Finite Group Databasebeta

← C2×#20286805 #28260740

Subgroups — C2×#20286805 #28260740

Order 13568.

2126 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×#16811278C211yesmaximal, characteristic
2#20286805C2116yesmaximal, direct product factor
3C2×#16810993C211yesmaximal, characteristic, complemented
4C2×#16810958C211yesmaximal, characteristic, complemented
5C2×#16810964C211yesmaximal, characteristic, complemented
6C2×#16810920C211yesmaximal, characteristic, complemented
7C2×#16810879C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810833C211yesmaximal, characteristic, complemented
10C2×#16810783C211yesmaximal, characteristic, complemented
11C2×#16810783C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810622C211yesmaximal, characteristic, complemented
15C2×#16810617C211yesmaximal, characteristic, complemented
16C2×C53×#552C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×#11719945C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24#16811278—24no—
25#16811278C2218yes—
26C2×#13133217C2211yescharacteristic
27C2×#13133199—21no—
28C2×#13133199—21no—
29C2×#13133196C2211yescharacteristic
30C2×#13133196C2211yescharacteristic
31C2×#13133188—21no—
32C2×C4×D212C2211yescharacteristic
33C2×C4⋊C4×D53—21no—
34#16810993C2218yescomplemented
35#16810964C2218yescomplemented
36#16810958C2218yescomplemented
37#16810920C2218yescomplemented
38#16810879C2218yescomplemented
39#16810862C2218yescomplemented
40#16810833C2218yescomplemented
41#16810783C2218yescomplemented
42#16810783C2218yescomplemented
43#16810721C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810622C2218yescomplemented
50#16810617C2218yescomplemented
51C2×#13133141C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C53×#552—24no—
65C53×#552C2218yescomplemented
66C2×#126×C53—21no—
67C2×#125×C53—21no—
68C2×#125×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×C22⋊Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×#117×C53—21no—
75C2×#117×C53C2211yescharacteristic
76C22×C4⋊C4×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—22no—
79C2×#11719945—24no—
80C2×#11719945—24no—
81C2×#11719945—42no—
82C2×#11719945—42no—
83C2×#11719945C2314yes—
84C2×#11719945C2314yes—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×D212C2311yescharacteristic
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C2×#11719925—42no—
94C2×#11719925—42no—
95C2×#11719925C2314yes—
96C2×#11719925C2314yes—
97C2×#11719924—24no—
98C2×#11719924C2314yes—
99C2×#11719917—42no—
100C2×#11719917C2314yes—
101C22×#88322—42no—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106C22×#88322C2314yes—
107#13133217—22no—
108#13133217C2314yes—
109#13133199—28no—
110#13133199—28no—
111#13133196—22no—
112#13133196—22no—
113#13133196C2314yes—
114#13133196C2314yes—
115#13133188—28no—
116C4×D212—22no—
117C4×D212C2314yes—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×#11719919—21no—
122C2×#11719919—21no—
123C4⋊C4×D53—28no—
124C2×C22⋊Dic53—21no—
125C2×C22⋊Dic53—21no—
126C2×#11719921—21no—
127#13133150C2314yes—
128#13133150C2314yes—
129#13133148C2314yes—
130C4⋊#88322C2314yes—
131#13133141C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133140C2314yes—
138#13133137C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141C22⋊#88322C2314yes—
142C22⋊#88322C2314yes—
143#13133128C2314yes—
144C22×Q8×C53C2311yescharacteristic
145C22×D4×C53D411yescharacteristic
146C23×C4×C53—21no—
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149#126×C53—28no—
150#125×C53—28no—
151#125×C53—22no—
152#125×C53C2314yes—
153#123×C53—28no—
154C22⋊Q8×C53—22no—
155C22⋊Q8×C53—22no—
156C22⋊Q8×C53C2314yes—
157C22⋊Q8×C53C2314yes—
158C4×Q8×C53—22no—
159C4×Q8×C53C2314yes—
160C4×D4×C53D414yes—
161C4×D4×C53C2314yes—
162#117×C53—28no—
163#117×C53—22no—
164#117×C53C2314yes—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—22no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2314yes—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53D411yescharacteristic
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C42×C53—21no—
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53C2412yes—
192C2×D4×C53—42no—
193C2×D4×C53C2×D414yes—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—22no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—24no—
203C22×C4×C53—44no—
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2×D412yes—
210C22×C4×C53C2412yes—
211C22×C4×C53C2412yes—
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—44no—
216C2×C22⋊D53—44no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220#11719945—28no—
221#11719945—28no—
222#11719945—44no—
223#11719945—44no—
224#11719945—48no—
225#11719945—48no—
226C2×D212—21no—
227C2×D212—22no—
228C2×D212#4114yes—
229C2×D212C2412yes—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—44no—
234C2×C4×D53—44no—
235C2×C4×D53—44no—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—21no—
241C2×Dic106—21no—
242C2×Dic106C2412yes—
243C2×Dic106C2412yes—
244C4⋊C4×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—24no—
247C4⋊C4×C53—24no—
248C4⋊C4×C53—24no—
249C4⋊C4×C53—24no—
250C4⋊C4×C53—24no—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53C2×D414yes—
254C4⋊C4×C53C2412yes—
255C4⋊C4×C53C2412yes—
256C4⋊C4×C53C2412yes—
257C22⋊C4×C53—24no—
258C22⋊C4×C53—24no—
259C22⋊C4×C53—24no—
260C22⋊C4×C53C2×D414yes—
261C22⋊C4×C53C2×D414yes—
262C42×C53—24no—
263C42×C53—24no—
264C42×C53C2×D412yes—
265C42×C53C2412yes—
266C22⋊Dic53—24no—
267C22⋊Dic53—24no—
268#11719925—44no—
269#11719925—44no—
270#11719924—28no—
271#11719921—24no—
272C4⋊Dic53—24no—
273C4⋊Dic53—24no—
274C4⋊Dic53—21no—
275C4⋊Dic53C2412yes—
276#11719919—24no—
277#11719919—24no—
278#11719917—44no—
279C2×#88322—22no—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322—22no—
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×C53C22×D412yes—
295C23×C53C22×D412yes—
296C23×C53C22×D411yescharacteristic
297C22×D53—24no—
298C22×D53—22no—
299C22×D53—42no—
300C22×D53—42no—
301Q8×C53—22no—
302Q8×C53—22no—
303Q8×C53—42no—
304D4×C53—44no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—24no—
310C2×C4×C53—24no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—48no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—42no—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D411yescharacteristic
329C2×C4×C53C2×#4112yes—
330C2×C4×C53H(5,𝔽2)12yes—
331C2×C4×C53C2511yescharacteristic
332C22⋊D53—48no—
333C22⋊D53—48no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340D212—24no—
341D212—22no—
342D212C2×#4114yes—
343C4×D53—48no—
344C4×D53—48no—
345C4×D53—48no—
346Dic106—22no—
347Dic106—22no—
348Dic106—22no—
349Dic106—22no—
350Dic106—42no—
351Dic106—42no—
352#88322—22no—
353#88322—22no—
354#88322—22no—
355#88322—22no—
356C2×#3315—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53#54612yes—
366C22×C53#57512yes—
367C22×C53#57812yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—24no—
370C2×D53—48no—
371C2×D53—42no—
372C2×D53—42no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—22no—
376C4×C53—22no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#54612yes—
382C4×C53C22×#4111yescharacteristic
383C4×C53C2×H(5,𝔽2)11yescharacteristic
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#552D5311yescharacteristic, complemented
388C2×#547—531no—
389#3315—5316no—
390C2×#491—531no—
391C2×#484—531no—
392C2×#485—531no—
393C2×#478—531no—
394C2×#470—531no—
395C2×#467—531no—
396C2×#462—531no—
397C2×#452—531no—
398C2×#452—531no—
399C2×#440—531no—
400C2×#435—531no—
401C2×#417—531no—
402C2×#416—531no—
403C2×C53—42no—
404C2×C53—42no—
405C2×C53#331514yescomplemented
406C2×C53C2×#54611yescharacteristic
407C2×C53C2×#57511yescharacteristic
408C2×C53C2×#57811yescharacteristic
409D53—44no—
410C22×#41—531no—
411C22×#41—531no—
412C22×Q16—531no—
413C22×Q16—531no—
414C22×SD16—531no—
415C22×M16—531no—
416C23×C8—531no—
417#552—24no—
418#552C2×D5318yescomplemented
419#547—538no—
420#547—1064no—
421C2×C4⋊Q8—531no—
422C2×#126—21no—
423C2×#125—21no—
424C2×#125C2×D5311yescharacteristic
425C2×#123—21no—
426C2×#123—1061no—
427C2×#123—1061no—
428C2×C22⋊Q8—531no—
429C2×C22⋊Q8—531no—
430C2×C22⋊Q8C2×D5311yescharacteristic
431C2×C22⋊Q8C2×D5311yescharacteristic
432C2×#121—1061no—
433C2×C4×Q8C2×D5311yescharacteristic
434C2×C4×D4—531no—
435C2×C4×D4C2×D5311yescharacteristic
436C2×#117—21no—
437C2×#117C2×D5311yescharacteristic
438C22×C4⋊C4—1061no—
439C22×C4⋊C4C2×D5311yescharacteristic
440#491—538no—
441#485—538no—
442#484—538no—
443#478—538no—
444#470—538no—
445#467—538no—
446#462—538no—
447#452—538no—
448#452—538no—
449#440—538no—
450#435—538no—
451C2×#107—531no—
452C2×#107—531no—
453C2×#106—531no—
454C2×C4⋊C8—531no—
455#417—538no—
456#416—538no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×C22⋊C8—531no—
468C2×C22⋊C8—531no—
469C2×#97—531no—
470C53C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—534no—
472C2×#41—534no—
473C2×#41—1064no—
474C2×#41—1064no—
475C2×#41—1062no—
476C2×#41—1062no—
477C2×#41—2122no—
478C2×#41—2122no—
479C22×Q8—531no—
480C22×Q8—531no—
481C22×Q8C22×D5311yescharacteristic
482C22×D4—531no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4C22⋊D5311yescharacteristic
486C23×C4—21no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4C22×D5311yescharacteristic
491C23×C4C22×D5311yescharacteristic
492C2×Q16—534no—
493C2×Q16—534no—
494C2×Q16—2122no—
495C2×Q16—2122no—
496C2×SD16—534no—
497C2×SD16—1064no—
498C2×M16—534no—
499C2×M16—2122no—
500C22×C8—531no—
501C22×C8—531no—
502C22×C8—531no—
503C22×C8—531no—
504C22×C8—534no—
505C22×C8—2122no—
506C4⋊Q8—534no—
507C4⋊Q8—1062no—
508#126—28no—
509#125—28no—
510#125—22no—
511#125C22×D5314yes—
512#123—28no—
513#123—1068no—
514#123—1068no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—534no—
518C22⋊Q8—534no—
519C22⋊Q8—1062no—
520C22⋊Q8—1062no—
521C22⋊Q8C22×D5314yes—
522C22⋊Q8C22×D5314yes—
523#121—1068no—
524C4×Q8—22no—
525C4×Q8C22×D5314yes—
526C4×D4—534no—
527C4×D4—1062no—
528C4×D4C22⋊D5314yes—
529C4×D4C22×D5314yes—
530#117—22no—
531#117—28no—
532#117C22×D5314yes—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1068no—
546C2×C4⋊C4C22⋊D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C4⋊C4C22×D5311yescharacteristic
549C2×C4⋊C4C22×D5314yes—
550C2×C4⋊C4C22×D5311yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C22⋊C4C22⋊D5311yescharacteristic
558C2×C22⋊C4C22⋊D5311yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
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—
578#97—534no—
579C24—1061no—
580C24C2×C22⋊D5311yescharacteristic
581C24C2×C22⋊D5311yescharacteristic
582#41—1068no—
583#41—1068no—
584#41—2124no—
585#41—2124no—
586#41—2128no—
587#41—2128no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—532no—
592C2×Q8—532no—
593C2×Q8—1061no—
594C2×Q8—1061no—
595C2×Q8—1062no—
596C2×Q8—1062no—
597C2×Q8—1062no—
598C2×Q8—1062no—
599C2×Q8C23×D5312yes—
600C2×D4—42no—
601C2×D4—534no—
602C2×D4—532no—
603C2×D4—1064no—
604C2×D4—1064no—
605C2×D4—1061no—
606C2×D4—1062no—
607C2×D4—2124no—
608C2×D4—2124no—
609C2×D4C2×C22⋊D5314yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—24no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—44no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1064no—
624C22×C4—1064no—
625C22×C4—1064no—
626C22×C4—2124no—
627C22×C4—2124no—
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—2124no—
639Q16—2124no—
640SD16—1068no—
641M16—2124no—
642C2×C8—532no—
643C2×C8—532no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1062no—
647C2×C8—1062no—
648C2×C8—1062no—
649C2×C8—1062no—
650C2×C8—2124no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—532no—
661C4⋊C4—1061no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4C2×C22⋊D5314yes—
667C4⋊C4C23×D5312yes—
668C4⋊C4C23×D5312yes—
669C4⋊C4C23×D5312yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—1064no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4C2×C22⋊D5314yes—
677C22⋊C4C2×C22⋊D5314yes—
678C42—24no—
679C42—24no—
680C42C2×C22⋊D5312yes—
681C42C23×D5312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—1062no—
689C23—1064no—
690C23—2122no—
691C23—2122no—
692C23C22×C22⋊D5312yes—
693C23C22×C22⋊D5312yes—
694C23C22×C22⋊D5311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—1062no—
699Q8—1062no—
700Q8—1062no—
701Q8—1062no—
702Q8—2122no—
703Q8—2122no—
704D4—44no—
705D4—534no—
706D4—1062no—
707D4—1064no—
708D4—2128no—
709D4—2128no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—2128no—
733C2×C4—2128no—
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×C4#41×D5312yes—
744C2×C4#1313326312yes—
745C2×C4C24×D5311yescharacteristic
746C8—1062no—
747C8—1062no—
748C8—1062no—
749C8—1062no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—1064no—
759C22—2128no—
760C22—2122no—
761C22—2122no—
762C22#1681126112yes—
763C22#1681142112yes—
764C22#1681143812yes—
765C22C23×C22⋊D5311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—2122no—
775C4—2122no—
776C4—2122no—
777C4#1681126112yes—
778C4C2×#41×D5311yescharacteristic
779C4C2×#1313326311yescharacteristic
780C2—42no—
781C2—42no—
782C2—2124no—
783C2#2028680514yesdirect product factor
784C2C2×#1681126111yescharacteristic
785C2C2×#1681142111yescharacteristic
786C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC2×#16811278C2
hypercenterC2×#552D53
hypocenterC53C2×#3315
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #20286805C2direct (N × H)
3. C2×#16810993C2semidirect
4. C2×#16810958C2semidirect
5. C2×#16810964C2semidirect
6. C2×#16810920C2semidirect
7. C2×#16810879C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810833C2semidirect
10. C2×#16810783C2semidirect
11. C2×#16810783C2semidirect
12. C2×#16810721C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810622C2semidirect
15. C2×#16810617C2semidirect
16. C2×C53×#552C2semidirect
34. #16810993C22semidirect
35. #16810964C22semidirect
36. #16810958C22semidirect
37. #16810920C22semidirect
38. #16810879C22semidirect
39. #16810862C22semidirect
40. #16810833C22semidirect
41. #16810783C22semidirect
42. #16810783C22semidirect
43. #16810721C22semidirect
44. #16810695C22semidirect
49. #16810622C22semidirect
50. #16810617C22semidirect
65. C53×#552C22semidirect
387. C2×#552D53semidirect
405. C2×C53#3315semidirect
418. #552C2×D53semidirect
470. C53C2×#3315semidirect
783. C2#20286805direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112782
#202868052
C2×#168109932
C2×#168109582
C2×#168109642
C2×#168109202
C2×#168108792
C2×#168108622
C2×#168108332
C2×#168107832
C2×#168107212
C2×#168106952
C2×#168106222
C2×#168106172
C2×C53×#5522
C2×#331553