Finite Group Databasebeta

← #14775226

Subgroups — #14775226

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×#10622580C211yesmaximal, characteristic
2#13071632C211yesmaximal, characteristic
3#13071485C211yesmaximal, characteristic, complemented
4#13069353C211yesmaximal, characteristic, complemented
5#13069314C211yesmaximal, characteristic, complemented
6#13069241C211yesmaximal, characteristic, complemented
7#13069211C211yesmaximal, characteristic, complemented
8#13069206C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068878C211yesmaximal, characteristic, complemented
11#13068809C211yesmaximal, characteristic, complemented
12#13068512C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic, complemented
15C2×C11×#340C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×#66979—21no—
22C2×#66946C2211yescharacteristic
23#10622826—21no—
24#10622825C2211yescharacteristic
25#10622824—21no—
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622603—21no—
33#10622602—21no—
34#10622601C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622594—21no—
38#10622594—21no—
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622580C418yescomplemented
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—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
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4C2×C414yescomplemented
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84#66983—22no—
85#66983C2×C414yes—
86C4×C22⋊D11—44no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91#66979—44no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66946—22no—
106#66946—41no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116C22⋊(C11⋊C8)C2×C414yescomplemented
117#66885—22no—
118#66885—41no—
119#66879—22no—
120#66879—41no—
121#66873C2×C414yescomplemented
122#66873C2×C414yescomplemented
123#66872—22no—
124#66872—41no—
125#66871C2×C414yescomplemented
126#66871C2×C414yescomplemented
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×C11—24no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—42no—
143C22×C4×C11—81no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—24no—
149C2×C22⋊D11—42no—
150C2×C22⋊D11—42no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
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—44no—
173C2×C8×C11#4112yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4C22×C412yes—
182C11×C4⋊C4C22×C412yes—
183C11×C4⋊C4#4112yes—
184C22⋊Dic11—22no—
185C22⋊Dic11—22no—
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—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11—42no—
198C4⋊Dic11C22×C412yes—
199Dic11⋊C4—42no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C22×C412yes—
212C2×C11⋊C8C22×C412yes—
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#1752—111no—
227C2×#340D1111yescharacteristic, complemented
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—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
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—48no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—84no—
263C2×C4×C11C4×D412yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C22⋊D11—48no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
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—
292D44—22no—
293D44—22no—
294D44—41no—
295D44—41no—
296C4×D11—84no—
297C8×C11—22no—
298C8×C11—41no—
299C11⋊C8—22no—
300C11⋊C8—22no—
301C23×C8C2×D1111yescharacteristic
302C2×#121—111no—
303C2×C4×D4—111no—
304C2×C4×D4—221no—
305C2×#117—221no—
306C22×C4⋊C4C2×D1111yescharacteristic
307C22×C4⋊C4C2×D1111yescharacteristic
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⋊C8—111no—
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#340C2×D1111yescharacteristic
340#340C2×D1111yescharacteristic
341#340C2×D1111yescharacteristic
342#340C2×D1111yescharacteristic
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#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—42no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11—81no—
371C4×C11C4×#4111yescharacteristic
372C4×C11#52011yescharacteristic
373C4×C11#55111yescharacteristic
374C4×C11#55211yescharacteristic
375Dic11—41no—
376Dic11—41no—
377Dic11—42no—
378Dic11—41no—
379Dic11—41no—
380Dic11—81no—
381Dic11—81no—
382C22×D4—111no—
383C22×D4—221no—
384C23×C4—21no—
385C23×C4—21no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C22×C8—22no—
389C22×C8—22no—
390C22×C8—41no—
391C22×C8—111no—
392C22×C8—111no—
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—21no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—41no—
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⋊C4C4×D1114yescomplemented
413C2×C4⋊C4C22×D1111yescharacteristic
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×C42—111no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
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⋊C8—114no—
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#235911yescharacteristic
451C2×C11C2×#44211yescharacteristic
452C2×C11#294711yescharacteristic
453C2×C11#330811yescharacteristic
454C2×C11#331011yescharacteristic
455C2×C11#334311yescharacteristic
456C2×C11#334511yescharacteristic
457D11—82no—
458C24—221no—
459C24D4×D1111yescharacteristic
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—24no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—881no—
493C22×C4C2×C4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4#434112yes—
496C22×C4C23×D1111yescharacteristic
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—44no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8#433912yes—
510C4⋊C4—24no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—112no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4C2×C4×D1112yes—
527C4⋊C4C2×C4×D1112yes—
528C4⋊C4#433912yes—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—224no—
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—222no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23(C22⋊D11)⋊C412yes—
556C23#6696412yes—
557C23#6696712yes—
558C23C2×D4×D1111yescharacteristic
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—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—48no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—84no—
584C2×C4—222no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
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—884no—
606C2×C4(C22⋊D11)⋊C412yes—
607C2×C4C22×C4×D1111yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×#433911yescharacteristic
610C2×C4C2×#434111yescharacteristic
611C2×C4#6703711yescharacteristic
612C2×C4#6704011yescharacteristic
613C8—22no—
614C8—41no—
615C8—222no—
616C8—222no—
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#1062239814yes—
631C22C2×(C22⋊D11)⋊C411yescharacteristic
632C22#1062302111yescharacteristic
633C22#1062303811yescharacteristic
634C22C2×#6696411yescharacteristic
635C22C2×#6696711yescharacteristic
636C22#1062329311yescharacteristic
637C22#1062329711yescharacteristic
638C4—22no—
639C4—42no—
640C4—42no—
641C4—42no—
642C4—81no—
643C4—441no—
644C4—441no—
645C4—442no—
646C4—441no—
647C4—441no—
648C4—881no—
649C4—881no—
650C4C4×#433911yescharacteristic
651C4#1062302611yescharacteristic
652C4#1062303511yescharacteristic
653C4#1062304411yescharacteristic
654C2—24no—
655C2—882no—
656C2#1307160411yescharacteristic
657C2C2×#1062239811yescharacteristic
658C2#1307745311yescharacteristic
659C2#1308060311yescharacteristic
660C2#1308063311yescharacteristic
661C2#1308105211yescharacteristic
662C2#1308108211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11#22938
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #13071485C2semidirect
4. #13069353C2semidirect
5. #13069314C2semidirect
6. #13069241C2semidirect
7. #13069211C2semidirect
8. #13069206C2semidirect
10. #13068878C2semidirect
11. #13068809C2semidirect
12. #13068512C2semidirect
13. #13068440C2semidirect
14. #13068392C2semidirect
15. C2×C11×#340C2semidirect
43. #10622580C4semidirect
76. C2×C11×C4⋊C4C2×C4semidirect
116. C22⋊(C11⋊C8)C2×C4semidirect
121. #66873C2×C4semidirect
122. #66873C2×C4semidirect
125. #66871C2×C4semidirect
126. #66871C2×C4semidirect
227. C2×#340D11semidirect
412. C2×C4⋊C4C4×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×#106225802
#130716322
#130714852
#130693532
#130693142
#130692412
#130692112
#130692062
#130690442
#130688782
#130688092
#130685122
#130684402
#130683922
C2×C11×#3402
#2293811