Finite Group Databasebeta

← #27352237

Subgroups — #27352237

Order 13568.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283729C211yesmaximal, characteristic, complemented
2#20283366C211yesmaximal, characteristic, complemented
3#20273350C211yesmaximal, characteristic, complemented
4#20273346C211yesmaximal, characteristic, complemented
5#20273346C211yesmaximal, characteristic, complemented
6#20273339C211yesmaximal, characteristic, complemented
7#20273335C211yesmaximal, characteristic, complemented
8#20273335C211yesmaximal, characteristic, complemented
9#20273326C211yesmaximal, characteristic, complemented
10#20273322C211yesmaximal, characteristic, complemented
11#20273313C211yesmaximal, characteristic, complemented
12#20273313C211yesmaximal, characteristic, complemented
13#20273303C211yesmaximal, characteristic, complemented
14C2×#16810363C211yesmaximal, characteristic, complemented
15C53×#3514C211yesmaximal, 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#16810680C2211yescharacteristic, complemented
25#16810680C2211yescharacteristic, complemented
26#16810680C2211yescharacteristic, complemented
27#16810680C2211yescharacteristic, complemented
28#16810680C2211yescharacteristic, complemented
29#16810650—21no—
30#16810590—21no—
31C4×#11719917C2211yescharacteristic, complemented
32C4×#11719917C2211yescharacteristic, complemented
33C2×#13133128C2211yescharacteristic, complemented
34C2×#13133128C2211yescharacteristic, complemented
35C2×#13133128C2211yescharacteristic, complemented
36#16810365C2211yescharacteristic, complemented
37#16810365C2211yescharacteristic, complemented
38#16810365C2211yescharacteristic, complemented
39#16810365C2211yescharacteristic, complemented
40#16810363C2211yescharacteristic
41#16810363C2211yescharacteristic
42#16810363C2211yescharacteristic
43#16810363C2211yescharacteristic
44#16810363C2211yescharacteristic, complemented
45#16810363C2211yescharacteristic, complemented
46#16810363C2211yescharacteristic, complemented
47#16810363C2211yescharacteristic, complemented
48#16810363C2211yescharacteristic, complemented
49#16810363C2211yescharacteristic, complemented
50#16810363C2211yescharacteristic, complemented
51#16810363C2211yescharacteristic, complemented
52C53×#559C411yescharacteristic
53C53×#556C411yescharacteristic
54C53×#555—21no—
55C53×#551—21no—
56C53×#551—21no—
57D4×Q8×C53C411yescharacteristic
58C53×#548C411yescharacteristic
59C53×#548C411yescharacteristic
60C53×#546—21no—
61C53×#546C411yescharacteristic
62C53×#546C411yescharacteristic
63D42×C53C411yescharacteristic
64C53×#542—21no—
65C53×#538—21no—
66C53×#538—21no—
67C53×#532C2211yescharacteristic
68C53×#529C2211yescharacteristic
69C53×#529C2211yescharacteristic
70C53×#529C2211yescharacteristic
71C2×#124×C53C2211yescharacteristic
72C2×#124×C53C2211yescharacteristic
73C53×#518—21no—
74C4×#41×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—
87C22⋊#88322—21no—
88C22⋊#88322—21no—
89C22⋊#88322—21no—
90C22⋊#88322—21no—
91C22⋊#88322—21no—
92C22⋊#88322—21no—
93C22⋊#88322—21no—
94#13133128—21no—
95#13133128—21no—
96#13133128—21no—
97#13133128C2311yescharacteristic
98#13133128C2311yescharacteristic
99#13133128C2311yescharacteristic
100#13133128C2311yescharacteristic
101#13133128C2311yescharacteristic
102#13133128C2311yescharacteristic
103#13133128C2311yescharacteristic
104#13133128C2311yescharacteristic
105C4×#88322—21no—
106C4×#88322—21no—
107C2×#41×C53C2×C411yescharacteristic
108C2×#41×C53C2×C411yescharacteristic
109C2×#41×C53D411yescharacteristic
110C22×Q8×C53C2×C411yescharacteristic
111C22×Q8×C53C2×C411yescharacteristic
112C22×D4×C53—21no—
113C22×D4×C53C2×C411yescharacteristic
114C22×D4×C53C2×C411yescharacteristic
115C4⋊Q8×C53—21no—
116C4⋊Q8×C53C2×C411yescharacteristic
117#127×C53C2×C411yescharacteristic
118#126×C53—21no—
119#126×C53—21no—
120#126×C53—21no—
121#126×C53—21no—
122#126×C53—21no—
123#125×C53C2311yescharacteristic
124#124×C53—21no—
125#124×C53—21no—
126#124×C53—21no—
127#124×C53—21no—
128#124×C53—21no—
129#124×C53—21no—
130#124×C53—21no—
131#124×C53C2×C411yescharacteristic
132#124×C53C2×C411yescharacteristic
133#124×C53C2×C411yescharacteristic
134#124×C53C2×C411yescharacteristic
135#124×C53C2311yescharacteristic
136#124×C53C2311yescharacteristic
137#124×C53C2311yescharacteristic
138#123×C53—21no—
139#123×C53—21no—
140#123×C53—21no—
141#123×C53—21no—
142#123×C53—21no—
143#123×C53—21no—
144#123×C53—21no—
145C22⋊Q8×C53—21no—
146C22⋊Q8×C53—21no—
147C22⋊Q8×C53—21no—
148C22⋊Q8×C53—21no—
149C22⋊Q8×C53—21no—
150C22⋊Q8×C53C2×C411yescharacteristic
151C22⋊Q8×C53C2×C411yescharacteristic
152C22⋊Q8×C53C2×C411yescharacteristic
153#121×C53—21no—
154#121×C53—21no—
155#121×C53—21no—
156#121×C53—21no—
157#121×C53—21no—
158#121×C53—21no—
159#121×C53—21no—
160#121×C53C2×C411yescharacteristic
161#121×C53C2×C411yescharacteristic
162#121×C53C2×C411yescharacteristic
163#120×C53—21no—
164#120×C53—21no—
165#120×C53—21no—
166#120×C53—21no—
167C4×Q8×C53C2×C411yescharacteristic
168C4×Q8×C53C2×C411yescharacteristic
169C4×Q8×C53C2×C411yescharacteristic
170C4×Q8×C53C2×C411yescharacteristic
171C4×Q8×C53D411yescharacteristic
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
186C4×D4×C53C2×C411yescharacteristic
187C4×D4×C53D411yescharacteristic
188C4×D4×C53D411yescharacteristic
189C4×D4×C53D411yescharacteristic
190#117×C53—21no—
191#117×C53—21no—
192#117×C53—21no—
193#117×C53—21no—
194#117×C53D411yescharacteristic
195#117×C53D411yescharacteristic
196#117×C53D411yescharacteristic
197C2×C22⋊C4×C53—21no—
198C2×C22⋊C4×C53—21no—
199C2×C22⋊C4×C53—21no—
200C2×C22⋊C4×C53—21no—
201C2×C22⋊C4×C53—21no—
202C2×C22⋊C4×C53—21no—
203C2×C42×C53C2311yescharacteristic
204C2×C42×C53C2311yescharacteristic
205C2×C42×C53C2311yescharacteristic
206C24×C53—21no—
207C24×C53—21no—
208#41×C53—42no—
209#41×C53—81no—
210#41×C53—81no—
211C2×Q8×C53—21no—
212C2×Q8×C53—21no—
213C2×Q8×C53—81no—
214C2×Q8×C53—81no—
215C2×Q8×C53C22⋊C411yescharacteristic
216C2×Q8×C53C22×C411yescharacteristic
217C2×Q8×C53C22×C411yescharacteristic
218C2×Q8×C53C22×C411yescharacteristic
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—44no—
229C2×D4×C53—81no—
230C2×D4×C53—81no—
231C2×D4×C53C22⋊C411yescharacteristic
232C2×D4×C53C22⋊C411yescharacteristic
233C2×D4×C53C22⋊C411yescharacteristic
234C2×D4×C53C22×C411yescharacteristic
235C2×D4×C53C22×C411yescharacteristic
236C2×D4×C53C22×C411yescharacteristic
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×C53C22×C411yescharacteristic
245C22×C4×C53C22×C411yescharacteristic
246C22×C4×C53C22×C411yescharacteristic
247C22×C4×C53C2×D411yescharacteristic
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2×D411yescharacteristic
250C22×C4×C53C2×D411yescharacteristic
251C22×C4×C53C2×D411yescharacteristic
252C22×C4×C53C2×D411yescharacteristic
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×C53C22⋊C411yescharacteristic
264C4⋊C4×C53C22⋊C411yescharacteristic
265C4⋊C4×C53C22⋊C411yescharacteristic
266C4⋊C4×C53C22⋊C411yescharacteristic
267C4⋊C4×C53C22⋊C411yescharacteristic
268C4⋊C4×C53C22⋊C411yescharacteristic
269C4⋊C4×C53C22×C411yescharacteristic
270C4⋊C4×C53C22×C411yescharacteristic
271C22⋊C4×C53—21no—
272C22⋊C4×C53—21no—
273C22⋊C4×C53—21no—
274C22⋊C4×C53—21no—
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×C53—21no—
289C22⋊C4×C53—21no—
290C22⋊C4×C53—21no—
291C22⋊C4×C53—21no—
292C22⋊C4×C53—21no—
293C22⋊C4×C53—21no—
294C22⋊C4×C53C22⋊C411yescharacteristic
295C22⋊C4×C53C22⋊C411yescharacteristic
296C22⋊C4×C53C22⋊C411yescharacteristic
297C22⋊C4×C53C22⋊C411yescharacteristic
298C22⋊C4×C53C22⋊C411yescharacteristic
299C22⋊C4×C53C22⋊C411yescharacteristic
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—42no—
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—42no—
325C2×#88322—42no—
326C23×C53—21no—
327C23×C53—21no—
328C23×C53—21no—
329C23×C53—42no—
330C23×C53—42no—
331C23×C53—81no—
332C23×C53—81no—
333C23×C53—81no—
334C23×C53—81no—
335C23×C53C2×C22⋊C411yescharacteristic
336C23×C53C2×C22⋊C411yescharacteristic
337C23×C53C2×C22⋊C411yescharacteristic
338Q8×C53—41no—
339Q8×C53—41no—
340Q8×C53—41no—
341Q8×C53—41no—
342Q8×C53—81no—
343Q8×C53—81no—
344D4×C53—22no—
345D4×C53—22no—
346D4×C53—41no—
347D4×C53—41no—
348D4×C53—41no—
349D4×C53—41no—
350D4×C53—42no—
351D4×C53—42no—
352D4×C53—42no—
353D4×C53—81no—
354D4×C53—81no—
355D4×C53—81no—
356D4×C53—81no—
357D4×C53—81no—
358D4×C53—81no—
359C2×C4×C53—22no—
360C2×C4×C53—21no—
361C2×C4×C53—21no—
362C2×C4×C53—21no—
363C2×C4×C53—21no—
364C2×C4×C53—21no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—42no—
374C2×C4×C53—81no—
375C2×C4×C53—81no—
376C2×C4×C53—81no—
377C2×C4×C53—81no—
378C2×C4×C53—81no—
379C2×C4×C53—81no—
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×C53C2×C22⋊C411yescharacteristic
388C2×C4×C53C2×C22⋊C411yescharacteristic
389C2×C4×C53C23×C411yescharacteristic
390C2×C4×C53C22×D411yescharacteristic
391C2×C4×C53C22×D411yescharacteristic
392#88322—22no—
393#88322—41no—
394#88322—41no—
395#88322—41no—
396#88322—41no—
397#88322—41no—
398#88322—41no—
399#88322—41no—
400#17679—531nomaximal, Sylow
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—21no—
405C22×C53—21no—
406C22×C53—21no—
407C22×C53—21no—
408C22×C53—21no—
409C22×C53—41no—
410C22×C53—41no—
411C22×C53—41no—
412C22×C53—41no—
413C22×C53—41no—
414C22×C53—41no—
415C22×C53—41no—
416C22×C53—41no—
417C22×C53—41no—
418C22×C53—162no—
419C22×C53—162no—
420C22×C53#42112yes—
421C22×C53C22×C22⋊C411yescharacteristic
422C4×C53—21no—
423C4×C53—21no—
424C4×C53—21no—
425C4×C53—21no—
426C4×C53—21no—
427C4×C53—21no—
428C4×C53—21no—
429C4×C53—21no—
430C4×C53—21no—
431C4×C53—21no—
432C4×C53—21no—
433C4×C53—21no—
434C4×C53—41no—
435C4×C53—41no—
436C4×C53—41no—
437C4×C53—41no—
438C4×C53—41no—
439#3514D5311yescharacteristic
440#2970—531no—
441#2923—531no—
442#1536—531no—
443#1535—531no—
444#1535—531no—
445#1533—531no—
446#1532—531no—
447#1532—531no—
448#1530—531no—
449#1529—531no—
450#1527—531no—
451#1527—531no—
452#1524—531no—
453C2×#329—531no—
454C2×C53—22no—
455C2×C53—41no—
456C2×C53—41no—
457C2×C53—81no—
458C2×C53—81no—
459C2×C53—81no—
460C2×C53#288811yescharacteristic
461C2×C53C2×#42111yescharacteristic
462C2×C53#290111yescharacteristic
463#559Dic5311yescharacteristic
464#556Dic5311yescharacteristic
465#555—21no—
466#551—21no—
467#551—21no—
468D4×Q8Dic5311yescharacteristic
469#548Dic5311yescharacteristic
470#548Dic5311yescharacteristic
471#546—21no—
472#546Dic5311yescharacteristic
473#546Dic5311yescharacteristic
474D42Dic5311yescharacteristic
475#542—21no—
476#538—21no—
477#538—21no—
478#532C2×D5311yescharacteristic
479#529C2×D5311yescharacteristic
480#529C2×D5311yescharacteristic
481#529C2×D5311yescharacteristic
482C2×#124C2×D5311yescharacteristic
483C2×#124C2×D5311yescharacteristic
484#518—21no—
485C4×#41C2×D5311yescharacteristic
486#446—1061no—
487#435—1061no—
488#435—1061no—
489C8×D4—1061no—
490#433—1061no—
491#433—1061no—
492#432—531no—
493#432—531no—
494#432—531no—
495#432—531no—
496#432—531no—
497#432—531no—
498#432—531no—
499#424—1061no—
500#408—1061no—
501C4×M16—531no—
502C4×M16—531no—
503C2×#97—531no—
504C2×#97—531no—
505C2×#97—531no—
506#330—531no—
507#330—531no—
508#330—531no—
509#330—531no—
510#329—531no—
511#329—531no—
512#329—531no—
513#329—531no—
514#329—531no—
515#329—531no—
516#329—531no—
517#329—531no—
518#329—531no—
519#329—531no—
520#329—531no—
521#329—531no—
522C53#1767911yescharacteristic, complemented, Sylow
523C2×#41C2×Dic5311yescharacteristic
524C2×#41C2×Dic5311yescharacteristic
525C2×#41C22⋊D5311yescharacteristic
526C22×Q8C2×Dic5311yescharacteristic
527C22×Q8C2×Dic5311yescharacteristic
528C22×D4—21no—
529C22×D4C2×Dic5311yescharacteristic
530C22×D4C2×Dic5311yescharacteristic
531C2×M16—1061no—
532C2×M16—1061no—
533C22×C8—1061no—
534C22×C8—1061no—
535C22×C8—1061no—
536C4⋊Q8—21no—
537C4⋊Q8C2×Dic5311yescharacteristic
538#127C2×Dic5311yescharacteristic
539#126—21no—
540#126—21no—
541#126—21no—
542#126—21no—
543#126—21no—
544#125C22×D5311yescharacteristic
545#124—21no—
546#124—21no—
547#124—21no—
548#124—21no—
549#124—21no—
550#124—21no—
551#124—21no—
552#124C2×Dic5311yescharacteristic
553#124C2×Dic5311yescharacteristic
554#124C2×Dic5311yescharacteristic
555#124C2×Dic5311yescharacteristic
556#124C22×D5311yescharacteristic
557#124C22×D5311yescharacteristic
558#124C22×D5311yescharacteristic
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566C22⋊Q8—21no—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—21no—
570C22⋊Q8—21no—
571C22⋊Q8C2×Dic5311yescharacteristic
572C22⋊Q8C2×Dic5311yescharacteristic
573C22⋊Q8C2×Dic5311yescharacteristic
574#121—21no—
575#121—21no—
576#121—21no—
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121C2×Dic5311yescharacteristic
582#121C2×Dic5311yescharacteristic
583#121C2×Dic5311yescharacteristic
584#120—21no—
585#120—21no—
586#120—21no—
587#120—21no—
588C4×Q8C2×Dic5311yescharacteristic
589C4×Q8C2×Dic5311yescharacteristic
590C4×Q8C2×Dic5311yescharacteristic
591C4×Q8C2×Dic5311yescharacteristic
592C4×Q8C22⋊D5311yescharacteristic
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—21no—
599C4×D4—21no—
600C4×D4—21no—
601C4×D4—21no—
602C4×D4C2×Dic5311yescharacteristic
603C4×D4C2×Dic5311yescharacteristic
604C4×D4C2×Dic5311yescharacteristic
605C4×D4C2×Dic5311yescharacteristic
606C4×D4C2×Dic5311yescharacteristic
607C4×D4C2×Dic5311yescharacteristic
608C4×D4C22⋊D5311yescharacteristic
609C4×D4C22⋊D5311yescharacteristic
610C4×D4C22⋊D5311yescharacteristic
611#117—21no—
612#117—21no—
613#117—21no—
614#117—21no—
615#117C22⋊D5311yescharacteristic
616#117C22⋊D5311yescharacteristic
617#117C22⋊D5311yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C42C22×D5311yescharacteristic
625C2×C42C22×D5311yescharacteristic
626C2×C42C22×D5311yescharacteristic
627C4⋊C8—1061no—
628C4⋊C8—1061no—
629C4⋊C8—1061no—
630C4⋊C8—1061no—
631C4⋊C8—1061no—
632C4⋊C8—1061no—
633C4⋊C8—1061no—
634C22⋊C8—1061no—
635C22⋊C8—1061no—
636C22⋊C8—1061no—
637C22⋊C8—1061no—
638C22⋊C8—1061no—
639C22⋊C8—1061no—
640C22⋊C8—1061no—
641#97—531no—
642#97—531no—
643#97—531no—
644#97—531no—
645#97—531no—
646#97—531no—
647#97—531no—
648#97—531no—
649#97—1061no—
650#97—1061no—
651#97—1061no—
652C4×C8—1061no—
653C4×C8—1061no—
654C24—21no—
655C24—21no—
656#41—42no—
657#41—81no—
658#41—81no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—81no—
662C2×Q8—81no—
663C2×Q8C22⋊Dic5311yescharacteristic
664C2×Q8C22×Dic5311yescharacteristic
665C2×Q8C22×Dic5311yescharacteristic
666C2×Q8C22×Dic5311yescharacteristic
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C22⋊Dic5311yescharacteristic
680C2×D4C22⋊Dic5311yescharacteristic
681C2×D4C22⋊Dic5311yescharacteristic
682C2×D4C22×Dic5311yescharacteristic
683C2×D4C22×Dic5311yescharacteristic
684C2×D4C22×Dic5311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4C22×Dic5311yescharacteristic
693C22×C4C22×Dic5311yescharacteristic
694C22×C4C22×Dic5311yescharacteristic
695C22×C4C2×C22⋊D5311yescharacteristic
696C22×C4C2×C22⋊D5311yescharacteristic
697C22×C4C2×C22⋊D5311yescharacteristic
698C22×C4C2×C22⋊D5311yescharacteristic
699C22×C4C2×C22⋊D5311yescharacteristic
700C22×C4C2×C22⋊D5311yescharacteristic
701M16—2122no—
702M16—2122no—
703C2×C8—1061no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—2122no—
712C2×C8—2122no—
713C2×C8—2122no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4C22⋊Dic5311yescharacteristic
725C4⋊C4C22⋊Dic5311yescharacteristic
726C4⋊C4C22⋊Dic5311yescharacteristic
727C4⋊C4C22⋊Dic5311yescharacteristic
728C4⋊C4C22⋊Dic5311yescharacteristic
729C4⋊C4C22⋊Dic5311yescharacteristic
730C4⋊C4C22×Dic5311yescharacteristic
731C4⋊C4C22×Dic5311yescharacteristic
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⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4C22⋊Dic5311yescharacteristic
756C22⋊C4C22⋊Dic5311yescharacteristic
757C22⋊C4C22⋊Dic5311yescharacteristic
758C22⋊C4C22⋊Dic5311yescharacteristic
759C22⋊C4C22⋊Dic5311yescharacteristic
760C22⋊C4C22⋊Dic5311yescharacteristic
761C42—21no—
762C42—21no—
763C42—21no—
764C42C22×Dic5311yescharacteristic
765C42C22×Dic5311yescharacteristic
766C42C22×Dic5311yescharacteristic
767C42C2×C22⋊D5311yescharacteristic
768C42C2×C22⋊D5311yescharacteristic
769C42C2×C22⋊D5311yescharacteristic
770C42C2×C22⋊D5311yescharacteristic
771C42C2×C22⋊D5311yescharacteristic
772C42C2×C22⋊D5311yescharacteristic
773C42C23×D5311yescharacteristic
774C23—21no—
775C23—21no—
776C23—21no—
777C23—42no—
778C23—42no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23C2×C22⋊Dic5311yescharacteristic
784C23C2×C22⋊Dic5311yescharacteristic
785C23C2×C22⋊Dic5311yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—42no—
799D4—42no—
800D4—42no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—42no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4C2×C22⋊Dic5311yescharacteristic
829C2×C4C2×C22⋊Dic5311yescharacteristic
830C2×C4C2×C22⋊Dic5311yescharacteristic
831C2×C4C2×C22⋊Dic5311yescharacteristic
832C2×C4C2×C22⋊Dic5311yescharacteristic
833C2×C4C2×C22⋊Dic5311yescharacteristic
834C2×C4C2×C22⋊Dic5311yescharacteristic
835C2×C4C2×C22⋊Dic5311yescharacteristic
836C2×C4C2×C22⋊Dic5311yescharacteristic
837C2×C4C23×Dic5311yescharacteristic
838C2×C4C22×C22⋊D5311yescharacteristic
839C2×C4C22×C22⋊D5311yescharacteristic
840C8—1062no—
841C8—2121no—
842C8—2121no—
843C8—2121no—
844C8—2121no—
845C8—2121no—
846C8—2121no—
847C8—2121no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—162no—
866C22—162no—
867C22#1681064012yes—
868C22C22×C22⋊Dic5311yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—41no—
882C4—41no—
883C4—41no—
884C4—41no—
885C4—41no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—81no—
890C2—81no—
891C2—81no—
892C2#2028319411yescharacteristic
893C2C2×#1681064011yescharacteristic
894C2#2028326211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
Fitting, prime radicalC53×#3514C2
socleC22×C53C22×C22⋊C4
cosocleC42×C53C24
hypercenter#3514D53
hypocenterC53#17679
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3514

Complements

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

NH ≅ G/Ntype
1. #20283729C2semidirect
2. #20283366C2semidirect
3. #20273350C2semidirect
4. #20273346C2semidirect
5. #20273346C2semidirect
6. #20273339C2semidirect
7. #20273335C2semidirect
8. #20273335C2semidirect
9. #20273326C2semidirect
10. #20273322C2semidirect
11. #20273313C2semidirect
12. #20273313C2semidirect
13. #20273303C2semidirect
14. C2×#16810363C2semidirect
22. #16810680C22semidirect
23. #16810680C22semidirect
24. #16810680C22semidirect
25. #16810680C22semidirect
26. #16810680C22semidirect
27. #16810680C22semidirect
28. #16810680C22semidirect
31. C4×#11719917C22semidirect
32. C4×#11719917C22semidirect
33. C2×#13133128C22semidirect
34. C2×#13133128C22semidirect
35. C2×#13133128C22semidirect
36. #16810365C22semidirect
37. #16810365C22semidirect
38. #16810365C22semidirect
39. #16810365C22semidirect
44. #16810363C22semidirect
45. #16810363C22semidirect
46. #16810363C22semidirect
47. #16810363C22semidirect
48. #16810363C22semidirect
49. #16810363C22semidirect
50. #16810363C22semidirect
51. #16810363C22semidirect
522. C53#17679semidirect

Maximal subgroups

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

subgroupindex
#202837292
#202833662
#202733502
#202733462
#202733392
#202733352
#202733262
#202733222
#202733132
#202733032
C2×#168103632
C53×#35142
#1767953