Subgroups — C₁₁×#33401 #14610594

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3407	C₂	1	2	yes	maximal
2	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2153	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₁×#364	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₁×#131	C₄	1	1	yes	characteristic
6	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
7	C₄×C₁₁×#41	C₄	1	1	yes	characteristic
8	C₁₁×#504	—	2	8	no	—
9	C₂×C₁₁×M₃₂	C₂²	1	12	yes	—
10	C₁₁×#405	C₄	1	3	yes	—
11	C₁₁×#405	C₂²	1	3	yes	—
12	C₄×C₁₁×M₁₆	C₄	1	3	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
14	C₁₁×#364	C₂²	1	4	yes	—
15	C₁₁×#364	C₂²	1	12	yes	—
16	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
17	C₁₁×#131	C₈	1	8	yes	—
18	C₁₁×#131	D₄	1	4	yes	—
19	C₁₁×#131	Q₈	1	4	yes	—
20	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
21	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
22	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
23	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
24	C₄×Q₈×C₁₁	—	2	1	no	—
25	C₄×D₄×C₁₁	—	2	3	no	—
26	C₁₁×#117	C₂×C₄	1	3	yes	—
27	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
28	C₁₁×M₃₂	—	2	12	no	—
29	C₁₁×M₃₂	C₂³	1	8	yes	—
30	C₂×C₁₁×C₁₆	—	2	12	no	—
31	C₁₁×#97	C₂×C₄	1	6	yes	—
32	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
33	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
34	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
35	C₄×C₈×C₁₁	C₂³	1	3	yes	—
36	#33401	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₁₁×#41	C₄⋊C₄	1	4	yes	—
38	C₁₁×#41	C₂×C₈	1	4	yes	—
39	C₂×Q₈×C₁₁	M₁₆	1	1	yes	characteristic
40	C₂×D₄×C₁₁	M₁₆	1	3	yes	—
41	C₂²×C₄×C₁₁	—	2	3	no	—
42	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
43	C₁₁×M₁₆	C₄⋊C₄	1	12	yes	—
44	C₁₁×M₁₆	C₂×C₈	1	12	yes	—
45	C₂×C₈×C₁₁	C₂×C₈	1	12	yes	—
46	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
47	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
49	C₂×C₈×C₁₁	C₂×D₄	1	6	yes	—
50	C₂×C₈×C₁₁	C₂×Q₈	1	6	yes	—
51	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
52	C₁₁×C₄⋊C₄	—	2	3	no	—
53	C₁₁×C₂²⋊C₄	—	2	3	no	—
54	C₄²×C₁₁	—	2	3	no	—
55	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
56	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
57	C₁₁×C₁₆	—	2	8	no	—
58	#3407	C₂×C₁₁	1	2	yes	—
59	C₄×#131	C₂×C₁₁	1	1	yes	characteristic
60	#2153	C₂×C₁₁	1	6	yes	complemented
61	C₂×#364	C₂×C₁₁	1	6	yes	complemented
62	C₂³×C₁₁	C₂×M₁₆	1	3	yes	—
63	Q₈×C₁₁	C₄⋊C₈	1	4	yes	—
64	D₄×C₁₁	C₄⋊C₈	1	12	yes	—
65	C₂×C₄×C₁₁	—	2	1	no	—
66	C₂×C₄×C₁₁	—	2	3	no	—
67	C₂×C₄×C₁₁	—	4	6	no	—
68	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
69	C₂×C₄×C₁₁	C₂²×C₈	1	6	yes	—
70	C₂×C₄×C₁₁	C₂×M₁₆	1	3	yes	—
71	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
72	C₈×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
73	C₈×C₁₁	C₂²×C₈	1	2	yes	—
74	C₈×C₁₁	C₂²×C₈	1	6	yes	—
75	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
76	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
77	C₂×#131	C₄×C₁₁	1	1	yes	characteristic
78	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
79	C₄×#41	C₄×C₁₁	1	1	yes	characteristic
80	#504	—	2	8	no	—
81	C₂×M₃₂	C₂²×C₁₁	1	12	yes	—
82	#405	C₄×C₁₁	1	3	yes	—
83	#405	C₂²×C₁₁	1	3	yes	—
84	C₄×M₁₆	C₄×C₁₁	1	3	yes	—
85	C₂×C₄×C₈	C₂²×C₁₁	1	3	yes	—
86	#364	C₂²×C₁₁	1	4	yes	—
87	#364	C₂²×C₁₁	1	12	yes	—
88	C₂²×C₁₁	—	4	3	no	—
89	C₂²×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
90	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
91	C₄×C₁₁	—	2	2	no	—
92	C₄×C₁₁	—	4	3	no	—
93	C₄×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
94	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
95	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
96	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
97	#131	C₈×C₁₁	1	8	yes	—
98	#131	D₄×C₁₁	1	4	yes	—
99	#131	Q₈×C₁₁	1	4	yes	—
100	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
101	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
102	C₂²×C₈	C₂×C₄×C₁₁	1	3	yes	—
103	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
104	C₄×Q₈	—	2	1	no	—
105	C₄×D₄	—	2	3	no	—
106	#117	C₂×C₄×C₁₁	1	3	yes	—
107	C₂×C₄²	C₂×C₄×C₁₁	1	3	yes	—
108	M₃₂	—	2	12	no	—
109	M₃₂	C₂³×C₁₁	1	8	yes	—
110	C₂×C₁₆	—	2	12	no	—
111	#97	C₂×C₄×C₁₁	1	6	yes	—
112	C₄×C₈	C₂×C₄×C₁₁	1	3	yes	—
113	C₄×C₈	C₂×C₄×C₁₁	1	3	yes	—
114	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
115	C₄×C₈	C₂³×C₁₁	1	3	yes	—
116	C₂×C₁₁	—	2	1	no	—
117	C₂×C₁₁	—	2	6	no	—
118	C₂×C₁₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
119	#41	C₁₁×C₄⋊C₄	1	4	yes	—
120	#41	C₂×C₈×C₁₁	1	4	yes	—
121	C₂×Q₈	C₁₁×M₁₆	1	1	yes	characteristic
122	C₂×D₄	C₁₁×M₁₆	1	3	yes	—
123	C₂²×C₄	—	2	3	no	—
124	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
125	M₁₆	C₁₁×C₄⋊C₄	1	12	yes	—
126	M₁₆	C₂×C₈×C₁₁	1	12	yes	—
127	C₂×C₈	C₂×C₈×C₁₁	1	12	yes	—
128	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
129	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
130	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
131	C₂×C₈	C₂×D₄×C₁₁	1	6	yes	—
132	C₂×C₈	C₂×Q₈×C₁₁	1	6	yes	—
133	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
134	C₄⋊C₄	—	2	3	no	—
135	C₂²⋊C₄	—	2	3	no	—
136	C₄²	—	2	3	no	—
137	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
138	C₄²	C₂²×C₄×C₁₁	1	3	yes	—
139	C₁₆	—	2	8	no	—
140	C₁₁	#33401	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³	C₂×C₁₁×M₁₆	1	3	yes	—
142	Q₈	C₁₁×C₄⋊C₈	1	4	yes	—
143	D₄	C₁₁×C₄⋊C₈	1	12	yes	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	3	no	—
146	C₂×C₄	—	4	6	no	—
147	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	6	yes	—
148	C₂×C₄	C₂²×C₈×C₁₁	1	6	yes	—
149	C₂×C₄	C₂×C₁₁×M₁₆	1	3	yes	—
150	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
151	C₈	C₂×C₁₁×C₄⋊C₄	1	6	yes	—
152	C₈	C₂²×C₈×C₁₁	1	2	yes	—
153	C₈	C₂²×C₈×C₁₁	1	6	yes	—
154	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
155	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
156	C₂²	—	4	3	no	—
157	C₂²	C₂×C₁₁×C₄⋊C₈	1	6	yes	—
158	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
159	C₄	—	2	2	no	—
160	C₄	—	4	3	no	—
161	C₄	C₂×C₁₁×C₄⋊C₈	1	6	yes	—
162	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
163	C₄	C₂³×C₈×C₁₁	1	1	yes	characteristic
164	C₂	—	2	1	no	—
165	C₂	—	2	6	no	—
166	C₂	C₂²×C₁₁×C₄⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₁	C₂²×D₄
commutator	C₄	C₂³×C₈×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂×C₁₁	C₂²×C₄⋊C₈
prime radical	C₂×C₁₁×#41	C₂×C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₁ ◁ C₂×C₁₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2153	C₂	semidirect
4. C₂×C₁₁×#364	C₂	semidirect
36. #33401	C₁₁	direct (N × H)
60. #2153	C₂×C₁₁	semidirect
61. C₂×#364	C₂×C₁₁	semidirect
140. C₁₁	#33401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3407	2
C₄×C₁₁×#131	2
C₁₁×#2153	2
C₂×C₁₁×#364	2
#33401	11

Subgroups — C11×#33401 #14610594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33401 #14610594