Finite Group Databasebeta

← C2×#20287077 #28262521

Subgroups — C2×#20287077 #28262521

Order 13568.

1866 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811313C211yesmaximal, characteristic
2#20287077C2116yesmaximal, direct product factor
3C2×#16811022C211yesmaximal, characteristic, complemented
4C2×#16810964C211yesmaximal, characteristic, complemented
5C2×#16810961C211yesmaximal, characteristic, complemented
6C2×#16810953C211yesmaximal, characteristic, complemented
7C2×#16810951C211yesmaximal, characteristic, complemented
8C2×#16810930C211yesmaximal, characteristic, complemented
9C2×#16810927C211yesmaximal, characteristic, complemented
10C2×#16810862C211yesmaximal, characteristic, complemented
11C2×#16810862C211yesmaximal, characteristic, complemented
12C2×C4×#11719925C211yesmaximal, characteristic, complemented
13C2×D4×#88322C211yesmaximal, characteristic
14C2×#16810659C211yesmaximal, characteristic, complemented
15C22×#13133150C211yesmaximal, characteristic, complemented
16C2×C53×#552C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811313—24no—
21#16811313C2218yes—
22C2×#13133210—21no—
23C2×#13133209C2211yescharacteristic
24C2×#13133207—21no—
25C2×#13133198—21no—
26C2×#13133196C2211yescharacteristic
27C2×#13133196C2211yescharacteristic
28C2×C4×Dic106C2211yescharacteristic
29C2×#13133176C2211yescharacteristic
30C2×#13133173—21no—
31C22×C4⋊Dic53C2211yescharacteristic
32#16811022C2218yescomplemented
33#16810964C2218yescomplemented
34#16810961C2218yescomplemented
35#16810953C2218yescomplemented
36#16810951C2218yescomplemented
37#16810930C2218yescomplemented
38#16810927C2218yescomplemented
39#16810862C2218yescomplemented
40#16810862C2218yescomplemented
41C4×#11719925C2218yescomplemented
42D4×#88322C2218yes—
43#16810659C2218yescomplemented
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133150C2218yescomplemented
50C2×#13133148C2211yescharacteristic
51C2×#13133148C2211yescharacteristic
52C2×#13133148C2211yescharacteristic
53C2×#13133148C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133140C2211yescharacteristic
59C2×#13133140C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
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×Dic106C2311yescharacteristic
78C23×Dic53—21no—
79C2×#11719925—24no—
80C2×#11719925C2314yes—
81C22×#88322—24no—
82C22×#88322—24no—
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2314yes—
87C22×#88322C2314yes—
88C22×#88322C2311yescharacteristic
89#13133210—28no—
90#13133209—22no—
91#13133209C2314yes—
92#13133207—28no—
93#13133198—28no—
94#13133196—22no—
95#13133196—22no—
96#13133196C2314yes—
97#13133196C2314yes—
98C4×Dic106—22no—
99C4×Dic106C2314yes—
100#13133176—22no—
101#13133176C2314yes—
102#13133173—28no—
103C2×C4⋊Dic53—22no—
104C2×C4⋊Dic53—21no—
105C2×C4⋊Dic53C2314yes—
106C2×C4⋊Dic53C2311yescharacteristic
107C2×C4⋊Dic53C2311yescharacteristic
108C2×C4⋊Dic53C2311yescharacteristic
109C2×#11719919—21no—
110C2×#11719919—21no—
111C2×#11719919—21no—
112C2×#11719919—21no—
113C2×#11719919—21no—
114C2×C22⋊Dic53—21no—
115C2×C22⋊Dic53—21no—
116C2×C22⋊Dic53—21no—
117C2×C4×Dic53—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133150C2314yes—
124#13133148C2314yes—
125#13133148C2314yes—
126#13133148C2314yes—
127#13133148C2314yes—
128C4⋊#88322C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133140C2314yes—
133#13133140C2314yes—
134#13133140C2314yes—
135C22⋊#88322C2314yes—
136C22⋊#88322C2314yes—
137C4×#88322C2314yes—
138C22×Q8×C53C2311yescharacteristic
139C22×D4×C53D411yescharacteristic
140C23×C4×C53—21no—
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143#126×C53—28no—
144#125×C53—28no—
145#125×C53—22no—
146#125×C53C2314yes—
147#123×C53—28no—
148C22⋊Q8×C53—22no—
149C22⋊Q8×C53—22no—
150C22⋊Q8×C53C2314yes—
151C22⋊Q8×C53C2314yes—
152C4×Q8×C53—22no—
153C4×Q8×C53C2314yes—
154C4×D4×C53D414yes—
155C4×D4×C53C2314yes—
156#117×C53—28no—
157#117×C53—22no—
158#117×C53C2314yes—
159C2×C4⋊C4×C53—21no—
160C2×C4⋊C4×C53—22no—
161C2×C4⋊C4×C53—21no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53D411yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2314yes—
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53D411yescharacteristic
175C2×C22⋊C4×C53D411yescharacteristic
176C2×C42×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C24×C53C2×D411yescharacteristic
180C24×C53C2×D411yescharacteristic
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53C2412yes—
185C2×D4×C53—24no—
186C2×D4×C53C2×D414yes—
187C22×C4×C53—22no—
188C22×C4×C53—22no—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—24no—
196C22×C4×C53—44no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D412yes—
202C22×C4×C53C2×D412yes—
203C22×C4×C53C2412yes—
204C22×C4×C53C2412yes—
205C22×C4×C53C2411yescharacteristic
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—24no—
211C22×Dic53—44no—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—21no—
215C2×Dic106C2412yes—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—24no—
219C4⋊C4×C53—24no—
220C4⋊C4×C53—24no—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53C2×D414yes—
226C4⋊C4×C53C2412yes—
227C4⋊C4×C53C2412yes—
228C4⋊C4×C53C2412yes—
229C22⋊C4×C53—24no—
230C22⋊C4×C53—24no—
231C22⋊C4×C53—24no—
232C22⋊C4×C53C2×D414yes—
233C22⋊C4×C53C2×D414yes—
234C42×C53—24no—
235C42×C53—24no—
236C42×C53C2×D412yes—
237C42×C53C2412yes—
238C22⋊Dic53—24no—
239C22⋊Dic53—24no—
240C22⋊Dic53—24no—
241#11719925—28no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—24no—
245C4⋊Dic53—21no—
246C4⋊Dic53C2412yes—
247C4⋊Dic53C2412yes—
248C4⋊Dic53C2412yes—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254C4×Dic53—24no—
255C4×Dic53—24no—
256C2×#88322—22no—
257C2×#88322—22no—
258C2×#88322—22no—
259C2×#88322—28no—
260C2×#88322—28no—
261C2×#88322#4114yes—
262C2×#88322C2412yes—
263C2×#88322C2412yes—
264C2×#88322C2412yes—
265C2×#88322C2412yes—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53#13514yes—
272C23×C53C22×D412yes—
273C23×C53C22×D412yes—
274C23×C53C22×D411yescharacteristic
275Q8×C53—22no—
276Q8×C53—22no—
277Q8×C53—42no—
278D4×C53—28no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—24no—
284C2×C4×C53—24no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—42no—
294C2×C4×C53—48no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53C22×D412yes—
299C2×C4×C53C22×D412yes—
300C2×C4×C53C22×D412yes—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C2×#4112yes—
304C2×C4×C532−1+412yes—
305C2×C4×C53C2511yescharacteristic
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—42no—
311C2×Dic53—48no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315Dic106—22no—
316Dic106—22no—
317Dic106—42no—
318#88322—22no—
319#88322—22no—
320#88322—22no—
321#88322C2×#4114yes—
322C2×#3336—531nomaximal, Sylow
323C22×C53—28no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—44no—
330C22×C53#54712yes—
331C22×C53C2×#13514yes—
332C22×C53C2×#13512yes—
333C22×C53#57812yes—
334C22×C53C23×D411yescharacteristic
335C4×C53—22no—
336C4×C53—22no—
337C4×C53—22no—
338C4×C53—22no—
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53—42no—
343C4×C53#54712yes—
344C4×C53C22×#4111yescharacteristic
345C4×C53C2×2−1+411yescharacteristic
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350C2×#552—531no—
351C2×#552D5311yescharacteristic
352#3336—5316no—
353C2×#499—531no—
354C2×#485—531no—
355C2×#485—531no—
356C2×#483—531no—
357C2×#483—531no—
358C2×#479—531no—
359C2×#479—531no—
360C2×#467—531no—
361C2×#467—531no—
362C2×C4×Q16—531no—
363C2×C8×D4—531no—
364C2×#427—531no—
365C22×#107—531no—
366C2×C53—24no—
367C2×C53—42no—
368C2×C53#333614yescomplemented
369C2×C53C2×#54711yescharacteristic
370C2×C53C22×#13511yescharacteristic
371C2×C53C2×#57811yescharacteristic
372C22×Q16—531no—
373C23×C8—531no—
374C23×C8—531no—
375#552—24no—
376#552—538no—
377#552—1064no—
378#552C2×D5318yes—
379C2×#126—21no—
380C2×#126—1061no—
381C2×#125—21no—
382C2×#125—531no—
383C2×#125—1061no—
384C2×#125C2×D5311yescharacteristic
385C2×#123—21no—
386C2×#123—1061no—
387C2×C22⋊Q8—531no—
388C2×C22⋊Q8—531no—
389C2×C22⋊Q8C2×D5311yescharacteristic
390C2×C22⋊Q8C2×D5311yescharacteristic
391C2×C4×Q8—531no—
392C2×C4×Q8C2×D5311yescharacteristic
393C2×C4×D4C2×D5311yescharacteristic
394C2×#117—21no—
395C2×#117—531no—
396C2×#117—1061no—
397C2×#117C2×D5311yescharacteristic
398C22×C4⋊C4—531no—
399C22×C4⋊C4C2×D5311yescharacteristic
400#499—538no—
401#485—538no—
402#485—538no—
403#483—538no—
404#483—538no—
405#479—538no—
406#479—538no—
407#467—538no—
408#467—538no—
409C4×Q16—538no—
410C8×D4—538no—
411#427—538no—
412C2×#107—531no—
413C2×#107—531no—
414C2×#107—538no—
415C2×#107—531no—
416C2×#107—531no—
417C2×#107—531no—
418C2×#106—531no—
419C2×#106—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8—531no—
423C2×#103—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×C22⋊C8—531no—
430C2×C22⋊C8—531no—
431C2×C4×C8—531no—
432C53C2×#333611yescharacteristic, complemented, Sylow
433C22×Q8—531no—
434C22×Q8C22×D5311yescharacteristic
435C22×D4C22⋊D5311yescharacteristic
436C23×C4—21no—
437C23×C4—1061no—
438C23×C4C22×D5311yescharacteristic
439C23×C4C22×D5311yescharacteristic
440C2×Q16—534no—
441C2×Q16—1064no—
442C22×C8—531no—
443C22×C8—531no—
444C22×C8—531no—
445C22×C8—534no—
446C22×C8—534no—
447C22×C8—531no—
448C22×C8—1064no—
449C22×C8—1064no—
450#126—28no—
451#126—1068no—
452#125—28no—
453#125—22no—
454#125—534no—
455#125—1068no—
456#125—1062no—
457#125C22×D5314yes—
458#123—28no—
459#123—1068no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—534no—
463C22⋊Q8—534no—
464C22⋊Q8—1062no—
465C22⋊Q8—1062no—
466C22⋊Q8C22×D5314yes—
467C22⋊Q8C22×D5314yes—
468C4×Q8—22no—
469C4×Q8—534no—
470C4×Q8—1062no—
471C4×Q8C22×D5314yes—
472C4×D4C22⋊D5314yes—
473C4×D4C22×D5314yes—
474#117—22no—
475#117—28no—
476#117—534no—
477#117—1062no—
478#117—1068no—
479#117C22×D5314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—531no—
488C2×C4⋊C4—531no—
489C2×C4⋊C4—534no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—1061no—
492C2×C4⋊C4—1062no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4C22⋊D5311yescharacteristic
499C2×C4⋊C4C22×D5311yescharacteristic
500C2×C4⋊C4C22×D5311yescharacteristic
501C2×C4⋊C4C22×D5314yes—
502C2×C4⋊C4C22×D5311yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1061no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4C22⋊D5311yescharacteristic
510C2×C22⋊C4C22⋊D5311yescharacteristic
511C2×C42—21no—
512C2×C42—21no—
513C2×C42—1061no—
514C2×C42—1061no—
515C2×C42C22×D5311yescharacteristic
516#107—534no—
517#107—534no—
518#107—534no—
519#107—534no—
520#107—534no—
521#106—534no—
522#106—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526#103—534no—
527#103—534no—
528#103—534no—
529#103—534no—
530#103—534no—
531#103—534no—
532C22⋊C8—534no—
533C22⋊C8—534no—
534C4×C8—534no—
535C24C2×C22⋊D5311yescharacteristic
536C24C2×C22⋊D5311yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—532no—
541C2×Q8—1061no—
542C2×Q8—1062no—
543C2×Q8—1062no—
544C2×Q8C23×D5312yes—
545C2×D4—24no—
546C2×D4C2×C22⋊D5314yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—44no—
557C22×C4—1064no—
558C22×C4—1061no—
559C22×C4—1061no—
560C22×C4—1061no—
561C22×C4—1061no—
562C22×C4—2124no—
563C22×C4C2×C22⋊D5312yes—
564C22×C4C2×C22⋊D5312yes—
565C22×C4C2×C22⋊D5311yescharacteristic
566C22×C4C2×C22⋊D5311yescharacteristic
567C22×C4C2×C22⋊D5311yescharacteristic
568C22×C4C2×C22⋊D5311yescharacteristic
569C22×C4C23×D5312yes—
570C22×C4C23×D5312yes—
571C22×C4C23×D5311yescharacteristic
572Q16—1068no—
573C2×C8—534no—
574C2×C8—532no—
575C2×C8—532no—
576C2×C8—532no—
577C2×C8—532no—
578C2×C8—1068no—
579C2×C8—1068no—
580C2×C8—1062no—
581C2×C8—1062no—
582C2×C8—1062no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—21no—
592C4⋊C4—532no—
593C4⋊C4—532no—
594C4⋊C4—532no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—1064no—
598C4⋊C4—1061no—
599C4⋊C4—1064no—
600C4⋊C4—1064no—
601C4⋊C4—1064no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4C2×C22⋊D5314yes—
605C4⋊C4C23×D5312yes—
606C4⋊C4C23×D5312yes—
607C4⋊C4C23×D5312yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—1064no—
612C22⋊C4—1064no—
613C22⋊C4—1064no—
614C22⋊C4C2×C22⋊D5314yes—
615C22⋊C4C2×C22⋊D5314yes—
616C42—24no—
617C42—24no—
618C42—1064no—
619C42—1064no—
620C42C2×C22⋊D5312yes—
621C42C23×D5312yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23#1313323714yes—
628C23C22×C22⋊D5312yes—
629C23C22×C22⋊D5312yes—
630C23C22×C22⋊D5311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—1062no—
635Q8—1062no—
636Q8—2122no—
637D4—28no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—42no—
653C2×C4—48no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—2122no—
662C2×C4—2128no—
663C2×C4—2122no—
664C2×C4—2122no—
665C2×C4—2122no—
666C2×C4C22×C22⋊D5312yes—
667C2×C4C22×C22⋊D5312yes—
668C2×C4C22×C22⋊D5312yes—
669C2×C4C22×C22⋊D5312yes—
670C2×C4C22×C22⋊D5311yescharacteristic
671C2×C4#41×D5312yes—
672C2×C4#1313326412yes—
673C2×C4C24×D5311yescharacteristic
674C8—534no—
675C8—1062no—
676C8—1062no—
677C8—1062no—
678C22—28no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22#1681127212yes—
686C22C2×#1313323714yes—
687C22C2×#1313323712yes—
688C22#1681143812yes—
689C22C23×C22⋊D5311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2122no—
699C4—2122no—
700C4—2122no—
701C4—2122no—
702C4#1681127212yes—
703C4C2×#41×D5311yescharacteristic
704C4C2×#1313326411yescharacteristic
705C2—24no—
706C2—42no—
707C2#2028707714yesdirect product factor
708C2C2×#1681127211yescharacteristic
709C2C22×#1313323711yescharacteristic
710C2C2×#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×#3336
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. #20287077C2direct (N × H)
3. C2×#16811022C2semidirect
4. C2×#16810964C2semidirect
5. C2×#16810961C2semidirect
6. C2×#16810953C2semidirect
7. C2×#16810951C2semidirect
8. C2×#16810930C2semidirect
9. C2×#16810927C2semidirect
10. C2×#16810862C2semidirect
11. C2×#16810862C2semidirect
12. C2×C4×#11719925C2semidirect
14. C2×#16810659C2semidirect
15. C22×#13133150C2semidirect
32. #16811022C22semidirect
33. #16810964C22semidirect
34. #16810961C22semidirect
35. #16810953C22semidirect
36. #16810951C22semidirect
37. #16810930C22semidirect
38. #16810927C22semidirect
39. #16810862C22semidirect
40. #16810862C22semidirect
41. C4×#11719925C22semidirect
43. #16810659C22semidirect
49. C2×#13133150C22semidirect
368. C2×C53#3336semidirect
432. C53C2×#3336semidirect
707. C2#20287077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113132
#202870772
C2×#168110222
C2×#168109642
C2×#168109612
C2×#168109532
C2×#168109512
C2×#168109302
C2×#168109272
C2×#168108622
C2×C4×#117199252
C2×D4×#883222
C2×#168106592
C22×#131331502
C2×C53×#5522
C2×#333653