Finite Group Databasebeta

← #14814518

Subgroups — #14814518

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072037C211yesmaximal, characteristic
2#13071567C211yesmaximal, characteristic, complemented
3#13070173C211yesmaximal, characteristic, complemented
4#13070054C211yesmaximal, characteristic, complemented
5#13069797C211yesmaximal, characteristic, complemented
6#13069240C211yesmaximal, characteristic, complemented
7#13069209C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic, complemented
9#13068935C211yesmaximal, characteristic, complemented
10#13068935C211yesmaximal, characteristic, complemented
11#13068907C211yesmaximal, characteristic, complemented
12#13068818C211yesmaximal, characteristic, complemented
13#13068709C211yesmaximal, characteristic, complemented
14#13068331C211yesmaximal, characteristic, complemented
15C11×#2071C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33#10622603—21no—
34#10622603—21no—
35#10622601—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39C4⋊C4×Dic11—21no—
40C2×#66872C2211yescharacteristic
41#10622573—21no—
42#10622572—21no—
43#10622570—21no—
44#10622564—21no—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×D44D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66991—22no—
78#66991—22no—
79#66991—22no—
80#66991—41no—
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)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—22no—
102C2×C8×D11—41no—
103C2×C8×D11—41no—
104#66945—22no—
105#66945—22no—
106#66945—22no—
107#66945—41no—
108#66945—41no—
109#66945—41no—
110C4×D44—22no—
111C4×D44—22no—
112C11×#102—41no—
113C11×#102—41no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121(C2×D11)⋊C8—22no—
122(C2×D11)⋊C8—41no—
123(C2×D11)⋊C8—41no—
124#66882—22no—
125#66872—41no—
126#26209—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D411yescharacteristic
129C23×D11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—42no—
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×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—41no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11#4112yes—
168C2×C4×D11#4112yes—
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—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—81no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—81no—
185C42×C11—21no—
186C42×C11—21no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
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—
197C4⋊Dic11—22no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11#4112yes—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—81no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C8×D11—44no—
218#2414—111no—
219#2354—111no—
220#2099—111no—
221#2077—111no—
222#2071D1111yescharacteristic, complemented
223#2033—111no—
224#1926—111no—
225#1921—111no—
226#1893—111no—
227#1875—111no—
228#1875—111no—
229#1869—111no—
230#1854—111no—
231#1825—111no—
232#1735—111no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C22×D411yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11#12312yes—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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#13512yes—
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C22⋊D11—84no—
281C22⋊D11—84no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—21no—
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—
299C2×Dic11#12312yes—
300D44—44no—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—41no—
306C4×D11—41no—
307C4×D11—41no—
308C4×D11—41no—
309C8×C11—41no—
310C8×C11—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C23×C8—111no—
314C2×#121—111no—
315C2×#121—111no—
316C2×C4×D4—111no—
317C2×#117—111no—
318C2×#117—111no—
319C2×#117—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102C2×D1111yescharacteristic
325C2×#102C2×D1111yescharacteristic
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329#394—221no—
330#392—221no—
331#390—221no—
332#390—221no—
333#390C2×D1111yescharacteristic
334#389—111no—
335#388—221no—
336#388—221no—
337#388—221no—
338#384C2×D1111yescharacteristic
339#380—111no—
340#380—111no—
341#380—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—221no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354#336—111no—
355#336C2×D1111yescharacteristic
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11C2×#12311yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11C2×#13511yescharacteristic
367C22×C11#57511yescharacteristic
368C22×C11#57611yescharacteristic
369C22×C11#57711yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C4×C11—22no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11#52911yescharacteristic
390C4×C11#53811yescharacteristic
391C4×C11#55311yescharacteristic
392C4×C11#55311yescharacteristic
393Dic11—22no—
394Dic11—41no—
395Dic11—42no—
396Dic11—42no—
397Dic11—81no—
398Dic11—81no—
399C22×D4—111no—
400C22×D4—221no—
401C22×D4—221no—
402C22×D4C22×D1111yescharacteristic
403C23×C4—111no—
404C23×C4—111no—
405C22×C8—111no—
406C22×C8—111no—
407C22×C8—222no—
408C22×C8—441no—
409C22×C8—441no—
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412#121—222no—
413#121—222no—
414#121—222no—
415#121—441no—
416C4×D4—222no—
417C4×D4—222no—
418#117—222no—
419#117—222no—
420#117—222no—
421#117—441no—
422#117—441no—
423#117—441no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—111no—
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⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C42—221no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452#107—222no—
453#106—441no—
454#102—41no—
455#102—41no—
456#102—222no—
457#102—441no—
458C22⋊C8—222no—
459C22⋊C8—441no—
460C22⋊C8—441no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11—161no—
467C2×C11#244411yescharacteristic
468C2×C11#309111yescharacteristic
469C2×C11#309611yescharacteristic
470C2×C11#330411yescharacteristic
471C2×C11#330511yescharacteristic
472C2×C11#330711yescharacteristic
473C2×C11#331911yescharacteristic
474D11—42no—
475D11—81no—
476C24—21no—
477C24—111no—
478C24—111no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—222no—
486C2×D4—222no—
487C2×D4—441no—
488C2×D4—442no—
489C2×D4—442no—
490C2×D4—442no—
491C2×D4—881no—
492C2×D4—881no—
493C2×D4—881no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—111no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—111no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4D4×D1111yescharacteristic
516C22×C4D4×D1111yescharacteristic
517C22×C4C23×D1111yescharacteristic
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—
530C2×C8—444no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—81no—
539C4⋊C4—112no—
540C4⋊C4—112no—
541C4⋊C4—222no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—881no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—881no—
559C22⋊C4—881no—
560C22⋊C4—881no—
561C42—21no—
562C42—21no—
563C42—442no—
564C42—442no—
565C42—442no—
566C42—442no—
567C11#2620911yescharacteristic, complemented, Sylow
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—112no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—221no—
588C23—221no—
589C23C2×D4×D1111yescharacteristic
590D4—41no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—444no—
595D4—884no—
596D4—884no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
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—112no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—221no—
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—441no—
636C2×C4—441no—
637C2×C4#6696512yes—
638C2×C4#6703711yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#6704211yescharacteristic
644C8—41no—
645C8—41no—
646C8—441no—
647C8—441no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—222no—
656C22—222no—
657C22—222no—
658C22—441no—
659C22—441no—
660C22—441no—
661C22—441no—
662C22—441no—
663C22—441no—
664C22—441no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22#1062314311yescharacteristic
670C22D11×#12311yescharacteristic
671C22#1062320711yescharacteristic
672C22C2×#6696511yescharacteristic
673C22#1062329311yescharacteristic
674C22#1062330511yescharacteristic
675C22#1062330811yescharacteristic
676C4—22no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—222no—
682C4—442no—
683C4—442no—
684C4—441no—
685C4—881no—
686C4—881no—
687C4#1062318811yescharacteristic
688C4#1062319211yescharacteristic
689C4#1062323711yescharacteristic
690C4#1062324011yescharacteristic
691C2—161no—
692C2—442no—
693C2—881no—
694C2#1307236911yescharacteristic
695C2#1307852411yescharacteristic
696C2#1307857311yescharacteristic
697C2#1308055411yescharacteristic
698C2#1308056911yescharacteristic
699C2#1308059911yescharacteristic
700C2#1308077111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2071C2
socleC23×C11C22×D4
prime radical#13072037C2
hypercenter#2071D11
hypocenterC11#26209
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
2. #13071567C2semidirect
3. #13070173C2semidirect
4. #13070054C2semidirect
5. #13069797C2semidirect
6. #13069240C2semidirect
7. #13069209C2semidirect
8. #13069041C2semidirect
9. #13068935C2semidirect
10. #13068935C2semidirect
11. #13068907C2semidirect
12. #13068818C2semidirect
13. #13068709C2semidirect
14. #13068331C2semidirect
15. C11×#2071C2semidirect
222. #2071D11semidirect
567. C11#26209semidirect

Maximal subgroups

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

subgroupindex
#130720372
#130715672
#130701732
#130700542
#130697972
#130692402
#130692092
#130690412
#130689352
#130689072
#130688182
#130687092
#130683312
C11×#20712
#2620911