Subgroups — #14668482

Order 2816.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070845	C₂	1	4	yes	maximal
2	#13068234	C₂	1	1	yes	maximal, characteristic
3	#13066533	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1710	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#500	C₂²	1	2	yes	—
6	C₁₁×#487	—	2	2	no	—
7	#10622312	C₂²	1	2	yes	—
8	#10622295	—	2	2	no	—
9	C₈²×C₁₁	C₂²	1	1	yes	characteristic
10	#10622130	—	2	8	no	—
11	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	—
12	C₁₁×C₄⋊Q₈	—	2	2	no	—
13	C₂×Dic₄₄	—	2	4	no	—
14	#66922	—	2	2	no	—
15	C₁₁×#107	—	2	4	no	—
16	C₁₁×#103	—	4	4	no	—
17	C₄×C₈×C₁₁	D₄	1	2	yes	—
18	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	#66882	—	4	4	no	—
20	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	—
21	#12514	—	11	1	no	maximal, Sylow
22	C₂×Q₈×C₁₁	—	4	2	no	—
23	C₂×Dic₂₂	—	4	2	no	—
24	C₂×C₈×C₁₁	D₈	1	4	yes	—
25	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
26	C₁₁×C₄⋊C₄	—	4	2	no	—
27	C₁₁×C₄⋊C₄	—	4	2	no	—
28	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
29	C₄⋊Dic₁₁	—	4	4	no	—
30	Dic₄₄	—	4	8	no	—
31	C₁₁⋊C₁₆	—	2	4	no	—
32	#2241	—	11	4	no	—
33	#1713	—	11	1	no	—
34	#1710	D₁₁	1	1	yes	characteristic
35	#1311	—	11	1	no	—
36	Q₈×C₁₁	—	8	4	no	—
37	C₂×C₄×C₁₁	—	8	2	no	—
38	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
39	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
40	C₂×Dic₁₁	—	8	2	no	—
41	Dic₂₂	—	8	4	no	—
42	C₈×C₁₁	—	2	4	no	—
43	C₈×C₁₁	#135	1	4	yes	—
44	#500	—	22	2	no	—
45	#500	C₂×D₁₁	1	2	yes	—
46	#494	—	11	2	no	—
47	#487	—	2	2	no	—
48	#358	—	22	8	no	—
49	C₄×C₁₆	—	11	2	no	—
50	C₈²	C₂×D₁₁	1	1	yes	characteristic
51	C₂²×C₁₁	#493	1	1	yes	characteristic
52	C₄×C₁₁	—	16	2	no	—
53	C₄×C₁₁	#495	1	2	yes	—
54	C₄×C₁₁	#510	1	4	yes	—
55	Dic₁₁	—	16	2	no	—
56	C₂×Q₁₆	—	22	4	no	—
57	C₄⋊Q₈	—	2	2	no	—
58	C₄⋊Q₈	—	22	2	no	—
59	C₂×C₁₆	—	11	4	no	—
60	#107	—	2	4	no	—
61	#107	—	44	4	no	—
62	#103	—	4	4	no	—
63	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
64	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
65	C₂×C₁₁	#1709	1	1	yes	characteristic
66	C₂×C₁₁	#2251	1	2	yes	—
67	C₂×Q₈	—	4	2	no	—
68	C₂×Q₈	—	44	2	no	—
69	Q₁₆	—	44	8	no	—
70	C₂×C₈	#4323	1	4	yes	—
71	C₂×C₈	D₄×D₁₁	1	2	yes	—
72	C₄⋊C₄	—	4	2	no	—
73	C₄⋊C₄	—	4	2	no	—
74	C₄⋊C₄	—	44	4	no	—
75	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
76	C₁₆	—	22	4	no	—
77	C₁₁	#12514	1	1	yes	characteristic, complemented, Sylow
78	Q₈	—	8	4	no	—
79	Q₈	—	88	4	no	—
80	C₂×C₄	—	8	2	no	—
81	C₂×C₄	—	88	2	no	—
82	C₂×C₄	C₂×#4323	1	2	yes	—
83	C₂×C₄	#66993	1	1	yes	characteristic
84	C₈	—	2	4	no	—
85	C₈	#66972	1	4	yes	—
86	C₂²	#10622686	1	1	yes	characteristic
87	C₄	—	16	2	no	—
88	C₄	—	176	2	no	—
89	C₄	#10622804	1	2	yes	—
90	C₄	#10622808	1	4	yes	—
91	C₂	#13068223	1	1	yes	characteristic
92	C₂	#13070888	1	2	yes	—

	subgroup	G/H
center	C₂²	#10622686
commutator, cosocle	C₄×C₈×C₁₁	C₂³
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₁₁×#1710	C₂
socle, prime radical	C₂²×C₁₁	#493
hypercenter	#1710	D₁₁
hypocenter	C₁₁	#12514
LCS	G ▷ C₄×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1710

Complements

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

N	H ≅ G/N	type
77. C₁₁	#12514	semidirect

Maximal subgroups

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

subgroup	index
#13070845	2
#13068234	2
#13066533	2
C₁₁×#1710	2
#12514	11