Subgroups — #13077310

Order 1408.

520 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	C₂³×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#10623322	C₂	1	1	yes	maximal, characteristic
3	C₂×#66954	C₂	1	1	yes	maximal, characteristic, complemented
4	#10622820	C₂	1	1	yes	maximal, characteristic, complemented
5	#10622724	C₂	1	4	yes	maximal, complemented
6	#10622723	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₂²⋊D₁₁	C₂	1	4	yes	maximal, complemented
8	#10622715	C₂	1	1	yes	maximal, characteristic, complemented
9	#10622714	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×#4339	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₁₁	—	2	4	no	—
13	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
16	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	#67006	C₄	1	2	yes	—
18	#66983	C₄	1	2	yes	—
19	#66982	C₄	1	2	yes	—
20	C₄×C₂²⋊D₁₁	C₂²	1	4	yes	—
21	#66979	C₂²	1	1	yes	characteristic
22	#66977	C₄	1	2	yes	—
23	C₂×#4318	C₂²	1	1	yes	characteristic
24	C₂×#4318	C₂²	1	1	yes	characteristic
25	#66954	—	2	4	no	—
26	C₂×#4313	C₂²	1	2	yes	complemented
27	C₂×C₈×D₁₁	C₂²	1	2	yes	complemented
28	C₂²⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
29	(C₂×D₁₁)⋊C₈	C₂²	1	4	yes	complemented
30	#66879	C₂²	1	2	yes	complemented
31	Dic₁₁⋊C₈	C₂²	1	4	yes	complemented
32	C₈×Dic₁₁	C₂²	1	2	yes	complemented
33	C₂⁴×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	—	2	2	no	—
35	C₂²×C₄×C₁₁	—	2	2	no	—
36	C₂²×C₄×C₁₁	C₂×C₄	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
40	C₂×C₂²⋊D₁₁	C₂×C₄	1	4	yes	—
41	C₂×C₂²⋊D₁₁	C₂×C₄	1	2	yes	—
42	#4339	—	2	2	no	—
43	#4339	—	2	2	no	—
44	C₂×D₄₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×D₁₁	C₂³	1	2	yes	—
46	C₂×Dic₂₂	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₁	—	2	4	no	—
48	C₂×C₈×C₁₁	—	2	4	no	—
49	C₂×C₈×C₁₁	—	2	2	no	—
50	C₂×C₈×C₁₁	D₄	1	4	yes	complemented
51	C₂×C₈×C₁₁	C₂³	1	2	yes	—
52	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²⋊Dic₁₁	C₂×C₄	1	4	yes	—
55	C₂²⋊Dic₁₁	C₂×C₄	1	2	yes	—
56	(C₂×D₁₁)⋊C₄	C₂×C₄	1	4	yes	—
57	C₄⋊Dic₁₁	C₂×C₄	1	2	yes	—
58	Dic₁₁⋊C₄	C₂×C₄	1	4	yes	—
59	C₄×Dic₁₁	C₂³	1	2	yes	—
60	#4318	—	2	2	no	—
61	#4318	—	2	2	no	—
62	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
63	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
64	#4313	—	2	4	no	—
65	C₈×D₁₁	—	2	4	no	—
66	#2929	—	11	1	no	maximal, Sylow
67	C₂³×C₁₁	—	2	2	no	—
68	C₂³×C₁₁	—	2	4	no	—
69	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂³×C₁₁	C₂²×C₄	1	2	yes	—
71	C₂²×D₁₁	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₁₁	—	2	2	no	—
73	C₂×C₄×C₁₁	—	2	4	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
77	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₁₁	#41	1	2	yes	—
80	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
81	C₂²⋊D₁₁	—	2	4	no	—
82	C₂²⋊D₁₁	—	2	8	no	—
83	C₂×Dic₁₁	C₂²×C₄	1	4	yes	—
84	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
85	D₄₄	—	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	C₂³×C₈	D₁₁	1	1	yes	characteristic, complemented
96	#525	—	11	1	no	—
97	#435	—	11	4	no	—
98	C₈×D₄	—	11	4	no	—
99	#424	—	11	1	no	—
100	#408	—	11	1	no	—
101	#407	—	11	1	no	—
102	#405	—	11	1	no	—
103	C₂²×C₁₁	—	2	8	no	—
104	C₂²×C₁₁	—	2	2	no	—
105	C₂²×C₁₁	—	2	2	no	—
106	C₂²×C₁₁	—	2	2	no	—
107	C₂²×C₁₁	C₄×D₄	1	2	yes	—
108	C₂²×C₁₁	#131	1	4	yes	complemented
109	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
110	C₂×D₁₁	—	2	2	no	—
111	C₂×D₁₁	—	2	4	no	—
112	C₄×C₁₁	—	2	2	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	4	no	—
118	C₂×#41	—	11	1	no	—
119	C₂³×C₄	C₂×D₁₁	1	1	yes	characteristic
120	#131	—	22	4	no	—
121	C₂×M₁₆	—	11	1	no	—
122	C₂×M₁₆	—	11	1	no	—
123	C₂×M₁₆	—	11	2	no	—
124	C₂²×C₈	—	2	4	no	—
125	C₂²×C₈	—	11	2	no	—
126	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
127	C₂²×C₈	C₂×D₁₁	1	2	yes	—
128	C₂²×C₈	C₂×D₁₁	1	2	yes	—
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	—	11	1	no	—
136	C₄⋊C₈	—	11	4	no	—
137	C₂²⋊C₈	—	11	4	no	—
138	C₂²⋊C₈	—	11	4	no	—
139	#97	—	11	2	no	—
140	C₄×C₈	—	11	2	no	—
141	C₂×C₁₁	—	2	2	no	—
142	C₂×C₁₁	—	2	4	no	—
143	C₂×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂×C₁₁	C₂×#131	1	2	yes	—
145	D₁₁	—	4	2	no	—
146	C₂⁴	C₄×D₁₁	1	1	yes	characteristic
147	#41	—	22	2	no	—
148	#41	—	22	2	no	—
149	C₂×Q₈	—	11	1	no	—
150	C₂×D₄	—	11	4	no	—
151	C₂×D₄	—	11	2	no	—
152	C₂×D₄	—	11	1	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	2	2	no	—
155	C₂²×C₄	—	11	2	no	—
156	C₂²×C₄	C₄×D₁₁	1	2	yes	—
157	C₂²×C₄	C₄×D₁₁	1	1	yes	characteristic
158	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
159	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
160	M₁₆	—	22	2	no	—
161	M₁₆	—	22	2	no	—
162	M₁₆	—	22	4	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	2	4	no	—
165	C₂×C₈	—	2	4	no	—
166	C₂×C₈	—	11	2	no	—
167	C₂×C₈	—	11	2	no	—
168	C₂×C₈	—	22	4	no	—
169	C₂×C₈	C₂²⋊D₁₁	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	2	no	—
174	C₄⋊C₄	—	11	4	no	—
175	C₂²⋊C₄	—	11	2	no	—
176	C₂²⋊C₄	—	11	4	no	—
177	C₂²⋊C₄	—	11	4	no	—
178	C₄²	—	11	2	no	—
179	C₁₁	#2929	1	1	yes	characteristic, complemented, Sylow
180	C₂³	—	2	4	no	—
181	C₂³	—	2	2	no	—
182	C₂³	—	11	2	no	—
183	C₂³	C₂×C₄×D₁₁	1	2	yes	—
184	C₂³	C₂×C₄×D₁₁	1	1	yes	characteristic
185	Q₈	—	22	2	no	—
186	D₄	—	22	8	no	—
187	D₄	—	22	4	no	—
188	D₄	—	22	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	11	4	no	—
194	C₂×C₄	—	11	2	no	—
195	C₂×C₄	—	22	2	no	—
196	C₂×C₄	—	22	2	no	—
197	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
198	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
199	C₂×C₄	#4339	1	2	yes	—
200	C₂×C₄	C₂×C₂²⋊D₁₁	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×C₂²⋊D₁₁	1	2	yes	—
206	C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
207	C₂²	—	2	8	no	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	2	2	no	—
211	C₂²	—	22	4	no	—
212	C₂²	—	22	2	no	—
213	C₂²	#66954	1	4	yes	complemented
214	C₂²	C₄×C₂²⋊D₁₁	1	2	yes	—
215	C₂²	C₂²×C₄×D₁₁	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	22	4	no	—
218	C₄	—	22	2	no	—
219	C₄	C₄×C₂²⋊D₁₁	1	2	yes	—
220	C₄	C₂×#4339	1	1	yes	characteristic
221	C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
222	C₂	—	2	4	no	—
223	C₂	—	2	2	no	—
224	C₂	—	44	2	no	—
225	C₂	C₂×#66954	1	2	yes	—
226	C₂	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₁
Fitting	C₂³×C₈×C₁₁	C₂
prime radical	#10623322	C₂
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	C₂³×C₈	D₁₁
hypocenter	C₁₁	#2929
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₈×C₁₁	C₂	semidirect
3. C₂×#66954	C₂	semidirect
4. #10622820	C₂	semidirect
5. #10622724	C₂	semidirect
6. #10622723	C₂	semidirect
7. C₈×C₂²⋊D₁₁	C₂	semidirect
8. #10622715	C₂	semidirect
9. #10622714	C₂	semidirect
26. C₂×#4313	C₂²	semidirect
27. C₂×C₈×D₁₁	C₂²	semidirect
29. (C₂×D₁₁)⋊C₈	C₂²	semidirect
30. #66879	C₂²	semidirect
31. Dic₁₁⋊C₈	C₂²	semidirect
32. C₈×Dic₁₁	C₂²	semidirect
50. C₂×C₈×C₁₁	D₄	semidirect
95. C₂³×C₈	D₁₁	semidirect
108. C₂²×C₁₁	#131	semidirect
169. C₂×C₈	C₂²⋊D₁₁	semidirect
179. C₁₁	#2929	semidirect
213. C₂²	#66954	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₈×C₁₁	2
#10623322	2
C₂×#66954	2
#10622820	2
#10622724	2
#10622723	2
C₈×C₂²⋊D₁₁	2
#10622715	2
#10622714	2
#2929	11