Subgroups — C₂×C₁₁×#3162 #14637850

Order 2816.

1902 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#533	C₂	1	2	yes	maximal
2	C₁₁×#3162	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#501	C₂	1	8	yes	maximal, complemented
4	C₂×C₁₁×#427	C₂	1	4	yes	maximal
5	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
7	C₁₁×#533	—	2	8	no	—
8	C₁₁×#533	C₂²	1	16	yes	—
9	C₂×C₁₁×C₄⋊Q₈	C₂²	1	4	yes	—
10	C₂×C₁₁×#125	C₂²	1	4	yes	—
11	C₂×C₁₁×C₂²⋊Q₈	—	2	4	no	—
12	C₂×C₄×Q₈×C₁₁	—	2	4	no	—
13	C₂×C₁₁×#117	C₂²	1	4	yes	—
14	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#501	C₂²	1	64	yes	complemented
16	C₁₁×#427	C₂²	1	32	yes	—
17	C₂×C₁₁×#107	C₂²	1	8	yes	—
18	C₂×C₁₁×#106	C₂²	1	8	yes	—
19	C₂×C₁₁×#97	C₂²	1	4	yes	—
20	C₂×C₁₁×#97	C₂²	1	8	yes	—
21	C₂²×Q₈×C₁₁	—	2	4	no	—
22	C₂³×C₄×C₁₁	D₄	1	2	yes	—
23	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	Q₈	1	16	yes	complemented
25	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
27	C₁₁×C₄⋊Q₈	—	2	8	no	—
28	C₁₁×C₄⋊Q₈	C₂³	1	16	yes	—
29	C₁₁×#125	—	2	8	no	—
30	C₁₁×#125	C₂³	1	16	yes	—
31	C₁₁×C₂²⋊Q₈	—	2	32	no	—
32	C₄×Q₈×C₁₁	—	2	32	no	—
33	C₁₁×#117	—	2	8	no	—
34	C₁₁×#117	C₂³	1	16	yes	—
35	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
36	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
37	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
38	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
39	C₂×C₄²×C₁₁	—	2	4	no	—
40	C₂×C₄²×C₁₁	D₄	1	4	yes	—
41	C₂×C₄²×C₁₁	D₄	1	2	yes	—
42	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
43	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
44	C₁₁×#107	C₂³	1	32	yes	—
45	C₁₁×#106	C₂³	1	32	yes	—
46	C₁₁×#97	C₂³	1	16	yes	—
47	C₂×#3162	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
49	C₂×Q₈×C₁₁	—	2	16	no	—
50	C₂×Q₈×C₁₁	—	4	16	no	—
51	C₂²×C₄×C₁₁	—	2	8	no	—
52	C₂²×C₄×C₁₁	—	4	4	no	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
54	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
55	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂×Q₈	1	8	yes	—
58	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
60	C₂×C₈×C₁₁	C₂×Q₈	1	16	yes	—
61	C₂×C₈×C₁₁	C₂×Q₈	1	32	yes	complemented
62	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
63	C₁₁×C₄⋊C₄	—	2	32	no	—
64	C₁₁×C₄⋊C₄	—	2	16	no	—
65	C₁₁×C₄⋊C₄	—	2	8	no	—
66	C₁₁×C₄⋊C₄	C₂⁴	1	16	yes	—
67	C₁₁×C₂²⋊C₄	—	2	16	no	—
68	C₄²×C₁₁	—	2	16	no	—
69	C₄²×C₁₁	C₂×D₄	1	8	yes	—
70	C₄²×C₁₁	C₂×D₄	1	4	yes	—
71	C₄²×C₁₁	C₂⁴	1	4	yes	—
72	C₂×#533	C₂×C₁₁	1	2	yes	—
73	#3162	C₂×C₁₁	1	16	yes	direct product factor
74	C₂×#501	C₂×C₁₁	1	8	yes	complemented
75	C₂×#427	C₂×C₁₁	1	4	yes	—
76	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic
77	C₂³×C₁₁	—	2	4	no	—
78	C₂³×C₁₁	C₄⋊Q₈	1	4	yes	—
79	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
80	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
81	Q₈×C₁₁	—	4	32	no	—
82	C₂×C₄×C₁₁	—	2	8	no	—
83	C₂×C₄×C₁₁	—	2	16	no	—
84	C₂×C₄×C₁₁	—	4	8	no	—
85	C₂×C₄×C₁₁	—	4	16	no	—
86	C₂×C₄×C₁₁	C₄⋊Q₈	1	8	yes	—
87	C₂×C₄×C₁₁	C₄⋊Q₈	1	4	yes	—
88	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
89	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
90	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂²×Q₈	1	4	yes	—
92	C₂×C₄×C₁₁	C₂²×Q₈	1	8	yes	—
93	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
94	C₈×C₁₁	C₂²×Q₈	1	16	yes	—
95	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
96	#533	—	2	8	no	—
97	#533	C₂²×C₁₁	1	16	yes	—
98	C₂×C₄⋊Q₈	C₂²×C₁₁	1	4	yes	—
99	C₂×#125	C₂²×C₁₁	1	4	yes	—
100	C₂×C₂²⋊Q₈	—	2	4	no	—
101	C₂×C₄×Q₈	—	2	4	no	—
102	C₂×#117	C₂²×C₁₁	1	4	yes	—
103	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
104	#501	C₂²×C₁₁	1	64	yes	complemented
105	#427	C₂²×C₁₁	1	32	yes	—
106	C₂×#107	C₂²×C₁₁	1	8	yes	—
107	C₂×#106	C₂²×C₁₁	1	8	yes	—
108	C₂×#97	C₂²×C₁₁	1	4	yes	—
109	C₂×#97	C₂²×C₁₁	1	8	yes	—
110	C₂²×C₁₁	—	2	8	no	—
111	C₂²×C₁₁	—	2	4	no	—
112	C₂²×C₁₁	C₂×C₄⋊Q₈	1	4	yes	—
113	C₂²×C₁₁	C₂×C₄⋊Q₈	1	2	yes	—
114	C₂²×C₁₁	#575	1	4	yes	—
115	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
116	C₄×C₁₁	—	2	8	no	—
117	C₄×C₁₁	—	4	16	no	—
118	C₄×C₁₁	C₂×C₄⋊Q₈	1	2	yes	—
119	C₄×C₁₁	C₂×C₄⋊Q₈	1	4	yes	—
120	C₄×C₁₁	C₂³×Q₈	1	2	yes	—
121	C₂²×Q₈	—	2	4	no	—
122	C₂³×C₄	D₄×C₁₁	1	2	yes	—
123	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
124	C₂²×C₈	Q₈×C₁₁	1	16	yes	complemented
125	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
126	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
127	C₄⋊Q₈	—	2	8	no	—
128	C₄⋊Q₈	C₂³×C₁₁	1	16	yes	—
129	#125	—	2	8	no	—
130	#125	C₂³×C₁₁	1	16	yes	—
131	C₂²⋊Q₈	—	2	32	no	—
132	C₄×Q₈	—	2	32	no	—
133	#117	—	2	8	no	—
134	#117	C₂³×C₁₁	1	16	yes	—
135	C₂×C₄⋊C₄	—	2	8	no	—
136	C₂×C₄⋊C₄	—	2	4	no	—
137	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
138	C₂×C₂²⋊C₄	—	2	4	no	—
139	C₂×C₄²	—	2	4	no	—
140	C₂×C₄²	D₄×C₁₁	1	2	yes	—
141	C₂×C₄²	D₄×C₁₁	1	4	yes	—
142	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
143	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
144	#107	C₂³×C₁₁	1	32	yes	—
145	#106	C₂³×C₁₁	1	32	yes	—
146	#97	C₂³×C₁₁	1	16	yes	—
147	C₂×C₁₁	—	2	4	no	—
148	C₂×C₁₁	#3162	1	4	yes	direct product factor
149	C₂×C₁₁	C₂²×C₄⋊Q₈	1	1	yes	characteristic
150	C₂×C₁₁	C₂×#575	1	2	yes	—
151	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
152	C₂×Q₈	—	2	16	no	—
153	C₂×Q₈	—	4	16	no	—
154	C₂²×C₄	—	2	8	no	—
155	C₂²×C₄	—	4	4	no	—
156	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
157	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
158	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
159	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
160	C₂²×C₄	C₂×Q₈×C₁₁	1	8	yes	—
161	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
162	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
163	C₂×C₈	C₂×Q₈×C₁₁	1	16	yes	—
164	C₂×C₈	C₂×Q₈×C₁₁	1	32	yes	complemented
165	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
166	C₄⋊C₄	—	2	32	no	—
167	C₄⋊C₄	—	2	16	no	—
168	C₄⋊C₄	—	2	8	no	—
169	C₄⋊C₄	C₂⁴×C₁₁	1	16	yes	—
170	C₂²⋊C₄	—	2	16	no	—
171	C₄²	—	2	16	no	—
172	C₄²	C₂×D₄×C₁₁	1	8	yes	—
173	C₄²	C₂×D₄×C₁₁	1	4	yes	—
174	C₄²	C₂⁴×C₁₁	1	4	yes	—
175	C₁₁	C₂×#3162	1	1	yes	characteristic, direct product factor, Sylow
176	C₂³	—	2	4	no	—
177	C₂³	C₁₁×C₄⋊Q₈	1	4	yes	—
178	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
179	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
180	Q₈	—	4	32	no	—
181	C₂×C₄	—	2	8	no	—
182	C₂×C₄	—	2	16	no	—
183	C₂×C₄	—	4	8	no	—
184	C₂×C₄	—	4	16	no	—
185	C₂×C₄	C₁₁×C₄⋊Q₈	1	8	yes	—
186	C₂×C₄	C₁₁×C₄⋊Q₈	1	4	yes	—
187	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
188	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
189	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
190	C₂×C₄	C₂²×Q₈×C₁₁	1	4	yes	—
191	C₂×C₄	C₂²×Q₈×C₁₁	1	8	yes	—
192	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
193	C₈	C₂²×Q₈×C₁₁	1	16	yes	—
194	C₂²	—	2	8	no	—
195	C₂²	—	2	4	no	—
196	C₂²	C₂×C₁₁×C₄⋊Q₈	1	4	yes	—
197	C₂²	C₂×C₁₁×C₄⋊Q₈	1	2	yes	—
198	C₂²	C₁₁×#575	1	4	yes	—
199	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
200	C₄	—	2	8	no	—
201	C₄	—	4	16	no	—
202	C₄	C₂×C₁₁×C₄⋊Q₈	1	4	yes	—
203	C₄	C₂×C₁₁×C₄⋊Q₈	1	2	yes	—
204	C₄	C₂³×Q₈×C₁₁	1	2	yes	—
205	C₂	—	2	4	no	—
206	C₂	C₁₁×#3162	1	4	yes	direct product factor
207	C₂	C₂²×C₁₁×C₄⋊Q₈	1	1	yes	characteristic
208	C₂	C₂×C₁₁×#575	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂²×D₄
prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#3162	C₂	direct (N × H)
3. C₂×C₁₁×#501	C₂	semidirect
15. C₁₁×#501	C₂²	semidirect
24. C₂²×C₈×C₁₁	Q₈	semidirect
47. C₂×#3162	C₁₁	direct (N × H)
61. C₂×C₈×C₁₁	C₂×Q₈	semidirect
73. #3162	C₂×C₁₁	direct (N × H)
74. C₂×#501	C₂×C₁₁	semidirect
104. #501	C₂²×C₁₁	semidirect
124. C₂²×C₈	Q₈×C₁₁	semidirect
148. C₂×C₁₁	#3162	direct (N × H)
164. C₂×C₈	C₂×Q₈×C₁₁	semidirect
175. C₁₁	C₂×#3162	direct (N × H)
206. C₂	C₁₁×#3162	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#533	2
C₁₁×#3162	2
C₂×C₁₁×#501	2
C₂×C₁₁×#427	2
C₂²×C₁₁×#97	2
C₂×#3162	11

Subgroups — C2×C11×#3162 #14637850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3162 #14637850