Finite Group Databasebeta

← #14814492

Subgroups — #14814492

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072048C211yesmaximal, characteristic
2#13071563C211yesmaximal, characteristic
3#13070175C211yesmaximal, characteristic, complemented
4#13070045C211yesmaximal, characteristic, complemented
5#13070024C211yesmaximal, characteristic, complemented
6#13069810C211yesmaximal, characteristic, complemented
7#13069194C211yesmaximal, characteristic, complemented
8#13069036C211yesmaximal, characteristic, complemented
9#13068925C211yesmaximal, characteristic, complemented
10#13068925C211yesmaximal, characteristic, complemented
11#13068907C211yesmaximal, characteristic
12#13068812C211yesmaximal, characteristic, complemented
13#13068710C211yesmaximal, characteristic, complemented
14#13068331C211yesmaximal, characteristic, complemented
15C11×#1928C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37#10622552—21no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11—21no—
40#10622541C2211yescharacteristic
41#10622288—21no—
42#10622285—21no—
43#10622283—21no—
44#10622283—21no—
45#10622282—21no—
46#10622260—21no—
47C11×#340C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44D411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70#66999—22no—
71#66999—22no—
72#66999—22no—
73#66999—41no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×C8×D11—22no—
100C2×C8×D11—41no—
101C2×C8×D11—41no—
102#66945—22no—
103#66945—22no—
104#66945—22no—
105#66945—41no—
106#66945—41no—
107#66945—41no—
108C4×D44—22no—
109C4×D44—22no—
110C11×#107—41no—
111C11×#103—22no—
112C11×#103—41no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116#66899—41no—
117#66899—41no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122(C2×D11)⋊C8—22no—
123(C2×D11)⋊C8—41no—
124(C2×D11)⋊C8—41no—
125#66872—22no—
126#26207—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C23×D11C2×D411yescharacteristic
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—41no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11#4112yes—
162C2×C4×D11#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4#4112yes—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—81no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—22no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11—81no—
198C4⋊Dic11#4112yes—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C8×D11—44no—
212#2415—111no—
213#2354—111no—
214#2099—111no—
215#2076—111no—
216#2072—111no—
217#2035—111no—
218#1928D1111yescharacteristic, complemented
219#1919—111no—
220#1892—111no—
221#1873—111no—
222#1873—111no—
223#1869—111no—
224#1854—111no—
225#1825—111no—
226#1735—111no—
227C23×C11C22×D411yescharacteristic
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11#12312yes—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
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#13512yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
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—
287C2×Dic11#12312yes—
288D44—44no—
289C4×D11—22no—
290C4×D11—22no—
291C4×D11—22no—
292C4×D11—22no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C8×C11—41no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C23×C8—111no—
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8—111no—
304C2×C4×D4—111no—
305C2×#117—111no—
306C2×#117—111no—
307C2×#117—111no—
308C2×#107C2×D1111yescharacteristic
309C2×#106—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103C2×D1111yescharacteristic
313C2×#103C2×D1111yescharacteristic
314C2×C22⋊C8—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317#397—221no—
318#394—221no—
319#391C2×D1111yescharacteristic
320#390—221no—
321#389—111no—
322#389—221no—
323#388—221no—
324#388—221no—
325#388—221no—
326#384—111no—
327#380—111no—
328#380—111no—
329#380—111no—
330C4×C4⋊C4—221no—
331C4×C4⋊C4C2×D1111yescharacteristic
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340C2×D1111yescharacteristic
342#336—111no—
343#336C2×D1111yescharacteristic
344C22×C11C2×#12311yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57811yescharacteristic
351C2×D11—22no—
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C4×C11—22no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11#52911yescharacteristic
372C4×C11#53811yescharacteristic
373C4×C11#55311yescharacteristic
374C4×C11#55311yescharacteristic
375Dic11—22no—
376Dic11—41no—
377Dic11—42no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8C22×D1111yescharacteristic
382C22×D4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—222no—
388C22×C8—441no—
389C22×C8—441no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395C22⋊Q8—441no—
396C4×D4—222no—
397C4×D4—222no—
398#117—222no—
399#117—222no—
400#117—222no—
401#117—441no—
402#117—441no—
403#117—441no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—111no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—21no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#107—41no—
433#106—222no—
434#103—22no—
435#103—41no—
436#103—441no—
437#103—441no—
438C22⋊C8—222no—
439C22⋊C8—441no—
440C22⋊C8—441no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11#244411yescharacteristic
449C2×C11#309111yescharacteristic
450C2×C11#309711yescharacteristic
451C2×C11#330211yescharacteristic
452C2×C11#330411yescharacteristic
453C2×C11#331511yescharacteristic
454C2×C11#332111yescharacteristic
455D11—42no—
456D11—81no—
457C24—111no—
458C24—111no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—441no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—111no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4D4×D1111yescharacteristic
491C22×C4D4×D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—444no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—112no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4#433912yes—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—881no—
535C22⋊C4—881no—
536C42—21no—
537C42—21no—
538C42—42no—
539C42—442no—
540C42—442no—
541C42—442no—
542C11#2620711yescharacteristic, complemented, Sylow
543C23—112no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23—221no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23C2×D4×D1111yescharacteristic
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—41no—
562D4—444no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—112no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4#6697212yes—
607C2×C4C2×#433911yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#6704211yescharacteristic
613C8—41no—
614C8—41no—
615C8—441no—
616C8—441no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—441no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—441no—
628C22—441no—
629C22—441no—
630C22—441no—
631C22#1062308111yescharacteristic
632C22#1062314311yescharacteristic
633C22D11×#12311yescharacteristic
634C22C2×#6697211yescharacteristic
635C22#1062330111yescharacteristic
636C22#1062330411yescharacteristic
637C22#1062331011yescharacteristic
638C4—22no—
639C4—41no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—222no—
645C4—442no—
646C4—441no—
647C4—881no—
648C4—881no—
649C4—881no—
650C4#1062305911yescharacteristic
651C4#1062308911yescharacteristic
652C4#1062320911yescharacteristic
653C4#1062324011yescharacteristic
654C2—442no—
655C2—881no—
656C2#1307237311yescharacteristic
657C2#1307853211yescharacteristic
658C2#1307858211yescharacteristic
659C2#1308053611yescharacteristic
660C2#1308055711yescharacteristic
661C2#1308071711yescharacteristic
662C2#1308080911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1928C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1928D11
hypocenterC11#26207
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1928

Complements

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

NH ≅ G/Ntype
3. #13070175C2semidirect
4. #13070045C2semidirect
5. #13070024C2semidirect
6. #13069810C2semidirect
7. #13069194C2semidirect
8. #13069036C2semidirect
9. #13068925C2semidirect
10. #13068925C2semidirect
12. #13068812C2semidirect
13. #13068710C2semidirect
14. #13068331C2semidirect
15. C11×#1928C2semidirect
218. #1928D11semidirect
542. C11#26207semidirect

Maximal subgroups

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

subgroupindex
#130720482
#130715632
#130701752
#130700452
#130700242
#130698102
#130691942
#130690362
#130689252
#130689072
#130688122
#130687102
#130683312
C11×#19282
#2620711