Subgroups — C₂×#13066665 #14665013

Order 2816.

414 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622096	C₂	1	1	yes	maximal, characteristic
3	#13066665	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×Q₁₆	—	2	1	no	—
6	C₂²×C₁₁×Q₁₆	C₄	1	2	yes	—
7	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
8	C₁₁×#494	—	2	1	no	—
9	C₁₁×#494	—	2	1	no	—
10	C₁₁×#494	C₄	1	2	yes	—
11	C₁₁×#494	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
14	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
15	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
16	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
17	#10622096	—	2	1	no	—
18	#10622096	C₂²	1	2	yes	—
19	C₂²×Q₈×C₁₁	—	2	2	no	—
20	C₂×C₁₁×Q₁₆	—	2	2	no	—
21	C₂×C₁₁×Q₁₆	—	2	2	no	—
22	C₂×C₁₁×Q₁₆	—	2	2	no	—
23	C₂×C₁₁×Q₁₆	—	4	4	no	—
24	C₂×C₁₁×Q₁₆	—	4	2	no	—
25	C₂×C₁₁×Q₁₆	—	4	2	no	—
26	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
29	C₁₁×C₄⋊Q₈	—	2	2	no	—
30	C₁₁×C₄⋊Q₈	—	2	2	no	—
31	C₁₁×C₄⋊Q₈	—	4	1	no	—
32	C₁₁×C₄⋊Q₈	—	4	1	no	—
33	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
34	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂²×C₁₁⋊C₈	—	4	1	no	—
37	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₂×C₁₁⋊C₁₆	—	2	2	no	—
42	C₂×C₁₁⋊C₁₆	—	4	2	no	—
43	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₁⋊C₈)	—	4	1	no	—
45	C₂×#1362	—	11	1	no	maximal, Sylow
46	C₂×Q₈×C₁₁	—	2	4	no	—
47	C₂×Q₈×C₁₁	—	4	2	no	—
48	C₂×Q₈×C₁₁	—	4	4	no	—
49	C₂×Q₈×C₁₁	—	4	4	no	—
50	C₂²×C₄×C₁₁	—	4	2	no	—
51	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
54	C₁₁×Q₁₆	—	4	4	no	—
55	C₁₁×Q₁₆	—	4	4	no	—
56	C₁₁×Q₁₆	—	4	2	no	—
57	C₁₁×Q₁₆	—	4	2	no	—
58	C₁₁×Q₁₆	—	4	4	no	—
59	C₂×C₈×C₁₁	—	2	2	no	—
60	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	D₈	1	2	yes	—
63	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
64	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₁₁×C₄⋊C₄	—	4	2	no	—
67	C₁₁×C₄⋊C₄	—	4	2	no	—
68	C₁₁×C₄⋊C₄	—	4	2	no	—
69	C₁₁×C₄⋊C₄	—	4	2	no	—
70	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₄²×C₁₁	D₈	1	1	yes	characteristic
72	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
73	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₂×C₁₁⋊C₈	—	4	2	no	—
75	C₂×C₁₁⋊C₈	—	8	2	no	—
76	C₁₁⋊C₁₆	—	4	2	no	—
77	C₂×#494	D₁₁	1	1	yes	characteristic
78	C₂×C₄⋊C₁₆	—	11	1	no	—
79	C₂×#335	—	11	1	no	—
80	#1362	—	11	4	no	—
81	C₂³×C₁₁	#102	1	1	yes	characteristic
82	Q₈×C₁₁	—	4	4	no	—
83	Q₈×C₁₁	—	4	4	no	—
84	Q₈×C₁₁	—	8	4	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	4	4	no	—
87	C₂×C₄×C₁₁	—	8	4	no	—
88	C₂×C₄×C₁₁	#100	1	2	yes	—
89	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
90	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
91	C₂×C₄×C₁₁	#102	1	2	yes	—
92	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
93	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
94	C₂×C₄×C₁₁	Q₃₂	1	2	yes	—
95	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
97	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
98	C₈×C₁₁	—	2	1	no	—
99	C₈×C₁₁	—	2	1	no	—
100	C₈×C₁₁	#102	1	2	yes	—
101	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
102	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
103	C₁₁⋊C₈	—	8	2	no	—
104	C₂²×Q₁₆	—	2	1	no	—
105	C₂²×Q₁₆	Dic₁₁	1	2	yes	—
106	C₂×C₄⋊Q₈	—	2	1	no	—
107	C₂²×C₁₆	—	22	1	no	—
108	#494	—	2	1	no	—
109	#494	—	2	1	no	—
110	#494	Dic₁₁	1	2	yes	—
111	#494	C₂×D₁₁	1	2	yes	—
112	C₂×C₄⋊C₈	—	22	1	no	—
113	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
114	C₄⋊C₁₆	—	11	2	no	—
115	C₄⋊C₁₆	—	22	1	no	—
116	#335	—	11	2	no	—
117	#335	—	22	1	no	—
118	C₂²×C₁₁	#331	1	2	yes	—
119	C₂²×C₁₁	#358	1	2	yes	—
120	C₂²×C₁₁	#362	1	2	yes	—
121	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
122	C₄×C₁₁	—	2	1	no	—
123	C₄×C₁₁	—	2	1	no	—
124	C₄×C₁₁	—	8	4	no	—
125	C₄×C₁₁	#331	1	2	yes	—
126	C₄×C₁₁	#358	1	2	yes	—
127	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
128	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
129	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
130	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
131	C₂²×Q₈	—	2	2	no	—
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×Q₁₆	—	2	2	no	—
134	C₂×Q₁₆	—	2	2	no	—
135	C₂×Q₁₆	—	4	4	no	—
136	C₂×Q₁₆	—	4	2	no	—
137	C₂×Q₁₆	—	4	2	no	—
138	C₂×Q₁₆	C₂×Dic₁₁	1	4	yes	—
139	C₂²×C₈	—	44	1	no	—
140	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
141	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	4	1	no	—
145	C₄⋊Q₈	—	4	1	no	—
146	C₂×C₄⋊C₄	—	4	1	no	—
147	C₂×C₄⋊C₄	—	4	1	no	—
148	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
149	C₂×C₁₆	—	22	2	no	—
150	C₂×C₁₆	—	44	2	no	—
151	C₄⋊C₈	—	22	2	no	—
152	C₄⋊C₈	—	44	1	no	—
153	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
154	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
155	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
156	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
157	C₂×C₁₁	#1362	1	4	yes	complemented
158	C₂×C₁₁	C₂×#331	1	1	yes	characteristic
159	C₂×C₁₁	C₂×#358	1	1	yes	characteristic
160	C₂×C₁₁	C₂×#362	1	1	yes	characteristic
161	C₂×Q₈	—	2	4	no	—
162	C₂×Q₈	—	4	2	no	—
163	C₂×Q₈	—	4	4	no	—
164	C₂×Q₈	—	4	4	no	—
165	C₂²×C₄	—	4	2	no	—
166	C₂²×C₄	#4323	1	1	yes	characteristic
167	C₂²×C₄	#4324	1	1	yes	characteristic
168	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
169	Q₁₆	—	4	4	no	—
170	Q₁₆	—	4	4	no	—
171	Q₁₆	—	4	4	no	—
172	Q₁₆	—	4	2	no	—
173	Q₁₆	—	4	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	44	2	no	—
176	C₂×C₈	—	88	2	no	—
177	C₂×C₈	#4323	1	2	yes	—
178	C₂×C₈	#4324	1	2	yes	—
179	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
180	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
181	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
182	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
183	C₄⋊C₄	—	4	2	no	—
184	C₄⋊C₄	—	4	2	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄²	#4323	1	1	yes	characteristic
188	C₄²	#4324	1	1	yes	characteristic
189	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
190	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
191	C₁₆	—	44	2	no	—
192	C₁₁	C₂×#1362	1	1	yes	characteristic, complemented, Sylow
193	C₂³	#66896	1	1	yes	characteristic
194	Q₈	—	4	4	no	—
195	Q₈	—	4	4	no	—
196	Q₈	—	8	4	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	8	4	no	—
200	C₂×C₄	#66892	1	2	yes	—
201	C₂×C₄	#66893	1	2	yes	—
202	C₂×C₄	#66896	1	1	yes	characteristic
203	C₂×C₄	#66896	1	2	yes	—
204	C₂×C₄	#66896	1	1	yes	characteristic
205	C₂×C₄	#66896	1	1	yes	characteristic
206	C₂×C₄	#66897	1	2	yes	—
207	C₂×C₄	C₂×#4323	1	1	yes	characteristic
208	C₂×C₄	C₂×#4324	1	1	yes	characteristic
209	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	88	2	no	—
213	C₈	#66896	1	2	yes	—
214	C₈	C₂×#4323	1	1	yes	characteristic
215	C₈	C₂×#4324	1	1	yes	characteristic
216	C₂²	#10622182	1	2	yes	—
217	C₂²	#10622202	1	2	yes	—
218	C₂²	#10622203	1	2	yes	—
219	C₂²	C₂×#66896	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	8	4	no	—
223	C₄	#10622182	1	2	yes	—
224	C₄	#10622202	1	2	yes	—
225	C₄	C₂×#66892	1	1	yes	characteristic
226	C₄	C₂×#66893	1	1	yes	characteristic
227	C₄	C₂×#66896	1	1	yes	characteristic
228	C₄	C₂×#66897	1	1	yes	characteristic
229	C₂	#13066665	1	4	yes	direct product factor
230	C₂	C₂×#10622182	1	1	yes	characteristic
231	C₂	C₂×#10622202	1	1	yes	characteristic
232	C₂	C₂×#10622203	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66896
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#494	C₂
socle, prime radical	C₂³×C₁₁	#102
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₂×#494	D₁₁
hypocenter	C₁₁	C₂×#1362
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#494

Complements

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

N	H ≅ G/N	type
3. #13066665	C₂	direct (N × H)
157. C₂×C₁₁	#1362	semidirect
192. C₁₁	C₂×#1362	semidirect
229. C₂	#13066665	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×C₄⋊(C₁₁⋊C₁₆)	2
C₂×#10622096	2
#13066665	2
C₂×C₁₁×#494	2
C₂×#1362	11

Subgroups — C2×#13066665 #14665013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066665 #14665013