Subgroups — #14662767

Order 2816.

322 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×#66876	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13066535	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×M₃₂	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×#66876	C₄	1	2	yes	—
8	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
9	C₁₁×#346	C₄	1	2	yes	—
10	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
11	#10622099	C₄	1	2	yes	—
12	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	—
13	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
15	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₁₁⋊C₈	C₈	1	4	yes	—
20	C₁₁×M₃₂	—	2	4	no	—
21	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	#66876	—	2	4	no	—
27	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
28	C₄×C₁₁⋊C₈	C₈	1	4	yes	—
29	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
30	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
31	#11402	—	11	1	no	maximal, Sylow
32	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
34	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
35	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
37	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
38	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₄²×C₁₁	C₄²	1	1	yes	characteristic
41	C₄²×C₁₁	C₂×C₈	1	2	yes	—
42	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₁₁⋊C₈	—	2	8	no	—
44	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
45	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
46	C₁₁×C₁₆	—	2	4	no	—
47	C₁₁⋊C₁₆	—	2	4	no	—
48	C₄×M₃₂	—	11	1	no	—
49	C₄×M₃₂	D₁₁	1	1	yes	characteristic
50	C₂×C₈²	—	11	1	no	—
51	#1312	—	11	4	no	—
52	C₂³×C₁₁	C₄×C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₁	—	2	4	no	—
54	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
55	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₁	#97	1	2	yes	—
57	C₂×C₄×C₁₁	#97	1	2	yes	—
58	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
60	C₈×C₁₁	#97	1	2	yes	—
61	C₈×C₁₁	#97	1	2	yes	—
62	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
63	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
64	C₁₁⋊C₈	—	2	4	no	—
65	C₁₁⋊C₈	M₃₂	1	8	yes	complemented
66	C₂×M₃₂	—	11	2	no	—
67	C₂×M₃₂	Dic₁₁	1	2	yes	—
68	C₂×C₄×C₈	—	11	2	no	—
69	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
70	#346	—	11	2	no	—
71	#346	Dic₁₁	1	2	yes	—
72	C₄×C₁₆	—	11	2	no	—
73	C₄×C₁₆	C₂×D₁₁	1	2	yes	—
74	C₈²	—	11	2	no	—
75	C₈²	—	11	1	no	—
76	C₈²	—	11	1	no	—
77	C₂²×C₁₁	—	2	2	no	—
78	C₂²×C₁₁	#322	1	2	yes	—
79	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
80	C₄×C₁₁	—	2	2	no	—
81	C₄×C₁₁	#322	1	2	yes	—
82	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
83	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
84	C₄×C₁₁	C₂×M₃₂	1	4	yes	—
85	C₂²×C₈	—	11	4	no	—
86	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
87	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
88	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
89	M₃₂	—	2	4	no	—
90	M₃₂	—	22	4	no	—
91	C₂×C₁₆	—	11	4	no	—
92	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	—
93	C₄×C₈	—	11	4	no	—
94	C₄×C₈	—	11	2	no	—
95	C₄×C₈	—	11	2	no	—
96	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
97	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
98	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
99	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
100	C₂×C₁₁	—	2	2	no	—
101	C₂×C₁₁	C₂×#322	1	1	yes	characteristic
102	C₂×C₁₁	C₄×M₃₂	1	2	yes	—
103	C₂²×C₄	C₈×D₁₁	1	2	yes	—
104	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
105	C₂×C₈	—	11	4	no	—
106	C₂×C₈	—	11	4	no	—
107	C₂×C₈	—	22	8	no	—
108	C₂×C₈	#4313	1	4	yes	—
109	C₂×C₈	#4318	1	4	yes	—
110	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
111	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
112	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
113	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
114	C₄²	C₈×D₁₁	1	2	yes	—
115	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
116	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
117	C₁₆	—	2	4	no	—
118	C₁₆	—	22	4	no	—
119	C₁₁	#11402	1	1	yes	characteristic, complemented, Sylow
120	C₂³	C₈×Dic₁₁	1	1	yes	characteristic
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	#66867	1	2	yes	—
123	C₂×C₄	C₈×Dic₁₁	1	2	yes	—
124	C₂×C₄	C₈×Dic₁₁	1	1	yes	characteristic
125	C₂×C₄	#66879	1	2	yes	—
126	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
127	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
128	C₈	—	11	8	no	—
129	C₈	—	22	4	no	—
130	C₈	#66867	1	2	yes	—
131	C₈	#66879	1	2	yes	—
132	C₈	C₂×#4313	1	2	yes	—
133	C₈	C₂×#4318	1	2	yes	—
134	C₂²	—	2	2	no	—
135	C₂²	#10622092	1	2	yes	—
136	C₂²	C₂×C₈×Dic₁₁	1	1	yes	characteristic
137	C₄	—	2	2	no	—
138	C₄	#10622092	1	2	yes	—
139	C₄	D₁₁×M₃₂	1	4	yes	—
140	C₄	C₂×#66867	1	1	yes	characteristic
141	C₄	C₂×#66879	1	1	yes	characteristic
142	C₂	—	2	2	no	—
143	C₂	C₂×#10622092	1	1	yes	characteristic
144	C₂	M₃₂×Dic₁₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₁₁
commutator, socle	C₂²×C₁₁	C₂×C₄×C₈
Fitting	C₄×C₁₁×M₃₂	C₂
prime radical	C₂³×C₁₁	C₄×C₈
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₄×M₃₂	D₁₁
hypocenter	C₁₁	#11402
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13066535	C₂	semidirect
65. C₁₁⋊C₈	M₃₂	semidirect
119. C₁₁	#11402	semidirect

Maximal subgroups

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

subgroup	index
C₄×#66876	2
C₂×C₈×C₁₁⋊C₈	2
#13066535	2
C₄×C₁₁×M₃₂	2
#11402	11