Finite Group Databasebeta

← #14770946

Subgroups — #14770946

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622385C211yesmaximal, characteristic
2#13071500C211yesmaximal, characteristic, complemented
3#13071455C211yesmaximal, characteristic
4#13069301C211yesmaximal, characteristic, complemented
5#13069239C211yesmaximal, characteristic, complemented
6#13069233C211yesmaximal, characteristic, complemented
7#13068871C211yesmaximal, characteristic, complemented
8#13068869C211yesmaximal, characteristic, complemented
9#13068710C211yesmaximal, characteristic, complemented
10#13068644C211yesmaximal, characteristic, complemented
11#13068553C211yesmaximal, characteristic
12C4×#66880C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
15C11×#1934C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622603—21no—
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622590—21no—
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622570—21no—
44#10622570—21no—
45#10622555—21no—
46C22⋊C4×Dic11—21no—
47C4×(C2×D11)⋊C4C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622385C418yescomplemented
50#10622283—21no—
51#10622261—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C2×#4341—22no—
64C2×#4341—22no—
65C2×#4341—22no—
66C2×#4341—41no—
67C2×#4341—41no—
68C2×#4341C2×C414yes—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—41no—
102C2×C8×D11—41no—
103C2×C8×D11C2×C414yes—
104#66945—22no—
105#66945C2×C414yes—
106#66940—22no—
107#66940—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×#102—41no—
111C11×#102C2×C414yes—
112C4×C8×C11—41no—
113C11×#95—21no—
114#66896—41no—
115#66896C2×C414yes—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123(C2×D11)⋊C8—22no—
124#66880—22no—
125#66880C2×C414yes—
126C8×Dic11—41no—
127#66874—22no—
128#66874C2×C414yes—
129#66871—41no—
130#66871—41no—
131#22573—111nomaximal, Sylow
132C24×C11—21no—
133C23×D11C2×D411yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C22×C412yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—24no—
147C2×C22⋊D11—42no—
148C2×C22⋊D11—42no—
149C22×Dic11—24no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159#4341—28no—
160#4341—44no—
161#4341—44no—
162#4341—44no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11C22×C412yes—
168C2×C4×D11#4112yes—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22C22×C412yes—
173C2×Dic22#4112yes—
174C2×Dic22#4112yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—81no—
187C11×C4⋊C4C22×C412yes—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—81no—
190C42×C11—21no—
191C42×C11—21no—
192C22⋊Dic11—42no—
193C22⋊Dic11—81no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—81no—
205C4⋊Dic11C22×C412yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—24no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C8×D11—44no—
222C2×#416—111no—
223#2346—111no—
224#2341—111no—
225#1934—111no—
226#1934D1111yescharacteristic, complemented
227#1925—111no—
228#1925—111no—
229#1863—111no—
230#1863—111no—
231#1825—111no—
232#1808—111no—
233#1788—111no—
234C4×#103—111no—
235C4×#103—111no—
236C8×C22⋊C4—111no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11C4×D412yes—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—41no—
255D4×C11—41no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
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#13512yes—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C22⋊D11—48no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—48no—
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×Dic11C4×D412yes—
299C2×Dic11#13512yes—
300C4×D11—22no—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—22no—
304Dic22—22no—
305Dic22—22no—
306Dic22—22no—
307Dic22#11714yes—
308C8×C11—22no—
309C8×C11—41no—
310C11⋊C8—22no—
311C11⋊C8—41no—
312C22×#41—111no—
313C23×C8—111no—
314C2×C4×Q8—111no—
315C2×C4×Q8—111no—
316C2×#117—111no—
317C2×#107—111no—
318C2×#107—111no—
319#416—118no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102C2×D1111yescharacteristic
327C2×#102C2×D1111yescharacteristic
328C2×C22⋊C8—111no—
329C2×C4×C8—111no—
330C2×C4×C8C2×D1111yescharacteristic
331#390—111no—
332#390—221no—
333#390—221no—
334#390C2×D1111yescharacteristic
335#389—111no—
336#389C2×D1111yescharacteristic
337#388—221no—
338#388—221no—
339#382—221no—
340#380—111no—
341#380—111no—
342#380—221no—
343C4×C4⋊C4—111no—
344C4×C4⋊C4—111no—
345C4×C22⋊C4—111no—
346C4×C22⋊C4—221no—
347#376—221no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354#336—111no—
355#336—111no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11C2×C4×D411yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#54611yescharacteristic
366C22×C11C2×#13511yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11#57611yescharacteristic
369C22×C11#57811yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C4×C11—22no—
378C4×C11—42no—
379C4×C11—41no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11C2×#11711yescharacteristic
383C4×C11#51811yescharacteristic
384C4×C11#55111yescharacteristic
385C4×C11#55111yescharacteristic
386Dic11—24no—
387Dic11—22no—
388Dic11—22no—
389Dic11—42no—
390Dic11—41no—
391Dic11—81no—
392Dic11—81no—
393C2×#41—114no—
394C2×#41—222no—
395C2×#41—222no—
396C2×#41—222no—
397C2×#41—441no—
398C2×#41—441no—
399C22×Q8—111no—
400C22×D4—221no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—111no—
403C23×C4—221no—
404C22×C8—111no—
405C22×C8—114no—
406C22×C8—111no—
407C22×C8—441no—
408C22×C8—441no—
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411C4×Q8—222no—
412C4×Q8—222no—
413C4×Q8—441no—
414C4×Q8—441no—
415#117—114no—
416#117—222no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—111no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#107—441no—
444#107—441no—
445#103—114no—
446#103—114no—
447#103—222no—
448#103—222no—
449#102—41no—
450#102—114no—
451#102—441no—
452#102C4×D1114yes—
453C22⋊C8—222no—
454C4×C8—41no—
455C4×C8—441no—
456#95—21no—
457#95—111no—
458#95—111no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464C2×C11—82no—
465C2×C11#234211yescharacteristic
466C2×C11C4×#13511yescharacteristic
467C2×C11#295111yescharacteristic
468C2×C11#330011yescharacteristic
469C2×C11#330011yescharacteristic
470C2×C11#330511yescharacteristic
471C2×C11#330511yescharacteristic
472D11—42no—
473C24—21no—
474C24—111no—
475#41—228no—
476#41—444no—
477#41—444no—
478#41—444no—
479C2×Q8—112no—
480C2×Q8—112no—
481C2×Q8—112no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—224no—
491C2×D4—442no—
492C2×D4—442no—
493C2×D4C2×C4×D1112yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—111no—
502C22×C4—224no—
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—442no—
512C22×C4—442no—
513C22×C4D4×D1111yescharacteristic
514C22×C4D4×D1111yescharacteristic
515C22×C4C23×D1111yescharacteristic
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—112no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—444no—
528C2×C8C2×C4×D1112yes—
529C4⋊C4—21no—
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—881no—
544C4⋊C4C2×C4×D1112yes—
545C22⋊C4—42no—
546C22⋊C4—81no—
547C22⋊C4—222no—
548C22⋊C4—224no—
549C22⋊C4—222no—
550C22⋊C4—442no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—21no—
555C42—21no—
556C42—224no—
557C42—221no—
558C42—221no—
559C42—442no—
560C42—442no—
561C42—442no—
562C42—442no—
563C11#2257311yescharacteristic, complemented, Sylow
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—112no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23C2×D4×D1111yescharacteristic
579Q8—114no—
580Q8—222no—
581Q8—222no—
582Q8—222no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4—448no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—221no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—221no—
619C2×C4—448no—
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#6696912yes—
629C2×C4C22×C4×D1111yescharacteristic
630C2×C4#6703711yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C2×C4#41×D1111yescharacteristic
634C2×C4#6704211yescharacteristic
635C8—22no—
636C8—41no—
637C8—222no—
638C8—441no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—441no—
650C22—441no—
651C22—441no—
652C22—441no—
653C22C4×D4×D1111yescharacteristic
654C22#1062314111yescharacteristic
655C22#1062320711yescharacteristic
656C22#1062328811yescharacteristic
657C22C2×#6696911yescharacteristic
658C22D11×#13511yescharacteristic
659C22#1062330211yescharacteristic
660C4—22no—
661C4—42no—
662C4—41no—
663C4—81no—
664C4—81no—
665C4—222no—
666C4—224no—
667C4—222no—
668C4—442no—
669C4—441no—
670C4—881no—
671C4—881no—
672C4D11×#11711yescharacteristic
673C4#1062307611yescharacteristic
674C4#1062319011yescharacteristic
675C4#1062323611yescharacteristic
676C2—82no—
677C2—442no—
678C2#1307146411yescharacteristic
679C2C4×#6696911yescharacteristic
680C2#1307748611yescharacteristic
681C2#1308050211yescharacteristic
682C2#1308050911yescharacteristic
683C2#1308056111yescharacteristic
684C2#1308056511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1934C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC22×C4×C11C24
hypercenter#1934D11
hypocenterC11#22573
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. #13071500C2semidirect
4. #13069301C2semidirect
5. #13069239C2semidirect
6. #13069233C2semidirect
7. #13068871C2semidirect
8. #13068869C2semidirect
9. #13068710C2semidirect
10. #13068644C2semidirect
12. C4×#66880C2semidirect
13. #13068435C2semidirect
14. C8×(C2×D11)⋊C4C2semidirect
15. C11×#1934C2semidirect
49. #10622385C4semidirect
226. #1934D11semidirect
563. C11#22573semidirect

Maximal subgroups

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

subgroupindex
C2×#106223852
#130715002
#130714552
#130693012
#130692392
#130692332
#130688712
#130688692
#130687102
#130686442
#130685532
C4×#668802
#130684352
C8×(C2×D11)⋊C42
C11×#19342
#2257311