Finite Group Databasebeta

← #14772095

Subgroups — #14772095

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622643C211yesmaximal, characteristic
2C2×#10622402C211yesmaximal, characteristic
3C2×#10622403C211yesmaximal, characteristic
4#13071535C211yesmaximal, characteristic
5#13071534C211yesmaximal, characteristic
6#13069353C211yesmaximal, characteristic
7#13069351C211yesmaximal, characteristic
8#13068873C211yesmaximal, characteristic
9#13068872C211yesmaximal, characteristic
10#13068867C211yesmaximal, characteristic
11#13068779C211yesmaximal, characteristic
12#13068630C211yesmaximal, characteristic
13#13068629C211yesmaximal, characteristic
14#13068482C211yesmaximal, characteristic
15C11×#1863C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622643—24no—
35#10622598C2211yescharacteristic
36#10622590—21no—
37#10622590C2211yescharacteristic
38#10622590C2211yescharacteristic
39C4⋊C4×Dic11—21no—
40#10622586—21no—
41#10622586C2211yescharacteristic
42#10622585—21no—
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622403C418yescomplemented
53#10622402—24no—
54#10622263—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77Q8×Dic11—41no—
78Q8×Dic11C2×C414yes—
79C2×#4326C2×C414yes—
80C2×#4326D414yes—
81C2×#4326Q814yes—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66940—22no—
105#66940—22no—
106#66940—41no—
107#66940C2×C414yes—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×#107—41no—
111C11×#103—22no—
112C11×#103C2×C414yes—
113C11×#95—21no—
114#66899—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66882—41no—
125#66880—22no—
126#66880C2×C414yes—
127#66879—22no—
128Dic11⋊C8—22no—
129C8×Dic11C2×C414yes—
130#66874—22no—
131#66872—22no—
132#66872—22no—
133#66871C2×C414yes—
134#66867—22no—
135#22675—111nomaximal, Sylow
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C22×C412yes—
140C2×Q8×C11C2×D412yes—
141C2×Q8×C11C2×Q812yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C22×C412yes—
161C2×Dic22C2×D412yes—
162C2×Dic22C2×Q812yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4C22×C412yes—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—42no—
180#4326C4⋊C4116yescomplemented
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—42no—
189C4⋊Dic11C22×C412yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—41no—
192Dic11⋊C4—41no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197C4×Dic11—24no—
198C4×Dic11—24no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11C22×C412yes—
205C4×Dic11#4112yes—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C412yes—
210C2×C11⋊C8C2×D412yes—
211C2×C11⋊C8C2×Q812yes—
212C2×#441—111no—
213C2×#441—111no—
214C2×C4×Q16—111no—
215#2351—111no—
216#2351—111no—
217#1943—111no—
218#1943—111no—
219#1863—111no—
220#1863—111no—
221#1863—111no—
222#1863D1111yescharacteristic
223#1846—111no—
224#1805—111no—
225#1805—111no—
226#1770—111no—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11C2×C4⋊C414yes—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11C4×D412yes—
279C2×Dic11C4×D412yes—
280Dic22—22no—
281Dic22—22no—
282Dic22—22no—
283Dic22C2×C4⋊C414yes—
284C8×C11—22no—
285C8×C11—41no—
286C11⋊C8—41no—
287C11⋊C8C2×C4⋊C414yes—
288C22×Q16—111no—
289C2×C4×Q8—111no—
290C2×C4×Q8—111no—
291C2×C4×Q8—111no—
292C2×C4×Q8—111no—
293C2×C4×Q8—111no—
294C2×C4×Q8C2×D1111yescharacteristic
295#441—224no—
296#441—224no—
297C4×Q16—118no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#107C2×D1111yescharacteristic
301C2×#106—111no—
302C2×#106—111no—
303C2×C4⋊C8—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103C2×D1111yescharacteristic
309C2×#103C2×D1111yescharacteristic
310C2×#97—111no—
311C2×#97—111no—
312C2×C4×C8—111no—
313#389—111no—
314#389—111no—
315#389—111no—
316#389—221no—
317#389—221no—
318#389—221no—
319#389—221no—
320#389C2×D1111yescharacteristic
321#382—111no—
322#382—111no—
323#382—221no—
324#382—221no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—221no—
327C4×C4⋊C4—221no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340C2×D1111yescharacteristic
332#336—111no—
333#336C2×D1111yescharacteristic
334C22×C11C2×C4×D411yescharacteristic
335C22×C11D4211yescharacteristic
336C22×C11D4×Q811yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57511yescharacteristic
339C22×C11#57811yescharacteristic
340C22×C11#57811yescharacteristic
341C4×C11—24no—
342C4×C11—42no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11C22×C4⋊C411yescharacteristic
348C4×C11#52011yescharacteristic
349C4×C11#54711yescharacteristic
350C4×C11#55411yescharacteristic
351Dic11—24no—
352Dic11—22no—
353Dic11—22no—
354Dic11—42no—
355Dic11—41no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359C22×Q8—111no—
360C22×Q8C22×D1111yescharacteristic
361C2×Q16—114no—
362C2×Q16—114no—
363C2×Q16—114no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8C22×D1111yescharacteristic
367C22×C8C22×D1111yescharacteristic
368C4×Q8—22no—
369C4×Q8—41no—
370C4×Q8—114no—
371C4×Q8—114no—
372C4×Q8—222no—
373C4×Q8—222no—
374C4×Q8—222no—
375C4×Q8—222no—
376C4×Q8—222no—
377C4×Q8—441no—
378C4×Q8—441no—
379C4×Q8—441no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C42—21no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—221no—
406C2×C42C22×D1111yescharacteristic
407#107—41no—
408#107—114no—
409#107—441no—
410#106—222no—
411#106—222no—
412C4⋊C8—222no—
413#103—22no—
414#103—114no—
415#103—222no—
416#103—222no—
417#103—222no—
418#103C4×D1114yes—
419#97—222no—
420#97—222no—
421C4×C8—114no—
422#95—21no—
423#95—111no—
424#95—111no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432C2×C11D4×C4⋊C411yescharacteristic
433C2×C11#294311yescharacteristic
434C2×C11#295011yescharacteristic
435C2×C11#327711yescharacteristic
436C2×C11#327711yescharacteristic
437C2×C11#339011yescharacteristic
438C2×C11#339011yescharacteristic
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—112no—
443C2×Q8—112no—
444C2×Q8—112no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8C2×C4×D1112yes—
449C2×Q8D4×D1112yes—
450C2×Q8Q8×D1112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4D4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465C22×C4C23×D1111yescharacteristic
466Q16—1116no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—112no—
473C2×C8—112no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8C2×C4×D1112yes—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—112no—
487C4⋊C4—224no—
488C4⋊C4—224no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4C2×C4×D1112yes—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—112no—
507C42—112no—
508C42—224no—
509C42—224no—
510C42—221no—
511C42—221no—
512C42—442no—
513C42—442no—
514C42—442no—
515C11#2267511yescharacteristic, complemented, Sylow
516C23C2×D4×D1111yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—22no—
520Q8—114no—
521Q8—222no—
522Q8—222no—
523Q8—222no—
524Q8C4⋊C4×D1114yes—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4C22×C4×D1111yescharacteristic
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4#6703711yescharacteristic
570C2×C4C2×Q8×D1111yescharacteristic
571C2×C4#41×D1111yescharacteristic
572C2×C4#6704311yescharacteristic
573C8—22no—
574C8—41no—
575C8—114no—
576C8—441no—
577C22C4×D4×D1111yescharacteristic
578C22#1062312111yescharacteristic
579C22#1062316311yescharacteristic
580C22#1062329711yescharacteristic
581C22#1062330211yescharacteristic
582C22#1062330411yescharacteristic
583C22#1062330811yescharacteristic
584C4—24no—
585C4—42no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—224no—
591C4—222no—
592C4—222no—
593C4—442no—
594C4—441no—
595C4—441no—
596C4—881no—
597C4—881no—
598C4C2×C4⋊C4×D1111yescharacteristic
599C4#1062307711yescharacteristic
600C4#1062316711yescharacteristic
601C4#1062318611yescharacteristic
602C2#1307151411yescharacteristic
603C2#1307741111yescharacteristic
604C2#1307747911yescharacteristic
605C2#1308026611yescharacteristic
606C2#1308027311yescharacteristic
607C2#1308157811yescharacteristic
608C2#1308158211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1863C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1863D11
hypocenterC11#22675
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
52. #10622403C4semidirect
180. #4326C4⋊C4semidirect
515. C11#22675semidirect

Maximal subgroups

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

subgroupindex
C2×#106226432
C2×#106224022
C2×#106224032
#130715352
#130715342
#130693532
#130693512
#130688732
#130688722
#130688672
#130687792
#130686302
#130686292
#130684822
C11×#18632
#2267511