Subgroups — C₂²×#10622142 #14906794

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66882	C₂	1	2	yes	maximal
2	C₂×#10622142	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
5	C₂²×C₄⋊Dic₁₁	—	2	2	no	—
6	C₂²×C₁₁×C₁₆	C₄	1	8	yes	complemented
7	C₂²×C₁₁×C₁₆	C₂²	1	6	yes	—
8	C₂×#66882	—	2	6	no	—
9	C₂×#66882	C₂²	1	12	yes	—
10	#10622142	C₂²	1	16	yes	direct product factor
11	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
12	C₂³×Dic₁₁	—	4	2	no	—
13	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
14	C₂²×C₈×C₁₁	D₄	1	3	yes	—
15	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
16	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
17	C₂×C₄⋊Dic₁₁	—	2	12	no	—
18	C₂×C₄⋊Dic₁₁	—	4	6	no	—
19	C₂×C₁₁×C₁₆	C₂×C₄	1	24	yes	complemented
20	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
21	#66882	—	2	12	no	—
22	#66882	C₂³	1	8	yes	—
23	C₂²×#366	—	11	1	no	maximal, Sylow
24	C₂⁴×C₁₁	D₈	1	1	yes	characteristic
25	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
26	C₂²×C₄×C₁₁	D₈	1	3	yes	—
27	C₂²×C₄×C₁₁	Q₁₆	1	4	yes	—
28	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
29	C₂²×Dic₁₁	—	4	12	no	—
30	C₂²×Dic₁₁	—	8	8	no	—
31	C₂×C₈×C₁₁	C₄⋊C₄	1	12	yes	—
32	C₂×C₈×C₁₁	C₂²×C₄	1	6	yes	—
33	C₂×C₈×C₁₁	C₂×D₄	1	3	yes	—
34	C₂×C₈×C₁₁	C₂×Q₈	1	6	yes	—
35	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
36	C₄⋊Dic₁₁	—	2	8	no	—
37	C₄⋊Dic₁₁	—	4	12	no	—
38	C₁₁×C₁₆	C₂²×C₄	1	8	yes	complemented
39	C₂³×C₁₆	D₁₁	1	1	yes	characteristic
40	C₂²×#107	—	11	2	no	—
41	C₂×#366	—	11	12	no	—
42	C₂³×C₁₁	#107	1	4	yes	—
43	C₂³×C₁₁	D₁₆	1	4	yes	—
44	C₂³×C₁₁	Q₃₂	1	4	yes	—
45	C₂³×C₁₁	C₂×D₈	1	3	yes	—
46	C₂×C₄×C₁₁	#107	1	12	yes	—
47	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
48	C₂×C₄×C₁₁	C₂×D₈	1	3	yes	—
49	C₂×C₄×C₁₁	C₂×Q₁₆	1	6	yes	—
50	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
51	C₂×Dic₁₁	—	4	8	no	—
52	C₂×Dic₁₁	—	8	24	no	—
53	C₈×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
54	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
55	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
56	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
57	C₂²×C₄⋊C₄	—	22	2	no	—
58	C₂²×C₁₆	Dic₁₁	1	8	yes	complemented
59	C₂²×C₁₆	C₂×D₁₁	1	6	yes	—
60	C₂×#107	—	11	12	no	—
61	C₂×#107	—	22	6	no	—
62	#366	—	11	16	no	—
63	C₂²×C₁₁	#366	1	16	yes	complemented
64	C₂²×C₁₁	C₂×#107	1	6	yes	—
65	C₂²×C₁₁	C₂×D₁₆	1	6	yes	—
66	C₂²×C₁₁	C₂×Q₃₂	1	6	yes	—
67	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
68	C₄×C₁₁	C₂×#107	1	6	yes	—
69	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
70	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
71	Dic₁₁	—	8	8	no	—
72	C₂³×C₄	—	44	2	no	—
73	C₂³×C₄	D₄₄	1	1	yes	characteristic
74	C₂²×C₈	Dic₂₂	1	4	yes	—
75	C₂²×C₈	D₄₄	1	3	yes	—
76	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
77	C₂²×C₈	C₂²×D₁₁	1	3	yes	—
78	C₂×C₄⋊C₄	—	22	12	no	—
79	C₂×C₄⋊C₄	—	44	6	no	—
80	C₂×C₁₆	C₂×Dic₁₁	1	24	yes	complemented
81	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
82	#107	—	11	8	no	—
83	#107	—	22	12	no	—
84	C₂×C₁₁	C₂×#366	1	12	yes	complemented
85	C₂×C₁₁	C₂²×#107	1	1	yes	characteristic
86	C₂×C₁₁	C₂²×D₁₆	1	1	yes	characteristic
87	C₂×C₁₁	C₂²×Q₃₂	1	1	yes	characteristic
88	C₂⁴	D₈₈	1	1	yes	characteristic
89	C₂²×C₄	—	44	12	no	—
90	C₂²×C₄	—	88	8	no	—
91	C₂²×C₄	D₈₈	1	3	yes	—
92	C₂²×C₄	Dic₄₄	1	4	yes	—
93	C₂²×C₄	C₄⋊Dic₁₁	1	4	yes	—
94	C₂²×C₄	C₂×D₄₄	1	3	yes	—
95	C₂×C₈	C₄⋊Dic₁₁	1	12	yes	—
96	C₂×C₈	C₂×Dic₂₂	1	6	yes	—
97	C₂×C₈	C₂×D₄₄	1	3	yes	—
98	C₂×C₈	C₂²×Dic₁₁	1	6	yes	—
99	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
100	C₄⋊C₄	—	22	8	no	—
101	C₄⋊C₄	—	44	12	no	—
102	C₁₆	C₂²×Dic₁₁	1	8	yes	complemented
103	C₁₁	C₂²×#366	1	1	yes	characteristic, complemented, Sylow
104	C₂³	D₁₇₆	1	4	yes	—
105	C₂³	Dic₈₈	1	4	yes	—
106	C₂³	#66882	1	4	yes	—
107	C₂³	C₂×D₈₈	1	3	yes	—
108	C₂×C₄	—	44	8	no	—
109	C₂×C₄	—	88	24	no	—
110	C₂×C₄	#66882	1	12	yes	—
111	C₂×C₄	C₂×D₈₈	1	3	yes	—
112	C₂×C₄	C₂×Dic₄₄	1	6	yes	—
113	C₂×C₄	C₂×C₄⋊Dic₁₁	1	6	yes	—
114	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
115	C₈	C₂×C₄⋊Dic₁₁	1	6	yes	—
116	C₈	C₂²×Dic₂₂	1	1	yes	characteristic
117	C₈	C₂³×Dic₁₁	1	1	yes	characteristic
118	C₂²	#10622142	1	16	yes	direct product factor
119	C₂²	C₂×D₁₇₆	1	6	yes	—
120	C₂²	C₂×Dic₈₈	1	6	yes	—
121	C₂²	C₂×#66882	1	6	yes	—
122	C₂²	C₂²×D₈₈	1	1	yes	characteristic
123	C₄	—	88	8	no	—
124	C₄	C₂×#66882	1	6	yes	—
125	C₄	C₂²×Dic₄₄	1	1	yes	characteristic
126	C₄	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
127	C₂	C₂×#10622142	1	12	yes	direct product factor
128	C₂	C₂²×#66882	1	1	yes	characteristic
129	C₂	C₂²×D₁₇₆	1	1	yes	characteristic
130	C₂	C₂²×Dic₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₈₈
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂³×C₁₁×C₁₆	C₂
socle, prime radical	C₂⁴×C₁₁	D₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂³×C₁₆	D₁₁
hypocenter	C₁₁	C₂²×#366
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#10622142	C₂	direct (N × H)
6. C₂²×C₁₁×C₁₆	C₄	semidirect
10. #10622142	C₂²	direct (N × H)
19. C₂×C₁₁×C₁₆	C₂×C₄	semidirect
38. C₁₁×C₁₆	C₂²×C₄	semidirect
58. C₂²×C₁₆	Dic₁₁	semidirect
63. C₂²×C₁₁	#366	semidirect
80. C₂×C₁₆	C₂×Dic₁₁	semidirect
84. C₂×C₁₁	C₂×#366	semidirect
102. C₁₆	C₂²×Dic₁₁	semidirect
103. C₁₁	C₂²×#366	semidirect
118. C₂²	#10622142	direct (N × H)
127. C₂	C₂×#10622142	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×#66882	2
C₂×#10622142	2
C₂³×C₁₁×C₁₆	2
C₂²×#366	11

Subgroups — C22×#10622142 #14906794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10622142 #14906794