Finite Group Databasebeta

← #14775232

Subgroups — #14775232

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
1C2×#10622349C211yesmaximal, characteristic
2#13071630C211yesmaximal, characteristic
3#13071483C211yesmaximal, characteristic, complemented
4#13069354C211yesmaximal, characteristic, complemented
5#13069313C211yesmaximal, characteristic, complemented
6#13069244C211yesmaximal, characteristic, complemented
7#13069209C211yesmaximal, characteristic, complemented
8#13069209C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068880C211yesmaximal, characteristic, complemented
11#13068811C211yesmaximal, characteristic, complemented
12#13068513C211yesmaximal, characteristic, complemented
13#13068442C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C11×#1752C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×(C22⋊D11)⋊C4—21no—
21C2×#66930—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622571—21no—
37#10622556—21no—
38#10622552C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622349C418yescomplemented
46#10622283—21no—
47#10622281—21no—
48#10622266—21no—
49#10622266—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78#66983—22no—
79#66983C2×C414yes—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11C2×C414yescomplemented
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103(C22⋊D11)⋊C4—44no—
104#66930—44no—
105C4×D44—22no—
106C4×D44—41no—
107C11×C22⋊C8C2×C414yescomplemented
108C11×#97—22no—
109C11×#97—41no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66885—22no—
120#66885—41no—
121#66885C2×C414yescomplemented
122#66885C2×C414yescomplemented
123#66882C2×C414yescomplemented
124#66882C2×C414yescomplemented
125#66881—22no—
126#66881—41no—
127#22938—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—42no—
145C22×Dic11—24no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—81no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C412yes—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—81no—
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—44no—
177C2×C8×C11C22×C412yes—
178C2×C8×C11C22×C412yes—
179C2×C8×C11#4112yes—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C22⋊Dic11—42no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—81no—
191C4⋊Dic11—24no—
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—42no—
203C4⋊Dic11C22×C412yes—
204C4⋊Dic11C22×C412yes—
205C4⋊Dic11C22×C412yes—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C2×#480—111no—
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#1752D1111yescharacteristic, complemented
227C2×#340—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11C4×D412yes—
233C23×C11AGL(1,ℤ/8)12yes—
234C23×C11AGL(1,ℤ/8)12yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
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—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11C4×D412yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C22⋊D11—48no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
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—48no—
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—84no—
292D44—22no—
293D44—22no—
294D44—41no—
295D44—41no—
296C4×D11—84no—
297C8×C11—22no—
298C8×C11—22no—
299C8×C11—22no—
300C8×C11—41no—
301C23×C8C2×D1111yescharacteristic
302C2×#121—111no—
303C2×C4×D4—111no—
304C2×C4×D4—221no—
305C2×#117—221no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308#480—118no—
309C2×#107—111no—
310C2×#107—111no—
311C2×#106—111no—
312C2×#106—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97C2×D1111yescharacteristic
319C2×#97C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
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#44214yes—
352C22×C11C2×C4×D411yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54711yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57811yescharacteristic
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C4×C11—22no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11C4×#4111yescharacteristic
372C4×C11#52011yescharacteristic
373C4×C11#55111yescharacteristic
374C4×C11#55211yescharacteristic
375Dic11—42no—
376Dic11—42no—
377Dic11—42no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382C22×D4—111no—
383C22×D4—221no—
384C23×C4—221no—
385C23×C4—221no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—41no—
391C22×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#121—114no—
396#121—222no—
397C4×D4—222no—
398C4×D4—441no—
399C4×D4—444no—
400#117—444no—
401C2×C4⋊C4—114no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—221no—
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×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4D4411yescharacteristic
423C2×C22⋊C4D4411yescharacteristic
424C2×C42—221no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429#107—114no—
430#107—114no—
431#106—222no—
432#106—441no—
433#102—114no—
434#102—114no—
435#102—222no—
436#102—441no—
437C22⋊C8C4×D1114yescomplemented
438#97—22no—
439#97—41no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95D4411yescharacteristic
448#95D4411yescharacteristic
449C2×C11—24no—
450C2×C11#235911yescharacteristic
451C2×C11C2×#44211yescharacteristic
452C2×C11#294711yescharacteristic
453C2×C11#330811yescharacteristic
454C2×C11#331011yescharacteristic
455C2×C11#334311yescharacteristic
456C2×C11#334511yescharacteristic
457D11—82no—
458C24—221no—
459C24C2×D4411yescharacteristic
460C2×D4—112no—
461C2×D4—224no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—442no—
468C2×D4—442no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—224no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—881no—
488C22×C4—881no—
489C22×C4C2×C4×D1112yes—
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C2×D4411yescharacteristic
493C22×C4C2×D4411yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4#433912yes—
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—44no—
507C2×C8C2×C4×D1112yes—
508C2×C8C2×C4×D1112yes—
509C2×C8#434112yes—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—112no—
513C4⋊C4—112no—
514C4⋊C4—224no—
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—224no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—881no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—442no—
541C42—442no—
542C42—442no—
543C11#2293811yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—222no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23C4×D4412yes—
556C23#6696112yes—
557C23#6696112yes—
558C23C22×D4411yescharacteristic
559D4—222no—
560D4—222no—
561D4—448no—
562D4—441no—
563D4—441no—
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—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
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—448no—
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×C4C4×D4412yes—
607C2×C4C22×C4×D1111yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—22no—
614C8—22no—
615C8—22no—
616C8—41no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—442no—
624C22—442no—
625C22—442no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22—881no—
630C22#1062232414yes—
631C22C2×C4×D4411yescharacteristic
632C22#1062308511yescharacteristic
633C22#1062308611yescharacteristic
634C22C2×#6696111yescharacteristic
635C22C2×#6696111yescharacteristic
636C22#1062328211yescharacteristic
637C22#1062328411yescharacteristic
638C4—22no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—41no—
643C4—442no—
644C4—442no—
645C4—442no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4—881no—
650C4#1062302611yescharacteristic
651C4#1062306211yescharacteristic
652C4C4×#434111yescharacteristic
653C4#1062307711yescharacteristic
654C2—24no—
655C2—882no—
656C2#1307161011yescharacteristic
657C2C2×#1062232411yescharacteristic
658C2#1307746111yescharacteristic
659C2#1308060911yescharacteristic
660C2#1308063911yescharacteristic
661C2#1308105811yescharacteristic
662C2#1308108811yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22938
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
3. #13071483C2semidirect
4. #13069354C2semidirect
5. #13069313C2semidirect
6. #13069244C2semidirect
7. #13069209C2semidirect
8. #13069209C2semidirect
10. #13068880C2semidirect
11. #13068811C2semidirect
12. #13068513C2semidirect
13. #13068442C2semidirect
14. C2×#10622189C2semidirect
15. C11×#1752C2semidirect
45. #10622349C4semidirect
89. C2×C4⋊Dic11C2×C4semidirect
107. C11×C22⋊C8C2×C4semidirect
121. #66885C2×C4semidirect
122. #66885C2×C4semidirect
123. #66882C2×C4semidirect
124. #66882C2×C4semidirect
226. #1752D11semidirect
437. C22⋊C8C4×D11semidirect
543. C11#22938semidirect

Maximal subgroups

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

subgroupindex
C2×#106223492
#130716302
#130714832
#130693542
#130693132
#130692442
#130692092
#130690442
#130688802
#130688112
#130685132
#130684422
C2×#106221892
C11×#17522
#2293811