Subgroups — #14643149

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#66867	C₂	1	2	yes	maximal
2	C₂×#10622092	C₂	1	2	yes	maximal
3	C₂×#10622093	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#97	C₄	1	4	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₄³×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×#66867	C₄	1	8	yes	—
11	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
12	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
13	#10622093	C₄	1	4	yes	complemented
14	#10622092	C₄	1	8	yes	complemented
15	C₈×C₁₁⋊C₈	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
21	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
22	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
23	C₁₁×#97	—	2	8	no	—
24	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
27	#66867	—	2	16	no	—
28	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
30	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
31	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
32	#7846	—	11	1	no	maximal, Sylow
33	C₂²×C₄×C₁₁	C₄²	1	4	yes	—
34	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
35	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₁	—	2	4	no	—
37	C₂×C₈×C₁₁	C₄²	1	4	yes	—
38	C₂×C₈×C₁₁	C₄²	1	4	yes	—
39	C₂×C₈×C₁₁	M₁₆	1	8	yes	—
40	C₄²×C₁₁	—	2	8	no	—
41	C₄²×C₁₁	—	2	4	no	—
42	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
43	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
44	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₁₁⋊C₈	—	2	8	no	—
46	C₂×C₁₁⋊C₈	C₄²	1	8	yes	—
47	C₂×C₁₁⋊C₈	C₄²	1	8	yes	—
48	C₂×C₁₁⋊C₈	M₁₆	1	16	yes	—
49	C₄×#97	—	11	2	no	—
50	C₄×#97	D₁₁	1	1	yes	characteristic
51	C₂×#322	—	11	1	no	—
52	C₂×#322	—	11	2	no	—
53	C₂×C₈²	—	11	1	no	—
54	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₁	—	2	8	no	—
56	C₂×C₄×C₁₁	—	2	4	no	—
57	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
58	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
59	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂×M₁₆	1	8	yes	—
62	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
63	C₈×C₁₁	—	2	4	no	—
64	C₈×C₁₁	#97	1	8	yes	complemented
65	C₁₁⋊C₈	—	2	8	no	—
66	C₁₁⋊C₈	#97	1	16	yes	complemented
67	C₂×#97	—	11	8	no	—
68	C₂×#97	Dic₁₁	1	4	yes	—
69	C₂×C₄×C₈	—	11	2	no	—
70	C₂×C₄×C₈	—	11	2	no	—
71	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
73	C₄³	C₂×D₁₁	1	1	yes	characteristic
74	#322	—	11	8	no	—
75	#322	—	11	4	no	—
76	C₈²	—	11	4	no	—
77	C₂²×C₁₁	C₄³	1	1	yes	characteristic
78	C₂²×C₁₁	C₄×M₁₆	1	4	yes	—
79	C₂²×C₁₁	C₄×M₁₆	1	2	yes	—
80	C₄×C₁₁	—	4	4	no	—
81	C₄×C₁₁	C₂×#97	1	2	yes	—
82	C₄×C₁₁	C₂×#97	1	4	yes	—
83	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
84	C₄×C₁₁	C₄×M₁₆	1	4	yes	—
85	C₂²×C₈	—	11	4	no	—
86	C₂²×C₈	—	11	4	no	—
87	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
88	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
89	C₂×C₄²	C₄×D₁₁	1	4	yes	—
90	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
91	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
92	#97	—	2	8	no	—
93	#97	—	22	16	no	—
94	C₄×C₈	—	11	4	no	—
95	C₄×C₈	—	11	4	no	—
96	C₄×C₈	—	11	4	no	—
97	C₄×C₈	—	11	4	no	—
98	C₄×C₈	C₄×D₁₁	1	2	yes	—
99	C₄×C₈	C₄×D₁₁	1	4	yes	—
100	C₄×C₈	C₄×D₁₁	1	2	yes	—
101	C₂×C₁₁	#1455	1	4	yes	—
102	C₂×C₁₁	C₄×#97	1	2	yes	—
103	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
104	C₂²×C₄	C₄×Dic₁₁	1	4	yes	—
105	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
106	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
107	C₂×C₈	—	2	4	no	—
108	C₂×C₈	—	11	8	no	—
109	C₂×C₈	—	11	16	no	—
110	C₂×C₈	—	11	8	no	—
111	C₂×C₈	—	22	8	no	—
112	C₂×C₈	#4318	1	8	yes	—
113	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
114	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
115	C₄²	—	2	8	no	—
116	C₄²	—	2	4	no	—
117	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
118	C₄²	C₂×C₄×D₁₁	1	2	yes	—
119	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
120	C₁₁	#7846	1	1	yes	characteristic, complemented, Sylow
121	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
122	C₂×C₄	—	2	8	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	C₄²×D₁₁	1	2	yes	—
125	C₂×C₄	C₄²×D₁₁	1	2	yes	—
126	C₂×C₄	M₁₆×D₁₁	1	8	yes	—
127	C₂×C₄	C₂×#4318	1	4	yes	—
128	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
129	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
130	C₈	—	2	4	no	—
131	C₈	—	11	16	no	—
132	C₈	—	22	8	no	—
133	C₈	#66867	1	8	yes	complemented
134	C₂²	C₄×#4318	1	2	yes	—
135	C₂²	C₄²×Dic₁₁	1	1	yes	characteristic
136	C₂²	M₁₆×Dic₁₁	1	4	yes	—
137	C₄	—	4	4	no	—
138	C₄	D₁₁×#97	1	4	yes	—
139	C₄	#10622320	1	4	yes	—
140	C₄	C₂×#66867	1	2	yes	—
141	C₄	C₄×#4318	1	2	yes	—
142	C₂	#13066919	1	4	yes	—
143	C₂	#97×Dic₁₁	1	2	yes	—
144	C₂	C₄×#66867	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₄³
Fitting	C₄×C₁₁×#97	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₄×#97	D₁₁
hypocenter	C₁₁	#7846
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
13. #10622093	C₄	semidirect
14. #10622092	C₄	semidirect
15. C₈×C₁₁⋊C₈	C₄	semidirect
64. C₈×C₁₁	#97	semidirect
66. C₁₁⋊C₈	#97	semidirect
120. C₁₁	#7846	semidirect
133. C₈	#66867	semidirect

Maximal subgroups

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

subgroup	index
C₄×#66867	2
C₂×#10622092	2
C₂×#10622093	2
C₂×C₈×C₁₁⋊C₈	2
C₄×C₁₁×#97	2
#7846	11