Finite Group Databasebeta

← #14814501

Subgroups — #14814501

Order 2816.

886 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072054C211yesmaximal, characteristic
2#13071542C211yesmaximal, characteristic, complemented
3#13070046C211yesmaximal, characteristic, complemented
4#13070030C211yesmaximal, characteristic, complemented
5#13069801C211yesmaximal, characteristic, complemented
6#13069237C211yesmaximal, characteristic, complemented
7#13069205C211yesmaximal, characteristic, complemented
8#13069043C211yesmaximal, characteristic, complemented
9#13068937C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068907C211yesmaximal, characteristic, complemented
12#13068805C211yesmaximal, characteristic, complemented
13#13068710C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#2101C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66948—21no—
18C2×#66948C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#382C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32#10622607—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622552C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622285—21no—
42#10622282—21no—
43#10622279—21no—
44#10622278—21no—
45#10622278—21no—
46#10622267—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44D411yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
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)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×C8×D11—22no—
96C2×C8×D11—41no—
97C2×C8×D11—41no—
98#66948—22no—
99#66948—22no—
100#66948—22no—
101#66948—41no—
102#66948—44no—
103#66945—22no—
104#66945—41no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C4⋊C4×D11—41no—
109C4×D44—22no—
110C4×D44—22no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—22no—
119#66885—41no—
120(C2×D11)⋊C8—22no—
121(C2×D11)⋊C8—41no—
122(C2×D11)⋊C8—41no—
123#66882—41no—
124#66873—41no—
125#66873—41no—
126#66871—22no—
127#26208—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11C2×D411yescharacteristic
130C23×D11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×D44—22no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44—42no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44—81no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C4×D11—81no—
174C2×C4×D11#4112yes—
175C2×C4×D11#4112yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4#4112yes—
191C42×C11—21no—
192C42×C11—21no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203C4⋊Dic11—22no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11#4112yes—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212C4×Dic11—42no—
213C4×Dic11—81no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C8×D11—44no—
221#2416—111no—
222#2352—111no—
223#2101D1111yescharacteristic, complemented
224#2076—111no—
225#2073—111no—
226#2033—111no—
227#1925—111no—
228#1921—111no—
229#1893—111no—
230#1875—111no—
231#1874—111no—
232#1869—111no—
233#1852—111no—
234#1825—111no—
235C2×#340—111no—
236C23×C11C22×D411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11#12312yes—
256C22×D11#13512yes—
257C22×D11AGL(1,ℤ/8)12yes—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11#12312yes—
297D44—44no—
298D44—41no—
299D44—41no—
300D44—41no—
301D44—41no—
302D44—84no—
303D44—84no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—22no—
308C4×D11—41no—
309C4×D11—41no—
310C4×D11—41no—
311C4×D11—41no—
312C4×D11—84no—
313C4×D11—84no—
314C8×C11—41no—
315C8×C11—41no—
316C11⋊C8—41no—
317C11⋊C8—41no—
318C23×C8—111no—
319C2×#121—111no—
320C2×#121—111no—
321C2×#121—221no—
322C2×C4×D4—111no—
323C2×#117—111no—
324C22×C4⋊C4—111no—
325C22×C4⋊C4—111no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×C22⋊C8—111no—
333C2×C22⋊C8—111no—
334C2×C22⋊C8—111no—
335#396—221no—
336#394—221no—
337#390—111no—
338#389C2×D1111yescharacteristic
339#388—221no—
340#387—221no—
341#386—221no—
342#386—221no—
343#382C2×D1111yescharacteristic
344#380—111no—
345#380—111no—
346#380—111no—
347C4×C4⋊C4—111no—
348C4×C22⋊C4—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340C2×D1111yescharacteristic
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#340C2×D1111yescharacteristic
359#336—111no—
360#336C2×D1111yescharacteristic
361C22×C11C2×#12311yescharacteristic
362C22×C11#54611yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11C2×#13511yescharacteristic
365C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C11#57611yescharacteristic
367C22×C11#57811yescharacteristic
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11#48214yes—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—42no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11—81no—
395C4×C11#52911yescharacteristic
396C4×C11#53811yescharacteristic
397C4×C11#55311yescharacteristic
398C4×C11#55311yescharacteristic
399Dic11—22no—
400Dic11—41no—
401Dic11—42no—
402Dic11—81no—
403Dic11—81no—
404C22×D4—111no—
405C22×D4—111no—
406C22×D4—221no—
407C22×D4—221no—
408C23×C4—111no—
409C23×C4—111no—
410C23×C4—221no—
411C23×C4—221no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—222no—
415C22×C8—441no—
416C22×C8—441no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419#121—222no—
420#121—222no—
421#121—222no—
422#121—441no—
423#121—444no—
424C4×D4—222no—
425C4×D4—222no—
426#117—222no—
427#117—441no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—222no—
434C2×C4⋊C4—222no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—441no—
438C2×C4⋊C4—441no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C42—221no—
454C2×C42—221no—
455C2×C42C22×D1111yescharacteristic
456#107—222no—
457#107—441no—
458#102—222no—
459#102—441no—
460#102—441no—
461#102—441no—
462C22⋊C8—222no—
463C22⋊C8—441no—
464C22⋊C8—441no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472C2×C11#244411yescharacteristic
473C2×C11C2×#48211yescharacteristic
474C2×C11#309811yescharacteristic
475C2×C11#329711yescharacteristic
476C2×C11#330011yescharacteristic
477C2×C11#330811yescharacteristic
478C2×C11#331811yescharacteristic
479D11—24no—
480D11—81no—
481D11—161no—
482C24—111no—
483C24—111no—
484C24—221no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—222no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—442no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—442no—
498C2×D4—442no—
499C2×D4—881no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4—881no—
526C22×C4—881no—
527C22×C4D4×D1111yescharacteristic
528C22×C4D4×D1111yescharacteristic
529C22×C4C23×D1111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—444no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—112no—
552C4⋊C4—222no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4#434312yes—
561C22⋊C4—222no—
562C22⋊C4—222no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—442no—
569C22⋊C4—881no—
570C22⋊C4—881no—
571C42—21no—
572C42—21no—
573C42—442no—
574C42—881no—
575C11#2620811yescharacteristic, complemented, Sylow
576C23—112no—
577C23—112no—
578C23—112no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23C2×D4×D1111yescharacteristic
598D4—444no—
599D4—441no—
600D4—441no—
601D4—441no—
602D4—441no—
603D4—884no—
604D4—884no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—112no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—222no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—884no—
647C2×C4—884no—
648C2×C4C2×#434311yescharacteristic
649C2×C4#41×D1111yescharacteristic
650C2×C4#41×D1111yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C2×C4#6704211yescharacteristic
653C2×C4#6704211yescharacteristic
654C8—41no—
655C8—41no—
656C8—441no—
657C8—441no—
658C22—114no—
659C22—222no—
660C22—222no—
661C22—222no—
662C22—222no—
663C22—222no—
664C22—222no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22—441no—
670C22—441no—
671C22—441no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22#1062316111yescharacteristic
680C22D11×#12311yescharacteristic
681C22#1062320711yescharacteristic
682C22D11×#13511yescharacteristic
683C22#1062330011yescharacteristic
684C22D11×AGL(1,ℤ/8)11yescharacteristic
685C22#1062331011yescharacteristic
686C4—41no—
687C4—42no—
688C4—41no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—222no—
693C4—442no—
694C4—441no—
695C4—881no—
696C4—881no—
697C4#1062322211yescharacteristic
698C4#1062322611yescharacteristic
699C4#1062323511yescharacteristic
700C4#1062324011yescharacteristic
701C2—224no—
702C2—881no—
703C2—1761no—
704C2#1307236711yescharacteristic
705C2D11×#48211yescharacteristic
706C2#1307859711yescharacteristic
707C2#1308046511yescharacteristic
708C2#1308050011yescharacteristic
709C2#1308060611yescharacteristic
710C2#1308075411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2101C2
socleC23×C11C22×D4
prime radical#13072054C2
hypercenter#2101D11
hypocenterC11#26208
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
2. #13071542C2semidirect
3. #13070046C2semidirect
4. #13070030C2semidirect
5. #13069801C2semidirect
6. #13069237C2semidirect
7. #13069205C2semidirect
8. #13069043C2semidirect
9. #13068937C2semidirect
10. #13068932C2semidirect
11. #13068907C2semidirect
12. #13068805C2semidirect
13. #13068710C2semidirect
14. D11×#340C2semidirect
15. C11×#2101C2semidirect
223. #2101D11semidirect
575. C11#26208semidirect

Maximal subgroups

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

subgroupindex
#130720542
#130715422
#130700462
#130700302
#130698012
#130692372
#130692052
#130690432
#130689372
#130689322
#130689072
#130688052
#130687102
D11×#3402
C11×#21012
#2620811