Finite Group Databasebeta

← #14823149

Subgroups — #14823149

Order 2816.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622658C211yesmaximal, characteristic
2C2×#10622407C211yesmaximal, characteristic, complemented
3#13072992C211yesmaximal, characteristic
4#13071647C211yesmaximal, characteristic
5#13069993C211yesmaximal, characteristic, complemented
6#13069948C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic
8#13069488C211yesmaximal, characteristic, complemented
9#13069259C211yesmaximal, characteristic, complemented
10#13069253C211yesmaximal, characteristic, complemented
11#13069226C211yesmaximal, characteristic
12#13068959C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic
14#13068512C211yesmaximal, characteristic, complemented
15C11×#2001C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622825C2211yescharacteristic
33C4×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622658—24no—
40#10622598C2211yescharacteristic
41#10622595—21no—
42#10622594—21no—
43C4⋊C4×Dic11—21no—
44C4⋊C4×Dic11C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46#10622587—21no—
47C2×#66872C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622564—21no—
51#10622564—21no—
52#10622560—21no—
53#10622558—21no—
54#10622407—24no—
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—41no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84Q8×Dic11—22no—
85Q8×Dic11—41no—
86#66979—22no—
87#66979—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66941—22no—
104#66941—41no—
105C11×#103—22no—
106C11×#103—22no—
107C11×C22⋊C8—22no—
108#66899—22no—
109#66899—22no—
110#66899—22no—
111#66899—22no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124C22⋊(C11⋊C8)—22no—
125#66882—22no—
126#66881—41no—
127#66879—22no—
128Dic11⋊C8—22no—
129#66872—22no—
130#66872—22no—
131#66871D414yes—
132#26810—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22—81no—
169C11×Q16—44no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11#4112yes—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C2×D412yes—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—42no—
184C22⋊Dic11—22no—
185C22⋊Dic11—41no—
186C22⋊Dic11—42no—
187C22⋊Dic11—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11C2×D412yes—
198Dic11⋊C4—42no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213C2×#485—111no—
214C2×#477—111no—
215#2492—111no—
216#2362—111no—
217#2066—111no—
218#2058—111no—
219#2035—111no—
220#2001D1111yescharacteristic
221#1971—111no—
222#1928—111no—
223#1927—111no—
224#1924—111no—
225#1878—111no—
226#1854—111no—
227#1776—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
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—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
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—41no—
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—41no—
292C2×Dic11#13712yes—
293Dic22—84no—
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16C2×D1111yescharacteristic
299C2×C4⋊Q8—111no—
300C2×C22⋊Q8C2×D1111yescharacteristic
301C2×C22⋊Q8C2×D1111yescharacteristic
302C2×C4×Q8—111no—
303C2×#117—111no—
304#485—224no—
305#477—224no—
306C2×#107—111no—
307C2×#107—111no—
308C2×#106—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103C2×D1111yescharacteristic
317C2×#103C2×D1111yescharacteristic
318C2×C22⋊C8—111no—
319C2×C22⋊C8C2×D1111yescharacteristic
320C2×#97—111no—
321#400—221no—
322#393—221no—
323#391—111no—
324#391—111no—
325#391—111no—
326#391—221no—
327#389—111no—
328#388—221no—
329#388—221no—
330#388—221no—
331#387—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—221no—
336C4×C22⋊C4—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340C2×D1111yescharacteristic
341#336—111no—
342#336—111no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11#52511yescharacteristic
351C22×C11D4211yescharacteristic
352C22×C11#54711yescharacteristic
353C22×C11C2×#13711yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57711yescharacteristic
356C22×C11#57811yescharacteristic
357C4×C11—42no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11#53211yescharacteristic
363C4×C11#54211yescharacteristic
364C4×C11#54811yescharacteristic
365C4×C11#55111yescharacteristic
366Dic11—22no—
367Dic11—41no—
368Dic11—41no—
369Dic11—41no—
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—221no—
375C22×Q8C22×D1111yescharacteristic
376C22×Q8C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C2×Q16—22no—
379C2×Q16—22no—
380C2×Q16—41no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C4⋊Q8—222no—
386C4⋊Q8—441no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—41no—
391C4×Q8—222no—
392C4×Q8—441no—
393#117—222no—
394#117—441no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—221no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418#107—114no—
419#107—222no—
420#106—222no—
421#106—222no—
422#106—441no—
423C4⋊C8—222no—
424#103—22no—
425#103—22no—
426#103—222no—
427#103—222no—
428#103—222no—
429#103—222no—
430C22⋊C8—22no—
431C22⋊C8—222no—
432#97—222no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445C2×C11—81no—
446C2×C11#246111yescharacteristic
447C2×C11#311611yescharacteristic
448C2×C11#312111yescharacteristic
449C2×C11#326711yescharacteristic
450C2×C11#327011yescharacteristic
451C2×C11#334911yescharacteristic
452C2×C11#335611yescharacteristic
453C24D4×D1111yescharacteristic
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—442no—
466C2×Q8—442no—
467C2×Q8—881no—
468C2×Q8#434112yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
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×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—44no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8#434112yes—
502C4⋊C4—24no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—112no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4D4×D1112yes—
518C4⋊C4#434112yes—
519C22⋊C4—24no—
520C22⋊C4—42no—
521C22⋊C4—222no—
522C22⋊C4—441no—
523C22⋊C4—442no—
524C22⋊C4—881no—
525C42—221no—
526C42—221no—
527C42—221no—
528C42—221no—
529C42—442no—
530C42—442no—
531C42—442no—
532C42—881no—
533C11#2681011yescharacteristic, complemented, Sylow
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23C2×D4×D1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—884no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—112no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
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×C4C2×D4×D1111yescharacteristic
595C2×C4C2×#434111yescharacteristic
596C2×C4C2×#434111yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#6704311yescharacteristic
600C8—22no—
601C8—41no—
602C8—222no—
603C8—441no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22#1062311711yescharacteristic
612C22#1062312111yescharacteristic
613C22#1062314211yescharacteristic
614C22#1062329711yescharacteristic
615C22#1062329911yescharacteristic
616C22D11×#13711yescharacteristic
617C22#1062330911yescharacteristic
618C4—42no—
619C4—41no—
620C4—42no—
621C4—42no—
622C4—81no—
623C4—222no—
624C4—441no—
625C4—441no—
626C4—442no—
627C4—441no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062311811yescharacteristic
632C4#1062312911yescharacteristic
633C4#1062313411yescharacteristic
634C4#1062324711yescharacteristic
635C2—81no—
636C2#1307257811yescharacteristic
637C2#1307877111yescharacteristic
638C2#1307884611yescharacteristic
639C2#1308014511yescharacteristic
640C2#1308018911yescharacteristic
641C2#1308115211yescharacteristic
642C2#1308122611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2001C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2001D11
hypocenterC11#26810
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#10622407C2semidirect
5. #13069993C2semidirect
6. #13069948C2semidirect
8. #13069488C2semidirect
9. #13069259C2semidirect
10. #13069253C2semidirect
12. #13068959C2semidirect
14. #13068512C2semidirect
533. C11#26810semidirect

Maximal subgroups

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

subgroupindex
C2×#106226582
C2×#106224072
#130729922
#130716472
#130699932
#130699482
#130698092
#130694882
#130692592
#130692532
#130692262
#130689592
#130688172
#130685122
C11×#20012
#2681011