Subgroups — C₂×C₁₁×#1367 #14589188

Order 2816.

286 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	C₂×C₁₁×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1367	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₁×C₁₆	—	2	2	no	—
5	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₁₁×C₄⋊C₁₆	—	2	2	no	—
9	C₁₁×C₄⋊C₁₆	C₂²	1	4	yes	—
10	C₈²×C₁₁	C₄	1	2	yes	—
11	C₈²×C₁₁	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₁	—	2	1	no	—
13	C₂²×C₈×C₁₁	C₈	1	1	yes	characteristic
14	C₂²×C₈×C₁₁	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₁×C₁₆	—	2	4	no	—
19	C₂×C₁₁×C₁₆	—	4	4	no	—
20	C₄×C₈×C₁₁	—	2	1	no	—
21	C₄×C₈×C₁₁	C₈	1	2	yes	—
22	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
27	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₂×#1367	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₁	—	2	4	no	—
33	C₂×C₈×C₁₁	—	2	2	no	—
34	C₂×C₈×C₁₁	—	2	2	no	—
35	C₂×C₈×C₁₁	—	2	2	no	—
36	C₂×C₈×C₁₁	C₁₆	1	4	yes	complemented
37	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
40	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
42	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
43	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
44	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
45	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
46	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
47	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
48	C₁₁×C₁₆	—	4	4	no	—
49	C₂×C₄⋊C₁₆	C₂×C₁₁	1	2	yes	—
50	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic
51	#1367	C₂×C₁₁	1	4	yes	direct product factor
52	C₂³×C₁₁	C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₁	—	2	2	no	—
54	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#106	1	2	yes	—
58	C₂×C₄×C₁₁	#108	1	2	yes	—
59	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
60	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
61	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
64	C₈×C₁₁	—	2	4	no	—
65	C₈×C₁₁	—	2	1	no	—
66	C₈×C₁₁	—	2	1	no	—
67	C₈×C₁₁	—	2	2	no	—
68	C₈×C₁₁	#106	1	2	yes	—
69	C₈×C₁₁	C₂×C₁₆	1	4	yes	complemented
70	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
71	C₂²×C₁₆	—	2	2	no	—
72	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
73	C₂×C₄×C₈	C₄×C₁₁	1	1	yes	characteristic
74	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
75	C₄⋊C₁₆	—	2	2	no	—
76	C₄⋊C₁₆	C₂²×C₁₁	1	4	yes	—
77	C₈²	C₄×C₁₁	1	2	yes	—
78	C₈²	C₂²×C₁₁	1	2	yes	—
79	C₂²×C₁₁	#334	1	2	yes	—
80	C₂²×C₁₁	C₄⋊C₁₆	1	2	yes	—
81	C₂²×C₁₁	#364	1	2	yes	—
82	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
83	C₄×C₁₁	—	2	1	no	—
84	C₄×C₁₁	—	2	1	no	—
85	C₄×C₁₁	#334	1	2	yes	—
86	C₄×C₁₁	C₄⋊C₁₆	1	2	yes	—
87	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
88	C₄×C₁₁	C₂×#108	1	1	yes	characteristic
89	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
90	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
91	C₂²×C₈	—	2	1	no	—
92	C₂²×C₈	C₈×C₁₁	1	1	yes	characteristic
93	C₂²×C₈	C₈×C₁₁	1	1	yes	characteristic
94	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
95	C₂²×C₈	Q₈×C₁₁	1	1	yes	characteristic
96	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
97	C₂×C₁₆	—	2	4	no	—
98	C₂×C₁₆	—	4	4	no	—
99	C₄×C₈	—	2	1	no	—
100	C₄×C₈	C₈×C₁₁	1	2	yes	—
101	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
102	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
103	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
104	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
105	C₄×C₈	Q₈×C₁₁	1	1	yes	characteristic
106	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
107	C₂×C₁₁	#1367	1	4	yes	direct product factor
108	C₂×C₁₁	C₂×#334	1	1	yes	characteristic
109	C₂×C₁₁	C₂×C₄⋊C₁₆	1	1	yes	characteristic
110	C₂×C₁₁	C₂×#364	1	1	yes	characteristic
111	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
113	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	2	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	C₁₁×C₁₆	1	4	yes	complemented
119	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
122	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
123	C₂×C₈	C₁₁×SD₁₆	1	4	yes	—
124	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
125	C₂×C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
126	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
127	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
128	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
129	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
130	C₁₆	—	4	4	no	—
131	C₁₁	C₂×#1367	1	1	yes	characteristic, direct product factor, Sylow
132	C₂³	C₁₁×C₄⋊C₈	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	C₁₁×C₄⋊C₈	1	1	yes	characteristic
135	C₂×C₄	C₁₁×C₄⋊C₈	1	1	yes	characteristic
136	C₂×C₄	C₁₁×C₄⋊C₈	1	1	yes	characteristic
137	C₂×C₄	C₁₁×#106	1	2	yes	—
138	C₂×C₄	C₁₁×#108	1	2	yes	—
139	C₂×C₄	C₂×C₁₁×C₁₆	1	2	yes	—
140	C₂×C₄	C₁₁×M₃₂	1	2	yes	—
141	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
143	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
144	C₈	—	2	4	no	—
145	C₈	—	2	2	no	—
146	C₈	—	2	1	no	—
147	C₈	—	2	1	no	—
148	C₈	C₁₁×#106	1	2	yes	—
149	C₈	C₂×C₁₁×C₁₆	1	4	yes	complemented
150	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
151	C₂²	C₁₁×#334	1	2	yes	—
152	C₂²	C₁₁×C₄⋊C₁₆	1	2	yes	—
153	C₂²	C₁₁×#364	1	2	yes	—
154	C₂²	C₂×C₁₁×C₄⋊C₈	1	1	yes	characteristic
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	C₁₁×#334	1	2	yes	—
158	C₄	C₁₁×C₄⋊C₁₆	1	2	yes	—
159	C₄	C₂×C₁₁×#106	1	1	yes	characteristic
160	C₄	C₂×C₁₁×#108	1	1	yes	characteristic
161	C₄	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
162	C₄	C₂×C₁₁×M₃₂	1	1	yes	characteristic
163	C₂	C₁₁×#1367	1	4	yes	direct product factor
164	C₂	C₂×C₁₁×#334	1	1	yes	characteristic
165	C₂	C₂×C₁₁×C₄⋊C₁₆	1	1	yes	characteristic
166	C₂	C₂×C₁₁×#364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₁₁	D₄
commutator	C₄	C₂²×C₁₁×C₁₆
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle, prime radical	C₂³×C₁₁	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1367	C₂	direct (N × H)
28. C₂×#1367	C₁₁	direct (N × H)
36. C₂×C₈×C₁₁	C₁₆	semidirect
51. #1367	C₂×C₁₁	direct (N × H)
69. C₈×C₁₁	C₂×C₁₆	semidirect
107. C₂×C₁₁	#1367	direct (N × H)
118. C₂×C₈	C₁₁×C₁₆	semidirect
131. C₁₁	C₂×#1367	direct (N × H)
149. C₈	C₂×C₁₁×C₁₆	semidirect
163. C₂	C₁₁×#1367	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×C₄⋊C₁₆	2
C₂×C₈²×C₁₁	2
C₁₁×#1367	2
C₂×#1367	11

Subgroups — C2×C11×#1367 #14589188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1367 #14589188