Subgroups — C₂×C₁₁×#2176 #14610642

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×Q₁₆	C₂	1	2	yes	maximal
3	C₁₁×#2176	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₁×#367	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#358	C₂	1	2	yes	maximal
6	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
8	C₂×C₄×Q₈×C₁₁	—	2	2	no	—
9	C₂×C₁₁×Q₃₂	C₄	1	8	yes	complemented
10	C₂×C₁₁×Q₃₂	C₂²	1	4	yes	—
11	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
13	C₄×C₁₁×Q₁₆	—	2	4	no	—
14	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	—
15	C₂×C₁₁×#107	C₂²	1	2	yes	—
16	C₂×C₁₁×#103	—	2	2	no	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#367	C₂²	1	4	yes	—
19	C₁₁×#358	C₂²	1	8	yes	—
20	C₁₁×#346	C₂²	1	4	yes	—
21	C₂²×Q₈×C₁₁	—	2	2	no	—
22	C₂×C₁₁×Q₁₆	—	2	2	no	—
23	C₂×C₁₁×Q₁₆	—	2	4	no	—
24	C₂×C₁₁×Q₁₆	C₂×C₄	1	8	yes	—
25	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
26	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₄×Q₈×C₁₁	—	2	8	no	—
29	C₄×Q₈×C₁₁	—	4	4	no	—
30	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
32	C₂×C₄²×C₁₁	—	4	2	no	—
33	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
34	C₁₁×Q₃₂	C₂×C₄	1	16	yes	complemented
35	C₂×C₁₁×C₁₆	—	2	2	no	—
36	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
37	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
38	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
39	C₁₁×#107	—	2	2	no	—
40	C₁₁×#107	C₂³	1	4	yes	—
41	C₁₁×#103	—	2	8	no	—
42	C₄×C₈×C₁₁	D₄	1	2	yes	—
43	C₄×C₈×C₁₁	C₂³	1	2	yes	—
44	C₂×#2176	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×Q₈×C₁₁	—	2	8	no	—
46	C₂×Q₈×C₁₁	—	2	4	no	—
47	C₂×Q₈×C₁₁	—	4	2	no	—
48	C₂×Q₈×C₁₁	—	4	4	no	—
49	C₂²×C₄×C₁₁	—	4	2	no	—
50	C₂²×C₄×C₁₁	—	4	2	no	—
51	C₂²×C₄×C₁₁	D₈	1	2	yes	—
52	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
53	C₁₁×Q₁₆	—	2	8	no	—
54	C₁₁×Q₁₆	—	2	4	no	—
55	C₁₁×Q₁₆	C₂²×C₄	1	8	yes	—
56	C₂×C₈×C₁₁	—	2	2	no	—
57	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
58	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₁	#41	1	2	yes	—
61	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
62	C₁₁×C₄⋊C₄	—	2	4	no	—
63	C₁₁×C₄⋊C₄	—	4	2	no	—
64	C₁₁×C₄⋊C₄	—	4	8	no	—
65	C₄²×C₁₁	—	4	8	no	—
66	C₄²×C₁₁	D₈	1	2	yes	—
67	C₄²×C₁₁	C₂×D₄	1	2	yes	—
68	C₁₁×C₁₆	—	2	2	no	—
69	C₁₁×C₁₆	C₂²×C₄	1	4	yes	—
70	C₂²×Q₃₂	C₂×C₁₁	1	1	yes	characteristic
71	C₂×C₄×Q₁₆	C₂×C₁₁	1	2	yes	—
72	#2176	C₂×C₁₁	1	8	yes	direct product factor
73	C₂×#367	C₂×C₁₁	1	1	yes	characteristic
74	C₂×#358	C₂×C₁₁	1	2	yes	—
75	C₂×#346	C₂×C₁₁	1	1	yes	characteristic
76	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
77	Q₈×C₁₁	—	2	8	no	—
78	Q₈×C₁₁	—	4	4	no	—
79	Q₈×C₁₁	—	4	8	no	—
80	C₂×C₄×C₁₁	—	2	4	no	—
81	C₂×C₄×C₁₁	—	4	4	no	—
82	C₂×C₄×C₁₁	—	4	8	no	—
83	C₂×C₄×C₁₁	—	4	4	no	—
84	C₂×C₄×C₁₁	—	8	4	no	—
85	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
86	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
87	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₁₁	#135	1	2	yes	—
89	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
90	C₈×C₁₁	—	2	2	no	—
91	C₈×C₁₁	C₄×D₄	1	2	yes	—
92	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
93	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
94	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
95	C₂×C₄×Q₈	—	2	2	no	—
96	C₂×Q₃₂	C₄×C₁₁	1	8	yes	complemented
97	C₂×Q₃₂	C₂²×C₁₁	1	4	yes	—
98	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
99	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
100	C₄×Q₁₆	—	2	4	no	—
101	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	—
102	C₂×#107	C₂²×C₁₁	1	2	yes	—
103	C₂×#103	—	2	2	no	—
104	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
105	#367	C₂²×C₁₁	1	4	yes	—
106	#358	C₂²×C₁₁	1	8	yes	—
107	#346	C₂²×C₁₁	1	4	yes	—
108	C₂²×C₁₁	C₄×D₈	1	2	yes	—
109	C₂²×C₁₁	#510	1	4	yes	—
110	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
111	C₄×C₁₁	—	2	4	no	—
112	C₄×C₁₁	—	4	8	no	—
113	C₄×C₁₁	—	8	4	no	—
114	C₄×C₁₁	C₄×D₈	1	2	yes	—
115	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
116	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
117	C₂²×Q₈	—	2	2	no	—
118	C₂×Q₁₆	—	2	2	no	—
119	C₂×Q₁₆	—	2	4	no	—
120	C₂×Q₁₆	C₂×C₄×C₁₁	1	8	yes	—
121	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
122	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
123	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
124	C₄×Q₈	—	2	8	no	—
125	C₄×Q₈	—	4	4	no	—
126	C₂×C₄⋊C₄	—	2	2	no	—
127	C₂×C₄⋊C₄	—	4	2	no	—
128	C₂×C₄²	—	4	2	no	—
129	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
130	Q₃₂	C₂×C₄×C₁₁	1	16	yes	complemented
131	C₂×C₁₆	—	2	2	no	—
132	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
133	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
134	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
135	#107	—	2	2	no	—
136	#107	C₂³×C₁₁	1	4	yes	—
137	#103	—	2	8	no	—
138	C₄×C₈	D₄×C₁₁	1	2	yes	—
139	C₄×C₈	C₂³×C₁₁	1	2	yes	—
140	C₂×C₁₁	#2176	1	4	yes	direct product factor
141	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
142	C₂×C₁₁	C₂×#510	1	2	yes	—
143	C₂×Q₈	—	2	8	no	—
144	C₂×Q₈	—	2	4	no	—
145	C₂×Q₈	—	4	2	no	—
146	C₂×Q₈	—	4	4	no	—
147	C₂²×C₄	—	4	2	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	C₁₁×D₈	1	2	yes	—
150	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
151	Q₁₆	—	2	8	no	—
152	Q₁₆	—	2	4	no	—
153	Q₁₆	C₂²×C₄×C₁₁	1	8	yes	—
154	C₂×C₈	—	2	2	no	—
155	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
156	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
157	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
158	C₂×C₈	C₁₁×#41	1	2	yes	—
159	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
160	C₄⋊C₄	—	2	4	no	—
161	C₄⋊C₄	—	4	2	no	—
162	C₄⋊C₄	—	4	8	no	—
163	C₄²	—	4	8	no	—
164	C₄²	C₁₁×D₈	1	2	yes	—
165	C₄²	C₂×D₄×C₁₁	1	2	yes	—
166	C₁₆	—	2	2	no	—
167	C₁₆	C₂²×C₄×C₁₁	1	4	yes	—
168	C₁₁	C₂×#2176	1	1	yes	characteristic, direct product factor, Sylow
169	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
170	Q₈	—	2	8	no	—
171	Q₈	—	4	4	no	—
172	Q₈	—	4	8	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	4	8	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	—	8	4	no	—
178	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
179	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
180	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
181	C₂×C₄	C₁₁×#135	1	2	yes	—
182	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
183	C₈	—	2	2	no	—
184	C₈	C₄×D₄×C₁₁	1	2	yes	—
185	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
186	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
187	C₂²	C₄×C₁₁×D₈	1	2	yes	—
188	C₂²	C₁₁×#510	1	4	yes	—
189	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
190	C₄	—	2	4	no	—
191	C₄	—	4	8	no	—
192	C₄	—	8	4	no	—
193	C₄	C₄×C₁₁×D₈	1	2	yes	—
194	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
195	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
196	C₂	C₁₁×#2176	1	4	yes	direct product factor
197	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
198	C₂	C₂×C₁₁×#510	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂×D₈
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2176	C₂	direct (N × H)
9. C₂×C₁₁×Q₃₂	C₄	semidirect
34. C₁₁×Q₃₂	C₂×C₄	semidirect
44. C₂×#2176	C₁₁	direct (N × H)
72. #2176	C₂×C₁₁	direct (N × H)
96. C₂×Q₃₂	C₄×C₁₁	semidirect
130. Q₃₂	C₂×C₄×C₁₁	semidirect
140. C₂×C₁₁	#2176	direct (N × H)
168. C₁₁	C₂×#2176	direct (N × H)
196. C₂	C₁₁×#2176	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×Q₃₂	2
C₂×C₄×C₁₁×Q₁₆	2
C₁₁×#2176	2
C₂×C₁₁×#367	2
C₂×C₁₁×#358	2
C₂×C₁₁×#346	2
C₂×#2176	11

Subgroups — C2×C11×#2176 #14610642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2176 #14610642