Subgroups — C₂×#13070518 #14907253

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₂₂	C₂	1	1	yes	maximal, characteristic
2	#13070518	C₂	1	8	yes	maximal, direct product factor
3	C₂×Dic₁₁⋊C₁₆	C₂	1	2	yes	maximal
4	C₂×C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₆×Dic₁₁	C₂	1	2	yes	maximal
6	C₂×C₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×Dic₂₂	C₄	1	1	yes	characteristic
8	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₁⋊C₈	C₄	1	2	yes	—
11	C₂×C₈×Dic₁₁	C₂²	1	2	yes	—
12	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	1	yes	characteristic
15	C₈×Dic₂₂	C₄	1	4	yes	—
16	C₈×Dic₂₂	C₂²	1	4	yes	—
17	C₁₁×C₄⋊C₁₆	C₂²	1	4	yes	—
18	Dic₁₁⋊C₁₆	C₂²	1	8	yes	—
19	C₁₆×Dic₁₁	C₂²	1	8	yes	—
20	C₄×C₁₁⋊C₁₆	C₂²	1	4	yes	—
21	C₂²×Dic₂₂	C₈	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₁	C₈	1	1	yes	characteristic
26	C₂×Dic₁₁⋊C₄	C₈	1	2	yes	—
27	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
28	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
29	C₄×Dic₂₂	C₈	1	4	yes	—
30	C₄×Dic₂₂	C₂×C₄	1	4	yes	—
31	C₂×C₁₁×C₁₆	—	2	4	no	—
32	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
33	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₁	C₂³	1	2	yes	—
35	Dic₁₁⋊C₈	C₂×C₄	1	8	yes	—
36	C₈×Dic₁₁	C₂×C₄	1	4	yes	—
37	C₈×Dic₁₁	C₂³	1	4	yes	—
38	C₂×C₁₁⋊C₁₆	—	2	2	no	—
39	C₂×C₁₁⋊C₁₆	Q₈	1	4	yes	complemented
40	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
41	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
42	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
43	C₂×Q₈×C₁₆	—	11	1	no	maximal, Sylow
44	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
47	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
48	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
49	C₂×Dic₂₂	C₁₆	1	8	yes	complemented
50	C₂×Dic₂₂	C₂×C₈	1	4	yes	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
53	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
55	C₂×C₈×C₁₁	#41	1	2	yes	—
56	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
57	C₄²×C₁₁	C₂×C₈	1	2	yes	—
58	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
59	C₄⋊Dic₁₁	C₂×C₈	1	4	yes	—
60	Dic₁₁⋊C₄	C₂×C₈	1	8	yes	—
61	C₄×Dic₁₁	C₂×C₈	1	4	yes	—
62	C₄×Dic₁₁	C₂²×C₄	1	4	yes	—
63	C₂×C₁₁⋊C₈	—	2	4	no	—
64	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
65	C₁₁×C₁₆	—	2	4	no	—
66	C₁₁⋊C₁₆	—	2	2	no	—
67	C₁₁⋊C₁₆	C₂×Q₈	1	4	yes	complemented
68	C₂×C₈×Q₈	—	11	1	no	—
69	Q₈×C₁₆	—	11	8	no	—
70	C₂×C₄⋊C₁₆	—	11	2	no	—
71	C₂×C₄⋊C₁₆	D₁₁	1	1	yes	characteristic
72	C₂×C₄×C₁₆	—	11	2	no	—
73	C₂×C₄×C₁₆	—	11	1	no	—
74	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	C₂×C₁₆	1	4	yes	—
77	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
78	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
79	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
81	C₂×C₄×C₁₁	#131	1	2	yes	—
82	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
83	C₂×Dic₁₁	—	2	4	no	—
84	C₂×Dic₁₁	C₂×C₁₆	1	8	yes	—
85	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
86	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
87	Dic₂₂	C₂×C₁₆	1	16	yes	complemented
88	C₈×C₁₁	—	2	2	no	—
89	C₈×C₁₁	C₄×Q₈	1	2	yes	—
90	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
91	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
92	C₁₁⋊C₈	—	2	4	no	—
93	C₂×C₄×Q₈	—	11	1	no	—
94	C₂²×C₁₆	—	11	1	no	—
95	C₂²×C₁₆	—	11	1	no	—
96	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
97	C₈×Q₈	—	11	4	no	—
98	C₈×Q₈	—	11	4	no	—
99	C₂×C₄⋊C₈	—	11	2	no	—
100	C₂×C₄⋊C₈	—	11	1	no	—
101	C₂×C₄×C₈	—	11	2	no	—
102	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
103	C₄⋊C₁₆	—	11	8	no	—
104	C₄⋊C₁₆	C₂×D₁₁	1	4	yes	—
105	C₄×C₁₆	—	11	8	no	—
106	C₄×C₁₆	—	11	4	no	—
107	C₂²×C₁₁	C₈×Q₈	1	2	yes	—
108	C₂²×C₁₁	C₂²×C₁₆	1	2	yes	—
109	C₂²×C₁₁	#504	1	2	yes	—
110	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
111	C₄×C₁₁	—	2	2	no	—
112	C₄×C₁₁	C₈×Q₈	1	2	yes	—
113	C₄×C₁₁	C₂²×C₁₆	1	4	yes	—
114	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
115	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
116	Dic₁₁	—	2	4	no	—
117	Dic₁₁	C₂²×C₁₆	1	8	yes	—
118	C₂²×Q₈	—	11	1	no	—
119	C₂²×C₈	—	11	2	no	—
120	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
121	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
122	C₄×Q₈	—	11	4	no	—
123	C₄×Q₈	—	11	4	no	—
124	C₂×C₄⋊C₄	—	11	2	no	—
125	C₂×C₄⋊C₄	—	11	1	no	—
126	C₂×C₄²	—	11	2	no	—
127	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
128	C₂×C₁₆	—	2	4	no	—
129	C₂×C₁₆	—	11	4	no	—
130	C₂×C₁₆	—	11	2	no	—
131	C₂×C₁₆	—	11	2	no	—
132	C₂×C₁₆	—	22	2	no	—
133	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
134	C₄⋊C₈	—	11	8	no	—
135	C₄⋊C₈	—	11	4	no	—
136	C₄×C₈	—	11	4	no	—
137	C₄×C₈	—	11	4	no	—
138	C₄×C₈	C₄×D₁₁	1	2	yes	—
139	C₄×C₈	C₂²×D₁₁	1	2	yes	—
140	C₂×C₁₁	Q₈×C₁₆	1	4	yes	complemented
141	C₂×C₁₁	C₂×C₈×Q₈	1	1	yes	characteristic
142	C₂×C₁₁	C₂³×C₁₆	1	1	yes	characteristic
143	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
144	C₂×Q₈	—	11	8	no	—
145	C₂×Q₈	—	11	4	no	—
146	C₂²×C₄	—	11	2	no	—
147	C₂²×C₄	—	11	2	no	—
148	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
149	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
151	C₂×C₈	—	2	2	no	—
152	C₂×C₈	—	11	4	no	—
153	C₂×C₈	—	22	4	no	—
154	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
155	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
156	C₂×C₈	#4341	1	2	yes	—
157	C₂×C₈	Q₈×D₁₁	1	2	yes	—
158	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
159	C₄⋊C₄	—	11	8	no	—
160	C₄⋊C₄	—	11	4	no	—
161	C₄²	—	11	4	no	—
162	C₄²	—	11	4	no	—
163	C₄²	C₈×D₁₁	1	2	yes	—
164	C₄²	C₂×C₄×D₁₁	1	2	yes	—
165	C₁₆	—	2	4	no	—
166	C₁₆	—	11	4	no	—
167	C₁₆	—	22	2	no	—
168	C₁₁	C₂×Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
169	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
170	Q₈	—	11	16	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	11	4	no	—
173	C₂×C₄	—	11	8	no	—
174	C₂×C₄	—	11	4	no	—
175	C₂×C₄	—	22	4	no	—
176	C₂×C₄	C₁₆×D₁₁	1	4	yes	—
177	C₂×C₄	#66940	1	2	yes	—
178	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
179	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
180	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
181	C₂×C₄	#66960	1	2	yes	—
182	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
183	C₈	—	2	2	no	—
184	C₈	—	22	4	no	—
185	C₈	#66940	1	2	yes	—
186	C₈	C₂×#4341	1	1	yes	characteristic
187	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
188	C₂²	#10622443	1	2	yes	—
189	C₂²	C₂×C₁₆×D₁₁	1	2	yes	—
190	C₂²	#10622520	1	2	yes	—
191	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
192	C₄	—	2	2	no	—
193	C₄	—	11	8	no	—
194	C₄	—	22	4	no	—
195	C₄	#10622443	1	2	yes	—
196	C₄	C₂×C₁₆×D₁₁	1	4	yes	—
197	C₄	C₂×#66940	1	1	yes	characteristic
198	C₄	C₂×#66960	1	1	yes	characteristic
199	C₂	#13070518	1	4	yes	direct product factor
200	C₂	C₂×#10622443	1	1	yes	characteristic
201	C₂	C₂²×C₁₆×D₁₁	1	1	yes	characteristic
202	C₂	C₂×#10622520	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₁₁
commutator	C₂×C₁₁	C₂³×C₁₆
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×C₄⋊C₁₆	D₁₁
hypocenter	C₁₁	C₂×Q₈×C₁₆
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #13070518	C₂	direct (N × H)
39. C₂×C₁₁⋊C₁₆	Q₈	semidirect
49. C₂×Dic₂₂	C₁₆	semidirect
67. C₁₁⋊C₁₆	C₂×Q₈	semidirect
87. Dic₂₂	C₂×C₁₆	semidirect
140. C₂×C₁₁	Q₈×C₁₆	semidirect
168. C₁₁	C₂×Q₈×C₁₆	semidirect
199. C₂	#13070518	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×C₈×Dic₂₂	2
#13070518	2
C₂×Dic₁₁⋊C₁₆	2
C₂×C₄×C₁₁⋊C₁₆	2
C₂×C₁₆×Dic₁₁	2
C₂×C₁₁×C₄⋊C₁₆	2
C₂×Q₈×C₁₆	11

Subgroups — C2×#13070518 #14907253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070518 #14907253