Finite Group Databasebeta

← #14775194

Subgroups — #14775194

Order 2816.

930 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622647C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic, complemented
3#13069356C211yesmaximal, characteristic, complemented
4#13069316C211yesmaximal, characteristic, complemented
5#13069233C211yesmaximal, characteristic, complemented
6#13069198C211yesmaximal, characteristic, complemented
7#13069194C211yesmaximal, characteristic, complemented
8#13069045C211yesmaximal, characteristic
9#13068863C211yesmaximal, characteristic, complemented
10#13068804C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic, complemented
13#13068394C211yesmaximal, characteristic, complemented
14C2×#10622167C211yesmaximal, characteristic, complemented
15C11×#2361C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#386—21no—
26C11×#385—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622647C418yescomplemented
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622555—21no—
41C22⋊C4×Dic11—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×#66867C2211yescharacteristic
48#10622267—21no—
49#10622267—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C11×#121—22no—
67C11×#121C2×C414yes—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C4×D4×C11—44no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2×C414yescomplemented
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8—41no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#66896—22no—
111#66896—41no—
112#66896C2×C414yescomplemented
113#66896C2×C414yescomplemented
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)C2×C414yescomplemented
120#66872C2×C414yescomplemented
121#66872C2×C414yescomplemented
122#66871—22no—
123#66871—41no—
124#66867—22no—
125#66867—41no—
126#22936—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—24no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11C22×C412yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11—81no—
151C22×C4×C11C22×C412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4112yes—
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—24no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—81no—
165C22×Dic11—81no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C22×C412yes—
173C11×C4⋊C4#4112yes—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—81no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—42no—
185C22⋊Dic11—42no—
186C4⋊Dic11—24no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C412yes—
194C4⋊Dic11C22×C412yes—
195Dic11⋊C4—81no—
196Dic11⋊C4—81no—
197C4×Dic11—81no—
198C4×Dic11—81no—
199C2×C11⋊C8—21no—
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—44no—
209C2×C11⋊C8C22×C412yes—
210C2×C11⋊C8C22×C412yes—
211C2×C11⋊C8#4112yes—
212C2×#481—111no—
213#2361D1111yescharacteristic
214#2345—111no—
215#1944—111no—
216#1936—111no—
217#1925—111no—
218#1920—111no—
219#1919—111no—
220#1893—111no—
221#1862—111no—
222#1852—111no—
223#1776—111no—
224#1762—111no—
225#1752—111no—
226C2×#340—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C4×D412yes—
239C23×C11AGL(1,ℤ/8)12yes—
240C23×C11#13712yes—
241C23×C11C22×D411yescharacteristic
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—48no—
245D4×C11—41no—
246D4×C11—41no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
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—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
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—84no—
275C2×C4×C11—84no—
276C2×C4×C11C4×D412yes—
277C2×C4×C11C23×C411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C2×Dic11—22no—
284C2×Dic11—22no—
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—
296C11⋊C8—22no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C23×C8—111no—
301C2×#121C2×D1111yescharacteristic
302C2×C4×D4—21no—
303C2×C4×D4C2×D1111yescharacteristic
304C22×C4⋊C4—111no—
305C22×C4⋊C4C2×D1111yescharacteristic
306#481—118no—
307C2×#107—111no—
308C2×#107—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×C22⋊C8—111no—
316C2×#97—111no—
317C2×#97—111no—
318#390C2×D1111yescharacteristic
319#389—111no—
320#389—111no—
321#389C2×D1111yescharacteristic
322#388—21no—
323#387—221no—
324#387—221no—
325#386—21no—
326#385—21no—
327#380—111no—
328#380—221no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4C2×D1111yescharacteristic
332C4×C22⋊C4—221no—
333C4×C22⋊C4C2×D1111yescharacteristic
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11#44014yes—
358C22×C11C2×C4×D411yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11#54711yescharacteristic
361C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C11C2×#13711yescharacteristic
363C22×C11#57611yescharacteristic
364C22×C11#57711yescharacteristic
365C4×C11—22no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11C4×#4111yescharacteristic
374C4×C11#52011yescharacteristic
375C4×C11#55111yescharacteristic
376C4×C11#55211yescharacteristic
377Dic11—42no—
378Dic11—42no—
379Dic11—81no—
380Dic11—81no—
381C22×D4—21no—
382C22×D4C22×D1111yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4—221no—
386C23×C4C22×D1111yescharacteristic
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—222no—
392C22×C8—222no—
393C22×C8—441no—
394#121—22no—
395#121C4×D1114yes—
396C4×D4—22no—
397C4×D4—41no—
398C4×D4—44no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—111no—
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—221no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4C22⋊D1111yescharacteristic
421C2×C22⋊C4C22⋊D1111yescharacteristic
422C2×C42—21no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427#107—222no—
428#107—441no—
429#106—114no—
430#106—114no—
431#102—114no—
432#102—114no—
433#102—222no—
434#102—441no—
435C22⋊C8—114no—
436#97—222no—
437#97—441no—
438#95—21no—
439#95—21no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95C22⋊D1111yescharacteristic
446#95C22⋊D1111yescharacteristic
447C2×C11—24no—
448C2×C11—82no—
449C2×C11#235911yescharacteristic
450C2×C11C2×#44011yescharacteristic
451C2×C11#294611yescharacteristic
452C2×C11#331611yescharacteristic
453C2×C11#331811yescharacteristic
454C2×C11#334511yescharacteristic
455C2×C11#334611yescharacteristic
456C24—21no—
457C24C2×C22⋊D1111yescharacteristic
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4C2×C4×D1112yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—224no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—881no—
486C22×C4—881no—
487C22×C4C2×C4×D1112yes—
488C22×C4#433912yes—
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495C2×C8—112no—
496C2×C8—112no—
497C2×C8—112no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—444no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—224no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—881no—
524C4⋊C4—881no—
525C4⋊C4C2×C4×D1112yes—
526C4⋊C4#434112yes—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—24no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—81no—
533C22⋊C4—442no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—42no—
539C42—881no—
540C42—881no—
541C11#2293611yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—22no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C4×C22⋊D1112yes—
554C23#6698512yes—
555C23#6700412yes—
556C23C22×C22⋊D1111yescharacteristic
557D4—22no—
558D4—22no—
559D4—48no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
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—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—222no—
592C2×C4—222no—
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—884no—
604C2×C4C4×C22⋊D1112yes—
605C2×C4C22×C4×D1111yescharacteristic
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704311yescharacteristic
611C8—222no—
612C8—222no—
613C8—222no—
614C8—441no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22#1062263114yes—
629C22C2×C4×C22⋊D1111yescharacteristic
630C22C2×#6698511yescharacteristic
631C22#1062333711yescharacteristic
632C22C2×#6700411yescharacteristic
633C22#1062335511yescharacteristic
634C22#1062336611yescharacteristic
635C22#1062336811yescharacteristic
636C4—22no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—41no—
643C4—81no—
644C4—442no—
645C4—442no—
646C4—881no—
647C4—881no—
648C4C4×#434111yescharacteristic
649C4#1062307211yescharacteristic
650C4#1062307711yescharacteristic
651C4#1062308711yescharacteristic
652C2—24no—
653C2—82no—
654C2#1307160211yescharacteristic
655C2C2×#1062263111yescharacteristic
656C2#1307744411yescharacteristic
657C2#1308072711yescharacteristic
658C2#1308075711yescharacteristic
659C2#1308108611yescharacteristic
660C2#1308110111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2361C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#2361D11
hypocenterC11#22936
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. #13071491C2semidirect
3. #13069356C2semidirect
4. #13069316C2semidirect
5. #13069233C2semidirect
6. #13069198C2semidirect
7. #13069194C2semidirect
9. #13068863C2semidirect
10. #13068804C2semidirect
11. #13068514C2semidirect
12. #13068441C2semidirect
13. #13068394C2semidirect
14. C2×#10622167C2semidirect
35. #10622647C4semidirect
90. C2×C4⋊Dic11C2×C4semidirect
112. #66896C2×C4semidirect
113. #66896C2×C4semidirect
119. C22⋊(C11⋊C8)C2×C4semidirect
120. #66872C2×C4semidirect
121. #66872C2×C4semidirect
541. C11#22936semidirect

Maximal subgroups

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

subgroupindex
C2×#106226472
#130714912
#130693562
#130693162
#130692332
#130691982
#130691942
#130690452
#130688632
#130688042
#130685142
#130684412
#130683942
C2×#106221672
C11×#23612
#2293611