Subgroups — #14665142

Order 2816.

292 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079130	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622101	C₂	1	1	yes	maximal, characteristic
3	#13066678	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic
5	#10623001	C₄	1	2	yes	—
6	C₂×C₁₁×M₃₂	—	2	1	no	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	#10622719	—	2	1	no	—
9	#10622719	—	2	1	no	—
10	C₂×#66876	—	2	1	no	—
11	#10622296	C₄	1	2	yes	—
12	#10622296	C₂²	1	2	yes	—
13	#10622295	—	2	1	no	—
14	#10622293	—	2	1	no	—
15	C₁₁×#364	—	2	1	no	—
16	C₁₁×#364	C₂²	1	2	yes	—
17	#10622101	—	2	1	no	—
18	#10622101	C₂²	1	2	yes	—
19	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
22	#66979	—	2	2	no	—
23	#66977	—	4	2	no	—
24	#66923	C₂×C₄	1	4	yes	—
25	#66922	—	2	2	no	—
26	C₄×Dic₂₂	—	4	2	no	—
27	C₁₁×M₃₂	—	2	2	no	—
28	C₁₁×M₃₂	—	4	1	no	—
29	C₂×C₁₁×C₁₆	—	4	1	no	—
30	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
32	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
33	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
34	#66882	—	2	2	no	—
35	#66882	—	2	2	no	—
36	#66881	—	2	2	no	—
37	#66881	—	2	2	no	—
38	#66876	—	2	2	no	—
39	#66876	—	4	1	no	—
40	C₂×C₁₁⋊C₁₆	—	4	1	no	—
41	#11956	—	11	1	no	maximal, Sylow
42	C₂²×C₄×C₁₁	—	2	1	no	—
43	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
44	C₂×Dic₂₂	—	4	2	no	—
45	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
49	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
50	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
51	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
52	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
53	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
54	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₄²×C₁₁	—	2	1	no	—
58	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
59	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
60	C₂²⋊Dic₁₁	—	4	2	no	—
61	C₄⋊Dic₁₁	—	2	4	no	—
62	C₄⋊Dic₁₁	—	4	2	no	—
63	Dic₁₁⋊C₄	—	4	4	no	—
64	C₄×Dic₁₁	—	4	2	no	—
65	C₁₁×C₁₆	—	4	2	no	—
66	C₁₁⋊C₁₆	—	4	2	no	—
67	#3160	—	11	1	no	—
68	C₂×#364	—	11	1	no	—
69	C₂×#364	D₁₁	1	1	yes	characteristic
70	#1366	—	11	4	no	—
71	C₂³×C₁₁	#100	1	1	yes	characteristic
72	C₂×C₄×C₁₁	—	2	1	no	—
73	C₂×C₄×C₁₁	—	2	1	no	—
74	C₂×C₄×C₁₁	—	4	2	no	—
75	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
76	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
77	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
78	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
81	C₂×Dic₁₁	—	4	4	no	—
82	Dic₂₂	—	8	4	no	—
83	C₈×C₁₁	#103	1	1	yes	characteristic
84	C₈×C₁₁	#103	1	1	yes	characteristic
85	C₈×C₁₁	#103	1	1	yes	characteristic
86	C₈×C₁₁	#103	1	1	yes	characteristic
87	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
88	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
89	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
90	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
91	#533	—	11	2	no	—
92	C₂×M₃₂	—	2	1	no	—
93	C₂×M₃₂	—	22	1	no	—
94	#500	—	22	1	no	—
95	#499	—	11	2	no	—
96	#499	—	11	2	no	—
97	#498	—	22	1	no	—
98	#427	—	22	1	no	—
99	#427	—	22	1	no	—
100	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
101	#364	—	2	1	no	—
102	#364	—	11	2	no	—
103	#364	—	22	1	no	—
104	#364	C₂×D₁₁	1	2	yes	—
105	C₂²×C₁₁	—	4	1	no	—
106	C₂²×C₁₁	#333	1	1	yes	characteristic
107	C₂²×C₁₁	#333	1	1	yes	characteristic
108	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
109	C₄×C₁₁	—	2	2	no	—
110	C₄×C₁₁	—	4	1	no	—
111	C₄×C₁₁	#333	1	1	yes	characteristic
112	C₄×C₁₁	#333	1	1	yes	characteristic
113	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
114	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
115	Dic₁₁	—	8	4	no	—
116	C₂²×C₈	D₄₄	1	1	yes	characteristic
117	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
118	C₄⋊Q₈	—	22	2	no	—
119	#125	—	11	4	no	—
120	C₂²⋊Q₈	—	44	2	no	—
121	C₄×Q₈	—	44	2	no	—
122	#117	—	22	2	no	—
123	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
124	M₃₂	—	2	2	no	—
125	M₃₂	—	4	1	no	—
126	M₃₂	—	22	2	no	—
127	M₃₂	—	44	1	no	—
128	C₂×C₁₆	—	4	1	no	—
129	C₂×C₁₆	—	44	1	no	—
130	#107	—	22	2	no	—
131	#107	—	22	2	no	—
132	#106	—	22	2	no	—
133	#106	—	22	2	no	—
134	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
135	C₄×C₈	D₄₄	1	1	yes	characteristic
136	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
137	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
138	C₂×C₁₁	—	2	1	no	—
139	C₂×C₁₁	—	2	1	no	—
140	C₂×C₁₁	—	2	1	no	—
141	C₂×C₁₁	C₂×#333	1	1	yes	characteristic
142	C₂×Q₈	—	44	2	no	—
143	C₂²×C₄	—	2	1	no	—
144	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
145	C₂×C₈	#4314	1	1	yes	characteristic
146	C₂×C₈	#4314	1	1	yes	characteristic
147	C₂×C₈	Dic₄₄	1	1	yes	characteristic
148	C₂×C₈	Dic₄₄	1	1	yes	characteristic
149	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
150	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
151	C₂×C₈	#4324	1	1	yes	characteristic
152	C₂×C₈	#4324	1	1	yes	characteristic
153	C₂×C₈	#4326	1	1	yes	characteristic
154	C₂×C₈	#4326	1	1	yes	characteristic
155	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
156	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
157	C₄⋊C₄	—	22	4	no	—
158	C₄⋊C₄	—	44	4	no	—
159	C₄⋊C₄	—	44	2	no	—
160	C₂²⋊C₄	—	44	2	no	—
161	C₄²	—	2	1	no	—
162	C₄²	—	44	2	no	—
163	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
164	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
165	C₁₆	—	4	2	no	—
166	C₁₆	—	44	2	no	—
167	C₁₁	#11956	1	1	yes	characteristic, complemented, Sylow
168	C₂³	#66887	1	1	yes	characteristic
169	Q₈	—	88	4	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	4	2	no	—
173	C₂×C₄	—	44	4	no	—
174	C₂×C₄	#66874	1	1	yes	characteristic
175	C₂×C₄	#66874	1	1	yes	characteristic
176	C₂×C₄	#66880	1	1	yes	characteristic
177	C₂×C₄	#66880	1	1	yes	characteristic
178	C₂×C₄	#66887	1	1	yes	characteristic
179	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
180	C₈	#66874	1	1	yes	characteristic
181	C₈	#66874	1	1	yes	characteristic
182	C₈	#66880	1	1	yes	characteristic
183	C₈	#66880	1	1	yes	characteristic
184	C₈	C₂×#4314	1	1	yes	characteristic
185	C₈	C₂×Dic₄₄	1	1	yes	characteristic
186	C₈	C₂×#4324	1	1	yes	characteristic
187	C₈	C₂×#4326	1	1	yes	characteristic
188	C₂²	—	4	1	no	—
189	C₂²	#10622119	1	1	yes	characteristic
190	C₂²	#10622119	1	1	yes	characteristic
191	C₂²	C₂×#66887	1	1	yes	characteristic
192	C₄	—	2	2	no	—
193	C₄	—	4	1	no	—
194	C₄	—	88	4	no	—
195	C₄	#10622119	1	1	yes	characteristic
196	C₄	#10622119	1	1	yes	characteristic
197	C₄	C₂×#66874	1	1	yes	characteristic
198	C₄	C₂×#66880	1	1	yes	characteristic
199	C₂	—	2	1	no	—
200	C₂	—	2	1	no	—
201	C₂	—	2	1	no	—
202	C₂	C₂×#10622119	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10622119
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#364	C₂
socle	C₂×C₁₁	C₂×#333
prime radical	C₂³×C₁₁	#100
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₂×#364	D₁₁
hypocenter	C₁₁	#11956
LCS	G ▷ C₄²×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
3. #13066678	C₂	semidirect
167. C₁₁	#11956	semidirect

Maximal subgroups

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

subgroup	index
#13079130	2
C₂×#10622101	2
#13066678	2
C₂×C₁₁×#364	2
#11956	11