Subgroups — #13077321

Order 1408.

492 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66954	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#4313	C₂	1	1	yes	maximal, characteristic, complemented
3	#10623055	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	#10622742	C₂	1	1	yes	maximal, characteristic, complemented
6	#10622739	C₂	1	1	yes	maximal, characteristic, complemented
7	#10622612	C₂	1	1	yes	maximal, characteristic, complemented
8	#10622319	C₂	1	4	yes	maximal, complemented
9	#10622301	C₂	1	4	yes	maximal, complemented
10	C₂×#4339	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#117	C₂²	1	1	yes	characteristic
15	C₂×#4318	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
17	#66954	—	2	4	no	—
18	C₂×#4313	—	2	4	no	—
19	C₂×#4313	C₂²	1	2	yes	—
20	C₂×#4313	C₂²	1	2	yes	—
21	C₂×#4313	C₂²	1	2	yes	complemented
22	C₂×C₈×D₁₁	C₂²	1	2	yes	complemented
23	#66950	C₄	1	2	yes	—
24	#66948	C₄	1	2	yes	—
25	#66939	C₄	1	2	yes	—
26	#66935	C₄	1	2	yes	—
27	C₄×D₄₄	C₂²	1	4	yes	—
28	C₁₁×#97	C₂²	1	2	yes	complemented
29	C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
30	(C₂×D₁₁)⋊C₈	C₂²	1	4	yes	—
31	(C₂×D₁₁)⋊C₈	C₂²	1	4	yes	complemented
32	C₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	complemented
33	C₂³×D₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
35	C₂×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
36	C₂²×Dic₁₁	C₂×C₄	1	1	yes	characteristic
37	#4339	—	2	2	no	—
38	#4339	—	2	2	no	—
39	C₂×D₄₄	C₂×C₄	1	1	yes	characteristic
40	C₂×D₄₄	C₂×C₄	1	4	yes	—
41	C₂×C₄×D₁₁	—	2	2	no	—
42	C₂×C₄×D₁₁	—	2	2	no	—
43	C₂×C₄×D₁₁	C₂×C₄	1	2	yes	—
44	C₂×C₄×D₁₁	C₂³	1	2	yes	—
45	C₂×C₄×D₁₁	C₂³	1	2	yes	—
46	C₂×Dic₂₂	C₂×C₄	1	1	yes	characteristic
47	C₁₁×M₁₆	—	2	2	no	—
48	C₂×C₈×C₁₁	D₄	1	4	yes	complemented
49	C₂×C₈×C₁₁	C₂³	1	2	yes	—
50	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₄²×C₁₁	C₂³	1	2	yes	—
55	(C₂×D₁₁)⋊C₄	C₂×C₄	1	4	yes	—
56	(C₂×D₁₁)⋊C₄	C₂×C₄	1	4	yes	—
57	C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
58	#4318	—	2	2	no	—
59	C₂×C₁₁⋊C₈	—	2	2	no	—
60	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
61	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
62	#4313	—	2	4	no	—
63	#4313	—	2	4	no	—
64	#4313	—	2	4	no	—
65	C₈×D₁₁	—	2	4	no	—
66	#2930	—	11	1	no	maximal, Sylow
67	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
68	C₂²×D₁₁	—	2	2	no	—
69	C₂²×D₁₁	—	4	2	no	—
70	C₂²×D₁₁	C₂²×C₄	1	2	yes	—
71	C₂²×D₁₁	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₁₁	C₂²×C₄	1	4	yes	—
73	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₁₁	#41	1	2	yes	—
76	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
77	C₂²⋊D₁₁	—	2	4	no	—
78	C₂×Dic₁₁	—	2	2	no	—
79	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
80	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
81	D₄₄	—	2	2	no	—
82	D₄₄	—	4	4	no	—
83	C₄×D₁₁	—	2	4	no	—
84	C₄×D₁₁	—	2	2	no	—
85	C₄×D₁₁	—	2	2	no	—
86	C₄×D₁₁	—	2	2	no	—
87	C₄×D₁₁	—	2	2	no	—
88	Dic₂₂	—	2	2	no	—
89	C₈×C₁₁	—	2	2	no	—
90	C₈×C₁₁	C₂×D₄	1	2	yes	—
91	C₈×C₁₁	C₂×D₄	1	2	yes	—
92	C₁₁⋊C₈	—	2	2	no	—
93	C₁₁⋊C₈	—	2	2	no	—
94	C₂×#131	—	11	1	no	—
95	C₂²×M₁₆	—	11	1	no	—
96	#525	—	11	1	no	—
97	#436	—	11	4	no	—
98	#435	—	11	4	no	—
99	#424	—	11	1	no	—
100	#408	—	11	1	no	—
101	#407	—	11	1	no	—
102	#405	D₁₁	1	1	yes	characteristic, complemented
103	C₂²×C₁₁	—	2	2	no	—
104	C₂²×C₁₁	C₄×D₄	1	2	yes	—
105	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
106	C₂×D₁₁	—	2	2	no	—
107	C₂×D₁₁	—	2	2	no	—
108	C₂×D₁₁	—	2	2	no	—
109	C₂×D₁₁	—	2	2	no	—
110	C₂×D₁₁	—	2	4	no	—
111	C₂×D₁₁	—	4	4	no	—
112	C₄×C₁₁	—	2	4	no	—
113	C₄×C₁₁	C₄×D₄	1	2	yes	—
114	C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
115	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
116	Dic₁₁	—	2	2	no	—
117	Dic₁₁	—	2	2	no	—
118	C₂×#41	—	11	1	no	—
119	C₂³×C₄	—	11	1	no	—
120	#131	—	22	4	no	—
121	C₂×M₁₆	—	11	1	no	—
122	C₂×M₁₆	—	11	2	no	—
123	C₂×M₁₆	—	11	2	no	—
124	C₂×M₁₆	—	11	2	no	—
125	C₂×M₁₆	—	22	4	no	—
126	C₂×M₁₆	C₂×D₁₁	1	1	yes	characteristic
127	C₂²×C₈	—	11	1	no	—
128	C₂²×C₈	—	11	2	no	—
129	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
130	#123	—	11	2	no	—
131	C₂²⋊Q₈	—	11	2	no	—
132	#121	—	11	2	no	—
133	#120	—	11	2	no	—
134	C₄×D₄	—	11	4	no	—
135	#117	C₂×D₁₁	1	1	yes	characteristic
136	C₄⋊C₈	—	11	4	no	—
137	C₂²⋊C₈	—	11	4	no	—
138	C₂²⋊C₈	—	11	4	no	—
139	#97	C₂×D₁₁	1	2	yes	complemented
140	C₄×C₈	C₂×D₁₁	1	2	yes	complemented
141	C₂×C₁₁	—	2	2	no	—
142	C₂×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
143	C₂×C₁₁	#568	1	2	yes	—
144	D₁₁	—	4	2	no	—
145	D₁₁	—	4	2	no	—
146	C₂⁴	—	11	1	no	—
147	#41	—	22	2	no	—
148	#41	—	22	2	no	—
149	C₂×Q₈	—	11	1	no	—
150	C₂×D₄	—	11	2	no	—
151	C₂×D₄	—	11	1	no	—
152	C₂×D₄	—	11	4	no	—
153	C₂²×C₄	—	11	1	no	—
154	C₂²×C₄	—	11	2	no	—
155	C₂²×C₄	—	11	2	no	—
156	C₂²×C₄	—	11	2	no	—
157	C₂²×C₄	—	22	2	no	—
158	C₂²×C₄	—	22	2	no	—
159	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
160	M₁₆	—	2	2	no	—
161	M₁₆	—	22	2	no	—
162	M₁₆	—	22	4	no	—
163	M₁₆	—	22	4	no	—
164	M₁₆	—	22	4	no	—
165	C₂×C₈	—	11	2	no	—
166	C₂×C₈	—	11	2	no	—
167	C₂×C₈	—	22	2	no	—
168	C₂×C₈	—	22	4	no	—
169	C₂×C₈	D₄₄	1	4	yes	complemented
170	C₂×C₈	C₂²×D₁₁	1	2	yes	—
171	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
172	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
173	C₄⋊C₄	—	11	4	no	—
174	C₄⋊C₄	C₄×D₁₁	1	2	yes	—
175	C₂²⋊C₄	—	11	4	no	—
176	C₂²⋊C₄	—	11	4	no	—
177	C₂²⋊C₄	C₄×D₁₁	1	2	yes	—
178	C₄²	C₂²×D₁₁	1	2	yes	—
179	C₁₁	#2930	1	1	yes	characteristic, complemented, Sylow
180	C₂³	—	11	2	no	—
181	C₂³	—	11	2	no	—
182	C₂³	—	22	2	no	—
183	C₂³	—	44	2	no	—
184	C₂³	C₂×C₄×D₁₁	1	1	yes	characteristic
185	Q₈	—	22	2	no	—
186	D₄	—	22	4	no	—
187	D₄	—	22	2	no	—
188	D₄	—	44	4	no	—
189	C₂×C₄	—	11	2	no	—
190	C₂×C₄	—	11	2	no	—
191	C₂×C₄	—	22	2	no	—
192	C₂×C₄	—	22	4	no	—
193	C₂×C₄	—	22	2	no	—
194	C₂×C₄	—	22	2	no	—
195	C₂×C₄	—	22	2	no	—
196	C₂×C₄	—	22	2	no	—
197	C₂×C₄	C₂×C₄×D₁₁	1	4	yes	—
198	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
199	C₂×C₄	C₂×D₄₄	1	2	yes	—
200	C₂×C₄	#4339	1	2	yes	—
201	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
202	C₈	—	2	2	no	—
203	C₈	—	22	2	no	—
204	C₈	—	22	2	no	—
205	C₈	C₂×D₄₄	1	2	yes	—
206	C₈	C₂×D₄₄	1	2	yes	—
207	C₂²	—	2	2	no	—
208	C₂²	—	22	2	no	—
209	C₂²	—	22	2	no	—
210	C₂²	—	22	2	no	—
211	C₂²	—	22	4	no	—
212	C₂²	—	22	2	no	—
213	C₂²	—	44	4	no	—
214	C₂²	C₄×D₄₄	1	2	yes	—
215	C₂²	C₂²×C₄×D₁₁	1	1	yes	characteristic
216	C₄	—	2	4	no	—
217	C₄	—	22	2	no	—
218	C₄	—	22	2	no	—
219	C₄	C₄×D₄₄	1	2	yes	—
220	C₄	C₂²×D₄₄	1	1	yes	characteristic
221	C₄	C₂×#4339	1	1	yes	characteristic
222	C₂	—	2	2	no	—
223	C₂	—	44	2	no	—
224	C₂	—	44	2	no	—
225	C₂	C₂×C₄×D₄₄	1	1	yes	characteristic
226	C₂	#10623281	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₄
Fitting	C₁₁×#405	C₂
prime radical	#10623055	C₂
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	#405	D₁₁
hypocenter	C₁₁	#2930
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
1. C₂×#66954	C₂	semidirect
2. C₂²×#4313	C₂	semidirect
4. C₁₁×#405	C₂	semidirect
5. #10622742	C₂	semidirect
6. #10622739	C₂	semidirect
7. #10622612	C₂	semidirect
8. #10622319	C₂	semidirect
9. #10622301	C₂	semidirect
21. C₂×#4313	C₂²	semidirect
22. C₂×C₈×D₁₁	C₂²	semidirect
28. C₁₁×#97	C₂²	semidirect
29. C₄×C₈×C₁₁	C₂²	semidirect
31. (C₂×D₁₁)⋊C₈	C₂²	semidirect
32. C₄⋊(C₁₁⋊C₈)	C₂²	semidirect
48. C₂×C₈×C₁₁	D₄	semidirect
102. #405	D₁₁	semidirect
139. #97	C₂×D₁₁	semidirect
140. C₄×C₈	C₂×D₁₁	semidirect
169. C₂×C₈	D₄₄	semidirect
179. C₁₁	#2930	semidirect

Maximal subgroups

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

subgroup	index
C₂×#66954	2
C₂²×#4313	2
#10623055	2
C₁₁×#405	2
#10622742	2
#10622739	2
#10622612	2
#10622319	2
#10622301	2
#2930	11