Finite Group Databasebeta

← C2×#23773593 #35156510

Subgroups — C2×#23773593 #35156510

Order 20224.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099043C211yesmaximal, characteristic, complemented
2#23773593C2116yesmaximal, direct product factor
3C2×#19098879C211yesmaximal, characteristic, complemented
4C2×#19098874C211yesmaximal, characteristic, complemented
5C2×#19098867C211yesmaximal, characteristic, complemented
6C2×#19098860C211yesmaximal, characteristic, complemented
7C2×#19098760C211yesmaximal, characteristic, complemented
8C2×#19098755C211yesmaximal, characteristic, complemented
9C2×#19098706C211yesmaximal, characteristic, complemented
10C2×#19098706C211yesmaximal, characteristic, complemented
11C2×#19098673C211yesmaximal, characteristic, complemented
12C2×#19098663C211yesmaximal, characteristic, complemented
13C2×C4×#11929612C211yesmaximal, characteristic, complemented
14C2×C4×#11929609C211yesmaximal, characteristic, complemented
15C2×#19098624C211yesmaximal, characteristic, complemented
16C2×#540×C79C211yesmaximal, characteristic, complemented
17C22×#11929624C2211yescharacteristic
18C22×#11929612C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20C22×#11929609C2211yescharacteristic
21C22×#11929609C2211yescharacteristic
22#19099043—24no—
23#19099043C2218yescomplemented
24C2×C4×Dic158C2211yescharacteristic
25C2×C4×Dic158C2211yescharacteristic
26C2×C4×D316C2211yescharacteristic
27C2×C4×D316C2211yescharacteristic
28C2×(C22⋊D79)⋊C4—21no—
29C2×(C22⋊D79)⋊C4—21no—
30C2×#14579119—21no—
31C22×C4⋊Dic79C2211yescharacteristic
32C2×C4⋊C4×D79—21no—
33#19098879C2218yescomplemented
34#19098874C2218yescomplemented
35#19098867C2218yescomplemented
36#19098860C2218yescomplemented
37#19098760C2218yescomplemented
38#19098755C2218yescomplemented
39#19098706C2218yescomplemented
40#19098706C2218yescomplemented
41#19098673C2218yescomplemented
42#19098663C2218yescomplemented
43C4×#11929612C2218yescomplemented
44C4×#11929609C2218yescomplemented
45#19098624C2218yescomplemented
46C2×#14579094C2211yescharacteristic
47C2×#14579094C2211yescharacteristic
48C2×#14579092C2211yescharacteristic
49C2×#14579092C2211yescharacteristic
50C2×C4⋊(C79⋊C8)C2211yescharacteristic
51C2×C4⋊(C79⋊C8)C2211yescharacteristic
52C2×#14579084C2211yescharacteristic
53C2×#14579084C2211yescharacteristic
54C2×#14579082C2211yescharacteristic
55C2×#14579082C2211yescharacteristic
56C2×#14579082C2211yescharacteristic
57C2×#14579082C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×C22⋊(C79⋊C8)C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#540×C79—24no—
65#540×C79C2218yescomplemented
66C2×#127×C79C2211yescharacteristic
67C2×#125×C79C2211yescharacteristic
68C2×#123×C79—21no—
69C2×#123×C79—21no—
70C2×#121×C79—21no—
71C2×#121×C79—21no—
72C2×#121×C79C2211yescharacteristic
73C2×#121×C79C2211yescharacteristic
74C2×C4×D4×C79C2211yescharacteristic
75C2×C4×D4×C79C2211yescharacteristic
76C2×#117×C79C2211yescharacteristic
77C2×#11929624—22no—
78C2×#11929624—24no—
79C2×#11929624—24no—
80C2×#11929624C2314yes—
81C22×Dic158C2311yescharacteristic
82C22×D316C2311yescharacteristic
83C22×C22⋊D79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C22×C4×D79—21no—
88C2×#11929612—24no—
89C2×#11929612—24no—
90C2×#11929612C2314yes—
91C2×#11929612C2314yes—
92C2×#11929609—24no—
93C2×#11929609—24no—
94C2×#11929609C2314yes—
95C2×#11929609C2314yes—
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98C22×C79⋊C8C2311yescharacteristic
99C22×C79⋊C8C2311yescharacteristic
100C4×Dic158—22no—
101C4×Dic158—22no—
102C4×Dic158C2314yes—
103C4×Dic158C2314yes—
104C4×D316—22no—
105C4×D316—22no—
106C4×D316C2314yes—
107C4×D316C2314yes—
108(C22⋊D79)⋊C4—28no—
109(C22⋊D79)⋊C4—28no—
110#14579119—28no—
111C2×C4⋊Dic79—21no—
112C2×C4⋊Dic79—22no—
113C2×C4⋊Dic79C2311yescharacteristic
114C2×C4⋊Dic79C2311yescharacteristic
115C2×C4⋊Dic79C2314yes—
116C2×Dic79⋊C4—21no—
117C2×Dic79⋊C4—21no—
118C4⋊C4×D79—28no—
119C2×(C2×D79)⋊C4—21no—
120C2×(C2×D79)⋊C4—21no—
121C2×C4×Dic79—21no—
122C2×C4×Dic79—21no—
123#14579094C2314yes—
124#14579094C2314yes—
125#14579092C2314yes—
126#14579092C2314yes—
127C4⋊(C79⋊C8)C2314yes—
128C4⋊(C79⋊C8)C2314yes—
129#14579084C2314yes—
130#14579084C2314yes—
131#14579082C2314yes—
132#14579082C2314yes—
133#14579082C2314yes—
134#14579082C2314yes—
135#14579081C2314yes—
136#14579081C2314yes—
137C22⋊(C79⋊C8)C2314yes—
138C22⋊(C79⋊C8)C2314yes—
139#14579072C2314yes—
140C4×C79⋊C8C2314yes—
141C22×D4×C79—21no—
142C22×D4×C79—21no—
143C22×D4×C79—21no—
144C22×D4×C79—21no—
145C22×D4×C79C2311yescharacteristic
146C22×D4×C79C2311yescharacteristic
147C23×C4×C79—21no—
148C23×C4×C79—21no—
149C23×C4×C79C2311yescharacteristic
150#127×C79—22no—
151#127×C79C2314yes—
152#125×C79—22no—
153#125×C79C2314yes—
154#123×C79—28no—
155#123×C79—28no—
156#121×C79—22no—
157#121×C79—22no—
158#121×C79—28no—
159#121×C79—28no—
160#121×C79C2314yes—
161#121×C79C2314yes—
162C4×D4×C79—22no—
163C4×D4×C79—22no—
164C4×D4×C79C2314yes—
165C4×D4×C79C2314yes—
166#117×C79D414yes—
167#117×C79C2314yes—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79D411yescharacteristic
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79D411yescharacteristic
179C2×C22⋊C4×C79D411yescharacteristic
180C2×C42×C79C2311yescharacteristic
181C2×C42×C79C2311yescharacteristic
182C23×D79—21no—
183#11929624—216no—
184#11929624—28no—
185#11929624—28no—
186C2×Dic158—21no—
187C2×Dic158—22no—
188C2×Dic158#4114yes—
189C2×Dic158C2412yes—
190C2×D316—21no—
191C2×D316—22no—
192C2×D316#4114yes—
193C2×D316C2412yes—
194C2×C22⋊D79—28no—
195C2×C22⋊D79—24no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—24no—
200C22×Dic79—82no—
201C2×C4×D79—28no—
202C2×C4×D79—24no—
203C2×C4×D79—24no—
204C2×C4×D79—24no—
205C2×C4×D79—82no—
206C2×C4×D79—82no—
207#11929612—28no—
208#11929612—28no—
209#11929609—28no—
210#11929609—28no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8—22no—
214C2×C79⋊C8—22no—
215C2×C79⋊C8C2412yes—
216C2×C79⋊C8C2412yes—
217C2×C79⋊C8C2412yes—
218C2×C79⋊C8C2412yes—
219C4⋊Dic79—24no—
220C4⋊Dic79—21no—
221C4⋊Dic79—21no—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226(C2×D79)⋊C4—24no—
227(C2×D79)⋊C4—24no—
228C4×Dic79—24no—
229C4×Dic79—24no—
230C24×C79—21no—
231C24×C79—21no—
232C24×C79C2×D411yescharacteristic
233C2×D4×C79—24no—
234C2×D4×C79—24no—
235C2×D4×C79—21no—
236C2×D4×C79—21no—
237C2×D4×C79—24no—
238C2×D4×C79—24no—
239C2×D4×C79—22no—
240C2×D4×C79—22no—
241C2×D4×C79—22no—
242C2×D4×C79—22no—
243C2×D4×C79—82no—
244C2×D4×C79—82no—
245C2×D4×C79—82no—
246C2×D4×C79—82no—
247C2×D4×C79C2412yes—
248C2×D4×C79C2412yes—
249C22×C4×C79—22no—
250C22×C4×C79—22no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79—24no—
254C22×C4×C79—24no—
255C22×C4×C79—82no—
256C22×C4×C79—82no—
257C22×C4×C79C2×D412yes—
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2×D411yescharacteristic
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2412yes—
264C22×C4×C79C2411yescharacteristic
265C4⋊C4×C79—24no—
266C4⋊C4×C79—24no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79—21no—
269C4⋊C4×C79C2×D414yes—
270C4⋊C4×C79C2×D414yes—
271C4⋊C4×C79C2412yes—
272C4⋊C4×C79C2412yes—
273C22⋊C4×C79—24no—
274C22⋊C4×C79—24no—
275C22⋊C4×C79—24no—
276C22⋊C4×C79—24no—
277C22⋊C4×C79C2×D414yes—
278C22⋊C4×C79C2×D414yes—
279C42×C79C2×D412yes—
280C42×C79C2×D412yes—
281C42×C79C2412yes—
282C42×C79C2412yes—
283C23×C79—22no—
284C23×C79—22no—
285C23×C79—22no—
286C23×C79—22no—
287C23×C79—22no—
288C23×C79—42no—
289C23×C79—42no—
290C23×C79—42no—
291C23×C79—42no—
292C23×C79—42no—
293C23×C79—42no—
294C23×C79C22×D412yes—
295C23×C79C22×D411yescharacteristic
296C22×D79—24no—
297C22×D79—22no—
298C22×D79—42no—
299C22×D79—42no—
300D4×C79—22no—
301D4×C79—22no—
302D4×C79—22no—
303D4×C79—22no—
304D4×C79—42no—
305D4×C79—42no—
306D4×C79—84no—
307D4×C79—84no—
308D4×C79—84no—
309D4×C79—84no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—22no—
314C2×C4×C79—22no—
315C2×C4×C79—24no—
316C2×C4×C79—22no—
317C2×C4×C79—22no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—42no—
321C2×C4×C79—42no—
322C2×C4×C79—84no—
323C2×C4×C79—84no—
324C2×C4×C79C22×D412yes—
325C2×C4×C79C22×D412yes—
326C2×C4×C79C22×D412yes—
327C2×C4×C79C22×D412yes—
328C2×C4×C79C22×D412yes—
329C2×C4×C79C22×D411yescharacteristic
330C2×C4×C79C2×#4112yes—
331C2×C4×C79C2×#4112yes—
332C2×C4×C79C2511yescharacteristic
333C22⋊D79—216no—
334C2×Dic79—24no—
335C2×Dic79—22no—
336C2×Dic79—22no—
337C2×Dic79—22no—
338C2×Dic79—42no—
339C2×Dic79—42no—
340C2×Dic79—84no—
341D316—24no—
342D316—22no—
343D316C2×#4114yes—
344C4×D79—216no—
345C4×D79—84no—
346C4×D79—84no—
347Dic158—24no—
348Dic158—22no—
349Dic158C2×#4114yes—
350C79⋊C8—22no—
351C79⋊C8—22no—
352C79⋊C8—22no—
353C79⋊C8—22no—
354C22×C79—22no—
355C22×C79—22no—
356C22×C79—22no—
357C22×C79—44no—
358C22×C79—42no—
359C22×C79—42no—
360C22×C79—42no—
361C22×C79—42no—
362C22×C79—42no—
363C22×C79—42no—
364C22×C79—84no—
365C22×C79—84no—
366C22×C79#52512yes—
367C22×C79#57612yes—
368C22×C79#57712yes—
369C22×C79C23×D411yescharacteristic
370C2×D79—24no—
371C2×D79—48no—
372C2×D79—42no—
373C2×D79—42no—
374C4×C79—22no—
375C4×C79—22no—
376C4×C79—22no—
377C4×C79—22no—
378C4×C79—22no—
379C4×C79—42no—
380C4×C79—42no—
381C4×C79#52512yes—
382C4×C79C22×#4111yescharacteristic
383C4×C79C22×#4111yescharacteristic
384Dic79—24no—
385Dic79—42no—
386Dic79—42no—
387C2×#3119—791nomaximal, Sylow
388C2×C79—42no—
389C2×C79—82no—
390C2×C79—82no—
391C2×C79#311914yescomplemented
392C2×C79C2×#52511yescharacteristic
393C2×C79C2×#57611yescharacteristic
394C2×C79C2×#57711yescharacteristic
395D79—44no—
396C2×#540D7911yescharacteristic, complemented
397C2×#520—791no—
398#3119—7916no—
399C2×#481—791no—
400C2×#480—791no—
401C2×#479—791no—
402C2×#478—791no—
403C2×#460—791no—
404C2×#459—791no—
405C2×#449—791no—
406C2×#449—791no—
407C2×#442—791no—
408C2×#440—791no—
409C2×C4×SD16—791no—
410C2×C4×D8—791no—
411C2×#433—791no—
412C79C2×#311911yescharacteristic, complemented, Sylow
413C22×#41—791no—
414C22×SD16—791no—
415C22×SD16—791no—
416C22×D8—791no—
417C22×D8—791no—
418#540—24no—
419#540C2×D7918yescomplemented
420C2×#127C2×D7911yescharacteristic
421C2×#125C2×D7911yescharacteristic
422C2×#123—21no—
423C2×#123—21no—
424C2×#121—21no—
425C2×#121—21no—
426C2×#121C2×D7911yescharacteristic
427C2×#121C2×D7911yescharacteristic
428#520—798no—
429#520—1584no—
430C2×C4×Q8—791no—
431C2×C4×Q8—791no—
432C2×C4×D4—791no—
433C2×C4×D4—791no—
434C2×C4×D4—1581no—
435C2×C4×D4—1581no—
436C2×C4×D4C2×D7911yescharacteristic
437C2×C4×D4C2×D7911yescharacteristic
438C2×#117—1581no—
439C2×#117C2×D7911yescharacteristic
440C22×C4⋊C4—791no—
441C22×C4⋊C4—1581no—
442#481—798no—
443#480—798no—
444#479—798no—
445#478—798no—
446#460—798no—
447#459—798no—
448#449—798no—
449#449—798no—
450#442—798no—
451#440—798no—
452C4×SD16—798no—
453C4×D8—798no—
454#433—798no—
455C2×#107—791no—
456C2×#107—791no—
457C2×#106—791no—
458C2×#106—791no—
459C2×C4⋊C8—791no—
460C2×C4⋊C8—791no—
461C2×#103—791no—
462C2×#103—791no—
463C2×#102—791no—
464C2×#102—791no—
465C2×#102—791no—
466C2×#102—791no—
467C2×#102—791no—
468C2×#102—791no—
469C2×C22⋊C8—791no—
470C2×C22⋊C8—791no—
471C2×#97—791no—
472C2×C4×C8—791no—
473C2×#41—794no—
474C2×#41—1584no—
475C2×#41—1584no—
476C2×#41—1582no—
477C22×Q8—791no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—791no—
483C22×D4—1581no—
484C22×D4C22×D7911yescharacteristic
485C22×D4C22×D7911yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—1581no—
489C23×C4—1581no—
490C23×C4—1581no—
491C23×C4—1581no—
492C23×C4C22×D7911yescharacteristic
493C2×SD16—794no—
494C2×SD16—794no—
495C2×SD16—1584no—
496C2×SD16—1584no—
497C2×D8—794no—
498C2×D8—794no—
499C2×D8—1584no—
500C2×D8—1584no—
501C22×C8—791no—
502C22×C8—791no—
503C22×C8—791no—
504C22×C8—791no—
505#127—22no—
506#127C22×D7914yes—
507#125—22no—
508#125C22×D7914yes—
509#123—28no—
510#123—28no—
511#121—22no—
512#121—22no—
513#121—28no—
514#121—28no—
515#121C22×D7914yes—
516#121C22×D7914yes—
517C4×Q8—794no—
518C4×Q8—794no—
519C4×Q8—1582no—
520C4×Q8—1582no—
521C4×D4—22no—
522C4×D4—22no—
523C4×D4—794no—
524C4×D4—794no—
525C4×D4—1588no—
526C4×D4—1588no—
527C4×D4—1582no—
528C4×D4—1582no—
529C4×D4C22×D7914yes—
530C4×D4C22×D7914yes—
531#117—1588no—
532#117C22⋊D7914yes—
533#117C22×D7914yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—791no—
537C2×C4⋊C4—791no—
538C2×C4⋊C4—794no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4—1582no—
541C2×C4⋊C4—1581no—
542C2×C4⋊C4—1581no—
543C2×C4⋊C4—1588no—
544C2×C4⋊C4C22⋊D7911yescharacteristic
545C2×C4⋊C4C22⋊D7911yescharacteristic
546C2×C4⋊C4C22×D7911yescharacteristic
547C2×C4⋊C4C22×D7911yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1581no—
553C2×C22⋊C4—1581no—
554C2×C22⋊C4C22⋊D7911yescharacteristic
555C2×C22⋊C4C22⋊D7911yescharacteristic
556C2×C42—1581no—
557C2×C42—1581no—
558C2×C42C22×D7911yescharacteristic
559C2×C42C22×D7911yescharacteristic
560#107—794no—
561#107—794no—
562#106—794no—
563#106—794no—
564C4⋊C8—794no—
565C4⋊C8—794no—
566#103—794no—
567#103—794no—
568#102—794no—
569#102—794no—
570#102—794no—
571#102—794no—
572#102—794no—
573#102—794no—
574C22⋊C8—794no—
575C22⋊C8—794no—
576#97—794no—
577C4×C8—794no—
578C24—21no—
579C24—21no—
580C24—1581no—
581C24C2×C22⋊D7911yescharacteristic
582#41—1588no—
583#41—1588no—
584#41—15816no—
585C2×Q8—794no—
586C2×Q8—792no—
587C2×Q8—1582no—
588C2×Q8—1581no—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—82no—
600C2×D4—82no—
601C2×D4—82no—
602C2×D4—82no—
603C2×D4—794no—
604C2×D4—792no—
605C2×D4—1588no—
606C2×D4—1584no—
607C2×D4—1582no—
608C2×D4—1581no—
609C2×D4C23×D7912yes—
610C2×D4C23×D7912yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—6322no—
620C22×C4—6322no—
621C22×C4—6322no—
622C22×C4—1588no—
623C22×C4—1581no—
624C22×C4—1581no—
625C22×C4—1584no—
626C22×C4—1584no—
627C22×C4—1584no—
628C22×C4—1581no—
629C22×C4—1584no—
630C22×C4C2×C22⋊D7912yes—
631C22×C4C2×C22⋊D7911yescharacteristic
632C22×C4C2×C22⋊D7911yescharacteristic
633C22×C4C2×C22⋊D7911yescharacteristic
634C22×C4C2×C22⋊D7911yescharacteristic
635C22×C4C2×C22⋊D7911yescharacteristic
636C22×C4C23×D7912yes—
637C22×C4C23×D7911yescharacteristic
638SD16—1588no—
639SD16—1588no—
640D8—1588no—
641D8—1588no—
642C2×C8—792no—
643C2×C8—792no—
644C2×C8—792no—
645C2×C8—792no—
646C2×C8—1582no—
647C2×C8—1582no—
648C2×C8—1582no—
649C2×C8—1582no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—792no—
655C4⋊C4—792no—
656C4⋊C4—1584no—
657C4⋊C4—1584no—
658C4⋊C4—1584no—
659C4⋊C4—1581no—
660C4⋊C4—1581no—
661C4⋊C4C2×C22⋊D7914yes—
662C4⋊C4C2×C22⋊D7914yes—
663C4⋊C4C23×D7912yes—
664C4⋊C4C23×D7912yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—1584no—
670C22⋊C4—1584no—
671C22⋊C4C2×C22⋊D7914yes—
672C22⋊C4C2×C22⋊D7914yes—
673C42—1584no—
674C42—1584no—
675C42C2×C22⋊D7912yes—
676C42C2×C22⋊D7912yes—
677C42C23×D7912yes—
678C42C23×D7912yes—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—3162no—
691C23—3162no—
692C23—1584no—
693C23—1582no—
694C23C22×C22⋊D7912yes—
695C23C22×C22⋊D7911yescharacteristic
696Q8—794no—
697Q8—1584no—
698Q8—1582no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—22no—
703D4—42no—
704D4—42no—
705D4—84no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—794no—
710D4—15816no—
711D4—1584no—
712D4—1582no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—3162no—
728C2×C4—3162no—
729C2×C4—6324no—
730C2×C4—6324no—
731C2×C4—6324no—
732C2×C4—15816no—
733C2×C4—1582no—
734C2×C4—1582no—
735C2×C4—1584no—
736C2×C4—1582no—
737C2×C4C22×C22⋊D7912yes—
738C2×C4C22×C22⋊D7912yes—
739C2×C4C22×C22⋊D7912yes—
740C2×C4C22×C22⋊D7912yes—
741C2×C4C22×C22⋊D7912yes—
742C2×C4C22×C22⋊D7911yescharacteristic
743C2×C4#41×D7912yes—
744C2×C4#41×D7912yes—
745C2×C4C24×D7911yescharacteristic
746C8—1582no—
747C8—1582no—
748C8—1582no—
749C8—1582no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—84no—
762C22—3162no—
763C22—3162no—
764C22—3168no—
765C22—1584no—
766C22#1909907012yes—
767C22#1909936612yes—
768C22#1909937412yes—
769C22C23×C22⋊D7911yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—42no—
776C4—42no—
777C4—3162no—
778C4—3162no—
779C4—1584no—
780C4#1909907012yes—
781C4C2×#41×D7911yescharacteristic
782C4C2×#41×D7911yescharacteristic
783C2—42no—
784C2—82no—
785C2—82no—
786C2—3164no—
787C2#2377359314yesdirect product factor
788C2C2×#1909907011yescharacteristic
789C2C2×#1909936611yescharacteristic
790C2C2×#1909937411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#540×C79C2
socleC23×C79C22×D4
hypercenterC2×#540D79
hypocenterC79C2×#3119
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#19099043C2semidirect
2. #23773593C2direct (N × H)
3. C2×#19098879C2semidirect
4. C2×#19098874C2semidirect
5. C2×#19098867C2semidirect
6. C2×#19098860C2semidirect
7. C2×#19098760C2semidirect
8. C2×#19098755C2semidirect
9. C2×#19098706C2semidirect
10. C2×#19098706C2semidirect
11. C2×#19098673C2semidirect
12. C2×#19098663C2semidirect
13. C2×C4×#11929612C2semidirect
14. C2×C4×#11929609C2semidirect
15. C2×#19098624C2semidirect
16. C2×#540×C79C2semidirect
23. #19099043C22semidirect
33. #19098879C22semidirect
34. #19098874C22semidirect
35. #19098867C22semidirect
36. #19098860C22semidirect
37. #19098760C22semidirect
38. #19098755C22semidirect
39. #19098706C22semidirect
40. #19098706C22semidirect
41. #19098673C22semidirect
42. #19098663C22semidirect
43. C4×#11929612C22semidirect
44. C4×#11929609C22semidirect
45. #19098624C22semidirect
65. #540×C79C22semidirect
391. C2×C79#3119semidirect
396. C2×#540D79semidirect
412. C79C2×#3119semidirect
419. #540C2×D79semidirect
787. C2#23773593direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990432
#237735932
C2×#190988792
C2×#190988742
C2×#190988672
C2×#190988602
C2×#190987602
C2×#190987552
C2×#190987062
C2×#190986732
C2×#190986632
C2×C4×#119296122
C2×C4×#119296092
C2×#190986242
C2×#540×C792
C2×#311979