Finite Group Databasebeta

← #14812853

Subgroups — #14812853

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073848C211yesmaximal, characteristic, complemented
2#13071588C211yesmaximal, characteristic
3#13070147C211yesmaximal, characteristic
4#13070004C211yesmaximal, characteristic
5#13070000C211yesmaximal, characteristic
6#13069382C211yesmaximal, characteristic, complemented
7#13069381C211yesmaximal, characteristic, complemented
8#13069371C211yesmaximal, characteristic, complemented
9#13069333C211yesmaximal, characteristic, complemented
10#13069202C211yesmaximal, characteristic, complemented
11#13069196C211yesmaximal, characteristic, complemented
12#13068777C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C11×#2092C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C11×#390C2211yescharacteristic
22C11×#382C2211yescharacteristic
23#10622834C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622590C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622558—21no—
40#10622557—21no—
41#10622556—21no—
42C22⋊C4×Dic11—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622271—21no—
48#10622270—21no—
49#10622266—21no—
50#10622265—21no—
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×Dic11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72D4×Dic11—22no—
73D4×Dic11Q814yes—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4D411yescharacteristic
83C2×Dic11⋊C4D411yescharacteristic
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11C2311yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C11×#107—41no—
92C11×#106—22no—
93C11×#102—22no—
94C11×#102—41no—
95C11×#95—21no—
96C11×#95—21no—
97#66896—22no—
98#66896—41no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66881—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114#66872—41no—
115#66871—41no—
116#66871—41no—
117C4⋊(C11⋊C8)—22no—
118#26096—111nomaximal, Sylow
119C24×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11C2×Q812yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—24no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—81no—
138C22×Dic11—81no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11#4112yes—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—81no—
157C42×C11—21no—
158C42×C11—21no—
159C22⋊Dic11—24no—
160C22⋊Dic11—42no—
161C22⋊Dic11—81no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—42no—
170C4⋊Dic11C2×Q812yes—
171Dic11⋊C4—22no—
172Dic11⋊C4—41no—
173Dic11⋊C4—42no—
174Dic11⋊C4—81no—
175Dic11⋊C4—81no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—81no—
179C4×Dic11—81no—
180C4×Dic11—81no—
181C4×Dic11C2×Q812yes—
182C4×Dic11#4112yes—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8#4112yes—
189#2570—111no—
190#2357—111no—
191#2094—111no—
192#2092D1111yescharacteristic
193#2067—111no—
194#2067—111no—
195#1949—111no—
196#1949—111no—
197#1947—111no—
198#1939—111no—
199#1920—111no—
200#1919—111no—
201#1846—111no—
202#1804—111no—
203C4×#102—111no—
204C23×C11—22no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11C22×D411yescharacteristic
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—41no—
215D4×C11—41no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11C22×Q811yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C112−1+411yescharacteristic
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—84no—
259C2×Dic11C22⋊Q812yes—
260C2×Dic11C22⋊Q812yes—
261C2×Dic11#13512yes—
262C8×C11—22no—
263C8×C11—41no—
264C11⋊C8—22no—
265C11⋊C8—41no—
266C2×C4×D4—111no—
267C2×#107—111no—
268C2×#107—111no—
269C2×#107C2×D1111yescharacteristic
270C2×#106—111no—
271C2×#106—111no—
272C2×#106C2×D1111yescharacteristic
273C2×C4⋊C8—111no—
274C2×C4⋊C8—111no—
275C2×C4⋊C8—111no—
276C2×#102—111no—
277C2×#102—111no—
278C2×#102C2×D1111yescharacteristic
279C2×#102C2×D1111yescharacteristic
280C2×C4×C8—111no—
281#400—221no—
282#398—221no—
283#390—111no—
284#390C2×D1111yescharacteristic
285#389—111no—
286#389—111no—
287#388—221no—
288#388—221no—
289#387—221no—
290#387—221no—
291#384—111no—
292#382—111no—
293#382—111no—
294#382C2×D1111yescharacteristic
295#381—221no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4—111no—
300C4×C22⋊C4—221no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#336—111no—
308#336C2×D1111yescharacteristic
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11C2×C22⋊Q811yescharacteristic
317C22×C11#54711yescharacteristic
318C22×C11#55011yescharacteristic
319C22×C11C2×#13511yescharacteristic
320C22×C11#57511yescharacteristic
321C22×C11#57611yescharacteristic
322C22×C11#57711yescharacteristic
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—81no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11#53311yescharacteristic
329C4×C11#54411yescharacteristic
330C4×C11#55211yescharacteristic
331C4×C11#55311yescharacteristic
332Dic11—22no—
333Dic11—22no—
334Dic11—22no—
335Dic11—42no—
336Dic11—41no—
337Dic11—81no—
338Dic11—81no—
339Dic11—81no—
340C22×D4C22×D1111yescharacteristic
341C23×C4—221no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346C4×D4—114no—
347C4×D4—222no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C42—111no—
367C2×C42—111no—
368C2×C42—221no—
369C2×C42—221no—
370C2×C42—221no—
371C2×C42C22×D1111yescharacteristic
372#107—41no—
373#107—441no—
374#107—441no—
375#106—22no—
376#106—222no—
377#106—441no—
378C4⋊C8—222no—
379C4⋊C8—222no—
380C4⋊C8—222no—
381#102—22no—
382#102—41no—
383#102—222no—
384#102—441no—
385C4×C8—222no—
386#95—21no—
387#95—21no—
388#95—111no—
389#95—111no—
390#95—221no—
391#95—221no—
392#95—221no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399C2×C11—82no—
400C2×C11#244111yescharacteristic
401C2×C11#307611yescharacteristic
402C2×C11#308111yescharacteristic
403C2×C11#333911yescharacteristic
404C2×C11#335111yescharacteristic
405C2×C11#339411yescharacteristic
406C2×C11#340311yescharacteristic
407C24—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4Q8×D1112yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—224no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—881no—
427C22×C4—881no—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—112no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8#434112yes—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—112no—
450C4⋊C4—222no—
451C4⋊C4—221no—
452C4⋊C4—221no—
453C4⋊C4—221no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—441no—
459C4⋊C4—442no—
460C4⋊C4—442no—
461C4⋊C4—881no—
462C4⋊C4—881no—
463C22⋊C4—42no—
464C22⋊C4—81no—
465C22⋊C4—224no—
466C22⋊C4—442no—
467C22⋊C4—881no—
468C42—21no—
469C42—21no—
470C42—112no—
471C42—112no—
472C42—221no—
473C42—221no—
474C42—881no—
475C42—881no—
476C42—881no—
477C11#2609611yescharacteristic, complemented, Sylow
478C23—22no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23C2×D4×D1111yescharacteristic
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—221no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—222no—
517C2×C4—221no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—884no—
530C2×C4C2×#434111yescharacteristic
531C2×C4#6703711yescharacteristic
532C2×C4C2×Q8×D1111yescharacteristic
533C2×C4#41×D1111yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—22no—
537C8—41no—
538C8—222no—
539C8—441no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22D11×C22⋊Q811yescharacteristic
548C22#1062318611yescharacteristic
549C22#1062324911yescharacteristic
550C22D11×#13511yescharacteristic
551C22#1062330111yescharacteristic
552C22#1062330411yescharacteristic
553C22#1062330511yescharacteristic
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—222no—
560C4—222no—
561C4—222no—
562C4—441no—
563C4—442no—
564C4—881no—
565C4—881no—
566C4—881no—
567C4#1062315311yescharacteristic
568C4#1062315411yescharacteristic
569C4#1062318111yescharacteristic
570C4#1062319211yescharacteristic
571C2—82no—
572C2#1307232211yescharacteristic
573C2#1307840111yescharacteristic
574C2#1307844611yescharacteristic
575C2#1308101111yescharacteristic
576C2#1308116911yescharacteristic
577C2#1308160911yescharacteristic
578C2#1308170111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2092C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2092D11
hypocenterC11#26096
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2092

Complements

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

NH ≅ G/Ntype
1. #13073848C2semidirect
6. #13069382C2semidirect
7. #13069381C2semidirect
8. #13069371C2semidirect
9. #13069333C2semidirect
10. #13069202C2semidirect
11. #13069196C2semidirect
12. #13068777C2semidirect
477. C11#26096semidirect

Maximal subgroups

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

subgroupindex
#130738482
#130715882
#130701472
#130700042
#130700002
#130693822
#130693812
#130693712
#130693332
#130692022
#130691962
#130687772
#130686242
#102×Dic112
C11×#20922
#2609611