Finite Group Databasebeta

← #14814359

Subgroups — #14814359

Order 2816.

844 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072034C211yesmaximal, characteristic
2#13070183C211yesmaximal, characteristic, complemented
3#13070052C211yesmaximal, characteristic, complemented
4#13070030C211yesmaximal, characteristic, complemented
5#13069798C211yesmaximal, characteristic, complemented
6#13069243C211yesmaximal, characteristic, complemented
7#13069187C211yesmaximal, characteristic, complemented
8#13069042C211yesmaximal, characteristic, complemented
9#13068938C211yesmaximal, characteristic, complemented
10#13068933C211yesmaximal, characteristic, complemented
11#13068909C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068706C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C11×#2352C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C11×#388—21no—
24C11×#387—21no—
25C11×#386—21no—
26C11×#382C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4—21no—
31#10622836—21no—
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622603—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622572—21no—
44#10622570—21no—
45#10622552C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C22⋊D11—21no—
65C22×D44C2311yescharacteristic
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88#66983—22no—
89#66983—22no—
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—
96#66979—22no—
97#66979—41no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—41no—
105C22×C11⋊C8—41no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120#66873—22no—
121#66873—41no—
122#66873—41no—
123#66873—41no—
124#66872—41no—
125#66871—22no—
126#26199—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—41no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
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—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11—81no—
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—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
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#4112yes—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—81no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11—81no—
191C22⋊Dic11—42no—
192C22⋊Dic11—81no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11#4112yes—
203Dic11⋊C4—81no—
204C4×Dic11—42no—
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—
217C2×C11⋊C8—44no—
218#2414—111no—
219#2352D1111yescharacteristic, complemented
220#2101—111no—
221#2077—111no—
222#2073—111no—
223#2033—111no—
224#1926—111no—
225#1918—111no—
226#1893—111no—
227#1875—111no—
228#1874—111no—
229#1869—111no—
230#1854—111no—
231#1824—111no—
232#1735—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11#12312yes—
246C23×C11#13512yes—
247C23×C11C22×D411yescharacteristic
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255D4×C11—44no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
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—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—84no—
288C2×C4×C11#12312yes—
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
295C22⋊D11—84no—
296C22⋊D11—84no—
297C2×Dic11—22no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306D44—41no—
307D44—41no—
308D44—41no—
309D44—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C23×C8—111no—
315C2×#121—111no—
316C2×#121—111no—
317C2×C4×D4C2×D1111yescharacteristic
318C2×#117—111no—
319C2×#117C2×D1111yescharacteristic
320C22×C4⋊C4C2×D1111yescharacteristic
321C2×#107—111no—
322C2×#106—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×C22⋊C8—111no—
330#394—221no—
331#392—221no—
332#390—111no—
333#390—221no—
334#389—111no—
335#388—21no—
336#388—221no—
337#387—21no—
338#386—21no—
339#382C2×D1111yescharacteristic
340#380—111no—
341#380C2×D1111yescharacteristic
342#380C2×D1111yescharacteristic
343C4×C4⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4—21no—
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#340—111no—
354#340—111no—
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11C2×#12311yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11C2×#13511yescharacteristic
375C22×C11#57511yescharacteristic
376C22×C11#57611yescharacteristic
377C22×C11#57711yescharacteristic
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C4×C11—22no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—42no—
390C4×C11—81no—
391C4×C11—81no—
392C4×C11—81no—
393C4×C11#52911yescharacteristic
394C4×C11#53811yescharacteristic
395C4×C11#55311yescharacteristic
396C4×C11#55311yescharacteristic
397Dic11—42no—
398Dic11—81no—
399Dic11—81no—
400C22×D4—111no—
401C22×D4—221no—
402C22×D4—221no—
403C22×D4C22⋊D1111yescharacteristic
404C23×C4—21no—
405C23×C4C22×D1111yescharacteristic
406C23×C4C22×D1111yescharacteristic
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—222no—
412C22×C8—441no—
413C22×C8—441no—
414#121—222no—
415#121—222no—
416#121—222no—
417#121—441no—
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—41no—
422#117—222no—
423#117—441no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22⋊D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4C22⋊D1111yescharacteristic
446C2×C22⋊C4C22⋊D1111yescharacteristic
447C2×C42—21no—
448C2×C42—21no—
449C2×C42—221no—
450C2×C42C22×D1111yescharacteristic
451#107—222no—
452#106—441no—
453#102—222no—
454#102—441no—
455#102—441no—
456#102—441no—
457C22⋊C8—222no—
458C22⋊C8—441no—
459C22⋊C8—441no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—221no—
466#95—221no—
467C2×C11—42no—
468C2×C11—42no—
469C2×C11#244411yescharacteristic
470C2×C11#309111yescharacteristic
471C2×C11#309611yescharacteristic
472C2×C11#329711yescharacteristic
473C2×C11#330111yescharacteristic
474C2×C11#331711yescharacteristic
475C2×C11#331911yescharacteristic
476D11—161no—
477C24—221no—
478C24C2×C22⋊D1111yescharacteristic
479C24C2×C22⋊D1111yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—442no—
490C2×D4—442no—
491C2×D4—442no—
492C2×D4—881no—
493C2×D4—881no—
494C2×D4—881no—
495C22×C4—21no—
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—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4#433912yes—
516C22×C4#433912yes—
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—444no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—112no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—881no—
551C4⋊C4#434112yes—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—81no—
567C42—442no—
568C11#2619911yescharacteristic, complemented, Sylow
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23#6698212yes—
589C23#6700312yes—
590C23C22×C22⋊D1111yescharacteristic
591D4—44no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—441no—
596D4—884no—
597D4—884no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
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—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4—222no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4#6698212yes—
640C2×C4C2×#433911yescharacteristic
641C2×C4C2×#433911yescharacteristic
642C2×C4C2×#434111yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4#41×D1111yescharacteristic
645C2×C4#6704211yescharacteristic
646C8—441no—
647C8—441no—
648C8—441no—
649C8—441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22—881no—
670C22—881no—
671C22C2×#6698211yescharacteristic
672C22#1062333711yescharacteristic
673C22C2×#6700311yescharacteristic
674C22#1062335311yescharacteristic
675C22#1062336011yescharacteristic
676C22#1062336611yescharacteristic
677C22#1062336811yescharacteristic
678C4—22no—
679C4—41no—
680C4—41no—
681C4—42no—
682C4—41no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4—442no—
687C4—881no—
688C4—881no—
689C4#1062306911yescharacteristic
690C4#1062307111yescharacteristic
691C4#1062309111yescharacteristic
692C4#1062309611yescharacteristic
693C2—42no—
694C2—42no—
695C2—1761no—
696C2#1307236011yescharacteristic
697C2#1307852911yescharacteristic
698C2#1307857411yescharacteristic
699C2#1308046011yescharacteristic
700C2#1308051811yescharacteristic
701C2#1308073611yescharacteristic
702C2#1308077211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2352C2
socleC23×C11C22×D4
prime radical#13072034C2
hypercenter#2352D11
hypocenterC11#26199
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13070183C2semidirect
3. #13070052C2semidirect
4. #13070030C2semidirect
5. #13069798C2semidirect
6. #13069243C2semidirect
7. #13069187C2semidirect
8. #13069042C2semidirect
9. #13068938C2semidirect
10. #13068933C2semidirect
11. #13068909C2semidirect
12. #13068813C2semidirect
13. #13068706C2semidirect
14. #13068332C2semidirect
15. C11×#2352C2semidirect
219. #2352D11semidirect
568. C11#26199semidirect

Maximal subgroups

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

subgroupindex
#130720342
#130701832
#130700522
#130700302
#130697982
#130692432
#130691872
#130690422
#130689382
#130689332
#130689092
#130688132
#130687062
#130683322
C11×#23522
#2619911