Finite Group Databasebeta

← C2×#20286760 #28260692

Subgroups — C2×#20286760 #28260692

Order 13568.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic106C211yesmaximal, characteristic
2#20286760C2116yesmaximal, direct product factor
3C2×#16810993C211yesmaximal, characteristic, complemented
4C2×#16810964C211yesmaximal, characteristic, complemented
5C2×#16810953C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810879C211yesmaximal, characteristic, complemented
8C2×#16810862C211yesmaximal, characteristic, complemented
9C2×#16810833C211yesmaximal, characteristic, complemented
10C2×#16810778C211yesmaximal, characteristic, complemented
11C2×#16810778C211yesmaximal, characteristic, complemented
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic
14C2×#16810631C211yesmaximal, characteristic, complemented
15C22×#13133140C211yesmaximal, characteristic, complemented
16C2×C53×#552C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C23×#88322C2211yescharacteristic
24D4×Dic106—24no—
25D4×Dic106C2218yes—
26C2×#13133217C2211yescharacteristic
27C2×#13133216—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133196C2211yescharacteristic
30C2×#13133194—21no—
31C2×#13133194—21no—
32C2×C4×Dic106C2211yescharacteristic
33C2×D4×Dic53—21no—
34#16810993C2218yescomplemented
35#16810964C2218yescomplemented
36#16810953C2218yescomplemented
37#16810927C2218yescomplemented
38#16810879C2218yescomplemented
39#16810862C2218yescomplemented
40#16810833C2218yescomplemented
41#16810778C2218yescomplemented
42#16810778C2218yescomplemented
43#16810728C2218yescomplemented
44#16810695C2218yes—
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810631C2218yescomplemented
50C2×#13133141C2211yescharacteristic
51C2×#13133140C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2218yescomplemented
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C53×#552—24no—
65C53×#552C2218yes—
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
77C22×Dic106—24no—
78C22×Dic106—24no—
79C22×Dic106—22no—
80C22×Dic106—22no—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106—42no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2314yes—
88C22×Dic106C2314yes—
89C22×Dic106C2311yescharacteristic
90C23×Dic53—21no—
91C23×Dic53—21no—
92C2×#11719925—24no—
93C2×#11719925—42no—
94C2×#11719925—42no—
95C2×#11719925C2314yes—
96C2×#11719925C2314yes—
97C2×#11719925C2314yes—
98C2×#11719917—42no—
99C2×#11719917C2314yes—
100C22×#88322—42no—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C22×#88322C2314yes—
106#13133217—22no—
107#13133217C2314yes—
108#13133216—28no—
109#13133196—22no—
110#13133196—22no—
111#13133196C2314yes—
112#13133196C2314yes—
113#13133194—28no—
114#13133194—28no—
115C4×Dic106—22no—
116C4×Dic106C2314yes—
117D4×Dic53—28no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×#11719919—21no—
122C2×#11719919—21no—
123C2×#11719919—21no—
124C2×C22⋊Dic53—21no—
125C2×C22⋊Dic53—21no—
126C2×C4×Dic53—21no—
127#13133150C2314yes—
128#13133148C2314yes—
129#13133148C2314yes—
130C4⋊#88322C2314yes—
131#13133141C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135#13133140C2314yes—
136#13133140C2314yes—
137#13133140C2314yes—
138#13133140C2314yes—
139#13133140C2314yes—
140#13133140C2314yes—
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
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×D4×C53—24no—
192C2×D4×C53C2×D414yes—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—44no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D412yes—
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2412yes—
210C22×C4×C53C2412yes—
211C22×C4×C53C2411yescharacteristic
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—24no—
217C22×Dic53—24no—
218C22×Dic53—44no—
219C22×Dic53—44no—
220C2×Dic106—21no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—28no—
227C2×Dic106—28no—
228C2×Dic106—24no—
229C2×Dic106—24no—
230C2×Dic106—21no—
231C2×Dic106—21no—
232C2×Dic106—44no—
233C2×Dic106—44no—
234C2×Dic106—48no—
235C2×Dic106—48no—
236C2×Dic106—44no—
237C2×Dic106—44no—
238C2×Dic106#4114yes—
239C2×Dic106C2412yes—
240C2×Dic106C2412yes—
241C2×Dic106C2412yes—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—24no—
245C4⋊C4×C53—24no—
246C4⋊C4×C53—24no—
247C4⋊C4×C53—24no—
248C4⋊C4×C53—24no—
249C4⋊C4×C53—24no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53C2×D414yes—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C4⋊C4×C53C2412yes—
255C22⋊C4×C53—24no—
256C22⋊C4×C53—24no—
257C22⋊C4×C53—24no—
258C22⋊C4×C53C2×D414yes—
259C22⋊C4×C53C2×D414yes—
260C42×C53—24no—
261C42×C53—24no—
262C42×C53C2×D412yes—
263C42×C53C2412yes—
264C22⋊Dic53—24no—
265C22⋊Dic53—24no—
266#11719925—28no—
267#11719925—44no—
268#11719925—44no—
269C4⋊Dic53—24no—
270C4⋊Dic53—24no—
271C4⋊Dic53—21no—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276C4×Dic53—24no—
277#11719917—44no—
278C2×#88322—22no—
279C2×#88322—22no—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322—44no—
283C2×#88322C2412yes—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53#13714yes—
293C23×C53C22×D412yes—
294C23×C53C22×D412yes—
295C23×C53C22×D411yescharacteristic
296Q8×C53—22no—
297Q8×C53—22no—
298Q8×C53—42no—
299D4×C53—28no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—24no—
305C2×C4×C53—24no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—42no—
315C2×C4×C53—48no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C2×#4112yes—
325C2×C4×C53H(5,𝔽2)12yes—
326C2×C4×C53C2511yescharacteristic
327C2×Dic53—24no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—48no—
333C2×Dic53—48no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337Dic106—24no—
338Dic106—22no—
339Dic106—22no—
340Dic106—22no—
341Dic106—22no—
342Dic106—22no—
343Dic106—48no—
344Dic106—48no—
345Dic106—42no—
346Dic106—42no—
347Dic106C2×#4114yes—
348#88322—22no—
349#88322—22no—
350#88322—22no—
351#88322—22no—
352C2×#3312—531nomaximal, Sylow
353C22×C53—22no—
354C22×C53—28no—
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—44no—
360C22×C53#54612yes—
361C22×C53C2×#13714yes—
362C22×C53C2×#13712yes—
363C22×C53#57812yes—
364C22×C53C23×D411yescharacteristic
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—22no—
368C4×C53—22no—
369C4×C53—42no—
370C4×C53—42no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53#54612yes—
374C4×C53C22×#4111yescharacteristic
375C4×C53C2×H(5,𝔽2)11yescharacteristic
376Dic53—24no—
377Dic53—42no—
378Dic53—42no—
379Dic53—42no—
380C2×#552D5311yescharacteristic
381C2×D4×Q8—531no—
382#3312—5316no—
383C2×#491—531no—
384C2×#485—531no—
385C2×#483—531no—
386C2×#479—531no—
387C2×#470—531no—
388C2×#467—531no—
389C2×#462—531no—
390C2×#451—531no—
391C2×#451—531no—
392C2×#441—531no—
393C2×#435—531no—
394C2×#419—531no—
395C22×#103—531no—
396C2×C53—24no—
397C2×C53—42no—
398C2×C53#331214yescomplemented
399C2×C53C2×#54611yescharacteristic
400C2×C53C22×#13711yescharacteristic
401C2×C53C2×#57811yescharacteristic
402C23×Q8—531no—
403C23×Q8—531no—
404C22×Q16—531no—
405C22×Q16—531no—
406C22×Q16—531no—
407C22×M16—531no—
408C23×C8—531no—
409#552—24no—
410#552C2×D5318yes—
411D4×Q8—538no—
412D4×Q8—1064no—
413C2×C4⋊Q8—531no—
414C2×C4⋊Q8—1061no—
415C2×#126—21no—
416C2×#125—21no—
417C2×#125C2×D5311yescharacteristic
418C2×#123—21no—
419C2×C22⋊Q8—531no—
420C2×C22⋊Q8—531no—
421C2×C22⋊Q8—1061no—
422C2×C22⋊Q8—1061no—
423C2×C22⋊Q8C2×D5311yescharacteristic
424C2×C22⋊Q8C2×D5311yescharacteristic
425C2×C4×Q8—531no—
426C2×C4×Q8C2×D5311yescharacteristic
427C2×C4×D4—1061no—
428C2×C4×D4C2×D5311yescharacteristic
429C2×#117—21no—
430C2×#117C2×D5311yescharacteristic
431C22×C4⋊C4C2×D5311yescharacteristic
432#491—538no—
433#485—538no—
434#483—538no—
435#479—538no—
436#470—538no—
437#467—538no—
438#462—538no—
439#451—538no—
440#451—538no—
441#441—538no—
442#435—538no—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8—531no—
447#419—538no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103—531no—
456C2×#103—531no—
457C2×#103—531no—
458C2×#103—538no—
459C2×C22⋊C8—531no—
460C2×C22⋊C8—531no—
461C2×#97—531no—
462C53C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—531no—
464C22×Q8—531no—
465C22×Q8—531no—
466C22×Q8—534no—
467C22×Q8—534no—
468C22×Q8—1064no—
469C22×Q8—1064no—
470C22×Q8—1061no—
471C22×Q8—1061no—
472C22×Q8—1062no—
473C22×Q8—1062no—
474C22×Q8—2122no—
475C22×Q8—2122no—
476C22×Q8C22×D5311yescharacteristic
477C22×D4C22⋊D5311yescharacteristic
478C23×C4—21no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4C22×D5311yescharacteristic
482C23×C4C22×D5311yescharacteristic
483C2×Q16—534no—
484C2×Q16—534no—
485C2×Q16—534no—
486C2×Q16—1064no—
487C2×Q16—2122no—
488C2×Q16—2122no—
489C2×M16—534no—
490C2×M16—2122no—
491C22×C8—531no—
492C22×C8—531no—
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—534no—
496C22×C8—2122no—
497C4⋊Q8—534no—
498C4⋊Q8—1068no—
499C4⋊Q8—1062no—
500#126—28no—
501#125—28no—
502#125—22no—
503#125C22×D5314yes—
504#123—28no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—534no—
508C22⋊Q8—534no—
509C22⋊Q8—1062no—
510C22⋊Q8—1062no—
511C22⋊Q8—1068no—
512C22⋊Q8—1068no—
513C22⋊Q8C22×D5314yes—
514C22⋊Q8C22×D5314yes—
515C4×Q8—22no—
516C4×Q8—534no—
517C4×Q8—1062no—
518C4×Q8C22×D5314yes—
519C4×D4—1068no—
520C4×D4C22⋊D5314yes—
521C4×D4C22×D5314yes—
522#117—22no—
523#117—28no—
524#117C22×D5314yes—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—1061no—
534C2×C4⋊C4—1061no—
535C2×C4⋊C4—1061no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4C22⋊D5311yescharacteristic
539C2×C4⋊C4C22×D5311yescharacteristic
540C2×C4⋊C4C22×D5311yescharacteristic
541C2×C4⋊C4C22×D5314yes—
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4C22⋊D5311yescharacteristic
549C2×C22⋊C4C22⋊D5311yescharacteristic
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—1061no—
553C2×C42C22×D5311yescharacteristic
554#107—534no—
555#106—534no—
556#106—534no—
557C4⋊C8—534no—
558#103—534no—
559#103—534no—
560#103—534no—
561#103—534no—
562#103—534no—
563#103—534no—
564#103—534no—
565#103—534no—
566#103—534no—
567#103—534no—
568C22⋊C8—534no—
569C22⋊C8—534no—
570#97—534no—
571C24C2×C22⋊D5311yescharacteristic
572C24C2×C22⋊D5311yescharacteristic
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—534no—
577C2×Q8—532no—
578C2×Q8—532no—
579C2×Q8—532no—
580C2×Q8—1068no—
581C2×Q8—1068no—
582C2×Q8—1061no—
583C2×Q8—1064no—
584C2×Q8—1064no—
585C2×Q8—1061no—
586C2×Q8—1061no—
587C2×Q8—1062no—
588C2×Q8—1062no—
589C2×Q8—1062no—
590C2×Q8—1062no—
591C2×Q8—1062no—
592C2×Q8—2124no—
593C2×Q8—2124no—
594C2×Q8—2124no—
595C2×Q8—2124no—
596C2×Q8—2128no—
597C2×Q8—2128no—
598C2×Q8C23×D5312yes—
599C2×D4—24no—
600C2×D4C2×C22⋊D5314yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—1061no—
612C22×C4—1064no—
613C22×C4—1064no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—2124no—
618C22×C4—2124no—
619C22×C4C2×C22⋊D5312yes—
620C22×C4C2×C22⋊D5312yes—
621C22×C4C2×C22⋊D5311yescharacteristic
622C22×C4C2×C22⋊D5311yescharacteristic
623C22×C4C2×C22⋊D5311yescharacteristic
624C22×C4C2×C22⋊D5311yescharacteristic
625C22×C4C23×D5312yes—
626C22×C4C23×D5312yes—
627C22×C4C23×D5311yescharacteristic
628Q16—1068no—
629Q16—2124no—
630Q16—2124no—
631M16—2124no—
632C2×C8—532no—
633C2×C8—532no—
634C2×C8—532no—
635C2×C8—532no—
636C2×C8—1062no—
637C2×C8—1062no—
638C2×C8—1062no—
639C2×C8—1062no—
640C2×C8—2124no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—21no—
650C4⋊C4—532no—
651C4⋊C4—1061no—
652C4⋊C4—1064no—
653C4⋊C4—1064no—
654C4⋊C4—1064no—
655C4⋊C4—1064no—
656C4⋊C4—1064no—
657C4⋊C4C2×C22⋊D5314yes—
658C4⋊C4C23×D5312yes—
659C4⋊C4C23×D5312yes—
660C4⋊C4C23×D5312yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C22⋊C4C2×C22⋊D5314yes—
667C22⋊C4C2×C22⋊D5314yes—
668C42—24no—
669C42—24no—
670C42—1064no—
671C42C2×C22⋊D5312yes—
672C42C23×D5312yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1313324714yes—
679C23C22×C22⋊D5312yes—
680C23C22×C22⋊D5312yes—
681C23C22×C22⋊D5311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—534no—
686Q8—1062no—
687Q8—1064no—
688Q8—1062no—
689Q8—1062no—
690Q8—1062no—
691Q8—1062no—
692Q8—2128no—
693Q8—2128no—
694Q8—2122no—
695Q8—2122no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—1062no—
717C2×C4—1064no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—2128no—
722C2×C4—2128no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4C22×C22⋊D5312yes—
727C2×C4C22×C22⋊D5312yes—
728C2×C4C22×C22⋊D5312yes—
729C2×C4C22×C22⋊D5312yes—
730C2×C4C22×C22⋊D5311yescharacteristic
731C2×C4#41×D5312yes—
732C2×C4#1313326312yes—
733C2×C4C24×D5311yescharacteristic
734C8—1062no—
735C8—1062no—
736C8—1062no—
737C8—1062no—
738C22—28no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1681126112yes—
746C22C2×#1313324714yes—
747C22C2×#1313324712yes—
748C22#1681143812yes—
749C22C23×C22⋊D5311yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—1064no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4#1681126112yes—
763C4C2×#41×D5311yescharacteristic
764C4C2×#1313326311yescharacteristic
765C2—24no—
766C2—42no—
767C2#2028676014yesdirect product factor
768C2C2×#1681126111yescharacteristic
769C2C22×#1313324711yescharacteristic
770C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×#552D53
hypocenterC53C2×#3312
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. #20286760C2direct (N × H)
3. C2×#16810993C2semidirect
4. C2×#16810964C2semidirect
5. C2×#16810953C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810879C2semidirect
8. C2×#16810862C2semidirect
9. C2×#16810833C2semidirect
10. C2×#16810778C2semidirect
11. C2×#16810778C2semidirect
12. C2×#16810728C2semidirect
14. C2×#16810631C2semidirect
15. C22×#13133140C2semidirect
34. #16810993C22semidirect
35. #16810964C22semidirect
36. #16810953C22semidirect
37. #16810927C22semidirect
38. #16810879C22semidirect
39. #16810862C22semidirect
40. #16810833C22semidirect
41. #16810778C22semidirect
42. #16810778C22semidirect
43. #16810728C22semidirect
49. #16810631C22semidirect
60. C2×#13133140C22semidirect
398. C2×C53#3312semidirect
462. C53C2×#3312semidirect
767. C2#20286760direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic1062
#202867602
C2×#168109932
C2×#168109642
C2×#168109532
C2×#168109272
C2×#168108792
C2×#168108622
C2×#168108332
C2×#168107782
C2×#168107282
C2×#168106952
C2×#168106312
C22×#131331402
C2×C53×#5522
C2×#331253