Finite Group Databasebeta

← #27351617

Subgroups — #27351617

Order 13568.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283750C211yesmaximal, characteristic, complemented
2#20277348C211yesmaximal, characteristic, complemented
3#20273292C211yesmaximal, characteristic, complemented
4#20273283C211yesmaximal, characteristic, complemented
5#20273275C211yesmaximal, characteristic, complemented
6#20273271C211yesmaximal, characteristic, complemented
7#20273262C211yesmaximal, characteristic, complemented
8#20273258C211yesmaximal, characteristic, complemented
9#20273253C211yesmaximal, characteristic, complemented
10#20273244C211yesmaximal, characteristic, complemented
11#20273231C211yesmaximal, characteristic, complemented
12#20273219C211yesmaximal, characteristic, complemented
13#20273206C211yesmaximal, characteristic, complemented
14C2×#16810357C211yesmaximal, characteristic, complemented
15C53×#3519C211yesmaximal, characteristic
16#16810701—21no—
17#16810695—21no—
18#16810695—21no—
19D4×#88322—21no—
20#16810680C2211yescharacteristic, complemented
21#16810676C2211yescharacteristic, complemented
22#16810587C2211yescharacteristic, complemented
23#16810587C2211yescharacteristic, complemented
24C2×C22⋊#88322C2211yescharacteristic, complemented
25C2×C22⋊#88322C2211yescharacteristic, complemented
26#16810516—21no—
27#16810509—21no—
28#16810503—21no—
29#16810498—21no—
30#16810491C2211yescharacteristic, complemented
31#16810489C2211yescharacteristic, complemented
32#16810486C2211yescharacteristic, complemented
33#16810483C2211yescharacteristic, complemented
34C4×C22⋊Dic53C2211yescharacteristic, complemented
35C2×#13133124C2211yescharacteristic, complemented
36#16810360C2211yescharacteristic, complemented
37#16810360C2211yescharacteristic, complemented
38#16810360C2211yescharacteristic, complemented
39#16810360C2211yescharacteristic, complemented
40#16810357C2211yescharacteristic
41#16810357C2211yescharacteristic
42#16810357C2211yescharacteristic
43#16810357C2211yescharacteristic
44#16810357C2211yescharacteristic, complemented
45#16810357C2211yescharacteristic, complemented
46#16810357C2211yescharacteristic, complemented
47#16810357C2211yescharacteristic, complemented
48#16810357C2211yescharacteristic, complemented
49#16810357C2211yescharacteristic, complemented
50#16810357C2211yescharacteristic, complemented
51#16810357C2211yescharacteristic, complemented
52C53×#555C411yescharacteristic, complemented
53C53×#554C411yescharacteristic, complemented
54C53×#553—21no—
55C53×#553C411yescharacteristic, complemented
56C53×#553C411yescharacteristic, complemented
57C53×#550C411yescharacteristic, complemented
58C53×#546—21no—
59C53×#546—21no—
60C53×#546C411yescharacteristic, complemented
61C53×#546C411yescharacteristic, complemented
62D42×C53—21no—
63D42×C53C411yescharacteristic, complemented
64C53×#540—21no—
65C53×#538—21no—
66C53×#538—21no—
67C53×#532C2211yescharacteristic
68C53×#529C2211yescharacteristic
69C53×#525C2211yescharacteristic
70C53×#525C2211yescharacteristic
71C2×#121×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#518—21no—
74C2×C4×D4×C53C2211yescharacteristic
75C23×Dic53—21no—
76C2×#11719917—21no—
77C2×#11719917—21no—
78C22×#88322—21no—
79C22×#88322—21no—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53—21no—
82C2×C22⋊Dic53—21no—
83C2×C22⋊Dic53—21no—
84C2×C22⋊Dic53—21no—
85C2×C4×Dic53—21no—
86C4⋊#88322—21no—
87C4⋊#88322—21no—
88C22⋊#88322—21no—
89C22⋊#88322—21no—
90C22⋊#88322—21no—
91C22⋊#88322—21no—
92C22⋊#88322C2311yescharacteristic
93C22⋊#88322C2311yescharacteristic
94C22⋊#88322C2311yescharacteristic
95C22⋊#88322C2311yescharacteristic
96#13133128—21no—
97C4×#88322—21no—
98#13133124—21no—
99#13133124—21no—
100#13133124—21no—
101#13133124—21no—
102#13133124—21no—
103#13133124C2311yescharacteristic
104#13133124C2311yescharacteristic
105#13133124C2311yescharacteristic
106#13133124C2311yescharacteristic
107C2×#41×C53—21no—
108C2×#41×C53C2×C411yescharacteristic
109C2×#41×C53C2×C411yescharacteristic, complemented
110C22×D4×C53—21no—
111C22×D4×C53—21no—
112C22×D4×C53—21no—
113C22×D4×C53C2×C411yescharacteristic
114C22×D4×C53C2×C411yescharacteristic, complemented
115C22×D4×C53D411yescharacteristic
116C23×C4×C53C2311yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C4⋊Q8×C53C2×C411yescharacteristic, complemented
119#127×C53—21no—
120#127×C53C2×C411yescharacteristic, complemented
121#126×C53—21no—
122#126×C53—21no—
123#126×C53—21no—
124#125×C53—21no—
125#125×C53C2×C411yescharacteristic, complemented
126#124×C53—21no—
127#124×C53—21no—
128#124×C53—21no—
129#124×C53C2×C411yescharacteristic, complemented
130#123×C53—21no—
131#123×C53—21no—
132#123×C53—21no—
133#123×C53—21no—
134#123×C53—21no—
135#123×C53—21no—
136#123×C53—21no—
137C22⋊Q8×C53—21no—
138C22⋊Q8×C53—21no—
139C22⋊Q8×C53C2×C411yescharacteristic
140C22⋊Q8×C53C2×C411yescharacteristic, complemented
141C22⋊Q8×C53C2311yescharacteristic
142#121×C53—21no—
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×C53—21no—
150#121×C53—21no—
151#121×C53—21no—
152#121×C53—21no—
153#121×C53—21no—
154#121×C53—21no—
155#121×C53C2×C411yescharacteristic
156#121×C53C2×C411yescharacteristic
157#121×C53C2×C411yescharacteristic
158#121×C53C2×C411yescharacteristic, complemented
159#121×C53C2×C411yescharacteristic, complemented
160#121×C53C2×C411yescharacteristic, complemented
161#121×C53C2311yescharacteristic
162#121×C53C2311yescharacteristic
163#121×C53C2311yescharacteristic
164#120×C53—21no—
165#120×C53—21no—
166#120×C53—21no—
167#120×C53—21no—
168#120×C53—21no—
169#120×C53—21no—
170C4×Q8×C53C2×C411yescharacteristic, complemented
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×C53—21no—
178C4×D4×C53—21no—
179C4×D4×C53—21no—
180C4×D4×C53—21no—
181C4×D4×C53C2×C411yescharacteristic
182C4×D4×C53C2×C411yescharacteristic
183C4×D4×C53C2×C411yescharacteristic
184C4×D4×C53C2×C411yescharacteristic
185C4×D4×C53C2×C411yescharacteristic, complemented
186C4×D4×C53C2×C411yescharacteristic, complemented
187C4×D4×C53C2×C411yescharacteristic, complemented
188C4×D4×C53D411yescharacteristic
189C4×D4×C53D411yescharacteristic
190C4×D4×C53D411yescharacteristic
191C4×D4×C53D411yescharacteristic
192#117×C53—21no—
193#117×C53—21no—
194#117×C53C2×C411yescharacteristic
195#117×C53C2×C411yescharacteristic, complemented
196C2×C4⋊C4×C53C2×C411yescharacteristic
197C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
198C2×C4⋊C4×C53D411yescharacteristic
199C2×C22⋊C4×C53—21no—
200C2×C22⋊C4×C53—21no—
201C2×C22⋊C4×C53—21no—
202C2×C22⋊C4×C53—21no—
203C2×C22⋊C4×C53D411yescharacteristic
204C2×C22⋊C4×C53D411yescharacteristic
205C2×C42×C53C2311yescharacteristic
206C24×C53—21no—
207C24×C53—21no—
208C24×C53C2×D411yescharacteristic
209C24×C53C2×D411yescharacteristic
210#41×C53—81no—
211#41×C53—81no—
212#41×C53—81no—
213#41×C53—81no—
214C2×Q8×C53—21no—
215C2×Q8×C53C22×C411yescharacteristic
216C2×D4×C53—21no—
217C2×D4×C53—21no—
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—21no—
228C2×D4×C53—21no—
229C2×D4×C53—21no—
230C2×D4×C53—21no—
231C2×D4×C53—42no—
232C2×D4×C53—44no—
233C2×D4×C53—81no—
234C2×D4×C53—81no—
235C2×D4×C53—81no—
236C2×D4×C53—81no—
237C2×D4×C53—81no—
238C2×D4×C53—81no—
239C2×D4×C53C22⋊C411yescharacteristic
240C2×D4×C53C22⋊C411yescharacteristic
241C2×D4×C53C22⋊C411yescharacteristic
242C2×D4×C53C22⋊C411yescharacteristic
243C2×D4×C53C22×C411yescharacteristic
244C2×D4×C53C22×C411yescharacteristic
245C2×D4×C53C22×C411yescharacteristic
246C22×C4×C53—21no—
247C22×C4×C53—21no—
248C22×C4×C53—21no—
249C22×C4×C53—21no—
250C22×C4×C53—21no—
251C22×C4×C53—21no—
252C22×C4×C53—21no—
253C22×C4×C53—81no—
254C22×C4×C53—81no—
255C22×C4×C53C22×C411yescharacteristic
256C22×C4×C53C22×C411yescharacteristic
257C22×C4×C53C22×C411yescharacteristic
258C22×C4×C53C22×C411yescharacteristic
259C22×C4×C53C2×D411yescharacteristic
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D411yescharacteristic
266C22×C4×C53C2×D411yescharacteristic
267C22×C4×C53C2411yescharacteristic
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—42no—
273C22×Dic53—81no—
274C22×Dic53—81no—
275C4⋊C4×C53—21no—
276C4⋊C4×C53—21no—
277C4⋊C4×C53—21no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53—21no—
281C4⋊C4×C53—21no—
282C4⋊C4×C53—21no—
283C4⋊C4×C53—21no—
284C4⋊C4×C53C22⋊C411yescharacteristic
285C4⋊C4×C53C22⋊C411yescharacteristic
286C4⋊C4×C53C22⋊C411yescharacteristic
287C4⋊C4×C53C22⋊C411yescharacteristic
288C4⋊C4×C53C22×C411yescharacteristic
289C4⋊C4×C53C22×C411yescharacteristic
290C4⋊C4×C53C22×C411yescharacteristic
291C4⋊C4×C53C22×C411yescharacteristic
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×C53—21no—
301C22⋊C4×C53—21no—
302C22⋊C4×C53—21no—
303C22⋊C4×C53—21no—
304C22⋊C4×C53—21no—
305C22⋊C4×C53—21no—
306C22⋊C4×C53—21no—
307C22⋊C4×C53—21no—
308C22⋊C4×C53—21no—
309C22⋊C4×C53—21no—
310C22⋊C4×C53—21no—
311C22⋊C4×C53C22⋊C411yescharacteristic
312C22⋊C4×C53C22⋊C411yescharacteristic
313C22⋊C4×C53C22⋊C411yescharacteristic
314C22⋊C4×C53C22⋊C411yescharacteristic
315C22⋊C4×C53C22⋊C411yescharacteristic
316C22⋊C4×C53C22⋊C411yescharacteristic
317C22⋊C4×C53C22⋊C411yescharacteristic
318C22⋊C4×C53C22⋊C411yescharacteristic
319C42×C53—21no—
320C42×C53—21no—
321C42×C53—21no—
322C42×C53C22×C411yescharacteristic
323C42×C53C22×C411yescharacteristic
324C42×C53C2×D411yescharacteristic
325C42×C53C2×D411yescharacteristic
326C22⋊Dic53—42no—
327C22⋊Dic53—81no—
328C22⋊Dic53—81no—
329C4⋊Dic53—81no—
330C4⋊Dic53—81no—
331C4×Dic53—81no—
332#11719917—81no—
333#11719917—81no—
334C2×#88322—21no—
335C2×#88322—21no—
336C2×#88322—21no—
337C2×#88322—21no—
338C2×#88322—81no—
339C2×#88322—81no—
340C23×C53—21no—
341C23×C53—21no—
342C23×C53—22no—
343C23×C53—21no—
344C23×C53—21no—
345C23×C53—21no—
346C23×C53—21no—
347C23×C53—21no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—42no—
352C23×C53—42no—
353C23×C53—81no—
354C23×C53—81no—
355C23×C53—81no—
356C23×C53—81no—
357C23×C53C2×C22⋊C411yescharacteristic
358C23×C53C2×C22⋊C411yescharacteristic
359C23×C53C2×C22⋊C411yescharacteristic
360C23×C53C2×C22⋊C411yescharacteristic
361C23×C53C22×D411yescharacteristic
362Q8×C53—41no—
363Q8×C53—81no—
364D4×C53—22no—
365D4×C53—22no—
366D4×C53—41no—
367D4×C53—41no—
368D4×C53—41no—
369D4×C53—41no—
370D4×C53—41no—
371D4×C53—42no—
372D4×C53—42no—
373D4×C53—41no—
374D4×C53—41no—
375D4×C53—41no—
376D4×C53—41no—
377D4×C53—41no—
378D4×C53—41no—
379D4×C53—42no—
380D4×C53—81no—
381D4×C53—81no—
382D4×C53—81no—
383D4×C53—81no—
384D4×C53—81no—
385D4×C53—81no—
386D4×C53—81no—
387D4×C53—81no—
388D4×C53—81no—
389C2×C4×C53—21no—
390C2×C4×C53—21no—
391C2×C4×C53—21no—
392C2×C4×C53—21no—
393C2×C4×C53—21no—
394C2×C4×C53—21no—
395C2×C4×C53—21no—
396C2×C4×C53—41no—
397C2×C4×C53—41no—
398C2×C4×C53—41no—
399C2×C4×C53—41no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—42no—
409C2×C4×C53—81no—
410C2×C4×C53—81no—
411C2×C4×C53—81no—
412C2×C4×C53—81no—
413C2×C4×C53—81no—
414C2×C4×C53—81no—
415C2×C4×C53C2×C22⋊C411yescharacteristic
416C2×C4×C53C2×C22⋊C411yescharacteristic
417C2×C4×C53C2×C22⋊C411yescharacteristic
418C2×C4×C53C2×C22⋊C411yescharacteristic
419C2×C4×C53C2×C22⋊C411yescharacteristic
420C2×C4×C53C2×C22⋊C411yescharacteristic
421C2×C4×C53C2×C22⋊C411yescharacteristic
422C2×C4×C53C2×C22⋊C411yescharacteristic
423C2×C4×C53C23×C411yescharacteristic
424C2×C4×C53C22×D411yescharacteristic
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430C2×Dic53—41no—
431C2×Dic53—41no—
432C2×Dic53—41no—
433C2×Dic53—41no—
434C2×Dic53—41no—
435C2×Dic53—41no—
436C2×Dic53—41no—
437C2×Dic53—84no—
438#88322—41no—
439#88322—41no—
440#88322—41no—
441#88322—41no—
442#17597—531nomaximal, Sylow
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—21no—
446C22×C53—21no—
447C22×C53—21no—
448C22×C53—21no—
449C22×C53—21no—
450C22×C53—21no—
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—21no—
454C22×C53—21no—
455C22×C53—21no—
456C22×C53—42no—
457C22×C53—42no—
458C22×C53—41no—
459C22×C53—41no—
460C22×C53—41no—
461C22×C53—41no—
462C22×C53—41no—
463C22×C53—41no—
464C22×C53—41no—
465C22×C53—41no—
466C22×C53—41no—
467C22×C53—81no—
468C22×C53—81no—
469C22×C53—162no—
470C22×C53—162no—
471C22×C53#42112yes—
472C22×C53C22×C22⋊C411yescharacteristic
473C22×C53#57611yescharacteristic
474C22×C53#57711yescharacteristic
475C4×C53—21no—
476C4×C53—21no—
477C4×C53—21no—
478C4×C53—21no—
479C4×C53—21no—
480C4×C53—21no—
481C4×C53—21no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—21no—
485C4×C53—41no—
486C4×C53—41no—
487C4×C53—41no—
488C4×C53—41no—
489C4×C53—41no—
490Dic53—81no—
491Dic53—81no—
492Dic53—81no—
493Dic53—81no—
494#3519D5311yescharacteristic
495#2974—531no—
496#2318—531no—
497#1521—531no—
498#1519—531no—
499#1517—531no—
500#1516—531no—
501#1514—531no—
502#1513—531no—
503#1512—531no—
504#1510—531no—
505#1507—531no—
506#1504—531no—
507#1501—531no—
508C2×#327—531no—
509C2×C53—21no—
510C2×C53—21no—
511C2×C53—22no—
512C2×C53—41no—
513C2×C53—41no—
514C2×C53—41no—
515C2×C53—81no—
516C2×C53—81no—
517C2×C53—81no—
518C2×C53#288311yescharacteristic
519C2×C53#289711yescharacteristic
520C2×C53C2×#42111yescharacteristic
521#555Dic5311yescharacteristic, complemented
522#554Dic5311yescharacteristic, complemented
523#553—21no—
524#553Dic5311yescharacteristic, complemented
525#553Dic5311yescharacteristic, complemented
526#550Dic5311yescharacteristic, complemented
527#546—21no—
528#546—21no—
529#546Dic5311yescharacteristic, complemented
530#546Dic5311yescharacteristic, complemented
531D42—21no—
532D42Dic5311yescharacteristic, complemented
533#540—21no—
534#538—21no—
535#538—21no—
536#532C2×D5311yescharacteristic
537#529C2×D5311yescharacteristic
538#525C2×D5311yescharacteristic
539#525C2×D5311yescharacteristic
540C2×#121C2×D5311yescharacteristic
541C2×#121C2×D5311yescharacteristic
542#518—21no—
543C2×C4×D4C2×D5311yescharacteristic
544#436—1061no—
545#435—1061no—
546#435—1061no—
547C8×D4—1061no—
548#432—531no—
549#431—531no—
550#407—531no—
551#407—531no—
552C2×C22⋊C8—531no—
553C2×C22⋊C8—531no—
554#388—1061no—
555#387—1061no—
556#386—1061no—
557#385—1061no—
558#383—531no—
559#382—531no—
560#381—531no—
561#380—531no—
562C4×C22⋊C4—531no—
563C2×#95—531no—
564#328—531no—
565#328—531no—
566#328—531no—
567#328—531no—
568#327—531no—
569#327—531no—
570#327—531no—
571#327—531no—
572#327—531no—
573#327—531no—
574#327—531no—
575#327—531no—
576#327—531no—
577#327—531no—
578#327—531no—
579#327—531no—
580C53#1759711yescharacteristic, complemented, Sylow
581C2×#41—21no—
582C2×#41C2×Dic5311yescharacteristic
583C2×#41C2×Dic5311yescharacteristic, complemented
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4C2×Dic5311yescharacteristic
588C22×D4C2×Dic5311yescharacteristic, complemented
589C22×D4C22⋊D5311yescharacteristic
590C23×C4—1061no—
591C23×C4C22×D5311yescharacteristic
592C23×C4C22×D5311yescharacteristic
593C2×M16—1061no—
594C2×M16—1061no—
595C22×C8—1061no—
596C22×C8—1061no—
597C4⋊Q8C2×Dic5311yescharacteristic, complemented
598#127—21no—
599#127C2×Dic5311yescharacteristic, complemented
600#126—21no—
601#126—21no—
602#126—21no—
603#125—21no—
604#125C2×Dic5311yescharacteristic, complemented
605#124—21no—
606#124—21no—
607#124—21no—
608#124C2×Dic5311yescharacteristic, complemented
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618C22⋊Q8C2×Dic5311yescharacteristic
619C22⋊Q8C2×Dic5311yescharacteristic, complemented
620C22⋊Q8C22×D5311yescharacteristic
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121C2×Dic5311yescharacteristic
635#121C2×Dic5311yescharacteristic
636#121C2×Dic5311yescharacteristic
637#121C2×Dic5311yescharacteristic, complemented
638#121C2×Dic5311yescharacteristic, complemented
639#121C2×Dic5311yescharacteristic, complemented
640#121C22×D5311yescharacteristic
641#121C22×D5311yescharacteristic
642#121C22×D5311yescharacteristic
643#120—21no—
644#120—21no—
645#120—21no—
646#120—21no—
647#120—21no—
648#120—21no—
649C4×Q8C2×Dic5311yescharacteristic, complemented
650C4×D4—21no—
651C4×D4—21no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—21no—
655C4×D4—21no—
656C4×D4—21no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—21no—
660C4×D4C2×Dic5311yescharacteristic
661C4×D4C2×Dic5311yescharacteristic
662C4×D4C2×Dic5311yescharacteristic
663C4×D4C2×Dic5311yescharacteristic
664C4×D4C2×Dic5311yescharacteristic, complemented
665C4×D4C2×Dic5311yescharacteristic, complemented
666C4×D4C2×Dic5311yescharacteristic, complemented
667C4×D4C22⋊D5311yescharacteristic
668C4×D4C22⋊D5311yescharacteristic
669C4×D4C22⋊D5311yescharacteristic
670C4×D4C22⋊D5311yescharacteristic
671#117—21no—
672#117—21no—
673#117C2×Dic5311yescharacteristic
674#117C2×Dic5311yescharacteristic, complemented
675C2×C4⋊C4—1061no—
676C2×C4⋊C4—1061no—
677C2×C4⋊C4C2×Dic5311yescharacteristic
678C2×C4⋊C4C2×Dic5311yescharacteristic, complemented
679C2×C4⋊C4C22⋊D5311yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—1061no—
685C2×C22⋊C4—1061no—
686C2×C22⋊C4—1061no—
687C2×C22⋊C4C22⋊D5311yescharacteristic
688C2×C22⋊C4C22⋊D5311yescharacteristic
689C2×C42—1061no—
690C2×C42C22×D5311yescharacteristic
691C4⋊C8—1061no—
692C4⋊C8—1061no—
693C22⋊C8—531no—
694C22⋊C8—531no—
695C22⋊C8—531no—
696C22⋊C8—531no—
697C22⋊C8—1061no—
698C22⋊C8—1061no—
699C22⋊C8—1061no—
700C22⋊C8—1061no—
701#97—1061no—
702C4×C8—1061no—
703#95—531no—
704#95—531no—
705#95—531no—
706#95—531no—
707#95—1061no—
708#95—1061no—
709#95—1061no—
710#95—1061no—
711#95—1061no—
712C24—21no—
713C24—21no—
714C24C2×C22⋊D5311yescharacteristic
715C24C2×C22⋊D5311yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719#41—81no—
720C2×Q8—21no—
721C2×Q8C22×Dic5311yescharacteristic
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C22⋊Dic5311yescharacteristic
746C2×D4C22⋊Dic5311yescharacteristic
747C2×D4C22⋊Dic5311yescharacteristic
748C2×D4C22⋊Dic5311yescharacteristic
749C2×D4C22×Dic5311yescharacteristic
750C2×D4C22×Dic5311yescharacteristic
751C2×D4C22×Dic5311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—81no—
760C22×C4—81no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—4241no—
766C22×C4—4241no—
767C22×C4—2122no—
768C22×C4C22×Dic5311yescharacteristic
769C22×C4C22×Dic5311yescharacteristic
770C22×C4C22×Dic5311yescharacteristic
771C22×C4C22×Dic5311yescharacteristic
772C22×C4C2×C22⋊D5311yescharacteristic
773C22×C4C2×C22⋊D5311yescharacteristic
774C22×C4C2×C22⋊D5311yescharacteristic
775C22×C4C2×C22⋊D5311yescharacteristic
776C22×C4C2×C22⋊D5311yescharacteristic
777C22×C4C2×C22⋊D5311yescharacteristic
778C22×C4C2×C22⋊D5311yescharacteristic
779C22×C4C2×C22⋊D5311yescharacteristic
780C22×C4C23×D5311yescharacteristic
781M16—4241no—
782M16—4241no—
783C2×C8—1061no—
784C2×C8—1061no—
785C2×C8—1061no—
786C2×C8—1061no—
787C2×C8—4241no—
788C2×C8—4241no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—4241no—
799C4⋊C4—4241no—
800C4⋊C4C22⋊Dic5311yescharacteristic
801C4⋊C4C22⋊Dic5311yescharacteristic
802C4⋊C4C22⋊Dic5311yescharacteristic
803C4⋊C4C22⋊Dic5311yescharacteristic
804C4⋊C4C22×Dic5311yescharacteristic
805C4⋊C4C22×Dic5311yescharacteristic
806C4⋊C4C22×Dic5311yescharacteristic
807C4⋊C4C22×Dic5311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—4241no—
828C22⋊C4—4241no—
829C22⋊C4—2122no—
830C22⋊C4C22⋊Dic5311yescharacteristic
831C22⋊C4C22⋊Dic5311yescharacteristic
832C22⋊C4C22⋊Dic5311yescharacteristic
833C22⋊C4C22⋊Dic5311yescharacteristic
834C22⋊C4C22⋊Dic5311yescharacteristic
835C22⋊C4C22⋊Dic5311yescharacteristic
836C22⋊C4C22⋊Dic5311yescharacteristic
837C22⋊C4C22⋊Dic5311yescharacteristic
838C42—21no—
839C42—21no—
840C42—21no—
841C42—4241no—
842C42C22×Dic5311yescharacteristic
843C42C22×Dic5311yescharacteristic
844C42C2×C22⋊D5311yescharacteristic
845C42C2×C22⋊D5311yescharacteristic
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C22⋊Dic5311yescharacteristic
864C23C2×C22⋊Dic5311yescharacteristic
865C23C2×C22⋊Dic5311yescharacteristic
866C23C2×C22⋊Dic5311yescharacteristic
867C23C22×C22⋊D5311yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—42no—
915C2×C4—81no—
916C2×C4—81no—
917C2×C4—81no—
918C2×C4—81no—
919C2×C4—81no—
920C2×C4—81no—
921C2×C4—4244no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4C2×C22⋊Dic5311yescharacteristic
935C2×C4C2×C22⋊Dic5311yescharacteristic
936C2×C4C2×C22⋊Dic5311yescharacteristic
937C2×C4C2×C22⋊Dic5311yescharacteristic
938C2×C4C2×C22⋊Dic5311yescharacteristic
939C2×C4C2×C22⋊Dic5311yescharacteristic
940C2×C4C2×C22⋊Dic5311yescharacteristic
941C2×C4C2×C22⋊Dic5311yescharacteristic
942C2×C4C23×Dic5311yescharacteristic
943C2×C4C22×C22⋊D5311yescharacteristic
944C8—2121no—
945C8—2121no—
946C8—2121no—
947C8—2121no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22#1681064012yes—
977C22C22×C22⋊Dic5311yescharacteristic
978C22#1681142611yescharacteristic
979C22#1681143411yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—4241no—
996C4—4241no—
997C4—4241no—
998C4—4241no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2#2028317611yescharacteristic
1009C2#2028324111yescharacteristic
1010C2C2×#1681064011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#3519C2
socleC22×C53C22×C22⋊C4
cosocleC22×C4×C53C24
hypercenter#3519D53
hypocenterC53#17597
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #20283750C2semidirect
2. #20277348C2semidirect
3. #20273292C2semidirect
4. #20273283C2semidirect
5. #20273275C2semidirect
6. #20273271C2semidirect
7. #20273262C2semidirect
8. #20273258C2semidirect
9. #20273253C2semidirect
10. #20273244C2semidirect
11. #20273231C2semidirect
12. #20273219C2semidirect
13. #20273206C2semidirect
14. C2×#16810357C2semidirect
20. #16810680C22semidirect
21. #16810676C22semidirect
22. #16810587C22semidirect
23. #16810587C22semidirect
24. C2×C22⋊#88322C22semidirect
25. C2×C22⋊#88322C22semidirect
30. #16810491C22semidirect
31. #16810489C22semidirect
32. #16810486C22semidirect
33. #16810483C22semidirect
34. C4×C22⋊Dic53C22semidirect
35. C2×#13133124C22semidirect
36. #16810360C22semidirect
37. #16810360C22semidirect
38. #16810360C22semidirect
39. #16810360C22semidirect
44. #16810357C22semidirect
45. #16810357C22semidirect
46. #16810357C22semidirect
47. #16810357C22semidirect
48. #16810357C22semidirect
49. #16810357C22semidirect
50. #16810357C22semidirect
51. #16810357C22semidirect
52. C53×#555C4semidirect
53. C53×#554C4semidirect
55. C53×#553C4semidirect
56. C53×#553C4semidirect
57. C53×#550C4semidirect
60. C53×#546C4semidirect
61. C53×#546C4semidirect
63. D42×C53C4semidirect
109. C2×#41×C53C2×C4semidirect
114. C22×D4×C53C2×C4semidirect
118. C4⋊Q8×C53C2×C4semidirect
120. #127×C53C2×C4semidirect
125. #125×C53C2×C4semidirect
129. #124×C53C2×C4semidirect
140. C22⋊Q8×C53C2×C4semidirect
158. #121×C53C2×C4semidirect
159. #121×C53C2×C4semidirect
160. #121×C53C2×C4semidirect
170. C4×Q8×C53C2×C4semidirect
185. C4×D4×C53C2×C4semidirect
186. C4×D4×C53C2×C4semidirect
187. C4×D4×C53C2×C4semidirect
195. #117×C53C2×C4semidirect
197. C2×C4⋊C4×C53C2×C4semidirect
521. #555Dic53semidirect
522. #554Dic53semidirect
524. #553Dic53semidirect
525. #553Dic53semidirect
526. #550Dic53semidirect
529. #546Dic53semidirect
530. #546Dic53semidirect
532. D42Dic53semidirect
580. C53#17597semidirect
583. C2×#41C2×Dic53semidirect
588. C22×D4C2×Dic53semidirect
597. C4⋊Q8C2×Dic53semidirect
599. #127C2×Dic53semidirect
604. #125C2×Dic53semidirect
608. #124C2×Dic53semidirect
619. C22⋊Q8C2×Dic53semidirect
637. #121C2×Dic53semidirect
638. #121C2×Dic53semidirect
639. #121C2×Dic53semidirect
649. C4×Q8C2×Dic53semidirect
664. C4×D4C2×Dic53semidirect
665. C4×D4C2×Dic53semidirect
666. C4×D4C2×Dic53semidirect
674. #117C2×Dic53semidirect
678. C2×C4⋊C4C2×Dic53semidirect

Maximal subgroups

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

subgroupindex
#202837502
#202773482
#202732922
#202732832
#202732752
#202732712
#202732622
#202732582
#202732532
#202732442
#202732312
#202732192
#202732062
C2×#168103572
C53×#35192
#1759753