Finite Group Databasebeta

← C2×#20286602 #28260499

Subgroups — C2×#20286602 #28260499

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811313C211yesmaximal, characteristic, complemented
2#20286602C2116yesmaximal, direct product factor
3C2×#16810977C211yesmaximal, characteristic, complemented
4C2×#16810961C211yesmaximal, characteristic, complemented
5C2×#16810934C211yesmaximal, characteristic, complemented
6C2×#16810930C211yesmaximal, characteristic, complemented
7C2×#16810862C211yesmaximal, characteristic, complemented
8C2×#16810850C211yesmaximal, characteristic, complemented
9C2×#16810842C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic, complemented
11C2×#16810779C211yesmaximal, characteristic, complemented
12C2×C4×#11719925C211yesmaximal, characteristic, complemented
13C2×D4×#88322C211yesmaximal, characteristic, complemented
14C2×#16810619C211yesmaximal, characteristic, complemented
15C22×#13133141C211yesmaximal, characteristic, complemented
16C2×C53×#548C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21C23×#88322C2211yescharacteristic
22#16811313—24no—
23#16811313C2218yescomplemented
24C2×#13133210—21no—
25C2×#13133209C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133198—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133196C2211yescharacteristic
30C2×C4×Dic106C2211yescharacteristic
31C2×#13133176C2211yescharacteristic
32C2×#13133173—21no—
33C22×C4⋊Dic53C2211yescharacteristic
34#16810977C2218yescomplemented
35#16810961C2218yescomplemented
36#16810934C2218yescomplemented
37#16810930C2218yescomplemented
38#16810862C2218yescomplemented
39#16810850C2218yescomplemented
40#16810842C2218yescomplemented
41#16810785C2218yescomplemented
42#16810779C2218yescomplemented
43C4×#11719925C2218yescomplemented
44D4×#88322C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810619C2218yescomplemented
50C2×#13133141C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133141C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2218yescomplemented
57C2×#13133140C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C22×#41×C53C2211yescharacteristic
65C23×Q8×C53C2211yescharacteristic
66C53×#548—24no—
67C53×#548C2218yes—
68C2×#124×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×C22⋊Q8×C53—21no—
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×#121×C53—21no—
73C2×#121×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C23×Dic53—21no—
79C2×#11719925—24no—
80C2×#11719925—42no—
81C2×#11719925C2314yes—
82C2×#11719925C2314yes—
83C2×#11719923—42no—
84C2×#11719923C2314yes—
85C22×#88322—42no—
86C22×#88322—42no—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C22×#88322C2314yes—
92C22×#88322C2314yes—
93#13133210—28no—
94#13133209—22no—
95#13133209C2314yes—
96#13133207—28no—
97#13133198—28no—
98#13133196—22no—
99#13133196—22no—
100#13133196C2314yes—
101#13133196C2314yes—
102C4×Dic106—22no—
103C4×Dic106C2314yes—
104#13133176—22no—
105#13133176C2314yes—
106#13133173—28no—
107C2×C4⋊Dic53—22no—
108C2×C4⋊Dic53—21no—
109C2×C4⋊Dic53C2314yes—
110C2×C4⋊Dic53C2311yescharacteristic
111C2×C4⋊Dic53C2311yescharacteristic
112C2×C4⋊Dic53C2311yescharacteristic
113C2×#11719919—21no—
114C2×#11719919—21no—
115C2×#11719919—21no—
116C2×#11719919—21no—
117C2×#11719919—21no—
118C2×C22⋊Dic53—21no—
119C2×C22⋊Dic53—21no—
120C2×C22⋊Dic53—21no—
121C2×C4×Dic53—21no—
122C2×C4×Dic53—21no—
123#13133150C2314yes—
124#13133150C2314yes—
125#13133148C2314yes—
126C4⋊#88322C2314yes—
127#13133141C2314yes—
128#13133141C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133141C2314yes—
133#13133140C2314yes—
134#13133138C2314yes—
135#13133138C2314yes—
136#13133138C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yes—
139C4×#88322C2314yes—
140C2×#41×C53—22no—
141C2×#41×C53—24no—
142C2×#41×C53—42no—
143C2×#41×C53C2314yes—
144C22×Q8×C53—21no—
145C22×Q8×C53—22no—
146C22×Q8×C53—24no—
147C22×Q8×C53—42no—
148C22×Q8×C53C2311yescharacteristic
149C22×Q8×C53C2314yes—
150C22×Q8×C53C2311yescharacteristic
151C22×D4×C53—21no—
152C22×D4×C53—21no—
153C22×D4×C53D411yescharacteristic
154C22×D4×C53C2311yescharacteristic
155C23×C4×C53—21no—
156C23×C4×C53—21no—
157C23×C4×C53C2311yescharacteristic
158C23×C4×C53C2311yescharacteristic
159#124×C53—28no—
160#124×C53—22no—
161#124×C53C2314yes—
162C22⋊Q8×C53—28no—
163C22⋊Q8×C53—22no—
164C22⋊Q8×C53C2314yes—
165#121×C53—28no—
166#121×C53—22no—
167#121×C53C2314yes—
168C4×Q8×C53—22no—
169C4×Q8×C53C2314yes—
170C4×D4×C53—28no—
171C4×D4×C53D414yes—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53D411yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C24×C53—21no—
186C24×C53C2×D411yescharacteristic
187C24×C53C2×D411yescharacteristic
188#41×C53—28no—
189#41×C53—44no—
190#41×C53—48no—
191C2×Q8×C53—21no—
192C2×Q8×C53—24no—
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—28no—
196C2×Q8×C53—22no—
197C2×Q8×C53—22no—
198C2×Q8×C53—44no—
199C2×Q8×C53—44no—
200C2×Q8×C53—48no—
201C2×Q8×C53#4114yes—
202C2×Q8×C53C2412yes—
203C2×Q8×C53C2412yes—
204C2×D4×C53—24no—
205C2×D4×C53—24no—
206C2×D4×C53—24no—
207C2×D4×C53—21no—
208C2×D4×C53—22no—
209C2×D4×C53—22no—
210C2×D4×C53—44no—
211C2×D4×C53—44no—
212C2×D4×C53C2×D414yes—
213C2×D4×C53C2412yes—
214C22×C4×C53—21no—
215C22×C4×C53—22no—
216C22×C4×C53—22no—
217C22×C4×C53—22no—
218C22×C4×C53—22no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—24no—
222C22×C4×C53—24no—
223C22×C4×C53—44no—
224C22×C4×C53—44no—
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D411yescharacteristic
229C22×C4×C53C2×D412yes—
230C22×C4×C53C2×D412yes—
231C22×C4×C53C2412yes—
232C22×C4×C53C2412yes—
233C22×C4×C53C2411yescharacteristic
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—24no—
239C22×Dic53—44no—
240C2×Dic106—22no—
241C2×Dic106—22no—
242C2×Dic106—21no—
243C2×Dic106C2412yes—
244C4⋊C4×C53—24no—
245C4⋊C4×C53—24no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53C2×D414yes—
248C4⋊C4×C53C2412yes—
249C22⋊C4×C53—24no—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—24no—
252C22⋊C4×C53—24no—
253C22⋊C4×C53C2×D414yes—
254C22⋊C4×C53C2×D414yes—
255C42×C53—24no—
256C42×C53C2×D412yes—
257C42×C53C2412yes—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261#11719925—28no—
262#11719925—44no—
263#11719923—44no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—24no—
267C4⋊Dic53—21no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270C4⋊Dic53C2412yes—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C2×#88322—22no—
279C2×#88322—22no—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322—44no—
283C2×#88322—44no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53#13514yes—
298C23×C53C22×D412yes—
299C23×C53C22×D412yes—
300C23×C53C22×D411yescharacteristic
301Q8×C53—24no—
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—48no—
306Q8×C53—42no—
307Q8×C53C2×#4114yes—
308D4×C53—28no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—48no—
312D4×C53—48no—
313D4×C53—42no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—24no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—24no—
321C2×C4×C53—24no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—48no—
329C2×C4×C53—48no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D412yes—
335C2×C4×C53C22×D412yes—
336C2×C4×C53C22×D411yescharacteristic
337C2×C4×C53C2×#4112yes—
338C2×C4×C53H(5,𝔽2)12yes—
339C2×C4×C53C2511yescharacteristic
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—42no—
345C2×Dic53—48no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349Dic106—22no—
350Dic106—22no—
351Dic106—42no—
352#88322—22no—
353#88322—22no—
354#88322—22no—
355#88322—22no—
356C2×#3300—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—28no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—44no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—84no—
368C22×C53#54612yes—
369C22×C53C2×#13514yes—
370C22×C53C2×#13512yes—
371C22×C53#57812yes—
372C22×C53C23×D411yescharacteristic
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—24no—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53#54612yes—
381C4×C53C22×#4111yescharacteristic
382C4×C53C2×H(5,𝔽2)11yescharacteristic
383Dic53—42no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#552—531no—
388C2×#548D5311yescharacteristic
389#3300—5316no—
390C2×#488—531no—
391C2×#485—531no—
392C2×#480—531no—
393C2×#479—531no—
394C2×#467—531no—
395C2×#465—531no—
396C2×#464—531no—
397C2×#452—531no—
398C2×#451—531no—
399C2×C4×Q16—531no—
400C2×C8×D4—531no—
401C2×#416—531no—
402C22×#103—531no—
403C2×C53—24no—
404C2×C53—42no—
405C2×C53—82no—
406C2×C53#330014yescomplemented
407C2×C53C2×#54611yescharacteristic
408C2×C53C22×#13511yescharacteristic
409C2×C53C2×#57811yescharacteristic
410C22×#41C2×D5311yescharacteristic
411C23×Q8C2×D5311yescharacteristic
412C22×Q16—531no—
413C22×Q16—531no—
414C22×SD16—531no—
415C23×C8—531no—
416C23×C8—531no—
417#552—538no—
418#552—1064no—
419#548—24no—
420#548C2×D5318yes—
421C2×#126—1061no—
422C2×#125—531no—
423C2×#125—1061no—
424C2×#124—21no—
425C2×#124C2×D5311yescharacteristic
426C2×#123—1061no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8C2×D5311yescharacteristic
431C2×#121—21no—
432C2×#121C2×D5311yescharacteristic
433C2×C4×Q8—531no—
434C2×C4×Q8C2×D5311yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C2×D5311yescharacteristic
437C2×#117—531no—
438C2×#117—1061no—
439C22×C4⋊C4—531no—
440#488—538no—
441#485—538no—
442#480—538no—
443#479—538no—
444#467—538no—
445#465—538no—
446#464—538no—
447#452—538no—
448#451—538no—
449C4×Q16—538no—
450C8×D4—538no—
451C2×#107—531no—
452C2×#107—531no—
453C2×#106—531no—
454C2×C4⋊C8—531no—
455#416—538no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—538no—
463C2×#103—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8—531no—
469C2×C4×C8—531no—
470C53C2×#330011yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D5314yes—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—531no—
480C22×Q8C22×D5311yescharacteristic
481C22×Q8C22×D5314yes—
482C22×Q8C22×D5311yescharacteristic
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C22⋊D5311yescharacteristic
486C22×D4C22×D5311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—1061no—
490C23×C4C22×D5311yescharacteristic
491C23×C4C22×D5311yescharacteristic
492C2×Q16—534no—
493C2×Q16—534no—
494C2×Q16—1064no—
495C2×Q16—2122no—
496C2×SD16—534no—
497C2×SD16—2122no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—531no—
501C22×C8—531no—
502C22×C8—534no—
503C22×C8—534no—
504C22×C8—2122no—
505C22×C8—2122no—
506#126—1068no—
507#125—534no—
508#125—1068no—
509#125—1062no—
510#124—28no—
511#124—22no—
512#124C22×D5314yes—
513#123—1068no—
514C22⋊Q8—22no—
515C22⋊Q8—28no—
516C22⋊Q8—534no—
517C22⋊Q8—534no—
518C22⋊Q8—1062no—
519C22⋊Q8—1062no—
520C22⋊Q8C22×D5314yes—
521#121—28no—
522#121—22no—
523#121C22×D5314yes—
524C4×Q8—22no—
525C4×Q8—534no—
526C4×Q8—1062no—
527C4×Q8C22×D5314yes—
528C4×D4—28no—
529C4×D4C22⋊D5314yes—
530C4×D4C22×D5314yes—
531#117—534no—
532#117—1062no—
533#117—1068no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—534no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1062no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4C22⋊D5311yescharacteristic
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4C22⋊D5311yescharacteristic
557C2×C22⋊C4C22⋊D5311yescharacteristic
558C2×C42—21no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42C22×D5311yescharacteristic
562#107—534no—
563#107—534no—
564#106—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#103—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#102—534no—
574#102—534no—
575#102—534no—
576C22⋊C8—534no—
577C22⋊C8—534no—
578C4×C8—534no—
579C24—21no—
580C24C2×C22⋊D5311yescharacteristic
581C24C2×C22⋊D5311yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—28no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—532no—
596C2×Q8—1061no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8#1171994714yes—
600C2×Q8C23×D5312yes—
601C2×Q8C23×D5312yes—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—21no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4C2×C22⋊D5314yes—
611C2×D4C23×D5312yes—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—24no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—1064no—
624C22×C4—1061no—
625C22×C4—1061no—
626C22×C4—1061no—
627C22×C4—1061no—
628C22×C4—2124no—
629C22×C4C2×C22⋊D5312yes—
630C22×C4C2×C22⋊D5312yes—
631C22×C4C2×C22⋊D5311yescharacteristic
632C22×C4C2×C22⋊D5311yescharacteristic
633C22×C4C2×C22⋊D5311yescharacteristic
634C22×C4C2×C22⋊D5311yescharacteristic
635C22×C4C23×D5312yes—
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638Q16—1068no—
639Q16—2124no—
640SD16—2124no—
641C2×C8—532no—
642C2×C8—532no—
643C2×C8—532no—
644C2×C8—532no—
645C2×C8—1062no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—1062no—
649C2×C8—2124no—
650C2×C8—2124no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—1061no—
658C4⋊C4—1061no—
659C4⋊C4—1064no—
660C4⋊C4—1061no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4C2×C22⋊D5314yes—
667C4⋊C4C23×D5312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4C2×C22⋊D5314yes—
676C22⋊C4C2×C22⋊D5314yes—
677C42—24no—
678C42—1064no—
679C42—1064no—
680C42C2×C22⋊D5312yes—
681C42C23×D5312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23#1313323714yes—
692C23C22×C22⋊D5312yes—
693C23C22×C22⋊D5312yes—
694C23C22×C22⋊D5311yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—42no—
701Q8—1062no—
702Q8—1062no—
703Q8—2122no—
704Q8C2×#1171994714yes—
705D4—28no—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—48no—
710D4—42no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—2122no—
734C2×C4—2128no—
735C2×C4—2122no—
736C2×C4—2122no—
737C2×C4—2122no—
738C2×C4C22×C22⋊D5312yes—
739C2×C4C22×C22⋊D5312yes—
740C2×C4C22×C22⋊D5312yes—
741C2×C4C22×C22⋊D5312yes—
742C2×C4C22×C22⋊D5311yescharacteristic
743C2×C4C2×#1171994712yes—
744C2×C4#1313326212yes—
745C2×C4C24×D5311yescharacteristic
746C8—1062no—
747C8—1062no—
748C8—1062no—
749C8—1062no—
750C22—28no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22#1681126712yes—
762C22C2×#1313323714yes—
763C22C2×#1313323712yes—
764C22#1681143812yes—
765C22C23×C22⋊D5311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—2122no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681126712yes—
778C4C22×#1171994711yescharacteristic
779C4C2×#1313326211yescharacteristic
780C2—24no—
781C2—42no—
782C2—82no—
783C2#2028660214yesdirect product factor
784C2C2×#1681126711yescharacteristic
785C2C22×#1313323711yescharacteristic
786C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC2×C53×#548C2
socleC23×C53C22×D4
hypercenterC2×#548D53
hypocenterC53C2×#3300
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16811313C2semidirect
2. #20286602C2direct (N × H)
3. C2×#16810977C2semidirect
4. C2×#16810961C2semidirect
5. C2×#16810934C2semidirect
6. C2×#16810930C2semidirect
7. C2×#16810862C2semidirect
8. C2×#16810850C2semidirect
9. C2×#16810842C2semidirect
10. C2×#16810785C2semidirect
11. C2×#16810779C2semidirect
12. C2×C4×#11719925C2semidirect
13. C2×D4×#88322C2semidirect
14. C2×#16810619C2semidirect
15. C22×#13133141C2semidirect
23. #16811313C22semidirect
34. #16810977C22semidirect
35. #16810961C22semidirect
36. #16810934C22semidirect
37. #16810930C22semidirect
38. #16810862C22semidirect
39. #16810850C22semidirect
40. #16810842C22semidirect
41. #16810785C22semidirect
42. #16810779C22semidirect
43. C4×#11719925C22semidirect
44. D4×#88322C22semidirect
49. #16810619C22semidirect
56. C2×#13133141C22semidirect
406. C2×C53#3300semidirect
470. C53C2×#3300semidirect
783. C2#20286602direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113132
#202866022
C2×#168109772
C2×#168109612
C2×#168109342
C2×#168109302
C2×#168108622
C2×#168108502
C2×#168108422
C2×#168107852
C2×#168107792
C2×C4×#117199252
C2×D4×#883222
C2×#168106192
C22×#131331412
C2×C53×#5482
C2×#330053