Finite Group Databasebeta

← #14822208

Subgroups — #14822208

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#13072970C211yesmaximal, characteristic, complemented
2#13071654C211yesmaximal, characteristic, complemented
3#13069925C211yesmaximal, characteristic, complemented
4#13069799C211yesmaximal, characteristic, complemented
5#13069761C211yesmaximal, characteristic, complemented
6#13069612C211yesmaximal, characteristic
7#13069572C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic, complemented
9#13069238C211yesmaximal, characteristic, complemented
10#13069232C211yesmaximal, characteristic, complemented
11#13069186C211yesmaximal, characteristic, complemented
12#13068961C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1875C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4323C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622835—21no—
26#10622834—21no—
27#10622834C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622601C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43#10622570—21no—
44#10622569—21no—
45#10622566—21no—
46#10622558—21no—
47#10622553—21no—
48C4×(C2×D11)⋊C4—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—22no—
68C11×#121—41no—
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84C2×#4323—22no—
85C2×#4323—41no—
86C2×#4323—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—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66946—22no—
106#66946—41no—
107#66943—22no—
108#66943—41no—
109C11×#102—22no—
110C11×#102—41no—
111C11×C22⋊C8—41no—
112#66896—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119C22⋊(C11⋊C8)—41no—
120#66885—22no—
121#66885—41no—
122#66882—22no—
123#66879—41no—
124Dic11⋊C8—41no—
125#66873—22no—
126#26747—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
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×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—24no—
151C2×C22⋊D11—81no—
152C2×C22⋊D11—81no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44#4112yes—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4#4112yes—
180C11×C4⋊C4#4112yes—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C42×C11—42no—
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186C22⋊Dic11—42no—
187C22⋊Dic11—81no—
188C22⋊Dic11—81no—
189C22⋊Dic11—81no—
190C22⋊Dic11—81no—
191#4323—44no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11#4112yes—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—81no—
210C4×Dic11—81no—
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#2363—111no—
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#1875D1111yescharacteristic, complemented
230#1825—111no—
231#1762—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—84no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
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×C11—41no—
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C22⋊D11—84no—
282C2×Dic11—22no—
283C2×Dic11—21no—
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—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303D44—22no—
304D44—22no—
305D44—41no—
306D44—41no—
307C4×D11—84no—
308C8×C11—41no—
309C8×C11—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C22×D8—111no—
313C2×#125—111no—
314C2×#121—111no—
315C2×#121C2×D1111yescharacteristic
316C2×C4×D4—111no—
317C2×#117C2×D1111yescharacteristic
318C2×#107—111no—
319C2×C4⋊C8—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102C2×D1111yescharacteristic
325C2×#102C2×D1111yescharacteristic
326C2×C22⋊C8—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×#97—111no—
329#397—221no—
330#394—221no—
331#390—111no—
332#390—111no—
333#390—111no—
334#390—221no—
335#390—221no—
336#389—111no—
337#388—221no—
338#388—221no—
339#386—221no—
340#380—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4—111no—
343C4×C22⋊C4—111no—
344C4×C22⋊C4—221no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340C2×D1111yescharacteristic
352#340C2×D1111yescharacteristic
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—81no—
363C22×C11—81no—
364C22×C11—81no—
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—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—41no—
384C4×C11—42no—
385C4×C11—42no—
386C4×C11—81no—
387C4×C11#52911yescharacteristic
388C4×C11#53811yescharacteristic
389C4×C11#55511yescharacteristic
390C4×C11#55911yescharacteristic
391Dic11—42no—
392Dic11—41no—
393Dic11—41no—
394Dic11—41no—
395Dic11—41no—
396Dic11—81no—
397Dic11—81no—
398C22×D4—21no—
399C22×D4—111no—
400C22×D4—221no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—221no—
403C23×C4C22×D1111yescharacteristic
404C2×D8—222no—
405C2×D8—441no—
406C2×D8—441no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411#125—222no—
412#125—441no—
413#121—22no—
414#121—41no—
415#121—222no—
416#121—222no—
417C4×D4—222no—
418C4×D4—441no—
419#117—22no—
420#117—41no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
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—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—221no—
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⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C42—21no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—221no—
447C2×C42—221no—
448#107—222no—
449C4⋊C8—441no—
450#102—22no—
451#102—41no—
452#102—222no—
453#102—222no—
454#102—222no—
455#102—441no—
456C22⋊C8—41no—
457C22⋊C8—441no—
458#97—441no—
459#95—111no—
460#95—111no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465C2×C11—81no—
466C2×C11—161no—
467C2×C11#245911yescharacteristic
468C2×C11#311111yescharacteristic
469C2×C11#312211yescharacteristic
470C2×C11#330911yescharacteristic
471C2×C11#330911yescharacteristic
472C2×C11#331911yescharacteristic
473C2×C11#332211yescharacteristic
474D11—82no—
475C24—21no—
476C24—221no—
477C24D4×D1111yescharacteristic
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—81no—
487C2×D4—112no—
488C2×D4—224no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—881no—
495C2×D4—881no—
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—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—881no—
515C22×C4D4×D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517D8—444no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
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—112no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—442no—
541C4⋊C4—442no—
542C4⋊C4—881no—
543C4⋊C4#433912yes—
544C4⋊C4#434112yes—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—224no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—441no—
551C22⋊C4—441no—
552C22⋊C4—442no—
553C22⋊C4—881no—
554C22⋊C4—881no—
555C22⋊C4—881no—
556C22⋊C4—881no—
557C22⋊C4—881no—
558C42—42no—
559C42—221no—
560C42—221no—
561C42—221no—
562C42—221no—
563C42—881no—
564C42—881no—
565C11#2674711yescharacteristic, complemented, Sylow
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—222no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23C2×D4×D1111yescharacteristic
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—84no—
593D4—222no—
594D4—222no—
595D4—441no—
596D4—441no—
597D4—884no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
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—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—222no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—884no—
636C2×C4C2×#433911yescharacteristic
637C2×C4C2×#434111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4#6703711yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C8—41no—
643C8—41no—
644C8—441no—
645C8—441no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22—881no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22#1062302111yescharacteristic
668C22#1062312211yescharacteristic
669C22#1062318711yescharacteristic
670C22#1062329911yescharacteristic
671C22#1062330011yescharacteristic
672C22#1062330411yescharacteristic
673C22#1062330511yescharacteristic
674C4—41no—
675C4—42no—
676C4—42no—
677C4—81no—
678C4—441no—
679C4—441no—
680C4—442no—
681C4—441no—
682C4—441no—
683C4—881no—
684C4—881no—
685C4#1062308811yescharacteristic
686C4#1062309011yescharacteristic
687C4#1062314411yescharacteristic
688C4#1062314711yescharacteristic
689C2—81no—
690C2—161no—
691C2—882no—
692C2#1307255211yescharacteristic
693C2#1307872011yescharacteristic
694C2#1307885511yescharacteristic
695C2#1308061811yescharacteristic
696C2#1308062611yescharacteristic
697C2#1308077311yescharacteristic
698C2#1308081011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenter#1875D11
hypocenterC11#26747
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. #13072970C2semidirect
2. #13071654C2semidirect
3. #13069925C2semidirect
4. #13069799C2semidirect
5. #13069761C2semidirect
7. #13069572C2semidirect
8. #13069310C2semidirect
9. #13069238C2semidirect
10. #13069232C2semidirect
11. #13069186C2semidirect
12. #13068961C2semidirect
13. #13068711C2semidirect
14. #13068440C2semidirect
15. C11×#1875C2semidirect
229. #1875D11semidirect
565. C11#26747semidirect

Maximal subgroups

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

subgroupindex
#130729702
#130716542
#130699252
#130697992
#130697612
#130696122
#130695722
#130693102
#130692382
#130692322
#130691862
#130689612
#130687112
#130684402
C11×#18752
#2674711