Subgroups — C₂×#13066758 #14673980

Order 2816.

294 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	C₂×#10622137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#13066758	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#504	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#131	C₄	1	1	yes	characteristic
6	C₁₁×#504	—	2	1	no	—
7	C₁₁×#504	—	2	1	no	—
8	C₁₁×#504	C₄	1	2	yes	—
9	C₁₁×#504	C₂²	1	2	yes	—
10	C₂×C₁₁×M₃₂	—	2	1	no	—
11	C₂×C₁₁×M₃₂	C₄	1	1	yes	characteristic
12	C₂²×C₁₁×C₁₆	—	2	1	no	—
13	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
14	#10622137	—	2	1	no	—
15	#10622137	C₂²	1	2	yes	complemented
16	C₂×C₁₁⋊C₃₂	—	2	1	no	—
17	C₂×C₁₁⋊C₃₂	—	2	1	no	—
18	C₂×C₁₁⋊C₃₂	—	2	1	no	—
19	C₂×C₁₁⋊C₃₂	C₂²	1	2	yes	complemented
20	C₂×C₁₁×#41	C₈	1	1	yes	characteristic
21	C₁₁×#131	—	2	1	no	—
22	C₁₁×#131	—	2	1	no	—
23	C₁₁×#131	C₈	1	2	yes	—
24	C₁₁×#131	C₂×C₄	1	2	yes	—
25	C₂×C₁₁×M₁₆	—	2	1	no	—
26	C₂×C₁₁×M₁₆	C₈	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	—	2	1	no	—
28	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₁₁×M₃₂	—	2	1	no	—
30	C₁₁×M₃₂	—	2	2	no	—
31	C₁₁×M₃₂	—	2	2	no	—
32	C₁₁×M₃₂	C₂×C₄	1	2	yes	—
33	C₂×C₁₁×C₁₆	—	2	1	no	—
34	C₂×C₁₁×C₁₆	—	2	2	no	—
35	C₂×C₁₁×C₁₆	—	2	2	no	—
36	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
38	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
39	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
40	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
41	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
42	C₁₁⋊C₃₂	—	2	2	no	—
43	C₁₁⋊C₃₂	—	2	2	no	—
44	C₂×#1401	—	11	1	no	maximal, Sylow
45	C₁₁×#41	—	2	1	no	—
46	C₁₁×#41	—	2	1	no	—
47	C₁₁×#41	C₁₆	1	2	yes	—
48	C₁₁×#41	C₂×C₈	1	2	yes	—
49	C₂×Q₈×C₁₁	C₁₆	1	1	yes	characteristic
50	C₂×D₄×C₁₁	—	2	1	no	—
51	C₂×D₄×C₁₁	C₁₆	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	—	2	1	no	—
53	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
54	C₁₁×M₁₆	—	2	2	no	—
55	C₁₁×M₁₆	—	2	2	no	—
56	C₁₁×M₁₆	—	2	1	no	—
57	C₁₁×M₁₆	C₂×C₈	1	2	yes	—
58	C₂×C₈×C₁₁	—	2	2	no	—
59	C₂×C₈×C₁₁	—	2	2	no	—
60	C₂×C₈×C₁₁	—	2	1	no	—
61	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
64	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
65	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
66	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
67	C₁₁×C₁₆	—	2	2	no	—
68	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
69	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
70	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
71	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
72	C₂×#504	D₁₁	1	1	yes	characteristic
73	C₂×M₆₄	—	11	1	no	—
74	C₂²×C₃₂	—	11	1	no	—
75	#1401	—	11	4	no	—
76	C₂³×C₁₁	—	2	1	no	—
77	C₂³×C₁₁	M₃₂	1	1	yes	characteristic
78	Q₈×C₁₁	—	2	1	no	—
79	Q₈×C₁₁	C₂×C₁₆	1	2	yes	—
80	D₄×C₁₁	—	2	2	no	—
81	D₄×C₁₁	—	2	2	no	—
82	D₄×C₁₁	—	2	1	no	—
83	D₄×C₁₁	C₂×C₁₆	1	2	yes	—
84	C₂×C₄×C₁₁	—	2	1	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
91	C₂×C₄×C₁₁	M₃₂	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
93	C₈×C₁₁	—	2	2	no	—
94	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
95	C₈×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
96	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
98	C₂×#131	Dic₁₁	1	1	yes	characteristic
99	#504	—	2	1	no	—
100	#504	—	2	1	no	—
101	#504	Dic₁₁	1	2	yes	—
102	#504	C₂×D₁₁	1	2	yes	—
103	C₂×M₃₂	—	2	1	no	—
104	C₂×M₃₂	Dic₁₁	1	1	yes	characteristic
105	C₂²×C₁₆	—	2	1	no	—
106	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
107	M₆₄	—	11	2	no	—
108	M₆₄	—	22	1	no	—
109	C₂×C₃₂	—	11	2	no	—
110	C₂×C₃₂	—	22	1	no	—
111	C₂×C₃₂	—	22	1	no	—
112	C₂×C₃₂	—	22	1	no	—
113	C₂²×C₁₁	—	2	2	no	—
114	C₂²×C₁₁	—	2	2	no	—
115	C₂²×C₁₁	—	4	2	no	—
116	C₂²×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
117	C₂²×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
118	C₂²×C₁₁	C₂×M₃₂	1	1	yes	characteristic
119	C₄×C₁₁	—	2	2	no	—
120	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
121	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
122	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
123	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
124	C₂×#41	C₁₁⋊C₈	1	1	yes	characteristic
125	#131	—	2	1	no	—
126	#131	—	2	1	no	—
127	#131	C₁₁⋊C₈	1	2	yes	—
128	#131	C₂×Dic₁₁	1	2	yes	—
129	C₂×M₁₆	—	2	1	no	—
130	C₂×M₁₆	C₁₁⋊C₈	1	1	yes	characteristic
131	C₂²×C₈	—	2	1	no	—
132	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
133	M₃₂	—	2	1	no	—
134	M₃₂	—	2	2	no	—
135	M₃₂	—	2	2	no	—
136	M₃₂	C₂×Dic₁₁	1	2	yes	—
137	C₂×C₁₆	—	2	1	no	—
138	C₂×C₁₆	—	2	2	no	—
139	C₂×C₁₆	—	2	2	no	—
140	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
141	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
142	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
143	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
144	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
145	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
146	C₃₂	—	22	2	no	—
147	C₃₂	—	22	2	no	—
148	C₂×C₁₁	—	2	1	no	—
149	C₂×C₁₁	—	2	1	no	—
150	C₂×C₁₁	—	4	2	no	—
151	C₂×C₁₁	#1401	1	2	yes	complemented
152	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
153	#41	—	2	1	no	—
154	#41	—	2	1	no	—
155	#41	C₁₁⋊C₁₆	1	2	yes	—
156	#41	C₂×C₁₁⋊C₈	1	2	yes	—
157	C₂×Q₈	C₁₁⋊C₁₆	1	1	yes	characteristic
158	C₂×D₄	—	2	1	no	—
159	C₂×D₄	C₁₁⋊C₁₆	1	1	yes	characteristic
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
162	M₁₆	—	2	1	no	—
163	M₁₆	—	2	2	no	—
164	M₁₆	—	2	2	no	—
165	M₁₆	C₂×C₁₁⋊C₈	1	2	yes	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
170	C₂×C₈	#4318	1	1	yes	characteristic
171	C₂×C₈	#4318	1	1	yes	characteristic
172	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
173	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
174	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
175	C₁₆	—	2	2	no	—
176	C₁₆	C₂²⋊Dic₁₁	1	1	yes	characteristic
177	C₁₆	C₂²⋊Dic₁₁	1	1	yes	characteristic
178	C₁₆	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
179	C₁₆	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
180	C₁₁	C₂×#1401	1	1	yes	characteristic, complemented, Sylow
181	C₂³	—	2	1	no	—
182	C₂³	#66876	1	1	yes	characteristic
183	Q₈	—	2	1	no	—
184	Q₈	C₂×C₁₁⋊C₁₆	1	2	yes	—
185	D₄	—	2	2	no	—
186	D₄	—	2	2	no	—
187	D₄	—	2	1	no	—
188	D₄	C₂×C₁₁⋊C₁₆	1	2	yes	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
193	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
194	C₂×C₄	#66876	1	1	yes	characteristic
195	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
196	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
197	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
198	C₈	—	2	2	no	—
199	C₈	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
200	C₈	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
201	C₈	C₂×#4318	1	1	yes	characteristic
202	C₈	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
203	C₂²	—	2	2	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	4	2	no	—
206	C₂²	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
207	C₂²	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
208	C₂²	C₂×#66876	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
211	C₄	C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
212	C₄	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic
213	C₄	C₂×C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
214	C₂	—	2	1	no	—
215	C₂	—	2	1	no	—
216	C₂	—	4	2	no	—
217	C₂	#13066758	1	2	yes	direct product factor
218	C₂	C₂×C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂²×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₂×C₁₁×#504	C₂
socle	C₂²×C₁₁	C₂²⋊C₁₆
prime radical	C₂×C₁₁×#41	C₈
cosocle	C₂×C₁₁×C₁₆	C₂³
hypercenter	C₂×#504	D₁₁
hypocenter	C₁₁	C₂×#1401
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×#10622137	C₂	semidirect
2. C₂²×C₁₁⋊C₃₂	C₂	semidirect
3. #13066758	C₂	direct (N × H)
15. #10622137	C₂²	semidirect
19. C₂×C₁₁⋊C₃₂	C₂²	semidirect
151. C₂×C₁₁	#1401	semidirect
180. C₁₁	C₂×#1401	semidirect
217. C₂	#13066758	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10622137	2
C₂²×C₁₁⋊C₃₂	2
#13066758	2
C₂×C₁₁×#504	2
C₂×#1401	11

Subgroups — C2×#13066758 #14673980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066758 #14673980