Finite Group Databasebeta

← #27351101

Subgroups — #27351101

Order 13568.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283840C211yesmaximal, characteristic, complemented
2#20283359C211yesmaximal, characteristic, complemented
3#20273184C211yesmaximal, characteristic, complemented
4#20273180C211yesmaximal, characteristic, complemented
5#20273175C211yesmaximal, characteristic, complemented
6#20273158C211yesmaximal, characteristic, complemented
7#20273149C211yesmaximal, characteristic, complemented
8#20273140C211yesmaximal, characteristic, complemented
9#20273128C211yesmaximal, characteristic, complemented
10#20273123C211yesmaximal, characteristic, complemented
11#20273114C211yesmaximal, characteristic, complemented
12#20273106C211yesmaximal, characteristic, complemented
13#20273102C211yesmaximal, characteristic, complemented
14C2×D4⋊#88322C211yesmaximal, characteristic, complemented
15C53×#3481C211yesmaximal, characteristic
16#16810754—21no—
17#16810695—21no—
18#16810695—21no—
19D4×#88322—21no—
20#16810684—21no—
21#16810684—21no—
22#16810680C2211yescharacteristic, complemented
23#16810680C2211yescharacteristic, complemented
24#16810676C2211yescharacteristic, complemented
25#16810676C2211yescharacteristic, complemented
26#16810676C2211yescharacteristic, complemented
27#16810676C2211yescharacteristic, complemented
28#16810676C2211yescharacteristic, complemented
29#16810650—21no—
30#16810647C2211yescharacteristic, complemented
31C2×C4⋊#88322C2211yescharacteristic, complemented
32C2×C4⋊#88322C2211yescharacteristic, complemented
33#16810590—21no—
34C4×#11719917C2211yescharacteristic, complemented
35C2×C4×#88322C2211yescharacteristic, complemented
36Q8⋊#88322C2211yescharacteristic, complemented
37Q8⋊#88322C2211yescharacteristic, complemented
38Q8⋊#88322C2211yescharacteristic, complemented
39Q8⋊#88322C2211yescharacteristic, complemented
40D4⋊#88322C2211yescharacteristic
41D4⋊#88322C2211yescharacteristic
42D4⋊#88322C2211yescharacteristic
43D4⋊#88322C2211yescharacteristic
44D4⋊#88322C2211yescharacteristic, complemented
45D4⋊#88322C2211yescharacteristic, complemented
46D4⋊#88322C2211yescharacteristic, complemented
47D4⋊#88322C2211yescharacteristic, complemented
48D4⋊#88322C2211yescharacteristic, complemented
49D4⋊#88322C2211yescharacteristic, complemented
50D4⋊#88322C2211yescharacteristic, complemented
51D4⋊#88322C2211yescharacteristic, complemented
52C53×#559C411yescharacteristic
53C53×#554C411yescharacteristic
54C53×#554C411yescharacteristic
55C53×#553—21no—
56C53×#553C411yescharacteristic
57C53×#553C411yescharacteristic
58C53×#551—21no—
59C53×#551—21no—
60C53×#546—21no—
61C53×#546C411yescharacteristic
62C53×#546C411yescharacteristic
63D42×C53C411yescharacteristic
64C53×#532C2211yescharacteristic
65C53×#529—21no—
66C53×#529C2211yescharacteristic
67C53×#529C2211yescharacteristic
68C53×#525—21no—
69C53×#525—21no—
70C4×#41×C53C2211yescharacteristic
71C4×#41×C53C2211yescharacteristic
72C2×C4×D4×C53—21no—
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×#11719917—21no—
76C2×#11719917—21no—
77C22×#88322—21no—
78C22×#88322—21no—
79C22×#88322—21no—
80C4⋊#88322—21no—
81C4⋊#88322—21no—
82C4⋊#88322—21no—
83C4⋊#88322—21no—
84C4⋊#88322—21no—
85C4⋊#88322—21no—
86C4⋊#88322—21no—
87C4⋊#88322C2311yescharacteristic
88C4⋊#88322C2311yescharacteristic
89C4⋊#88322C2311yescharacteristic
90C4⋊#88322C2311yescharacteristic
91C22⋊#88322—21no—
92C22⋊#88322—21no—
93C22⋊#88322—21no—
94C22⋊#88322—21no—
95C22⋊#88322—21no—
96C22⋊#88322—21no—
97C22⋊#88322—21no—
98#13133128—21no—
99#13133128—21no—
100#13133128—21no—
101C4×#88322—21no—
102C4×#88322—21no—
103C4×#88322C2311yescharacteristic
104C4×#88322C2311yescharacteristic
105C4×#88322C2311yescharacteristic
106C4×#88322C2311yescharacteristic
107C2×#41×C53—21no—
108C2×#41×C53C2×C411yescharacteristic
109C2×#41×C53D411yescharacteristic
110C22×D4×C53—21no—
111C22×D4×C53C2×C411yescharacteristic
112C22×D4×C53C2×C411yescharacteristic
113C23×C4×C53—21no—
114C23×C4×C53—21no—
115C4⋊Q8×C53C2×C411yescharacteristic
116#127×C53C2×C411yescharacteristic
117#126×C53—21no—
118#126×C53—21no—
119#126×C53—21no—
120#126×C53—21no—
121#125×C53—21no—
122#125×C53C2×C411yescharacteristic
123#125×C53C2×C411yescharacteristic
124#124×C53—21no—
125#124×C53—21no—
126#124×C53C2×C411yescharacteristic
127#124×C53C2×C411yescharacteristic
128#123×C53—21no—
129#123×C53—21no—
130#123×C53—21no—
131#123×C53—21no—
132#123×C53—21no—
133#123×C53—21no—
134#123×C53—21no—
135#123×C53—21no—
136C22⋊Q8×C53—21no—
137C22⋊Q8×C53—21no—
138C22⋊Q8×C53—21no—
139C22⋊Q8×C53—21no—
140C22⋊Q8×C53—21no—
141C22⋊Q8×C53C2×C411yescharacteristic
142C22⋊Q8×C53C2×C411yescharacteristic
143#121×C53—21no—
144#121×C53—21no—
145#121×C53—21no—
146#121×C53—21no—
147#121×C53—21no—
148#121×C53—21no—
149#121×C53C2×C411yescharacteristic
150#121×C53C2×C411yescharacteristic
151#121×C53C2×C411yescharacteristic
152#121×C53C2×C411yescharacteristic
153#120×C53—21no—
154#120×C53—21no—
155#120×C53—21no—
156#120×C53—21no—
157C4×Q8×C53C2×C411yescharacteristic
158C4×Q8×C53C2×C411yescharacteristic
159C4×Q8×C53D411yescharacteristic
160C4×Q8×C53C2311yescharacteristic
161C4×D4×C53—21no—
162C4×D4×C53—21no—
163C4×D4×C53—21no—
164C4×D4×C53—21no—
165C4×D4×C53—21no—
166C4×D4×C53—21no—
167C4×D4×C53—21no—
168C4×D4×C53—21no—
169C4×D4×C53—21no—
170C4×D4×C53—21no—
171C4×D4×C53—21no—
172C4×D4×C53—21no—
173C4×D4×C53—21no—
174C4×D4×C53C2×C411yescharacteristic
175C4×D4×C53C2×C411yescharacteristic
176C4×D4×C53C2×C411yescharacteristic
177C4×D4×C53C2×C411yescharacteristic
178C4×D4×C53C2×C411yescharacteristic
179C4×D4×C53C2×C411yescharacteristic
180C4×D4×C53C2×C411yescharacteristic
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53D411yescharacteristic
183C4×D4×C53D411yescharacteristic
184C4×D4×C53D411yescharacteristic
185C4×D4×C53C2311yescharacteristic
186C4×D4×C53C2311yescharacteristic
187C4×D4×C53C2311yescharacteristic
188#117×C53—21no—
189#117×C53—21no—
190#117×C53—21no—
191#117×C53C2×C411yescharacteristic
192#117×C53D411yescharacteristic
193#117×C53D411yescharacteristic
194#117×C53D411yescharacteristic
195C2×C4⋊C4×C53—21no—
196C2×C4⋊C4×C53C2×C411yescharacteristic
197C2×C4⋊C4×C53C2×C411yescharacteristic
198C2×C22⋊C4×C53—21no—
199C2×C22⋊C4×C53—21no—
200C2×C22⋊C4×C53—21no—
201C2×C22⋊C4×C53—21no—
202C2×C42×C53—21no—
203C2×C42×C53C2311yescharacteristic
204C2×C42×C53C2311yescharacteristic
205C2×C42×C53C2311yescharacteristic
206C24×C53—21no—
207C24×C53—21no—
208#41×C53—22no—
209#41×C53—42no—
210#41×C53—41no—
211#41×C53—81no—
212#41×C53—81no—
213C2×Q8×C53—21no—
214C2×Q8×C53C22⋊C411yescharacteristic
215C2×Q8×C53C22×C411yescharacteristic
216C2×D4×C53—22no—
217C2×D4×C53—22no—
218C2×D4×C53—21no—
219C2×D4×C53—21no—
220C2×D4×C53—21no—
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—21no—
224C2×D4×C53—21no—
225C2×D4×C53—21no—
226C2×D4×C53—21no—
227C2×D4×C53—41no—
228C2×D4×C53—41no—
229C2×D4×C53—44no—
230C2×D4×C53C22⋊C411yescharacteristic
231C2×D4×C53C22⋊C411yescharacteristic
232C2×D4×C53C22⋊C411yescharacteristic
233C2×D4×C53C22×C411yescharacteristic
234C2×D4×C53C22×C411yescharacteristic
235C2×D4×C53C22×C411yescharacteristic
236C22×C4×C53—21no—
237C22×C4×C53—21no—
238C22×C4×C53—21no—
239C22×C4×C53—21no—
240C22×C4×C53—21no—
241C22×C4×C53—21no—
242C22×C4×C53—21no—
243C22×C4×C53—21no—
244C22×C4×C53—21no—
245C22×C4×C53—21no—
246C22×C4×C53—21no—
247C22×C4×C53—81no—
248C22×C4×C53—81no—
249C22×C4×C53—81no—
250C22×C4×C53—81no—
251C22×C4×C53C22×C411yescharacteristic
252C22×C4×C53C22×C411yescharacteristic
253C22×C4×C53C22×C411yescharacteristic
254C22×C4×C53C2×D411yescharacteristic
255C22×C4×C53C2×D411yescharacteristic
256C22×C4×C53C2×D411yescharacteristic
257C22×C4×C53C2×D411yescharacteristic
258C22×C4×C53C2×D411yescharacteristic
259C22×C4×C53C2×D411yescharacteristic
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53—21no—
266C4⋊C4×C53—21no—
267C4⋊C4×C53—21no—
268C4⋊C4×C53—21no—
269C4⋊C4×C53—21no—
270C4⋊C4×C53—21no—
271C4⋊C4×C53C22⋊C411yescharacteristic
272C4⋊C4×C53C22⋊C411yescharacteristic
273C4⋊C4×C53C22⋊C411yescharacteristic
274C4⋊C4×C53C22⋊C411yescharacteristic
275C4⋊C4×C53C22⋊C411yescharacteristic
276C4⋊C4×C53C22⋊C411yescharacteristic
277C4⋊C4×C53C22×C411yescharacteristic
278C4⋊C4×C53C22×C411yescharacteristic
279C4⋊C4×C53C22×C411yescharacteristic
280C4⋊C4×C53C22×C411yescharacteristic
281C22⋊C4×C53—21no—
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C22⋊C4×C53—21no—
286C22⋊C4×C53—21no—
287C22⋊C4×C53—21no—
288C22⋊C4×C53—21no—
289C22⋊C4×C53—21no—
290C22⋊C4×C53—21no—
291C22⋊C4×C53—21no—
292C22⋊C4×C53—21no—
293C22⋊C4×C53—21no—
294C22⋊C4×C53—21no—
295C22⋊C4×C53—21no—
296C22⋊C4×C53—21no—
297C22⋊C4×C53—21no—
298C22⋊C4×C53—21no—
299C22⋊C4×C53—21no—
300C22⋊C4×C53C22⋊C411yescharacteristic
301C22⋊C4×C53C22⋊C411yescharacteristic
302C22⋊C4×C53C22⋊C411yescharacteristic
303C22⋊C4×C53C22⋊C411yescharacteristic
304C22⋊C4×C53C22⋊C411yescharacteristic
305C22⋊C4×C53C22⋊C411yescharacteristic
306C42×C53—21no—
307C42×C53—21no—
308C42×C53—21no—
309C42×C53C22×C411yescharacteristic
310C42×C53C22×C411yescharacteristic
311C42×C53C22×C411yescharacteristic
312C42×C53C2×D411yescharacteristic
313C42×C53C2×D411yescharacteristic
314C42×C53C2×D411yescharacteristic
315C42×C53C2×D411yescharacteristic
316C42×C53C2×D411yescharacteristic
317C42×C53C2×D411yescharacteristic
318C42×C53C2411yescharacteristic
319#11719917—42no—
320#11719917—81no—
321C2×#88322—21no—
322C2×#88322—21no—
323C2×#88322—21no—
324C2×#88322—21no—
325C2×#88322—21no—
326C2×#88322—21no—
327C2×#88322—21no—
328C2×#88322—21no—
329C2×#88322—42no—
330C2×#88322—81no—
331C2×#88322—81no—
332C23×C53—21no—
333C23×C53—21no—
334C23×C53—21no—
335C23×C53—42no—
336C23×C53—42no—
337C23×C53—42no—
338C23×C53—42no—
339C23×C53—81no—
340C23×C53—81no—
341C23×C53C2×C22⋊C411yescharacteristic
342C23×C53C2×C22⋊C411yescharacteristic
343C23×C53C2×C22⋊C411yescharacteristic
344Q8×C53—21no—
345Q8×C53—21no—
346Q8×C53—41no—
347Q8×C53—81no—
348D4×C53—22no—
349D4×C53—22no—
350D4×C53—21no—
351D4×C53—21no—
352D4×C53—21no—
353D4×C53—21no—
354D4×C53—21no—
355D4×C53—41no—
356D4×C53—42no—
357D4×C53—42no—
358D4×C53—42no—
359D4×C53—42no—
360D4×C53—42no—
361D4×C53—42no—
362D4×C53—81no—
363D4×C53—81no—
364D4×C53—81no—
365D4×C53#13112yes—
366C2×C4×C53—22no—
367C2×C4×C53—21no—
368C2×C4×C53—21no—
369C2×C4×C53—21no—
370C2×C4×C53—21no—
371C2×C4×C53—21no—
372C2×C4×C53—21no—
373C2×C4×C53—21no—
374C2×C4×C53—21no—
375C2×C4×C53—21no—
376C2×C4×C53—21no—
377C2×C4×C53—21no—
378C2×C4×C53—21no—
379C2×C4×C53—21no—
380C2×C4×C53—21no—
381C2×C4×C53—21no—
382C2×C4×C53—21no—
383C2×C4×C53—21no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—42no—
387C2×C4×C53—42no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—41no—
391C2×C4×C53—41no—
392C2×C4×C53—41no—
393C2×C4×C53—41no—
394C2×C4×C53—81no—
395C2×C4×C53—81no—
396C2×C4×C53—81no—
397C2×C4×C53—81no—
398C2×C4×C53—81no—
399C2×C4×C53—81no—
400C2×C4×C53C2×C22⋊C411yescharacteristic
401C2×C4×C53C2×C22⋊C411yescharacteristic
402C2×C4×C53C2×C22⋊C411yescharacteristic
403C2×C4×C53C2×C22⋊C411yescharacteristic
404C2×C4×C53C2×C22⋊C411yescharacteristic
405C2×C4×C53C2×C22⋊C411yescharacteristic
406C2×C4×C53C2×C22⋊C411yescharacteristic
407C2×C4×C53C2×C22⋊C411yescharacteristic
408C2×C4×C53C2×C22⋊C411yescharacteristic
409C2×C4×C53C23×C411yescharacteristic
410C2×C4×C53C22×D411yescharacteristic
411C2×C4×C53C22×D411yescharacteristic
412#88322—41no—
413#88322—41no—
414#88322—41no—
415#88322—41no—
416#88322—41no—
417#88322—41no—
418#88322—41no—
419#88322—41no—
420#17521—531nomaximal, Sylow
421C22×C53—21no—
422C22×C53—21no—
423C22×C53—21no—
424C22×C53—21no—
425C22×C53—22no—
426C22×C53—21no—
427C22×C53—21no—
428C22×C53—21no—
429C22×C53—21no—
430C22×C53—41no—
431C22×C53—41no—
432C22×C53—41no—
433C22×C53—41no—
434C22×C53—41no—
435C22×C53—41no—
436C22×C53—41no—
437C22×C53—41no—
438C22×C53—84no—
439C22×C53—84no—
440C22×C53#42112yes—
441C22×C53C22×C22⋊C411yescharacteristic
442C4×C53—21no—
443C4×C53—21no—
444C4×C53—21no—
445C4×C53—21no—
446C4×C53—21no—
447C4×C53—21no—
448C4×C53—21no—
449C4×C53—21no—
450C4×C53—21no—
451C4×C53—21no—
452C4×C53—41no—
453C4×C53—41no—
454C4×C53—41no—
455C4×C53—41no—
456C4×C53—41no—
457C4×C53C2×#13111yescharacteristic
458C4×C53#56811yescharacteristic
459C4×C53#57611yescharacteristic
460C4×C53#57711yescharacteristic
461#3481D5311yescharacteristic
462#2990—531no—
463#2922—531no—
464#1496—531no—
465#1495—531no—
466#1494—531no—
467#1490—531no—
468#1488—531no—
469#1486—531no—
470#1483—531no—
471#1482—531no—
472#1480—531no—
473#1478—531no—
474#1477—531no—
475C2×D4⋊C8—531no—
476C2×C53—22no—
477C2×C53—41no—
478C2×C53—41no—
479C2×C53—42no—
480C2×C53—81no—
481C2×C53—81no—
482C2×C53#288011yescharacteristic
483C2×C53#289711yescharacteristic
484C2×C53C2×#42111yescharacteristic
485#559Dic5311yescharacteristic
486#554Dic5311yescharacteristic
487#554Dic5311yescharacteristic
488#553—21no—
489#553Dic5311yescharacteristic
490#553Dic5311yescharacteristic
491#551—21no—
492#551—21no—
493#546—21no—
494#546Dic5311yescharacteristic
495#546Dic5311yescharacteristic
496D42Dic5311yescharacteristic
497#532C2×D5311yescharacteristic
498#529—21no—
499#529C2×D5311yescharacteristic
500#529C2×D5311yescharacteristic
501#525—21no—
502#525—21no—
503C4×#41C2×D5311yescharacteristic
504C4×#41C2×D5311yescharacteristic
505C2×C4×D4—21no—
506C2×C4×D4C2×D5311yescharacteristic
507C2×C4×D4C2×D5311yescharacteristic
508#446—1061no—
509#435—1061no—
510#435—1061no—
511C8×D4—1061no—
512#433—1061no—
513#433—1061no—
514#432—531no—
515#432—531no—
516#431—531no—
517#431—531no—
518#431—531no—
519#431—531no—
520#431—531no—
521#424—1061no—
522#423—531no—
523C2×C4⋊C8—531no—
524C2×C4⋊C8—531no—
525#408—1061no—
526C4×M16—531no—
527C2×C4×C8—531no—
528Q8⋊C8—531no—
529Q8⋊C8—531no—
530Q8⋊C8—531no—
531Q8⋊C8—531no—
532D4⋊C8—531no—
533D4⋊C8—531no—
534D4⋊C8—531no—
535D4⋊C8—531no—
536D4⋊C8—531no—
537D4⋊C8—531no—
538D4⋊C8—531no—
539D4⋊C8—531no—
540D4⋊C8—531no—
541D4⋊C8—531no—
542D4⋊C8—531no—
543D4⋊C8—531no—
544C53#1752111yescharacteristic, complemented, Sylow
545C2×#41—21no—
546C2×#41C2×Dic5311yescharacteristic
547C2×#41C22⋊D5311yescharacteristic
548C22×D4—21no—
549C22×D4C2×Dic5311yescharacteristic
550C22×D4C2×Dic5311yescharacteristic
551C23×C4—21no—
552C23×C4—21no—
553C2×M16—1061no—
554C2×M16—1061no—
555C22×C8—1061no—
556C22×C8—1061no—
557C22×C8—1061no—
558C4⋊Q8C2×Dic5311yescharacteristic
559#127C2×Dic5311yescharacteristic
560#126—21no—
561#126—21no—
562#126—21no—
563#126—21no—
564#125—21no—
565#125C2×Dic5311yescharacteristic
566#125C2×Dic5311yescharacteristic
567#124—21no—
568#124—21no—
569#124C2×Dic5311yescharacteristic
570#124C2×Dic5311yescharacteristic
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8C2×Dic5311yescharacteristic
585C22⋊Q8C2×Dic5311yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121C2×Dic5311yescharacteristic
593#121C2×Dic5311yescharacteristic
594#121C2×Dic5311yescharacteristic
595#121C2×Dic5311yescharacteristic
596#120—21no—
597#120—21no—
598#120—21no—
599#120—21no—
600C4×Q8C2×Dic5311yescharacteristic
601C4×Q8C2×Dic5311yescharacteristic
602C4×Q8C22⋊D5311yescharacteristic
603C4×Q8C22×D5311yescharacteristic
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4C2×Dic5311yescharacteristic
618C4×D4C2×Dic5311yescharacteristic
619C4×D4C2×Dic5311yescharacteristic
620C4×D4C2×Dic5311yescharacteristic
621C4×D4C2×Dic5311yescharacteristic
622C4×D4C2×Dic5311yescharacteristic
623C4×D4C2×Dic5311yescharacteristic
624C4×D4C2×Dic5311yescharacteristic
625C4×D4C22⋊D5311yescharacteristic
626C4×D4C22⋊D5311yescharacteristic
627C4×D4C22⋊D5311yescharacteristic
628C4×D4C22×D5311yescharacteristic
629C4×D4C22×D5311yescharacteristic
630C4×D4C22×D5311yescharacteristic
631#117—21no—
632#117—21no—
633#117—21no—
634#117C2×Dic5311yescharacteristic
635#117C22⋊D5311yescharacteristic
636#117C22⋊D5311yescharacteristic
637#117C22⋊D5311yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4C2×Dic5311yescharacteristic
640C2×C4⋊C4C2×Dic5311yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C42—21no—
646C2×C42C22×D5311yescharacteristic
647C2×C42C22×D5311yescharacteristic
648C2×C42C22×D5311yescharacteristic
649C4⋊C8—531no—
650C4⋊C8—531no—
651C4⋊C8—531no—
652C4⋊C8—531no—
653C4⋊C8—1061no—
654C4⋊C8—1061no—
655C4⋊C8—1061no—
656C4⋊C8—1061no—
657C4⋊C8—1061no—
658C4⋊C8—1061no—
659C4⋊C8—1061no—
660C22⋊C8—1061no—
661C22⋊C8—1061no—
662C22⋊C8—1061no—
663C22⋊C8—1061no—
664C22⋊C8—1061no—
665C22⋊C8—1061no—
666C22⋊C8—1061no—
667#97—1061no—
668#97—1061no—
669#97—1061no—
670C4×C8—531no—
671C4×C8—531no—
672C4×C8—531no—
673C4×C8—531no—
674C4×C8—1061no—
675C4×C8—1061no—
676C24—21no—
677C24—21no—
678#41—22no—
679#41—42no—
680#41—41no—
681#41—81no—
682#41—81no—
683C2×Q8—21no—
684C2×Q8C22⋊Dic5311yescharacteristic
685C2×Q8C22×Dic5311yescharacteristic
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—41no—
698C2×D4—41no—
699C2×D4—44no—
700C2×D4C22⋊Dic5311yescharacteristic
701C2×D4C22⋊Dic5311yescharacteristic
702C2×D4C22⋊Dic5311yescharacteristic
703C2×D4C22×Dic5311yescharacteristic
704C2×D4C22×Dic5311yescharacteristic
705C2×D4C22×Dic5311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—81no—
720C22×C4—81no—
721C22×C4C22×Dic5311yescharacteristic
722C22×C4C22×Dic5311yescharacteristic
723C22×C4C22×Dic5311yescharacteristic
724C22×C4C2×C22⋊D5311yescharacteristic
725C22×C4C2×C22⋊D5311yescharacteristic
726C22×C4C2×C22⋊D5311yescharacteristic
727C22×C4C2×C22⋊D5311yescharacteristic
728C22×C4C2×C22⋊D5311yescharacteristic
729C22×C4C2×C22⋊D5311yescharacteristic
730M16—4241no—
731M16—2122no—
732C2×C8—1061no—
733C2×C8—1061no—
734C2×C8—1061no—
735C2×C8—1061no—
736C2×C8—1061no—
737C2×C8—1061no—
738C2×C8—1061no—
739C2×C8—1061no—
740C2×C8—4241no—
741C2×C8—4241no—
742C2×C8—2122no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4C22⋊Dic5311yescharacteristic
755C4⋊C4C22⋊Dic5311yescharacteristic
756C4⋊C4C22⋊Dic5311yescharacteristic
757C4⋊C4C22⋊Dic5311yescharacteristic
758C4⋊C4C22⋊Dic5311yescharacteristic
759C4⋊C4C22⋊Dic5311yescharacteristic
760C4⋊C4C22×Dic5311yescharacteristic
761C4⋊C4C22×Dic5311yescharacteristic
762C4⋊C4C22×Dic5311yescharacteristic
763C4⋊C4C22×Dic5311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4C22⋊Dic5311yescharacteristic
784C22⋊C4C22⋊Dic5311yescharacteristic
785C22⋊C4C22⋊Dic5311yescharacteristic
786C22⋊C4C22⋊Dic5311yescharacteristic
787C22⋊C4C22⋊Dic5311yescharacteristic
788C22⋊C4C22⋊Dic5311yescharacteristic
789C42—21no—
790C42—21no—
791C42—21no—
792C42C22×Dic5311yescharacteristic
793C42C22×Dic5311yescharacteristic
794C42C22×Dic5311yescharacteristic
795C42C2×C22⋊D5311yescharacteristic
796C42C2×C22⋊D5311yescharacteristic
797C42C2×C22⋊D5311yescharacteristic
798C42C2×C22⋊D5311yescharacteristic
799C42C2×C22⋊D5311yescharacteristic
800C42C2×C22⋊D5311yescharacteristic
801C42C23×D5311yescharacteristic
802C23—21no—
803C23—21no—
804C23—21no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—81no—
810C23—81no—
811C23C2×C22⋊Dic5311yescharacteristic
812C23C2×C22⋊Dic5311yescharacteristic
813C23C2×C22⋊Dic5311yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—41no—
817Q8—81no—
818D4—22no—
819D4—22no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—21no—
825D4—41no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—42no—
831D4—42no—
832D4—81no—
833D4—81no—
834D4—81no—
835D4#1313322412yes—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—81no—
865C2×C4—81no—
866C2×C4—81no—
867C2×C4—81no—
868C2×C4—81no—
869C2×C4—81no—
870C2×C4C2×C22⋊Dic5311yescharacteristic
871C2×C4C2×C22⋊Dic5311yescharacteristic
872C2×C4C2×C22⋊Dic5311yescharacteristic
873C2×C4C2×C22⋊Dic5311yescharacteristic
874C2×C4C2×C22⋊Dic5311yescharacteristic
875C2×C4C2×C22⋊Dic5311yescharacteristic
876C2×C4C2×C22⋊Dic5311yescharacteristic
877C2×C4C2×C22⋊Dic5311yescharacteristic
878C2×C4C2×C22⋊Dic5311yescharacteristic
879C2×C4C23×Dic5311yescharacteristic
880C2×C4C22×C22⋊D5311yescharacteristic
881C2×C4C22×C22⋊D5311yescharacteristic
882C8—2121no—
883C8—2121no—
884C8—2121no—
885C8—2121no—
886C8—2121no—
887C8—2121no—
888C8—2121no—
889C8—2121no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—22no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—84no—
908C22—84no—
909C22#1681064012yes—
910C22C22×C22⋊Dic5311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—41no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—41no—
926C4C2×#1313322411yescharacteristic
927C4#1681139011yescharacteristic
928C4#1681142611yescharacteristic
929C4#1681143411yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—42no—
934C2—81no—
935C2—81no—
936C2#2028316411yescharacteristic
937C2#2028324111yescharacteristic
938C2C2×#1681064011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
Fitting, prime radicalC53×#3481C2
socleC22×C53C22×C22⋊C4
cosocleC42×C53C24
hypercenter#3481D53
hypocenterC53#17521
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3481

Complements

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

NH ≅ G/Ntype
1. #20283840C2semidirect
2. #20283359C2semidirect
3. #20273184C2semidirect
4. #20273180C2semidirect
5. #20273175C2semidirect
6. #20273158C2semidirect
7. #20273149C2semidirect
8. #20273140C2semidirect
9. #20273128C2semidirect
10. #20273123C2semidirect
11. #20273114C2semidirect
12. #20273106C2semidirect
13. #20273102C2semidirect
14. C2×D4⋊#88322C2semidirect
22. #16810680C22semidirect
23. #16810680C22semidirect
24. #16810676C22semidirect
25. #16810676C22semidirect
26. #16810676C22semidirect
27. #16810676C22semidirect
28. #16810676C22semidirect
30. #16810647C22semidirect
31. C2×C4⋊#88322C22semidirect
32. C2×C4⋊#88322C22semidirect
34. C4×#11719917C22semidirect
35. C2×C4×#88322C22semidirect
36. Q8⋊#88322C22semidirect
37. Q8⋊#88322C22semidirect
38. Q8⋊#88322C22semidirect
39. Q8⋊#88322C22semidirect
44. D4⋊#88322C22semidirect
45. D4⋊#88322C22semidirect
46. D4⋊#88322C22semidirect
47. D4⋊#88322C22semidirect
48. D4⋊#88322C22semidirect
49. D4⋊#88322C22semidirect
50. D4⋊#88322C22semidirect
51. D4⋊#88322C22semidirect
544. C53#17521semidirect

Maximal subgroups

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

subgroupindex
#202838402
#202833592
#202731842
#202731802
#202731752
#202731582
#202731492
#202731402
#202731282
#202731232
#202731142
#202731062
#202731022
C2×D4⋊#883222
C53×#34812
#1752153