Finite Group Databasebeta

← #14823209

Subgroups — #14823209

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622658C211yesmaximal, characteristic, complemented
2C2×#10622374C211yesmaximal, characteristic, complemented
3#13072992C211yesmaximal, characteristic, complemented
4#13071658C211yesmaximal, characteristic
5#13070007C211yesmaximal, characteristic, complemented
6#13069943C211yesmaximal, characteristic, complemented
7#13069795C211yesmaximal, characteristic
8#13069499C211yesmaximal, characteristic, complemented
9#13069252C211yesmaximal, characteristic, complemented
10#13069239C211yesmaximal, characteristic, complemented
11#13069226C211yesmaximal, characteristic, complemented
12#13068952C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068512C211yesmaximal, characteristic, complemented
15C11×#2000C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622834—21no—
30#10622834C2211yescharacteristic
31#10622833—21no—
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622825C2211yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41#10622658—24no—
42#10622598C2211yescharacteristic
43#10622595—21no—
44C4⋊C4×Dic11C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46#10622587—21no—
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622564—21no—
51#10622560—21no—
52#10622558—21no—
53C22⋊C4×Dic11—21no—
54#10622374—24no—
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C22×Dic22—21no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16—41no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—41no—
74C11×#121—22no—
75C11×#121—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11D411yescharacteristic
87C2×C22⋊Dic11D411yescharacteristic
88D4×Dic11—22no—
89D4×Dic11—41no—
90#66979—22no—
91#66979—41no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
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#66941—22no—
106#66941—41no—
107C11×#103—22no—
108C11×#102—22no—
109C11×C22⋊C8—22no—
110#66899—22no—
111#66899—22no—
112#66896—22no—
113#66896—22no—
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—41no—
126#66881—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129#66872D414yescomplemented
130#66871—22no—
131#66871—22no—
132#26814—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
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×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—81no—
148C2×D4×C11—81no—
149C2×D4×C11#4112yes—
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×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—81no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C2×Dic22—42no—
173C2×Dic22—42no—
174C2×Dic22—81no—
175C11×SD16—44no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11#4112yes—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4#4112yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—42no—
189C22⋊Dic11—22no—
190C22⋊Dic11—41no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—81no—
195C22⋊Dic11—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—81no—
204C4⋊Dic11C2×D412yes—
205Dic11⋊C4—42no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C4×Dic11—81no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C2×D412yes—
219C2×#485—111no—
220C2×#476—111no—
221#2492—111no—
222#2363—111no—
223#2068—111no—
224#2057—111no—
225#2033—111no—
226#2000D1111yescharacteristic
227#1973—111no—
228#1927—111no—
229#1925—111no—
230#1924—111no—
231#1877—111no—
232#1854—111no—
233#1776—111no—
234C23×C11—22no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—84no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—84no—
304C2×Dic11#13712yes—
305Dic22—84no—
306C8×C11—22no—
307C8×C11—41no—
308C11⋊C8—22no—
309C11⋊C8—41no—
310C22×SD16C2×D1111yescharacteristic
311C2×C4⋊Q8—111no—
312C2×C22⋊Q8C2×D1111yescharacteristic
313C2×#121C2×D1111yescharacteristic
314C2×C4×D4—111no—
315C2×#117—111no—
316#485—224no—
317#476—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103C2×D1111yescharacteristic
327C2×#102—111no—
328C2×#102—111no—
329C2×#102C2×D1111yescharacteristic
330C2×C22⋊C8—111no—
331C2×C22⋊C8C2×D1111yescharacteristic
332C2×#97—111no—
333#400—221no—
334#393—221no—
335#391—111no—
336#391—111no—
337#391—221no—
338#390—111no—
339#390—221no—
340#389—111no—
341#388—221no—
342#388—221no—
343#386—221no—
344#380—111no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C22⋊C4—111no—
348C4×C22⋊C4—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#336—111no—
354#336—111no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—41no—
362C22×C11—42no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11#52511yescharacteristic
370C22×C11D4211yescharacteristic
371C22×C11#54711yescharacteristic
372C22×C11C2×#13711yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57611yescharacteristic
375C22×C11#57711yescharacteristic
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11#53211yescharacteristic
381C4×C11#54211yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55111yescharacteristic
384Dic11—22no—
385Dic11—41no—
386Dic11—41no—
387Dic11—42no—
388Dic11—41no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392C22×Q8—221no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—21no—
395C22×D4C22×D1111yescharacteristic
396C23×C4—221no—
397C23×C4C22×D1111yescharacteristic
398C2×SD16—22no—
399C2×SD16—22no—
400C2×SD16—41no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—222no—
406C4⋊Q8—441no—
407C22⋊Q8—22no—
408C22⋊Q8—41no—
409#121—22no—
410#121—22no—
411C4×D4—222no—
412C4×D4—441no—
413#117—222no—
414#117—441no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438#107—222no—
439#107—222no—
440#107—441no—
441#106—114no—
442#106—222no—
443C4⋊C8—222no—
444#103—22no—
445#103—222no—
446#103—222no—
447#102—22no—
448#102—222no—
449#102—222no—
450C22⋊C8—22no—
451C22⋊C8—222no—
452#97—222no—
453#95—111no—
454#95—111no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463C2×C11—81no—
464C2×C11—82no—
465C2×C11#246111yescharacteristic
466C2×C11#311611yescharacteristic
467C2×C11#311811yescharacteristic
468C2×C11#326611yescharacteristic
469C2×C11#326811yescharacteristic
470C2×C11#335011yescharacteristic
471C2×C11#335711yescharacteristic
472C24—21no—
473C24D4×D1111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—442no—
481C2×Q8—442no—
482C2×Q8—881no—
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—81no—
490C2×D4—81no—
491C2×D4#434112yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—881no—
512C22×C4D4×D1111yescharacteristic
513C22×C4C23×D1111yescharacteristic
514SD16—44no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—112no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8#434112yes—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—112no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—442no—
539C4⋊C4—881no—
540C4⋊C4D4×D1112yes—
541C4⋊C4#434112yes—
542C22⋊C4—24no—
543C22⋊C4—42no—
544C22⋊C4—222no—
545C22⋊C4—441no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—881no—
550C22⋊C4—881no—
551C42—221no—
552C42—221no—
553C42—221no—
554C42—221no—
555C42—442no—
556C42—881no—
557C42—881no—
558C11#2681411yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—22no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C2×D4×D1111yescharacteristic
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—884no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583D4—84no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—112no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—222no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—884no—
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4C2×#434111yescharacteristic
627C2×C4C2×#434111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4#6703711yescharacteristic
630C2×C4#6704311yescharacteristic
631C8—22no—
632C8—41no—
633C8—222no—
634C8—441no—
635C22—41no—
636C22—42no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—41no—
644C22—42no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22#1062311711yescharacteristic
650C22#1062312111yescharacteristic
651C22#1062314211yescharacteristic
652C22#1062329311yescharacteristic
653C22#1062329911yescharacteristic
654C22#1062330511yescharacteristic
655C22D11×#13711yescharacteristic
656C4—42no—
657C4—42no—
658C4—41no—
659C4—81no—
660C4—222no—
661C4—442no—
662C4—441no—
663C4—441no—
664C4—441no—
665C4—881no—
666C4—881no—
667C4—881no—
668C4#1062311811yescharacteristic
669C4#1062312911yescharacteristic
670C4#1062313411yescharacteristic
671C4#1062324711yescharacteristic
672C2—81no—
673C2—82no—
674C2#1307257811yescharacteristic
675C2#1307877111yescharacteristic
676C2#1307880111yescharacteristic
677C2#1308012911yescharacteristic
678C2#1308016011yescharacteristic
679C2#1308116711yescharacteristic
680C2#1308123711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2000C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2000D11
hypocenterC11#26814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#10622658C2semidirect
2. C2×#10622374C2semidirect
3. #13072992C2semidirect
5. #13070007C2semidirect
6. #13069943C2semidirect
8. #13069499C2semidirect
9. #13069252C2semidirect
10. #13069239C2semidirect
11. #13069226C2semidirect
12. #13068952C2semidirect
13. #13068817C2semidirect
14. #13068512C2semidirect
129. #66872D4semidirect
558. C11#26814semidirect

Maximal subgroups

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

subgroupindex
C2×#106226582
C2×#106223742
#130729922
#130716582
#130700072
#130699432
#130697952
#130694992
#130692522
#130692392
#130692262
#130689522
#130688172
#130685122
C11×#20002
#2681411