Subgroups — #14906967

Order 2816.

674 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×#10622520	C₂	1	2	yes	maximal, complemented
2	#13077329	C₂	1	1	yes	maximal, characteristic
3	#13070440	C₂	1	8	yes	maximal, complemented
4	#13070231	C₂	1	2	yes	maximal, complemented
5	C₂×#10622099	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#66954	C₂²	1	2	yes	—
8	#10623008	C₄	1	1	yes	characteristic
9	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	#10622723	C₄	1	2	yes	—
12	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
14	#10622537	C₄	1	1	yes	characteristic
15	#10622520	—	2	8	no	—
16	C₂×#66862	C₂²	1	4	yes	—
17	C₂×C₁₆×D₁₁	C₂²	1	4	yes	—
18	#10622301	C₄	1	4	yes	—
19	C₈×D₄₄	C₂²	1	4	yes	—
20	C₁₁×C₄⋊C₁₆	C₂²	1	4	yes	—
21	(C₂×D₁₁)⋊C₁₆	C₂²	1	8	yes	—
22	#10622099	C₂²	1	4	yes	—
23	C₂×#4339	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	#66983	C₈	1	4	yes	—
28	C₂×#4318	C₂×C₄	1	2	yes	—
29	#66954	—	2	4	no	—
30	#66954	—	2	4	no	—
31	C₂×#4313	C₂×C₄	1	4	yes	—
32	C₂×C₈×D₁₁	C₂³	1	4	yes	—
33	#66928	C₈	1	2	yes	—
34	#66927	C₈	1	1	yes	characteristic
35	C₄×D₄₄	C₂×C₄	1	4	yes	—
36	#66922	C₈	1	1	yes	characteristic
37	C₁₁×M₃₂	—	2	4	no	—
38	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
39	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₁₁	C₂³	1	2	yes	—
41	(C₂×D₁₁)⋊C₈	C₂×C₄	1	8	yes	—
42	C₂×C₁₁⋊C₁₆	—	2	2	no	—
43	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	complemented
44	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
45	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
46	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
47	#66862	—	2	8	no	—
48	C₁₆×D₁₁	—	2	8	no	—
49	#33435	—	11	1	no	maximal, Sylow
50	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊D₁₁	C₂×C₈	1	4	yes	—
53	#4339	—	2	4	no	—
54	#4339	—	2	4	no	—
55	C₂×D₄₄	C₂×C₈	1	2	yes	—
56	C₂×D₄₄	C₂×C₈	1	4	yes	—
57	C₂×C₄×D₁₁	C₂²×C₄	1	4	yes	—
58	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
59	C₂×C₈×C₁₁	—	2	2	no	—
60	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
61	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₁₁	#41	1	2	yes	—
64	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
65	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
66	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
67	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
68	(C₂×D₁₁)⋊C₄	C₂×C₈	1	8	yes	—
69	C₄⋊Dic₁₁	C₂×C₈	1	4	yes	—
70	#4318	—	2	4	no	—
71	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
72	#4313	—	2	8	no	—
73	C₈×D₁₁	—	2	4	no	—
74	C₈×D₁₁	—	2	4	no	—
75	C₁₁×C₁₆	—	2	4	no	—
76	C₁₁⋊C₁₆	—	2	2	no	—
77	C₁₁⋊C₁₆	C₂×D₄	1	4	yes	—
78	C₂×#504	—	11	2	no	—
79	#2931	—	11	1	no	—
80	#2168	—	11	8	no	—
81	#2150	D₁₁	1	1	yes	characteristic, complemented
82	#2113	—	11	2	no	—
83	C₂×#346	—	11	1	no	—
84	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
85	C₂²×D₁₁	C₂²×C₈	1	4	yes	—
86	C₂×C₄×C₁₁	—	4	2	no	—
87	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
89	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
90	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
91	C₂×C₄×C₁₁	#131	1	2	yes	—
92	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
93	C₂²⋊D₁₁	—	2	8	no	—
94	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
95	D₄₄	—	2	4	no	—
96	D₄₄	—	4	4	no	—
97	C₄×D₁₁	—	2	4	no	—
98	C₄×D₁₁	—	2	4	no	—
99	Dic₂₂	—	2	4	no	—
100	C₈×C₁₁	—	2	2	no	—
101	C₈×C₁₁	C₄×D₄	1	2	yes	—
102	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
103	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
104	C₁₁⋊C₈	—	2	4	no	—
105	C₂×#131	—	11	2	no	—
106	#532	—	11	1	no	—
107	#504	—	22	8	no	—
108	C₂×M₃₂	—	11	4	no	—
109	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
110	C₂²×C₁₆	—	11	1	no	—
111	C₂²×C₁₆	—	11	1	no	—
112	C₂²×C₁₆	—	11	4	no	—
113	#436	—	11	4	no	—
114	C₈×D₄	—	11	4	no	—
115	#423	—	11	1	no	—
116	#408	—	11	2	no	—
117	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
118	C₄⋊C₁₆	C₂×D₁₁	1	4	yes	—
119	C₂²⋊C₁₆	—	11	8	no	—
120	#346	—	11	4	no	—
121	C₂²×C₁₁	—	2	2	no	—
122	C₂²×C₁₁	C₈×D₄	1	2	yes	—
123	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
124	C₂×D₁₁	—	2	8	no	—
125	C₂×D₁₁	—	2	4	no	—
126	C₄×C₁₁	—	2	2	no	—
127	C₄×C₁₁	—	2	2	no	—
128	C₄×C₁₁	C₈×D₄	1	2	yes	—
129	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
130	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
131	Dic₁₁	—	2	4	no	—
132	C₂×#41	—	11	2	no	—
133	#131	—	22	4	no	—
134	#131	—	22	4	no	—
135	C₂×M₁₆	—	11	2	no	—
136	C₂×M₁₆	—	11	4	no	—
137	C₂²×C₈	—	11	4	no	—
138	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
139	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
140	C₄⋊Q₈	—	11	1	no	—
141	#127	—	11	1	no	—
142	#124	—	11	2	no	—
143	#121	—	11	4	no	—
144	C₄×D₄	—	11	4	no	—
145	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
146	M₃₂	—	2	4	no	—
147	M₃₂	—	22	8	no	—
148	C₂×C₁₆	—	11	4	no	—
149	C₂×C₁₆	—	11	2	no	—
150	C₂×C₁₆	—	11	2	no	—
151	C₂×C₁₆	—	22	8	no	—
152	C₂×C₁₆	—	22	2	no	—
153	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
154	C₄⋊C₈	—	11	4	no	—
155	C₂²⋊C₈	—	11	8	no	—
156	C₄×C₈	C₄×D₁₁	1	2	yes	—
157	C₄×C₈	C₂²×D₁₁	1	2	yes	—
158	C₂×C₁₁	—	2	2	no	—
159	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
160	C₂×C₁₁	#3407	1	2	yes	—
161	D₁₁	—	4	4	no	—
162	#41	—	22	4	no	—
163	#41	—	22	4	no	—
164	C₂×Q₈	—	11	2	no	—
165	C₂×D₄	—	11	4	no	—
166	C₂×D₄	—	11	2	no	—
167	C₂×D₄	—	11	4	no	—
168	C₂²×C₄	—	11	4	no	—
169	C₂²×C₄	C₈×D₁₁	1	2	yes	—
170	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
171	M₁₆	—	22	4	no	—
172	M₁₆	—	22	8	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	11	4	no	—
175	C₂×C₈	—	22	4	no	—
176	C₂×C₈	—	22	4	no	—
177	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
178	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
179	C₂×C₈	D₄×D₁₁	1	2	yes	—
180	C₂×C₈	#4343	1	2	yes	—
181	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
182	C₄⋊C₄	—	11	4	no	—
183	C₂²⋊C₄	—	11	8	no	—
184	C₄²	C₈×D₁₁	1	1	yes	characteristic
185	C₄²	C₈×D₁₁	1	1	yes	characteristic
186	C₄²	C₂×C₄×D₁₁	1	2	yes	—
187	C₁₆	—	2	4	no	—
188	C₁₆	—	11	4	no	—
189	C₁₆	—	22	2	no	—
190	C₁₁	#33435	1	1	yes	characteristic, complemented, Sylow
191	C₂³	—	11	4	no	—
192	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
193	Q₈	—	22	4	no	—
194	D₄	—	22	8	no	—
195	D₄	—	22	4	no	—
196	D₄	—	44	4	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	11	4	no	—
199	C₂×C₄	—	22	4	no	—
200	C₂×C₄	—	22	4	no	—
201	C₂×C₄	#66946	1	2	yes	—
202	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
203	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
204	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
205	C₂×C₄	#66960	1	2	yes	—
206	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	22	4	no	—
209	C₈	#66946	1	2	yes	—
210	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
211	C₈	C₂×#4343	1	1	yes	characteristic
212	C₂²	—	2	2	no	—
213	C₂²	—	22	4	no	—
214	C₂²	—	22	8	no	—
215	C₂²	#10622447	1	2	yes	—
216	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	22	4	no	—
220	C₄	#10622447	1	2	yes	—
221	C₄	C₂×#66946	1	1	yes	characteristic
222	C₄	C₂×#66960	1	1	yes	characteristic
223	C₂	—	2	2	no	—
224	C₂	—	44	4	no	—
225	C₂	C₂×#10622447	1	1	yes	characteristic
226	C₂	#13081718	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2150	C₂
prime radical	#10623008	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2150	D₁₁
hypocenter	C₁₁	#33435
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
1. C₂×#10622520	C₂	semidirect
3. #13070440	C₂	semidirect
4. #13070231	C₂	semidirect
5. C₂×#10622099	C₂	semidirect
6. C₁₁×#2150	C₂	semidirect
43. C₂×C₁₁⋊C₁₆	D₄	semidirect
81. #2150	D₁₁	semidirect
190. C₁₁	#33435	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622520	2
#13077329	2
#13070440	2
#13070231	2
C₂×#10622099	2
C₁₁×#2150	2
#33435	11