Subgroups — C₂²×C₁₁×#494 #14637823

Order 2816.

3262 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×Q₁₆	C₂	1	4	yes	maximal
2	C₂²×C₁₁×C₄⋊Q₈	C₂	1	2	yes	maximal
3	C₂×C₁₁×#494	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂³×Q₈×C₁₁	C₂²	1	4	yes	—
6	C₂²×C₁₁×Q₁₆	—	2	32	no	—
7	C₂²×C₁₁×Q₁₆	C₂²	1	48	yes	—
8	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
9	C₂×C₁₁×C₄⋊Q₈	—	2	12	no	—
10	C₂×C₁₁×C₄⋊Q₈	C₂²	1	24	yes	—
11	C₂²×C₁₁×C₄⋊C₄	—	2	4	no	—
12	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#494	C₂²	1	64	yes	direct product factor
14	C₂×C₄×C₈×C₁₁	C₂²	1	12	yes	—
15	C₂²×Q₈×C₁₁	—	2	12	no	—
16	C₂²×Q₈×C₁₁	—	2	32	no	—
17	C₂²×Q₈×C₁₁	C₂³	1	24	yes	—
18	C₂³×C₄×C₁₁	—	2	4	no	—
19	C₂³×C₄×C₁₁	D₄	1	2	yes	—
20	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₁₁×Q₁₆	—	2	192	no	—
22	C₂×C₁₁×Q₁₆	C₂³	1	64	yes	—
23	C₂²×C₈×C₁₁	D₄	1	16	yes	—
24	C₂²×C₈×C₁₁	C₂³	1	12	yes	—
25	C₁₁×C₄⋊Q₈	—	2	48	no	—
26	C₁₁×C₄⋊Q₈	C₂³	1	32	yes	—
27	C₂×C₁₁×C₄⋊C₄	—	2	48	no	—
28	C₂×C₄²×C₁₁	D₄	1	6	yes	—
29	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
30	C₄×C₈×C₁₁	C₂³	1	16	yes	—
31	C₂²×#494	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
33	C₂×Q₈×C₁₁	—	2	24	no	—
34	C₂×Q₈×C₁₁	—	2	96	no	—
35	C₂×Q₈×C₁₁	—	4	48	no	—
36	C₂×Q₈×C₁₁	C₂⁴	1	16	yes	—
37	C₂²×C₄×C₁₁	—	2	24	no	—
38	C₂²×C₄×C₁₁	—	4	16	no	—
39	C₂²×C₄×C₁₁	Q₁₆	1	16	yes	complemented
40	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
41	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
42	C₂²×C₄×C₁₁	C₂×D₄	1	12	yes	—
43	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
44	C₁₁×Q₁₆	—	2	128	no	—
45	C₂×C₈×C₁₁	C₂×D₄	1	48	yes	—
46	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
47	C₁₁×C₄⋊C₄	—	2	64	no	—
48	C₄²×C₁₁	C₂×D₄	1	12	yes	—
49	C₄²×C₁₁	C₂⁴	1	4	yes	—
50	C₂³×Q₁₆	C₂×C₁₁	1	4	yes	—
51	C₂²×C₄⋊Q₈	C₂×C₁₁	1	2	yes	—
52	C₂×#494	C₂×C₁₁	1	24	yes	direct product factor
53	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
54	C₂³×C₁₁	#127	1	4	yes	—
55	C₂³×C₁₁	C₂×Q₁₆	1	8	yes	—
56	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
57	Q₈×C₁₁	—	2	32	no	—
58	Q₈×C₁₁	—	4	48	no	—
59	C₂×C₄×C₁₁	—	2	16	no	—
60	C₂×C₄×C₁₁	—	4	48	no	—
61	C₂×C₄×C₁₁	#127	1	12	yes	—
62	C₂×C₄×C₁₁	C₂×Q₁₆	1	48	yes	complemented
63	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
64	C₂×C₄×C₁₁	C₂²×D₄	1	12	yes	—
65	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
66	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
67	C₈×C₁₁	C₂²×D₄	1	16	yes	—
68	C₂³×Q₈	C₂²×C₁₁	1	4	yes	—
69	C₂²×Q₁₆	—	2	32	no	—
70	C₂²×Q₁₆	C₂²×C₁₁	1	48	yes	—
71	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
72	C₂×C₄⋊Q₈	—	2	12	no	—
73	C₂×C₄⋊Q₈	C₂²×C₁₁	1	24	yes	—
74	C₂²×C₄⋊C₄	—	2	4	no	—
75	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
76	#494	C₂²×C₁₁	1	64	yes	direct product factor
77	C₂×C₄×C₈	C₂²×C₁₁	1	12	yes	—
78	C₂²×C₁₁	#494	1	16	yes	direct product factor
79	C₂²×C₁₁	C₂×#127	1	6	yes	—
80	C₂²×C₁₁	C₂²×Q₁₆	1	12	yes	—
81	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
82	C₄×C₁₁	—	4	16	no	—
83	C₄×C₁₁	C₂×#127	1	6	yes	—
84	C₄×C₁₁	C₂²×Q₁₆	1	16	yes	complemented
85	C₄×C₁₁	C₂³×D₄	1	2	yes	—
86	C₂²×Q₈	—	2	12	no	—
87	C₂²×Q₈	—	2	32	no	—
88	C₂²×Q₈	C₂³×C₁₁	1	24	yes	—
89	C₂³×C₄	—	2	4	no	—
90	C₂³×C₄	D₄×C₁₁	1	2	yes	—
91	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
92	C₂×Q₁₆	—	2	192	no	—
93	C₂×Q₁₆	C₂³×C₁₁	1	64	yes	—
94	C₂²×C₈	D₄×C₁₁	1	16	yes	—
95	C₂²×C₈	C₂³×C₁₁	1	12	yes	—
96	C₄⋊Q₈	—	2	48	no	—
97	C₄⋊Q₈	C₂³×C₁₁	1	32	yes	—
98	C₂×C₄⋊C₄	—	2	48	no	—
99	C₂×C₄²	D₄×C₁₁	1	6	yes	—
100	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
101	C₄×C₈	C₂³×C₁₁	1	16	yes	—
102	C₂×C₁₁	C₂×#494	1	12	yes	direct product factor
103	C₂×C₁₁	C₂²×#127	1	1	yes	characteristic
104	C₂×C₁₁	C₂³×Q₁₆	1	2	yes	—
105	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
106	C₂×Q₈	—	2	24	no	—
107	C₂×Q₈	—	2	96	no	—
108	C₂×Q₈	—	4	48	no	—
109	C₂×Q₈	C₂⁴×C₁₁	1	16	yes	—
110	C₂²×C₄	—	2	24	no	—
111	C₂²×C₄	—	4	16	no	—
112	C₂²×C₄	C₁₁×Q₁₆	1	16	yes	complemented
113	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
114	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
115	C₂²×C₄	C₂×D₄×C₁₁	1	12	yes	—
116	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
117	Q₁₆	—	2	128	no	—
118	C₂×C₈	C₂×D₄×C₁₁	1	48	yes	—
119	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
120	C₄⋊C₄	—	2	64	no	—
121	C₄²	C₂×D₄×C₁₁	1	12	yes	—
122	C₄²	C₂⁴×C₁₁	1	4	yes	—
123	C₁₁	C₂²×#494	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³	C₁₁×#127	1	4	yes	—
125	C₂³	C₂×C₁₁×Q₁₆	1	8	yes	—
126	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
127	Q₈	—	2	32	no	—
128	Q₈	—	4	48	no	—
129	C₂×C₄	—	2	16	no	—
130	C₂×C₄	—	4	48	no	—
131	C₂×C₄	C₁₁×#127	1	12	yes	—
132	C₂×C₄	C₂×C₁₁×Q₁₆	1	48	yes	complemented
133	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
134	C₂×C₄	C₂²×D₄×C₁₁	1	12	yes	—
135	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
136	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
137	C₈	C₂²×D₄×C₁₁	1	16	yes	—
138	C₂²	C₁₁×#494	1	16	yes	direct product factor
139	C₂²	C₂×C₁₁×#127	1	6	yes	—
140	C₂²	C₂²×C₁₁×Q₁₆	1	12	yes	—
141	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
142	C₄	—	4	16	no	—
143	C₄	C₂×C₁₁×#127	1	6	yes	—
144	C₄	C₂²×C₁₁×Q₁₆	1	16	yes	complemented
145	C₄	C₂³×D₄×C₁₁	1	2	yes	—
146	C₂	C₂×C₁₁×#494	1	12	yes	direct product factor
147	C₂	C₂²×C₁₁×#127	1	1	yes	characteristic
148	C₂	C₂³×C₁₁×Q₁₆	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×#494	C₂	direct (N × H)
13. C₁₁×#494	C₂²	direct (N × H)
31. C₂²×#494	C₁₁	direct (N × H)
39. C₂²×C₄×C₁₁	Q₁₆	semidirect
52. C₂×#494	C₂×C₁₁	direct (N × H)
62. C₂×C₄×C₁₁	C₂×Q₁₆	semidirect
76. #494	C₂²×C₁₁	direct (N × H)
78. C₂²×C₁₁	#494	direct (N × H)
84. C₄×C₁₁	C₂²×Q₁₆	semidirect
102. C₂×C₁₁	C₂×#494	direct (N × H)
112. C₂²×C₄	C₁₁×Q₁₆	semidirect
123. C₁₁	C₂²×#494	direct (N × H)
132. C₂×C₄	C₂×C₁₁×Q₁₆	semidirect
138. C₂²	C₁₁×#494	direct (N × H)
144. C₄	C₂²×C₁₁×Q₁₆	semidirect
146. C₂	C₂×C₁₁×#494	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×Q₁₆	2
C₂²×C₁₁×C₄⋊Q₈	2
C₂×C₁₁×#494	2
C₂²×C₄×C₈×C₁₁	2
C₂²×#494	11

Subgroups — C22×C11×#494 #14637823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#494 #14637823