Finite Group Databasebeta

← #27351138

Subgroups — #27351138

Order 13568.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 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#20273188C211yesmaximal, characteristic, complemented
4#20273180C211yesmaximal, characteristic, complemented
5#20273175C211yesmaximal, characteristic, complemented
6#20273162C211yesmaximal, characteristic, complemented
7#20273149C211yesmaximal, characteristic, complemented
8#20273144C211yesmaximal, characteristic, complemented
9#20273128C211yesmaximal, characteristic, complemented
10#20273123C211yesmaximal, characteristic, complemented
11#20273118C211yesmaximal, characteristic, complemented
12#20273110C211yesmaximal, characteristic, complemented
13#20273102C211yesmaximal, characteristic, complemented
14C2×Q8⋊#88322C211yesmaximal, characteristic, complemented
15C53×#3482C211yesmaximal, characteristic
16#16810754—21no—
17#16810695—21no—
18#16810695—21no—
19D4×#88322—21no—
20#16810684—21no—
21#16810684—21no—
22#16810680C2211yescharacteristic
23#16810680C2211yescharacteristic
24#16810676C2211yescharacteristic
25#16810676C2211yescharacteristic
26#16810676C2211yescharacteristic
27#16810676C2211yescharacteristic
28#16810676C2211yescharacteristic
29#16810650—21no—
30#16810647C2211yescharacteristic
31C2×C4⋊#88322C2211yescharacteristic
32C2×C4⋊#88322C2211yescharacteristic
33#16810590—21no—
34C4×#11719917C2211yescharacteristic
35C2×C4×#88322C2211yescharacteristic
36Q8⋊#88322C2211yescharacteristic
37Q8⋊#88322C2211yescharacteristic
38Q8⋊#88322C2211yescharacteristic
39Q8⋊#88322C2211yescharacteristic
40Q8⋊#88322C2211yescharacteristic
41Q8⋊#88322C2211yescharacteristic
42Q8⋊#88322C2211yescharacteristic
43Q8⋊#88322C2211yescharacteristic
44Q8⋊#88322C2211yescharacteristic
45Q8⋊#88322C2211yescharacteristic
46Q8⋊#88322C2211yescharacteristic
47Q8⋊#88322C2211yescharacteristic
48D4⋊#88322C2211yescharacteristic
49D4⋊#88322C2211yescharacteristic
50D4⋊#88322C2211yescharacteristic
51D4⋊#88322C2211yescharacteristic
52C53×#557C411yescharacteristic
53C53×#556—21no—
54C53×#556C411yescharacteristic
55C53×#552—21no—
56C53×#552—21no—
57C53×#552C411yescharacteristic
58C53×#552C411yescharacteristic
59D4×Q8×C53C411yescharacteristic
60C53×#548C411yescharacteristic
61C53×#548C411yescharacteristic
62C53×#547—21no—
63C53×#547C411yescharacteristic
64C53×#533—21no—
65C53×#533C2211yescharacteristic
66C53×#529—21no—
67C53×#529—21no—
68C53×#529C2211yescharacteristic
69C53×#529C2211yescharacteristic
70C4×#41×C53—21no—
71C4×#41×C53C2211yescharacteristic
72C4×#41×C53C2211yescharacteristic
73C2×C4×Q8×C53C2211yescharacteristic
74C2×C4×Q8×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×Q8×C53C2×C411yescharacteristic
111C22×Q8×C53C2×C411yescharacteristic
112C4⋊Q8×C53—21no—
113C4⋊Q8×C53—21no—
114C4⋊Q8×C53C2×C411yescharacteristic
115C4⋊Q8×C53C2×C411yescharacteristic
116#126×C53—21no—
117#126×C53—21no—
118#126×C53—21no—
119#126×C53—21no—
120#126×C53—21no—
121#126×C53—21no—
122#125×C53—21no—
123#125×C53—21no—
124#125×C53—21no—
125#125×C53—21no—
126#125×C53—21no—
127#125×C53C2×C411yescharacteristic
128#125×C53C2×C411yescharacteristic
129#124×C53—21no—
130#124×C53—21no—
131#124×C53C2×C411yescharacteristic
132#124×C53C2×C411yescharacteristic
133#123×C53—21no—
134#123×C53—21no—
135#123×C53—21no—
136#123×C53—21no—
137#123×C53—21no—
138#123×C53—21no—
139C22⋊Q8×C53—21no—
140C22⋊Q8×C53—21no—
141C22⋊Q8×C53—21no—
142C22⋊Q8×C53—21no—
143C22⋊Q8×C53—21no—
144C22⋊Q8×C53—21no—
145C22⋊Q8×C53—21no—
146C22⋊Q8×C53C2×C411yescharacteristic
147C22⋊Q8×C53C2×C411yescharacteristic
148C22⋊Q8×C53C2×C411yescharacteristic
149C22⋊Q8×C53C2×C411yescharacteristic
150#121×C53—21no—
151#121×C53—21no—
152#121×C53C2×C411yescharacteristic
153#121×C53C2×C411yescharacteristic
154C4×Q8×C53—21no—
155C4×Q8×C53—21no—
156C4×Q8×C53—21no—
157C4×Q8×C53—21no—
158C4×Q8×C53—21no—
159C4×Q8×C53—21no—
160C4×Q8×C53C2×C411yescharacteristic
161C4×Q8×C53C2×C411yescharacteristic
162C4×Q8×C53C2×C411yescharacteristic
163C4×Q8×C53C2×C411yescharacteristic
164C4×Q8×C53C2×C411yescharacteristic
165C4×Q8×C53C2×C411yescharacteristic
166C4×Q8×C53D411yescharacteristic
167C4×Q8×C53C2311yescharacteristic
168C4×Q8×C53C2311yescharacteristic
169C4×Q8×C53C2311yescharacteristic
170C4×D4×C53—21no—
171C4×D4×C53—21no—
172C4×D4×C53—21no—
173C4×D4×C53—21no—
174C4×D4×C53—21no—
175C4×D4×C53—21no—
176C4×D4×C53—21no—
177C4×D4×C53C2×C411yescharacteristic
178C4×D4×C53C2×C411yescharacteristic
179C4×D4×C53C2×C411yescharacteristic
180C4×D4×C53C2×C411yescharacteristic
181C4×D4×C53D411yescharacteristic
182C4×D4×C53D411yescharacteristic
183C4×D4×C53D411yescharacteristic
184C4×D4×C53C2311yescharacteristic
185#117×C53—21no—
186#117×C53—21no—
187#117×C53—21no—
188#117×C53—21no—
189#117×C53—21no—
190#117×C53—21no—
191#117×C53—21no—
192#117×C53C2×C411yescharacteristic
193#117×C53D411yescharacteristic
194#117×C53D411yescharacteristic
195#117×C53D411yescharacteristic
196C2×C4⋊C4×C53—21no—
197C2×C4⋊C4×C53—21no—
198C2×C4⋊C4×C53C2×C411yescharacteristic
199C2×C4⋊C4×C53C2×C411yescharacteristic
200C2×C42×C53—21no—
201C2×C42×C53—21no—
202C2×C42×C53—21no—
203C2×C42×C53C2311yescharacteristic
204C2×C42×C53C2311yescharacteristic
205C2×C42×C53C2311yescharacteristic
206#41×C53—22no—
207#41×C53—42no—
208#41×C53—41no—
209#41×C53—44no—
210C2×Q8×C53—21no—
211C2×Q8×C53—21no—
212C2×Q8×C53—21no—
213C2×Q8×C53—22no—
214C2×Q8×C53—22no—
215C2×Q8×C53—41no—
216C2×Q8×C53—41no—
217C2×Q8×C53C22⋊C411yescharacteristic
218C2×Q8×C53C22×C411yescharacteristic
219C2×Q8×C53C22×C411yescharacteristic
220C2×Q8×C53C22×C411yescharacteristic
221C2×D4×C53—21no—
222C2×D4×C53—21no—
223C2×D4×C53—21no—
224C2×D4×C53C22⋊C411yescharacteristic
225C2×D4×C53C22⋊C411yescharacteristic
226C2×D4×C53C22⋊C411yescharacteristic
227C2×D4×C53C22×C411yescharacteristic
228C22×C4×C53—21no—
229C22×C4×C53—21no—
230C22×C4×C53—21no—
231C22×C4×C53—21no—
232C22×C4×C53—21no—
233C22×C4×C53—21no—
234C22×C4×C53—21no—
235C22×C4×C53C22×C411yescharacteristic
236C22×C4×C53C22×C411yescharacteristic
237C22×C4×C53C22×C411yescharacteristic
238C22×C4×C53C2×D411yescharacteristic
239C22×C4×C53C2×D411yescharacteristic
240C22×C4×C53C2×D411yescharacteristic
241C22×C4×C53C2×D411yescharacteristic
242C22×C4×C53C2×D411yescharacteristic
243C22×C4×C53C2×D411yescharacteristic
244C4⋊C4×C53—21no—
245C4⋊C4×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53—21no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53—21no—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53—21no—
265C4⋊C4×C53C22⋊C411yescharacteristic
266C4⋊C4×C53C22⋊C411yescharacteristic
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22⋊C411yescharacteristic
270C4⋊C4×C53C22⋊C411yescharacteristic
271C4⋊C4×C53C22×C411yescharacteristic
272C4⋊C4×C53C22×C411yescharacteristic
273C4⋊C4×C53C22×C411yescharacteristic
274C4⋊C4×C53C22×C411yescharacteristic
275C22⋊C4×C53—21no—
276C22⋊C4×C53—21no—
277C22⋊C4×C53—21no—
278C22⋊C4×C53—21no—
279C22⋊C4×C53—21no—
280C22⋊C4×C53—21no—
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×C53C22⋊C411yescharacteristic
289C22⋊C4×C53C22⋊C411yescharacteristic
290C22⋊C4×C53C22⋊C411yescharacteristic
291C22⋊C4×C53C22⋊C411yescharacteristic
292C22⋊C4×C53C22⋊C411yescharacteristic
293C22⋊C4×C53C22⋊C411yescharacteristic
294C42×C53—21no—
295C42×C53—21no—
296C42×C53—21no—
297C42×C53—21no—
298C42×C53—21no—
299C42×C53—21no—
300C42×C53—21no—
301C42×C53—21no—
302C42×C53—21no—
303C42×C53C22×C411yescharacteristic
304C42×C53C22×C411yescharacteristic
305C42×C53C22×C411yescharacteristic
306C42×C53C2×D411yescharacteristic
307C42×C53C2×D411yescharacteristic
308C42×C53C2×D411yescharacteristic
309C42×C53C2×D411yescharacteristic
310C42×C53C2×D411yescharacteristic
311C42×C53C2×D411yescharacteristic
312C42×C53C2411yescharacteristic
313#11719917—42no—
314#11719917—81no—
315C2×#88322—21no—
316C2×#88322—21no—
317C2×#88322—21no—
318C2×#88322—21no—
319C2×#88322—21no—
320C2×#88322—21no—
321C2×#88322—21no—
322C2×#88322—21no—
323C2×#88322—42no—
324C2×#88322—81no—
325C2×#88322—81no—
326C23×C53—21no—
327C23×C53C2×C22⋊C411yescharacteristic
328C23×C53C2×C22⋊C411yescharacteristic
329C23×C53C2×C22⋊C411yescharacteristic
330Q8×C53—21no—
331Q8×C53—21no—
332Q8×C53—21no—
333Q8×C53—21no—
334Q8×C53—21no—
335Q8×C53—41no—
336Q8×C53—42no—
337Q8×C53—42no—
338Q8×C53—42no—
339Q8×C53#13112yes—
340D4×C53—22no—
341D4×C53—22no—
342D4×C53—21no—
343D4×C53—21no—
344D4×C53—41no—
345D4×C53—42no—
346D4×C53—42no—
347D4×C53—42no—
348C2×C4×C53—21no—
349C2×C4×C53—22no—
350C2×C4×C53—21no—
351C2×C4×C53—21no—
352C2×C4×C53—21no—
353C2×C4×C53—21no—
354C2×C4×C53—21no—
355C2×C4×C53—21no—
356C2×C4×C53—21no—
357C2×C4×C53—21no—
358C2×C4×C53—21no—
359C2×C4×C53—21no—
360C2×C4×C53—21no—
361C2×C4×C53—21no—
362C2×C4×C53—21no—
363C2×C4×C53—21no—
364C2×C4×C53—21no—
365C2×C4×C53—21no—
366C2×C4×C53—21no—
367C2×C4×C53—21no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—42no—
371C2×C4×C53—42no—
372C2×C4×C53—42no—
373C2×C4×C53—42no—
374C2×C4×C53—42no—
375C2×C4×C53—42no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53C2×C22⋊C411yescharacteristic
379C2×C4×C53C2×C22⋊C411yescharacteristic
380C2×C4×C53C2×C22⋊C411yescharacteristic
381C2×C4×C53C2×C22⋊C411yescharacteristic
382C2×C4×C53C2×C22⋊C411yescharacteristic
383C2×C4×C53C2×C22⋊C411yescharacteristic
384C2×C4×C53C2×C22⋊C411yescharacteristic
385C2×C4×C53C2×C22⋊C411yescharacteristic
386C2×C4×C53C2×C22⋊C411yescharacteristic
387C2×C4×C53C23×C411yescharacteristic
388C2×C4×C53C22×D411yescharacteristic
389C2×C4×C53C22×D411yescharacteristic
390#88322—41no—
391#88322—41no—
392#88322—41no—
393#88322—41no—
394#88322—41no—
395#88322—41no—
396#88322—41no—
397#88322—41no—
398#17524—531nomaximal, Sylow
399C22×C53—21no—
400C22×C53—21no—
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—21no—
407C22×C53—41no—
408C22×C53—41no—
409C22×C53—41no—
410C22×C53#42112yes—
411C22×C53C22×C22⋊C411yescharacteristic
412C4×C53—21no—
413C4×C53—21no—
414C4×C53—21no—
415C4×C53—22no—
416C4×C53—21no—
417C4×C53—21no—
418C4×C53—21no—
419C4×C53—21no—
420C4×C53—21no—
421C4×C53—21no—
422C4×C53—21no—
423C4×C53—41no—
424C4×C53—41no—
425C4×C53—41no—
426C4×C53—41no—
427C4×C53—41no—
428C4×C53—41no—
429C4×C53C2×#13111yescharacteristic
430C4×C53#56811yescharacteristic
431C4×C53#57711yescharacteristic
432C4×C53#57811yescharacteristic
433#3482D5311yescharacteristic
434#2990—531no—
435#2922—531no—
436#1497—531no—
437#1495—531no—
438#1494—531no—
439#1491—531no—
440#1488—531no—
441#1487—531no—
442#1483—531no—
443#1482—531no—
444#1481—531no—
445#1479—531no—
446#1477—531no—
447C2×Q8⋊C8—531no—
448C2×C53—22no—
449C2×C53—41no—
450C2×C53—41no—
451C2×C53—81no—
452C2×C53#288011yescharacteristic
453C2×C53#289811yescharacteristic
454C2×C53C2×#42111yescharacteristic
455#557Dic5311yescharacteristic
456#556—21no—
457#556Dic5311yescharacteristic
458#552—21no—
459#552—21no—
460#552Dic5311yescharacteristic
461#552Dic5311yescharacteristic
462D4×Q8Dic5311yescharacteristic
463#548Dic5311yescharacteristic
464#548Dic5311yescharacteristic
465#547—21no—
466#547Dic5311yescharacteristic
467#533—21no—
468#533C2×D5311yescharacteristic
469#529—21no—
470#529—21no—
471#529C2×D5311yescharacteristic
472#529C2×D5311yescharacteristic
473C4×#41—21no—
474C4×#41C2×D5311yescharacteristic
475C4×#41C2×D5311yescharacteristic
476C2×C4×Q8C2×D5311yescharacteristic
477C2×C4×Q8C2×D5311yescharacteristic
478#446—1061no—
479#435—1061no—
480#435—1061no—
481C8×D4—1061no—
482#433—1061no—
483#433—1061no—
484#432—531no—
485#432—531no—
486#431—531no—
487#431—531no—
488#431—531no—
489#431—531no—
490#431—531no—
491#424—1061no—
492#423—531no—
493C2×C4⋊C8—531no—
494C2×C4⋊C8—531no—
495#408—1061no—
496C4×M16—531no—
497C2×C4×C8—531no—
498Q8⋊C8—531no—
499Q8⋊C8—531no—
500Q8⋊C8—531no—
501Q8⋊C8—531no—
502Q8⋊C8—531no—
503Q8⋊C8—531no—
504Q8⋊C8—531no—
505Q8⋊C8—531no—
506Q8⋊C8—531no—
507Q8⋊C8—531no—
508Q8⋊C8—531no—
509Q8⋊C8—531no—
510D4⋊C8—531no—
511D4⋊C8—531no—
512D4⋊C8—531no—
513D4⋊C8—531no—
514C53#1752411yescharacteristic, complemented, Sylow
515C2×#41—21no—
516C2×#41C2×Dic5311yescharacteristic
517C2×#41C22⋊D5311yescharacteristic
518C22×Q8C2×Dic5311yescharacteristic
519C22×Q8C2×Dic5311yescharacteristic
520C2×M16—1061no—
521C2×M16—1061no—
522C22×C8—1061no—
523C22×C8—1061no—
524C22×C8—1061no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8C2×Dic5311yescharacteristic
528C4⋊Q8C2×Dic5311yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#125—21no—
536#125—21no—
537#125—21no—
538#125—21no—
539#125—21no—
540#125C2×Dic5311yescharacteristic
541#125C2×Dic5311yescharacteristic
542#124—21no—
543#124—21no—
544#124C2×Dic5311yescharacteristic
545#124C2×Dic5311yescharacteristic
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8C2×Dic5311yescharacteristic
560C22⋊Q8C2×Dic5311yescharacteristic
561C22⋊Q8C2×Dic5311yescharacteristic
562C22⋊Q8C2×Dic5311yescharacteristic
563#121—21no—
564#121—21no—
565#121C2×Dic5311yescharacteristic
566#121C2×Dic5311yescharacteristic
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C2×Dic5311yescharacteristic
574C4×Q8C2×Dic5311yescharacteristic
575C4×Q8C2×Dic5311yescharacteristic
576C4×Q8C2×Dic5311yescharacteristic
577C4×Q8C2×Dic5311yescharacteristic
578C4×Q8C2×Dic5311yescharacteristic
579C4×Q8C22⋊D5311yescharacteristic
580C4×Q8C22×D5311yescharacteristic
581C4×Q8C22×D5311yescharacteristic
582C4×Q8C22×D5311yescharacteristic
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4C2×Dic5311yescharacteristic
591C4×D4C2×Dic5311yescharacteristic
592C4×D4C2×Dic5311yescharacteristic
593C4×D4C2×Dic5311yescharacteristic
594C4×D4C22⋊D5311yescharacteristic
595C4×D4C22⋊D5311yescharacteristic
596C4×D4C22⋊D5311yescharacteristic
597C4×D4C22×D5311yescharacteristic
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117C2×Dic5311yescharacteristic
606#117C22⋊D5311yescharacteristic
607#117C22⋊D5311yescharacteristic
608#117C22⋊D5311yescharacteristic
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4C2×Dic5311yescharacteristic
612C2×C4⋊C4C2×Dic5311yescharacteristic
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C22×D5311yescharacteristic
617C2×C42C22×D5311yescharacteristic
618C2×C42C22×D5311yescharacteristic
619C4⋊C8—531no—
620C4⋊C8—531no—
621C4⋊C8—531no—
622C4⋊C8—531no—
623C4⋊C8—1061no—
624C4⋊C8—1061no—
625C4⋊C8—1061no—
626C4⋊C8—1061no—
627C4⋊C8—1061no—
628C4⋊C8—1061no—
629C4⋊C8—1061no—
630C22⋊C8—1061no—
631C22⋊C8—1061no—
632C22⋊C8—1061no—
633C22⋊C8—1061no—
634C22⋊C8—1061no—
635C22⋊C8—1061no—
636C22⋊C8—1061no—
637#97—1061no—
638#97—1061no—
639#97—1061no—
640C4×C8—531no—
641C4×C8—531no—
642C4×C8—531no—
643C4×C8—531no—
644C4×C8—1061no—
645C4×C8—1061no—
646#41—22no—
647#41—42no—
648#41—41no—
649#41—44no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—41no—
656C2×Q8—41no—
657C2×Q8C22⋊Dic5311yescharacteristic
658C2×Q8C22×Dic5311yescharacteristic
659C2×Q8C22×Dic5311yescharacteristic
660C2×Q8C22×Dic5311yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22⋊Dic5311yescharacteristic
665C2×D4C22⋊Dic5311yescharacteristic
666C2×D4C22⋊Dic5311yescharacteristic
667C2×D4C22×Dic5311yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4C22×Dic5311yescharacteristic
676C22×C4C22×Dic5311yescharacteristic
677C22×C4C22×Dic5311yescharacteristic
678C22×C4C2×C22⋊D5311yescharacteristic
679C22×C4C2×C22⋊D5311yescharacteristic
680C22×C4C2×C22⋊D5311yescharacteristic
681C22×C4C2×C22⋊D5311yescharacteristic
682C22×C4C2×C22⋊D5311yescharacteristic
683C22×C4C2×C22⋊D5311yescharacteristic
684M16—4241no—
685M16—2122no—
686C2×C8—1061no—
687C2×C8—1061no—
688C2×C8—1061no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—4241no—
695C2×C8—4241no—
696C2×C8—2122no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4C22⋊Dic5311yescharacteristic
719C4⋊C4C22⋊Dic5311yescharacteristic
720C4⋊C4C22⋊Dic5311yescharacteristic
721C4⋊C4C22⋊Dic5311yescharacteristic
722C4⋊C4C22⋊Dic5311yescharacteristic
723C4⋊C4C22⋊Dic5311yescharacteristic
724C4⋊C4C22×Dic5311yescharacteristic
725C4⋊C4C22×Dic5311yescharacteristic
726C4⋊C4C22×Dic5311yescharacteristic
727C4⋊C4C22×Dic5311yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4C22⋊Dic5311yescharacteristic
742C22⋊C4C22⋊Dic5311yescharacteristic
743C22⋊C4C22⋊Dic5311yescharacteristic
744C22⋊C4C22⋊Dic5311yescharacteristic
745C22⋊C4C22⋊Dic5311yescharacteristic
746C22⋊C4C22⋊Dic5311yescharacteristic
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42C22×Dic5311yescharacteristic
757C42C22×Dic5311yescharacteristic
758C42C22×Dic5311yescharacteristic
759C42C2×C22⋊D5311yescharacteristic
760C42C2×C22⋊D5311yescharacteristic
761C42C2×C22⋊D5311yescharacteristic
762C42C2×C22⋊D5311yescharacteristic
763C42C2×C22⋊D5311yescharacteristic
764C42C2×C22⋊D5311yescharacteristic
765C42C23×D5311yescharacteristic
766C23—21no—
767C23C2×C22⋊Dic5311yescharacteristic
768C23C2×C22⋊Dic5311yescharacteristic
769C23C2×C22⋊Dic5311yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—41no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8#1313322412yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4C2×C22⋊Dic5311yescharacteristic
819C2×C4C2×C22⋊Dic5311yescharacteristic
820C2×C4C2×C22⋊Dic5311yescharacteristic
821C2×C4C2×C22⋊Dic5311yescharacteristic
822C2×C4C2×C22⋊Dic5311yescharacteristic
823C2×C4C2×C22⋊Dic5311yescharacteristic
824C2×C4C2×C22⋊Dic5311yescharacteristic
825C2×C4C2×C22⋊Dic5311yescharacteristic
826C2×C4C2×C22⋊Dic5311yescharacteristic
827C2×C4C23×Dic5311yescharacteristic
828C2×C4C22×C22⋊D5311yescharacteristic
829C2×C4C22×C22⋊D5311yescharacteristic
830C8—2121no—
831C8—2121no—
832C8—2121no—
833C8—2121no—
834C8—2121no—
835C8—2121no—
836C8—2121no—
837C8—2121no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22#1681064012yes—
850C22C22×C22⋊Dic5311yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—22no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4C2×#1313322411yescharacteristic
869C4#1681139011yescharacteristic
870C4#1681143111yescharacteristic
871C4#1681143811yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—81no—
876C2#2028316411yescharacteristic
877C2#2028324811yescharacteristic
878C2C2×#1681064011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
Fitting, prime radicalC53×#3482C2
socleC22×C53C22×C22⋊C4
cosocleC42×C53C24
hypercenter#3482D53
hypocenterC53#17524
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #20283840C2semidirect
2. #20283359C2semidirect
3. #20273188C2semidirect
4. #20273180C2semidirect
5. #20273175C2semidirect
6. #20273162C2semidirect
7. #20273149C2semidirect
8. #20273144C2semidirect
9. #20273128C2semidirect
10. #20273123C2semidirect
11. #20273118C2semidirect
12. #20273110C2semidirect
13. #20273102C2semidirect
14. C2×Q8⋊#88322C2semidirect
514. C53#17524semidirect

Maximal subgroups

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

subgroupindex
#202838402
#202833592
#202731882
#202731802
#202731752
#202731622
#202731492
#202731442
#202731282
#202731232
#202731182
#202731102
#202731022
C2×Q8⋊#883222
C53×#34822
#1752453