Finite Group Databasebeta

← #14813701

Subgroups — #14813701

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622658C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic, complemented
3#13071565C211yesmaximal, characteristic
4#13070159C211yesmaximal, characteristic, complemented
5#13070092C211yesmaximal, characteristic, complemented
6#13070052C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069254C211yesmaximal, characteristic, complemented
9#13069205C211yesmaximal, characteristic, complemented
10#13069050C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic, complemented
12#13068914C211yesmaximal, characteristic
13#13068813C211yesmaximal, characteristic, complemented
14#13068809C211yesmaximal, characteristic, complemented
15C11×#2417C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#398—21no—
24C11×#396—21no—
25C11×#391C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#386—21no—
28C11×#380—21no—
29C11×#380C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622834—21no—
35#10622825C2211yescharacteristic
36#10622825C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622658—24no—
41C4⋊C4×Dic11—21no—
42#10622577—24no—
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622564—21no—
50#10622564—21no—
51#10622548C2211yescharacteristic
52C4×C4⋊Dic11C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—41no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—41no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92#66979—22no—
93#66979—22no—
94#66979—41no—
95#66979—41no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×#4318—22no—
106C2×#4318—22no—
107C2×#4318—22no—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116#66899—22no—
117#66899—22no—
118#66899—22no—
119#66899—41no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)—22no—
126#66872—22no—
127#66872—22no—
128#66872—22no—
129#66872—41no—
130#66871—22no—
131#66871D414yescomplemented
132#26155—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—41no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—81no—
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4112yes—
166C22×C4×C11#4112yes—
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—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—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4C2×D412yes—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—81no—
188C42×C11—21no—
189C42×C11—21no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—81no—
193C22⋊Dic11—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—81no—
203C4⋊Dic11C2×D412yes—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207#4318—28no—
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—21no—
218C2×C11⋊C8C2×D412yes—
219C2×C11⋊C8#4112yes—
220C2×#485—111no—
221C2×#428—111no—
222#2417D1111yescharacteristic
223#2354—111no—
224#2096—111no—
225#2084—111no—
226#2077—111no—
227#2035—111no—
228#1928—111no—
229#1921—111no—
230#1894—111no—
231#1873—111no—
232#1870—111no—
233#1854—111no—
234#1853—111no—
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—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11#12312yes—
249C23×C11C22×D411yescharacteristic
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254D4×C11—44no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
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—41no—
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—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—84no—
286C2×C4×C11#12312yes—
287C2×C4×C11#13712yes—
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C112−1+411yescharacteristic
294C2×Dic11—22no—
295C2×Dic11—41no—
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×Dic11—41no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C22×M16—111no—
311C2×C22⋊Q8C2×D1111yescharacteristic
312C2×C22⋊Q8C2×D1111yescharacteristic
313C2×C4×D4C2×D1111yescharacteristic
314C2×#117—111no—
315C2×#117—111no—
316C22×C4⋊C4C2×D1111yescharacteristic
317#485—224no—
318#428—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#106—111no—
324C2×#106—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×C22⋊C8—111no—
330C2×C22⋊C8—111no—
331C2×C22⋊C8—111no—
332#398—21no—
333#396—21no—
334#391C2×D1111yescharacteristic
335#390—221no—
336#389C2×D1111yescharacteristic
337#388—221no—
338#388—221no—
339#386—21no—
340#384—111no—
341#380—21no—
342#380—111no—
343#380—111no—
344#380C2×D1111yescharacteristic
345C4×C4⋊C4—111no—
346C4×C4⋊C4—221no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336—111no—
354#336—111no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11C2×#12311yescharacteristic
370C22×C11D4211yescharacteristic
371C22×C11#54711yescharacteristic
372C22×C11C2×#13711yescharacteristic
373C22×C11#57511yescharacteristic
374C22×C11#57711yescharacteristic
375C22×C11#57711yescharacteristic
376C4×C11—22no—
377C4×C11—22no—
378C4×C11—41no—
379C4×C11—41no—
380C4×C11—42no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11#52511yescharacteristic
385C4×C11#53911yescharacteristic
386C4×C11#54811yescharacteristic
387C4×C11#55311yescharacteristic
388Dic11—42no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392C22×Q8C22×D1111yescharacteristic
393C22×D4C22⋊D1111yescharacteristic
394C23×C4—21no—
395C23×C4C22×D1111yescharacteristic
396C23×C4C22×D1111yescharacteristic
397C2×M16—222no—
398C2×M16—222no—
399C2×M16—222no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—111no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—41no—
408C4×D4—22no—
409C4×D4—22no—
410#117—222no—
411#117—222no—
412#117—441no—
413#117—441no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4C22⋊D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4C22⋊D1111yescharacteristic
438C2×C22⋊C4C22⋊D1111yescharacteristic
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#107—114no—
444#107—222no—
445#106—222no—
446#106—222no—
447#106—222no—
448#106—441no—
449#103—222no—
450#103—222no—
451#103—222no—
452#103—441no—
453C22⋊C8—222no—
454C22⋊C8—222no—
455C22⋊C8—222no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—221no—
461#95—221no—
462#95—221no—
463C2×C11—42no—
464C2×C11—81no—
465C2×C11#244311yescharacteristic
466C2×C11#309511yescharacteristic
467C2×C11#309911yescharacteristic
468C2×C11#326711yescharacteristic
469C2×C11#327811yescharacteristic
470C2×C11#334811yescharacteristic
471C2×C11#335611yescharacteristic
472C24C2×C22⋊D1111yescharacteristic
473C24C2×C22⋊D1111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4#434112yes—
505C22×C4#434112yes—
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511M16—228no—
512C2×C8—112no—
513C2×C8—112no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—112no—
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—881no—
544C4⋊C4D4×D1112yes—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—442no—
551C22⋊C4—442no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—21no—
555C42—21no—
556C42—442no—
557C42—442no—
558C42—442no—
559C11#2615511yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23#6698812yes—
574C23C22×C22⋊D1111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—44no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
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—84no—
611C2×C4—222no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4#6698812yes—
624C2×C4#6699512yes—
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4C2×#434111yescharacteristic
627C2×C4C2×#434111yescharacteristic
628C2×C4#6703711yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#6704311yescharacteristic
631C8—222no—
632C8—222no—
633C8—441no—
634C8—441no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×#6698811yescharacteristic
650C22D4×C22⋊D1111yescharacteristic
651C22C2×#6699511yescharacteristic
652C22#1062335311yescharacteristic
653C22#1062335511yescharacteristic
654C22#1062336711yescharacteristic
655C22#1062336811yescharacteristic
656C4—22no—
657C4—22no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—442no—
665C4—881no—
666C4—881no—
667C4—881no—
668C4#1062312911yescharacteristic
669C4#1062313211yescharacteristic
670C4#1062313311yescharacteristic
671C4#1062313711yescharacteristic
672C2—42no—
673C2—81no—
674C2#1307234711yescharacteristic
675C2#1307856011yescharacteristic
676C2#1307860111yescharacteristic
677C2#1308013711yescharacteristic
678C2#1308027811yescharacteristic
679C2#1308112511yescharacteristic
680C2#1308123111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2417C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2417D11
hypocenterC11#26155
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#10622658C2semidirect
2. C2×#10622577C2semidirect
4. #13070159C2semidirect
5. #13070092C2semidirect
6. #13070052C2semidirect
7. #13069809C2semidirect
8. #13069254C2semidirect
9. #13069205C2semidirect
10. #13069050C2semidirect
11. #13068929C2semidirect
13. #13068813C2semidirect
14. #13068809C2semidirect
131. #66871D4semidirect
559. C11#26155semidirect

Maximal subgroups

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

subgroupindex
C2×#106226582
C2×#106225772
#130715652
#130701592
#130700922
#130700522
#130698092
#130692542
#130692052
#130690502
#130689292
#130689142
#130688132
#130688092
C11×#24172
#2615511