Subgroups — C₂²×C₁₁×#433 #14637309

Order 2816.

2310 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#433	C₂	1	24	yes	maximal, direct product factor
3	C₂²×C₁₁×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₁×C₂²⋊C₈	C₂	1	2	yes	maximal
5	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
9	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
10	C₂×C₁₁×#117	C₄	1	12	yes	—
11	C₂×C₁₁×#117	C₂²	1	12	yes	—
12	C₂²×C₁₁×C₄⋊C₄	C₄	1	2	yes	—
13	C₂²×C₁₁×C₂²⋊C₄	C₄	1	2	yes	—
14	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#433	C₂²	1	64	yes	direct product factor
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	24	yes	complemented
18	C₂×C₁₁×C₂²⋊C₈	C₂²	1	24	yes	—
19	C₂×C₁₁×#97	C₂²	1	12	yes	complemented
20	C₂×C₄×C₈×C₁₁	C₂²	1	12	yes	complemented
21	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₁	—	2	8	no	—
23	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₁	C₂×C₄	1	6	yes	—
27	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
28	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	—	2	8	no	—
30	C₂²×C₈×C₁₁	—	2	8	no	—
31	C₂²×C₈×C₁₁	C₂³	1	12	yes	—
32	C₂²×C₈×C₁₁	C₂³	1	12	yes	—
33	C₁₁×#117	C₂×C₄	1	48	yes	—
34	C₁₁×#117	C₂³	1	16	yes	—
35	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	24	yes	—
36	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	24	yes	—
37	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
38	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
39	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
40	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
41	C₁₁×C₄⋊C₈	C₂³	1	32	yes	complemented
42	C₁₁×C₂²⋊C₈	C₂³	1	32	yes	—
43	C₁₁×#97	C₂³	1	16	yes	complemented
44	C₄×C₈×C₁₁	C₂³	1	16	yes	complemented
45	C₂²×#433	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁴×C₁₁	—	2	4	no	—
47	C₂⁴×C₁₁	—	2	8	no	—
48	C₂⁴×C₁₁	C₂²×C₄	1	6	yes	—
49	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	—	2	4	no	—
51	C₂²×C₄×C₁₁	—	2	8	no	—
52	C₂²×C₄×C₁₁	—	2	8	no	—
53	C₂²×C₄×C₁₁	—	2	24	no	—
54	C₂²×C₄×C₁₁	—	2	24	no	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
57	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
58	C₂²×C₄×C₁₁	C₂²×C₄	1	12	yes	—
59	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
60	C₂²×C₄×C₁₁	#41	1	8	yes	—
61	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
62	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
63	C₂×C₈×C₁₁	—	2	24	no	—
64	C₂×C₈×C₁₁	—	2	24	no	—
65	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
66	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
67	C₁₁×C₄⋊C₄	C₂²×C₄	1	32	yes	—
68	C₁₁×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
69	C₄²×C₁₁	C₂²×C₄	1	12	yes	—
70	C₄²×C₁₁	C₂²×C₄	1	12	yes	—
71	C₄²×C₁₁	C₂⁴	1	4	yes	—
72	C₄²×C₁₁	C₂⁴	1	4	yes	—
73	C₂²×#117	C₂×C₁₁	1	1	yes	characteristic
74	C₂×#433	C₂×C₁₁	1	24	yes	direct product factor
75	C₂²×C₄⋊C₈	C₂×C₁₁	1	2	yes	complemented
76	C₂²×C₂²⋊C₈	C₂×C₁₁	1	2	yes	—
77	C₂²×#97	C₂×C₁₁	1	1	yes	characteristic, complemented
78	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
79	C₂³×C₁₁	—	2	12	no	—
80	C₂³×C₁₁	—	2	24	no	—
81	C₂³×C₁₁	—	4	16	no	—
82	C₂³×C₁₁	#117	1	4	yes	—
83	C₂³×C₁₁	#131	1	8	yes	—
84	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
85	C₂³×C₁₁	C₂³×C₄	1	3	yes	—
86	C₂×C₄×C₁₁	—	2	12	no	—
87	C₂×C₄×C₁₁	—	2	24	no	—
88	C₂×C₄×C₁₁	—	2	24	no	—
89	C₂×C₄×C₁₁	—	2	24	no	—
90	C₂×C₄×C₁₁	—	2	8	no	—
91	C₂×C₄×C₁₁	#117	1	12	yes	—
92	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
93	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
94	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
95	C₂×C₄×C₁₁	C₂³×C₄	1	3	yes	—
96	C₂×C₄×C₁₁	C₂×#41	1	12	yes	—
97	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
98	C₈×C₁₁	—	2	8	no	—
99	C₈×C₁₁	—	2	8	no	—
100	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
101	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
102	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
103	C₂×#117	C₄×C₁₁	1	12	yes	—
104	C₂×#117	C₂²×C₁₁	1	12	yes	—
105	C₂²×C₄⋊C₄	C₄×C₁₁	1	2	yes	—
106	C₂²×C₂²⋊C₄	C₄×C₁₁	1	2	yes	—
107	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
108	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
109	#433	C₂²×C₁₁	1	64	yes	direct product factor
110	C₂×C₄⋊C₈	C₂²×C₁₁	1	24	yes	complemented
111	C₂×C₂²⋊C₈	C₂²×C₁₁	1	24	yes	—
112	C₂×#97	C₂²×C₁₁	1	12	yes	complemented
113	C₂×C₄×C₈	C₂²×C₁₁	1	12	yes	complemented
114	C₂²×C₁₁	—	2	4	no	—
115	C₂²×C₁₁	—	2	8	no	—
116	C₂²×C₁₁	—	4	24	no	—
117	C₂²×C₁₁	#433	1	16	yes	direct product factor
118	C₂²×C₁₁	C₂×#117	1	6	yes	—
119	C₂²×C₁₁	C₂×#131	1	12	yes	—
120	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
121	C₄×C₁₁	—	2	4	no	—
122	C₄×C₁₁	—	2	8	no	—
123	C₄×C₁₁	—	2	8	no	—
124	C₄×C₁₁	C₂×#117	1	6	yes	—
125	C₄×C₁₁	C₂²×#41	1	2	yes	—
126	C₂⁵	C₂×C₄×C₁₁	1	1	yes	characteristic
127	C₂³×C₄	—	2	8	no	—
128	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
129	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
130	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
131	C₂³×C₄	C₂×C₄×C₁₁	1	6	yes	—
132	C₂³×C₄	C₂³×C₁₁	1	6	yes	—
133	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
134	C₂²×C₈	—	2	8	no	—
135	C₂²×C₈	—	2	8	no	—
136	C₂²×C₈	C₂³×C₁₁	1	12	yes	—
137	C₂²×C₈	C₂³×C₁₁	1	12	yes	—
138	#117	C₂×C₄×C₁₁	1	48	yes	—
139	#117	C₂³×C₁₁	1	16	yes	—
140	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	24	yes	—
141	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	24	yes	—
142	C₂×C₄²	C₂×C₄×C₁₁	1	6	yes	—
143	C₂×C₄²	C₂×C₄×C₁₁	1	6	yes	—
144	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
145	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
146	C₄⋊C₈	C₂³×C₁₁	1	32	yes	complemented
147	C₂²⋊C₈	C₂³×C₁₁	1	32	yes	—
148	#97	C₂³×C₁₁	1	16	yes	complemented
149	C₄×C₈	C₂³×C₁₁	1	16	yes	complemented
150	C₂×C₁₁	—	4	4	no	—
151	C₂×C₁₁	C₂×#433	1	12	yes	direct product factor
152	C₂×C₁₁	C₂²×#117	1	1	yes	characteristic
153	C₂×C₁₁	C₂²×#131	1	2	yes	—
154	C₂⁴	—	2	4	no	—
155	C₂⁴	—	2	8	no	—
156	C₂⁴	C₂²×C₄×C₁₁	1	6	yes	—
157	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	—	2	8	no	—
160	C₂²×C₄	—	2	8	no	—
161	C₂²×C₄	—	2	24	no	—
162	C₂²×C₄	—	2	24	no	—
163	C₂²×C₄	C₂²×C₄×C₁₁	1	12	yes	—
164	C₂²×C₄	C₂²×C₄×C₁₁	1	12	yes	—
165	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
166	C₂²×C₄	C₂²×C₄×C₁₁	1	12	yes	—
167	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
168	C₂²×C₄	C₁₁×#41	1	8	yes	—
169	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
170	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
171	C₂×C₈	—	2	24	no	—
172	C₂×C₈	—	2	24	no	—
173	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
174	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
175	C₄⋊C₄	C₂²×C₄×C₁₁	1	32	yes	—
176	C₂²⋊C₄	C₂²×C₄×C₁₁	1	32	yes	—
177	C₄²	C₂²×C₄×C₁₁	1	12	yes	—
178	C₄²	C₂²×C₄×C₁₁	1	12	yes	—
179	C₄²	C₂⁴×C₁₁	1	4	yes	—
180	C₄²	C₂⁴×C₁₁	1	4	yes	—
181	C₁₁	C₂²×#433	1	1	yes	characteristic, direct product factor, Sylow
182	C₂³	—	2	12	no	—
183	C₂³	—	2	24	no	—
184	C₂³	—	4	16	no	—
185	C₂³	C₁₁×#117	1	4	yes	—
186	C₂³	C₁₁×#131	1	8	yes	—
187	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
188	C₂³	C₂³×C₄×C₁₁	1	3	yes	—
189	C₂×C₄	—	2	12	no	—
190	C₂×C₄	—	2	24	no	—
191	C₂×C₄	—	2	24	no	—
192	C₂×C₄	—	2	24	no	—
193	C₂×C₄	—	2	8	no	—
194	C₂×C₄	C₁₁×#117	1	12	yes	—
195	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
196	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
197	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
198	C₂×C₄	C₂³×C₄×C₁₁	1	3	yes	—
199	C₂×C₄	C₂×C₁₁×#41	1	12	yes	—
200	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
201	C₈	—	2	8	no	—
202	C₈	—	2	8	no	—
203	C₂²	—	2	4	no	—
204	C₂²	—	2	8	no	—
205	C₂²	—	4	24	no	—
206	C₂²	C₁₁×#433	1	16	yes	direct product factor
207	C₂²	C₂×C₁₁×#117	1	6	yes	—
208	C₂²	C₂×C₁₁×#131	1	12	yes	—
209	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
210	C₄	—	2	4	no	—
211	C₄	—	2	8	no	—
212	C₄	—	2	8	no	—
213	C₄	C₂×C₁₁×#117	1	6	yes	—
214	C₄	C₂²×C₁₁×#41	1	2	yes	—
215	C₂	—	4	4	no	—
216	C₂	C₂×C₁₁×#433	1	12	yes	direct product factor
217	C₂	C₂²×C₁₁×#117	1	1	yes	characteristic
218	C₂	C₂²×C₁₁×#131	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂⁴×C₁₁	C₂²×C₄
prime radical	C₂⁵×C₁₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#433	C₂	direct (N × H)
3. C₂²×C₁₁×C₄⋊C₈	C₂	semidirect
5. C₂²×C₁₁×#97	C₂	semidirect
6. C₂²×C₄×C₈×C₁₁	C₂	semidirect
16. C₁₁×#433	C₂²	direct (N × H)
17. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
19. C₂×C₁₁×#97	C₂²	semidirect
20. C₂×C₄×C₈×C₁₁	C₂²	semidirect
41. C₁₁×C₄⋊C₈	C₂³	semidirect
43. C₁₁×#97	C₂³	semidirect
44. C₄×C₈×C₁₁	C₂³	semidirect
45. C₂²×#433	C₁₁	direct (N × H)
74. C₂×#433	C₂×C₁₁	direct (N × H)
75. C₂²×C₄⋊C₈	C₂×C₁₁	semidirect
77. C₂²×#97	C₂×C₁₁	semidirect
78. C₂²×C₄×C₈	C₂×C₁₁	semidirect
109. #433	C₂²×C₁₁	direct (N × H)
110. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
112. C₂×#97	C₂²×C₁₁	semidirect
113. C₂×C₄×C₈	C₂²×C₁₁	semidirect
117. C₂²×C₁₁	#433	direct (N × H)
146. C₄⋊C₈	C₂³×C₁₁	semidirect
148. #97	C₂³×C₁₁	semidirect
149. C₄×C₈	C₂³×C₁₁	semidirect
151. C₂×C₁₁	C₂×#433	direct (N × H)
181. C₁₁	C₂²×#433	direct (N × H)
206. C₂²	C₁₁×#433	direct (N × H)
216. C₂	C₂×C₁₁×#433	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#117	2
C₂×C₁₁×#433	2
C₂²×C₁₁×C₄⋊C₈	2
C₂²×C₁₁×C₂²⋊C₈	2
C₂²×C₁₁×#97	2
C₂²×C₄×C₈×C₁₁	2
C₂²×#433	11

Subgroups — C22×C11×#433 #14637309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#433 #14637309