Subgroups — C₂×#13066594 #14663571

Order 2816.

382 conjugacy classes of subgroups.

The subgroup lattice has 240 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	C₂×C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#13066594	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₂₂	C₄	1	1	yes	characteristic
6	C₂²×C₁₁×C₁₆	—	2	1	no	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₁⋊C₈	—	2	1	no	—
9	C₂×C₈×Dic₁₁	—	2	1	no	—
10	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
11	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	1	yes	characteristic
12	C₈×Dic₂₂	—	2	1	no	—
13	C₈×Dic₂₂	—	2	1	no	—
14	C₈×Dic₂₂	C₄	1	2	yes	—
15	C₈×Dic₂₂	C₂²	1	2	yes	—
16	C₁₁×C₄⋊C₁₆	—	2	1	no	—
17	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
18	C₄×C₁₁⋊C₁₆	—	2	1	no	—
19	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	—
20	C₂²×Dic₂₂	C₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₁	C₈	1	1	yes	characteristic
25	C₂×Dic₁₁⋊C₄	—	2	1	no	—
26	C₂×C₄×Dic₁₁	—	2	1	no	—
27	C₂²×C₁₁⋊C₈	—	2	1	no	—
28	C₄×Dic₂₂	—	2	1	no	—
29	C₄×Dic₂₂	—	2	1	no	—
30	C₄×Dic₂₂	C₈	1	2	yes	—
31	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
32	C₂×C₁₁×C₁₆	—	2	2	no	—
33	C₂×C₁₁×C₁₆	—	4	2	no	—
34	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
36	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
38	Dic₁₁⋊C₈	—	2	2	no	—
39	Dic₁₁⋊C₈	—	2	2	no	—
40	C₈×Dic₁₁	—	2	2	no	—
41	C₈×Dic₁₁	—	2	2	no	—
42	C₂×C₁₁⋊C₁₆	—	2	4	no	—
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
45	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
46	C₂×Q₈⋊C₁₆	—	11	1	no	maximal, Sylow
47	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
50	C₂²×Dic₁₁	—	2	1	no	—
51	C₂²×Dic₁₁	—	2	1	no	—
52	C₂×Dic₂₂	—	2	1	no	—
53	C₂×Dic₂₂	—	2	2	no	—
54	C₂×Dic₂₂	C₁₆	1	4	yes	complemented
55	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
56	C₂×C₈×C₁₁	—	2	2	no	—
57	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
60	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
61	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
65	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
66	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
67	C₄⋊Dic₁₁	—	2	1	no	—
68	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
69	Dic₁₁⋊C₄	—	2	2	no	—
70	Dic₁₁⋊C₄	—	2	2	no	—
71	C₄×Dic₁₁	—	2	2	no	—
72	C₄×Dic₁₁	—	2	2	no	—
73	C₂×C₁₁⋊C₈	—	2	2	no	—
74	C₂×C₁₁⋊C₈	—	4	2	no	—
75	C₁₁×C₁₆	—	4	2	no	—
76	C₁₁⋊C₁₆	—	2	4	no	—
77	C₂×C₈×Q₈	—	11	1	no	—
78	C₂×C₄⋊C₁₆	D₁₁	1	1	yes	characteristic
79	C₂×C₄×C₁₆	—	11	1	no	—
80	Q₈⋊C₁₆	—	11	4	no	—
81	C₂³×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
86	C₂×C₄×C₁₁	#103	1	2	yes	—
87	C₂×C₄×C₁₁	#104	1	2	yes	—
88	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
89	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
90	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
93	C₂×Dic₁₁	—	2	4	no	—
94	C₂×Dic₁₁	—	2	2	no	—
95	C₂×Dic₁₁	—	2	2	no	—
96	C₂×Dic₁₁	—	4	2	no	—
97	Dic₂₂	—	2	4	no	—
98	Dic₂₂	—	2	2	no	—
99	Dic₂₂	C₂×C₁₆	1	4	yes	complemented
100	C₈×C₁₁	—	2	1	no	—
101	C₈×C₁₁	—	2	1	no	—
102	C₈×C₁₁	#103	1	2	yes	—
103	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
104	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
105	C₁₁⋊C₈	—	4	2	no	—
106	C₂×C₄×Q₈	—	11	1	no	—
107	C₂²×C₁₆	—	2	1	no	—
108	C₂²×C₁₆	—	22	1	no	—
109	C₈×Q₈	—	11	2	no	—
110	C₈×Q₈	—	11	2	no	—
111	C₈×Q₈	—	22	1	no	—
112	C₈×Q₈	—	22	1	no	—
113	C₂×C₄⋊C₈	—	11	1	no	—
114	C₂×C₄⋊C₈	—	22	1	no	—
115	C₂×C₄×C₈	—	22	1	no	—
116	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
117	C₄⋊C₁₆	—	2	1	no	—
118	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
119	C₄×C₁₆	—	11	2	no	—
120	C₄×C₁₆	—	22	1	no	—
121	C₂²×C₁₁	Q₈⋊C₈	1	2	yes	—
122	C₂²×C₁₁	C₂²⋊C₁₆	1	2	yes	—
123	C₂²×C₁₁	#350	1	2	yes	—
124	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₄×C₁₁	—	2	1	no	—
126	C₄×C₁₁	—	2	1	no	—
127	C₄×C₁₁	Q₈⋊C₈	1	2	yes	—
128	C₄×C₁₁	C₂²⋊C₁₆	1	2	yes	—
129	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
130	C₄×C₁₁	C₂×#104	1	1	yes	characteristic
131	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
132	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
133	Dic₁₁	—	2	4	no	—
134	Dic₁₁	—	4	2	no	—
135	C₂²×Q₈	—	11	1	no	—
136	C₂²×C₈	—	22	1	no	—
137	C₂²×C₈	D₄₄	1	1	yes	characteristic
138	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
139	C₄×Q₈	—	11	2	no	—
140	C₄×Q₈	—	11	2	no	—
141	C₄×Q₈	—	22	1	no	—
142	C₄×Q₈	—	22	1	no	—
143	C₂×C₄⋊C₄	—	11	1	no	—
144	C₂×C₄⋊C₄	—	22	1	no	—
145	C₂×C₄²	—	22	1	no	—
146	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
147	C₂×C₁₆	—	2	2	no	—
148	C₂×C₁₆	—	4	2	no	—
149	C₂×C₁₆	—	22	4	no	—
150	C₂×C₁₆	—	22	2	no	—
151	C₄⋊C₈	—	11	2	no	—
152	C₄⋊C₈	—	22	2	no	—
153	C₄⋊C₈	—	22	2	no	—
154	C₄⋊C₈	—	22	1	no	—
155	C₄×C₈	—	22	2	no	—
156	C₄×C₈	—	22	2	no	—
157	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
158	C₄×C₈	D₄₄	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
160	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
161	C₂×C₁₁	Q₈⋊C₁₆	1	4	yes	complemented
162	C₂×C₁₁	C₂×Q₈⋊C₈	1	1	yes	characteristic
163	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
164	C₂×C₁₁	C₂×#350	1	1	yes	characteristic
165	C₂×Q₈	—	11	4	no	—
166	C₂×Q₈	—	11	2	no	—
167	C₂×Q₈	—	22	2	no	—
168	C₂×Q₈	—	22	1	no	—
169	C₂²×C₄	—	22	1	no	—
170	C₂²×C₄	—	22	1	no	—
171	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
172	C₂²×C₄	#4313	1	1	yes	characteristic
173	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	22	2	no	—
176	C₂×C₈	—	44	2	no	—
177	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
178	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
179	C₂×C₈	#4324	1	2	yes	—
180	C₂×C₈	#4326	1	2	yes	—
181	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
182	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
183	C₄⋊C₄	—	11	2	no	—
184	C₄⋊C₄	—	22	1	no	—
185	C₄⋊C₄	—	22	2	no	—
186	C₄⋊C₄	—	22	2	no	—
187	C₄²	—	22	2	no	—
188	C₄²	—	22	2	no	—
189	C₄²	C₈×D₁₁	1	1	yes	characteristic
190	C₄²	#4313	1	1	yes	characteristic
191	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
192	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
193	C₁₆	—	4	2	no	—
194	C₁₆	—	22	4	no	—
195	C₁₁	C₂×Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
196	C₂³	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
197	Q₈	—	11	4	no	—
198	Q₈	—	22	2	no	—
199	Q₈	—	22	4	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	22	2	no	—
202	C₂×C₄	—	22	4	no	—
203	C₂×C₄	—	22	2	no	—
204	C₂×C₄	—	44	2	no	—
205	C₂×C₄	C₁₆×D₁₁	1	2	yes	—
206	C₂×C₄	#66862	1	2	yes	—
207	C₂×C₄	#66874	1	2	yes	—
208	C₂×C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
209	C₂×C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
210	C₂×C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
211	C₂×C₄	#66889	1	2	yes	—
212	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
213	C₂×C₄	C₂×#4313	1	1	yes	characteristic
214	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
215	C₈	—	2	1	no	—
216	C₈	—	2	1	no	—
217	C₈	—	44	2	no	—
218	C₈	#66874	1	2	yes	—
219	C₈	C₂×#4324	1	1	yes	characteristic
220	C₈	C₂×#4326	1	1	yes	characteristic
221	C₂²	#10622122	1	2	yes	—
222	C₂²	(C₂×D₁₁)⋊C₁₆	1	2	yes	—
223	C₂²	#10622153	1	2	yes	—
224	C₂²	C₂×(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	22	4	no	—
228	C₄	—	44	2	no	—
229	C₄	#10622122	1	2	yes	—
230	C₄	(C₂×D₁₁)⋊C₁₆	1	2	yes	—
231	C₄	C₂×C₁₆×D₁₁	1	1	yes	characteristic
232	C₄	C₂×#66862	1	1	yes	characteristic
233	C₄	C₂×#66874	1	1	yes	characteristic
234	C₄	C₂×#66889	1	1	yes	characteristic
235	C₂	#13066594	1	4	yes	direct product factor
236	C₂	C₂×#10622122	1	1	yes	characteristic
237	C₂	C₂×(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
238	C₂	C₂×#10622153	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #13066594	C₂	direct (N × H)
54. C₂×Dic₂₂	C₁₆	semidirect
99. Dic₂₂	C₂×C₁₆	semidirect
161. C₂×C₁₁	Q₈⋊C₁₆	semidirect
195. C₁₁	C₂×Q₈⋊C₁₆	semidirect
235. C₂	#13066594	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
C₂×C₄×C₁₁⋊C₁₆	2
#13066594	2
C₂×C₁₁×C₄⋊C₁₆	2
C₂×Q₈⋊C₁₆	11

Subgroups — C2×#13066594 #14663571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066594 #14663571