Subgroups — C₂³×(C₂×D₁₁)⋊C₈ #15617199

Order 2816.

7646 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×(C₂×D₁₁)⋊C₈	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁵×D₁₁	C₄	1	1	yes	characteristic
6	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₂⁴×Dic₁₁	C₄	1	1	yes	characteristic
8	C₂³×C₄×D₁₁	—	2	8	no	—
9	C₂³×C₄×D₁₁	—	2	8	no	—
10	C₂³×C₄×D₁₁	C₄	1	14	yes	—
11	C₂³×C₄×D₁₁	C₂²	1	14	yes	—
12	C₂³×C₈×C₁₁	—	2	8	no	—
13	C₂³×C₈×C₁₁	C₂²	1	14	yes	complemented
14	C₂³×C₁₁⋊C₈	—	2	8	no	—
15	C₂³×C₁₁⋊C₈	C₂²	1	14	yes	complemented
16	C₂×(C₂×D₁₁)⋊C₈	C₂²	1	112	yes	direct product factor
17	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂⁴×D₁₁	—	2	8	no	—
19	C₂⁴×D₁₁	—	2	8	no	—
20	C₂⁴×D₁₁	C₈	1	16	yes	complemented
21	C₂⁴×D₁₁	C₂×C₄	1	14	yes	—
22	C₂³×C₄×C₁₁	C₂×C₄	1	7	yes	—
23	C₂³×C₄×C₁₁	D₄	1	8	yes	—
24	C₂³×C₄×C₁₁	D₄	1	8	yes	—
25	C₂³×C₄×C₁₁	C₂³	1	7	yes	—
26	C₂³×Dic₁₁	—	2	8	no	—
27	C₂³×Dic₁₁	C₂×C₄	1	14	yes	—
28	C₂²×C₄×D₁₁	—	2	112	no	—
29	C₂²×C₄×D₁₁	—	2	56	no	—
30	C₂²×C₄×D₁₁	—	2	56	no	—
31	C₂²×C₄×D₁₁	C₂×C₄	1	84	yes	—
32	C₂²×C₄×D₁₁	C₂³	1	28	yes	—
33	C₂²×C₈×C₁₁	—	2	56	no	—
34	C₂²×C₈×C₁₁	C₂³	1	28	yes	complemented
35	C₂²×C₁₁⋊C₈	—	2	56	no	—
36	C₂²×C₁₁⋊C₈	C₂³	1	28	yes	complemented
37	(C₂×D₁₁)⋊C₈	C₂³	1	64	yes	direct product factor
38	C₂³×C₂²⋊C₈	—	11	1	no	maximal, Sylow
39	C₂⁴×C₁₁	C₂²⋊C₄	1	8	yes	—
40	C₂⁴×C₁₁	C₂×C₈	1	8	yes	—
41	C₂⁴×C₁₁	M₁₆	1	8	yes	—
42	C₂⁴×C₁₁	C₂²×C₄	1	7	yes	—
43	C₂³×D₁₁	—	2	128	no	—
44	C₂³×D₁₁	—	2	56	no	—
45	C₂³×D₁₁	—	2	56	no	—
46	C₂³×D₁₁	C₂×C₈	1	112	yes	complemented
47	C₂³×D₁₁	C₂²×C₄	1	28	yes	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	56	yes	—
49	C₂²×C₄×C₁₁	C₂²×C₄	1	21	yes	—
50	C₂²×C₄×C₁₁	C₂×D₄	1	28	yes	—
51	C₂²×C₄×C₁₁	C₂×D₄	1	28	yes	—
52	C₂²×C₄×C₁₁	C₂⁴	1	7	yes	—
53	C₂²×Dic₁₁	—	2	56	no	—
54	C₂²×Dic₁₁	C₂²×C₄	1	28	yes	—
55	C₂×C₄×D₁₁	—	2	336	no	—
56	C₂×C₄×D₁₁	—	2	56	no	—
57	C₂×C₄×D₁₁	—	2	56	no	—
58	C₂×C₄×D₁₁	C₂²×C₄	1	56	yes	—
59	C₂×C₄×D₁₁	C₂⁴	1	8	yes	—
60	C₂×C₈×C₁₁	—	2	56	no	—
61	C₂×C₈×C₁₁	C₂⁴	1	8	yes	complemented
62	C₂×C₁₁⋊C₈	—	2	56	no	—
63	C₂×C₁₁⋊C₈	C₂⁴	1	8	yes	complemented
64	C₂⁵×C₄	—	11	1	no	—
65	C₂⁴×C₈	—	11	1	no	—
66	C₂⁴×C₈	D₁₁	1	1	yes	characteristic, complemented
67	C₂²×C₂²⋊C₈	—	11	28	no	—
68	C₂³×C₁₁	C₂²⋊C₈	1	64	yes	complemented
69	C₂³×C₁₁	C₂×C₂²⋊C₄	1	28	yes	—
70	C₂³×C₁₁	C₂²×C₈	1	28	yes	—
71	C₂³×C₁₁	C₂×M₁₆	1	28	yes	—
72	C₂³×C₁₁	C₂³×C₄	1	7	yes	—
73	C₂²×D₁₁	—	2	56	no	—
74	C₂²×D₁₁	—	2	56	no	—
75	C₂²×D₁₁	—	2	448	no	—
76	C₂²×D₁₁	C₂²×C₈	1	112	yes	complemented
77	C₂²×D₁₁	C₂³×C₄	1	8	yes	—
78	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	84	yes	—
79	C₂×C₄×C₁₁	C₂³×C₄	1	7	yes	—
80	C₂×C₄×C₁₁	C₂²×D₄	1	14	yes	—
81	C₂×C₄×C₁₁	C₂²×D₄	1	14	yes	—
82	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
83	C₂×Dic₁₁	—	2	56	no	—
84	C₂×Dic₁₁	C₂³×C₄	1	8	yes	—
85	C₄×D₁₁	—	2	112	no	—
86	C₄×D₁₁	—	2	8	no	—
87	C₄×D₁₁	—	2	8	no	—
88	C₈×C₁₁	—	2	8	no	—
89	C₁₁⋊C₈	—	2	8	no	—
90	C₂⁶	—	11	1	no	—
91	C₂⁴×C₄	—	11	1	no	—
92	C₂⁴×C₄	—	11	14	no	—
93	C₂⁴×C₄	—	11	14	no	—
94	C₂⁴×C₄	—	22	8	no	—
95	C₂⁴×C₄	—	22	8	no	—
96	C₂⁴×C₄	C₂×D₁₁	1	1	yes	characteristic
97	C₂³×C₈	—	2	8	no	—
98	C₂³×C₈	—	11	14	no	—
99	C₂³×C₈	—	22	8	no	—
100	C₂³×C₈	C₂×D₁₁	1	14	yes	complemented
101	C₂×C₂²⋊C₈	—	11	112	no	—
102	C₂²×C₁₁	C₂×C₂²⋊C₈	1	112	yes	complemented
103	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	14	yes	—
104	C₂²×C₁₁	C₂³×C₈	1	14	yes	—
105	C₂²×C₁₁	C₂²×M₁₆	1	14	yes	—
106	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
107	C₂×D₁₁	—	2	224	no	—
108	C₂×D₁₁	—	2	8	no	—
109	C₂×D₁₁	—	2	8	no	—
110	C₂×D₁₁	C₂³×C₈	1	16	yes	complemented
111	C₄×C₁₁	C₂²×C₂²⋊C₄	1	14	yes	—
112	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
113	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
114	Dic₁₁	—	2	8	no	—
115	C₂⁵	—	11	16	no	—
116	C₂⁵	—	11	14	no	—
117	C₂⁵	—	22	8	no	—
118	C₂⁵	—	22	8	no	—
119	C₂⁵	C₄×D₁₁	1	1	yes	characteristic
120	C₂³×C₄	—	11	14	no	—
121	C₂³×C₄	—	11	84	no	—
122	C₂³×C₄	—	11	28	no	—
123	C₂³×C₄	—	22	8	no	—
124	C₂³×C₄	—	22	112	no	—
125	C₂³×C₄	—	22	56	no	—
126	C₂³×C₄	—	22	56	no	—
127	C₂³×C₄	C₄×D₁₁	1	7	yes	—
128	C₂³×C₄	D₄₄	1	8	yes	—
129	C₂³×C₄	C₂²⋊D₁₁	1	8	yes	—
130	C₂³×C₄	C₂²×D₁₁	1	7	yes	—
131	C₂²×C₈	—	2	56	no	—
132	C₂²×C₈	—	11	28	no	—
133	C₂²×C₈	—	22	56	no	—
134	C₂²×C₈	C₂²×D₁₁	1	28	yes	complemented
135	C₂²⋊C₈	—	11	64	no	—
136	C₂×C₁₁	C₂²×C₂²⋊C₈	1	28	yes	complemented
137	C₂×C₁₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₁₁	C₂⁴×C₈	1	1	yes	characteristic
139	C₂×C₁₁	C₂³×M₁₆	1	1	yes	characteristic
140	D₁₁	—	2	16	no	—
141	C₂⁴	—	11	112	no	—
142	C₂⁴	—	11	28	no	—
143	C₂⁴	—	22	128	no	—
144	C₂⁴	—	22	56	no	—
145	C₂⁴	—	22	56	no	—
146	C₂⁴	C₈×D₁₁	1	8	yes	—
147	C₂⁴	#4313	1	8	yes	—
148	C₂⁴	(C₂×D₁₁)⋊C₄	1	8	yes	—
149	C₂⁴	C₂×C₄×D₁₁	1	7	yes	—
150	C₂²×C₄	—	11	28	no	—
151	C₂²×C₄	—	11	56	no	—
152	C₂²×C₄	—	11	8	no	—
153	C₂²×C₄	—	22	56	no	—
154	C₂²×C₄	—	22	336	no	—
155	C₂²×C₄	—	22	56	no	—
156	C₂²×C₄	—	22	56	no	—
157	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	56	yes	—
158	C₂²×C₄	C₂×C₄×D₁₁	1	21	yes	—
159	C₂²×C₄	C₂×D₄₄	1	28	yes	—
160	C₂²×C₄	C₂×C₂²⋊D₁₁	1	28	yes	—
161	C₂²×C₄	C₂³×D₁₁	1	7	yes	—
162	C₂×C₈	—	2	56	no	—
163	C₂×C₈	—	11	8	no	—
164	C₂×C₈	—	22	56	no	—
165	C₂×C₈	C₂³×D₁₁	1	8	yes	complemented
166	C₁₁	C₂³×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
167	C₂³	—	11	112	no	—
168	C₂³	—	11	8	no	—
169	C₂³	—	22	448	no	—
170	C₂³	—	22	56	no	—
171	C₂³	—	22	56	no	—
172	C₂³	(C₂×D₁₁)⋊C₈	1	64	yes	direct product factor
173	C₂³	C₂×C₈×D₁₁	1	28	yes	—
174	C₂³	C₂×#4313	1	28	yes	—
175	C₂³	C₂×(C₂×D₁₁)⋊C₄	1	28	yes	—
176	C₂³	C₂²×C₄×D₁₁	1	7	yes	—
177	C₂×C₄	—	11	8	no	—
178	C₂×C₄	—	22	56	no	—
179	C₂×C₄	—	22	112	no	—
180	C₂×C₄	—	22	8	no	—
181	C₂×C₄	—	22	8	no	—
182	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	84	yes	—
183	C₂×C₄	C₂²×C₄×D₁₁	1	7	yes	—
184	C₂×C₄	C₂²×D₄₄	1	14	yes	—
185	C₂×C₄	C₂²×C₂²⋊D₁₁	1	14	yes	—
186	C₂×C₄	C₂⁴×D₁₁	1	1	yes	characteristic
187	C₈	—	2	8	no	—
188	C₈	—	22	8	no	—
189	C₂²	—	11	16	no	—
190	C₂²	—	22	224	no	—
191	C₂²	—	22	8	no	—
192	C₂²	—	22	8	no	—
193	C₂²	C₂×(C₂×D₁₁)⋊C₈	1	112	yes	direct product factor
194	C₂²	C₂²×C₈×D₁₁	1	14	yes	—
195	C₂²	C₂²×#4313	1	14	yes	—
196	C₂²	C₂²×(C₂×D₁₁)⋊C₄	1	14	yes	—
197	C₂²	C₂³×C₄×D₁₁	1	1	yes	characteristic
198	C₄	—	22	8	no	—
199	C₄	C₂²×(C₂×D₁₁)⋊C₄	1	14	yes	—
200	C₄	C₂³×D₄₄	1	1	yes	characteristic
201	C₄	C₂³×C₂²⋊D₁₁	1	1	yes	characteristic
202	C₂	—	22	16	no	—
203	C₂	C₂²×(C₂×D₁₁)⋊C₈	1	28	yes	direct product factor
204	C₂	C₂³×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
205	C₂	C₂³×C₈×D₁₁	1	1	yes	characteristic
206	C₂	C₂³×#4313	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₄	C₂×D₁₁
commutator	C₂×C₁₁	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₁₁
Fitting	C₂⁴×C₈×C₁₁	C₂
socle	C₂⁵×C₁₁	C₂×C₄
prime radical	C₂⁵×D₁₁	C₄
cosocle	C₂×C₄×C₁₁	C₂⁵
hypercenter	C₂⁴×C₈	D₁₁
hypocenter	C₁₁	C₂³×C₂²⋊C₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴×C₄ ◁ C₂⁴×C₈

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₁₁⋊C₈	C₂	semidirect
3. C₂²×(C₂×D₁₁)⋊C₈	C₂	direct (N × H)
4. C₂⁴×C₈×C₁₁	C₂	semidirect
13. C₂³×C₈×C₁₁	C₂²	semidirect
15. C₂³×C₁₁⋊C₈	C₂²	semidirect
16. C₂×(C₂×D₁₁)⋊C₈	C₂²	direct (N × H)
20. C₂⁴×D₁₁	C₈	semidirect
34. C₂²×C₈×C₁₁	C₂³	semidirect
36. C₂²×C₁₁⋊C₈	C₂³	semidirect
37. (C₂×D₁₁)⋊C₈	C₂³	direct (N × H)
46. C₂³×D₁₁	C₂×C₈	semidirect
61. C₂×C₈×C₁₁	C₂⁴	semidirect
63. C₂×C₁₁⋊C₈	C₂⁴	semidirect
66. C₂⁴×C₈	D₁₁	semidirect
68. C₂³×C₁₁	C₂²⋊C₈	semidirect
76. C₂²×D₁₁	C₂²×C₈	semidirect
100. C₂³×C₈	C₂×D₁₁	semidirect
102. C₂²×C₁₁	C₂×C₂²⋊C₈	semidirect
110. C₂×D₁₁	C₂³×C₈	semidirect
134. C₂²×C₈	C₂²×D₁₁	semidirect
136. C₂×C₁₁	C₂²×C₂²⋊C₈	semidirect
165. C₂×C₈	C₂³×D₁₁	semidirect
166. C₁₁	C₂³×C₂²⋊C₈	semidirect
172. C₂³	(C₂×D₁₁)⋊C₈	direct (N × H)
193. C₂²	C₂×(C₂×D₁₁)⋊C₈	direct (N × H)
203. C₂	C₂²×(C₂×D₁₁)⋊C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×D₁₁	2
C₂⁴×C₁₁⋊C₈	2
C₂²×(C₂×D₁₁)⋊C₈	2
C₂⁴×C₈×C₁₁	2
C₂³×C₂²⋊C₈	11

Subgroups — C23×(C2×D11)⋊C8 #15617199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×(C₂×D₁₁)⋊C₈ #15617199