Finite Group Databasebeta

← C2×#23773662 #35156584

Subgroups — C2×#23773662 #35156584

Order 20224.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099184C211yesmaximal, characteristic, complemented
2#23773662C2116yesmaximal, direct product factor
3C2×#19098898C211yesmaximal, characteristic, complemented
4C2×#19098876C211yesmaximal, characteristic, complemented
5C2×#19098858C211yesmaximal, characteristic, complemented
6C2×#19098843C211yesmaximal, characteristic, complemented
7C2×#19098785C211yesmaximal, characteristic, complemented
8C2×#19098778C211yesmaximal, characteristic, complemented
9C2×#19098725C211yesmaximal, characteristic, complemented
10C2×#19098708C211yesmaximal, characteristic
11C2×#19098663C211yesmaximal, characteristic, complemented
12C2×#19098661C211yesmaximal, characteristic, complemented
13C2×C4×#11929614C211yesmaximal, characteristic, complemented
14C2×C4×#11929609C211yesmaximal, characteristic, complemented
15C2×#19098624C211yesmaximal, characteristic, complemented
16C2×#520×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929612C2211yescharacteristic
19C22×#11929611C2211yescharacteristic
20C22×#11929609C2211yescharacteristic
21#19099184—24no—
22#19099184C2218yescomplemented
23C2×#14579161C2211yescharacteristic
24C2×#14579156—21no—
25C2×#14579149C2211yescharacteristic
26C2×#14579147—21no—
27C2×#14579143—21no—
28C2×#14579140C2211yescharacteristic
29C2×#14579139—21no—
30C2×#14579135C2211yescharacteristic
31C2×C4×Dic158C2211yescharacteristic
32C2×C4×D316C2211yescharacteristic
33#19098898C2218yescomplemented
34#19098876C2218yescomplemented
35#19098858C2218yescomplemented
36#19098843C2218yescomplemented
37#19098785C2218yescomplemented
38#19098778C2218yescomplemented
39#19098725C2218yescomplemented
40#19098708C2218yes—
41#19098663C2218yescomplemented
42#19098661C2218yescomplemented
43C4×#11929614C2218yescomplemented
44C4×#11929609C2218yescomplemented
45#19098624C2218yescomplemented
46C2×#14579094C2211yescharacteristic
47C2×#14579094C2211yescharacteristic
48C2×#14579094C2211yescharacteristic
49C2×#14579094C2211yescharacteristic
50C2×C4⋊(C79⋊C8)C2211yescharacteristic
51C2×C4⋊(C79⋊C8)C2211yescharacteristic
52C2×#14579085C2211yescharacteristic
53C2×#14579085C2211yescharacteristic
54C2×#14579084C2211yescharacteristic
55C2×#14579084C2211yescharacteristic
56C2×#14579082C2211yescharacteristic
57C2×#14579082C2211yescharacteristic
58C2×#14579081C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×C22⋊(C79⋊C8)C2211yescharacteristic
61C2×C22⋊(C79⋊C8)C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64C22×#41×C79C2211yescharacteristic
65#520×C79—24no—
66#520×C79C2218yescomplemented
67C2×C4×Q8×C79C2211yescharacteristic
68C2×C4×Q8×C79C2211yescharacteristic
69C2×C4×D4×C79—21no—
70C2×C4×D4×C79—21no—
71C2×C4×D4×C79C2211yescharacteristic
72C2×C4×D4×C79C2211yescharacteristic
73C2×#117×C79—21no—
74C2×#117×C79C2211yescharacteristic
75C22×C4⋊C4×C79—21no—
76C22×C4⋊C4×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×Dic158C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C4×D79—21no—
82C2×#11929614—24no—
83C2×#11929614C2314yes—
84C2×#11929612—24no—
85C2×#11929612C2314yes—
86C2×#11929611—24no—
87C2×#11929611C2314yes—
88C2×#11929609—24no—
89C2×#11929609C2314yes—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C22×C79⋊C8C2311yescharacteristic
94#14579161—22no—
95#14579161C2314yes—
96#14579156—28no—
97#14579149—22no—
98#14579149C2314yes—
99#14579147—28no—
100#14579143—28no—
101#14579140—22no—
102#14579140C2314yes—
103#14579139—28no—
104#14579135—22no—
105#14579135C2314yes—
106C4×Dic158—22no—
107C4×Dic158C2314yes—
108C4×D316—22no—
109C4×D316C2314yes—
110C2×C4⋊Dic79—21no—
111C2×C4⋊Dic79C2311yescharacteristic
112C2×C4⋊Dic79C2311yescharacteristic
113C2×Dic79⋊C4—21no—
114C2×Dic79⋊C4—21no—
115C2×C22⋊Dic79—21no—
116C2×(C2×D79)⋊C4—21no—
117C2×(C2×D79)⋊C4—21no—
118C2×(C2×D79)⋊C4—21no—
119C2×(C2×D79)⋊C4—21no—
120C2×C4×Dic79—21no—
121#14579094C2314yes—
122#14579094C2314yes—
123#14579094C2314yes—
124#14579094C2314yes—
125C4⋊(C79⋊C8)C2314yes—
126C4⋊(C79⋊C8)C2314yes—
127#14579085C2314yes—
128#14579085C2314yes—
129#14579084C2314yes—
130#14579084C2314yes—
131#14579082C2314yes—
132#14579082C2314yes—
133#14579081C2314yes—
134#14579081C2314yes—
135C22⋊(C79⋊C8)C2314yes—
136C22⋊(C79⋊C8)C2314yes—
137#14579072C2314yes—
138C4×C79⋊C8C2314yes—
139C2×#41×C79—24no—
140C2×#41×C79—24no—
141C2×#41×C79—22no—
142C2×#41×C79C2314yes—
143C22×Q8×C79C2311yescharacteristic
144C22×D4×C79—21no—
145C22×D4×C79C2311yescharacteristic
146C23×C4×C79—21no—
147C23×C4×C79—21no—
148C23×C4×C79—21no—
149C23×C4×C79—21no—
150C23×C4×C79C2311yescharacteristic
151C4×Q8×C79—22no—
152C4×Q8×C79—22no—
153C4×Q8×C79C2314yes—
154C4×Q8×C79C2314yes—
155C4×D4×C79—28no—
156C4×D4×C79—28no—
157C4×D4×C79—22no—
158C4×D4×C79—22no—
159C4×D4×C79C2314yes—
160C4×D4×C79C2314yes—
161#117×C79—28no—
162#117×C79D414yes—
163#117×C79C2314yes—
164C2×C4⋊C4×C79—21no—
165C2×C4⋊C4×C79—21no—
166C2×C4⋊C4×C79—21no—
167C2×C4⋊C4×C79—22no—
168C2×C4⋊C4×C79—28no—
169C2×C4⋊C4×C79D411yescharacteristic
170C2×C4⋊C4×C79D411yescharacteristic
171C2×C4⋊C4×C79C2314yes—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79D411yescharacteristic
177C2×C22⋊C4×C79D411yescharacteristic
178C2×C42×C79—21no—
179C2×C42×C79—21no—
180C2×C42×C79C2311yescharacteristic
181C2×C42×C79C2311yescharacteristic
182C23×D79—21no—
183C2×Dic158—21no—
184C2×Dic158—24no—
185C2×Dic158—22no—
186C2×Dic158—22no—
187C2×Dic158—82no—
188C2×Dic158C2412yes—
189C2×D316—21no—
190C2×D316—22no—
191C2×D316—22no—
192C2×D316C2412yes—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—82no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C2×C4×D79—24no—
199C2×C4×D79—82no—
200#11929614—28no—
201#11929612—28no—
202#11929611—28no—
203#11929609—28no—
204C2×C79⋊C8—22no—
205C2×C79⋊C8—22no—
206C2×C79⋊C8—22no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8C2412yes—
209C2×C79⋊C8C2412yes—
210C2×C79⋊C8C2412yes—
211C2×C79⋊C8C2412yes—
212C4⋊Dic79—24no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79C2412yes—
216C4⋊Dic79C2412yes—
217Dic79⋊C4—24no—
218Dic79⋊C4—24no—
219C22⋊Dic79—24no—
220(C2×D79)⋊C4—24no—
221(C2×D79)⋊C4—24no—
222(C2×D79)⋊C4—24no—
223(C2×D79)⋊C4—24no—
224C4×Dic79—24no—
225C24×C79—21no—
226C24×C79C2×D411yescharacteristic
227#41×C79—216no—
228#41×C79—28no—
229#41×C79—28no—
230C2×Q8×C79—21no—
231C2×Q8×C79—22no—
232C2×Q8×C79#4114yes—
233C2×Q8×C79C2412yes—
234C2×D4×C79—28no—
235C2×D4×C79—24no—
236C2×D4×C79—21no—
237C2×D4×C79—22no—
238C2×D4×C79#4114yes—
239C2×D4×C79C2412yes—
240C22×C4×C79—28no—
241C22×C4×C79—21no—
242C22×C4×C79—24no—
243C22×C4×C79—22no—
244C22×C4×C79—22no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—24no—
248C22×C4×C79—24no—
249C22×C4×C79—24no—
250C22×C4×C79—82no—
251C22×C4×C79—82no—
252C22×C4×C79—82no—
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D412yes—
259C22×C4×C79C2412yes—
260C22×C4×C79C2411yescharacteristic
261C4⋊C4×C79—24no—
262C4⋊C4×C79—24no—
263C4⋊C4×C79—24no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79C2×D414yes—
267C4⋊C4×C79C2×D414yes—
268C4⋊C4×C79C2412yes—
269C4⋊C4×C79C2412yes—
270C22⋊C4×C79—24no—
271C22⋊C4×C79—24no—
272C22⋊C4×C79C2×D414yes—
273C22⋊C4×C79C2×D414yes—
274C42×C79—24no—
275C42×C79—24no—
276C42×C79C2×D412yes—
277C42×C79C2×D412yes—
278C42×C79C2412yes—
279C42×C79C2412yes—
280C23×C79—22no—
281C23×C79—24no—
282C23×C79—22no—
283C23×C79—22no—
284C23×C79—22no—
285C23×C79—42no—
286C23×C79—42no—
287C23×C79C22×D412yes—
288C23×C79C22×D411yescharacteristic
289C22×D79—22no—
290C22×D79—42no—
291C22×D79—42no—
292C22×D79—42no—
293Q8×C79—24no—
294Q8×C79—22no—
295Q8×C79C2×#4114yes—
296D4×C79—216no—
297D4×C79—24no—
298D4×C79—22no—
299D4×C79C2×#4114yes—
300C2×C4×C79—216no—
301C2×C4×C79—22no—
302C2×C4×C79—24no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—24no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—42no—
314C2×C4×C79—42no—
315C2×C4×C79—84no—
316C2×C4×C79—84no—
317C2×C4×C79—84no—
318C2×C4×C79C22×D412yes—
319C2×C4×C79C22×D412yes—
320C2×C4×C79C22×D412yes—
321C2×C4×C79C22×D412yes—
322C2×C4×C79C22×D412yes—
323C2×C4×C79C22×D411yescharacteristic
324C2×C4×C79C2×#4112yes—
325C2×C4×C79C2×#4112yes—
326C2×C4×C79C2511yescharacteristic
327C22⋊D79—84no—
328C2×Dic79—22no—
329C2×Dic79—22no—
330C2×Dic79—22no—
331C2×Dic79—42no—
332C2×Dic79—42no—
333C2×Dic79—42no—
334D316—22no—
335D316—22no—
336D316—42no—
337C4×D79—84no—
338Dic158—22no—
339Dic158—22no—
340Dic158—42no—
341Dic158—84no—
342C79⋊C8—22no—
343C79⋊C8—22no—
344C79⋊C8—22no—
345C79⋊C8—22no—
346C22×C79—22no—
347C22×C79—24no—
348C22×C79—22no—
349C22×C79—22no—
350C22×C79—44no—
351C22×C79—48no—
352C22×C79—42no—
353C22×C79—42no—
354C22×C79#52512yes—
355C22×C79#57612yes—
356C22×C79#57812yes—
357C22×C79C23×D411yescharacteristic
358C2×D79—42no—
359C2×D79—42no—
360C2×D79—42no—
361C2×D79—84no—
362C4×C79—22no—
363C4×C79—24no—
364C4×C79—22no—
365C4×C79—22no—
366C4×C79—22no—
367C4×C79—22no—
368C4×C79—42no—
369C4×C79—42no—
370C4×C79#52512yes—
371C4×C79C22×#4111yescharacteristic
372C4×C79C22×#4111yescharacteristic
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376C2×#3124—791nomaximal, Sylow
377C2×C79—42no—
378C2×C79—44no—
379C2×C79#312414yescomplemented
380C2×C79C2×#52511yescharacteristic
381C2×C79C2×#57611yescharacteristic
382C2×C79C2×#57811yescharacteristic
383D79—82no—
384C2×#542—791no—
385C2×#520D7911yescharacteristic, complemented
386#3124—7916no—
387C2×#484—791no—
388C2×#480—791no—
389C2×#477—791no—
390C2×#474—791no—
391C2×#464—791no—
392C2×#463—791no—
393C2×#452—791no—
394C2×#449—791no—
395C2×#440—791no—
396C2×#440—791no—
397C2×C4×Q16—791no—
398C2×C4×D8—791no—
399C2×#433—791no—
400C79C2×#312411yescharacteristic, complemented, Sylow
401C22×#41C2×D7911yescharacteristic
402C22×Q16—791no—
403C22×SD16—791no—
404C22×SD16—791no—
405C22×D8—791no—
406#542—798no—
407#542—1584no—
408C2×C4⋊Q8—791no—
409C2×#126—1581no—
410C2×#124—791no—
411C2×#124—1581no—
412C2×#123—1581no—
413C2×C22⋊Q8—791no—
414C2×C22⋊Q8—1581no—
415C2×#121—791no—
416#520—24no—
417#520C2×D7918yescomplemented
418C2×C4×Q8—791no—
419C2×C4×Q8C2×D7911yescharacteristic
420C2×C4×Q8C2×D7911yescharacteristic
421C2×C4×D4—21no—
422C2×C4×D4—21no—
423C2×C4×D4—791no—
424C2×C4×D4C2×D7911yescharacteristic
425C2×C4×D4C2×D7911yescharacteristic
426C2×#117—21no—
427C2×#117C2×D7911yescharacteristic
428C22×C4⋊C4—21no—
429C22×C4⋊C4C2×D7911yescharacteristic
430#484—798no—
431#480—798no—
432#477—798no—
433#474—798no—
434#464—798no—
435#463—798no—
436#452—798no—
437#449—798no—
438#440—798no—
439#440—798no—
440C4×Q16—798no—
441C4×D8—798no—
442#433—798no—
443C2×#107—791no—
444C2×#107—791no—
445C2×#107—791no—
446C2×#107—791no—
447C2×C4⋊C8—791no—
448C2×C4⋊C8—791no—
449C2×#103—791no—
450C2×#103—791no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#102—791no—
454C2×#102—791no—
455C2×#102—791no—
456C2×#102—791no—
457C2×C22⋊C8—791no—
458C2×C22⋊C8—791no—
459C2×#97—791no—
460C2×C4×C8—791no—
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D7914yes—
465C22×Q8—791no—
466C22×Q8—1581no—
467C22×Q8C22×D7911yescharacteristic
468C22×D4—21no—
469C22×D4—791no—
470C22×D4—1581no—
471C22×D4C22×D7911yescharacteristic
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—1581no—
477C23×C4C22×D7911yescharacteristic
478C2×Q16—794no—
479C2×Q16—1584no—
480C2×SD16—794no—
481C2×SD16—794no—
482C2×SD16—1584no—
483C2×SD16—1584no—
484C2×D8—794no—
485C2×D8—1584no—
486C22×C8—791no—
487C22×C8—791no—
488C22×C8—791no—
489C22×C8—791no—
490C4⋊Q8—794no—
491C4⋊Q8—1582no—
492#126—1588no—
493#124—794no—
494#124—1588no—
495#124—1582no—
496#123—1588no—
497C22⋊Q8—794no—
498C22⋊Q8—1582no—
499C22⋊Q8—1588no—
500#121—794no—
501#121—1582no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—794no—
505C4×Q8—1582no—
506C4×Q8C22×D7914yes—
507C4×Q8C22×D7914yes—
508C4×D4—28no—
509C4×D4—28no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—794no—
513C4×D4—1582no—
514C4×D4C22×D7914yes—
515C4×D4C22×D7914yes—
516#117—28no—
517#117C22⋊D7914yes—
518#117C22×D7914yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—791no—
525C2×C4⋊C4—791no—
526C2×C4⋊C4—1581no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C4⋊C4C22⋊D7911yescharacteristic
530C2×C4⋊C4C22⋊D7911yescharacteristic
531C2×C4⋊C4C22×D7911yescharacteristic
532C2×C4⋊C4C22×D7911yescharacteristic
533C2×C4⋊C4C22×D7914yes—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—1581no—
537C2×C22⋊C4—1581no—
538C2×C22⋊C4—1581no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C22⋊C4C22⋊D7911yescharacteristic
542C2×C22⋊C4C22⋊D7911yescharacteristic
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1581no—
546C2×C42C22×D7911yescharacteristic
547C2×C42C22×D7911yescharacteristic
548#107—794no—
549#107—794no—
550#107—794no—
551#107—794no—
552C4⋊C8—794no—
553C4⋊C8—794no—
554#103—794no—
555#103—794no—
556#103—794no—
557#103—794no—
558#102—794no—
559#102—794no—
560#102—794no—
561#102—794no—
562C22⋊C8—794no—
563C22⋊C8—794no—
564#97—794no—
565C4×C8—794no—
566C24—21no—
567C24—1581no—
568C24C2×C22⋊D7911yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—22no—
573C2×Q8—21no—
574C2×Q8—792no—
575C2×Q8—6322no—
576C2×Q8—1582no—
577C2×Q8—1582no—
578C2×Q8—1581no—
579C2×Q8—1584no—
580C2×Q8#1192962414yes—
581C2×Q8C23×D7912yes—
582C2×D4—28no—
583C2×D4—24no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—792no—
587C2×D4—6322no—
588C2×D4—1584no—
589C2×D4—1582no—
590C2×D4—1582no—
591C2×D4—1581no—
592C2×D4#1192962414yes—
593C2×D4C23×D7912yes—
594C22×C4—28no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—6322no—
608C22×C4—1581no—
609C22×C4—1581no—
610C22×C4—1581no—
611C22×C4—1584no—
612C22×C4C2×C22⋊D7912yes—
613C22×C4C2×C22⋊D7911yescharacteristic
614C22×C4C2×C22⋊D7911yescharacteristic
615C22×C4C2×C22⋊D7911yescharacteristic
616C22×C4C2×C22⋊D7911yescharacteristic
617C22×C4C2×C22⋊D7911yescharacteristic
618C22×C4C23×D7912yes—
619C22×C4C23×D7911yescharacteristic
620Q16—1588no—
621SD16—1588no—
622SD16—1588no—
623D8—1588no—
624C2×C8—792no—
625C2×C8—792no—
626C2×C8—792no—
627C2×C8—792no—
628C2×C8—1582no—
629C2×C8—1582no—
630C2×C8—1582no—
631C2×C8—1582no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—792no—
638C4⋊C4—792no—
639C4⋊C4—1584no—
640C4⋊C4—1584no—
641C4⋊C4—1581no—
642C4⋊C4—1581no—
643C4⋊C4—1584no—
644C4⋊C4C2×C22⋊D7914yes—
645C4⋊C4C2×C22⋊D7914yes—
646C4⋊C4C23×D7912yes—
647C4⋊C4C23×D7912yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—1584no—
651C22⋊C4—1584no—
652C22⋊C4—1584no—
653C22⋊C4—1584no—
654C22⋊C4—1584no—
655C22⋊C4C2×C22⋊D7914yes—
656C22⋊C4C2×C22⋊D7914yes—
657C42—24no—
658C42—24no—
659C42—1584no—
660C42C2×C22⋊D7912yes—
661C42C2×C22⋊D7912yes—
662C42C23×D7912yes—
663C42C23×D7912yes—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—3162no—
672C23—3162no—
673C23—3162no—
674C23—1582no—
675C23C22×C22⋊D7912yes—
676C23C22×C22⋊D7911yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—3162no—
680Q8—6324no—
681Q8—1582no—
682Q8—1582no—
683Q8C2×#1192962414yes—
684D4—216no—
685D4—24no—
686D4—22no—
687D4—3162no—
688D4—6324no—
689D4—1582no—
690D4—1582no—
691D4C2×#1192962414yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—3162no—
711C2×C4—3162no—
712C2×C4—3162no—
713C2×C4—6324no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1582no—
717C2×C4C22×C22⋊D7912yes—
718C2×C4C22×C22⋊D7912yes—
719C2×C4C22×C22⋊D7912yes—
720C2×C4C22×C22⋊D7912yes—
721C2×C4C22×C22⋊D7912yes—
722C2×C4C22×C22⋊D7911yescharacteristic
723C2×C4C2×#1192962412yes—
724C2×C4C2×#1192962412yes—
725C2×C4C24×D7911yescharacteristic
726C8—1582no—
727C8—1582no—
728C8—1582no—
729C8—1582no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—48no—
738C22—3162no—
739C22—3162no—
740C22—3162no—
741C22—6324no—
742C22#1909907412yes—
743C22#1909936612yes—
744C22#1909937812yes—
745C22C23×C22⋊D7911yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—3162no—
755C4—3162no—
756C4—3162no—
757C4#1909907412yes—
758C4C22×#1192962411yescharacteristic
759C4C22×#1192962411yescharacteristic
760C2—42no—
761C2—44no—
762C2—6322no—
763C2#2377366214yesdirect product factor
764C2C2×#1909907411yescharacteristic
765C2C2×#1909936611yescharacteristic
766C2C2×#1909937811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#520×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098708C2
hypercenterC2×#520D79
hypocenterC79C2×#3124
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#19099184C2semidirect
2. #23773662C2direct (N × H)
3. C2×#19098898C2semidirect
4. C2×#19098876C2semidirect
5. C2×#19098858C2semidirect
6. C2×#19098843C2semidirect
7. C2×#19098785C2semidirect
8. C2×#19098778C2semidirect
9. C2×#19098725C2semidirect
11. C2×#19098663C2semidirect
12. C2×#19098661C2semidirect
13. C2×C4×#11929614C2semidirect
14. C2×C4×#11929609C2semidirect
15. C2×#19098624C2semidirect
16. C2×#520×C79C2semidirect
22. #19099184C22semidirect
33. #19098898C22semidirect
34. #19098876C22semidirect
35. #19098858C22semidirect
36. #19098843C22semidirect
37. #19098785C22semidirect
38. #19098778C22semidirect
39. #19098725C22semidirect
41. #19098663C22semidirect
42. #19098661C22semidirect
43. C4×#11929614C22semidirect
44. C4×#11929609C22semidirect
45. #19098624C22semidirect
66. #520×C79C22semidirect
379. C2×C79#3124semidirect
385. C2×#520D79semidirect
400. C79C2×#3124semidirect
417. #520C2×D79semidirect
763. C2#23773662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991842
#237736622
C2×#190988982
C2×#190988762
C2×#190988582
C2×#190988432
C2×#190987852
C2×#190987782
C2×#190987252
C2×#190987082
C2×#190986632
C2×#190986612
C2×C4×#119296142
C2×C4×#119296092
C2×#190986242
C2×#520×C792
C2×#312479