Subgroups — #13066913

Order 1408.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#10622538	C₂	1	2	yes	maximal
3	#10622093	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622092	C₂	1	2	yes	maximal, complemented
5	C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×M₁₆	C₄	1	2	yes	—
7	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×#97	C₄	1	2	yes	—
9	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂²⋊(C₁₁⋊C₈)	C₄	1	4	yes	—
12	C₄⋊(C₁₁⋊C₈)	C₄	1	4	yes	—
13	C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
14	C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
15	C₂²×C₄×C₁₁	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₁₁×M₁₆	—	2	4	no	—
18	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
20	C₄²×C₁₁	C₂×C₄	1	2	yes	—
21	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
24	C₂×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
25	#1453	—	11	1	no	maximal, Sylow
26	C₂³×C₁₁	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₁₁	—	2	2	no	—
28	C₂×C₄×C₁₁	—	2	4	no	—
29	C₂×C₄×C₁₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₁₁	C₄²	1	2	yes	—
31	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
32	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₁	—	2	2	no	—
34	C₈×C₁₁	M₁₆	1	4	yes	—
35	C₁₁⋊C₈	—	2	4	no	—
36	C₁₁⋊C₈	—	2	4	no	—
37	#431	—	11	2	no	—
38	C₄×M₁₆	D₁₁	1	1	yes	characteristic
39	#322	—	11	2	no	—
40	#322	—	11	1	no	—
41	C₈²	—	11	1	no	—
42	C₂²×C₁₁	—	2	1	no	—
43	C₂²×C₁₁	—	2	2	no	—
44	C₂²×C₁₁	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₁₁	—	2	1	no	—
46	C₄×C₁₁	—	2	2	no	—
47	C₄×C₁₁	C₂×M₁₆	1	2	yes	—
48	C₄×C₁₁	#131	1	4	yes	—
49	C₂×M₁₆	Dic₁₁	1	2	yes	—
50	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
51	C₄⋊C₈	—	11	4	no	—
52	C₂²⋊C₈	—	11	4	no	—
53	#97	Dic₁₁	1	2	yes	—
54	C₄×C₈	—	11	2	no	—
55	C₄×C₈	—	11	2	no	—
56	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
57	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
58	C₂×C₁₁	—	4	1	no	—
59	C₂×C₁₁	C₄×M₁₆	1	1	yes	characteristic
60	C₂×C₁₁	#405	1	2	yes	—
61	C₂²×C₄	C₄×D₁₁	1	2	yes	—
62	C₂²×C₄	C₂×Dic₁₁	1	1	yes	characteristic
63	M₁₆	—	2	4	no	—
64	C₂×C₈	—	11	4	no	—
65	C₂×C₈	—	11	4	no	—
66	C₂×C₈	C₂×Dic₁₁	1	2	yes	—
67	C₂×C₈	C₂×Dic₁₁	1	2	yes	—
68	C₄²	C₄×D₁₁	1	2	yes	—
69	C₄²	C₂×Dic₁₁	1	1	yes	characteristic
70	C₄²	C₂²×D₁₁	1	1	yes	characteristic
71	C₁₁	#1453	1	1	yes	characteristic, complemented, Sylow
72	C₂³	C₄×Dic₁₁	1	1	yes	characteristic
73	C₂×C₄	—	2	4	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	C₄×Dic₁₁	1	1	yes	characteristic
76	C₂×C₄	C₄×Dic₁₁	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
78	C₂×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	22	4	no	—
81	C₈	—	22	4	no	—
82	C₈	#4318	1	4	yes	—
83	C₂²	—	2	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	C₂×C₄×Dic₁₁	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	#66960	1	4	yes	—
89	C₄	C₂×#4318	1	2	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×#4318	1	1	yes	characteristic
92	C₂	#10622735	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₁₁
commutator, socle	C₂²×C₁₁	C₂×C₄²
Fitting	C₄×C₁₁×M₁₆	C₂
prime radical	C₂³×C₁₁	C₄²
cosocle	C₄²×C₁₁	C₂³
hypercenter	C₄×M₁₆	D₁₁
hypocenter	C₁₁	#1453
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #10622093	C₂	semidirect
4. #10622092	C₂	semidirect
5. C₈×C₁₁⋊C₈	C₂	semidirect
71. C₁₁	#1453	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₁×M₁₆	2
#10622538	2
#10622093	2
#10622092	2
C₈×C₁₁⋊C₈	2
#1453	11