Subgroups — C₂×#13070474 #14907047

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622486	C₂	1	2	yes	maximal
3	#13070474	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622130	C₂	1	2	yes	maximal
5	C₂×C₁₆×Dic₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#366	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₄₄	C₂²	1	2	yes	—
8	C₂×#66940	—	2	2	no	—
9	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×#107	C₂²	1	2	yes	—
11	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₂×#66874	—	2	2	no	—
14	C₂×Dic₈₈	C₄	1	8	yes	complemented
15	C₂×Dic₈₈	C₂²	1	4	yes	—
16	#10622486	—	2	4	no	—
17	#10622486	C₂²	1	8	yes	—
18	C₁₁×#366	C₂²	1	4	yes	—
19	C₁₆×Dic₁₁	C₂²	1	4	yes	—
20	#10622130	C₂²	1	8	yes	—
21	C₂²×Dic₂₂	—	2	2	no	—
22	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
24	C₂×Dic₁₁⋊C₄	—	4	2	no	—
25	C₂×C₄×Dic₁₁	—	4	2	no	—
26	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
27	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
28	C₂×Dic₄₄	—	2	2	no	—
29	C₂×Dic₄₄	—	2	4	no	—
30	C₂×Dic₄₄	C₂×C₄	1	8	yes	—
31	C₂×Dic₄₄	C₂³	1	4	yes	—
32	#66940	—	2	8	no	—
33	#66940	—	4	4	no	—
34	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
35	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
36	C₁₁×#107	—	2	2	no	—
37	C₁₁×#107	C₂³	1	4	yes	—
38	C₈×Dic₁₁	D₄	1	2	yes	—
39	C₈×Dic₁₁	C₂³	1	2	yes	—
40	C₂×C₁₁⋊C₁₆	—	2	2	no	—
41	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
42	#66874	—	2	8	no	—
43	Dic₈₈	C₂×C₄	1	16	yes	complemented
44	C₂×C₄×Q₃₂	—	11	1	no	maximal, Sylow
45	C₂²×C₄×C₁₁	—	4	2	no	—
46	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₂²×Dic₁₁	—	4	2	no	—
48	C₂²×Dic₁₁	D₈	1	1	yes	characteristic
49	C₂²×Dic₁₁	D₈	1	1	yes	characteristic
50	C₂×Dic₂₂	—	2	8	no	—
51	C₂×Dic₂₂	—	2	4	no	—
52	C₂×Dic₂₂	—	4	2	no	—
53	C₂×Dic₂₂	—	4	4	no	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
55	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	#41	1	2	yes	—
57	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	—	2	4	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	Dic₁₁⋊C₄	—	4	8	no	—
61	C₄×Dic₁₁	—	4	8	no	—
62	C₄×Dic₁₁	D₈	1	2	yes	—
63	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
64	C₂×C₁₁⋊C₈	—	2	2	no	—
65	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
66	Dic₄₄	—	2	8	no	—
67	Dic₄₄	—	2	4	no	—
68	Dic₄₄	C₂²×C₄	1	8	yes	—
69	C₁₁×C₁₆	C₂²×C₄	1	4	yes	—
70	C₁₁⋊C₁₆	—	2	2	no	—
71	C₂²×Q₃₂	—	11	1	no	—
72	C₂×C₄×Q₁₆	—	11	2	no	—
73	C₄×Q₃₂	—	11	8	no	—
74	C₂×#366	D₁₁	1	1	yes	characteristic
75	C₂×#358	—	11	2	no	—
76	C₂×C₄×C₁₆	—	11	1	no	—
77	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
78	C₂×C₄×C₁₁	—	4	4	no	—
79	C₂×C₄×C₁₁	—	8	4	no	—
80	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
81	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	#135	1	2	yes	—
83	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
84	C₂×Dic₁₁	—	2	2	no	—
85	C₂×Dic₁₁	—	4	4	no	—
86	C₂×Dic₁₁	—	4	8	no	—
87	C₂×Dic₁₁	Q₃₂	1	4	yes	complemented
88	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
89	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
90	Dic₂₂	—	2	8	no	—
91	Dic₂₂	—	4	4	no	—
92	Dic₂₂	—	4	8	no	—
93	C₈×C₁₁	C₄×D₄	1	2	yes	—
94	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
95	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
96	C₁₁⋊C₈	—	2	2	no	—
97	C₂²×Q₁₆	—	11	2	no	—
98	C₂×C₄×Q₈	—	22	2	no	—
99	C₂×Q₃₂	—	11	4	no	—
100	C₂×Q₃₂	—	11	8	no	—
101	C₂²×C₁₆	—	11	1	no	—
102	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
103	C₄×Q₁₆	—	11	8	no	—
104	C₄×Q₁₆	—	22	4	no	—
105	C₂×#107	C₂×D₁₁	1	2	yes	—
106	C₂×#103	—	22	2	no	—
107	C₂×C₄×C₈	—	11	1	no	—
108	#366	C₂×D₁₁	1	4	yes	—
109	#358	—	11	8	no	—
110	C₄×C₁₆	—	11	4	no	—
111	C₂²×C₁₁	C₄×D₈	1	2	yes	—
112	C₂²×C₁₁	C₂×Q₃₂	1	2	yes	—
113	C₂²×C₁₁	#508	1	2	yes	—
114	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
115	C₄×C₁₁	—	8	4	no	—
116	C₄×C₁₁	C₄×D₈	1	2	yes	—
117	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
118	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
119	Dic₁₁	—	2	2	no	—
120	Dic₁₁	—	4	8	no	—
121	Dic₁₁	C₂×Q₃₂	1	4	yes	complemented
122	C₂²×Q₈	—	22	2	no	—
123	C₂×Q₁₆	—	11	8	no	—
124	C₂×Q₁₆	—	11	4	no	—
125	C₂×Q₁₆	—	22	2	no	—
126	C₂×Q₁₆	—	22	4	no	—
127	C₂²×C₈	—	11	1	no	—
128	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
129	C₄×Q₈	—	22	8	no	—
130	C₄×Q₈	—	44	4	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	44	2	no	—
133	C₂×C₄²	—	11	1	no	—
134	C₂×C₄²	—	44	2	no	—
135	Q₃₂	—	11	16	no	—
136	C₂×C₁₆	—	11	2	no	—
137	C₂×C₁₆	—	22	2	no	—
138	C₂×C₁₆	C₄×D₁₁	1	4	yes	—
139	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
140	#107	—	2	2	no	—
141	#107	C₂²×D₁₁	1	4	yes	—
142	#103	—	22	8	no	—
143	C₄×C₈	—	11	2	no	—
144	C₄×C₈	—	11	2	no	—
145	C₂×C₁₁	C₄×Q₃₂	1	4	yes	complemented
146	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
147	C₂×C₁₁	C₂²×Q₃₂	1	1	yes	characteristic
148	C₂×C₁₁	C₂×#508	1	1	yes	characteristic
149	C₂×Q₈	—	22	8	no	—
150	C₂×Q₈	—	22	4	no	—
151	C₂×Q₈	—	44	2	no	—
152	C₂×Q₈	—	44	4	no	—
153	C₂²×C₄	—	4	2	no	—
154	C₂²×C₄	—	11	1	no	—
155	C₂²×C₄	—	11	1	no	—
156	C₂²×C₄	—	44	2	no	—
157	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
158	Q₁₆	—	11	8	no	—
159	Q₁₆	—	22	8	no	—
160	Q₁₆	—	22	4	no	—
161	C₂×C₈	—	11	2	no	—
162	C₂×C₈	—	22	2	no	—
163	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
164	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
165	C₂×C₈	#4343	1	2	yes	—
166	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
167	C₄⋊C₄	—	2	4	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	44	8	no	—
170	C₄²	—	11	2	no	—
171	C₄²	—	11	2	no	—
172	C₄²	—	44	8	no	—
173	C₁₆	—	22	2	no	—
174	C₁₆	C₂×C₄×D₁₁	1	4	yes	—
175	C₁₁	C₂×C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
176	C₂³	D₈×D₁₁	1	1	yes	characteristic
177	Q₈	—	22	8	no	—
178	Q₈	—	44	8	no	—
179	Q₈	—	44	4	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	8	4	no	—
182	C₂×C₄	—	11	2	no	—
183	C₂×C₄	—	11	4	no	—
184	C₂×C₄	—	11	2	no	—
185	C₂×C₄	—	22	2	no	—
186	C₂×C₄	—	44	8	no	—
187	C₂×C₄	—	44	4	no	—
188	C₂×C₄	#66946	1	2	yes	—
189	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
190	C₂×C₄	#66972	1	2	yes	—
191	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
192	C₈	—	22	2	no	—
193	C₈	#66946	1	2	yes	—
194	C₈	C₂²×C₄×D₁₁	1	1	yes	characteristic
195	C₈	C₂×#4343	1	1	yes	characteristic
196	C₂²	#10622485	1	2	yes	—
197	C₂²	#10622525	1	2	yes	—
198	C₂²	D₁₁×Q₃₂	1	2	yes	—
199	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
200	C₄	—	8	4	no	—
201	C₄	—	11	4	no	—
202	C₄	—	22	2	no	—
203	C₄	—	44	8	no	—
204	C₄	#10622485	1	2	yes	—
205	C₄	C₂×#66946	1	1	yes	characteristic
206	C₄	C₂×#66972	1	1	yes	characteristic
207	C₂	#13070474	1	4	yes	direct product factor
208	C₂	C₂×#10622485	1	1	yes	characteristic
209	C₂	C₂×D₁₁×Q₃₂	1	1	yes	characteristic
210	C₂	C₂×#10622525	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₁
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#366	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×#366	D₁₁
hypocenter	C₁₁	C₂×C₄×Q₃₂
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
3. #13070474	C₂	direct (N × H)
14. C₂×Dic₈₈	C₄	semidirect
43. Dic₈₈	C₂×C₄	semidirect
87. C₂×Dic₁₁	Q₃₂	semidirect
121. Dic₁₁	C₂×Q₃₂	semidirect
145. C₂×C₁₁	C₄×Q₃₂	semidirect
175. C₁₁	C₂×C₄×Q₃₂	semidirect
207. C₂	#13070474	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₈₈	2
C₂×#10622486	2
#13070474	2
C₂×#10622130	2
C₂×C₁₆×Dic₁₁	2
C₂×C₁₁×#366	2
C₂×C₄×Q₃₂	11

Subgroups — C2×#13070474 #14907047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070474 #14907047