Subgroups — C₂×#13066671 #14665051

Order 2816.

350 conjugacy classes of subgroups.

The subgroup lattice has 218 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	#13066671	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
6	C₁₁×#500	—	2	1	no	—
7	C₁₁×#500	—	2	1	no	—
8	C₁₁×#500	C₄	1	2	yes	—
9	C₁₁×#500	C₂²	1	2	yes	—
10	C₂×C₁₁×#107	—	2	1	no	—
11	C₂×C₁₁×#107	C₄	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	—	4	1	no	—
20	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
22	C₁₁×C₄⋊Q₈	—	2	2	no	—
23	C₁₁×C₄⋊Q₈	—	2	2	no	—
24	C₁₁×C₄⋊Q₈	—	4	1	no	—
25	C₁₁×C₄⋊Q₈	—	4	1	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
28	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
29	C₂²×C₁₁⋊C₈	—	4	1	no	—
30	C₁₁×#107	—	2	2	no	—
31	C₁₁×#107	—	2	2	no	—
32	C₁₁×#107	—	2	2	no	—
33	C₁₁×#107	C₂×C₄	1	4	yes	—
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	C₂×C₁₁⋊C₁₆	—	2	2	no	—
39	C₂×C₁₁⋊C₁₆	—	4	2	no	—
40	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	4	1	no	—
42	C₂×#1364	—	11	1	no	maximal, Sylow
43	C₂×Q₈×C₁₁	—	4	2	no	—
44	C₂×Q₈×C₁₁	—	4	2	no	—
45	C₂×Q₈×C₁₁	—	8	2	no	—
46	C₂×Q₈×C₁₁	—	8	2	no	—
47	C₂²×C₄×C₁₁	—	4	2	no	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
55	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
56	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	—	2	4	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₁₁×C₄⋊C₄	—	4	2	no	—
62	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₁	D₈	1	1	yes	characteristic
64	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
65	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₂×C₁₁⋊C₈	—	4	2	no	—
67	C₂×C₁₁⋊C₈	—	8	2	no	—
68	C₁₁⋊C₁₆	—	4	2	no	—
69	C₂×#500	D₁₁	1	1	yes	characteristic
70	C₂×C₄⋊C₁₆	—	11	1	no	—
71	C₂×#335	—	11	1	no	—
72	#1364	—	11	4	no	—
73	C₂³×C₁₁	#102	1	1	yes	characteristic
74	Q₈×C₁₁	—	8	4	no	—
75	Q₈×C₁₁	—	8	2	no	—
76	Q₈×C₁₁	—	8	2	no	—
77	C₂×C₄×C₁₁	—	2	2	no	—
78	C₂×C₄×C₁₁	—	4	4	no	—
79	C₂×C₄×C₁₁	—	8	4	no	—
80	C₂×C₄×C₁₁	#101	1	2	yes	—
81	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
82	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
83	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
84	C₂×C₄×C₁₁	#103	1	2	yes	—
85	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
86	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
87	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
90	C₈×C₁₁	—	2	1	no	—
91	C₈×C₁₁	—	2	1	no	—
92	C₈×C₁₁	#103	1	2	yes	—
93	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
94	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
95	C₁₁⋊C₈	—	8	2	no	—
96	C₂×C₄⋊Q₈	—	2	1	no	—
97	C₂²×C₁₆	—	22	1	no	—
98	#500	—	2	1	no	—
99	#500	—	2	1	no	—
100	#500	Dic₁₁	1	2	yes	—
101	#500	C₂×D₁₁	1	2	yes	—
102	C₂×#107	—	2	1	no	—
103	C₂×#107	Dic₁₁	1	2	yes	—
104	C₂×C₄⋊C₈	—	22	1	no	—
105	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
106	C₄⋊C₁₆	—	11	2	no	—
107	C₄⋊C₁₆	—	22	1	no	—
108	#335	—	11	2	no	—
109	#335	—	22	1	no	—
110	C₂²×C₁₁	#332	1	2	yes	—
111	C₂²×C₁₁	#357	1	2	yes	—
112	C₂²×C₁₁	#362	1	2	yes	—
113	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
114	C₄×C₁₁	—	2	1	no	—
115	C₄×C₁₁	—	2	1	no	—
116	C₄×C₁₁	—	8	4	no	—
117	C₄×C₁₁	#332	1	2	yes	—
118	C₄×C₁₁	#357	1	2	yes	—
119	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
120	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
121	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
122	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
123	C₂²×Q₈	—	4	1	no	—
124	C₂²×C₈	—	44	1	no	—
125	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
126	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
127	C₄⋊Q₈	—	2	2	no	—
128	C₄⋊Q₈	—	2	2	no	—
129	C₄⋊Q₈	—	4	1	no	—
130	C₄⋊Q₈	—	4	1	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	4	1	no	—
133	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
134	C₂×C₁₆	—	22	2	no	—
135	C₂×C₁₆	—	44	2	no	—
136	#107	—	2	2	no	—
137	#107	—	2	2	no	—
138	#107	—	2	2	no	—
139	#107	C₂×Dic₁₁	1	4	yes	—
140	C₄⋊C₈	—	22	2	no	—
141	C₄⋊C₈	—	44	1	no	—
142	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
143	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
144	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
145	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
146	C₂×C₁₁	#1364	1	4	yes	complemented
147	C₂×C₁₁	C₂×#332	1	1	yes	characteristic
148	C₂×C₁₁	C₂×#357	1	1	yes	characteristic
149	C₂×C₁₁	C₂×#362	1	1	yes	characteristic
150	C₂×Q₈	—	4	2	no	—
151	C₂×Q₈	—	4	2	no	—
152	C₂×Q₈	—	8	2	no	—
153	C₂×Q₈	—	8	2	no	—
154	C₂²×C₄	—	4	2	no	—
155	C₂²×C₄	#4323	1	1	yes	characteristic
156	C₂²×C₄	#4324	1	1	yes	characteristic
157	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	44	2	no	—
160	C₂×C₈	—	88	2	no	—
161	C₂×C₈	#4325	1	2	yes	—
162	C₂×C₈	#4326	1	2	yes	—
163	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
164	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
165	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
166	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
167	C₄⋊C₄	—	2	4	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄²	#4323	1	1	yes	characteristic
172	C₄²	#4324	1	1	yes	characteristic
173	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
174	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
175	C₁₆	—	44	2	no	—
176	C₁₁	C₂×#1364	1	1	yes	characteristic, complemented, Sylow
177	C₂³	#66896	1	1	yes	characteristic
178	Q₈	—	8	2	no	—
179	Q₈	—	8	2	no	—
180	Q₈	—	8	4	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	8	4	no	—
184	C₂×C₄	#66890	1	2	yes	—
185	C₂×C₄	#66891	1	2	yes	—
186	C₂×C₄	#66896	1	1	yes	characteristic
187	C₂×C₄	#66896	1	1	yes	characteristic
188	C₂×C₄	#66896	1	1	yes	characteristic
189	C₂×C₄	#66899	1	2	yes	—
190	C₂×C₄	#66900	1	2	yes	—
191	C₂×C₄	C₂×#4323	1	1	yes	characteristic
192	C₂×C₄	C₂×#4324	1	1	yes	characteristic
193	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
194	C₈	—	2	1	no	—
195	C₈	—	2	1	no	—
196	C₈	—	88	2	no	—
197	C₈	#66899	1	2	yes	—
198	C₈	C₂×#4325	1	1	yes	characteristic
199	C₈	C₂×#4326	1	1	yes	characteristic
200	C₂²	#10622185	1	2	yes	—
201	C₂²	#10622200	1	2	yes	—
202	C₂²	#10622203	1	2	yes	—
203	C₂²	C₂×#66896	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	—	8	4	no	—
207	C₄	#10622185	1	2	yes	—
208	C₄	#10622200	1	2	yes	—
209	C₄	C₂×#66890	1	1	yes	characteristic
210	C₄	C₂×#66891	1	1	yes	characteristic
211	C₄	C₂×#66899	1	1	yes	characteristic
212	C₄	C₂×#66900	1	1	yes	characteristic
213	C₂	#13066671	1	4	yes	direct product factor
214	C₂	C₂×#10622185	1	1	yes	characteristic
215	C₂	C₂×#10622200	1	1	yes	characteristic
216	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×#500	C₂
socle, prime radical	C₂³×C₁₁	#102
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₂×#500	D₁₁
hypocenter	C₁₁	C₂×#1364
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#500

Complements

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

N	H ≅ G/N	type
3. #13066671	C₂	direct (N × H)
146. C₂×C₁₁	#1364	semidirect
176. C₁₁	C₂×#1364	semidirect
213. C₂	#13066671	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
#13066671	2
C₂×C₁₁×#500	2
C₂×#1364	11

Subgroups — C2×#13066671 #14665051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066671 #14665051