Finite Group Databasebeta

← #14823133

Subgroups — #14823133

Order 2816.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622609C211yesmaximal, characteristic
2C2×#10622635C211yesmaximal, characteristic, complemented
3#13072957C211yesmaximal, characteristic
4#13070008C211yesmaximal, characteristic, complemented
5#13069954C211yesmaximal, characteristic, complemented
6#13069816C211yesmaximal, characteristic
7#13069624C211yesmaximal, characteristic
8#13069486C211yesmaximal, characteristic, complemented
9#13069257C211yesmaximal, characteristic, complemented
10#13069254C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic, complemented
13#13068815C211yesmaximal, characteristic
14#13068514C211yesmaximal, characteristic, complemented
15C11×#2362C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#388—21no—
26C11×#387—21no—
27C4×C11×C4⋊C4—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622635—24no—
37#10622609—24no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622565—21no—
47#10622557—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53#10622271—21no—
54#10622263—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×#4326—22no—
88C2×#4326—22no—
89C2×#4326—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93#66977—22no—
94#66977—41no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66923—22no—
104#66923—41no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111#66899—22no—
112#66899—22no—
113#66899—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122#66874—22no—
123#66874—22no—
124#66874—22no—
125#66872—41no—
126#66872D414yes—
127#66871—22no—
128#66871—22no—
129#66871—22no—
130C4⋊(C11⋊C8)—22no—
131#66867—22no—
132#26809—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4C2×D412yes—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—42no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C42×C11—42no—
185C42×C11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188#4326—44no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2×D412yes—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C2×D412yes—
210C2×C11⋊C8#4112yes—
211C2×#485—111no—
212C2×#479—111no—
213#2489—111no—
214#2362D1111yescharacteristic
215#2068—111no—
216#2059—111no—
217#2036—111no—
218#2001—111no—
219#1971—111no—
220#1928—111no—
221#1928—111no—
222#1924—111no—
223#1878—111no—
224#1854—111no—
225#1776—111no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11C22×D411yescharacteristic
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—41no—
237Q8×C11—41no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291C11⋊C8—22no—
292C11⋊C8—22no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C22×Q16—111no—
296C2×#125—111no—
297C2×C22⋊Q8—111no—
298C2×C22⋊Q8C2×D1111yescharacteristic
299C2×C4×Q8C2×D1111yescharacteristic
300C2×#117C2×D1111yescharacteristic
301#485—224no—
302#479—224no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#107—111no—
306C2×#106—111no—
307C2×#106—111no—
308C2×C4⋊C8—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×#97—111no—
318#400—221no—
319#397—221no—
320#391—111no—
321#391—111no—
322#391C2×D1111yescharacteristic
323#389C2×D1111yescharacteristic
324#388—21no—
325#388—21no—
326#388—221no—
327#387—21no—
328#382—221no—
329#380—111no—
330C4×C4⋊C4—21no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4C2×D1111yescharacteristic
333C4×C22⋊C4C2×D1111yescharacteristic
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336—111no—
339#336—111no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11#52511yescharacteristic
348C22×C11D4211yescharacteristic
349C22×C11#54711yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57511yescharacteristic
352C22×C11#57811yescharacteristic
353C22×C11#57811yescharacteristic
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—81no—
363C4×C11#53211yescharacteristic
364C4×C11#54211yescharacteristic
365C4×C11#54811yescharacteristic
366C4×C11#55111yescharacteristic
367Dic11—42no—
368Dic11—81no—
369Dic11—81no—
370Dic11—81no—
371C22×Q8—111no—
372C22×Q8C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C2×Q16—222no—
375C2×Q16—222no—
376C2×Q16—441no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—111no—
381#125—222no—
382#125—441no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—222no—
386C22⋊Q8—441no—
387C4×Q8—22no—
388C4×Q8—41no—
389#117—22no—
390#117—41no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4C22⋊D1111yescharacteristic
408C2×C22⋊C4C22⋊D1111yescharacteristic
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415#107—222no—
416#107—222no—
417#107—222no—
418#106—114no—
419#106—441no—
420C4⋊C8—222no—
421#103—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103—222no—
427C22⋊C8—222no—
428C22⋊C8—222no—
429#97—222no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95C22⋊D1111yescharacteristic
441#95C22⋊D1111yescharacteristic
442C2×C11—81no—
443C2×C11#246111yescharacteristic
444C2×C11#311111yescharacteristic
445C2×C11#312711yescharacteristic
446C2×C11#326911yescharacteristic
447C2×C11#326911yescharacteristic
448C2×C11#334911yescharacteristic
449C2×C11#335211yescharacteristic
450C24C2×C22⋊D1111yescharacteristic
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8#433912yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483Q16—444no—
484C2×C8—112no—
485C2×C8—112no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C4⋊C4—24no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—112no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4#433912yes—
513C4⋊C4D4×D1112yes—
514C22⋊C4—24no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—42no—
518C22⋊C4—442no—
519C22⋊C4—442no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—42no—
525C42—42no—
526C42—42no—
527C42—442no—
528C11#2680911yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23C22×C22⋊D1111yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—441no—
542Q8—441no—
543Q8—441no—
544Q8—441no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—222no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4C2×#433911yescharacteristic
589C2×C4C2×#433911yescharacteristic
590C2×C4C2×D4×D1111yescharacteristic
591C2×C4#6703711yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#6704311yescharacteristic
594C8—222no—
595C8—222no—
596C8—441no—
597C8—441no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1062332211yescharacteristic
606C22D4×C22⋊D1111yescharacteristic
607C22#1062335311yescharacteristic
608C22#1062335311yescharacteristic
609C22#1062335511yescharacteristic
610C22#1062336911yescharacteristic
611C22#1062336911yescharacteristic
612C4—41no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—41no—
617C4—41no—
618C4—42no—
619C4—42no—
620C4—81no—
621C4—442no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4#1062307911yescharacteristic
626C4#1062308311yescharacteristic
627C4#1062308711yescharacteristic
628C4#1062309211yescharacteristic
629C2—81no—
630C2#1307257711yescharacteristic
631C2#1307872511yescharacteristic
632C2#1307891611yescharacteristic
633C2#1308016711yescharacteristic
634C2#1308017211yescharacteristic
635C2#1308114011yescharacteristic
636C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2362C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2362D11
hypocenterC11#26809
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×#10622635C2semidirect
4. #13070008C2semidirect
5. #13069954C2semidirect
8. #13069486C2semidirect
9. #13069257C2semidirect
10. #13069254C2semidirect
12. #13068957C2semidirect
14. #13068514C2semidirect
528. C11#26809semidirect

Maximal subgroups

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

subgroupindex
C2×#106226092
C2×#106226352
#130729572
#130700082
#130699542
#130698162
#130696242
#130694862
#130692572
#130692542
#130692312
#130689572
#130688152
#130685142
C11×#23622
#2680911