Subgroups — #13066773

Order 1408.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#496	C₂	1	1	yes	maximal, characteristic
2	#10622180	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622179	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×SD₁₆	—	2	1	no	—
5	C₂×C₁₁×D₈	—	2	1	no	—
6	C₁₁×#127	C₄	1	1	yes	characteristic, complemented
7	C₁₁×#124	C₂²	1	1	yes	characteristic
8	C₁₁×#97	C₄	1	1	yes	characteristic, complemented
9	#66900	—	2	1	no	—
10	#66898	—	2	1	no	—
11	C₂×Q₈×C₁₁	D₄	1	1	yes	characteristic
12	C₂×D₄×C₁₁	—	2	1	no	—
13	C₂×D₄×C₁₁	—	4	1	no	—
14	C₂×D₄×C₁₁	D₄	1	1	yes	characteristic
15	C₁₁×SD₁₆	—	4	2	no	—
16	C₁₁×D₈	—	4	2	no	—
17	C₂×C₈×C₁₁	—	2	1	no	—
18	C₁₁×C₂²⋊C₄	—	4	1	no	—
19	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂²⋊Dic₁₁	—	4	1	no	—
21	#4318	—	4	1	no	—
22	#1406	—	11	1	no	maximal, Sylow
23	C₂³×C₁₁	—	2	1	no	—
24	C₂³×C₁₁	—	4	1	no	—
25	Q₈×C₁₁	—	4	1	no	—
26	D₄×C₁₁	—	4	1	no	—
27	D₄×C₁₁	—	4	1	no	—
28	D₄×C₁₁	—	4	1	no	—
29	D₄×C₁₁	—	8	2	no	—
30	C₂×C₄×C₁₁	—	2	1	no	—
31	C₂×C₄×C₁₁	—	2	1	no	—
32	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×Dic₁₁	—	8	1	no	—
34	C₈×C₁₁	—	2	2	no	—
35	C₁₁⋊C₈	—	8	1	no	—
36	#496	D₁₁	1	1	yes	characteristic
37	#355	—	11	1	no	—
38	#354	—	11	1	no	—
39	C₂²×C₁₁	—	4	1	no	—
40	C₂²×C₁₁	—	8	1	no	—
41	C₂²×C₁₁	—	8	2	no	—
42	C₂²×C₁₁	—	8	1	no	—
43	C₂²×C₁₁	#99	1	1	yes	characteristic
44	C₄×C₁₁	—	2	1	no	—
45	C₄×C₁₁	—	4	1	no	—
46	C₄×C₁₁	—	4	1	no	—
47	Dic₁₁	—	16	1	no	—
48	C₂×SD₁₆	—	2	1	no	—
49	C₂×D₈	—	2	1	no	—
50	#127	Dic₁₁	1	1	yes	characteristic, complemented
51	#124	C₂×D₁₁	1	1	yes	characteristic
52	#101	—	22	1	no	—
53	#99	—	22	1	no	—
54	#97	Dic₁₁	1	1	yes	characteristic, complemented
55	C₂×C₁₁	—	2	1	no	—
56	C₂×C₁₁	—	8	1	no	—
57	C₂×C₁₁	—	16	1	no	—
58	C₂×C₁₁	#353	1	1	yes	characteristic
59	C₂×Q₈	C₂²⋊D₁₁	1	1	yes	characteristic
60	C₂×D₄	—	2	1	no	—
61	C₂×D₄	—	4	1	no	—
62	C₂×D₄	C₂²⋊D₁₁	1	1	yes	characteristic
63	SD₁₆	—	4	2	no	—
64	D₈	—	4	2	no	—
65	M₁₆	—	44	1	no	—
66	C₂×C₈	—	2	1	no	—
67	C₂²⋊C₄	—	4	1	no	—
68	C₂²⋊C₄	—	44	1	no	—
69	C₄²	C₂×Dic₁₁	1	1	yes	characteristic
70	C₁₁	#1406	1	1	yes	characteristic, complemented, Sylow
71	C₂³	—	2	1	no	—
72	C₂³	—	4	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	4	1	no	—
77	D₄	—	8	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	88	1	no	—
81	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	88	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	8	2	no	—
87	C₂²	—	8	1	no	—
88	C₂²	#66898	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	176	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	16	1	no	—
96	C₂	#10622183	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10622183
commutator	C₄²×C₁₁	C₂×C₄
Frattini	#124	C₂×D₁₁
Fitting, prime radical	C₁₁×#496	C₂
socle	C₂×C₁₁	#353
cosocle	C₁₁×#124	C₂²
hypercenter	#496	D₁₁
hypocenter	C₁₁	#1406
LCS	G ▷ C₄²×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #496

Complements

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

N	H ≅ G/N	type
2. #10622180	C₂	semidirect
3. #10622179	C₂	semidirect
6. C₁₁×#127	C₄	semidirect
8. C₁₁×#97	C₄	semidirect
50. #127	Dic₁₁	semidirect
54. #97	Dic₁₁	semidirect
70. C₁₁	#1406	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#496	2
#10622180	2
#10622179	2
#1406	11