Subgroups — #14670173

Order 2816.

342 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066694	C₂	1	6	yes	maximal
2	C₄²×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₁₁	C₄	1	3	yes	—
4	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
5	C₄³×C₁₁	C₄	1	1	yes	characteristic
6	C₂²×C₁₁⋊C₁₆	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
8	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
9	C₂×C₄²×C₁₁	C₈	1	3	yes	—
10	C₂×C₄²×C₁₁	C₈	1	1	yes	characteristic
11	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
12	C₄×C₈×C₁₁	—	2	6	no	—
13	C₄×C₈×C₁₁	—	2	6	no	—
14	C₂×C₁₁⋊C₁₆	—	2	12	no	—
15	#12894	—	11	1	no	maximal, Sylow
16	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
17	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
18	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	—	2	3	no	—
20	C₂×C₈×C₁₁	—	2	3	no	—
21	C₂×C₈×C₁₁	M₁₆	1	6	yes	—
22	C₂×C₈×C₁₁	#41	1	6	yes	—
23	C₄²×C₁₁	—	2	6	no	—
24	C₄²×C₁₁	—	2	3	no	—
25	C₄²×C₁₁	—	2	3	no	—
26	C₄²×C₁₁	C₁₆	1	4	yes	complemented
27	C₁₁⋊C₁₆	—	4	4	no	—
28	C₄²×C₈	D₁₁	1	1	yes	characteristic
29	#1374	—	11	6	no	—
30	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
31	C₂×C₄×C₁₁	—	2	3	no	—
32	C₂×C₄×C₁₁	—	2	3	no	—
33	C₂×C₄×C₁₁	—	2	3	no	—
34	C₂×C₄×C₁₁	—	2	3	no	—
35	C₂×C₄×C₁₁	C₂×C₁₆	1	6	yes	—
36	C₂×C₄×C₁₁	M₃₂	1	6	yes	—
37	C₂×C₄×C₁₁	#117	1	3	yes	—
38	C₂×C₄×C₁₁	C₂×M₁₆	1	3	yes	—
39	C₈×C₁₁	—	2	6	no	—
40	C₈×C₁₁	#126	1	4	yes	—
41	C₂²×C₁₆	—	11	4	no	—
42	C₂×C₄×C₈	Dic₁₁	1	3	yes	—
43	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
44	C₄³	Dic₁₁	1	1	yes	characteristic
45	C₂²×C₁₁	#431	1	3	yes	—
46	C₂²×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
47	C₂²×C₁₁	C₂×M₃₂	1	3	yes	—
48	C₄×C₁₁	—	2	6	no	—
49	C₄×C₁₁	—	2	6	no	—
50	C₄×C₁₁	#383	1	1	yes	characteristic
51	C₄×C₁₁	#432	1	3	yes	—
52	C₂²×C₈	C₂×Dic₁₁	1	3	yes	—
53	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
54	C₂×C₄²	C₁₁⋊C₈	1	3	yes	—
55	C₂×C₄²	C₁₁⋊C₈	1	1	yes	characteristic
56	C₂×C₄²	C₂×Dic₁₁	1	3	yes	—
57	C₂×C₁₆	—	22	12	no	—
58	C₄×C₈	—	2	6	no	—
59	C₄×C₈	—	2	6	no	—
60	C₂×C₁₁	#1839	1	1	yes	characteristic
61	C₂×C₁₁	#2162	1	3	yes	—
62	C₂×C₁₁	#2163	1	3	yes	—
63	C₂²×C₄	C₂×C₁₁⋊C₈	1	3	yes	—
64	C₂²×C₄	C₂×C₁₁⋊C₈	1	3	yes	—
65	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
66	C₂×C₈	—	2	3	no	—
67	C₂×C₈	—	2	3	no	—
68	C₂×C₈	#4318	1	6	yes	—
69	C₂×C₈	#4339	1	6	yes	—
70	C₄²	—	2	6	no	—
71	C₄²	—	2	3	no	—
72	C₄²	—	2	3	no	—
73	C₄²	C₁₁⋊C₁₆	1	4	yes	complemented
74	C₁₆	—	44	4	no	—
75	C₁₁	#12894	1	1	yes	characteristic, complemented, Sylow
76	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	2	3	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	C₂×C₁₁⋊C₁₆	1	6	yes	—
82	C₂×C₄	#66876	1	6	yes	—
83	C₂×C₄	C₂×#4318	1	3	yes	—
84	C₂×C₄	#66979	1	3	yes	—
85	C₈	—	2	6	no	—
86	C₈	#66929	1	4	yes	—
87	C₂²	#10622538	1	3	yes	—
88	C₂²	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic
89	C₂²	C₂×#66876	1	3	yes	—
90	C₄	—	2	6	no	—
91	C₄	—	2	6	no	—
92	C₄	#10622539	1	3	yes	—
93	C₄	#10622550	1	1	yes	characteristic
94	C₂	#13068759	1	1	yes	characteristic
95	C₂	#13070415	1	3	yes	—
96	C₂	#13070419	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₁
commutator	C₂²×C₁₁	C₂²×C₁₆
Fitting	C₄²×C₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₄²×C₈	D₁₁
hypocenter	C₁₁	#12894
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
26. C₄²×C₁₁	C₁₆	semidirect
73. C₄²	C₁₁⋊C₁₆	semidirect
75. C₁₁	#12894	semidirect

Maximal subgroups

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

subgroup	index
#13066694	2
C₄²×C₈×C₁₁	2
#12894	11