Subgroups — C₂²×C₁₁×#491 #14637801

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#125	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#491	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₁₁×#103	C₂	1	4	yes	maximal
5	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
7	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂×C₁₁×C₄⋊Q₈	—	2	6	no	—
9	C₂×C₁₁×C₄⋊Q₈	C₂²	1	12	yes	—
10	C₂×C₁₁×#125	—	2	6	no	—
11	C₂×C₁₁×#125	C₂²	1	12	yes	—
12	C₂²×C₁₁×C₄⋊C₄	—	2	2	no	—
13	C₂²×C₁₁×C₄⋊C₄	—	2	2	no	—
14	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#491	C₂²	1	64	yes	direct product factor
17	C₂×C₁₁×#103	C₂²	1	48	yes	—
18	C₂×C₁₁×#97	C₂²	1	12	yes	—
19	C₂²×Q₈×C₁₁	—	2	6	no	—
20	C₂²×Q₈×C₁₁	—	2	16	no	—
21	C₂²×Q₈×C₁₁	C₂³	1	12	yes	—
22	C₂³×C₄×C₁₁	—	2	2	no	—
23	C₂³×C₄×C₁₁	—	2	2	no	—
24	C₂³×C₄×C₁₁	D₄	1	2	yes	—
25	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	—	2	8	no	—
27	C₂²×C₈×C₁₁	C₂³	1	12	yes	—
28	C₁₁×C₄⋊Q₈	—	2	24	no	—
29	C₁₁×C₄⋊Q₈	C₂³	1	16	yes	—
30	C₁₁×#125	—	2	24	no	—
31	C₁₁×#125	C₂³	1	16	yes	—
32	C₂×C₁₁×C₄⋊C₄	—	2	24	no	—
33	C₂×C₁₁×C₄⋊C₄	—	2	24	no	—
34	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
35	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
36	C₂×C₄²×C₁₁	D₄	1	6	yes	—
37	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
38	C₁₁×#103	C₂³	1	64	yes	—
39	C₁₁×#97	C₂³	1	16	yes	—
40	C₂²×#491	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
42	C₂×Q₈×C₁₁	—	2	12	no	—
43	C₂×Q₈×C₁₁	—	2	48	no	—
44	C₂×Q₈×C₁₁	—	4	24	no	—
45	C₂×Q₈×C₁₁	C₂⁴	1	8	yes	—
46	C₂²×C₄×C₁₁	—	2	8	no	—
47	C₂²×C₄×C₁₁	—	2	12	no	—
48	C₂²×C₄×C₁₁	—	2	12	no	—
49	C₂²×C₄×C₁₁	—	4	8	no	—
50	C₂²×C₄×C₁₁	—	4	8	no	—
51	C₂²×C₄×C₁₁	C₂×D₄	1	12	yes	—
52	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
53	C₂²×C₄×C₁₁	#41	1	8	yes	—
54	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
55	C₂×C₈×C₁₁	—	2	24	no	—
56	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
57	C₁₁×C₄⋊C₄	—	2	32	no	—
58	C₁₁×C₄⋊C₄	—	2	32	no	—
59	C₁₁×C₄⋊C₄	—	2	12	no	—
60	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
61	C₄²×C₁₁	C₂×D₄	1	12	yes	—
62	C₄²×C₁₁	C₂⁴	1	4	yes	—
63	C₂²×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
64	C₂²×#125	C₂×C₁₁	1	1	yes	characteristic
65	C₂×#491	C₂×C₁₁	1	24	yes	direct product factor
66	C₂²×#103	C₂×C₁₁	1	4	yes	—
67	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic
68	C₂³×C₁₁	#124	1	4	yes	—
69	C₂³×C₁₁	#137	1	8	yes	—
70	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
71	Q₈×C₁₁	—	2	16	no	—
72	Q₈×C₁₁	—	4	24	no	—
73	C₂×C₄×C₁₁	—	2	24	no	—
74	C₂×C₄×C₁₁	—	2	8	no	—
75	C₂×C₄×C₁₁	—	2	8	no	—
76	C₂×C₄×C₁₁	—	4	24	no	—
77	C₂×C₄×C₁₁	—	4	24	no	—
78	C₂×C₄×C₁₁	#124	1	12	yes	—
79	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
80	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
81	C₂×C₄×C₁₁	C₂×#41	1	12	yes	—
82	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
83	C₈×C₁₁	—	2	8	no	—
84	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
85	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
86	C₂×C₄⋊Q₈	—	2	6	no	—
87	C₂×C₄⋊Q₈	C₂²×C₁₁	1	12	yes	—
88	C₂×#125	—	2	6	no	—
89	C₂×#125	C₂²×C₁₁	1	12	yes	—
90	C₂²×C₄⋊C₄	—	2	2	no	—
91	C₂²×C₄⋊C₄	—	2	2	no	—
92	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
93	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
94	#491	C₂²×C₁₁	1	64	yes	direct product factor
95	C₂×#103	C₂²×C₁₁	1	48	yes	—
96	C₂×#97	C₂²×C₁₁	1	12	yes	—
97	C₂²×C₁₁	#491	1	16	yes	direct product factor
98	C₂²×C₁₁	C₂×#124	1	6	yes	—
99	C₂²×C₁₁	C₂×#137	1	12	yes	—
100	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
101	C₄×C₁₁	—	2	8	no	—
102	C₄×C₁₁	—	4	8	no	—
103	C₄×C₁₁	—	4	8	no	—
104	C₄×C₁₁	C₂×#124	1	6	yes	—
105	C₄×C₁₁	C₂²×#41	1	2	yes	—
106	C₂²×Q₈	—	2	6	no	—
107	C₂²×Q₈	—	2	16	no	—
108	C₂²×Q₈	C₂³×C₁₁	1	12	yes	—
109	C₂³×C₄	—	2	2	no	—
110	C₂³×C₄	—	2	2	no	—
111	C₂³×C₄	D₄×C₁₁	1	2	yes	—
112	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
113	C₂²×C₈	—	2	8	no	—
114	C₂²×C₈	C₂³×C₁₁	1	12	yes	—
115	C₄⋊Q₈	—	2	24	no	—
116	C₄⋊Q₈	C₂³×C₁₁	1	16	yes	—
117	#125	—	2	24	no	—
118	#125	C₂³×C₁₁	1	16	yes	—
119	C₂×C₄⋊C₄	—	2	24	no	—
120	C₂×C₄⋊C₄	—	2	24	no	—
121	C₂×C₄⋊C₄	—	2	6	no	—
122	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
123	C₂×C₄²	D₄×C₁₁	1	6	yes	—
124	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
125	#103	C₂³×C₁₁	1	64	yes	—
126	#97	C₂³×C₁₁	1	16	yes	—
127	C₂×C₁₁	C₂×#491	1	12	yes	direct product factor
128	C₂×C₁₁	C₂²×#124	1	1	yes	characteristic
129	C₂×C₁₁	C₂²×#137	1	2	yes	—
130	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
131	C₂×Q₈	—	2	12	no	—
132	C₂×Q₈	—	2	48	no	—
133	C₂×Q₈	—	4	24	no	—
134	C₂×Q₈	C₂⁴×C₁₁	1	8	yes	—
135	C₂²×C₄	—	2	8	no	—
136	C₂²×C₄	—	2	12	no	—
137	C₂²×C₄	—	2	12	no	—
138	C₂²×C₄	—	4	8	no	—
139	C₂²×C₄	—	4	8	no	—
140	C₂²×C₄	C₂×D₄×C₁₁	1	12	yes	—
141	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
142	C₂²×C₄	C₁₁×#41	1	8	yes	—
143	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
144	C₂×C₈	—	2	24	no	—
145	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
146	C₄⋊C₄	—	2	32	no	—
147	C₄⋊C₄	—	2	32	no	—
148	C₄⋊C₄	—	2	12	no	—
149	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
150	C₄²	C₂×D₄×C₁₁	1	12	yes	—
151	C₄²	C₂⁴×C₁₁	1	4	yes	—
152	C₁₁	C₂²×#491	1	1	yes	characteristic, direct product factor, Sylow
153	C₂³	C₁₁×#124	1	4	yes	—
154	C₂³	C₁₁×#137	1	8	yes	—
155	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
156	Q₈	—	2	16	no	—
157	Q₈	—	4	24	no	—
158	C₂×C₄	—	2	24	no	—
159	C₂×C₄	—	2	8	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	4	24	no	—
162	C₂×C₄	—	4	24	no	—
163	C₂×C₄	C₁₁×#124	1	12	yes	—
164	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
165	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
166	C₂×C₄	C₂×C₁₁×#41	1	12	yes	—
167	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
168	C₈	—	2	8	no	—
169	C₂²	C₁₁×#491	1	16	yes	direct product factor
170	C₂²	C₂×C₁₁×#124	1	6	yes	—
171	C₂²	C₂×C₁₁×#137	1	12	yes	—
172	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
173	C₄	—	2	8	no	—
174	C₄	—	4	8	no	—
175	C₄	—	4	8	no	—
176	C₄	C₂×C₁₁×#124	1	6	yes	—
177	C₄	C₂²×C₁₁×#41	1	2	yes	—
178	C₂	C₂×C₁₁×#491	1	12	yes	direct product factor
179	C₂	C₂²×C₁₁×#124	1	1	yes	characteristic
180	C₂	C₂²×C₁₁×#137	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₁×#491	C₂	direct (N × H)
16. C₁₁×#491	C₂²	direct (N × H)
40. C₂²×#491	C₁₁	direct (N × H)
65. C₂×#491	C₂×C₁₁	direct (N × H)
94. #491	C₂²×C₁₁	direct (N × H)
97. C₂²×C₁₁	#491	direct (N × H)
127. C₂×C₁₁	C₂×#491	direct (N × H)
152. C₁₁	C₂²×#491	direct (N × H)
169. C₂²	C₁₁×#491	direct (N × H)
178. C₂	C₂×C₁₁×#491	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×C₄⋊Q₈	2
C₂²×C₁₁×#125	2
C₂×C₁₁×#491	2
C₂²×C₁₁×#103	2
C₂²×C₁₁×#97	2
C₂²×#491	11

Subgroups — C22×C11×#491 #14637801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#491 #14637801