Subgroups — C₂²×#10622093 #14719341

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁⋊C₈	C₂	1	2	yes	maximal
2	C₂×#10622093	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₁	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂³×C₁₁⋊C₈	C₄	1	4	yes	—
7	C₂×C₄×C₈×C₁₁	C₄	1	6	yes	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	6	yes	—
9	C₂×C₄×C₁₁⋊C₈	C₄	1	12	yes	—
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	12	yes	—
11	#10622093	C₂²	1	16	yes	direct product factor
12	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
13	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₁	C₈	1	16	yes	complemented
15	C₂²×C₈×C₁₁	C₂×C₄	1	12	yes	—
16	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
17	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
18	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
19	C₂²×C₁₁⋊C₈	—	2	16	no	—
20	C₂²×C₁₁⋊C₈	C₂×C₄	1	24	yes	—
21	C₄×C₈×C₁₁	C₂×C₄	1	12	yes	—
22	C₄×C₈×C₁₁	C₂³	1	4	yes	—
23	C₄×C₁₁⋊C₈	C₂×C₄	1	24	yes	—
24	C₄×C₁₁⋊C₈	C₂³	1	8	yes	—
25	C₂²×#322	—	11	1	no	maximal, Sylow
26	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
27	C₂²×C₄×C₁₁	C₄²	1	3	yes	—
28	C₂²×C₄×C₁₁	C₄²	1	6	yes	—
29	C₂²×C₄×C₁₁	C₂×C₈	1	8	yes	—
30	C₂²×C₄×C₁₁	M₁₆	1	16	yes	—
31	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
32	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
33	C₂×C₈×C₁₁	C₂×C₈	1	48	yes	complemented
34	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
35	C₄²×C₁₁	C₄²	1	6	yes	—
36	C₄²×C₁₁	C₂²×C₄	1	6	yes	—
37	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
38	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
39	C₂×C₁₁⋊C₈	—	2	48	no	—
40	C₂×C₁₁⋊C₈	C₂²×C₄	1	16	yes	—
41	C₂²×C₄×C₈	—	11	2	no	—
42	C₂²×C₄×C₈	D₁₁	1	1	yes	characteristic
43	C₂×#322	—	11	12	no	—
44	C₂³×C₁₁	C₄×C₈	1	4	yes	—
45	C₂³×C₁₁	#97	1	8	yes	—
46	C₂³×C₁₁	C₂×C₄²	1	3	yes	—
47	C₂×C₄×C₁₁	C₄×C₈	1	12	yes	—
48	C₂×C₄×C₁₁	#97	1	24	yes	—
49	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
50	C₂×C₄×C₁₁	C₂×C₄²	1	6	yes	—
51	C₂×C₄×C₁₁	C₂²×C₈	1	12	yes	—
52	C₂×C₄×C₁₁	C₂×M₁₆	1	24	yes	—
53	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
54	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
55	C₈×C₁₁	C₂²×C₈	1	16	yes	complemented
56	C₁₁⋊C₈	—	2	16	no	—
57	C₂³×C₈	—	11	4	no	—
58	C₂³×C₈	Dic₁₁	1	2	yes	—
59	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
60	C₂×C₄×C₈	—	11	12	no	—
61	C₂×C₄×C₈	—	11	12	no	—
62	C₂×C₄×C₈	Dic₁₁	1	6	yes	—
63	C₂×C₄×C₈	C₂×D₁₁	1	6	yes	—
64	#322	—	11	16	no	—
65	C₂²×C₁₁	#322	1	16	yes	complemented
66	C₂²×C₁₁	C₂×C₄×C₈	1	6	yes	—
67	C₂²×C₁₁	C₂×#97	1	12	yes	—
68	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
69	C₄×C₁₁	C₂×C₄×C₈	1	6	yes	—
70	C₄×C₁₁	C₂×#97	1	12	yes	—
71	C₄×C₁₁	C₂³×C₈	1	2	yes	—
72	C₄×C₁₁	C₂²×M₁₆	1	4	yes	—
73	C₂³×C₄	C₄×D₁₁	1	2	yes	—
74	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
75	C₂²×C₈	—	11	24	no	—
76	C₂²×C₈	—	22	16	no	—
77	C₂²×C₈	C₁₁⋊C₈	1	16	yes	complemented
78	C₂²×C₈	C₂×Dic₁₁	1	12	yes	—
79	C₂×C₄²	C₄×D₁₁	1	6	yes	—
80	C₂×C₄²	C₂×Dic₁₁	1	3	yes	—
81	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
82	C₄×C₈	—	11	24	no	—
83	C₄×C₈	—	11	8	no	—
84	C₄×C₈	C₂×Dic₁₁	1	12	yes	—
85	C₄×C₈	C₂²×D₁₁	1	4	yes	—
86	C₂×C₁₁	C₂×#322	1	12	yes	complemented
87	C₂×C₁₁	C₂²×C₄×C₈	1	1	yes	characteristic
88	C₂×C₁₁	C₂²×#97	1	2	yes	—
89	C₂⁴	C₄×Dic₁₁	1	1	yes	characteristic
90	C₂²×C₄	#4313	1	16	yes	—
91	C₂²×C₄	C₂×C₁₁⋊C₈	1	8	yes	—
92	C₂²×C₄	C₄×Dic₁₁	1	3	yes	—
93	C₂²×C₄	C₄×Dic₁₁	1	6	yes	—
94	C₂²×C₄	C₂×C₄×D₁₁	1	6	yes	—
95	C₂²×C₄	C₂²×Dic₁₁	1	3	yes	—
96	C₂×C₈	—	11	16	no	—
97	C₂×C₈	—	22	48	no	—
98	C₂×C₈	C₂×C₁₁⋊C₈	1	48	yes	complemented
99	C₂×C₈	C₂²×Dic₁₁	1	8	yes	—
100	C₄²	C₄×Dic₁₁	1	6	yes	—
101	C₄²	C₂×C₄×D₁₁	1	6	yes	—
102	C₄²	C₂²×Dic₁₁	1	3	yes	—
103	C₄²	C₂³×D₁₁	1	1	yes	characteristic
104	C₁₁	C₂²×#322	1	1	yes	characteristic, complemented, Sylow
105	C₂³	C₄×C₁₁⋊C₈	1	4	yes	—
106	C₂³	#66879	1	8	yes	—
107	C₂³	C₂×C₄×Dic₁₁	1	3	yes	—
108	C₂×C₄	C₄×C₁₁⋊C₈	1	12	yes	—
109	C₂×C₄	#66879	1	24	yes	—
110	C₂×C₄	C₂×#4313	1	24	yes	—
111	C₂×C₄	C₂²×C₁₁⋊C₈	1	12	yes	—
112	C₂×C₄	C₂×C₄×Dic₁₁	1	3	yes	—
113	C₂×C₄	C₂×C₄×Dic₁₁	1	6	yes	—
114	C₂×C₄	C₂²×C₄×D₁₁	1	2	yes	—
115	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
116	C₈	—	22	16	no	—
117	C₈	C₂²×C₁₁⋊C₈	1	16	yes	complemented
118	C₂²	#10622093	1	16	yes	direct product factor
119	C₂²	C₂×C₄×C₁₁⋊C₈	1	6	yes	—
120	C₂²	C₂×#66879	1	12	yes	—
121	C₂²	C₂²×C₄×Dic₁₁	1	1	yes	characteristic
122	C₄	C₂×C₄×C₁₁⋊C₈	1	6	yes	—
123	C₄	C₂×#66879	1	12	yes	—
124	C₄	C₂²×#4313	1	4	yes	—
125	C₄	C₂³×C₁₁⋊C₈	1	2	yes	—
126	C₂	C₂×#10622093	1	12	yes	direct product factor
127	C₂	C₂²×C₄×C₁₁⋊C₈	1	1	yes	characteristic
128	C₂	C₂²×#66879	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂²×C₄×C₈×C₁₁	C₂
socle, prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂²×C₄×C₈	D₁₁
hypocenter	C₁₁	C₂²×#322
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#10622093	C₂	direct (N × H)
11. #10622093	C₂²	direct (N × H)
14. C₂²×C₈×C₁₁	C₈	semidirect
33. C₂×C₈×C₁₁	C₂×C₈	semidirect
55. C₈×C₁₁	C₂²×C₈	semidirect
65. C₂²×C₁₁	#322	semidirect
77. C₂²×C₈	C₁₁⋊C₈	semidirect
86. C₂×C₁₁	C₂×#322	semidirect
98. C₂×C₈	C₂×C₁₁⋊C₈	semidirect
104. C₁₁	C₂²×#322	semidirect
117. C₈	C₂²×C₁₁⋊C₈	semidirect
118. C₂²	#10622093	direct (N × H)
126. C₂	C₂×#10622093	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₁⋊C₈	2
C₂×#10622093	2
C₂²×C₄×C₈×C₁₁	2
C₂²×#322	11

Subgroups — C22×#10622093 #14719341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10622093 #14719341