791no—
396C2×#388—791no—
397C2×#387—791no—
398C2×#386—791no—
399C2×#386—791no—
400C2×#386D7911yescharacteristic
401C2×#385—791no—
402C2×#383—791no—
403C2×#380—791no—
404C2×C4×C22⋊C4—791no—
405C22×#95—791no—
406C79C2×#251011yescharacteristic, complemented, Sylow
407C23×D4C2×D7911yescharacteristic
408C24×C4—791no—
409C24×C4—791no—
410C24×C4C2×D7911yescharacteristic
411C22×C4⋊C4—791no—
412C22×C4⋊C4—791no—
413C22×C4⋊C4—791no—
414C22×C4⋊C4—791no—
415C22×C22⋊C4—791no—
416C22×C22⋊C4—791no—
417C22×C22⋊C4—791no—
418C22×C22⋊C4—791no—
419C22×C22⋊C4—791no—
420C22×C22⋊C4—791no—
421C22×C22⋊C4C2×D7911yescharacteristic
422C22×C22⋊C4C2×D7911yescharacteristic
423C22×C22⋊C4C2×D7911yescharacteristic
424C22×C42—791no—
425C22×C42—791no—
426#401—798no—
427#400—798no—
428#397—798no—
429#397—798no—
430#388—798no—
431#388—798no—
432#387—798no—
433#386—798no—
434#386—798no—
435#386C2×D7918yes—
436#385—798no—
437#383—798no—
438#380—798no—
439C4×C22⋊C4—798no—
440C2×#95—791no—
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×#95—798no—
455C2×#95C2×D7911yescharacteristic
456C2×#95C2×D7911yescharacteristic
457C25C22×D7911yescharacteristic
458C25C22×D7911yescharacteristic
459C22×D4—24no—
460C22×D4—24no—
461C22×D4—24no—
462C22×D4C22×D7914yes—
463C23×C4—24no—
464C23×C4—24no—
465C23×C4—42no—
466C23×C4—3162no—
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—791no—
479C23×C4—1584no—
480C23×C4—1584no—
481C23×C4—1584no—
482C23×C4C22×D7911yescharacteristic
483C23×C4C22×D7911yescharacteristic
484C23×C4C22×D7911yescharacteristic
485C23×C4C22×D7911yescharacteristic
486C23×C4C22×D7914yes—
487C23×C4C22×D7911yescharacteristic
488C2×C4⋊C4—3162no—
489C2×C4⋊C4—3162no—
490C2×C4⋊C4—3162no—
491C2×C4⋊C4—794no—
492C2×C4⋊C4—794no—
493C2×C4⋊C4—794no—
494C2×C4⋊C4—794no—
495C2×C4⋊C4—1584no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—3162no—
500C2×C22⋊C4—3162no—
501C2×C22⋊C4—3162no—
502C2×C22⋊C4—794no—
503C2×C22⋊C4—794no—
504C2×C22⋊C4—794no—
505C2×C22⋊C4—794no—
506C2×C22⋊C4—794no—
507C2×C22⋊C4—794no—
508C2×C22⋊C4—1584no—
509C2×C22⋊C4—1584no—
510C2×C22⋊C4—1584no—
511C2×C22⋊C4C22×D7914yes—
512C2×C22⋊C4C22×D7914yes—
513C2×C22⋊C4C22×D7914yes—
514C2×C42—3162no—
515C2×C42—794no—
516C2×C42—794no—
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#95—794no—
532#95C22×D7914yes—
533#95C22×D7914yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24#1192962314yes—
546C24#1192962314yes—
547C24#1192962414yes—
548C24C23×D7912yes—
549C24C23×D7912yes—
550C24C23×D7911yescharacteristic
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—416no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
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—28no—
571C22×C4—44no—
572C22×C4—416no—
573C22×C4—31616no—
574C22×C4—31616no—
575C22×C4—3164no—
576C22×C4—3164no—
577C22×C4—3164no—
578C22×C4—794no—
579C22×C4—792no—
580C22×C4—792no—
581C22×C4—792no—
582C22×C4—792no—
583C22×C4—792no—
584C22×C4—792no—
585C22×C4—792no—
586C22×C4—792no—
587C22×C4—1588no—
588C22×C4—1582no—
589C22×C4—1582no—
590C22×C4—1582no—
591C22×C4—1582no—
592C22×C4—1582no—
593C22×C4—1588no—
594C22×C4—1582no—
595C22×C4—1582no—
596C22×C4—1582no—
597C22×C4—1588no—
598C22×C4—1582no—
599C22×C4—1582no—
600C22×C4—1582no—
601C22×C4—1582no—
602C22×C4—1582no—
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—1582no—
613C22×C4#1192962314yes—
614C22×C4C23×D7912yes—
615C22×C4C23×D7912yes—
616C22×C4C23×D7912yes—
617C22×C4C23×D7912yes—
618C22×C4C23×D7912yes—
619C4⋊C4—3164no—
620C4⋊C4—3164no—
621C4⋊C4—3164no—
622C4⋊C4—1588no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—44no—
626C22⋊C4—3164no—
627C22⋊C4—3164no—
628C22⋊C4—3164no—
629C22⋊C4—1588no—
630C22⋊C4—1588no—
631C22⋊C4—1588no—
632C42—3164no—
633C42—1588no—
634C23—22no—
635C23—22no—
636C23—28no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—28no—
641C23—28no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23#14579154116yes—
659C23#41×D7912yes—
660C23C2×#1192962314yes—
661C23C2×#1192962314yes—
662C23C2×#1192962312yes—
663C23C2×#1192962312yes—
664C23C2×#1192962312yes—
665C23C2×#1192962414yes—
666C23C2×#1192962412yes—
667C23#1457920612yes—
668C23#1457920712yes—
669C23C24×D7911yescharacteristic
670D4—416no—
671C2×C4—22no—
672C2×C4—28no—
673C2×C4—22no—
674C2×C4—22no—
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—416no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—31616no—
692C2×C4—3164no—
693C2×C4—3164no—
694C2×C4—3164no—
695C2×C4—3164no—
696C2×C4—3164no—
697C2×C4—3164no—
698C2×C4—3164no—
699C2×C4—31616no—
700C2×C4—794no—
701C2×C4—1582no—
702C2×C4—1582no—
703C2×C4—1582no—
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—1582no—
722C2×C4—1582no—
723C2×C4—1588no—
724C2×C4—1582no—
725C2×C4C2×#1192962314yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—232no—
732C22—24no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—88no—
741C22C2×#1457915418yes—
742C22C2×#1457915414yes—
743C22#1909909414yes—
744C22#1909915014yes—
745C22#1909923614yes—
746C22#1909924414yes—
747C22#1909925914yes—
748C22#1909926214yes—
749C22C2×#41×D7911yescharacteristic
750C22C22×#1192962311yescharacteristic
751C22C22×#1192962311yescharacteristic
752C22C22×#1192962311yescharacteristic
753C22C22×#1192962411yescharacteristic
754C22C2×#1457920611yescharacteristic
755C22C2×#1457920711yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—3162no—
762C4—3162no—
763C4—3162no—
764C4—3162no—
765C4—3162no—
766C4—3162no—
767C4—3162no—
768C4—1584no—
769C2—28no—
770C2—82no—
771C2#2376796418yesdirect product factor
772C2C22×#1457915411yescharacteristic
773C2C2×#1909909411yescharacteristic
774C2C2×#1909915011yescharacteristic
775C2C2×#1909923611yescharacteristic
776C2C2×#1909924411yescharacteristic
777C2C2×#1909925911yescharacteristic
778C2C2×#1909926211yescharacteristic
subgroupG/H
centerC24C23×D79
commutator, cosocleC23×C79C25
FrattiniC23C24×D79
FittingC2×#386×C79C2
socleC24×C79C24
prime radicalC23×D4×C79C22
hypercenterC2×#386D79
hypocenterC79C2×#2510
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. #23767964C2direct (N × H)
2. C2×C79⋊#401C2semidirect
3. C2×#19098505C2semidirect
4. C2×#19098491C2semidirect
5. C2×#19098488C2semidirect
6. C2×#19098457C2semidirect
7. C2×#19098456C2semidirect
8. C2×#19098448C2semidirect
11. C2×#19098435C2semidirect
12. C2×#19098430C2semidirect
13. C2×#19098423C2semidirect
14. C2×C22⋊C4×Dic79C2semidirect
15. C22×C79⋊#95C2semidirect
31. C79⋊#401C22semidirect
32. #19098505C22semidirect
33. #19098491C22semidirect
34. #19098488C22semidirect
35. #19098457C22semidirect
36. #19098456C22semidirect
37. #19098448C22semidirect
40. #19098435C22semidirect
41. #19098430C22semidirect
42. #19098423C22semidirect
43. C22⋊C4×Dic79C22semidirect
58. C2×C79⋊#95C22semidirect
382. C2×C79#2510semidirect
406. C79C2×#2510semidirect
771. C2#23767964direct (N × H)

Maximal subgroups

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

subgroupindex
#237679642
C2×C79⋊#4012
C2×#190985052
C2×#190984912
C2×#190984882
C2×#190984572
C2×#190984562
C2×#190984482
C2×#190984432
C2×#190984352
C2×#190984302
C2×#190984232
C2×C22⋊C4×Dic792
C22×C79⋊#952
C2×#386×C792
C2×#251079