Subgroups — #13070902

Order 1408.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622296	C₂	1	1	yes	maximal, characteristic
2	#10622295	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#346	C₂	1	1	yes	maximal, characteristic
4	#10622143	C₂	1	2	yes	maximal
5	#10622142	C₂	1	2	yes	maximal
6	#66923	—	2	1	no	—
7	#66922	—	2	1	no	—
8	C₂×C₁₁×C₁₆	C₂²	1	2	yes	—
9	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	#66882	—	2	1	no	—
11	#66882	C₂²	1	2	yes	—
12	#66882	C₂²	1	1	yes	characteristic
13	#66882	C₂²	1	1	yes	characteristic
14	#66881	—	2	1	no	—
15	C₂×Dic₂₂	—	4	1	no	—
16	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	C₄²×C₁₁	D₄	1	1	yes	characteristic
19	C₄⋊Dic₁₁	—	2	1	no	—
20	C₄⋊Dic₁₁	—	2	1	no	—
21	C₄⋊Dic₁₁	—	2	2	no	—
22	C₄⋊Dic₁₁	—	4	1	no	—
23	Dic₁₁⋊C₄	—	4	1	no	—
24	Dic₁₁⋊C₄	—	4	1	no	—
25	C₁₁×C₁₆	Q₈	1	4	yes	complemented
26	#2255	—	11	1	no	maximal, Sylow
27	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
30	C₂×Dic₁₁	—	4	1	no	—
31	C₂×Dic₁₁	—	4	1	no	—
32	C₂×Dic₁₁	—	4	2	no	—
33	Dic₂₂	—	8	2	no	—
34	C₈×C₁₁	Q₁₆	1	2	yes	—
35	C₈×C₁₁	C₂×Q₈	1	2	yes	—
36	#500	—	11	1	no	—
37	#499	—	11	1	no	—
38	#367	—	11	2	no	—
39	#366	—	11	2	no	—
40	#346	D₁₁	1	1	yes	characteristic
41	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₁	—	2	1	no	—
43	C₄×C₁₁	—	2	1	no	—
44	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
45	C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
46	Dic₁₁	—	8	2	no	—
47	Dic₁₁	—	8	1	no	—
48	Dic₁₁	—	8	1	no	—
49	C₄⋊Q₈	—	22	1	no	—
50	#125	—	22	1	no	—
51	C₂×C₁₆	C₂×D₁₁	1	2	yes	—
52	#107	—	11	1	no	—
53	#107	—	11	2	no	—
54	#107	—	11	1	no	—
55	#107	—	22	1	no	—
56	#106	—	22	1	no	—
57	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
58	C₂×C₁₁	#500	1	1	yes	characteristic
59	C₂×C₁₁	#509	1	1	yes	characteristic
60	C₂×C₁₁	#510	1	1	yes	characteristic
61	C₂×Q₈	—	44	1	no	—
62	C₂×C₈	D₄₄	1	1	yes	characteristic
63	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
64	C₄⋊C₄	—	22	1	no	—
65	C₄⋊C₄	—	22	1	no	—
66	C₄⋊C₄	—	22	2	no	—
67	C₄⋊C₄	—	44	1	no	—
68	C₄⋊C₄	—	44	1	no	—
69	C₄⋊C₄	—	44	1	no	—
70	C₄²	D₄₄	1	1	yes	characteristic
71	C₁₆	Dic₂₂	1	4	yes	complemented
72	C₁₁	#2255	1	1	yes	characteristic, complemented, Sylow
73	Q₈	—	88	2	no	—
74	C₂×C₄	—	44	1	no	—
75	C₂×C₄	—	44	1	no	—
76	C₂×C₄	—	44	2	no	—
77	C₂×C₄	D₈₈	1	1	yes	characteristic
78	C₂×C₄	D₈₈	1	1	yes	characteristic
79	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
80	C₈	Dic₄₄	1	2	yes	—
81	C₈	C₂×Dic₂₂	1	2	yes	—
82	C₂²	C₂×D₈₈	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	88	2	no	—
86	C₄	—	88	1	no	—
87	C₄	—	88	1	no	—
88	C₄	#66922	1	1	yes	characteristic
89	C₄	C₂×Dic₄₄	1	1	yes	characteristic
90	C₂	#10622295	1	1	yes	characteristic
91	C₂	#10622521	1	1	yes	characteristic
92	C₂	#10622522	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#346	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₈
hypercenter	#346	D₁₁
hypocenter	C₁₁	#2255
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
25. C₁₁×C₁₆	Q₈	semidirect
71. C₁₆	Dic₂₂	semidirect
72. C₁₁	#2255	semidirect

Maximal subgroups

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

subgroup	index
#10622296	2
#10622295	2
C₁₁×#346	2
#10622143	2
#10622142	2
#2255	11