Finite Group Databasebeta

← C2×#20287155 #28262623

Subgroups — C2×#20287155 #28262623

Order 13568.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811277C211yesmaximal, characteristic
2#20287155C2116yesmaximal, direct product factor
3C2×#16811033C211yesmaximal, characteristic, complemented
4C2×#16810956C211yesmaximal, characteristic, complemented
5C2×#16810947C211yesmaximal, characteristic, complemented
6C2×#16810951C211yesmaximal, characteristic, complemented
7C2×#16810936C211yesmaximal, characteristic, complemented
8C2×#16810918C211yesmaximal, characteristic, complemented
9C2×#16810920C211yesmaximal, characteristic, complemented
10C2×#16810871C211yesmaximal, characteristic, complemented
11C2×#16810854C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810666C211yesmaximal, characteristic, complemented
15C22×#13133150C211yesmaximal, characteristic, complemented
16C2×C53×#552C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719924C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811277—24no—
22#16811277C2218yes—
23C2×#13133217C2211yescharacteristic
24C2×#13133201—21no—
25C2×#13133201—21no—
26C2×#13133197—21no—
27C2×#13133191C2211yescharacteristic
28C2×#13133191C2211yescharacteristic
29C2×C4×D212C2211yescharacteristic
30C22×C4⋊Dic53C2211yescharacteristic
31C22×C4⋊Dic53C2211yescharacteristic
32#16811033C2218yescomplemented
33#16810956C2218yescomplemented
34#16810951C2218yescomplemented
35#16810947C2218yescomplemented
36#16810936C2218yescomplemented
37#16810920C2218yescomplemented
38#16810918C2218yescomplemented
39#16810871C2218yescomplemented
40#16810854C2218yescomplemented
41#16810721C2218yescomplemented
42#16810695C2218yescomplemented
43#16810666C2218yescomplemented
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133150C2211yescharacteristic
50C2×#13133150C2218yescomplemented
51C2×#13133148C2211yescharacteristic
52C2×#13133148C2211yescharacteristic
53C2×#13133148C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
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×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C2×#11719924—24no—
87C2×#11719924C2314yes—
88C2×#11719917—24no—
89C2×#11719917C2314yes—
90C22×#88322—24no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yes—
95C22×#88322C2311yescharacteristic
96#13133217—22no—
97#13133217C2314yes—
98#13133201—28no—
99#13133201—28no—
100#13133197—28no—
101#13133191—22no—
102#13133191—22no—
103#13133191C2314yes—
104#13133191C2314yes—
105C4×D212—22no—
106C4×D212C2314yes—
107C2×C4⋊Dic53—22no—
108C2×C4⋊Dic53—22no—
109C2×C4⋊Dic53—21no—
110C2×C4⋊Dic53—21no—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53C2314yes—
113C2×C4⋊Dic53C2314yes—
114C2×C4⋊Dic53C2311yescharacteristic
115C2×C4⋊Dic53C2311yescharacteristic
116C2×C4⋊Dic53C2311yescharacteristic
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×#11719921—21no—
120#13133150C2314yes—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133150C2314yes—
124#13133150C2314yes—
125#13133150C2314yes—
126#13133148C2314yes—
127#13133148C2314yes—
128#13133148C2314yes—
129C4⋊#88322C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133141C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135#13133137C2314yes—
136C22⋊#88322C2314yes—
137C22⋊#88322C2314yes—
138#13133128C2314yes—
139C22×Q8×C53C2311yescharacteristic
140C22×D4×C53D411yescharacteristic
141C23×C4×C53—21no—
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144#126×C53—28no—
145#125×C53—28no—
146#125×C53—22no—
147#125×C53C2314yes—
148#123×C53—28no—
149C22⋊Q8×C53—22no—
150C22⋊Q8×C53—22no—
151C22⋊Q8×C53C2314yes—
152C22⋊Q8×C53C2314yes—
153C4×Q8×C53—22no—
154C4×Q8×C53C2314yes—
155C4×D4×C53D414yes—
156C4×D4×C53C2314yes—
157#117×C53—28no—
158#117×C53—22no—
159#117×C53C2314yes—
160C2×C4⋊C4×C53—21no—
161C2×C4⋊C4×C53—22no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53D411yescharacteristic
176C2×C22⋊C4×C53D411yescharacteristic
177C2×C42×C53—21no—
178C2×C42×C53—21no—
179C2×C42×C53C2311yescharacteristic
180C24×C53C2×D411yescharacteristic
181C24×C53C2×D411yescharacteristic
182C23×D53—21no—
183C2×Q8×C53—21no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53C2412yes—
187C2×D4×C53—24no—
188C2×D4×C53C2×D414yes—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—44no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D412yes—
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2412yes—
206C22×C4×C53C2412yes—
207C22×C4×C53C2411yescharacteristic
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—44no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—24no—
216C22×Dic53—24no—
217C22×Dic53—44no—
218C22×Dic53—44no—
219#11719947—432no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—21no—
223C2×D212C2412yes—
224C2×C4×D53—24no—
225C2×C4×D53—44no—
226C2×Dic106—24no—
227C2×Dic106—44no—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—21no—
230C4⋊C4×C53—24no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—24no—
233C4⋊C4×C53—24no—
234C4⋊C4×C53—24no—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53C2×D414yes—
238C4⋊C4×C53C2412yes—
239C4⋊C4×C53C2412yes—
240C4⋊C4×C53C2412yes—
241C22⋊C4×C53—24no—
242C22⋊C4×C53—24no—
243C22⋊C4×C53—24no—
244C22⋊C4×C53C2×D414yes—
245C22⋊C4×C53C2×D414yes—
246C42×C53—24no—
247C42×C53—24no—
248C42×C53C2×D412yes—
249C42×C53C2412yes—
250#11719924—28no—
251#11719921—24no—
252#11719921—24no—
253#11719921—24no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—24no—
258C4⋊Dic53—24no—
259C4⋊Dic53—24no—
260C4⋊Dic53C2412yes—
261C4⋊Dic53C2412yes—
262C4⋊Dic53C2412yes—
263#11719917—28no—
264C2×#88322—22no—
265C2×#88322—22no—
266C2×#88322—22no—
267C2×#88322—28no—
268C2×#88322#4114yescomplemented
269C2×#88322C2412yes—
270C2×#88322C2412yes—
271C2×#88322C2412yes—
272C2×#88322C2412yes—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53—22no—
276C23×C53—22no—
277C23×C53—22no—
278C23×C53AGL(1,ℤ/8)14yes—
279C23×C53C22×D412yes—
280C23×C53C22×D412yes—
281C23×C53C22×D411yescharacteristic
282C22×D53—22no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286Q8×C53—22no—
287Q8×C53—22no—
288Q8×C53—42no—
289D4×C53—28no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—24no—
295C2×C4×C53—24no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—42no—
305C2×C4×C53—48no—
306C2×C4×C53—42no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D411yescharacteristic
314C2×C4×C53C2×#4112yes—
315C2×C4×C532−1+412yes—
316C2×C4×C53C2511yescharacteristic
317C22⋊D53—48no—
318C22⋊D53—48no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—48no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53—42no—
326C2×Dic53—48no—
327D212—22no—
328D212—22no—
329D212—42no—
330C4×D53—48no—
331Dic106—48no—
332#88322—22no—
333#88322—22no—
334#88322—22no—
335#88322C2×#4114yescomplemented
336C2×#3343—531nomaximal, Sylow
337C22×C53—28no—
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—44no—
344C22×C53#54712yes—
345C22×C53C2×AGL(1,ℤ/8)14yes—
346C22×C53C2×AGL(1,ℤ/8)12yes—
347C22×C53#57812yes—
348C22×C53C23×D411yescharacteristic
349C2×D53—42no—
350C2×D53—42no—
351C2×D53—42no—
352C2×D53—84no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53—22no—
356C4×C53—22no—
357C4×C53—42no—
358C4×C53—42no—
359C4×C53—42no—
360C4×C53—42no—
361C4×C53#54712yes—
362C4×C53C22×#4111yescharacteristic
363C4×C53C2×2−1+411yescharacteristic
364Dic53—42no—
365Dic53—42no—
366Dic53—42no—
367C2×#552D5311yescharacteristic, complemented
368C2×#547—531no—
369#3343—5316no—
370C2×#501—531no—
371C2×#484—531no—
372C2×#482—531no—
373C2×#483—531no—
374C2×#480—531no—
375C2×#477—531no—
376C2×#478—531no—
377C2×#468—531no—
378C2×#465—531no—
379C2×#440—531no—
380C2×#435—531no—
381C2×#428—531no—
382C22×#107—531no—
383C2×C53—24no—
384C2×C53—42no—
385C2×C53#334314yescomplemented
386C2×C53C2×#54711yescharacteristic
387C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C53C2×#57811yescharacteristic
389D53—82no—
390C22×#41—1061no—
391C22×SD16—531no—
392C22×M16—531no—
393C23×C8—531no—
394#552—24no—
395#552C2×D5318yescomplemented
396#547—538no—
397#547—1064no—
398C2×C4⋊Q8—531no—
399C2×#126—21no—
400C2×#125—21no—
401C2×#125C2×D5311yescharacteristic
402C2×#123—21no—
403C2×#123—1061no—
404C2×#123—1061no—
405C2×C22⋊Q8—1061no—
406C2×C22⋊Q8C2×D5311yescharacteristic
407C2×C22⋊Q8C2×D5311yescharacteristic
408C2×#121—531no—
409C2×#121—531no—
410C2×C4×Q8C2×D5311yescharacteristic
411C2×C4×D4—531no—
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117—21no—
414C2×#117C2×D5311yescharacteristic
415C22×C4⋊C4—531no—
416C22×C4⋊C4—531no—
417C22×C4⋊C4C2×D5311yescharacteristic
418#501—538no—
419#484—538no—
420#483—538no—
421#482—538no—
422#480—538no—
423#478—538no—
424#477—538no—
425#468—538no—
426#465—538no—
427#440—538no—
428#435—538no—
429#428—538no—
430C2×#107—531no—
431C2×#107—531no—
432C2×#107—531no—
433C2×#107—531no—
434C2×#107—538no—
435C2×#107—531no—
436C2×#107—531no—
437C2×#106—531no—
438C2×#106—531no—
439C2×#106—531no—
440C2×C4⋊C8—531no—
441C2×#103—531no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×#102—531no—
447C2×C22⋊C8—531no—
448C2×C22⋊C8—531no—
449C2×#97—531no—
450C53C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—1068no—
452C2×#41—2128no—
453C22×Q8—1061no—
454C22×Q8C22×D5311yescharacteristic
455C22×D4—531no—
456C22×D4—1061no—
457C22×D4—1061no—
458C22×D4C22⋊D5311yescharacteristic
459C23×C4—21no—
460C23×C4—1061no—
461C23×C4—1061no—
462C23×C4—1061no—
463C23×C4C22×D5311yescharacteristic
464C23×C4C22×D5311yescharacteristic
465C2×SD16—534no—
466C2×SD16—1064no—
467C2×M16—534no—
468C2×M16—1064no—
469C22×C8—531no—
470C22×C8—531no—
471C22×C8—534no—
472C22×C8—531no—
473C22×C8—531no—
474C22×C8—1064no—
475C4⋊Q8—534no—
476C4⋊Q8—1062no—
477#126—28no—
478#125—28no—
479#125—22no—
480#125C22×D5314yes—
481#123—28no—
482#123—1068no—
483#123—1068no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—1068no—
487C22⋊Q8C22×D5314yes—
488C22⋊Q8C22×D5314yes—
489#121—534no—
490#121—534no—
491#121—1062no—
492#121—1062no—
493C4×Q8—22no—
494C4×Q8C22×D5314yes—
495C4×D4—534no—
496C4×D4—1062no—
497C4×D4C22⋊D5314yes—
498C4×D4C22×D5314yes—
499#117—22no—
500#117—28no—
501#117C22×D5314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—534no—
513C2×C4⋊C4—534no—
514C2×C4⋊C4—1061no—
515C2×C4⋊C4—1061no—
516C2×C4⋊C4—1062no—
517C2×C4⋊C4—1062no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4C22⋊D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C4⋊C4C22×D5314yes—
523C2×C4⋊C4C22×D5311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4C22⋊D5311yescharacteristic
531C2×C22⋊C4C22⋊D5311yescharacteristic
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C22×D5311yescharacteristic
535#107—534no—
536#107—534no—
537#107—534no—
538#107—534no—
539#107—534no—
540#107—534no—
541#106—534no—
542#106—534no—
543#106—534no—
544C4⋊C8—534no—
545#103—534no—
546#103—534no—
547#103—534no—
548#102—534no—
549#102—534no—
550#102—534no—
551C22⋊C8—534no—
552C22⋊C8—534no—
553#97—534no—
554C24—1061no—
555C24C2×C22⋊D5311yescharacteristic
556C24C2×C22⋊D5311yescharacteristic
557#41—21232no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—1064no—
562C2×Q8—2124no—
563C2×Q8C23×D5312yes—
564C2×D4—24no—
565C2×D4—532no—
566C2×D4—1064no—
567C2×D4—1064no—
568C2×D4—1061no—
569C2×D4—1062no—
570C2×D4—1062no—
571C2×D4—2124no—
572C2×D4—2124no—
573C2×D4C2×C22⋊D5314yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—1064no—
585C22×C4—1064no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1064no—
590C22×C4—2124no—
591C22×C4—2124no—
592C22×C4—2124no—
593C22×C4C2×C22⋊D5312yes—
594C22×C4C2×C22⋊D5312yes—
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C2×C22⋊D5311yescharacteristic
599C22×C4C23×D5312yes—
600C22×C4C23×D5312yes—
601C22×C4C23×D5311yescharacteristic
602SD16—1068no—
603M16—1068no—
604C2×C8—534no—
605C2×C8—532no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—532no—
609C2×C8—1068no—
610C2×C8—1062no—
611C2×C8—1062no—
612C2×C8—1062no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—532no—
623C4⋊C4—532no—
624C4⋊C4—532no—
625C4⋊C4—1061no—
626C4⋊C4—1061no—
627C4⋊C4—1061no—
628C4⋊C4—1064no—
629C4⋊C4—1064no—
630C4⋊C4—1064no—
631C4⋊C4C2×C22⋊D5314yes—
632C4⋊C4C23×D5312yes—
633C4⋊C4C23×D5312yes—
634C4⋊C4C23×D5312yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1064no—
639C22⋊C4—1064no—
640C22⋊C4—1064no—
641C22⋊C4C2×C22⋊D5314yes—
642C22⋊C4C2×C22⋊D5314yes—
643C42—24no—
644C42—24no—
645C42C2×C22⋊D5312yes—
646C42C23×D5312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—1062no—
653C23—2122no—
654C23—2122no—
655C23—2122no—
656C23#1313324214yes—
657C23C22×C22⋊D5312yes—
658C23C22×C22⋊D5312yes—
659C23C22×C22⋊D5311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—2128no—
664D4—28no—
665D4—1062no—
666D4—1062no—
667D4—2128no—
668D4—2128no—
669D4—2122no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—1062no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—2128no—
693C2×C4—2128no—
694C2×C4—2122no—
695C2×C4—2122no—
696C2×C4—2122no—
697C2×C4—2128no—
698C2×C4C22×C22⋊D5312yes—
699C2×C4C22×C22⋊D5312yes—
700C2×C4C22×C22⋊D5312yes—
701C2×C4C22×C22⋊D5312yes—
702C2×C4C22×C22⋊D5311yescharacteristic
703C2×C4#41×D5312yes—
704C2×C4#1313326412yes—
705C2×C4C24×D5311yescharacteristic
706C8—534no—
707C8—1062no—
708C8—1062no—
709C8—1062no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—4244no—
718C22—2122no—
719C22—2122no—
720C22—2122no—
721C22#1681127212yes—
722C22C2×#1313324214yes—
723C22C2×#1313324212yes—
724C22#1681143812yes—
725C22C23×C22⋊D5311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4#1681127212yes—
738C4C2×#41×D5311yescharacteristic
739C4C2×#1313326411yescharacteristic
740C2—24no—
741C2—42no—
742C2—4242no—
743C2#2028715514yesdirect product factor
744C2C2×#1681127211yescharacteristic
745C2C22×#1313324211yescharacteristic
746C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#552C2
socleC23×C53C22×D4
prime radicalC2×#16811277C2
hypercenterC2×#552D53
hypocenterC53C2×#3343
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. #20287155C2direct (N × H)
3. C2×#16811033C2semidirect
4. C2×#16810956C2semidirect
5. C2×#16810947C2semidirect
6. C2×#16810951C2semidirect
7. C2×#16810936C2semidirect
8. C2×#16810918C2semidirect
9. C2×#16810920C2semidirect
10. C2×#16810871C2semidirect
11. C2×#16810854C2semidirect
12. C2×#16810721C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810666C2semidirect
15. C22×#13133150C2semidirect
16. C2×C53×#552C2semidirect
32. #16811033C22semidirect
33. #16810956C22semidirect
34. #16810951C22semidirect
35. #16810947C22semidirect
36. #16810936C22semidirect
37. #16810920C22semidirect
38. #16810918C22semidirect
39. #16810871C22semidirect
40. #16810854C22semidirect
41. #16810721C22semidirect
42. #16810695C22semidirect
43. #16810666C22semidirect
50. C2×#13133150C22semidirect
65. C53×#552C22semidirect
268. C2×#88322#41semidirect
335. #88322C2×#41semidirect
367. C2×#552D53semidirect
385. C2×C53#3343semidirect
395. #552C2×D53semidirect
450. C53C2×#3343semidirect
743. C2#20287155direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112772
#202871552
C2×#168110332
C2×#168109562
C2×#168109472
C2×#168109512
C2×#168109362
C2×#168109182
C2×#168109202
C2×#168108712
C2×#168108542
C2×#168107212
C2×#168106952
C2×#168106662
C22×#131331502
C2×C53×#5522
C2×#334353