Subgroups — C₁₁×#13556 #14590749

Order 2816.

290 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#504	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×M₆₄	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1400	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#131	C₄	1	1	yes	characteristic
5	C₁₁×#504	—	2	2	no	—
6	C₁₁×#504	—	2	2	no	—
7	C₂×C₁₁×M₃₂	C₄	1	1	yes	characteristic
8	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
9	C₂²×C₁₁×C₁₆	C₄	1	2	yes	—
10	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	C₁₁×M₆₄	—	2	2	no	—
12	C₁₁×M₆₄	C₂²	1	4	yes	—
13	C₂×C₁₁×C₃₂	—	2	2	no	—
14	C₂×C₁₁×#41	C₈	1	1	yes	characteristic
15	C₁₁×#131	—	2	2	no	—
16	C₁₁×#131	—	2	2	no	—
17	C₂×C₁₁×M₁₆	C₈	1	1	yes	characteristic
18	C₂×C₁₁×M₁₆	C₈	1	2	yes	—
19	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₁₁×M₃₂	—	2	2	no	—
22	C₁₁×M₃₂	—	2	4	no	—
23	C₂×C₁₁×C₁₆	—	2	2	no	—
24	C₂×C₁₁×C₁₆	—	2	2	no	—
25	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
26	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
28	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
29	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
30	C₁₁×C₃₂	—	2	4	no	—
31	#13556	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₁₁×#41	—	2	2	no	—
33	C₁₁×#41	—	2	2	no	—
34	C₂×Q₈×C₁₁	C₁₆	1	1	yes	characteristic
35	C₂×D₄×C₁₁	C₁₆	1	2	yes	—
36	C₂×D₄×C₁₁	C₁₆	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
38	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
39	C₁₁×M₁₆	—	2	4	no	—
40	C₁₁×M₁₆	—	2	2	no	—
41	C₂×C₈×C₁₁	—	2	2	no	—
42	C₂×C₈×C₁₁	—	2	2	no	—
43	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
45	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
46	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
47	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
48	C₁₁×C₁₆	—	2	2	no	—
49	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
50	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
51	C₁₁×C₁₆	C₂×D₄	1	2	yes	—
52	C₂×#504	C₂×C₁₁	1	1	yes	characteristic
53	C₂×M₆₄	C₂×C₁₁	1	2	yes	complemented
54	#1400	C₂×C₁₁	1	4	yes	complemented
55	C₂³×C₁₁	C₂×C₁₆	1	2	yes	—
56	C₂³×C₁₁	C₂×C₁₆	1	1	yes	characteristic
57	Q₈×C₁₁	—	2	2	no	—
58	D₄×C₁₁	—	2	4	no	—
59	D₄×C₁₁	—	2	2	no	—
60	C₂×C₄×C₁₁	—	2	2	no	—
61	C₂×C₄×C₁₁	—	2	2	no	—
62	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
63	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
64	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
65	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
66	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
67	C₈×C₁₁	—	2	2	no	—
68	C₈×C₁₁	C₂²⋊C₈	1	2	yes	—
69	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
70	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
71	C₂×#131	C₄×C₁₁	1	1	yes	characteristic
72	#504	—	2	2	no	—
73	#504	—	2	2	no	—
74	C₂×M₃₂	C₄×C₁₁	1	1	yes	characteristic
75	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
76	C₂²×C₁₆	C₄×C₁₁	1	2	yes	—
77	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
78	M₆₄	—	2	2	no	—
79	M₆₄	C₂²×C₁₁	1	4	yes	—
80	C₂×C₃₂	—	2	2	no	—
81	C₂²×C₁₁	—	2	2	no	—
82	C₂²×C₁₁	—	4	1	no	—
83	C₂²×C₁₁	—	4	2	no	—
84	C₂²×C₁₁	C₂²⋊C₁₆	1	2	yes	—
85	C₂²×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
86	C₄×C₁₁	—	2	2	no	—
87	C₄×C₁₁	C₂²⋊C₁₆	1	2	yes	—
88	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
89	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
90	C₂×#41	C₈×C₁₁	1	1	yes	characteristic
91	#131	—	2	2	no	—
92	#131	—	2	2	no	—
93	C₂×M₁₆	C₈×C₁₁	1	1	yes	characteristic
94	C₂×M₁₆	C₈×C₁₁	1	2	yes	—
95	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
96	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
97	M₃₂	—	2	2	no	—
98	M₃₂	—	2	4	no	—
99	C₂×C₁₆	—	2	2	no	—
100	C₂×C₁₆	—	2	2	no	—
101	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
102	C₂×C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
103	C₂×C₁₆	D₄×C₁₁	1	2	yes	—
104	C₂×C₁₆	D₄×C₁₁	1	2	yes	—
105	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
106	C₃₂	—	2	4	no	—
107	C₂×C₁₁	—	2	1	no	—
108	C₂×C₁₁	—	2	2	no	—
109	C₂×C₁₁	—	4	2	no	—
110	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
111	#41	—	2	2	no	—
112	#41	—	2	2	no	—
113	C₂×Q₈	C₁₁×C₁₆	1	1	yes	characteristic
114	C₂×D₄	C₁₁×C₁₆	1	2	yes	—
115	C₂×D₄	C₁₁×C₁₆	1	1	yes	characteristic
116	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
117	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
118	M₁₆	—	2	2	no	—
119	M₁₆	—	2	4	no	—
120	C₂×C₈	—	2	2	no	—
121	C₂×C₈	—	2	2	no	—
122	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
123	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
124	C₂×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
125	C₂×C₈	C₁₁×M₁₆	1	2	yes	—
126	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
127	C₁₆	—	2	2	no	—
128	C₁₆	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
129	C₁₆	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
130	C₁₆	C₂×D₄×C₁₁	1	2	yes	—
131	C₁₁	#13556	1	1	yes	characteristic, direct product factor, Sylow
132	C₂³	C₂×C₁₁×C₁₆	1	2	yes	—
133	C₂³	C₂×C₁₁×C₁₆	1	1	yes	characteristic
134	Q₈	—	2	2	no	—
135	D₄	—	2	4	no	—
136	D₄	—	2	2	no	—
137	C₂×C₄	—	2	2	no	—
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
140	C₂×C₄	C₂×C₁₁×C₁₆	1	2	yes	—
141	C₂×C₄	C₂×C₁₁×C₁₆	1	1	yes	characteristic
142	C₂×C₄	C₁₁×M₃₂	1	2	yes	—
143	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
144	C₈	—	2	2	no	—
145	C₈	C₁₁×C₂²⋊C₈	1	2	yes	—
146	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
147	C₈	C₂×C₁₁×M₁₆	1	1	yes	characteristic
148	C₂²	—	2	2	no	—
149	C₂²	—	4	1	no	—
150	C₂²	—	4	2	no	—
151	C₂²	C₁₁×C₂²⋊C₁₆	1	2	yes	—
152	C₂²	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
153	C₄	—	2	2	no	—
154	C₄	C₁₁×C₂²⋊C₁₆	1	2	yes	—
155	C₄	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
156	C₄	C₂×C₁₁×M₃₂	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	2	no	—
159	C₂	—	4	2	no	—
160	C₂	C₂×C₁₁×C₂²⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₁×C₁₆	C₂²⋊C₄
commutator	C₂²	C₂²×C₁₁×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₁
socle	C₂×C₁₁	C₂×C₂²⋊C₁₆
prime radical	C₂×C₁₁×#41	C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₁×C₁₆ ◁ C₂²×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×M₆₄	C₂	semidirect
3. C₁₁×#1400	C₂	semidirect
31. #13556	C₁₁	direct (N × H)
53. C₂×M₆₄	C₂×C₁₁	semidirect
54. #1400	C₂×C₁₁	semidirect
131. C₁₁	#13556	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×#504	2
C₂×C₁₁×M₆₄	2
C₁₁×#1400	2
#13556	11

Subgroups — C11×#13556 #14590749

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#13556 #14590749