Subgroups — #14669113

Order 2816.

330 conjugacy classes of subgroups.

The subgroup lattice has 208 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×#10622150	C₂	1	2	yes	maximal
3	#13068302	C₂	1	1	yes	maximal, characteristic
4	#13066699	C₂	1	2	yes	maximal
5	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66879	C₂²	1	1	yes	characteristic
9	C₂×#66879	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
12	C₂×#66876	C₂²	1	2	yes	—
13	#10622545	C₄	1	1	yes	characteristic
14	C₂×#66867	C₄	1	1	yes	characteristic
15	C₁₁×#364	C₄	1	4	yes	complemented
16	#10622150	—	2	4	no	—
17	#10622101	C₄	1	4	yes	complemented
18	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₁₁×M₃₂	—	2	2	no	—
26	C₁₁×M₃₂	C₂×C₄	1	4	yes	—
27	C₂×C₁₁×C₁₆	—	2	2	no	—
28	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
29	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
30	C₁₁⋊#95	—	2	2	no	—
31	#66879	—	2	1	no	—
32	#66879	—	2	1	no	—
33	#66879	D₄	1	2	yes	—
34	#66879	Q₈	1	2	yes	—
35	C₈×Dic₁₁	—	2	2	no	—
36	C₈×Dic₁₁	—	2	2	no	—
37	#66876	—	2	2	no	—
38	#66876	C₂×C₄	1	4	yes	—
39	C₂×C₁₁⋊C₁₆	—	2	2	no	—
40	#66867	—	2	2	no	—
41	#12660	—	11	1	no	maximal, Sylow
42	C₂²×C₄×C₁₁	—	2	1	no	—
43	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂²×Dic₁₁	—	2	1	no	—
45	C₂²×Dic₁₁	M₁₆	1	2	yes	—
46	C₂×C₈×C₁₁	C₄²	1	2	yes	—
47	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
49	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
54	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
55	C₄²×C₁₁	—	2	1	no	—
56	C₄²×C₁₁	C₄²	1	2	yes	—
57	C₄×Dic₁₁	—	2	1	no	—
58	C₄×Dic₁₁	—	2	1	no	—
59	C₄×Dic₁₁	—	2	1	no	—
60	C₄×Dic₁₁	C₄⋊C₄	1	2	yes	—
61	C₂×C₁₁⋊C₈	—	2	1	no	—
62	C₂×C₁₁⋊C₈	—	2	1	no	—
63	C₂×C₁₁⋊C₈	—	2	1	no	—
64	C₂×C₁₁⋊C₈	—	2	1	no	—
65	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
66	C₂×C₁₁⋊C₈	M₁₆	1	2	yes	—
67	C₁₁×C₁₆	—	2	4	no	—
68	C₁₁⋊C₁₆	—	2	4	no	—
69	C₂×#364	—	11	1	no	—
70	C₂×#364	D₁₁	1	1	yes	characteristic
71	C₂×#347	—	11	2	no	—
72	#1726	—	11	1	no	—
73	#1377	—	11	2	no	—
74	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	4	2	no	—
77	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₁₁	—	2	2	no	—
84	C₂×Dic₁₁	—	2	2	no	—
85	C₂×Dic₁₁	—	4	2	no	—
86	C₂×Dic₁₁	—	4	2	no	—
87	C₈×C₁₁	#97	1	4	yes	—
88	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
89	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
90	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
91	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
92	C₁₁⋊C₈	—	2	2	no	—
93	C₁₁⋊C₈	—	2	2	no	—
94	C₂×M₃₂	—	11	2	no	—
95	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
96	C₂×#97	—	11	1	no	—
97	C₂×#97	—	11	1	no	—
98	C₂×#97	—	11	1	no	—
99	C₂×C₄×C₈	—	11	1	no	—
100	C₂×C₄×C₈	—	11	1	no	—
101	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
102	#376	—	11	1	no	—
103	#364	—	11	4	no	—
104	#364	Dic₁₁	1	4	yes	complemented
105	#347	—	22	4	no	—
106	C₂²×C₁₁	—	2	2	no	—
107	C₂²×C₁₁	C₄×M₁₆	1	1	yes	characteristic
108	C₂²×C₁₁	#423	1	1	yes	characteristic
109	C₂²×C₁₁	#432	1	1	yes	characteristic
110	C₄×C₁₁	—	4	2	no	—
111	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
112	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
113	C₄×C₁₁	#423	1	1	yes	characteristic
114	C₄×C₁₁	#432	1	1	yes	characteristic
115	Dic₁₁	—	4	2	no	—
116	Dic₁₁	—	4	2	no	—
117	C₂²×C₈	—	11	1	no	—
118	C₂²×C₈	—	11	1	no	—
119	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
120	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
121	C₂×C₄²	—	11	1	no	—
122	C₂×C₄²	—	11	1	no	—
123	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
124	M₃₂	—	2	2	no	—
125	M₃₂	—	11	4	no	—
126	M₃₂	—	22	2	no	—
127	M₃₂	C₂×Dic₁₁	1	4	yes	—
128	C₂×C₁₆	—	2	2	no	—
129	C₂×C₁₆	—	22	2	no	—
130	#97	—	11	2	no	—
131	#97	—	11	2	no	—
132	#97	—	22	2	no	—
133	#97	—	22	1	no	—
134	#97	—	22	1	no	—
135	C₄×C₈	—	22	2	no	—
136	C₄×C₈	—	22	2	no	—
137	C₄×C₈	C₄×D₁₁	1	2	yes	—
138	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
139	#95	—	22	2	no	—
140	C₂×C₁₁	—	2	1	no	—
141	C₂×C₁₁	—	2	1	no	—
142	C₂×C₁₁	#1767	1	1	yes	characteristic
143	C₂×C₁₁	#2166	1	2	yes	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	11	2	no	—
146	C₂²×C₄	—	22	1	no	—
147	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
148	C₂×C₈	—	11	2	no	—
149	C₂×C₈	—	11	2	no	—
150	C₂×C₈	—	22	1	no	—
151	C₂×C₈	—	22	1	no	—
152	C₂×C₈	—	22	1	no	—
153	C₂×C₈	—	22	1	no	—
154	C₂×C₈	#4313	1	2	yes	—
155	C₂×C₈	#4313	1	2	yes	—
156	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
157	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
158	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
159	C₂×C₈	#4341	1	1	yes	characteristic
160	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
161	C₂×C₈	#4343	1	1	yes	characteristic
162	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
163	C₄²	—	2	1	no	—
164	C₄²	—	11	2	no	—
165	C₄²	—	22	1	no	—
166	C₄²	—	22	1	no	—
167	C₄²	—	22	1	no	—
168	C₄²	C₄×Dic₁₁	1	2	yes	—
169	C₁₆	—	2	4	no	—
170	C₁₆	—	22	4	no	—
171	C₁₁	#12660	1	1	yes	characteristic, complemented, Sylow
172	C₂³	M₁₆×D₁₁	1	1	yes	characteristic
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	22	2	no	—
176	C₂×C₄	—	22	2	no	—
177	C₂×C₄	—	44	2	no	—
178	C₂×C₄	—	44	2	no	—
179	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
180	C₂×C₄	#66945	1	1	yes	characteristic
181	C₂×C₄	C₂×#4313	1	1	yes	characteristic
182	C₂×C₄	C₂×#4313	1	1	yes	characteristic
183	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
184	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
185	C₈	—	22	2	no	—
186	C₈	—	22	2	no	—
187	C₈	#66879	1	4	yes	—
188	C₈	#66940	1	1	yes	characteristic
189	C₈	#66946	1	1	yes	characteristic
190	C₈	D₄×Dic₁₁	1	1	yes	characteristic
191	C₈	Q₈×Dic₁₁	1	1	yes	characteristic
192	C₂²	—	2	2	no	—
193	C₂²	#10622448	1	1	yes	characteristic
194	C₂²	#10622450	1	1	yes	characteristic
195	C₂²	M₁₆×Dic₁₁	1	1	yes	characteristic
196	C₄	—	4	2	no	—
197	C₄	—	44	2	no	—
198	C₄	—	44	2	no	—
199	C₄	#10622448	1	1	yes	characteristic
200	C₄	#10622450	1	1	yes	characteristic
201	C₄	C₄⋊C₄×Dic₁₁	1	1	yes	characteristic
202	C₄	C₂×#66879	1	1	yes	characteristic
203	C₂	—	2	1	no	—
204	C₂	—	2	1	no	—
205	C₂	#13068471	1	1	yes	characteristic
206	C₂	#13070431	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#66945
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#364	C₂
socle	C₂²×C₁₁	#432
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#364	D₁₁
hypocenter	C₁₁	#12660
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
15. C₁₁×#364	C₄	semidirect
17. #10622101	C₄	semidirect
104. #364	Dic₁₁	semidirect
171. C₁₁	#12660	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
C₂×#10622150	2
#13068302	2
#13066699	2
C₂×C₁₁×#364	2
#12660	11