Subgroups — #14640661

Order 2816.

200 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622101	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622101	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×M₃₂	C₄	1	1	yes	characteristic
5	C₂×C₁₁×M₃₂	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×#66876	—	2	1	no	—
8	C₂×#66876	—	2	1	no	—
9	C₁₁×#346	—	2	1	no	—
10	C₄×C₁₁×C₁₆	—	2	1	no	—
11	#10622101	—	2	1	no	—
12	#10622101	—	2	1	no	—
13	#10622101	C₄	1	2	yes	—
14	#10622101	C₄	1	2	yes	—
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
18	C₁₁×M₃₂	—	2	1	no	—
19	C₁₁×M₃₂	—	2	1	no	—
20	C₁₁×M₃₂	C₈	1	2	yes	—
21	C₁₁×M₃₂	C₈	1	2	yes	—
22	C₂×C₁₁×C₁₆	—	2	1	no	—
23	C₂×C₁₁×C₁₆	—	2	1	no	—
24	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
27	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
28	#66876	—	2	2	no	—
29	#66876	—	2	2	no	—
30	#66876	—	4	1	no	—
31	#66876	—	4	1	no	—
32	C₂×C₁₁⋊C₁₆	—	4	1	no	—
33	C₂×C₁₁⋊C₁₆	—	4	1	no	—
34	#7162	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	—	2	1	no	—
36	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
43	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
46	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
49	C₄²×C₁₁	—	2	1	no	—
50	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
51	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₁₁×C₁₆	—	2	2	no	—
53	C₁₁×C₁₆	—	2	2	no	—
54	C₁₁⋊C₁₆	—	4	2	no	—
55	C₁₁⋊C₁₆	—	4	2	no	—
56	C₂×#364	—	11	1	no	—
57	C₂×#364	—	11	1	no	—
58	C₄×M₃₂	D₁₁	1	1	yes	characteristic
59	C₂³×C₁₁	#108	1	1	yes	characteristic
60	C₂×C₄×C₁₁	—	2	1	no	—
61	C₂×C₄×C₁₁	—	2	1	no	—
62	C₂×C₄×C₁₁	—	4	2	no	—
63	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
67	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#108	1	1	yes	characteristic
69	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
70	C₈×C₁₁	#97	1	1	yes	characteristic
71	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
72	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
73	C₈×C₁₁	#102	1	1	yes	characteristic
74	C₈×C₁₁	#102	1	1	yes	characteristic
75	C₈×C₁₁	#103	1	1	yes	characteristic
76	C₈×C₁₁	#103	1	1	yes	characteristic
77	C₂×M₃₂	—	22	1	no	—
78	C₂×M₃₂	—	22	1	no	—
79	C₂×M₃₂	Dic₁₁	1	1	yes	characteristic
80	C₂×M₃₂	Dic₁₁	1	1	yes	characteristic
81	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
82	#364	—	11	2	no	—
83	#364	—	11	2	no	—
84	#364	—	22	1	no	—
85	#364	—	22	1	no	—
86	#346	—	2	1	no	—
87	C₄×C₁₆	—	2	1	no	—
88	C₂²×C₁₁	—	4	1	no	—
89	C₂²×C₁₁	#334	1	1	yes	characteristic
90	C₂²×C₁₁	#335	1	1	yes	characteristic
91	C₂²×C₁₁	#341	1	1	yes	characteristic
92	C₄×C₁₁	—	2	2	no	—
93	C₄×C₁₁	—	4	1	no	—
94	C₄×C₁₁	#334	1	1	yes	characteristic
95	C₄×C₁₁	#335	1	1	yes	characteristic
96	C₄×C₁₁	#336	1	1	yes	characteristic
97	C₄×C₁₁	#340	1	1	yes	characteristic
98	C₂²×C₈	D₄₄	1	1	yes	characteristic
99	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
100	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
101	M₃₂	—	2	1	no	—
102	M₃₂	—	2	1	no	—
103	M₃₂	—	22	2	no	—
104	M₃₂	—	22	2	no	—
105	M₃₂	—	44	1	no	—
106	M₃₂	—	44	1	no	—
107	M₃₂	C₁₁⋊C₈	1	2	yes	—
108	M₃₂	C₁₁⋊C₈	1	2	yes	—
109	C₂×C₁₆	—	2	1	no	—
110	C₂×C₁₆	—	2	1	no	—
111	C₂×C₁₆	—	44	1	no	—
112	C₂×C₁₆	—	44	1	no	—
113	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
114	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
115	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
116	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
117	C₂×C₁₁	—	2	1	no	—
118	C₂×C₁₁	—	2	1	no	—
119	C₂×C₁₁	—	2	1	no	—
120	C₂×C₁₁	#1277	1	1	yes	characteristic
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
123	C₂×C₈	#4314	1	1	yes	characteristic
124	C₂×C₈	#4314	1	1	yes	characteristic
125	C₂×C₈	D₈₈	1	1	yes	characteristic
126	C₂×C₈	Dic₄₄	1	1	yes	characteristic
127	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
128	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
129	C₂×C₈	#4318	1	1	yes	characteristic
130	C₂×C₈	#4318	1	1	yes	characteristic
131	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
132	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
133	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
134	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
135	C₄²	—	2	1	no	—
136	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
137	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
138	C₁₆	—	2	2	no	—
139	C₁₆	—	2	2	no	—
140	C₁₆	—	44	2	no	—
141	C₁₆	—	44	2	no	—
142	C₁₁	#7162	1	1	yes	characteristic, complemented, Sylow
143	C₂³	#66883	1	1	yes	characteristic
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	4	2	no	—
147	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
148	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
149	C₂×C₄	#66881	1	1	yes	characteristic
150	C₂×C₄	#66882	1	1	yes	characteristic
151	C₂×C₄	#66883	1	1	yes	characteristic
152	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
153	C₈	C₄×C₁₁⋊C₈	1	1	yes	characteristic
154	C₈	#66867	1	1	yes	characteristic
155	C₈	#66880	1	1	yes	characteristic
156	C₈	#66880	1	1	yes	characteristic
157	C₈	#66885	1	1	yes	characteristic
158	C₈	#66885	1	1	yes	characteristic
159	C₈	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
160	C₈	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
161	C₂²	—	4	1	no	—
162	C₂²	#10622095	1	1	yes	characteristic
163	C₂²	#10622096	1	1	yes	characteristic
164	C₂²	#10622190	1	1	yes	characteristic
165	C₄	—	2	2	no	—
166	C₄	—	4	1	no	—
167	C₄	#10622095	1	1	yes	characteristic
168	C₄	#10622096	1	1	yes	characteristic
169	C₄	#10622162	1	1	yes	characteristic
170	C₄	#10622189	1	1	yes	characteristic
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	—	2	1	no	—
174	C₂	#13066451	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66885
commutator	C₈×C₁₁	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₄×C₁₁×M₃₂	C₂
socle	C₂×C₁₁	#1277
prime radical	C₂³×C₁₁	#108
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	C₄×M₃₂	D₁₁
hypocenter	C₁₁	#7162
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
142. C₁₁	#7162	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622101	2
C₄×C₁₁×M₃₂	2
#7162	11