Finite Group Databasebeta

← #14775230

Subgroups — #14775230

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#13071630C211yesmaximal, characteristic
3#13069351C211yesmaximal, characteristic, complemented
4#13069312C211yesmaximal, characteristic, complemented
5#13069243C211yesmaximal, characteristic, complemented
6#13069208C211yesmaximal, characteristic, complemented
7#13069205C211yesmaximal, characteristic, complemented
8#13069042C211yesmaximal, characteristic
9#13068876C211yesmaximal, characteristic, complemented
10#13068808C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12#13068444C211yesmaximal, characteristic, complemented
13#13068394C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C11×#2344C211yesmaximal, characteristic, complemented
16C2×C11×#117—21no—
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×(C22⋊D11)⋊C4—21no—
22C2×C4×D44C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#387—21no—
26C11×#387—21no—
27C11×#381—21no—
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622580C418yescomplemented
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622571—21no—
43#10622552C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48#10622283—21no—
49#10622281—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C11×#117—44no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2×C414yescomplemented
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83#66983—22no—
84#66983C2×C414yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—41no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104(C22⋊D11)⋊C4—44no—
105C4×D44—22no—
106C4×D44—41no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114C11⋊#95—21no—
115C11⋊#95—21no—
116C22⋊(C11⋊C8)C2×C414yescomplemented
117#66873—22no—
118#66873—41no—
119#66873C2×C414yescomplemented
120#66873C2×C414yescomplemented
121#66872—22no—
122#66872—41no—
123#66871C2×C414yescomplemented
124#66871C2×C414yescomplemented
125#66867—22no—
126#66867—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×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×C11C22×C412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—24no—
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
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—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C22×C412yes—
177C11×C4⋊C4C22×C412yes—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—42no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186C42×C11—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—42no—
196C4⋊Dic11C22×C412yes—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—42no—
199C4×Dic11—42no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—44no—
210C2×C11⋊C8C22×C412yes—
211C2×C11⋊C8C22×C412yes—
212C2×C11⋊C8#4112yes—
213C2×#480—111no—
214#2361—111no—
215#2344D1111yescharacteristic, complemented
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×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—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×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—48no—
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×C11C4×D412yes—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C112−1+411yescharacteristic
281C22⋊D11—48no—
282C2×Dic11—22no—
283C2×Dic11—22no—
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—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C23×C8—111no—
302C2×#121—111no—
303C2×C4×D4—111no—
304C2×C4×D4—221no—
305C2×#117—21no—
306C22×C4⋊C4—111no—
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#389C2×D1111yescharacteristic
323#389C2×D1111yescharacteristic
324#388—221no—
325#387—21no—
326#387—21no—
327#386—221no—
328#385—221no—
329#381—21no—
330#380C2×D1111yescharacteristic
331C4×C4⋊C4—111no—
332C4×C4⋊C4C2×D1111yescharacteristic
333C4×C4⋊C4C2×D1111yescharacteristic
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#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—41no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11C4×#4111yescharacteristic
376C4×C11#52011yescharacteristic
377C4×C11#55111yescharacteristic
378C4×C11#55211yescharacteristic
379Dic11—42no—
380Dic11—42no—
381Dic11—81no—
382C22×D4—111no—
383C22×D4—221no—
384C23×C4—21no—
385C23×C4—221no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—222no—
393C22×C8—222no—
394C22×C8—441no—
395#121—114no—
396#121—222no—
397C4×D4—222no—
398C4×D4—441no—
399C4×D4—444no—
400#117—44no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—441no—
412C2×C4⋊C4C4×D1114yescomplemented
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4C22⋊D1111yescharacteristic
423C2×C22⋊C4C22⋊D1111yescharacteristic
424C2×C42—21no—
425C2×C42—21no—
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⋊C8—114no—
438#97—222no—
439#97—441no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—221no—
446#95—221no—
447#95C22⋊D1111yescharacteristic
448#95C22⋊D1111yescharacteristic
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×C22⋊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—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—881no—
488C22×C4—881no—
489C22×C4C2×C4×D1112yes—
490C22×C4#433912yes—
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497C2×C8—112no—
498C2×C8—112no—
499C2×C8—112no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—444no—
510C4⋊C4—24no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4C2×C4×D1112yes—
528C4⋊C4C2×C4×D1112yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—42no—
532C22⋊C4—224no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—881no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—42no—
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×C22⋊D1112yes—
556C23#6698512yes—
557C23#6700212yes—
558C23C22×C22⋊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—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—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—48no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—222no—
596C2×C4—222no—
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×C22⋊D1112yes—
607C2×C4C22×C4×D1111yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704211yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—222no—
614C8—222no—
615C8—222no—
616C8—441no—
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#1062262714yes—
631C22C2×C4×C22⋊D1111yescharacteristic
632C22C2×#6698511yescharacteristic
633C22C2×#6700211yescharacteristic
634C22#1062335511yescharacteristic
635C22#1062336011yescharacteristic
636C22#1062336811yescharacteristic
637C22#1062336911yescharacteristic
638C4—22no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—42no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—81no—
647C4—442no—
648C4—442no—
649C4—881no—
650C4#1062305311yescharacteristic
651C4#1062305411yescharacteristic
652C4#1062305811yescharacteristic
653C4#1062306211yescharacteristic
654C2—24no—
655C2—882no—
656C2#1307160811yescharacteristic
657C2C2×#1062262711yescharacteristic
658C2#1307745911yescharacteristic
659C2#1308060111yescharacteristic
660C2#1308063111yescharacteristic
661C2#1308105611yescharacteristic
662C2#1308108611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2344C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#2344D11
hypocenterC11#22938
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #13069351C2semidirect
4. #13069312C2semidirect
5. #13069243C2semidirect
6. #13069208C2semidirect
7. #13069205C2semidirect
9. #13068876C2semidirect
10. #13068808C2semidirect
11. #13068514C2semidirect
12. #13068444C2semidirect
13. #13068394C2semidirect
14. C2×#10622167C2semidirect
15. C11×#2344C2semidirect
33. #10622580C4semidirect
71. C2×C11×C4⋊C4C2×C4semidirect
116. C22⋊(C11⋊C8)C2×C4semidirect
119. #66873C2×C4semidirect
120. #66873C2×C4semidirect
123. #66871C2×C4semidirect
124. #66871C2×C4semidirect
215. #2344D11semidirect
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
#130716302
#130693512
#130693122
#130692432
#130692082
#130692052
#130690422
#130688762
#130688082
#130685142
#130684442
#130683942
C2×#106221672
C11×#23442
#2293811