Finite Group Databasebeta

← C2×#23772238 #35152373

Subgroups — C2×#23772238 #35152373

Order 20224.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14579193C211yesmaximal, characteristic
2C2×#19099045C211yesmaximal, characteristic
3C2×#19099039C211yesmaximal, characteristic, complemented
4#23772238C2116yesmaximal, direct product factor
5C2×#19098670C211yesmaximal, characteristic, complemented
6C2×#19098668C211yesmaximal, characteristic, complemented
7C2×#19098662C211yesmaximal, characteristic, complemented
8C2×#19098661C211yesmaximal, characteristic, complemented
9C2×#19098655C211yesmaximal, characteristic, complemented
10C2×C4×#11929613C211yesmaximal, characteristic, complemented
11C2×#19098648C211yesmaximal, characteristic, complemented
12C2×#19098604C211yesmaximal, characteristic, complemented
13C2×#19098558C211yesmaximal, characteristic
14C2×#103×D79C211yesmaximal, characteristic, complemented
15C2×#19098517C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C79C211yesmaximal, characteristic, complemented
17C22×#11929625C2211yescharacteristic
18C22×Q8×D79C2211yescharacteristic
19C2×#14579193C4116yescomplemented
20C2×#14579193C2218yes—
21C22×#11929614C2211yescharacteristic
22C22×#11929613C2211yescharacteristic
23C22×#11929611C2211yescharacteristic
24C22×#11929607C2211yescharacteristic
25C22×C8×D79C2211yescharacteristic
26#19099045—24no—
27#19099045C2218yes—
28#19099039—24no—
29#19099039C2218yescomplemented
30C2×Q8×Dic79C2211yescharacteristic
31C2×Q8×Dic79C2211yescharacteristic
32C2×C4×Dic158—21no—
33C2×C4×Dic158C2211yescharacteristic
34C2×#14579126—21no—
35C2×#14579126C2211yescharacteristic
36C2×C4×D316—21no—
37C2×C4×D316C2211yescharacteristic
38C2×#14579123—21no—
39C2×#14579123C2211yescharacteristic
40C2×#14579119—21no—
41C2×#14579119C2211yescharacteristic
42C2×#14579118—21no—
43C2×#14579118—21no—
44C2×#14579118C2211yescharacteristic
45C2×C4⋊C4×D79—21no—
46C2×C4⋊C4×D79C2211yescharacteristic
47#19098670C2218yescomplemented
48#19098668C2218yescomplemented
49#19098662C2218yescomplemented
50#19098661C2218yescomplemented
51#19098655C2218yescomplemented
52C4×#11929613C2218yescomplemented
53#19098648C2218yescomplemented
54#19098604C2218yescomplemented
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58#19098558C2218yes—
59C2×#14579086C2211yescharacteristic
60C2×#14579085C2211yescharacteristic
61C2×#14579085C2211yescharacteristic
62C2×#14579084C2211yescharacteristic
63#103×D79C2218yescomplemented
64C2×#14579083C2211yescharacteristic
65C2×#14579081C2211yescharacteristic
66#19098517C2218yescomplemented
67C2×#14579072C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C2×C8×Dic79C2211yescharacteristic
70C22×Q16×C79C2211yescharacteristic
71C2×C4×Q8×C79C2211yescharacteristic
72C2×C4×Q8×C79C2211yescharacteristic
73C4×Q16×C79C2218yescomplemented
74C2×#107×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#103×C79C2211yescharacteristic
77C2×C4×C8×C79C2211yescharacteristic
78C2×#11929625—22no—
79C2×#11929625—24no—
80C2×#11929625C2×C418yes—
81C2×#11929625C2314yes—
82C22×Dic158—21no—
83C22×Dic158C2311yescharacteristic
84C2×Q8×D79—22no—
85C2×Q8×D79—24no—
86C2×Q8×D79C2×C418yescomplemented
87C2×Q8×D79C2314yes—
88C22×D316—21no—
89C22×D316C2311yescharacteristic
90C22×C4×D79—21no—
91C22×C4×D79—21no—
92C22×C4×D79—21no—
93C22×C4×D79—21no—
94C22×C4×D79—21no—
95C22×C4×D79C2311yescharacteristic
96#14579193C2×C4164yescomplemented
97C2×#11929614C2×C418yescomplemented
98C2×#11929614C2314yes—
99C2×#11929613C2×C418yescomplemented
100C2×#11929613C2314yes—
101C2×#11929611C2×C418yescomplemented
102C2×#11929611C2314yes—
103C2×#11929607C2×C418yescomplemented
104C2×#11929607C2314yes—
105C22×C79⋊C8C2311yescharacteristic
106C22×C79⋊C8C2311yescharacteristic
107C2×C8×D79—24no—
108C2×C8×D79C2314yes—
109Q8×Dic79—22no—
110Q8×Dic79—22no—
111Q8×Dic79C2314yes—
112Q8×Dic79C2314yes—
113C4×Dic158—22no—
114C4×Dic158—28no—
115C4×Dic158C2314yes—
116#14579126—28no—
117#14579126—22no—
118#14579126C2314yes—
119C4×D316—22no—
120C4×D316—28no—
121C4×D316C2314yes—
122#14579123—28no—
123#14579123—22no—
124#14579123C2314yes—
125#14579119—22no—
126#14579119—28no—
127#14579119C2314yes—
128#14579118—28no—
129#14579118—28no—
130#14579118D414yes—
131#14579118C2314yes—
132C2×C4⋊Dic79—21no—
133C2×C4⋊Dic79—21no—
134C2×C4⋊Dic79C2311yescharacteristic
135C2×C4⋊Dic79C2311yescharacteristic
136C2×Dic79⋊C4—21no—
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4D411yescharacteristic
140C2×Dic79⋊C4D411yescharacteristic
141C4⋊C4×D79—22no—
142C4⋊C4×D79—28no—
143C4⋊C4×D79C2314yes—
144C2×(C2×D79)⋊C4—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4D411yescharacteristic
148C2×(C2×D79)⋊C4D411yescharacteristic
149C2×C4×Dic79—21no—
150C2×C4×Dic79—21no—
151C2×C4×Dic79—21no—
152C2×C4×Dic79—21no—
153C2×C4×Dic79—21no—
154C2×C4×Dic79C2311yescharacteristic
155#14579094C2314yes—
156#14579093C2314yes—
157#14579092C2314yes—
158#14579086C2314yes—
159#14579085C2314yes—
160#14579085C2314yes—
161#14579084C2314yes—
162#14579083C2314yes—
163#14579081C2314yes—
164#14579072C2314yes—
165#14579071C2314yes—
166C8×Dic79C2314yes—
167C22×Q8×C79C2311yescharacteristic
168C22×Q8×C79C2311yescharacteristic
169C2×Q16×C79C2×C418yescomplemented
170C2×Q16×C79C2314yes—
171C22×C8×C79C2311yescharacteristic
172C22×C8×C79C2311yescharacteristic
173C4×Q8×C79—22no—
174C4×Q8×C79—22no—
175C4×Q8×C79C2314yes—
176C4×Q8×C79C2314yes—
177C2×C4⋊C4×C79—21no—
178C2×C4⋊C4×C79—21no—
179C2×C4⋊C4×C79C2311yescharacteristic
180C2×C4⋊C4×C79C2311yescharacteristic
181C2×C42×C79—21no—
182C2×C42×C79—21no—
183C2×C42×C79C2311yescharacteristic
184#107×C79C2314yes—
185#103×C79C2314yes—
186#103×C79C2314yes—
187C4×C8×C79C2314yes—
188C23×D79—21no—
189C23×D79C2×D411yescharacteristic
190#11929625—216no—
191#11929625—28no—
192#11929625C22×C4116yes—
193C2×Dic158—28no—
194C2×Dic158—24no—
195C2×Dic158—21no—
196C2×Dic158—22no—
197C2×Dic158C22×C414yes—
198C2×Dic158C2412yes—
199Q8×D79—216no—
200Q8×D79—28no—
201Q8×D79C22×C4116yescomplemented
202C2×D316—28no—
203C2×D316—24no—
204C2×D316—21no—
205C2×D316—22no—
206C2×D316C22×C414yes—
207C2×D316C2412yes—
208C22×Dic79—21no—
209C22×Dic79—21no—
210C22×Dic79—21no—
211C22×Dic79C2×D411yescharacteristic
212C22×Dic79C2×D411yescharacteristic
213C22×Dic79C2×D411yescharacteristic
214C2×C4×D79—28no—
215C2×C4×D79—24no—
216C2×C4×D79—24no—
217C2×C4×D79—28no—
218C2×C4×D79—24no—
219C2×C4×D79—24no—
220C2×C4×D79—24no—
221C2×C4×D79—82no—
222C2×C4×D79—82no—
223C2×C4×D79—82no—
224C2×C4×D79C22×C414yes—
225C2×C4×D79C2×D412yes—
226C2×C4×D79#4114yes—
227C2×C4×D79C2412yes—
228#11929614C22×C4116yescomplemented
229#11929613C22×C4116yescomplemented
230#11929611C22×C4116yescomplemented
231#11929607C22×C4116yescomplemented
232C2×C79⋊C8—22no—
233C2×C79⋊C8C22×C414yes—
234C2×C79⋊C8C2412yes—
235C2×C79⋊C8C2412yes—
236C8×D79—28no—
237C4⋊Dic79—24no—
238C4⋊Dic79—24no—
239C4⋊Dic79—21no—
240C4⋊Dic79—21no—
241C4⋊Dic79C2412yes—
242C4⋊Dic79C2412yes—
243Dic79⋊C4—24no—
244Dic79⋊C4—24no—
245Dic79⋊C4—24no—
246Dic79⋊C4C2×D414yes—
247Dic79⋊C4C2×D414yes—
248(C2×D79)⋊C4—24no—
249(C2×D79)⋊C4—24no—
250(C2×D79)⋊C4—24no—
251(C2×D79)⋊C4C2×D414yes—
252(C2×D79)⋊C4C2×D414yes—
253C4×Dic79—24no—
254C4×Dic79—24no—
255C4×Dic79—24no—
256C4×Dic79—24no—
257C4×Dic79—24no—
258C4×Dic79C2×D412yes—
259C4×Dic79C2412yes—
260C2×Q8×C79—21no—
261C2×Q8×C79—21no—
262C2×Q8×C79—22no—
263C2×Q8×C79—22no—
264C2×Q8×C79C22×C414yes—
265C2×Q8×C79C22×C414yes—
266C2×Q8×C79C2412yes—
267C2×Q8×C79C2412yes—
268C22×C4×C79—21no—
269C22×C4×C79—21no—
270C22×C4×C79—21no—
271C22×C4×C79—21no—
272C22×C4×C79C2×D411yescharacteristic
273C22×C4×C79C2×D411yescharacteristic
274C22×C4×C79C2411yescharacteristic
275Q16×C79C22×C4116yescomplemented
276C2×C8×C79—22no—
277C2×C8×C79C22×C414yes—
278C2×C8×C79C2412yes—
279C2×C8×C79C2412yes—
280C4⋊C4×C79—24no—
281C4⋊C4×C79—24no—
282C4⋊C4×C79—21no—
283C4⋊C4×C79—21no—
284C4⋊C4×C79C2412yes—
285C4⋊C4×C79C2412yes—
286C42×C79—24no—
287C42×C79—24no—
288C42×C79C2×D412yes—
289C42×C79C2412yes—
290C23×C79C22×D411yescharacteristic
291C22×D79—22no—
292C22×D79—22no—
293C22×D79—24no—
294C22×D79—22no—
295C22×D79—42no—
296C22×D79—42no—
297C22×D79C4×D414yes—
298C22×D79C22×D412yes—
299Q8×C79—24no—
300Q8×C79—24no—
301Q8×C79—22no—
302Q8×C79—22no—
303Q8×C79C23×C414yes—
304Q8×C79C23×C414yes—
305C2×C4×C79—24no—
306C2×C4×C79—24no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
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×C79C23×C412yes—
316C2×C4×C79C22×D412yes—
317C2×C4×C79C22×D412yes—
318C2×C4×C79C22×D411yescharacteristic
319C2×C4×C79C2×#4112yes—
320C2×C4×C79C2511yescharacteristic
321C2×Dic79—24no—
322C2×Dic79—22no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—22no—
327C2×Dic79—42no—
328C2×Dic79—42no—
329C2×Dic79C4×D414yes—
330C2×Dic79C22×D412yes—
331C2×Dic79C22×D412yes—
332C2×Dic79C22×D412yes—
333D316—216no—
334D316—24no—
335D316—22no—
336D316C23×C414yes—
337C4×D79—216no—
338C4×D79—216no—
339C4×D79—84no—
340C4×D79—84no—
341C4×D79—84no—
342C4×D79C4×D418yes—
343C4×D79C23×C414yes—
344C4×D79C2×#4114yes—
345Dic158—24no—
346Dic158—22no—
347Dic158—216no—
348Dic158C23×C414yes—
349C8×C79—22no—
350C8×C79C23×C414yes—
351C79⋊C8—22no—
352C79⋊C8C23×C414yes—
353C22×C79C2×C4×D412yes—
354C22×C79#57712yes—
355C22×C79#57812yes—
356C22×C79C23×D411yescharacteristic
357C2×D79—28no—
358C2×D79—22no—
359C2×D79—22no—
360C2×D79—24no—
361C2×D79—48no—
362C2×D79—42no—
363C2×D79—42no—
364C2×D79C2×C4×D414yes—
365C4×C79—24no—
366C4×C79—24no—
367C4×C79—22no—
368C4×C79—22no—
369C4×C79—42no—
370C4×C79—42no—
371C4×C79C2×C4×D412yes—
372C4×C79C24×C411yescharacteristic
373C4×C79C22×#4111yescharacteristic
374Dic79—24no—
375Dic79—22no—
376Dic79—22no—
377Dic79—42no—
378Dic79—42no—
379Dic79C2×C4×D414yes—
380C2×#2947—791nomaximal, Sylow
381C2×C79#294714yescomplemented
382C2×C79C22×C4×D411yescharacteristic
383C2×C79C2×#57711yescharacteristic
384C2×C79C2×#57811yescharacteristic
385D79—24no—
386D79—44no—
387C22×#137—791no—
388C2×#520—791no—
389C2×#519—791no—
390#2947—7916no—
391C2×#441—791no—
392C2×#441—791no—
393C2×#440—791no—
394C2×#440—791no—
395C2×C4×Q16—791no—
396C2×C4×Q16D7911yescharacteristic, complemented
397C2×C4×SD16—791no—
398C2×C4×SD16—791no—
399C2×#428—791no—
400C2×#416—791no—
401C22×#103—791no—
402C2×#405—791no—
403C79C2×#294711yescharacteristic, complemented, Sylow
404C22×#41—791no—
405C23×Q8—791no—
406C2×#137—798no—
407C2×#137—7916no—
408C22×Q16—791no—
409C22×Q16C2×D7911yescharacteristic
410C22×SD16—791no—
411C22×SD16—791no—
412C22×M16—791no—
413C23×C8—791no—
414#520—798no—
415#520—1584no—
416#519—798no—
417#519—1584no—
418C2×C4×Q8—791no—
419C2×C4×Q8—791no—
420C2×C4×Q8—791no—
421C2×C4×Q8—791no—
422C2×C4×Q8—1581no—
423C2×C4×Q8—1581no—
424C2×C4×Q8C2×D7911yescharacteristic
425C2×C4×Q8C2×D7911yescharacteristic
426C2×C4×D4—791no—
427C2×C4×D4—791no—
428C2×C4×D4—1581no—
429C2×C4×D4—1581no—
430C2×#117—791no—
431C2×#117—791no—
432C2×#117—1581no—
433C2×#117—1581no—
434C2×#117—1581no—
435C22×C4⋊C4—791no—
436C22×C4⋊C4—1581no—
437#441—798no—
438#441—798no—
439#440—798no—
440#440—798no—
441C4×Q16—798no—
442C4×Q16C2×D7918yescomplemented
443C4×SD16—798no—
444C4×SD16—798no—
445#428—798no—
446C2×#107—791no—
447C2×#107C2×D7911yescharacteristic
448C2×#106—791no—
449C2×#106—791no—
450#416—798no—
451C2×#103—791no—
452C2×#103—791no—
453C2×#103—791no—
454C2×#103—791no—
455C2×#103—798no—
456C2×#103C2×D7911yescharacteristic
457C2×#103C2×D7911yescharacteristic
458C2×#102—791no—
459C2×#102—791no—
460#405—798no—
461C2×#97—791no—
462C2×#97—791no—
463C2×C4×C8—791no—
464C2×C4×C8C2×D7911yescharacteristic
465C2×#41—798no—
466C2×#41—794no—
467C2×#41—1582no—
468C2×#41—1584no—
469C22×Q8—798no—
470C22×Q8—794no—
471C22×Q8—791no—
472C22×Q8—1581no—
473C22×Q8—1582no—
474C22×Q8—1584no—
475C22×Q8C22×D7911yescharacteristic
476C22×Q8C22×D7911yescharacteristic
477C22×D4—791no—
478C22×D4—1581no—
479C23×C4—791no—
480C23×C4—1581no—
481C23×C4—1581no—
482C23×C4—1581no—
483C23×C4—1581no—
484C23×C4—1581no—
485#137—7964no—
486C2×Q16—798no—
487C2×Q16—794no—
488C2×Q16C4×D7918yescomplemented
489C2×Q16C22×D7914yes—
490C2×SD16—798no—
491C2×SD16—794no—
492C2×SD16—798no—
493C2×SD16—794no—
494C2×M16—798no—
495C2×M16—794no—
496C22×C8—791no—
497C22×C8—791no—
498C22×C8—794no—
499C22×C8—1584no—
500C22×C8C22×D7911yescharacteristic
501C22×C8C22×D7911yescharacteristic
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—794no—
505C4×Q8—794no—
506C4×Q8—794no—
507C4×Q8—794no—
508C4×Q8—1588no—
509C4×Q8—1582no—
510C4×Q8—1582no—
511C4×Q8—1582no—
512C4×Q8—1588no—
513C4×Q8—1582no—
514C4×Q8C22×D7914yes—
515C4×Q8C22×D7914yes—
516C4×D4—794no—
517C4×D4—794no—
518C4×D4—1588no—
519C4×D4—1582no—
520C4×D4—1588no—
521C4×D4—1582no—
522#117—794no—
523#117—794no—
524#117—794no—
525#117—1588no—
526#117—1588no—
527#117—1588no—
528#117—1582no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—791no—
532C2×C4⋊C4—791no—
533C2×C4⋊C4—791no—
534C2×C4⋊C4—791no—
535C2×C4⋊C4—794no—
536C2×C4⋊C4—1588no—
537C2×C4⋊C4—1582no—
538C2×C4⋊C4—1581no—
539C2×C4⋊C4—1581no—
540C2×C4⋊C4—1581no—
541C2×C4⋊C4—1581no—
542C2×C4⋊C4—1581no—
543C2×C4⋊C4C22×D7911yescharacteristic
544C2×C4⋊C4C22×D7911yescharacteristic
545C2×C22⋊C4—791no—
546C2×C22⋊C4—791no—
547C2×C22⋊C4—1581no—
548C2×C22⋊C4—1581no—
549C2×C22⋊C4—1581no—
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—791no—
553C2×C42—1581no—
554C2×C42—1581no—
555C2×C42—1581no—
556C2×C42—1581no—
557C2×C42—1581no—
558C2×C42C22×D7911yescharacteristic
559#107—794no—
560#107C22×D7914yes—
561#106—794no—
562#106—794no—
563#103—794no—
564#103—794no—
565#103—794no—
566#103—794no—
567#103C22×D7914yes—
568#103C22×D7914yes—
569#102—794no—
570#102—794no—
571#97—794no—
572#97—794no—
573C4×C8—794no—
574C4×C8C22×D7914yes—
575C24—791no—
576C24—1581no—
577#41—7916no—
578#41—15816no—
579#41—1588no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—7916no—
585C2×Q8—792no—
586C2×Q8—794no—
587C2×Q8—1584no—
588C2×Q8—1588no—
589C2×Q8—15816no—
590C2×Q8—1588no—
591C2×Q8—1582no—
592C2×Q8—1581no—
593C2×Q8C2×C4×D7914yes—
594C2×Q8C2×C4×D7914yes—
595C2×Q8C23×D7912yes—
596C2×Q8C23×D7912yes—
597C2×D4—792no—
598C2×D4—794no—
599C2×D4—1584no—
600C2×D4—1588no—
601C2×D4—1582no—
602C2×D4—1581no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—791no—
608C22×C4—794no—
609C22×C4—792no—
610C22×C4—794no—
611C22×C4—792no—
612C22×C4—791no—
613C22×C4—791no—
614C22×C4—6322no—
615C22×C4—6322no—
616C22×C4—6322no—
617C22×C4—1584no—
618C22×C4—1584no—
619C22×C4—1588no—
620C22×C4—1584no—
621C22×C4—1584no—
622C22×C4—1588no—
623C22×C4—1581no—
624C22×C4—1581no—
625C22×C4—1584no—
626C22×C4—1581no—
627C22×C4D4×D7911yescharacteristic
628C22×C4D4×D7911yescharacteristic
629C22×C4C23×D7911yescharacteristic
630Q16—7916no—
631Q16C2×C4×D79116yescomplemented
632SD16—7916no—
633SD16—7916no—
634M16—7916no—
635C2×C8—22no—
636C2×C8—792no—
637C2×C8—794no—
638C2×C8—792no—
639C2×C8—1588no—
640C2×C8—1582no—
641C2×C8C2×C4×D7914yes—
642C2×C8C23×D7912yes—
643C2×C8C23×D7912yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—794no—
649C4⋊C4—794no—
650C4⋊C4—792no—
651C4⋊C4—792no—
652C4⋊C4—1584no—
653C4⋊C4—1584no—
654C4⋊C4—1584no—
655C4⋊C4—1584no—
656C4⋊C4—1584no—
657C4⋊C4—1581no—
658C4⋊C4—1581no—
659C4⋊C4C23×D7912yes—
660C4⋊C4C23×D7912yes—
661C22⋊C4—794no—
662C22⋊C4—794no—
663C22⋊C4—1584no—
664C22⋊C4—1584no—
665C22⋊C4—1584no—
666C42—24no—
667C42—24no—
668C42—792no—
669C42—792no—
670C42—1584no—
671C42—1584no—
672C42—1584no—
673C42—1584no—
674C42—1584no—
675C42D4×D7912yes—
676C42C23×D7912yes—
677C23—3162no—
678C23—3162no—
679C23—794no—
680C23—792no—
681C23—1584no—
682C23—1582no—
683C23—1582no—
684C23—1582no—
685C23C2×D4×D7911yescharacteristic
686Q8—24no—
687Q8—24no—
688Q8—22no—
689Q8—22no—
690Q8—794no—
691Q8—15816no—
692Q8—1584no—
693Q8—1582no—
694Q8C22×C4×D7914yes—
695Q8C22×C4×D7914yes—
696D4—794no—
697D4—15816no—
698D4—1584no—
699D4—1582no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—3162no—
711C2×C4—3162no—
712C2×C4—794no—
713C2×C4—792no—
714C2×C4—798no—
715C2×C4—794no—
716C2×C4—794no—
717C2×C4—792no—
718C2×C4—792no—
719C2×C4—6324no—
720C2×C4—6324no—
721C2×C4—6324no—
722C2×C4—15816no—
723C2×C4—15816no—
724C2×C4—1582no—
725C2×C4—1582no—
726C2×C4—1584no—
727C2×C4—1582no—
728C2×C4—1582no—
729C2×C4—1582no—
730C2×C4C22×C4×D7912yes—
731C2×C4C2×D4×D7912yes—
732C2×C4C2×D4×D7912yes—
733C2×C4C2×D4×D7911yescharacteristic
734C2×C4#41×D7912yes—
735C2×C4C24×D7911yescharacteristic
736C8—22no—
737C8—794no—
738C8—1582no—
739C8C22×C4×D7914yes—
740C22—3168no—
741C22—3162no—
742C22—3162no—
743C22—794no—
744C22—1584no—
745C22—1588no—
746C22—1582no—
747C22—1582no—
748C22C4×D4×D7912yes—
749C22#1909937012yes—
750C22#1909937612yes—
751C22C22×D4×D7911yescharacteristic
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—3162no—
759C4—3162no—
760C4—794no—
761C4—1584no—
762C4—1582no—
763C4—1582no—
764C4C4×D4×D7912yes—
765C4C23×C4×D7911yescharacteristic
766C4C2×#41×D7911yescharacteristic
767C2—3164no—
768C2—1584no—
769C2#2377223814yesdirect product factor
770C2C2×C4×D4×D7911yescharacteristic
771C2C2×#1909937011yescharacteristic
772C2C2×#1909937611yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC4×C79C24×C4
FrattiniC2×C4C24×D79
FittingC2×C4×Q16×C79C2
socleC23×C79C22×D4
prime radicalC22×#11929625C22
cosocleC2×C4×C79C25
hypercenterC2×C4×Q16D79
hypocenterC79C2×#2947
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. C2×#19099039C2semidirect
4. #23772238C2direct (N × H)
5. C2×#19098670C2semidirect
6. C2×#19098668C2semidirect
7. C2×#19098662C2semidirect
8. C2×#19098661C2semidirect
9. C2×#19098655C2semidirect
10. C2×C4×#11929613C2semidirect
11. C2×#19098648C2semidirect
12. C2×#19098604C2semidirect
14. C2×#103×D79C2semidirect
15. C2×#19098517C2semidirect
16. C2×C4×Q16×C79C2semidirect
19. C2×#14579193C4semidirect
29. #19099039C22semidirect
47. #19098670C22semidirect
48. #19098668C22semidirect
49. #19098662C22semidirect
50. #19098661C22semidirect
51. #19098655C22semidirect
52. C4×#11929613C22semidirect
53. #19098648C22semidirect
54. #19098604C22semidirect
63. #103×D79C22semidirect
66. #19098517C22semidirect
73. C4×Q16×C79C22semidirect
86. C2×Q8×D79C2×C4semidirect
96. #14579193C2×C4semidirect
97. C2×#11929614C2×C4semidirect
99. C2×#11929613C2×C4semidirect
101. C2×#11929611C2×C4semidirect
103. C2×#11929607C2×C4semidirect
169. C2×Q16×C79C2×C4semidirect
201. Q8×D79C22×C4semidirect
228. #11929614C22×C4semidirect
229. #11929613C22×C4semidirect
230. #11929611C22×C4semidirect
231. #11929607C22×C4semidirect
275. Q16×C79C22×C4semidirect
381. C2×C79#2947semidirect
396. C2×C4×Q16D79semidirect
403. C79C2×#2947semidirect
442. C4×Q16C2×D79semidirect
488. C2×Q16C4×D79semidirect
631. Q16C2×C4×D79semidirect
769. C2#23772238direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145791932
C2×#190990452
C2×#190990392
#237722382
C2×#190986702
C2×#190986682
C2×#190986622
C2×#190986612
C2×#190986552
C2×C4×#119296132
C2×#190986482
C2×#190986042
C2×#190985582
C2×#103×D792
C2×#190985172
C2×C4×Q16×C792
C2×#294779