Subgroups — C₂×#10623350 #13083326

Order 1408.

1460 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×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
2	#10623350	C₂	1	16	yes	maximal, direct product factor
3	C₂×#67001	C₂	1	8	yes	maximal, complemented
4	C₂²×#4318	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₁×#41	C₄	1	4	yes	—
6	C₂×C₁₁×#41	C₄	1	8	yes	—
7	C₂×C₁₁×#41	C₂²	1	4	yes	—
8	C₂×C₁₁×#41	C₂²	1	8	yes	—
9	C₂²×Q₈×C₁₁	C₄	1	1	yes	characteristic
10	C₂²×D₄×C₁₁	C₄	1	3	yes	—
11	C₂³×C₄×C₁₁	C₂²	1	3	yes	—
12	#67001	C₂²	1	64	yes	complemented
13	C₂×#4318	C₂²	1	4	yes	—
14	C₂×#4318	C₂²	1	12	yes	complemented
15	C₂×#4318	C₂²	1	48	yes	complemented
16	C₂²×C₁₁⋊C₈	C₂²	1	12	yes	complemented
17	C₂⁴×C₁₁	C₂×C₄	1	3	yes	—
18	C₁₁×#41	C₂×C₄	1	16	yes	—
19	C₁₁×#41	C₂×C₄	1	32	yes	—
20	C₁₁×#41	C₂³	1	16	yes	—
21	C₂×Q₈×C₁₁	C₂×C₄	1	4	yes	—
22	C₂×Q₈×C₁₁	C₂×C₄	1	8	yes	—
23	C₂×D₄×C₁₁	C₂×C₄	1	12	yes	—
24	C₂×D₄×C₁₁	C₂×C₄	1	24	yes	—
25	C₂²×C₄×C₁₁	C₂×C₄	1	3	yes	—
26	C₂²×C₄×C₁₁	C₂×C₄	1	6	yes	—
27	C₂²×C₄×C₁₁	C₂×C₄	1	12	yes	—
28	C₂²×C₄×C₁₁	C₂³	1	6	yes	—
29	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₁₁	C₂³	1	12	yes	—
31	#4318	C₂³	1	16	yes	—
32	#4318	C₂³	1	48	yes	complemented
33	C₂×C₁₁⋊C₈	C₂³	1	8	yes	—
34	C₂×C₁₁⋊C₈	C₂³	1	48	yes	complemented
35	C₂×#568	—	11	1	no	maximal, Sylow
36	C₂³×C₁₁	—	4	6	no	—
37	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
38	C₂³×C₁₁	C₂²×C₄	1	6	yes	—
39	C₂³×C₁₁	C₂²×C₄	1	12	yes	—
40	Q₈×C₁₁	C₂²×C₄	1	16	yes	—
41	D₄×C₁₁	C₂²×C₄	1	48	yes	—
42	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₁	C₂²×C₄	1	12	yes	—
45	C₂×C₄×C₁₁	C₂²×C₄	1	6	yes	—
46	C₂×C₄×C₁₁	C₂²×C₄	1	12	yes	—
47	C₂×C₄×C₁₁	C₂²×C₄	1	24	yes	—
48	C₂×C₄×C₁₁	C₂⁴	1	12	yes	—
49	C₂×C₄×C₁₁	C₂⁴	1	2	yes	—
50	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
51	C₁₁⋊C₈	C₂⁴	1	16	yes	—
52	C₂²×#41	D₁₁	1	1	yes	characteristic
53	#568	—	11	16	no	—
54	C₂×#131	—	11	8	no	—
55	C₂²×M₁₆	—	11	6	no	—
56	C₂²×C₁₁	—	2	2	no	—
57	C₂²×C₁₁	—	2	12	no	—
58	C₂²×C₁₁	—	4	12	no	—
59	C₂²×C₁₁	C₂³×C₄	1	2	yes	—
60	C₂²×C₁₁	C₂³×C₄	1	12	yes	—
61	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₁₁	C₂³×C₄	1	2	yes	—
63	C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
64	C₄×C₁₁	C₂³×C₄	1	12	yes	—
65	C₄×C₁₁	C₂⁵	1	1	yes	characteristic
66	C₂×#41	Dic₁₁	1	4	yes	—
67	C₂×#41	Dic₁₁	1	8	yes	—
68	C₂×#41	C₂×D₁₁	1	4	yes	—
69	C₂×#41	C₂×D₁₁	1	8	yes	—
70	C₂²×Q₈	Dic₁₁	1	1	yes	characteristic
71	C₂²×D₄	Dic₁₁	1	3	yes	—
72	C₂³×C₄	C₂×D₁₁	1	3	yes	—
73	#131	—	11	64	no	—
74	C₂×M₁₆	—	11	4	no	—
75	C₂×M₁₆	—	11	12	no	—
76	C₂×M₁₆	—	11	48	no	—
77	C₂²×C₈	—	11	12	no	—
78	C₂×C₁₁	—	2	2	no	—
79	C₂×C₁₁	—	2	12	no	—
80	C₂×C₁₁	#568	1	2	yes	complemented
81	C₂×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
82	C₂⁴	C₂×Dic₁₁	1	3	yes	—
83	#41	C₂×Dic₁₁	1	16	yes	—
84	#41	C₂×Dic₁₁	1	32	yes	—
85	#41	C₂²×D₁₁	1	16	yes	—
86	C₂×Q₈	C₂×Dic₁₁	1	4	yes	—
87	C₂×Q₈	C₂×Dic₁₁	1	8	yes	—
88	C₂×D₄	C₂×Dic₁₁	1	12	yes	—
89	C₂×D₄	C₂×Dic₁₁	1	24	yes	—
90	C₂²×C₄	C₂×Dic₁₁	1	3	yes	—
91	C₂²×C₄	C₂×Dic₁₁	1	6	yes	—
92	C₂²×C₄	C₂×Dic₁₁	1	12	yes	—
93	C₂²×C₄	C₂²×D₁₁	1	12	yes	—
94	C₂²×C₄	C₂²×D₁₁	1	6	yes	—
95	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
96	M₁₆	—	11	16	no	—
97	M₁₆	—	11	48	no	—
98	C₂×C₈	—	11	48	no	—
99	C₂×C₈	—	11	8	no	—
100	C₁₁	C₂×#568	1	1	yes	characteristic, complemented, Sylow
101	C₂³	—	4	6	no	—
102	C₂³	C₂²×Dic₁₁	1	1	yes	characteristic
103	C₂³	C₂²×Dic₁₁	1	6	yes	—
104	C₂³	C₂²×Dic₁₁	1	12	yes	—
105	Q₈	C₂²×Dic₁₁	1	16	yes	—
106	D₄	C₂²×Dic₁₁	1	48	yes	—
107	C₂×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
108	C₂×C₄	C₂²×Dic₁₁	1	2	yes	—
109	C₂×C₄	C₂²×Dic₁₁	1	12	yes	—
110	C₂×C₄	C₂²×Dic₁₁	1	6	yes	—
111	C₂×C₄	C₂²×Dic₁₁	1	24	yes	—
112	C₂×C₄	C₂²×Dic₁₁	1	12	yes	—
113	C₂×C₄	C₂³×D₁₁	1	12	yes	—
114	C₂×C₄	C₂³×D₁₁	1	2	yes	—
115	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
116	C₈	—	11	16	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	2	12	no	—
119	C₂²	—	4	12	no	—
120	C₂²	C₂³×Dic₁₁	1	2	yes	—
121	C₂²	C₂³×Dic₁₁	1	12	yes	—
122	C₂²	C₂³×Dic₁₁	1	1	yes	characteristic
123	C₄	C₂³×Dic₁₁	1	2	yes	—
124	C₄	C₂³×Dic₁₁	1	1	yes	characteristic
125	C₄	C₂³×Dic₁₁	1	12	yes	—
126	C₄	C₂⁴×D₁₁	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	12	no	—
129	C₂	#10623350	1	2	yes	direct product factor
130	C₂	C₂⁴×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₁
commutator	C₂×C₁₁	C₂⁴×C₄
Frattini	C₄	C₂⁴×D₁₁
Fitting, prime radical	C₂²×C₁₁×#41	C₂
socle	C₂²×C₁₁	C₂³×C₄
cosocle	C₄×C₁₁	C₂⁵
hypercenter	C₂²×#41	D₁₁
hypocenter	C₁₁	C₂×#568
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
2. #10623350	C₂	direct (N × H)
3. C₂×#67001	C₂	semidirect
4. C₂²×#4318	C₂	semidirect
12. #67001	C₂²	semidirect
14. C₂×#4318	C₂²	semidirect
15. C₂×#4318	C₂²	semidirect
16. C₂²×C₁₁⋊C₈	C₂²	semidirect
32. #4318	C₂³	semidirect
34. C₂×C₁₁⋊C₈	C₂³	semidirect
80. C₂×C₁₁	#568	semidirect
100. C₁₁	C₂×#568	semidirect
129. C₂	#10623350	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×C₁₁×#41	2
#10623350	2
C₂×#67001	2
C₂²×#4318	2
C₂×#568	11

Subgroups — C2×#10623350 #13083326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10623350 #13083326