Finite Group Databasebeta

← #14775234

Subgroups — #14775234

Order 2816.

958 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#13071636C211yesmaximal, characteristic
2#13071485C211yesmaximal, characteristic, complemented
3#13069355C211yesmaximal, characteristic, complemented
4#13069315C211yesmaximal, characteristic, complemented
5#13069245C211yesmaximal, characteristic, complemented
6#13069210C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic
9#13068879C211yesmaximal, characteristic, complemented
10#13068811C211yesmaximal, characteristic, complemented
11#13068515C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#13068395C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C2×C11×#480C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×D4×Dic11—21no—
19C2×D4×Dic11C2211yescharacteristic
20C2×#66979—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#480C418yescomplemented
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622833—21no—
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34#10622824—21no—
35C4×C22⋊Dic11C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622598C2211yescharacteristic
43#10622594—21no—
44#10622594—21no—
45C4⋊C4×Dic11C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48#10622564—21no—
49#10622563—21no—
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#121—22no—
69C11×#121C2×C414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4C2×C414yescomplemented
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83D4×Dic11—22no—
84D4×Dic11—41no—
85D4×Dic11—44no—
86#66979—44no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—41no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C11×#107C2×C414yescomplemented
108C11×#107C2×C414yescomplemented
109C11×#102C2×C414yescomplemented
110C11×#102C2×C414yescomplemented
111C11×C22⋊C8C2×C414yescomplemented
112#66896—22no—
113#66896—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66881—22no—
124#66881—41no—
125#66879—22no—
126#66879—41no—
127#22938—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11C22×C412yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C22×C412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—81no—
162C22×Dic11—81no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C412yes—
172C2×C8×C11C22×C412yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C22×C412yes—
178C11×C4⋊C4C22×C412yes—
179C11×C4⋊C4C22×C412yes—
180C11×C22⋊C4—24no—
181C22⋊Dic11—22no—
182C22⋊Dic11—22no—
183C22⋊Dic11—42no—
184C22⋊Dic11—42no—
185C22⋊Dic11—42no—
186C22⋊Dic11—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11#4112yes—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—44no—
212C2×C11⋊C8#4112yes—
213C2×#480D1111yescharacteristic
214#2361—111no—
215#2344—111no—
216#1943—111no—
217#1936—111no—
218#1926—111no—
219#1921—111no—
220#1921—111no—
221#1893—111no—
222#1864—111no—
223#1853—111no—
224#1776—111no—
225#1762—111no—
226#1752—111no—
227C2×#340—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—22no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C4×D412yes—
240C23×C11AGL(1,ℤ/8)12yes—
241C23×C11AGL(1,ℤ/8)12yes—
242C23×C11C22×D411yescharacteristic
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—48no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
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—48no—
264C2×C4×C11C4×D412yes—
265C2×C4×C11C23×C411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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—41no—
294C2×Dic11—41no—
295C2×Dic11—84no—
296C2×Dic11—84no—
297C8×C11—22no—
298C8×C11—22no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C23×C8—111no—
302C2×#121C2×D1111yescharacteristic
303C2×C4×D4—111no—
304C2×C4×D4—221no—
305C2×#117—221no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4C2×D1111yescharacteristic
308#480Dic1118yescomplemented
309C2×#107C2×D1111yescharacteristic
310C2×#107C2×D1111yescharacteristic
311C2×#106—111no—
312C2×#106—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102C2×D1111yescharacteristic
316C2×#102C2×D1111yescharacteristic
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97—111no—
319C2×#97—111no—
320#390—111no—
321#389—111no—
322#389—111no—
323#389—111no—
324#388—221no—
325#387—221no—
326#387—221no—
327#386—221no—
328#385—221no—
329#381—221no—
330#380—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—111no—
333C4×C4⋊C4—111no—
334C4×C22⋊C4—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#336—111no—
344#336—111no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11#44214yes—
359C22×C11C2×C4×D411yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11#54711yescharacteristic
362C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57811yescharacteristic
366C4×C11—22no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11C4×#4111yescharacteristic
371C4×C11#52011yescharacteristic
372C4×C11#55111yescharacteristic
373C4×C11#55211yescharacteristic
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382C22×D4—21no—
383C22×D4C22×D1111yescharacteristic
384C23×C4—21no—
385C23×C4—221no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—222no—
391C22×C8—222no—
392C22×C8—441no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#121—22no—
396#121C2×Dic1114yes—
397C4×D4—222no—
398C4×D4—441no—
399C4×D4—444no—
400#117—444no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—441no—
413C2×C4⋊C4C2×Dic1114yescomplemented
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429#107C2×Dic1114yescomplemented
430#107C2×Dic1114yescomplemented
431#106—222no—
432#106—441no—
433#102—222no—
434#102—441no—
435#102C2×Dic1114yescomplemented
436#102C2×Dic1114yescomplemented
437C22⋊C8C2×Dic1114yescomplemented
438#97—222no—
439#97—441no—
440#95—111no—
441#95—111no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449C2×C11—24no—
450C2×C11—82no—
451C2×C11#235911yescharacteristic
452C2×C11C2×#44211yescharacteristic
453C2×C11#294711yescharacteristic
454C2×C11#330811yescharacteristic
455C2×C11#331011yescharacteristic
456C2×C11#334311yescharacteristic
457C2×C11#334511yescharacteristic
458C24—21no—
459C24D4×D1111yescharacteristic
460C2×D4—24no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4C22×Dic1112yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4—881no—
493C22×C4D4×D1111yescharacteristic
494C22×C4#434112yes—
495C22×C4C22×Dic1112yes—
496C22×C4C23×D1111yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—112no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—444no—
508C2×C8C22×Dic1112yes—
509C2×C8C22×Dic1112yes—
510C4⋊C4—24no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—112no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4C22×Dic1112yes—
527C4⋊C4C22×Dic1112yes—
528C4⋊C4C22×Dic1112yes—
529C22⋊C4—24no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—881no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—221no—
540C42—442no—
541C42—442no—
542C42—442no—
543C11#2293811yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23#6696412yes—
556C23#6696412yes—
557C23D4×Dic1112yes—
558C23C2×D4×D1111yescharacteristic
559D4—22no—
560D4—22no—
561D4—48no—
562D4—41no—
563D4—41no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—48no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—221no—
592C2×C4—221no—
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—884no—
605C2×C4—884no—
606C2×C4D4×Dic1112yes—
607C2×C4C2×#434111yescharacteristic
608C2×C4#41×D1111yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704211yescharacteristic
611C2×C4#6704311yescharacteristic
612C2×C4C23×Dic1111yescharacteristic
613C8—22no—
614C8—22no—
615C8—222no—
616C8—441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22#1062276514yes—
631C22#1062318511yescharacteristic
632C22#1062318611yescharacteristic
633C22C2×#6696411yescharacteristic
634C22C2×#6696411yescharacteristic
635C22#1062330911yescharacteristic
636C22#1062331011yescharacteristic
637C22C2×D4×Dic1111yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—441no—
643C4—441no—
644C4—441no—
645C4—442no—
646C4—441no—
647C4—881no—
648C4—881no—
649C4—881no—
650C4#1062318111yescharacteristic
651C4#1062318911yescharacteristic
652C4#41×Dic1111yescharacteristic
653C4#1062335811yescharacteristic
654C2—24no—
655C2—82no—
656C2#1307161211yescharacteristic
657C2C2×#1062276511yescharacteristic
658C2#1307746011yescharacteristic
659C2#1308060511yescharacteristic
660C2#1308063511yescharacteristic
661C2#1308106011yescharacteristic
662C2#1308109011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#480C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC2×#480D11
hypocenterC11#22938
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. #13071485C2semidirect
3. #13069355C2semidirect
4. #13069315C2semidirect
5. #13069245C2semidirect
6. #13069210C2semidirect
7. #13069210C2semidirect
9. #13068879C2semidirect
10. #13068811C2semidirect
11. #13068515C2semidirect
12. #13068443C2semidirect
13. #13068395C2semidirect
14. C2×#10622167C2semidirect
23. C11×#480C4semidirect
72. C2×C11×C4⋊C4C2×C4semidirect
107. C11×#107C2×C4semidirect
108. C11×#107C2×C4semidirect
109. C11×#102C2×C4semidirect
110. C11×#102C2×C4semidirect
111. C11×C22⋊C8C2×C4semidirect
308. #480Dic11semidirect
413. C2×C4⋊C4C2×Dic11semidirect
429. #107C2×Dic11semidirect
430. #107C2×Dic11semidirect
435. #102C2×Dic11semidirect
436. #102C2×Dic11semidirect
437. C22⋊C8C2×Dic11semidirect
543. C11#22938semidirect

Maximal subgroups

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

subgroupindex
#130716362
#130714852
#130693552
#130693152
#130692452
#130692102
#130690452
#130688792
#130688112
#130685152
#130684432
#130683952
C2×#106221672
C2×C11×#4802
#2293811