Finite Group Databasebeta

← #14822207

Subgroups — #14822207

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#13071652C211yesmaximal, characteristic, complemented
3#13069927C211yesmaximal, characteristic, complemented
4#13069799C211yesmaximal, characteristic, complemented
5#13069763C211yesmaximal, characteristic, complemented
6#13069614C211yesmaximal, characteristic
7#13069571C211yesmaximal, characteristic, complemented
8#13069313C211yesmaximal, characteristic, complemented
9#13069237C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13068963C211yesmaximal, characteristic, complemented
12#13068936C211yesmaximal, characteristic, complemented
13#13068712C211yesmaximal, characteristic, complemented
14#13068442C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×D88C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35#10622572—21no—
36#10622570—21no—
37#10622570—21no—
38#10622569—21no—
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622552C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622288—21no—
46#10622282—21no—
47#10622282—21no—
48#10622279—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75#66983—22no—
76#66983—22no—
77#66983—22no—
78#66983—41no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88#66979—22no—
89#66979—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×D88—22no—
103C2×D88—41no—
104C2×D88—41no—
105C4×D44—22no—
106C4×D44—41no—
107#66923—22no—
108#66923—41no—
109C11×C4⋊C8—41no—
110C11×C22⋊C8—41no—
111C11×C22⋊C8—41no—
112C11×#97—41no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119#66885—22no—
120#66885—22no—
121#66885—22no—
122#66885—22no—
123#66885—41no—
124#66885—41no—
125#66882—22no—
126#26747—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C23×D11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—42no—
145C2×C22⋊D11—81no—
146C2×C22⋊D11—81no—
147C2×C22⋊D11—81no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
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—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C22⋊Dic11—42no—
188C22⋊Dic11—81no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11#4112yes—
208C4⋊Dic11#4112yes—
209C4⋊Dic11#4112yes—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—81no—
213C4×Dic11—42no—
214C4×Dic11—81no—
215C4×Dic11—81no—
216D88—44no—
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#1924D1111yescharacteristic, complemented
227#1918—111no—
228#1879—111no—
229#1875—111no—
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×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
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×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C22⋊D11—84no—
280C22⋊D11—84no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299D44—22no—
300D44—22no—
301D44—41no—
302D44—41no—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307C4×D11—84no—
308C8×C11—41no—
309C8×C11—41no—
310C8×C11—41no—
311C8×C11—41no—
312C22×D8—111no—
313C2×#125—111no—
314C2×#121—111no—
315C2×#121—111no—
316C2×C4×D4—111no—
317C2×#117—111no—
318C2×#107—111no—
319C2×C4⋊C8C2×D1111yescharacteristic
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×C22⋊C8C2×D1111yescharacteristic
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×#97C2×D1111yescharacteristic
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—221no—
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#336C2×D1111yescharacteristic
354#336C2×D1111yescharacteristic
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×C11#54611yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57511yescharacteristic
367C22×C11#57611yescharacteristic
368C22×C11#57611yescharacteristic
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11#52911yescharacteristic
389C4×C11#53811yescharacteristic
390C4×C11#55511yescharacteristic
391C4×C11#55911yescharacteristic
392Dic11—42no—
393Dic11—42no—
394Dic11—42no—
395Dic11—81no—
396Dic11—81no—
397Dic11—81no—
398C22×D4—111no—
399C22×D4—111no—
400C22×D4—221no—
401C22×D4—221no—
402C23×C4—221no—
403C23×C4C22×D1111yescharacteristic
404C2×D8—222no—
405C2×D8—441no—
406C2×D8—441no—
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411#125—222no—
412#125—441no—
413#121—222no—
414#121—222no—
415#121—222no—
416#121—441no—
417C4×D4—222no—
418C4×D4—441no—
419#117—222no—
420#117—441no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
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⋊C4D4411yescharacteristic
442C2×C22⋊C4D4411yescharacteristic
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448#107—222no—
449C4⋊C8—41no—
450#102—222no—
451#102—222no—
452#102—222no—
453#102—222no—
454#102—441no—
455#102—441no—
456C22⋊C8—41no—
457C22⋊C8—41no—
458#97—41no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95D4411yescharacteristic
464#95D4411yescharacteristic
465C2×C11—81no—
466C2×C11#245911yescharacteristic
467C2×C11#311111yescharacteristic
468C2×C11#312211yescharacteristic
469C2×C11#330911yescharacteristic
470C2×C11#330911yescharacteristic
471C2×C11#331911yescharacteristic
472C2×C11#332211yescharacteristic
473D11—82no—
474D11—161no—
475C24—221no—
476C24—221no—
477C24C2×D4411yescharacteristic
478C2×D4—112no—
479C2×D4—224no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—442no—
492C2×D4—442no—
493C2×D4—881no—
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—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—881no—
511C22×C4C2×D4411yescharacteristic
512C22×C4C2×D4411yescharacteristic
513C22×C4C2×D4411yescharacteristic
514C22×C4C2×D4411yescharacteristic
515C22×C4C2×D4411yescharacteristic
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—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C4⋊C4—112no—
531C4⋊C4—112no—
532C4⋊C4—112no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—881no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—224no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—881no—
554C22⋊C4—881no—
555C22⋊C4—881no—
556C22⋊C4—881no—
557C22⋊C4—881no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—442no—
563C42—881no—
564C42—881no—
565C11#2674711yescharacteristic, complemented, Sylow
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—222no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23C22×D4411yescharacteristic
588D4—222no—
589D4—222no—
590D4—441no—
591D4—441no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—441no—
596D4—884no—
597D4—884no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
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—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
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×C4#6703711yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C8—41no—
643C8—41no—
644C8—41no—
645C8—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—442no—
654C22—442no—
655C22—442no—
656C22—881no—
657C22—881no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22—881no—
662C22—881no—
663C22—881no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22#1062305511yescharacteristic
668C22#1062308511yescharacteristic
669C22#1062308511yescharacteristic
670C22#1062327911yescharacteristic
671C22#1062327911yescharacteristic
672C22#1062328311yescharacteristic
673C22#1062328311yescharacteristic
674C4—41no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—442no—
680C4—442no—
681C4—442no—
682C4—881no—
683C4—881no—
684C4—881no—
685C4#1062314411yescharacteristic
686C4#1062319511yescharacteristic
687C4#1062320111yescharacteristic
688C4#1062323711yescharacteristic
689C2—81no—
690C2—882no—
691C2—1761no—
692C2#1307255111yescharacteristic
693C2#1307872711yescharacteristic
694C2#1307886011yescharacteristic
695C2#1308062411yescharacteristic
696C2#1308062411yescharacteristic
697C2#1308077411yescharacteristic
698C2#1308081911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1924C2
socleC23×C11C22×D4
prime radical#13069614C2
hypercenter#1924D11
hypocenterC11#26747
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. #13072968C2semidirect
2. #13071652C2semidirect
3. #13069927C2semidirect
4. #13069799C2semidirect
5. #13069763C2semidirect
7. #13069571C2semidirect
8. #13069313C2semidirect
9. #13069237C2semidirect
10. #13069188C2semidirect
11. #13068963C2semidirect
12. #13068936C2semidirect
13. #13068712C2semidirect
14. #13068442C2semidirect
15. C11×#1924C2semidirect
226. #1924D11semidirect
565. C11#26747semidirect

Maximal subgroups

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

subgroupindex
#130729682
#130716522
#130699272
#130697992
#130697632
#130696142
#130695712
#130693132
#130692372
#130691882
#130689632
#130689362
#130687122
#130684422
C11×#19242
#2674711