Subgroups — C₂³×C₁₁×#102 #14637270

Order 2816.

7646 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₁×#102	C₂	1	28	yes	maximal, direct product factor
5	C₂⁶×C₁₁	—	2	1	no	—
6	C₂³×D₄×C₁₁	—	2	7	no	—
7	C₂³×D₄×C₁₁	—	2	8	no	—
8	C₂³×D₄×C₁₁	C₄	1	16	yes	complemented
9	C₂³×D₄×C₁₁	C₂²	1	14	yes	—
10	C₂⁴×C₄×C₁₁	—	2	1	no	—
11	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₁	—	2	8	no	—
13	C₂³×C₈×C₁₁	C₂²	1	14	yes	complemented
14	C₂²×C₁₁×C₄⋊C₄	—	2	7	no	—
15	C₂²×C₁₁×C₄⋊C₄	C₂²	1	14	yes	complemented
16	C₂×C₁₁×#102	C₂²	1	112	yes	direct product factor
17	C₂⁵×C₁₁	—	2	16	no	—
18	C₂⁵×C₁₁	—	2	14	no	—
19	C₂⁵×C₁₁	—	4	8	no	—
20	C₂⁵×C₁₁	—	4	8	no	—
21	C₂⁵×C₁₁	D₄	1	1	yes	characteristic
22	C₂²×D₄×C₁₁	—	2	112	no	—
23	C₂²×D₄×C₁₁	—	2	42	no	—
24	C₂²×D₄×C₁₁	—	2	56	no	—
25	C₂²×D₄×C₁₁	C₂×C₄	1	112	yes	complemented
26	C₂²×D₄×C₁₁	C₂³	1	28	yes	—
27	C₂³×C₄×C₁₁	—	2	14	no	—
28	C₂³×C₄×C₁₁	—	4	8	no	—
29	C₂³×C₄×C₁₁	C₂×C₄	1	8	yes	—
30	C₂³×C₄×C₁₁	D₄	1	7	yes	—
31	C₂³×C₄×C₁₁	D₄	1	8	yes	—
32	C₂³×C₄×C₁₁	C₂³	1	7	yes	—
33	C₂²×C₈×C₁₁	—	2	56	no	—
34	C₂²×C₈×C₁₁	C₂³	1	28	yes	complemented
35	C₂×C₁₁×C₄⋊C₄	—	2	42	no	—
36	C₂×C₁₁×C₄⋊C₄	C₂³	1	28	yes	complemented
37	C₁₁×#102	C₂³	1	64	yes	direct product factor
38	C₂³×#102	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂⁴×C₁₁	—	2	112	no	—
40	C₂⁴×C₁₁	—	2	28	no	—
41	C₂⁴×C₁₁	—	4	128	no	—
42	C₂⁴×C₁₁	—	4	56	no	—
43	C₂⁴×C₁₁	—	4	56	no	—
44	C₂⁴×C₁₁	C₂²⋊C₄	1	8	yes	—
45	C₂⁴×C₁₁	D₈	1	8	yes	—
46	C₂⁴×C₁₁	SD₁₆	1	8	yes	—
47	C₂⁴×C₁₁	C₂×D₄	1	7	yes	—
48	C₂×D₄×C₁₁	—	2	336	no	—
49	C₂×D₄×C₁₁	—	2	28	no	—
50	C₂×D₄×C₁₁	—	2	56	no	—
51	C₂×D₄×C₁₁	C₂²×C₄	1	112	yes	complemented
52	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
53	C₂²×C₄×C₁₁	—	2	28	no	—
54	C₂²×C₄×C₁₁	—	4	56	no	—
55	C₂²×C₄×C₁₁	C₂²⋊C₄	1	56	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	28	yes	—
57	C₂²×C₄×C₁₁	C₂×D₄	1	21	yes	—
58	C₂²×C₄×C₁₁	C₂×D₄	1	28	yes	—
59	C₂²×C₄×C₁₁	C₂⁴	1	7	yes	—
60	C₂×C₈×C₁₁	—	2	56	no	—
61	C₂×C₈×C₁₁	C₂⁴	1	8	yes	complemented
62	C₁₁×C₄⋊C₄	—	2	28	no	—
63	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	complemented
64	C₂⁴×D₄	C₂×C₁₁	1	1	yes	characteristic
65	C₂⁴×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
66	C₂³×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
67	C₂²×#102	C₂×C₁₁	1	28	yes	direct product factor
68	C₂³×C₁₁	—	2	112	no	—
69	C₂³×C₁₁	—	2	8	no	—
70	C₂³×C₁₁	—	4	56	no	—
71	C₂³×C₁₁	—	4	56	no	—
72	C₂³×C₁₁	—	4	448	no	—
73	C₂³×C₁₁	#102	1	64	yes	direct product factor
74	C₂³×C₁₁	C₂×C₂²⋊C₄	1	28	yes	—
75	C₂³×C₁₁	C₂×D₈	1	28	yes	—
76	C₂³×C₁₁	C₂×SD₁₆	1	28	yes	—
77	C₂³×C₁₁	C₂²×D₄	1	7	yes	—
78	D₄×C₁₁	—	2	112	no	—
79	D₄×C₁₁	—	2	8	no	—
80	D₄×C₁₁	C₂³×C₄	1	16	yes	complemented
81	C₂×C₄×C₁₁	—	2	8	no	—
82	C₂×C₄×C₁₁	—	4	56	no	—
83	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	84	yes	—
84	C₂×C₄×C₁₁	C₂³×C₄	1	14	yes	—
85	C₂×C₄×C₁₁	C₂²×D₄	1	7	yes	—
86	C₂×C₄×C₁₁	C₂²×D₄	1	14	yes	—
87	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
88	C₈×C₁₁	—	2	8	no	—
89	C₂⁶	—	2	1	no	—
90	C₂³×D₄	—	2	7	no	—
91	C₂³×D₄	—	2	8	no	—
92	C₂³×D₄	C₄×C₁₁	1	16	yes	complemented
93	C₂³×D₄	C₂²×C₁₁	1	14	yes	—
94	C₂⁴×C₄	—	2	1	no	—
95	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
96	C₂³×C₈	—	2	8	no	—
97	C₂³×C₈	C₂²×C₁₁	1	14	yes	complemented
98	C₂²×C₄⋊C₄	—	2	7	no	—
99	C₂²×C₄⋊C₄	C₂²×C₁₁	1	14	yes	complemented
100	C₂×#102	C₂²×C₁₁	1	112	yes	direct product factor
101	C₂²×C₁₁	—	2	16	no	—
102	C₂²×C₁₁	—	4	224	no	—
103	C₂²×C₁₁	—	4	8	no	—
104	C₂²×C₁₁	—	4	8	no	—
105	C₂²×C₁₁	C₂×#102	1	112	yes	direct product factor
106	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	14	yes	—
107	C₂²×C₁₁	C₂²×D₈	1	14	yes	—
108	C₂²×C₁₁	C₂²×SD₁₆	1	14	yes	—
109	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
110	C₄×C₁₁	—	4	8	no	—
111	C₄×C₁₁	C₂²×C₂²⋊C₄	1	14	yes	—
112	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
113	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
114	C₂⁵	—	2	16	no	—
115	C₂⁵	—	2	14	no	—
116	C₂⁵	—	4	8	no	—
117	C₂⁵	—	4	8	no	—
118	C₂⁵	D₄×C₁₁	1	1	yes	characteristic
119	C₂²×D₄	—	2	112	no	—
120	C₂²×D₄	—	2	42	no	—
121	C₂²×D₄	—	2	56	no	—
122	C₂²×D₄	C₂×C₄×C₁₁	1	112	yes	complemented
123	C₂²×D₄	C₂³×C₁₁	1	28	yes	—
124	C₂³×C₄	—	2	14	no	—
125	C₂³×C₄	—	4	8	no	—
126	C₂³×C₄	C₂×C₄×C₁₁	1	8	yes	—
127	C₂³×C₄	D₄×C₁₁	1	7	yes	—
128	C₂³×C₄	D₄×C₁₁	1	8	yes	—
129	C₂³×C₄	C₂³×C₁₁	1	7	yes	—
130	C₂²×C₈	—	2	56	no	—
131	C₂²×C₈	C₂³×C₁₁	1	28	yes	complemented
132	C₂×C₄⋊C₄	—	2	42	no	—
133	C₂×C₄⋊C₄	C₂³×C₁₁	1	28	yes	complemented
134	#102	C₂³×C₁₁	1	64	yes	direct product factor
135	C₂×C₁₁	—	4	16	no	—
136	C₂×C₁₁	C₂²×#102	1	28	yes	direct product factor
137	C₂×C₁₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₁₁	C₂³×D₈	1	1	yes	characteristic
139	C₂×C₁₁	C₂³×SD₁₆	1	1	yes	characteristic
140	C₂⁴	—	2	112	no	—
141	C₂⁴	—	2	28	no	—
142	C₂⁴	—	4	128	no	—
143	C₂⁴	—	4	56	no	—
144	C₂⁴	—	4	56	no	—
145	C₂⁴	C₁₁×C₂²⋊C₄	1	8	yes	—
146	C₂⁴	C₁₁×D₈	1	8	yes	—
147	C₂⁴	C₁₁×SD₁₆	1	8	yes	—
148	C₂⁴	C₂×D₄×C₁₁	1	7	yes	—
149	C₂×D₄	—	2	336	no	—
150	C₂×D₄	—	2	28	no	—
151	C₂×D₄	—	2	56	no	—
152	C₂×D₄	C₂²×C₄×C₁₁	1	112	yes	complemented
153	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
154	C₂²×C₄	—	2	28	no	—
155	C₂²×C₄	—	4	56	no	—
156	C₂²×C₄	C₁₁×C₂²⋊C₄	1	56	yes	—
157	C₂²×C₄	C₂²×C₄×C₁₁	1	28	yes	—
158	C₂²×C₄	C₂×D₄×C₁₁	1	21	yes	—
159	C₂²×C₄	C₂×D₄×C₁₁	1	28	yes	—
160	C₂²×C₄	C₂⁴×C₁₁	1	7	yes	—
161	C₂×C₈	—	2	56	no	—
162	C₂×C₈	C₂⁴×C₁₁	1	8	yes	complemented
163	C₄⋊C₄	—	2	28	no	—
164	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	complemented
165	C₁₁	C₂³×#102	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³	—	2	112	no	—
167	C₂³	—	2	8	no	—
168	C₂³	—	4	448	no	—
169	C₂³	—	4	56	no	—
170	C₂³	—	4	56	no	—
171	C₂³	C₁₁×#102	1	64	yes	direct product factor
172	C₂³	C₂×C₁₁×C₂²⋊C₄	1	28	yes	—
173	C₂³	C₂×C₁₁×D₈	1	28	yes	—
174	C₂³	C₂×C₁₁×SD₁₆	1	28	yes	—
175	C₂³	C₂²×D₄×C₁₁	1	7	yes	—
176	D₄	—	2	112	no	—
177	D₄	—	2	8	no	—
178	D₄	C₂³×C₄×C₁₁	1	16	yes	complemented
179	C₂×C₄	—	2	8	no	—
180	C₂×C₄	—	4	56	no	—
181	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	84	yes	—
182	C₂×C₄	C₂³×C₄×C₁₁	1	14	yes	—
183	C₂×C₄	C₂²×D₄×C₁₁	1	7	yes	—
184	C₂×C₄	C₂²×D₄×C₁₁	1	14	yes	—
185	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
186	C₈	—	2	8	no	—
187	C₂²	—	2	16	no	—
188	C₂²	—	4	224	no	—
189	C₂²	—	4	8	no	—
190	C₂²	—	4	8	no	—
191	C₂²	C₂×C₁₁×#102	1	112	yes	direct product factor
192	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	14	yes	—
193	C₂²	C₂²×C₁₁×D₈	1	14	yes	—
194	C₂²	C₂²×C₁₁×SD₁₆	1	14	yes	—
195	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
196	C₄	—	4	8	no	—
197	C₄	C₂²×C₁₁×C₂²⋊C₄	1	14	yes	—
198	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
199	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
200	C₂	—	4	16	no	—
201	C₂	C₂²×C₁₁×#102	1	28	yes	direct product factor
202	C₂	C₂³×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
203	C₂	C₂³×C₁₁×D₈	1	1	yes	characteristic
204	C₂	C₂³×C₁₁×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁵×C₁₁	D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂⁴×D₄×C₁₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₁ ◁ C₂⁴×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₈×C₁₁	C₂	semidirect
3. C₂³×C₁₁×C₄⋊C₄	C₂	semidirect
4. C₂²×C₁₁×#102	C₂	direct (N × H)
8. C₂³×D₄×C₁₁	C₄	semidirect
13. C₂³×C₈×C₁₁	C₂²	semidirect
15. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
16. C₂×C₁₁×#102	C₂²	direct (N × H)
25. C₂²×D₄×C₁₁	C₂×C₄	semidirect
34. C₂²×C₈×C₁₁	C₂³	semidirect
36. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
37. C₁₁×#102	C₂³	direct (N × H)
38. C₂³×#102	C₁₁	direct (N × H)
51. C₂×D₄×C₁₁	C₂²×C₄	semidirect
61. C₂×C₈×C₁₁	C₂⁴	semidirect
63. C₁₁×C₄⋊C₄	C₂⁴	semidirect
65. C₂⁴×C₈	C₂×C₁₁	semidirect
66. C₂³×C₄⋊C₄	C₂×C₁₁	semidirect
67. C₂²×#102	C₂×C₁₁	direct (N × H)
73. C₂³×C₁₁	#102	direct (N × H)
80. D₄×C₁₁	C₂³×C₄	semidirect
92. C₂³×D₄	C₄×C₁₁	semidirect
97. C₂³×C₈	C₂²×C₁₁	semidirect
99. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
100. C₂×#102	C₂²×C₁₁	direct (N × H)
105. C₂²×C₁₁	C₂×#102	direct (N × H)
122. C₂²×D₄	C₂×C₄×C₁₁	semidirect
131. C₂²×C₈	C₂³×C₁₁	semidirect
133. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
134. #102	C₂³×C₁₁	direct (N × H)
136. C₂×C₁₁	C₂²×#102	direct (N × H)
152. C₂×D₄	C₂²×C₄×C₁₁	semidirect
162. C₂×C₈	C₂⁴×C₁₁	semidirect
164. C₄⋊C₄	C₂⁴×C₁₁	semidirect
165. C₁₁	C₂³×#102	direct (N × H)
171. C₂³	C₁₁×#102	direct (N × H)
178. D₄	C₂³×C₄×C₁₁	semidirect
191. C₂²	C₂×C₁₁×#102	direct (N × H)
201. C₂	C₂²×C₁₁×#102	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×D₄×C₁₁	2
C₂⁴×C₈×C₁₁	2
C₂³×C₁₁×C₄⋊C₄	2
C₂²×C₁₁×#102	2
C₂³×#102	11

Subgroups — C23×C11×#102 #14637270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₁×#102 #14637270