Subgroups — C₂×#13066755 #14673973

Order 2816.

306 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66862	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622137	C₂	1	1	yes	maximal, characteristic, complemented
3	#13066755	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
6	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁⋊C₁₆	C₄	1	1	yes	characteristic
8	C₂×#66862	—	2	1	no	—
9	C₂×#66862	—	2	1	no	—
10	C₂×#66862	—	2	1	no	—
11	C₂×#66862	—	2	1	no	—
12	C₂×#66862	C₄	1	2	yes	—
13	C₂×#66862	C₂²	1	2	yes	—
14	C₁₁×M₆₄	—	2	1	no	—
15	C₁₁×M₆₄	C₂²	1	2	yes	complemented
16	C₂×C₁₁×C₃₂	—	2	1	no	—
17	#10622137	—	2	1	no	—
18	#10622137	C₂²	1	2	yes	complemented
19	C₂×C₁₁⋊C₃₂	—	2	1	no	—
20	C₂²×C₄×D₁₁	C₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₁₁⋊C₈	C₈	1	1	yes	characteristic
23	C₂×C₈×D₁₁	—	2	1	no	—
24	C₂×C₈×D₁₁	—	2	1	no	—
25	C₂×C₈×D₁₁	—	2	1	no	—
26	C₂×C₈×D₁₁	—	2	1	no	—
27	C₂×C₈×D₁₁	C₈	1	2	yes	—
28	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
31	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
32	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
33	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
34	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
35	C₂×C₁₁⋊C₁₆	—	2	1	no	—
36	C₂×C₁₁⋊C₁₆	—	2	1	no	—
37	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
38	#66862	—	2	2	no	—
39	#66862	—	2	2	no	—
40	#66862	—	2	2	no	—
41	#66862	—	2	2	no	—
42	C₁₁×C₃₂	—	2	2	no	—
43	C₁₁⋊C₃₂	—	2	2	no	—
44	C₂×#1400	—	11	1	no	maximal, Sylow
45	C₂³×D₁₁	C₁₆	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
47	C₂²×Dic₁₁	C₁₆	1	1	yes	characteristic
48	C₂×C₄×D₁₁	—	2	1	no	—
49	C₂×C₄×D₁₁	—	2	1	no	—
50	C₂×C₄×D₁₁	—	2	1	no	—
51	C₂×C₄×D₁₁	—	2	1	no	—
52	C₂×C₄×D₁₁	C₁₆	1	2	yes	—
53	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
54	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
57	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
58	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
59	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₁₁⋊C₈	—	2	1	no	—
61	C₂×C₁₁⋊C₈	—	2	1	no	—
62	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	—
63	C₈×D₁₁	—	2	2	no	—
64	C₈×D₁₁	—	2	2	no	—
65	C₈×D₁₁	—	2	2	no	—
66	C₈×D₁₁	—	2	2	no	—
67	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
68	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
69	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
70	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
71	C₁₁⋊C₁₆	—	2	2	no	—
72	C₂²×M₃₂	—	11	1	no	—
73	C₂×M₆₄	—	11	1	no	—
74	C₂×M₆₄	D₁₁	1	1	yes	characteristic, complemented
75	#1400	—	11	4	no	—
76	C₂³×C₁₁	C₂×C₁₆	1	1	yes	characteristic
77	C₂²×D₁₁	—	2	1	no	—
78	C₂²×D₁₁	—	2	1	no	—
79	C₂²×D₁₁	—	4	2	no	—
80	C₂²×D₁₁	C₂×C₁₆	1	2	yes	—
81	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
84	C₂×C₄×C₁₁	M₃₂	1	1	yes	characteristic
85	C₂×C₄×C₁₁	M₃₂	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
87	C₂×Dic₁₁	—	2	1	no	—
88	C₂×Dic₁₁	—	2	1	no	—
89	C₂×Dic₁₁	C₂×C₁₆	1	2	yes	—
90	C₄×D₁₁	—	2	2	no	—
91	C₄×D₁₁	—	2	2	no	—
92	C₄×D₁₁	—	2	2	no	—
93	C₄×D₁₁	—	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	C₁₁⋊C₈	—	2	2	no	—
99	C₂³×C₈	—	11	1	no	—
100	C₂×M₃₂	—	11	2	no	—
101	C₂×M₃₂	—	11	2	no	—
102	C₂×M₃₂	—	22	1	no	—
103	C₂×M₃₂	—	22	1	no	—
104	C₂×M₃₂	—	22	1	no	—
105	C₂×M₃₂	—	22	1	no	—
106	C₂²×C₁₆	—	11	1	no	—
107	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
108	M₆₄	—	2	1	no	—
109	M₆₄	—	11	2	no	—
110	M₆₄	—	22	1	no	—
111	M₆₄	C₂×D₁₁	1	2	yes	complemented
112	C₂×C₃₂	—	2	1	no	—
113	C₂×C₃₂	—	22	1	no	—
114	C₂²×C₁₁	—	2	2	no	—
115	C₂²×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
116	C₂²×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
117	C₂²×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
118	C₂×D₁₁	—	2	2	no	—
119	C₂×D₁₁	—	4	2	no	—
120	C₂×D₁₁	—	4	2	no	—
121	C₂×D₁₁	—	4	2	no	—
122	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
123	C₄×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
124	C₄×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
126	Dic₁₁	—	2	2	no	—
127	C₂³×C₄	—	11	1	no	—
128	C₂²×C₈	—	11	1	no	—
129	C₂²×C₈	—	11	2	no	—
130	C₂²×C₈	—	11	2	no	—
131	C₂²×C₈	—	22	1	no	—
132	C₂²×C₈	—	22	1	no	—
133	C₂²×C₈	—	22	1	no	—
134	C₂²×C₈	—	22	1	no	—
135	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
136	M₃₂	—	22	2	no	—
137	M₃₂	—	22	2	no	—
138	M₃₂	—	22	2	no	—
139	M₃₂	—	22	2	no	—
140	C₂×C₁₆	—	11	2	no	—
141	C₂×C₁₆	—	22	1	no	—
142	C₂×C₁₆	—	22	1	no	—
143	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
144	C₂×C₁₆	D₄₄	1	1	yes	characteristic
145	C₂×C₁₆	D₄₄	1	1	yes	characteristic
146	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
147	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
148	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
149	C₃₂	—	2	2	no	—
150	C₃₂	—	22	2	no	—
151	C₂×C₁₁	—	2	1	no	—
152	C₂×C₁₁	—	2	1	no	—
153	C₂×C₁₁	#1400	1	2	yes	complemented
154	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
155	D₁₁	—	4	2	no	—
156	C₂⁴	—	11	1	no	—
157	C₂²×C₄	—	11	1	no	—
158	C₂²×C₄	—	11	2	no	—
159	C₂²×C₄	—	11	2	no	—
160	C₂²×C₄	—	22	1	no	—
161	C₂²×C₄	—	22	1	no	—
162	C₂²×C₄	—	22	1	no	—
163	C₂²×C₄	—	22	1	no	—
164	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
165	C₂×C₈	—	11	2	no	—
166	C₂×C₈	—	22	1	no	—
167	C₂×C₈	—	22	1	no	—
168	C₂×C₈	—	22	2	no	—
169	C₂×C₈	—	22	2	no	—
170	C₂×C₈	—	22	2	no	—
171	C₂×C₈	—	22	2	no	—
172	C₂×C₈	C₈×D₁₁	1	1	yes	characteristic
173	C₂×C₈	#4313	1	1	yes	characteristic
174	C₂×C₈	#4313	1	1	yes	characteristic
175	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
176	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
177	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
178	C₁₆	—	22	2	no	—
179	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
180	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
181	C₁₆	C₂×D₄₄	1	1	yes	characteristic
182	C₁₆	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
183	C₁₁	C₂×#1400	1	1	yes	characteristic, complemented, Sylow
184	C₂³	—	11	2	no	—
185	C₂³	—	22	1	no	—
186	C₂³	—	22	1	no	—
187	C₂³	—	44	2	no	—
188	C₂³	C₁₆×D₁₁	1	1	yes	characteristic
189	C₂×C₄	—	11	2	no	—
190	C₂×C₄	—	22	1	no	—
191	C₂×C₄	—	22	1	no	—
192	C₂×C₄	—	22	2	no	—
193	C₂×C₄	—	22	2	no	—
194	C₂×C₄	—	22	2	no	—
195	C₂×C₄	—	22	2	no	—
196	C₂×C₄	C₁₆×D₁₁	1	1	yes	characteristic
197	C₂×C₄	#66862	1	1	yes	characteristic
198	C₂×C₄	#66862	1	1	yes	characteristic
199	C₂×C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
200	C₂×C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
201	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
202	C₈	—	22	2	no	—
203	C₈	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
204	C₈	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
205	C₈	C₂×#4313	1	1	yes	characteristic
206	C₈	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
207	C₂²	—	2	2	no	—
208	C₂²	—	22	2	no	—
209	C₂²	—	44	2	no	—
210	C₂²	—	44	2	no	—
211	C₂²	—	44	2	no	—
212	C₂²	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
213	C₂²	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
214	C₂²	C₂×C₁₆×D₁₁	1	1	yes	characteristic
215	C₄	—	22	2	no	—
216	C₄	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
217	C₄	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
218	C₄	C₂×#66862	1	1	yes	characteristic
219	C₄	C₂×(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	—	44	2	no	—
223	C₂	#13066755	1	2	yes	direct product factor
224	C₂	C₂×(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₁₁)⋊C₄
commutator	C₂²×C₁₁	C₂²×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₂×C₁₁×M₆₄	C₂
socle	C₂²×C₁₁	C₂²⋊C₁₆
prime radical	C₂³×D₁₁	C₁₆
cosocle	C₂×C₁₁×C₁₆	C₂³
hypercenter	C₂×M₆₄	D₁₁
hypocenter	C₁₁	C₂×#1400
LCS	G ▷ C₂²×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
2. C₂×#10622137	C₂	semidirect
3. #13066755	C₂	direct (N × H)
4. C₂×C₁₁×M₆₄	C₂	semidirect
15. C₁₁×M₆₄	C₂²	semidirect
18. #10622137	C₂²	semidirect
74. C₂×M₆₄	D₁₁	semidirect
111. M₆₄	C₂×D₁₁	semidirect
153. C₂×C₁₁	#1400	semidirect
183. C₁₁	C₂×#1400	semidirect
223. C₂	#13066755	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×#66862	2
C₂×#10622137	2
#13066755	2
C₂×C₁₁×M₆₄	2
C₂×#1400	11

Subgroups — C2×#13066755 #14673973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066755 #14673973