Finite Group Databasebeta

← #14823210

Subgroups — #14823210

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×#10622697C211yesmaximal, characteristic, complemented
3#13071652C211yesmaximal, characteristic
4#13070011C211yesmaximal, characteristic, complemented
5#13069941C211yesmaximal, characteristic, complemented
6#13069798C211yesmaximal, characteristic
7#13069617C211yesmaximal, characteristic
8#13069500C211yesmaximal, characteristic, complemented
9#13069247C211yesmaximal, characteristic, complemented
10#13069236C211yesmaximal, characteristic, complemented
11#13069231C211yesmaximal, characteristic, complemented
12#13068953C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068514C211yesmaximal, characteristic, complemented
15C11×#2492C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C11×#400—21no—
23C11×#393—21no—
24C11×#391—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#388—21no—
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622697—24no—
37#10622658—24no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622570—21no—
47#10622569—21no—
48#10622552C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53#10622282—21no—
54#10622279—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—41no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—41no—
87#66983—22no—
88#66983—22no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93#66979—22no—
94#66979—41no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×D44—22no—
106C4×D44—41no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115#66899—22no—
116#66899—22no—
117#66899—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C22⋊(C11⋊C8)—22no—
121C22⋊(C11⋊C8)—22no—
122#66873—22no—
123#66873—22no—
124#66873—22no—
125#66872—22no—
126#66872D414yescomplemented
127#66871—22no—
128#66871—22no—
129#66871—41no—
130C4⋊(C11⋊C8)—22no—
131#66867—22no—
132#26814—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—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—42no—
142C2×Q8×C11—42no—
143C2×Q8×C11—81no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—81no—
162C2×C22⋊D11—81no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44#4112yes—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—81no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—81no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—81no—
192C22⋊Dic11—42no—
193#4325—44no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—81no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C2×D412yes—
203C4⋊Dic11#4112yes—
204Dic11⋊C4—81no—
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⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C2×D412yes—
218C2×C11⋊C8#4112yes—
219C2×#485—111no—
220C2×#476—111no—
221#2492D1111yescharacteristic, complemented
222#2363—111no—
223#2068—111no—
224#2057—111no—
225#2033—111no—
226#2000—111no—
227#1973—111no—
228#1927—111no—
229#1925—111no—
230#1924—111no—
231#1877—111no—
232#1854—111no—
233#1776—111no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11C22×D411yescharacteristic
242C22×D11—22no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—84no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
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—21no—
268C2×C4×C11—21no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
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×C11#13712yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C112−1+411yescharacteristic
291C22⋊D11—84no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301D44—22no—
302D44—22no—
303D44—41no—
304D44—41no—
305C4×D11—84no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C22×SD16—111no—
311C2×C4⋊Q8C2×D1111yescharacteristic
312C2×C22⋊Q8C2×D1111yescharacteristic
313C2×#121—111no—
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×#103—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×C22⋊C8—111no—
331C2×C22⋊C8—111no—
332C2×#97—111no—
333#400—21no—
334#393—21no—
335#391—21no—
336#391C2×D1111yescharacteristic
337#391C2×D1111yescharacteristic
338#390—111no—
339#390—221no—
340#389—111no—
341#388—21no—
342#388—221no—
343#386—221no—
344#380C2×D1111yescharacteristic
345C4×C4⋊C4—111no—
346C4×C4⋊C4C2×D1111yescharacteristic
347C4×C22⋊C4—221no—
348C4×C22⋊C4C2×D1111yescharacteristic
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336—111no—
354#336—111no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11#52511yescharacteristic
363C22×C11D4211yescharacteristic
364C22×C11#54711yescharacteristic
365C22×C11C2×#13711yescharacteristic
366C22×C11#57511yescharacteristic
367C22×C11#57611yescharacteristic
368C22×C11#57711yescharacteristic
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11#53211yescharacteristic
386C4×C11#54211yescharacteristic
387C4×C11#54811yescharacteristic
388C4×C11#55111yescharacteristic
389Dic11—42no—
390Dic11—42no—
391Dic11—81no—
392C22×Q8—21no—
393C22×Q8C22×D1111yescharacteristic
394C22×D4—111no—
395C22×D4—221no—
396C23×C4—221no—
397C23×C4C22×D1111yescharacteristic
398C2×SD16—222no—
399C2×SD16—222no—
400C2×SD16—441no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—111no—
405C4⋊Q8—22no—
406C4⋊Q8—41no—
407C22⋊Q8—22no—
408C22⋊Q8—41no—
409#121—222no—
410#121—222no—
411C4×D4—222no—
412C4×D4—441no—
413#117—222no—
414#117—441no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4C22⋊D1111yescharacteristic
432C2×C22⋊C4C22⋊D1111yescharacteristic
433C2×C42—21no—
434C2×C42—221no—
435C2×C42—221no—
436C2×C42C22×D1111yescharacteristic
437C2×C42C22×D1111yescharacteristic
438#107—222no—
439#107—222no—
440#107—441no—
441#106—114no—
442#106—222no—
443C4⋊C8—222no—
444#103—222no—
445#103—222no—
446#103—222no—
447#102—222no—
448#102—222no—
449#102—222no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452#97—222no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—221no—
460#95—221no—
461#95C22⋊D1111yescharacteristic
462#95C22⋊D1111yescharacteristic
463C2×C11—81no—
464C2×C11#246111yescharacteristic
465C2×C11#311611yescharacteristic
466C2×C11#311811yescharacteristic
467C2×C11#326611yescharacteristic
468C2×C11#326811yescharacteristic
469C2×C11#335011yescharacteristic
470C2×C11#335711yescharacteristic
471D11—82no—
472C24—221no—
473C24C2×C22⋊D1111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—81no—
483C2×D4—112no—
484C2×D4—224no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—881no—
491C2×D4—881no—
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—21no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—881no—
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C2×C22⋊D1111yescharacteristic
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C23×D1111yescharacteristic
514SD16—444no—
515C2×C8—112no—
516C2×C8—112no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—112no—
535C4⋊C4—112no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—881no—
541C4⋊C4D4×D1112yes—
542C22⋊C4—22no—
543C22⋊C4—41no—
544C22⋊C4—42no—
545C22⋊C4—81no—
546C22⋊C4—224no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—881no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—81no—
556C42—442no—
557C42—881no—
558C11#2681411yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—222no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23C22×C22⋊D1111yescharacteristic
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—84no—
579D4—222no—
580D4—222no—
581D4—441no—
582D4—441no—
583D4—884no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—884no—
624C2×C4#6699512yes—
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4#6703711yescharacteristic
627C2×C4#41×D1111yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#6704311yescharacteristic
631C8—222no—
632C8—222no—
633C8—441no—
634C8—441no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—442no—
643C22—442no—
644C22—442no—
645C22—881no—
646C22—881no—
647C22—881no—
648C22—881no—
649C22D4×C22⋊D1111yescharacteristic
650C22C2×#6699511yescharacteristic
651C22#1062335311yescharacteristic
652C22#1062335511yescharacteristic
653C22#1062335911yescharacteristic
654C22#1062336611yescharacteristic
655C22#1062336811yescharacteristic
656C4—22no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—442no—
666C4—442no—
667C4—881no—
668C4#1062319911yescharacteristic
669C4#1062320011yescharacteristic
670C4#1062320811yescharacteristic
671C4#1062321011yescharacteristic
672C2—81no—
673C2—882no—
674C2#1307257911yescharacteristic
675C2#1307877211yescharacteristic
676C2#1307879411yescharacteristic
677C2#1308012711yescharacteristic
678C2#1308015211yescharacteristic
679C2#1308116111yescharacteristic
680C2#1308124211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2492C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2492D11
hypocenterC11#26814
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2492

Complements

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

NH ≅ G/Ntype
1. C2×#10622658C2semidirect
2. C2×#10622697C2semidirect
4. #13070011C2semidirect
5. #13069941C2semidirect
8. #13069500C2semidirect
9. #13069247C2semidirect
10. #13069236C2semidirect
11. #13069231C2semidirect
12. #13068953C2semidirect
13. #13068813C2semidirect
14. #13068514C2semidirect
15. C11×#2492C2semidirect
126. #66872D4semidirect
221. #2492D11semidirect
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×#106226972
#130716522
#130700112
#130699412
#130697982
#130696172
#130695002
#130692472
#130692362
#130692312
#130689532
#130688132
#130685142
C11×#24922
#2681411