Finite Group Databasebeta

← #14810967

Subgroups — #14810967

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622407C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic
3#13072308C211yesmaximal, characteristic, complemented
4#13071457C211yesmaximal, characteristic
5#13070139C211yesmaximal, characteristic, complemented
6#13070002C211yesmaximal, characteristic, complemented
7#13070000C211yesmaximal, characteristic, complemented
8#13069750C211yesmaximal, characteristic, complemented
9#13068886C211yesmaximal, characteristic, complemented
10#13068868C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068643C211yesmaximal, characteristic, complemented
14#13068629C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622846—24no—
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622834—21no—
32#10622834—21no—
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622825—21no—
38#10622825C2211yescharacteristic
39C4×C22⋊Dic11—21no—
40C4×C22⋊Dic11C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66881C2211yescharacteristic
43C2×Dic11⋊C8C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45#10622598C2211yescharacteristic
46#10622590C2211yescharacteristic
47#10622586C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622561—21no—
51#10622560—21no—
52#10622407—24no—
53#10622267—21no—
54#10622259—21no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—41no—
65C2×C11×#41—41no—
66C2×C11×#41Q814yescomplemented
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×Dic22—21no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86Q8×Dic11—22no—
87Q8×Dic11—22no—
88Q8×Dic11—41no—
89Q8×Dic11—41no—
90#66979—22no—
91#66979—41no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8—22no—
107C22×C11⋊C8—22no—
108C22×C11⋊C8—41no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111#66941—22no—
112#66941—41no—
113C11×#103—22no—
114C11×#103—22no—
115C11×#102—41no—
116C11×#102—41no—
117C11×C22⋊C8—22no—
118C11×#95—21no—
119#66899—22no—
120#66899D414yes—
121#66896—22no—
122#66896—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66882—22no—
131#66881—41no—
132Dic11⋊C8—22no—
133Dic11⋊C8—41no—
134#66871—22no—
135#66871—41no—
136#25959—111nomaximal, Sylow
137C24×C11—21no—
138C24×C11C2×D411yescharacteristic
139C11×#41—28no—
140C11×#41—44no—
141C11×#41—44no—
142C11×#41—44no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D412yes—
147C2×Q8×C11C2×Q812yes—
148C2×Q8×C11#4112yes—
149C2×D4×C11—24no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—42no—
156C2×D4×C11—42no—
157C2×D4×C11C2×Q812yes—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×Q812yes—
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C2×Dic22—42no—
181C2×Dic22—42no—
182C2×Dic22—81no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C22⋊C4—81no—
194C22⋊Dic11—22no—
195C22⋊Dic11—41no—
196C22⋊Dic11—42no—
197C22⋊Dic11—42no—
198C22⋊Dic11—42no—
199C22⋊Dic11—81no—
200C22⋊Dic11—81no—
201C22⋊Dic11—81no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—42no—
210C4⋊Dic11—42no—
211C4⋊Dic11—42no—
212C4⋊Dic11C2×D412yes—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—42no—
220C4×Dic11—42no—
221C4×Dic11—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—44no—
228C2×C11⋊C8C2×D412yes—
229C2×#477—111no—
230C2×#416—111no—
231#2439—111no—
232#2341—111no—
233#2092—111no—
234#2067—111no—
235#2067—111no—
236#2023—111no—
237#1865—111no—
238#1863—111no—
239#1854—111no—
240#1850—111no—
241#1808—111no—
242#1805—111no—
243#1788D1111yescharacteristic
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—22no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11C22⋊Q812yes—
258C23×C11C22×D411yescharacteristic
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—22no—
262Q8×C11C22⋊Q814yes—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—48no—
266D4×C11—41no—
267D4×C11—41no—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—48no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11C22⋊Q812yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×Q811yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—22no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11#13512yes—
315Dic22—84no—
316C8×C11—41no—
317C8×C11—41no—
318C11⋊C8—22no—
319C11⋊C8—41no—
320C22×#41C2×D1111yescharacteristic
321C23×C8—111no—
322C2×C4⋊Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×#117—111no—
326#477—224no—
327C2×#107—111no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#106—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—111no—
333#416—224no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103C2×D1111yescharacteristic
337C2×#103C2×D1111yescharacteristic
338C2×#102—111no—
339C2×#102—111no—
340C2×#102C2×D1111yescharacteristic
341C2×#102C2×D1111yescharacteristic
342C2×C22⋊C8C2×D1111yescharacteristic
343#396—221no—
344#393—221no—
345#391—221no—
346#390—111no—
347#390—111no—
348#390—221no—
349#390—221no—
350#389—111no—
351#389—111no—
352#387—221no—
353#382—111no—
354#380—111no—
355#380—221no—
356#380C2×D1111yescharacteristic
357C4×C22⋊C4—111no—
358C4×C22⋊C4—221no—
359#340—111no—
360#340—111no—
361#340—111no—
362#340—111no—
363#336—111no—
364#336—111no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11C2×C22⋊Q811yescharacteristic
380C22×C11D4211yescharacteristic
381C22×C11#54611yescharacteristic
382C22×C11C2×#13511yescharacteristic
383C22×C11#57511yescharacteristic
384C22×C11#57611yescharacteristic
385C22×C11#57811yescharacteristic
386C4×C11—22no—
387C4×C11—24no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11C2×C22⋊Q811yescharacteristic
391C4×C11#54311yescharacteristic
392C4×C11#54611yescharacteristic
393C4×C11#55111yescharacteristic
394Dic11—22no—
395Dic11—41no—
396Dic11—42no—
397Dic11—41no—
398Dic11—41no—
399Dic11—81no—
400Dic11—81no—
401Dic11—81no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—41no—
406C2×#41—41no—
407C2×#41Dic2214yescomplemented
408C22×Q8—221no—
409C22×Q8C22×D1111yescharacteristic
410C22×D4—21no—
411C22×D4C22×D1111yescharacteristic
412C23×C4—21no—
413C23×C4C22×D1111yescharacteristic
414C22×C8—111no—
415C22×C8—111no—
416C22×C8—222no—
417C22×C8—222no—
418C22×C8—441no—
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C4⋊Q8—222no—
422C4⋊Q8—441no—
423C4×Q8—222no—
424C4×Q8—222no—
425C4×Q8—441no—
426C4×Q8—441no—
427#117—222no—
428#117—441no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—111no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42—221no—
454#107—222no—
455#107—222no—
456#107—441no—
457#106—441no—
458C4⋊C8—222no—
459C4⋊C8—441no—
460#103—22no—
461#103—22no—
462#103—114no—
463#103—222no—
464#102—41no—
465#102—41no—
466#102—222no—
467#102—222no—
468C22⋊C8—22no—
469#95—21no—
470#95—111no—
471#95—111no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477C2×C11—42no—
478C2×C11—82no—
479C2×C11#243711yescharacteristic
480C2×C11#307611yescharacteristic
481C2×C11#308311yescharacteristic
482C2×C11#326811yescharacteristic
483C2×C11#328511yescharacteristic
484C2×C11#330511yescharacteristic
485C2×C11#331311yescharacteristic
486C24—21no—
487C24D4×D1111yescharacteristic
488#41—28no—
489#41—44no—
490#41—44no—
491#41—44no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—442no—
496C2×Q8—442no—
497C2×Q8—881no—
498C2×Q8C2×Dic2212yes—
499C2×Q8D4×D1112yes—
500C2×Q8#434112yes—
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×Dic2212yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—111no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4C2×Dic2212yes—
529C22×C4D4×D1111yescharacteristic
530C22×C4#434112yes—
531C22×C4C23×D1111yescharacteristic
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—112no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—444no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—112no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4—442no—
561C4⋊C4—881no—
562C22⋊C4—81no—
563C22⋊C4—222no—
564C22⋊C4—442no—
565C22⋊C4—441no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—881no—
569C22⋊C4—881no—
570C22⋊C4—881no—
571C42—221no—
572C42—221no—
573C42—221no—
574C42—221no—
575C42—442no—
576C42—442no—
577C42—442no—
578C11#2595911yescharacteristic, complemented, Sylow
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23#6693112yes—
593C23C2×D4×D1111yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—884no—
598Q8#6693114yes—
599D4—22no—
600D4—22no—
601D4—48no—
602D4—41no—
603D4—41no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—48no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—112no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—222no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4#6693112yes—
645C2×C4C22×Dic2211yescharacteristic
646C2×C4C2×D4×D1111yescharacteristic
647C2×C4C2×#434111yescharacteristic
648C2×C4C2×#434111yescharacteristic
649C2×C4#6703711yescharacteristic
650C2×C4#6703711yescharacteristic
651C8—41no—
652C8—41no—
653C8—222no—
654C8—441no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×#6693111yescharacteristic
670C22#1062312111yescharacteristic
671C22#1062312211yescharacteristic
672C22D11×#13511yescharacteristic
673C22#1062329911yescharacteristic
674C22#1062330511yescharacteristic
675C22#1062331011yescharacteristic
676C4—22no—
677C4—24no—
678C4—81no—
679C4—81no—
680C4—222no—
681C4—441no—
682C4—442no—
683C4—441no—
684C4—441no—
685C4—881no—
686C4—881no—
687C4—881no—
688C4C2×#6693111yescharacteristic
689C4#1062301411yescharacteristic
690C4#1062311811yescharacteristic
691C4#1062312211yescharacteristic
692C2—42no—
693C2—82no—
694C2#1307228211yescharacteristic
695C2#1307840011yescharacteristic
696C2#1307847111yescharacteristic
697C2#1308014911yescharacteristic
698C2#1308035511yescharacteristic
699C2#1308055911yescharacteristic
700C2#1308068611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#1788D11
hypocenterC11#25959
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
1. C2×#10622407C2semidirect
3. #13072308C2semidirect
5. #13070139C2semidirect
6. #13070002C2semidirect
7. #13070000C2semidirect
8. #13069750C2semidirect
9. #13068886C2semidirect
10. #13068868C2semidirect
11. #13068817C2semidirect
12. #13068793C2semidirect
13. #13068643C2semidirect
14. #13068629C2semidirect
66. C2×C11×#41Q8semidirect
407. C2×#41Dic22semidirect
578. C11#25959semidirect

Maximal subgroups

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

subgroupindex
C2×#106224072
C2×#106228462
#130723082
#130714572
#130701392
#130700022
#130700002
#130697502
#130688862
#130688682
#130688172
#130687932
#130686432
#130686292
C11×#17882
#2595911