Finite Group Databasebeta

← #14775247

Subgroups — #14775247

Order 2816.

802 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×#10622336C211yesmaximal, characteristic
2#13071641C211yesmaximal, characteristic
3#13071499C211yesmaximal, characteristic
4#13069359C211yesmaximal, characteristic, complemented
5#13069306C211yesmaximal, characteristic, complemented
6#13069258C211yesmaximal, characteristic, complemented
7#13069209C211yesmaximal, characteristic, complemented
8#13069195C211yesmaximal, characteristic, complemented
9#13069039C211yesmaximal, characteristic
10#13068887C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic
12#13068513C211yesmaximal, characteristic, complemented
13#13068447C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic
15C11×#1752C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622825C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34#10622558—21no—
35#10622557—21no—
36#10622557—21no—
37#10622557—21no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622336C418yescomplemented
46#10622265—21no—
47#10622263—21no—
48#10622262—21no—
49#10622261—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4D411yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66979—22no—
78#66979—22no—
79#66979—41no—
80#66979C2×C414yes—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88#66977—22no—
89#66977C2×C414yes—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C4×Dic22—22no—
102C4×Dic22—41no—
103C11×C22⋊C8C2×C414yes—
104C11×#97—22no—
105C11×#97—41no—
106C11×#95D411yescharacteristic
107C11×#95D411yescharacteristic
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66882—41no—
118#66882C2×C414yes—
119#66881—22no—
120#66881C2×C414yes—
121#66880—22no—
122#66880—41no—
123#66880C2×C414yes—
124#66880C2×C414yes—
125#22939—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C412yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—44no—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C2×C8×C11#4112yes—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C22⋊Dic11—24no—
173C22⋊Dic11—24no—
174C22⋊Dic11—42no—
175C22⋊Dic11—81no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C412yes—
187C4⋊Dic11C22×C412yes—
188C4⋊Dic11C22×C412yes—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195C4×Dic11—24no—
196C4×Dic11—42no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201C2×#485—111no—
202#2362—111no—
203#2346—111no—
204#1944—111no—
205#1935—111no—
206#1928—111no—
207#1921—111no—
208#1919—111no—
209#1892—111no—
210#1865—111no—
211#1854—111no—
212#1776—111no—
213#1763—111no—
214#1752D1111yescharacteristic
215#1735—111no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11C4×D412yes—
223C23×C11C22×D411yescharacteristic
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
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×C11C4×D412yes—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—22no—
278C8×C11—22no—
279C8×C11—22no—
280C8×C11—41no—
281C23×C8C2×D1111yescharacteristic
282C2×C22⋊Q8—111no—
283C2×C4×Q8—111no—
284C2×#117—111no—
285C2×#117—111no—
286#485—118no—
287C2×#107—111no—
288C2×#107—111no—
289C2×#106—111no—
290C2×#106—111no—
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—111no—
295C2×C22⋊C8C2×D1111yescharacteristic
296C2×#97C2×D1111yescharacteristic
297C2×#97C2×D1111yescharacteristic
298#391—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#388—221no—
303#388—221no—
304#388—221no—
305#388—221no—
306#387—221no—
307#382—221no—
308#380—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—221no—
313C4×C22⋊C4C2×D1111yescharacteristic
314#376—221no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#336C2×D1111yescharacteristic
324#336C2×D1111yescharacteristic
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#54611yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—22no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11C4×#4111yescharacteristic
345C4×C11#52011yescharacteristic
346C4×C11#55111yescharacteristic
347C4×C11#55211yescharacteristic
348Dic11—42no—
349Dic11—42no—
350Dic11—42no—
351Dic11—42no—
352Dic11—42no—
353Dic11—81no—
354Dic11—81no—
355Dic11—81no—
356C22×Q8—111no—
357C23×C4C22×D1111yescharacteristic
358C22×C8—22no—
359C22×C8—22no—
360C22×C8—41no—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22⋊Q8—114no—
366C22⋊Q8—222no—
367C4×Q8—222no—
368C4×Q8—441no—
369#117—114no—
370#117—222no—
371#117—222no—
372#117—441no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4D4411yescharacteristic
390C2×C22⋊C4D4411yescharacteristic
391C2×C42—221no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399#107—114no—
400#107—441no—
401#106—114no—
402#106—222no—
403#103—114no—
404#103—114no—
405#103—222no—
406#103—441no—
407C22⋊C8C4×D1114yes—
408#97—22no—
409#97—41no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95D4411yescharacteristic
420#95D4411yescharacteristic
421C2×C11—42no—
422C2×C11#235911yescharacteristic
423C2×C11#294311yescharacteristic
424C2×C11#294711yescharacteristic
425C2×C11#331511yescharacteristic
426C2×C11#332111yescharacteristic
427C2×C11#334811yescharacteristic
428C2×C11#334911yescharacteristic
429C24C2×D4411yescharacteristic
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4C2×C4×D1112yes—
449C22×C4C2×D4411yescharacteristic
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×D4411yescharacteristic
454C22×C4#433912yes—
455C22×C4C23×D1111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—44no—
466C2×C8C2×C4×D1112yes—
467C2×C8C2×C4×D1112yes—
468C2×C8#434112yes—
469C4⋊C4—112no—
470C4⋊C4—112no—
471C4⋊C4—112no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—224no—
499C42—442no—
500C42—442no—
501C42—442no—
502C42—442no—
503C42—442no—
504C11#2293911yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23C4×D4412yes—
512C23C22×D4411yescharacteristic
513Q8—222no—
514Q8—222no—
515Q8—441no—
516Q8—441no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4C4×D4412yes—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×#434111yescharacteristic
563C2×C4#6703711yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#6704311yescharacteristic
566C8—22no—
567C8—22no—
568C8—22no—
569C8—41no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×C4×D4411yescharacteristic
578C22#1062308511yescharacteristic
579C22#1062308611yescharacteristic
580C22#1062327911yescharacteristic
581C22#1062327911yescharacteristic
582C22#1062328211yescharacteristic
583C22#1062328411yescharacteristic
584C4—22no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—442no—
590C4—442no—
591C4—442no—
592C4—442no—
593C4—442no—
594C4—881no—
595C4—881no—
596C4—881no—
597C4#1062302611yescharacteristic
598C4#1062306211yescharacteristic
599C4C4×#434111yescharacteristic
600C4#1062307711yescharacteristic
601C2—42no—
602C2#1307161011yescharacteristic
603C2#1307741811yescharacteristic
604C2#1307746111yescharacteristic
605C2#1308071411yescharacteristic
606C2#1308080411yescharacteristic
607C2#1308113311yescharacteristic
608C2#1308114811yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
4. #13069359C2semidirect
5. #13069306C2semidirect
6. #13069258C2semidirect
7. #13069209C2semidirect
8. #13069195C2semidirect
10. #13068887C2semidirect
12. #13068513C2semidirect
13. #13068447C2semidirect
45. #10622336C4semidirect
504. C11#22939semidirect

Maximal subgroups

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

subgroupindex
C2×#106223362
#130716412
#130714992
#130693592
#130693062
#130692582
#130692092
#130691952
#130690392
#130688872
#130688172
#130685132
#130684472
#130683332
C11×#17522
#2293911