Finite Group Databasebeta

← #27352252

Subgroups — #27352252

Order 13568.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 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#20273353C211yesmaximal, characteristic, complemented
4#20273346C211yesmaximal, characteristic, complemented
5#20273346C211yesmaximal, characteristic, complemented
6#20273342C211yesmaximal, characteristic, complemented
7#20273335C211yesmaximal, characteristic, complemented
8#20273335C211yesmaximal, characteristic, complemented
9#20273330C211yesmaximal, characteristic, complemented
10#20273322C211yesmaximal, characteristic, complemented
11#20273317C211yesmaximal, characteristic, complemented
12#20273317C211yesmaximal, characteristic, complemented
13#20273303C211yesmaximal, characteristic, complemented
14C2×#16810365C211yesmaximal, characteristic, complemented
15C53×#3515C211yesmaximal, characteristic
16#16810754—21no—
17#16810695—21no—
18#16810695—21no—
19D4×#88322—21no—
20#16810684—21no—
21#16810684—21no—
22#16810680C2211yescharacteristic
23#16810680C2211yescharacteristic
24#16810680C2211yescharacteristic
25#16810680C2211yescharacteristic
26#16810680C2211yescharacteristic
27#16810680C2211yescharacteristic
28#16810680C2211yescharacteristic
29#16810650—21no—
30#16810590—21no—
31C4×#11719917C2211yescharacteristic
32C4×#11719917C2211yescharacteristic
33C2×#13133128C2211yescharacteristic
34C2×#13133128C2211yescharacteristic
35C2×#13133128C2211yescharacteristic
36#16810365C2211yescharacteristic
37#16810365C2211yescharacteristic
38#16810365C2211yescharacteristic
39#16810365C2211yescharacteristic
40#16810365C2211yescharacteristic
41#16810365C2211yescharacteristic
42#16810365C2211yescharacteristic
43#16810365C2211yescharacteristic
44#16810365C2211yescharacteristic
45#16810365C2211yescharacteristic
46#16810365C2211yescharacteristic
47#16810365C2211yescharacteristic
48#16810363C2211yescharacteristic
49#16810363C2211yescharacteristic
50#16810363C2211yescharacteristic
51#16810363C2211yescharacteristic
52C53×#557C411yescharacteristic
53C53×#554C411yescharacteristic
54C53×#554C411yescharacteristic
55C53×#553C411yescharacteristic
56C53×#553C411yescharacteristic
57C53×#552—21no—
58C53×#552—21no—
59C53×#552—21no—
60C53×#552C411yescharacteristic
61C53×#552C411yescharacteristic
62C53×#547—21no—
63C53×#547C411yescharacteristic
64C53×#541—21no—
65C53×#539—21no—
66C53×#539—21no—
67C53×#533C2211yescharacteristic
68C53×#529C2211yescharacteristic
69C53×#529C2211yescharacteristic
70C53×#529C2211yescharacteristic
71C2×#125×C53C2211yescharacteristic
72C2×#125×C53C2211yescharacteristic
73C53×#520—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×C53—21no—
108C2×#41×C53D411yescharacteristic
109C4⋊Q8×C53—21no—
110C4⋊Q8×C53C2×C411yescharacteristic
111C4⋊Q8×C53C2×C411yescharacteristic
112#126×C53—21no—
113#126×C53—21no—
114#126×C53—21no—
115#126×C53—21no—
116#126×C53—21no—
117#126×C53—21no—
118#126×C53—21no—
119#125×C53—21no—
120#125×C53—21no—
121#125×C53—21no—
122#125×C53—21no—
123#125×C53—21no—
124#125×C53—21no—
125#125×C53—21no—
126#125×C53—21no—
127#125×C53—21no—
128#125×C53C2×C411yescharacteristic
129#125×C53C2×C411yescharacteristic
130#125×C53C2×C411yescharacteristic
131#125×C53C2×C411yescharacteristic
132#125×C53C2311yescharacteristic
133#125×C53C2311yescharacteristic
134#125×C53C2311yescharacteristic
135#124×C53C2311yescharacteristic
136#123×C53—21no—
137#123×C53—21no—
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×C53—21no—
151C22⋊Q8×C53—21no—
152C22⋊Q8×C53—21no—
153C22⋊Q8×C53C2×C411yescharacteristic
154C22⋊Q8×C53C2×C411yescharacteristic
155C22⋊Q8×C53C2×C411yescharacteristic
156#121×C53—21no—
157#121×C53—21no—
158#121×C53C2×C411yescharacteristic
159#121×C53C2×C411yescharacteristic
160#121×C53C2×C411yescharacteristic
161C4×Q8×C53—21no—
162C4×Q8×C53—21no—
163C4×Q8×C53—21no—
164C4×Q8×C53C2×C411yescharacteristic
165C4×Q8×C53C2×C411yescharacteristic
166C4×Q8×C53C2×C411yescharacteristic
167C4×Q8×C53C2×C411yescharacteristic
168C4×Q8×C53D411yescharacteristic
169C4×D4×C53—21no—
170C4×D4×C53—21no—
171C4×D4×C53—21no—
172C4×D4×C53—21no—
173C4×D4×C53—21no—
174C4×D4×C53—21no—
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×C53D411yescharacteristic
182C4×D4×C53D411yescharacteristic
183C4×D4×C53D411yescharacteristic
184#117×C53—21no—
185#117×C53—21no—
186#117×C53—21no—
187#117×C53—21no—
188#117×C53—21no—
189#117×C53C2×C411yescharacteristic
190#117×C53C2×C411yescharacteristic
191#117×C53D411yescharacteristic
192#117×C53D411yescharacteristic
193#117×C53D411yescharacteristic
194C2×C4⋊C4×C53—21no—
195C2×C4⋊C4×C53—21no—
196C2×C4⋊C4×C53—21no—
197C2×C4⋊C4×C53—21no—
198C2×C4⋊C4×C53—21no—
199C2×C4⋊C4×C53C2×C411yescharacteristic
200C2×C4⋊C4×C53C2×C411yescharacteristic
201C2×C4⋊C4×C53C2×C411yescharacteristic
202C2×C4⋊C4×C53C2×C411yescharacteristic
203C2×C42×C53C2311yescharacteristic
204C2×C42×C53C2311yescharacteristic
205C2×C42×C53C2311yescharacteristic
206#41×C53—42no—
207#41×C53—44no—
208C2×Q8×C53—21no—
209C2×Q8×C53—21no—
210C2×Q8×C53C22⋊C411yescharacteristic
211C2×Q8×C53C22×C411yescharacteristic
212C2×D4×C53—21no—
213C2×D4×C53—21no—
214C2×D4×C53—21no—
215C2×D4×C53C22⋊C411yescharacteristic
216C2×D4×C53C22⋊C411yescharacteristic
217C2×D4×C53C22⋊C411yescharacteristic
218C2×D4×C53C22×C411yescharacteristic
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53C22×C411yescharacteristic
227C22×C4×C53C22×C411yescharacteristic
228C22×C4×C53C22×C411yescharacteristic
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D411yescharacteristic
234C22×C4×C53C2×D411yescharacteristic
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
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×C53C22⋊C411yescharacteristic
262C4⋊C4×C53C22⋊C411yescharacteristic
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
271C4⋊C4×C53C22×C411yescharacteristic
272C4⋊C4×C53C22×C411yescharacteristic
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×C53C22⋊C411yescharacteristic
287C22⋊C4×C53C22⋊C411yescharacteristic
288C22⋊C4×C53C22⋊C411yescharacteristic
289C22⋊C4×C53C22⋊C411yescharacteristic
290C22⋊C4×C53C22⋊C411yescharacteristic
291C22⋊C4×C53C22⋊C411yescharacteristic
292C42×C53—21no—
293C42×C53—21no—
294C42×C53—21no—
295C42×C53—21no—
296C42×C53—21no—
297C42×C53C22×C411yescharacteristic
298C42×C53C22×C411yescharacteristic
299C42×C53C22×C411yescharacteristic
300C42×C53C2×D411yescharacteristic
301C42×C53C2×D411yescharacteristic
302C42×C53C2×D411yescharacteristic
303C42×C53C2×D411yescharacteristic
304C42×C53C2×D411yescharacteristic
305C42×C53C2×D411yescharacteristic
306C42×C53C2411yescharacteristic
307#11719917—42no—
308#11719917—42no—
309C2×#88322—21no—
310C2×#88322—21no—
311C2×#88322—21no—
312C2×#88322—21no—
313C2×#88322—21no—
314C2×#88322—21no—
315C2×#88322—21no—
316C2×#88322—21no—
317C2×#88322—42no—
318C2×#88322—42no—
319C2×#88322—42no—
320C23×C53—21no—
321C23×C53C2×C22⋊C411yescharacteristic
322C23×C53C2×C22⋊C411yescharacteristic
323C23×C53C2×C22⋊C411yescharacteristic
324Q8×C53—41no—
325Q8×C53—42no—
326Q8×C53—41no—
327Q8×C53—81no—
328D4×C53—22no—
329D4×C53—22no—
330D4×C53—41no—
331D4×C53—41no—
332D4×C53—42no—
333D4×C53—42no—
334D4×C53—81no—
335C2×C4×C53—22no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—42no—
352C2×C4×C53—42no—
353C2×C4×C53—42no—
354C2×C4×C53—81no—
355C2×C4×C53—81no—
356C2×C4×C53—81no—
357C2×C4×C53—81no—
358C2×C4×C53C2×C22⋊C411yescharacteristic
359C2×C4×C53C2×C22⋊C411yescharacteristic
360C2×C4×C53C2×C22⋊C411yescharacteristic
361C2×C4×C53C2×C22⋊C411yescharacteristic
362C2×C4×C53C2×C22⋊C411yescharacteristic
363C2×C4×C53C2×C22⋊C411yescharacteristic
364C2×C4×C53C2×C22⋊C411yescharacteristic
365C2×C4×C53C2×C22⋊C411yescharacteristic
366C2×C4×C53C2×C22⋊C411yescharacteristic
367C2×C4×C53C23×C411yescharacteristic
368C2×C4×C53C22×D411yescharacteristic
369C2×C4×C53C22×D411yescharacteristic
370#88322—22no—
371#88322—41no—
372#88322—41no—
373#88322—41no—
374#88322—41no—
375#88322—41no—
376#88322—41no—
377#88322—41no—
378#17680—531nomaximal, Sylow
379C22×C53—21no—
380C22×C53—21no—
381C22×C53—21no—
382C22×C53—21no—
383C22×C53—21no—
384C22×C53—21no—
385C22×C53—21no—
386C22×C53—21no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53#42112yes—
391C22×C53C22×C22⋊C411yescharacteristic
392C4×C53—21no—
393C4×C53—21no—
394C4×C53—21no—
395C4×C53—21no—
396C4×C53—21no—
397C4×C53—21no—
398C4×C53—21no—
399C4×C53—21no—
400C4×C53—21no—
401C4×C53—21no—
402C4×C53—21no—
403C4×C53—21no—
404C4×C53—41no—
405C4×C53—41no—
406C4×C53—41no—
407C4×C53—41no—
408C4×C53—41no—
409C4×C53—41no—
410C4×C53—41no—
411#3515D5311yescharacteristic
412#2970—531no—
413#2923—531no—
414#1537—531no—
415#1535—531no—
416#1535—531no—
417#1534—531no—
418#1532—531no—
419#1532—531no—
420#1531—531no—
421#1529—531no—
422#1528—531no—
423#1528—531no—
424#1524—531no—
425C2×#330—531no—
426C2×C53—22no—
427C2×C53—41no—
428C2×C53—41no—
429C2×C53—81no—
430C2×C53#288911yescharacteristic
431C2×C53C2×#42111yescharacteristic
432C2×C53#290111yescharacteristic
433#557Dic5311yescharacteristic
434#554Dic5311yescharacteristic
435#554Dic5311yescharacteristic
436#553Dic5311yescharacteristic
437#553Dic5311yescharacteristic
438#552—21no—
439#552—21no—
440#552—21no—
441#552Dic5311yescharacteristic
442#552Dic5311yescharacteristic
443#547—21no—
444#547Dic5311yescharacteristic
445#541—21no—
446#539—21no—
447#539—21no—
448#533C2×D5311yescharacteristic
449#529C2×D5311yescharacteristic
450#529C2×D5311yescharacteristic
451#529C2×D5311yescharacteristic
452C2×#125C2×D5311yescharacteristic
453C2×#125C2×D5311yescharacteristic
454#520—21no—
455C4×#41C2×D5311yescharacteristic
456#446—1061no—
457#435—1061no—
458#435—1061no—
459C8×D4—1061no—
460#433—1061no—
461#433—1061no—
462#432—531no—
463#432—531no—
464#432—531no—
465#432—531no—
466#432—531no—
467#432—531no—
468#432—531no—
469#424—1061no—
470#408—1061no—
471C4×M16—531no—
472C4×M16—531no—
473C2×#97—531no—
474C2×#97—531no—
475C2×#97—531no—
476#330—531no—
477#330—531no—
478#330—531no—
479#330—531no—
480#330—531no—
481#330—531no—
482#330—531no—
483#330—531no—
484#330—531no—
485#330—531no—
486#330—531no—
487#330—531no—
488#329—531no—
489#329—531no—
490#329—531no—
491#329—531no—
492C53#1768011yescharacteristic, complemented, Sylow
493C2×#41—21no—
494C2×#41C22⋊D5311yescharacteristic
495C2×M16—1061no—
496C2×M16—1061no—
497C22×C8—1061no—
498C22×C8—1061no—
499C22×C8—1061no—
500C4⋊Q8—21no—
501C4⋊Q8C2×Dic5311yescharacteristic
502C4⋊Q8C2×Dic5311yescharacteristic
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#125—21no—
511#125—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125C2×Dic5311yescharacteristic
520#125C2×Dic5311yescharacteristic
521#125C2×Dic5311yescharacteristic
522#125C2×Dic5311yescharacteristic
523#125C22×D5311yescharacteristic
524#125C22×D5311yescharacteristic
525#125C22×D5311yescharacteristic
526#124C22×D5311yescharacteristic
527#123—21no—
528#123—21no—
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536C22⋊Q8—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8C2×Dic5311yescharacteristic
545C22⋊Q8C2×Dic5311yescharacteristic
546C22⋊Q8C2×Dic5311yescharacteristic
547#121—21no—
548#121—21no—
549#121C2×Dic5311yescharacteristic
550#121C2×Dic5311yescharacteristic
551#121C2×Dic5311yescharacteristic
552C4×Q8—21no—
553C4×Q8—21no—
554C4×Q8—21no—
555C4×Q8C2×Dic5311yescharacteristic
556C4×Q8C2×Dic5311yescharacteristic
557C4×Q8C2×Dic5311yescharacteristic
558C4×Q8C2×Dic5311yescharacteristic
559C4×Q8C22⋊D5311yescharacteristic
560C4×D4—21no—
561C4×D4—21no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4C2×Dic5311yescharacteristic
567C4×D4C2×Dic5311yescharacteristic
568C4×D4C2×Dic5311yescharacteristic
569C4×D4C2×Dic5311yescharacteristic
570C4×D4C2×Dic5311yescharacteristic
571C4×D4C2×Dic5311yescharacteristic
572C4×D4C22⋊D5311yescharacteristic
573C4×D4C22⋊D5311yescharacteristic
574C4×D4C22⋊D5311yescharacteristic
575#117—21no—
576#117—21no—
577#117—21no—
578#117—21no—
579#117—21no—
580#117C2×Dic5311yescharacteristic
581#117C2×Dic5311yescharacteristic
582#117C22⋊D5311yescharacteristic
583#117C22⋊D5311yescharacteristic
584#117C22⋊D5311yescharacteristic
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4C2×Dic5311yescharacteristic
591C2×C4⋊C4C2×Dic5311yescharacteristic
592C2×C4⋊C4C2×Dic5311yescharacteristic
593C2×C4⋊C4C2×Dic5311yescharacteristic
594C2×C42C22×D5311yescharacteristic
595C2×C42C22×D5311yescharacteristic
596C2×C42C22×D5311yescharacteristic
597C4⋊C8—1061no—
598C4⋊C8—1061no—
599C4⋊C8—1061no—
600C4⋊C8—1061no—
601C4⋊C8—1061no—
602C4⋊C8—1061no—
603C4⋊C8—1061no—
604C22⋊C8—1061no—
605C22⋊C8—1061no—
606C22⋊C8—1061no—
607C22⋊C8—1061no—
608C22⋊C8—1061no—
609C22⋊C8—1061no—
610C22⋊C8—1061no—
611#97—531no—
612#97—531no—
613#97—531no—
614#97—531no—
615#97—531no—
616#97—531no—
617#97—531no—
618#97—531no—
619#97—1061no—
620#97—1061no—
621#97—1061no—
622C4×C8—1061no—
623C4×C8—1061no—
624#41—42no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8C22⋊Dic5311yescharacteristic
629C2×Q8C22×Dic5311yescharacteristic
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4C22⋊Dic5311yescharacteristic
634C2×D4C22⋊Dic5311yescharacteristic
635C2×D4C22⋊Dic5311yescharacteristic
636C2×D4C22×Dic5311yescharacteristic
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4C22×Dic5311yescharacteristic
645C22×C4C22×Dic5311yescharacteristic
646C22×C4C22×Dic5311yescharacteristic
647C22×C4C2×C22⋊D5311yescharacteristic
648C22×C4C2×C22⋊D5311yescharacteristic
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653M16—2122no—
654M16—2122no—
655C2×C8—1061no—
656C2×C8—1061no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—1061no—
660C2×C8—1061no—
661C2×C8—1061no—
662C2×C8—1061no—
663C2×C8—2122no—
664C2×C8—2122no—
665C2×C8—2122no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4C22⋊Dic5311yescharacteristic
693C4⋊C4C22⋊Dic5311yescharacteristic
694C4⋊C4C22⋊Dic5311yescharacteristic
695C4⋊C4C22⋊Dic5311yescharacteristic
696C4⋊C4C22⋊Dic5311yescharacteristic
697C4⋊C4C22⋊Dic5311yescharacteristic
698C4⋊C4C22×Dic5311yescharacteristic
699C4⋊C4C22×Dic5311yescharacteristic
700C4⋊C4C22×Dic5311yescharacteristic
701C4⋊C4C22×Dic5311yescharacteristic
702C4⋊C4C22×Dic5311yescharacteristic
703C4⋊C4C22×Dic5311yescharacteristic
704C22⋊C4—21no—
705C22⋊C4—21no—
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⋊C4C22⋊Dic5311yescharacteristic
718C22⋊C4C22⋊Dic5311yescharacteristic
719C22⋊C4C22⋊Dic5311yescharacteristic
720C22⋊C4C22⋊Dic5311yescharacteristic
721C22⋊C4C22⋊Dic5311yescharacteristic
722C22⋊C4C22⋊Dic5311yescharacteristic
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42C22×Dic5311yescharacteristic
729C42C22×Dic5311yescharacteristic
730C42C22×Dic5311yescharacteristic
731C42C2×C22⋊D5311yescharacteristic
732C42C2×C22⋊D5311yescharacteristic
733C42C2×C22⋊D5311yescharacteristic
734C42C2×C22⋊D5311yescharacteristic
735C42C2×C22⋊D5311yescharacteristic
736C42C2×C22⋊D5311yescharacteristic
737C42C23×D5311yescharacteristic
738C23—21no—
739C23C2×C22⋊Dic5311yescharacteristic
740C23C2×C22⋊Dic5311yescharacteristic
741C23C2×C22⋊Dic5311yescharacteristic
742Q8—41no—
743Q8—41no—
744Q8—42no—
745Q8—81no—
746D4—22no—
747D4—22no—
748D4—41no—
749D4—41no—
750D4—42no—
751D4—42no—
752D4—81no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4C2×C22⋊Dic5311yescharacteristic
777C2×C4C2×C22⋊Dic5311yescharacteristic
778C2×C4C2×C22⋊Dic5311yescharacteristic
779C2×C4C2×C22⋊Dic5311yescharacteristic
780C2×C4C2×C22⋊Dic5311yescharacteristic
781C2×C4C2×C22⋊Dic5311yescharacteristic
782C2×C4C2×C22⋊Dic5311yescharacteristic
783C2×C4C2×C22⋊Dic5311yescharacteristic
784C2×C4C2×C22⋊Dic5311yescharacteristic
785C2×C4C23×Dic5311yescharacteristic
786C2×C4C22×C22⋊D5311yescharacteristic
787C2×C4C22×C22⋊D5311yescharacteristic
788C8—1062no—
789C8—2121no—
790C8—2121no—
791C8—2121no—
792C8—2121no—
793C8—2121no—
794C8—2121no—
795C8—2121no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22#1681064012yes—
808C22C22×C22⋊Dic5311yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C2—22no—
829C2—41no—
830C2—41no—
831C2—81no—
832C2#2028319811yescharacteristic
833C2C2×#1681064011yescharacteristic
834C2#2028326211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
Fitting, prime radicalC53×#3515C2
socleC22×C53C22×C22⋊C4
cosocleC42×C53C24
hypercenter#3515D53
hypocenterC53#17680
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3515

Complements

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

NH ≅ G/Ntype
1. #20283729C2semidirect
2. #20283366C2semidirect
3. #20273353C2semidirect
4. #20273346C2semidirect
5. #20273346C2semidirect
6. #20273342C2semidirect
7. #20273335C2semidirect
8. #20273335C2semidirect
9. #20273330C2semidirect
10. #20273322C2semidirect
11. #20273317C2semidirect
12. #20273317C2semidirect
13. #20273303C2semidirect
14. C2×#16810365C2semidirect
492. C53#17680semidirect

Maximal subgroups

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

subgroupindex
#202837292
#202833662
#202733532
#202733462
#202733422
#202733352
#202733302
#202733222
#202733172
#202733032
C2×#168103652
C53×#35152
#1768053