Finite Group Databasebeta

← #14822203

Subgroups — #14822203

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072968C211yesmaximal, characteristic, complemented
2#13069926C211yesmaximal, characteristic, complemented
3#13069795C211yesmaximal, characteristic, complemented
4#13069762C211yesmaximal, characteristic, complemented
5#13069612C211yesmaximal, characteristic
6#13069573C211yesmaximal, characteristic, complemented
7#13069312C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13069231C211yesmaximal, characteristic, complemented
10#13069184C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#390—21no—
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#386—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622572—21no—
41#10622570—21no—
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622288—21no—
48#10622282—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C11×#121—22no—
66C11×#121—22no—
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×#4323—22no—
88C2×#4323—41no—
89C2×#4323—41no—
90#66983—22no—
91#66983—41no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66923—22no—
108#66923—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66896—22no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120#66873—22no—
121#66873—22no—
122#66873—41no—
123#66871—22no—
124C4⋊(C11⋊C8)—41no—
125#66867—41no—
126#26747—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—81no—
137C2×D4×C11—81no—
138C2×D4×C11#4112yes—
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—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—81no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4#4112yes—
175C11×C4⋊C4#4112yes—
176C11×C22⋊C4—24no—
177C11×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—81no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188C42×C11—81no—
189C22⋊Dic11—81no—
190#4323—44no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
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—
217#2490—111no—
218#2363D1111yescharacteristic, complemented
219#2054—111no—
220#2033—111no—
221#2025—111no—
222#1999—111no—
223#1989—111no—
224#1936—111no—
225#1925—111no—
226#1924—111no—
227#1918—111no—
228#1879—111no—
229#1875—111no—
230#1825—111no—
231#1762—111no—
232C23×C11—22no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—84no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
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—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
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—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—84no—
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C22⋊D11—84no—
295C2×Dic11—22no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C22×D8—111no—
313C2×#125—111no—
314C2×#121—111no—
315C2×#121C2×D1111yescharacteristic
316C2×C4×D4C2×D1111yescharacteristic
317C2×#117C2×D1111yescharacteristic
318C2×#107—111no—
319C2×C4⋊C8—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328C2×#97—111no—
329#397—221no—
330#394—221no—
331#390—21no—
332#390—111no—
333#390—111no—
334#390—221no—
335#390C2×D1111yescharacteristic
336#389C2×D1111yescharacteristic
337#388—21no—
338#388—221no—
339#386—21no—
340#380—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4C2×D1111yescharacteristic
343C4×C22⋊C4—21no—
344C4×C22⋊C4C2×D1111yescharacteristic
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336—111no—
354#336—111no—
355C22×C11—41no—
356C22×C11—42no—
357C22×C11—41no—
358C22×C11—42no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11#52511yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11#54611yescharacteristic
372C22×C11#57511yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57611yescharacteristic
375C22×C11#57611yescharacteristic
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—42no—
390C4×C11—81no—
391C4×C11#52911yescharacteristic
392C4×C11#53811yescharacteristic
393C4×C11#55511yescharacteristic
394C4×C11#55911yescharacteristic
395Dic11—42no—
396Dic11—81no—
397Dic11—81no—
398C22×D4—21no—
399C22×D4—111no—
400C22×D4—221no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—21no—
403C23×C4C22×D1111yescharacteristic
404C2×D8—222no—
405C2×D8—441no—
406C2×D8—441no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—111no—
411#125—222no—
412#125—441no—
413#121—22no—
414#121—22no—
415#121—222no—
416#121—441no—
417C4×D4—22no—
418C4×D4—41no—
419#117—22no—
420#117—41no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4C22⋊D1111yescharacteristic
442C2×C22⋊C4C22⋊D1111yescharacteristic
443C2×C42—21no—
444C2×C42—21no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448#107—222no—
449C4⋊C8—441no—
450#102—222no—
451#102—222no—
452#102—222no—
453#102—222no—
454#102—441no—
455#102—441no—
456C22⋊C8—441no—
457C22⋊C8—441no—
458#97—441no—
459#95—21no—
460#95—21no—
461#95—221no—
462#95—221no—
463#95C22⋊D1111yescharacteristic
464#95C22⋊D1111yescharacteristic
465C2×C11—81no—
466C2×C11—82no—
467C2×C11#245911yescharacteristic
468C2×C11#311111yescharacteristic
469C2×C11#312211yescharacteristic
470C2×C11#330911yescharacteristic
471C2×C11#330911yescharacteristic
472C2×C11#331911yescharacteristic
473C2×C11#332211yescharacteristic
474D11—161no—
475C24—21no—
476C24—221no—
477C24C2×C22⋊D1111yescharacteristic
478C2×D4—24no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—442no—
493C2×D4—442no—
494C2×D4—881no—
495C2×D4#433912yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—81no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517D8—444no—
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—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—81no—
535C4⋊C4—112no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4#433912yes—
544C4⋊C4#434112yes—
545C22⋊C4—24no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—81no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—881no—
555C22⋊C4—881no—
556C22⋊C4—881no—
557C22⋊C4—881no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—42no—
563C42—81no—
564C42—881no—
565C11#2674711yescharacteristic, complemented, Sylow
566C23—22no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23C22×C22⋊D1111yescharacteristic
588D4—22no—
589D4—22no—
590D4—41no—
591D4—41no—
592D4—84no—
593D4—441no—
594D4—441no—
595D4—441no—
596D4—441no—
597D4—884no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—84no—
627C2×C4—222no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4C2×#433911yescharacteristic
637C2×C4C2×#433911yescharacteristic
638C2×C4C2×#434111yescharacteristic
639C2×C4#6703711yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#6704211yescharacteristic
642C8—441no—
643C8—441no—
644C8—441no—
645C8—441no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—42no—
650C22—41no—
651C22—42no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—41no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—881no—
661C22—881no—
662C22—881no—
663C22—881no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22#1062332211yescharacteristic
668C22#1062333711yescharacteristic
669C22#1062335311yescharacteristic
670C22#1062335311yescharacteristic
671C22#1062336011yescharacteristic
672C22#1062336611yescharacteristic
673C22#1062336611yescharacteristic
674C4—41no—
675C4—41no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—42no—
681C4—81no—
682C4—442no—
683C4—881no—
684C4—881no—
685C4#1062306911yescharacteristic
686C4#1062309011yescharacteristic
687C4#1062309111yescharacteristic
688C4#1062309411yescharacteristic
689C2—81no—
690C2—82no—
691C2—1761no—
692C2#1307254711yescharacteristic
693C2#1307872511yescharacteristic
694C2#1307885911yescharacteristic
695C2#1308061611yescharacteristic
696C2#1308062211yescharacteristic
697C2#1308076611yescharacteristic
698C2#1308081711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenter#2363D11
hypocenterC11#26747
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #13072968C2semidirect
2. #13069926C2semidirect
3. #13069795C2semidirect
4. #13069762C2semidirect
6. #13069573C2semidirect
7. #13069312C2semidirect
8. #13069236C2semidirect
9. #13069231C2semidirect
10. #13069184C2semidirect
11. #13068964C2semidirect
12. #13068938C2semidirect
13. #13068711C2semidirect
14. #13068441C2semidirect
15. C11×#2363C2semidirect
218. #2363D11semidirect
565. C11#26747semidirect

Maximal subgroups

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

subgroupindex
#130729682
#130699262
#130697952
#130697622
#130696122
#130695732
#130693122
#130692362
#130692312
#130691842
#130689642
#130689382
#130687112
#130684412
C11×#23632
#2674711