Subgroups — #13077013

Order 1408.

648 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66941	C₂	1	6	yes	maximal
2	C₁₁×#384	C₂	1	1	yes	maximal, characteristic
3	#10622589	C₂	1	6	yes	maximal
4	#10622548	C₂	1	1	yes	maximal, characteristic
5	C₄²×Dic₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₂	C₂²	1	4	yes	—
7	C₂×C₁₁×C₄⋊C₄	C₂²	1	6	yes	—
8	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₁	C₂²	1	6	yes	—
10	C₂×Dic₁₁⋊C₄	C₂²	1	12	yes	—
11	C₂×C₄×Dic₁₁	C₂²	1	3	yes	—
12	C₂×C₄×Dic₁₁	C₂²	1	3	yes	—
13	#66941	—	2	24	no	—
14	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
15	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
16	C₂²×Dic₁₁	C₂³	1	4	yes	—
17	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
18	C₂²×Dic₁₁	C₂³	1	3	yes	—
19	C₂×Dic₂₂	—	2	24	no	—
20	C₁₁×C₄⋊C₄	—	2	12	no	—
21	C₄²×C₁₁	Q₈	1	4	yes	complemented
22	C₄⋊Dic₁₁	—	2	12	no	—
23	Dic₁₁⋊C₄	—	2	24	no	—
24	C₄×Dic₁₁	D₄	1	12	yes	—
25	C₄×Dic₁₁	Q₈	1	12	yes	complemented
26	#2868	—	11	1	no	maximal, Sylow
27	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₁₁	—	2	12	no	—
29	C₂×C₄×C₁₁	C₂×D₄	1	6	yes	—
30	C₂×C₄×C₁₁	C₂×Q₈	1	6	yes	—
31	C₂×C₄×C₁₁	C₂×Q₈	1	6	yes	—
32	C₂×Dic₁₁	—	2	12	no	—
33	C₂×Dic₁₁	C₂×D₄	1	6	yes	—
34	C₂×Dic₁₁	C₂×D₄	1	6	yes	—
35	C₂×Dic₁₁	C₂×Q₈	1	12	yes	—
36	Dic₂₂	—	4	16	no	—
37	C₂×C₄⋊Q₈	—	11	6	no	—
38	#384	—	11	6	no	—
39	#384	—	11	1	no	—
40	#384	D₁₁	1	1	yes	characteristic
41	C₄³	—	11	1	no	—
42	C₂²×C₁₁	C₂²×D₄	1	3	yes	—
43	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
44	C₂²×C₁₁	C₂²×Q₈	1	3	yes	—
45	C₄×C₁₁	—	4	4	no	—
46	C₄×C₁₁	C₄⋊Q₈	1	12	yes	complemented
47	Dic₁₁	—	4	4	no	—
48	Dic₁₁	#127	1	4	yes	—
49	Dic₁₁	C₄⋊Q₈	1	12	yes	complemented
50	C₂²×Q₈	—	11	4	no	—
51	C₄⋊Q₈	—	22	24	no	—
52	C₂×C₄⋊C₄	—	11	12	no	—
53	C₂×C₄⋊C₄	—	11	6	no	—
54	C₂×C₄⋊C₄	C₂×D₁₁	1	6	yes	—
55	C₂×C₄²	—	11	3	no	—
56	C₂×C₄²	—	11	3	no	—
57	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
58	C₂×C₁₁	C₂×#127	1	1	yes	characteristic
59	C₂×C₁₁	C₂×C₄⋊Q₈	1	3	yes	—
60	C₂×C₁₁	C₂×C₄⋊Q₈	1	3	yes	—
61	C₂×Q₈	—	22	24	no	—
62	C₂²×C₄	—	11	3	no	—
63	C₂²×C₄	—	11	1	no	—
64	C₂²×C₄	—	11	4	no	—
65	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
66	C₂²×C₄	C₂²×D₁₁	1	3	yes	—
67	C₄⋊C₄	—	2	12	no	—
68	C₄⋊C₄	—	22	24	no	—
69	C₄⋊C₄	—	22	12	no	—
70	C₄²	—	11	12	no	—
71	C₄²	—	11	12	no	—
72	C₄²	Dic₂₂	1	4	yes	complemented
73	C₁₁	#2868	1	1	yes	characteristic, complemented, Sylow
74	C₂³	C₂³×D₁₁	1	1	yes	characteristic
75	Q₈	—	44	16	no	—
76	C₂×C₄	—	2	12	no	—
77	C₂×C₄	—	11	6	no	—
78	C₂×C₄	—	11	6	no	—
79	C₂×C₄	—	11	12	no	—
80	C₂×C₄	—	22	12	no	—
81	C₂×C₄	C₂×Dic₂₂	1	6	yes	—
82	C₂×C₄	D₄×D₁₁	1	6	yes	—
83	C₂×C₄	Q₈×D₁₁	1	6	yes	—
84	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
85	C₂²	C₂×D₄×D₁₁	1	3	yes	—
86	C₂²	C₂×Q₈×D₁₁	1	3	yes	—
87	C₄	—	4	4	no	—
88	C₄	—	11	4	no	—
89	C₄	—	11	12	no	—
90	C₄	—	44	4	no	—
91	C₄	#66941	1	12	yes	complemented
92	C₂	C₂×#66941	1	3	yes	—
93	C₂	D₁₁×#127	1	1	yes	characteristic
94	C₂	D₁₁×C₄⋊Q₈	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#384	C₂
hypercenter	#384	D₁₁
hypocenter	C₁₁	#2868
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #384

Complements

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

N	H ≅ G/N	type
21. C₄²×C₁₁	Q₈	semidirect
25. C₄×Dic₁₁	Q₈	semidirect
46. C₄×C₁₁	C₄⋊Q₈	semidirect
49. Dic₁₁	C₄⋊Q₈	semidirect
72. C₄²	Dic₂₂	semidirect
73. C₁₁	#2868	semidirect
91. C₄	#66941	semidirect

Maximal subgroups

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

subgroup	index
C₂×#66941	2
C₁₁×#384	2
#10622589	2
#10622548	2
C₄²×Dic₁₁	2
#2868	11