Finite Group Databasebeta

← #14810883

Subgroups — #14810883

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622700C211yesmaximal, characteristic, complemented
2C2×#10622417C211yesmaximal, characteristic
3#13072303C211yesmaximal, characteristic, complemented
4#13071445C211yesmaximal, characteristic
5#13070166C211yesmaximal, characteristic, complemented
6#13070011C211yesmaximal, characteristic, complemented
7#13070007C211yesmaximal, characteristic, complemented
8#13068880C211yesmaximal, characteristic, complemented
9#13068864C211yesmaximal, characteristic, complemented
10#13068816C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068644C211yesmaximal, characteristic, complemented
13#13068625C211yesmaximal, characteristic, complemented
14#13068555C211yesmaximal, characteristic
15C11×#2024C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#391C2211yescharacteristic
25#10622844—21no—
26#10622843—21no—
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622700—24no—
36#10622607—21no—
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622591—21no—
41#10622590C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622417—24no—
51#10622278—21no—
52#10622278—21no—
53#10622277—21no—
54D11×#95—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C2×#4343—22no—
64C2×#4343—22no—
65C2×#4343—22no—
66C2×#4343—41no—
67C2×#4343—41no—
68C2×#4343Q814yescomplemented
69C22×D44—21no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—22no—
78C11×C4⋊Q8—41no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102C2×C8×D11—41no—
103#66946—22no—
104#66946—41no—
105#66945—22no—
106#66945—41no—
107C4×D44—22no—
108C4×D44—41no—
109C11×#103—22no—
110C11×#103—41no—
111C11×#95—21no—
112C11×#95—21no—
113#66899—22no—
114#66899—41no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66885—22no—
126#66885—22no—
127(C2×D11)⋊C8—22no—
128#66881—41no—
129Dic11⋊C8—41no—
130#66873—22no—
131#66873D414yes—
132#66871—22no—
133#66871—22no—
134#66871—41no—
135C4⋊(C11⋊C8)—22no—
136#25954—111nomaximal, Sylow
137C23×D11—21no—
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—42no—
145C2×Q8×C11—42no—
146C2×Q8×C11—81no—
147C2×Q8×C11C2×Q812yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161#4343—28no—
162#4343—44no—
163#4343—44no—
164#4343—44no—
165C2×D44—24no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—42no—
170C2×D44—42no—
171C2×D44C2×D412yes—
172C2×D44C2×Q812yes—
173C2×D44#4112yes—
174C2×C4×D11—24no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—42no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×C4×D11—42no—
184C2×C4×D11—42no—
185C2×C4×D11—81no—
186C2×C4×D11—81no—
187C2×C4×D11C2×Q812yes—
188C2×C4×D11#4112yes—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4C2×D412yes—
202C42×C11—21no—
203C42×C11—21no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—42no—
207(C2×D11)⋊C4—42no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—81no—
210(C2×D11)⋊C4—81no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—81no—
218Dic11⋊C4—42no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8C2×D412yes—
228C8×D11—44no—
229C2×#474—111no—
230C2×#416—111no—
231#2439—111no—
232#2339—111no—
233#2097—111no—
234#2068—111no—
235#2068—111no—
236#2024D1111yescharacteristic, complemented
237#1864—111no—
238#1862—111no—
239#1854—111no—
240#1850—111no—
241#1808—111no—
242#1804—111no—
243#1788—111no—
244C23×C11C22×D411yescharacteristic
245C22×D11—22no—
246C22×D11—21no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11C22⋊Q812yes—
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—84no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—41no—
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#13512yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×Q811yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11C22⋊Q812yes—
306D44—22no—
307D44—22no—
308D44—22no—
309D44—48no—
310D44C22⋊Q814yes—
311C4×D11—22no—
312C4×D11—22no—
313C4×D11—22no—
314C4×D11—22no—
315C4×D11—48no—
316C4×D11—84no—
317C4×D11—84no—
318C8×C11—41no—
319C8×C11—41no—
320C11⋊C8—22no—
321C11⋊C8—41no—
322C22×#41—111no—
323C23×C8—111no—
324C2×C4⋊Q8C2×D1111yescharacteristic
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×#117—111no—
328#474—224no—
329C2×#107—111no—
330C2×#107—111no—
331C2×#107—111no—
332C2×#106—111no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335#416—224no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103C2×D1111yescharacteristic
339C2×#103C2×D1111yescharacteristic
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#102—111no—
344C2×C22⋊C8—111no—
345#396—221no—
346#393—221no—
347#391—111no—
348#391—221no—
349#391C2×D1111yescharacteristic
350#389—111no—
351#389—111no—
352#387—221no—
353#386—221no—
354#386—221no—
355#382—111no—
356#381—221no—
357#380—111no—
358#380—111no—
359C4×C22⋊C4—111no—
360C2×#95—221no—
361#340—111no—
362#340—111no—
363#340C2×D1111yescharacteristic
364#340C2×D1111yescharacteristic
365#336—111no—
366#336C2×D1111yescharacteristic
367C22×C11C2×C22⋊Q811yescharacteristic
368C22×C11D4211yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11C2×#13511yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57611yescharacteristic
373C22×C11#57811yescharacteristic
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—24no—
377C2×D11—22no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—41no—
381C2×D11—42no—
382C2×D11—41no—
383C2×D11—42no—
384C2×D11—41no—
385C2×D11—42no—
386C2×D11—41no—
387C2×D11—42no—
388C4×C11—22no—
389C4×C11—42no—
390C4×C11—41no—
391C4×C11—42no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11C2×C22⋊Q811yescharacteristic
395C4×C11#54311yescharacteristic
396C4×C11#54611yescharacteristic
397C4×C11#55111yescharacteristic
398Dic11—22no—
399Dic11—41no—
400Dic11—41no—
401Dic11—81no—
402Dic11—81no—
403Dic11—81no—
404C2×#41—114no—
405C2×#41—222no—
406C2×#41—222no—
407C2×#41—222no—
408C2×#41—441no—
409C2×#41—441no—
410C22×Q8—21no—
411C22×Q8C22×D1111yescharacteristic
412C22×D4—111no—
413C22×D4—221no—
414C23×C4—111no—
415C23×C4—221no—
416C23×C4—221no—
417C23×C4—221no—
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—222no—
421C22×C8—222no—
422C22×C8—441no—
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C4⋊Q8—22no—
426C4⋊Q8—41no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—441no—
430C4×D4—441no—
431#117—222no—
432#117—441no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—111no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C42—111no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452#107—222no—
453#107—222no—
454#107—441no—
455#106—441no—
456C4⋊C8—222no—
457C4⋊C8—441no—
458#103—22no—
459#103—41no—
460#103—222no—
461#103—441no—
462#102—114no—
463#102—222no—
464#102—222no—
465#102—222no—
466C22⋊C8—222no—
467#95—21no—
468#95—21no—
469#95—111no—
470#95—111no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479C2×C11#243711yescharacteristic
480C2×C11#307611yescharacteristic
481C2×C11#308311yescharacteristic
482C2×C11#326911yescharacteristic
483C2×C11#328011yescharacteristic
484C2×C11#330211yescharacteristic
485C2×C11#331911yescharacteristic
486D11—42no—
487D11—44no—
488C24—111no—
489C24—221no—
490#41—228no—
491#41—444no—
492#41—444no—
493#41—444no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—81no—
502C2×Q8Q8×D1112yes—
503C2×D4—112no—
504C2×D4—112no—
505C2×D4—112no—
506C2×D4—224no—
507C2×D4—221no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—442no—
511C2×D4—442no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—111no—
517C22×C4—112no—
518C22×C4—112no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—224no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—442no—
535C22×C4—881no—
536C22×C4—881no—
537C22×C4D4×D1111yescharacteristic
538C22×C4D4×D1111yescharacteristic
539C22×C4C23×D1111yescharacteristic
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—112no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—444no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—442no—
566C4⋊C4—881no—
567C4⋊C4D4×D1112yes—
568C22⋊C4—222no—
569C22⋊C4—441no—
570C22⋊C4—442no—
571C22⋊C4—442no—
572C22⋊C4—442no—
573C22⋊C4—881no—
574C22⋊C4—881no—
575C42—21no—
576C42—21no—
577C42—221no—
578C42—221no—
579C42—442no—
580C11#2595411yescharacteristic, complemented, Sylow
581C23—112no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—222no—
588C23—222no—
589C23—222no—
590C23—221no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23—441no—
595C23C2×D4×D1111yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600Q8—84no—
601D4—114no—
602D4—222no—
603D4—222no—
604D4—222no—
605D4—448no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—41no—
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—112no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—448no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—884no—
647C2×C4—884no—
648C2×C4#6696912yes—
649C2×C4C2×D4×D1111yescharacteristic
650C2×C4#6703711yescharacteristic
651C2×C4C2×Q8×D1111yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C2×C4#6704211yescharacteristic
655C8—41no—
656C8—41no—
657C8—222no—
658C8—441no—
659C22—222no—
660C22—222no—
661C22—224no—
662C22—222no—
663C22—441no—
664C22—442no—
665C22—442no—
666C22—442no—
667C22—442no—
668C22—441no—
669C22—441no—
670C22—442no—
671C22—442no—
672C22—441no—
673C22#1062312111yescharacteristic
674C22D11×C22⋊Q811yescharacteristic
675C22#1062320711yescharacteristic
676C22C2×#6696911yescharacteristic
677C22#1062329711yescharacteristic
678C22#1062330511yescharacteristic
679C22#1062330811yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—42no—
684C4—81no—
685C4—81no—
686C4—222no—
687C4—441no—
688C4—441no—
689C4—881no—
690C4—881no—
691C4—881no—
692C4D11×C22⋊Q811yescharacteristic
693C4#1062316511yescharacteristic
694C4#1062320711yescharacteristic
695C4#1062321011yescharacteristic
696C2—442no—
697C2—444no—
698C2#1307227611yescharacteristic
699C2#1307839911yescharacteristic
700C2#1307846411yescharacteristic
701C2#1308017411yescharacteristic
702C2#1308029411yescharacteristic
703C2#1308053211yescharacteristic
704C2#1308077111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2024C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenter#2024D11
hypocenterC11#25954
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
3. #13072303C2semidirect
5. #13070166C2semidirect
6. #13070011C2semidirect
7. #13070007C2semidirect
8. #13068880C2semidirect
9. #13068864C2semidirect
10. #13068816C2semidirect
11. #13068795C2semidirect
12. #13068644C2semidirect
13. #13068625C2semidirect
15. C11×#2024C2semidirect
68. C2×#4343Q8semidirect
236. #2024D11semidirect
580. C11#25954semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×#106224172
#130723032
#130714452
#130701662
#130700112
#130700072
#130688802
#130688642
#130688162
#130687952
#130686442
#130686252
#130685552
C11×#20242
#2595411