Subgroups — #13070133

Order 1408.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622739	C₂	1	3	yes	maximal
2	#10622738	C₂	1	3	yes	maximal, complemented
3	C₁₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₁₁×M₁₆	C₂²	1	3	yes	—
6	C₂×#4318	C₂²	1	3	yes	—
7	(C₂×D₁₁)⋊C₈	—	2	6	no	—
8	#66883	—	2	6	no	—
9	C₂³×D₁₁	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
11	C₂²×Dic₁₁	Q₈	1	1	yes	characteristic
12	C₂×C₄×D₁₁	—	2	3	no	—
13	C₂×C₄×D₁₁	—	2	3	no	—
14	C₁₁×M₁₆	—	2	6	no	—
15	C₂×C₈×C₁₁	D₄	1	6	yes	—
16	#4318	—	2	6	no	—
17	C₂×C₁₁⋊C₈	—	2	3	no	—
18	#2091	—	11	1	no	maximal, Sylow
19	C₂³×C₁₁	C₂×Q₈	1	1	yes	characteristic
20	C₂²×D₁₁	—	2	3	no	—
21	C₂²×D₁₁	—	4	2	no	—
22	C₂×C₄×C₁₁	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₁₁	#41	1	3	yes	—
24	C₂×Dic₁₁	—	2	3	no	—
25	C₄×D₁₁	—	4	3	no	—
26	C₄×D₁₁	—	4	1	no	—
27	C₈×C₁₁	—	2	6	no	—
28	C₁₁⋊C₈	—	4	3	no	—
29	#430	—	11	3	no	—
30	#407	—	11	3	no	—
31	#338	D₁₁	1	1	yes	characteristic, complemented
32	C₂²×C₁₁	—	4	1	no	—
33	C₂²×C₁₁	C₂²⋊Q₈	1	3	yes	—
34	C₂×D₁₁	—	2	6	no	—
35	C₂×D₁₁	—	4	3	no	—
36	C₂×D₁₁	—	4	1	no	—
37	C₄×C₁₁	#123	1	3	yes	—
38	C₄×C₁₁	#127	1	1	yes	characteristic
39	Dic₁₁	—	4	1	no	—
40	C₂³×C₄	—	11	1	no	—
41	C₂×M₁₆	—	11	3	no	—
42	C₂×M₁₆	C₂×D₁₁	1	3	yes	—
43	#108	—	22	6	no	—
44	C₂²⋊C₈	—	22	6	no	—
45	C₂×C₁₁	—	2	3	no	—
46	C₂×C₁₁	#399	1	1	yes	characteristic
47	D₁₁	—	4	2	no	—
48	C₂⁴	—	11	1	no	—
49	C₂²×C₄	—	11	1	no	—
50	C₂²×C₄	—	22	3	no	—
51	C₂²×C₄	—	22	3	no	—
52	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
53	M₁₆	—	2	6	no	—
54	M₁₆	—	22	6	no	—
55	C₂×C₈	—	22	3	no	—
56	C₂×C₈	D₄₄	1	6	yes	—
57	C₁₁	#2091	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	22	3	no	—
59	C₂³	—	44	2	no	—
60	C₂³	Q₈×D₁₁	1	1	yes	characteristic
61	C₂×C₄	—	22	3	no	—
62	C₂×C₄	—	44	1	no	—
63	C₂×C₄	—	44	3	no	—
64	C₂×C₄	C₂×D₄₄	1	3	yes	—
65	C₂×C₄	#4341	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	44	3	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	22	6	no	—
70	C₂²	—	44	3	no	—
71	C₂²	—	44	1	no	—
72	C₂²	#66950	1	3	yes	—
73	C₄	—	44	1	no	—
74	C₄	#66927	1	1	yes	characteristic
75	C₄	#66939	1	3	yes	—
76	C₂	—	2	3	no	—
77	C₂	—	44	2	no	—
78	C₂	#10622290	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#66927
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#338	C₂
socle	C₂×C₁₁	#399
prime radical	C₂³×D₁₁	Q₈
hypercenter	#338	D₁₁
hypocenter	C₁₁	#2091
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
2. #10622738	C₂	semidirect
3. C₁₁×#338	C₂	semidirect
31. #338	D₁₁	semidirect
57. C₁₁	#2091	semidirect

Maximal subgroups

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

subgroup	index
#10622739	2
#10622738	2
C₁₁×#338	2
#2091	11