Finite Group Databasebeta

← #14814393

Subgroups — #14814393

Order 2816.

794 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072045C211yesmaximal, characteristic
2#13071545C211yesmaximal, characteristic
3#13070185C211yesmaximal, characteristic, complemented
4#13070039C211yesmaximal, characteristic, complemented
5#13070036C211yesmaximal, characteristic, complemented
6#13069813C211yesmaximal, characteristic, complemented
7#13069258C211yesmaximal, characteristic, complemented
8#13069202C211yesmaximal, characteristic, complemented
9#13069039C211yesmaximal, characteristic, complemented
10#13068926C211yesmaximal, characteristic, complemented
11#13068921C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068707C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622835—21no—
27#10622833—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622594—21no—
38#10622585—21no—
39#10622565—21no—
40#10622564—21no—
41#10622558—21no—
42C22⋊C4×Dic11—21no—
43#10622549C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22C2311yescharacteristic
64C22×C8×C11—22no—
65C22×C8×C11—41no—
66C22×C8×C11—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66979—22no—
85#66979—22no—
86#66979—41no—
87#66979—41no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—41no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—22no—
99#66977—22no—
100#66977—22no—
101#66977—41no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C11×C22⋊C8—22no—
109C11×C22⋊C8—41no—
110C11×C22⋊C8—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66882—41no—
121#66881—22no—
122#66880—22no—
123#66880—41no—
124#66880—41no—
125#66880—41no—
126#26201—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11#4112yes—
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—44no—
179C11×C4⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C42×C11—21no—
183C42×C11—21no—
184C22⋊Dic11—42no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11#4112yes—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212#2415—111no—
213#2352—111no—
214#2101—111no—
215#2075—111no—
216#2074—111no—
217#2035—111no—
218#1928—111no—
219#1920—111no—
220#1892—111no—
221#1873—111no—
222#1872—111no—
223#1869D1111yescharacteristic
224#1854—111no—
225#1824—111no—
226#1735—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11#12312yes—
240C23×C11#13512yes—
241C23×C11C22×D411yescharacteristic
242D4×C11—44no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
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—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11#12312yes—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
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—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—84no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297Dic22—41no—
298C8×C11—41no—
299C8×C11—41no—
300C8×C11—41no—
301C8×C11—41no—
302C23×C8C2×D1111yescharacteristic
303C2×C22⋊Q8—111no—
304C2×C22⋊Q8—111no—
305C2×C4×D4C2×D1111yescharacteristic
306C2×#117—111no—
307C2×#117—111no—
308C22×C4⋊C4—111no—
309C2×#107—111no—
310C2×#106—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×C22⋊C8C2×D1111yescharacteristic
316C2×C22⋊C8C2×D1111yescharacteristic
317C2×C22⋊C8C2×D1111yescharacteristic
318#397—221no—
319#394—221no—
320#391—111no—
321#389—111no—
322#389—221no—
323#388—221no—
324#388—221no—
325#387—221no—
326#386—221no—
327#382—111no—
328#380—111no—
329#380—111no—
330#380—111no—
331C4×C4⋊C4—111no—
332C4×C22⋊C4—221no—
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#340—111no—
342#340—111no—
343#336C2×D1111yescharacteristic
344#336C2×D1111yescharacteristic
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11C2×#12311yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11#54611yescharacteristic
362C22×C11C2×#13511yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57811yescharacteristic
366C4×C11—22no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11#52911yescharacteristic
371C4×C11#53811yescharacteristic
372C4×C11#55311yescharacteristic
373C4×C11#55311yescharacteristic
374Dic11—42no—
375Dic11—42no—
376Dic11—81no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382C22×Q8—111no—
383C22×D4D4411yescharacteristic
384C23×C4—221no—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C22×C8—22no—
388C22×C8—41no—
389C22×C8—41no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394C22⋊Q8—222no—
395C22⋊Q8—222no—
396C22⋊Q8—222no—
397C22⋊Q8—441no—
398C4×D4—22no—
399C4×D4—22no—
400#117—222no—
401#117—222no—
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—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—441no—
417C2×C4⋊C4D4411yescharacteristic
418C2×C22⋊C4—221no—
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⋊C4D4411yescharacteristic
426C2×C22⋊C4D4411yescharacteristic
427C2×C42—221no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42C22×D1111yescharacteristic
431#107—441no—
432#106—222no—
433#103—222no—
434#103—441no—
435#103—441no—
436#103—441no—
437C22⋊C8—22no—
438C22⋊C8—41no—
439C22⋊C8—41no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449C2×C11—42no—
450C2×C11—42no—
451C2×C11#244411yescharacteristic
452C2×C11#309111yescharacteristic
453C2×C11#309711yescharacteristic
454C2×C11#330011yescharacteristic
455C2×C11#330111yescharacteristic
456C2×C11#331111yescharacteristic
457C2×C11#331511yescharacteristic
458C24C2×D4411yescharacteristic
459C24C2×D4411yescharacteristic
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—41no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
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—442no—
488C22×C4—442no—
489C22×C4—881no—
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4#434112yes—
495C22×C4#434112yes—
496C22×C4C23×D1111yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—44no—
510C4⋊C4—22no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—881no—
538C42—21no—
539C42—21no—
540C42—442no—
541C42—442no—
542C42—881no—
543C11#2620111yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23#6693912yes—
557C23#6695712yes—
558C23C22×D4411yescharacteristic
559Q8—441no—
560Q8—441no—
561Q8—441no—
562Q8—441no—
563D4—44no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
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—441no—
607C2×C4—884no—
608C2×C4#6693912yes—
609C2×C4C2×#434111yescharacteristic
610C2×C4C2×#434111yescharacteristic
611C2×C4#6703711yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C8—41no—
616C8—41no—
617C8—41no—
618C8—41no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22C2×#6693911yescharacteristic
634C22#1062308511yescharacteristic
635C22#1062308511yescharacteristic
636C22C2×#6695711yescharacteristic
637C22#1062327911yescharacteristic
638C22#1062328211yescharacteristic
639C22#1062328411yescharacteristic
640C4—22no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—442no—
645C4—442no—
646C4—881no—
647C4—881no—
648C4—881no—
649C4—881no—
650C4—881no—
651C4—881no—
652C4#1062312411yescharacteristic
653C4#1062313211yescharacteristic
654C4#1062313211yescharacteristic
655C4#1062318011yescharacteristic
656C2—42no—
657C2—42no—
658C2#1307236411yescharacteristic
659C2#1307853111yescharacteristic
660C2#1307858611yescharacteristic
661C2#1308050511yescharacteristic
662C2#1308052011yescharacteristic
663C2#1308065411yescharacteristic
664C2#1308071411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1869C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1869D11
hypocenterC11#26201
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
3. #13070185C2semidirect
4. #13070039C2semidirect
5. #13070036C2semidirect
6. #13069813C2semidirect
7. #13069258C2semidirect
8. #13069202C2semidirect
9. #13069039C2semidirect
10. #13068926C2semidirect
11. #13068921C2semidirect
12. #13068817C2semidirect
13. #13068707C2semidirect
14. #13068333C2semidirect
543. C11#26201semidirect

Maximal subgroups

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

subgroupindex
#130720452
#130715452
#130701852
#130700392
#130700362
#130698132
#130692582
#130692022
#130690392
#130689262
#130689212
#130688172
#130687072
#130683332
C11×#18692
#2620111