Subgroups — C₂²×#10623343 #15660358

Order 2816.

11230 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10623343	C₂	1	48	yes	maximal, direct product factor
2	C₂²×Q₈×Dic₁₁	C₂	1	8	yes	maximal, complemented
3	C₂²×#66979	C₂	1	6	yes	maximal
4	C₂⁴×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂³×Q₈×C₁₁	C₄	1	32	yes	complemented
6	C₂³×Q₈×C₁₁	C₂²	1	4	yes	—
7	C₂³×Q₈×C₁₁	C₂²	1	24	yes	—
8	C₂⁴×C₄×C₁₁	C₂²	1	3	yes	—
9	C₂²×C₂²⋊Dic₁₁	C₂²	1	4	yes	—
10	#10623343	C₂²	1	256	yes	direct product factor
11	C₂×Q₈×Dic₁₁	C₂²	1	192	yes	complemented
12	C₂×#66979	C₂²	1	144	yes	—
13	C₂²×C₄⋊Dic₁₁	C₂²	1	12	yes	—
14	C₂²×C₄×Dic₁₁	C₂²	1	12	yes	—
15	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
16	C₂²×Q₈×C₁₁	C₂×C₄	1	64	yes	—
17	C₂²×Q₈×C₁₁	C₂×C₄	1	384	yes	complemented
18	C₂²×Q₈×C₁₁	C₂³	1	48	yes	—
19	C₂²×Q₈×C₁₁	C₂³	1	64	yes	—
20	C₂³×C₄×C₁₁	C₂×C₄	1	48	yes	—
21	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
22	C₂³×C₄×C₁₁	C₂³	1	36	yes	—
23	C₂³×Dic₁₁	C₂³	1	8	yes	—
24	C₂×C₂²⋊Dic₁₁	C₂³	1	48	yes	—
25	Q₈×Dic₁₁	C₂³	1	512	yes	complemented
26	#66979	C₂³	1	384	yes	—
27	C₂×C₄⋊Dic₁₁	C₂³	1	144	yes	—
28	C₂×C₄×Dic₁₁	C₂³	1	144	yes	—
29	C₂²×#519	—	11	1	no	maximal, Sylow
30	C₂⁴×C₁₁	—	2	8	no	—
31	C₂⁴×C₁₁	C₂²×C₄	1	8	yes	—
32	C₂⁴×C₁₁	C₂⁴	1	6	yes	—
33	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
34	C₂×Q₈×C₁₁	C₂²×C₄	1	384	yes	—
35	C₂×Q₈×C₁₁	C₂²×C₄	1	512	yes	complemented
36	C₂×Q₈×C₁₁	C₂⁴	1	64	yes	—
37	C₂²×C₄×C₁₁	C₂²×C₄	1	48	yes	—
38	C₂²×C₄×C₁₁	C₂²×C₄	1	288	yes	—
39	C₂²×C₄×C₁₁	C₂⁴	1	36	yes	—
40	C₂²×C₄×C₁₁	C₂⁴	1	48	yes	—
41	C₂²×Dic₁₁	—	2	32	no	—
42	C₂²×Dic₁₁	C₂⁴	1	48	yes	—
43	C₂²⋊Dic₁₁	C₂⁴	1	64	yes	—
44	C₄⋊Dic₁₁	C₂⁴	1	192	yes	—
45	C₄×Dic₁₁	C₂⁴	1	192	yes	—
46	C₂⁴×Q₈	D₁₁	1	1	yes	characteristic
47	C₂×#519	—	11	48	no	—
48	C₂²×C₄×Q₈	—	11	8	no	—
49	C₂²×#117	—	11	6	no	—
50	C₂³×C₁₁	—	2	32	no	—
51	C₂³×C₁₁	—	2	24	no	—
52	C₂³×C₁₁	C₂³×C₄	1	24	yes	—
53	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
54	C₂³×C₁₁	2₋¹⁺⁴	1	8	yes	—
55	C₂³×C₁₁	C₂⁵	1	4	yes	—
56	C₂³×C₁₁	C₂⁵	1	3	yes	—
57	Q₈×C₁₁	C₂³×C₄	1	256	yes	—
58	C₂×C₄×C₁₁	C₂³×C₄	1	144	yes	—
59	C₂×C₄×C₁₁	C₂³×C₄	1	192	yes	—
60	C₂×C₄×C₁₁	C₂⁵	1	24	yes	—
61	C₂×Dic₁₁	—	2	96	no	—
62	C₂×Dic₁₁	C₂⁵	1	32	yes	—
63	C₂³×Q₈	Dic₁₁	1	32	yes	complemented
64	C₂³×Q₈	C₂×D₁₁	1	4	yes	—
65	C₂³×Q₈	C₂×D₁₁	1	24	yes	—
66	C₂⁴×C₄	C₂×D₁₁	1	3	yes	—
67	#519	—	11	256	no	—
68	C₂×C₄×Q₈	—	11	192	no	—
69	C₂×#117	—	11	144	no	—
70	C₂²×C₄⋊C₄	—	11	12	no	—
71	C₂²×C₂²⋊C₄	—	11	4	no	—
72	C₂²×C₄²	—	11	12	no	—
73	C₂²×C₁₁	—	2	8	no	—
74	C₂²×C₁₁	—	2	48	no	—
75	C₂²×C₁₁	#519	1	16	yes	complemented
76	C₂²×C₁₁	C₂⁴×C₄	1	8	yes	—
77	C₂²×C₁₁	C₂⁴×C₄	1	6	yes	—
78	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	12	yes	—
79	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
80	C₄×C₁₁	C₂⁴×C₄	1	48	yes	—
81	Dic₁₁	—	2	32	no	—
82	C₂⁵	C₂²×D₁₁	1	1	yes	characteristic
83	C₂²×Q₈	C₂×Dic₁₁	1	64	yes	—
84	C₂²×Q₈	C₂×Dic₁₁	1	384	yes	complemented
85	C₂²×Q₈	C₂²×D₁₁	1	48	yes	—
86	C₂²×Q₈	C₂²×D₁₁	1	64	yes	—
87	C₂³×C₄	—	11	8	no	—
88	C₂³×C₄	C₂×Dic₁₁	1	48	yes	—
89	C₂³×C₄	C₂²×D₁₁	1	36	yes	—
90	C₂³×C₄	C₂²×D₁₁	1	6	yes	—
91	C₄×Q₈	—	11	512	no	—
92	#117	—	11	384	no	—
93	C₂×C₄⋊C₄	—	11	144	no	—
94	C₂×C₂²⋊C₄	—	11	48	no	—
95	C₂×C₄²	—	11	144	no	—
96	C₂×C₁₁	—	2	8	no	—
97	C₂×C₁₁	C₂×#519	1	12	yes	complemented
98	C₂×C₁₁	C₂⁵×C₄	1	1	yes	characteristic
99	C₂×C₁₁	C₂²×2₋¹⁺⁴	1	2	yes	—
100	C₂⁴	—	2	8	no	—
101	C₂⁴	C₂²×Dic₁₁	1	8	yes	—
102	C₂⁴	C₂³×D₁₁	1	6	yes	—
103	C₂⁴	C₂³×D₁₁	1	1	yes	characteristic
104	C₂×Q₈	C₂²×Dic₁₁	1	384	yes	—
105	C₂×Q₈	C₂²×Dic₁₁	1	512	yes	complemented
106	C₂×Q₈	C₂³×D₁₁	1	64	yes	—
107	C₂²×C₄	—	11	48	no	—
108	C₂²×C₄	—	22	32	no	—
109	C₂²×C₄	C₂²×Dic₁₁	1	48	yes	—
110	C₂²×C₄	C₂²×Dic₁₁	1	288	yes	—
111	C₂²×C₄	C₂³×D₁₁	1	36	yes	—
112	C₂²×C₄	C₂³×D₁₁	1	48	yes	—
113	C₄⋊C₄	—	11	192	no	—
114	C₂²⋊C₄	—	11	64	no	—
115	C₄²	—	11	192	no	—
116	C₁₁	C₂²×#519	1	1	yes	characteristic, complemented, Sylow
117	C₂³	—	2	32	no	—
118	C₂³	—	2	24	no	—
119	C₂³	#67040	1	8	yes	—
120	C₂³	C₂³×Dic₁₁	1	24	yes	—
121	C₂³	C₂³×Dic₁₁	1	4	yes	—
122	C₂³	C₂⁴×D₁₁	1	4	yes	—
123	C₂³	C₂⁴×D₁₁	1	3	yes	—
124	Q₈	C₂³×Dic₁₁	1	256	yes	—
125	C₂×C₄	—	11	32	no	—
126	C₂×C₄	—	22	96	no	—
127	C₂×C₄	C₂³×Dic₁₁	1	144	yes	—
128	C₂×C₄	C₂³×Dic₁₁	1	192	yes	—
129	C₂×C₄	C₂⁴×D₁₁	1	24	yes	—
130	C₂²	—	2	8	no	—
131	C₂²	—	2	48	no	—
132	C₂²	#10623343	1	16	yes	direct product factor
133	C₂²	C₂×#67040	1	12	yes	—
134	C₂²	C₂⁴×Dic₁₁	1	8	yes	—
135	C₂²	C₂⁴×Dic₁₁	1	6	yes	—
136	C₂²	C₂⁵×D₁₁	1	1	yes	characteristic
137	C₄	—	22	32	no	—
138	C₄	C₂⁴×Dic₁₁	1	48	yes	—
139	C₂	—	2	8	no	—
140	C₂	C₂×#10623343	1	12	yes	direct product factor
141	C₂	C₂⁵×Dic₁₁	1	1	yes	characteristic
142	C₂	C₂²×#67040	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₁
commutator	C₂×C₁₁	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₁
Fitting	C₂⁴×Q₈×C₁₁	C₂
socle	C₂⁴×C₁₁	C₂⁴
prime radical	C₂⁵×C₁₁	C₂³
cosocle	C₂²×C₁₁	C₂⁶
hypercenter	C₂⁴×Q₈	D₁₁
hypocenter	C₁₁	C₂²×#519
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#10623343	C₂	direct (N × H)
2. C₂²×Q₈×Dic₁₁	C₂	semidirect
5. C₂³×Q₈×C₁₁	C₄	semidirect
10. #10623343	C₂²	direct (N × H)
11. C₂×Q₈×Dic₁₁	C₂²	semidirect
17. C₂²×Q₈×C₁₁	C₂×C₄	semidirect
25. Q₈×Dic₁₁	C₂³	semidirect
35. C₂×Q₈×C₁₁	C₂²×C₄	semidirect
63. C₂³×Q₈	Dic₁₁	semidirect
75. C₂²×C₁₁	#519	semidirect
84. C₂²×Q₈	C₂×Dic₁₁	semidirect
97. C₂×C₁₁	C₂×#519	semidirect
105. C₂×Q₈	C₂²×Dic₁₁	semidirect
116. C₁₁	C₂²×#519	semidirect
132. C₂²	#10623343	direct (N × H)
140. C₂	C₂×#10623343	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10623343	2
C₂²×Q₈×Dic₁₁	2
C₂²×#66979	2
C₂⁴×Q₈×C₁₁	2
C₂²×#519	11

Subgroups — C22×#10623343 #15660358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10623343 #15660358