Subgroups — C₂×#13070902 #14909270

Order 2816.

518 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622295	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622296	C₂	1	1	yes	maximal, characteristic
3	#13070902	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622143	C₂	1	2	yes	maximal
5	C₂×#10622142	C₂	1	2	yes	maximal
6	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
7	C₂×#66923	—	2	1	no	—
8	C₂×#66922	—	2	1	no	—
9	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×#66882	—	2	1	no	—
12	C₂×#66882	C₂²	1	1	yes	characteristic
13	C₂×#66882	C₂²	1	2	yes	—
14	C₂×#66882	C₂²	1	1	yes	characteristic
15	C₂×#66881	—	2	1	no	—
16	#10622296	—	2	2	no	—
17	#10622296	C₂²	1	4	yes	—
18	#10622295	—	2	2	no	—
19	#10622295	C₂²	1	4	yes	—
20	C₁₁×#346	C₂²	1	4	yes	—
21	#10622143	C₂²	1	8	yes	—
22	#10622142	C₂²	1	8	yes	—
23	C₂²×Dic₂₂	—	4	1	no	—
24	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₁	—	2	2	no	—
28	C₂×C₄⋊Dic₁₁	—	2	1	no	—
29	C₂×C₄⋊Dic₁₁	—	2	1	no	—
30	C₂×C₄⋊Dic₁₁	—	4	1	no	—
31	C₂×Dic₁₁⋊C₄	—	4	1	no	—
32	C₂×Dic₁₁⋊C₄	—	4	1	no	—
33	#66923	—	2	4	no	—
34	#66923	—	4	2	no	—
35	#66922	—	2	4	no	—
36	#66922	—	4	2	no	—
37	C₂×C₁₁×C₁₆	Q₈	1	8	yes	complemented
38	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
39	C₄×C₈×C₁₁	D₄	1	2	yes	—
40	C₄×C₈×C₁₁	C₂³	1	2	yes	—
41	#66882	—	2	2	no	—
42	#66882	—	2	4	no	—
43	#66882	—	2	1	no	—
44	#66882	—	2	1	no	—
45	#66882	C₂³	1	4	yes	—
46	#66882	C₂³	1	2	yes	—
47	#66882	C₂³	1	2	yes	—
48	#66881	—	2	4	no	—
49	C₂×#2255	—	11	1	no	maximal, Sylow
50	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
53	C₂²×Dic₁₁	—	4	1	no	—
54	C₂²×Dic₁₁	—	4	1	no	—
55	C₂²×Dic₁₁	—	4	2	no	—
56	C₂×Dic₂₂	—	4	4	no	—
57	C₂×Dic₂₂	—	8	4	no	—
58	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
59	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
62	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
63	C₄²×C₁₁	D₈	1	2	yes	—
64	C₄²×C₁₁	C₂×D₄	1	2	yes	—
65	C₄⋊Dic₁₁	—	2	2	no	—
66	C₄⋊Dic₁₁	—	2	2	no	—
67	C₄⋊Dic₁₁	—	2	4	no	—
68	C₄⋊Dic₁₁	—	4	4	no	—
69	C₄⋊Dic₁₁	—	4	2	no	—
70	C₄⋊Dic₁₁	—	4	1	no	—
71	C₄⋊Dic₁₁	—	4	1	no	—
72	Dic₁₁⋊C₄	—	4	4	no	—
73	Dic₁₁⋊C₄	—	4	4	no	—
74	C₁₁×C₁₆	C₂×Q₈	1	8	yes	complemented
75	C₂×#500	—	11	1	no	—
76	C₂×#499	—	11	1	no	—
77	#2255	—	11	8	no	—
78	C₂×#367	—	11	2	no	—
79	C₂×#366	—	11	2	no	—
80	C₂×#346	D₁₁	1	1	yes	characteristic
81	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
85	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
86	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
87	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
88	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
90	C₂×Dic₁₁	—	4	2	no	—
91	C₂×Dic₁₁	—	4	2	no	—
92	C₂×Dic₁₁	—	4	4	no	—
93	C₂×Dic₁₁	—	8	4	no	—
94	C₂×Dic₁₁	—	8	2	no	—
95	C₂×Dic₁₁	—	8	2	no	—
96	Dic₂₂	—	8	8	no	—
97	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
98	C₈×C₁₁	C₂×Q₁₆	1	4	yes	—
99	C₈×C₁₁	C₂²×Q₈	1	2	yes	—
100	C₂×C₄⋊Q₈	—	22	1	no	—
101	C₂×#125	—	22	1	no	—
102	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
103	#500	—	11	4	no	—
104	#500	—	22	2	no	—
105	#499	—	11	4	no	—
106	#499	—	22	2	no	—
107	C₂×#107	—	11	1	no	—
108	C₂×#107	—	11	1	no	—
109	C₂×#107	—	11	2	no	—
110	C₂×#107	—	22	1	no	—
111	C₂×#106	—	22	1	no	—
112	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
113	#367	—	11	8	no	—
114	#366	—	11	8	no	—
115	#346	C₂×D₁₁	1	4	yes	—
116	C₂²×C₁₁	#500	1	2	yes	—
117	C₂²×C₁₁	#509	1	2	yes	—
118	C₂²×C₁₁	#510	1	2	yes	—
119	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
120	C₄×C₁₁	—	2	2	no	—
121	C₄×C₁₁	—	2	2	no	—
122	C₄×C₁₁	#500	1	2	yes	—
123	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
124	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
125	Dic₁₁	—	8	4	no	—
126	Dic₁₁	—	8	2	no	—
127	Dic₁₁	—	8	2	no	—
128	C₂²×Q₈	—	44	1	no	—
129	C₂²×C₈	D₄₄	1	1	yes	characteristic
130	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
131	C₄⋊Q₈	—	22	4	no	—
132	C₄⋊Q₈	—	44	2	no	—
133	#125	—	22	4	no	—
134	#125	—	44	2	no	—
135	C₂×C₄⋊C₄	—	22	1	no	—
136	C₂×C₄⋊C₄	—	22	1	no	—
137	C₂×C₄⋊C₄	—	22	2	no	—
138	C₂×C₄⋊C₄	—	44	1	no	—
139	C₂×C₄⋊C₄	—	44	1	no	—
140	C₂×C₄⋊C₄	—	44	1	no	—
141	C₂×C₄²	D₄₄	1	1	yes	characteristic
142	C₂×C₁₆	Dic₂₂	1	8	yes	complemented
143	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
144	#107	—	11	2	no	—
145	#107	—	11	4	no	—
146	#107	—	11	2	no	—
147	#107	—	22	1	no	—
148	#107	—	22	1	no	—
149	#107	—	22	2	no	—
150	#107	—	22	4	no	—
151	#106	—	22	4	no	—
152	C₄×C₈	D₄₄	1	2	yes	—
153	C₄×C₈	C₂²×D₁₁	1	2	yes	—
154	C₂×C₁₁	#2255	1	4	yes	complemented
155	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
156	C₂×C₁₁	C₂×#509	1	1	yes	characteristic
157	C₂×C₁₁	C₂×#510	1	1	yes	characteristic
158	C₂×Q₈	—	44	4	no	—
159	C₂×Q₈	—	88	4	no	—
160	C₂²×C₄	—	44	1	no	—
161	C₂²×C₄	—	44	1	no	—
162	C₂²×C₄	—	44	2	no	—
163	C₂²×C₄	D₈₈	1	1	yes	characteristic
164	C₂²×C₄	D₈₈	1	1	yes	characteristic
165	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
166	C₂×C₈	Dic₄₄	1	4	yes	—
167	C₂×C₈	C₂×Dic₂₂	1	4	yes	—
168	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
169	C₂×C₈	C₂×D₄₄	1	2	yes	—
170	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
171	C₄⋊C₄	—	22	2	no	—
172	C₄⋊C₄	—	22	2	no	—
173	C₄⋊C₄	—	22	4	no	—
174	C₄⋊C₄	—	44	1	no	—
175	C₄⋊C₄	—	44	1	no	—
176	C₄⋊C₄	—	44	2	no	—
177	C₄⋊C₄	—	44	4	no	—
178	C₄⋊C₄	—	44	4	no	—
179	C₄⋊C₄	—	44	4	no	—
180	C₄²	D₈₈	1	2	yes	—
181	C₄²	C₂×D₄₄	1	2	yes	—
182	C₁₆	C₂×Dic₂₂	1	8	yes	complemented
183	C₁₁	C₂×#2255	1	1	yes	characteristic, complemented, Sylow
184	C₂³	C₂×D₈₈	1	1	yes	characteristic
185	Q₈	—	88	8	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	44	2	no	—
189	C₂×C₄	—	44	2	no	—
190	C₂×C₄	—	44	4	no	—
191	C₂×C₄	—	88	4	no	—
192	C₂×C₄	—	88	2	no	—
193	C₂×C₄	—	88	2	no	—
194	C₂×C₄	#66922	1	2	yes	—
195	C₂×C₄	C₂×D₈₈	1	2	yes	—
196	C₂×C₄	C₂×D₈₈	1	2	yes	—
197	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
198	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
199	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
200	C₈	#66922	1	2	yes	—
201	C₈	C₂×Dic₄₄	1	4	yes	—
202	C₈	C₂²×Dic₂₂	1	2	yes	—
203	C₂²	#10622295	1	2	yes	—
204	C₂²	#10622521	1	2	yes	—
205	C₂²	#10622522	1	2	yes	—
206	C₂²	C₂²×D₈₈	1	1	yes	characteristic
207	C₄	—	2	2	no	—
208	C₄	—	2	2	no	—
209	C₄	—	88	4	no	—
210	C₄	—	88	2	no	—
211	C₄	—	88	2	no	—
212	C₄	#10622295	1	2	yes	—
213	C₄	C₂×#66922	1	1	yes	characteristic
214	C₄	C₂²×Dic₄₄	1	1	yes	characteristic
215	C₂	#13070902	1	4	yes	direct product factor
216	C₂	C₂×#10622295	1	1	yes	characteristic
217	C₂	C₂×#10622521	1	1	yes	characteristic
218	C₂	C₂×#10622522	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	C₂×#2255
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
3. #13070902	C₂	direct (N × H)
37. C₂×C₁₁×C₁₆	Q₈	semidirect
74. C₁₁×C₁₆	C₂×Q₈	semidirect
142. C₂×C₁₆	Dic₂₂	semidirect
154. C₂×C₁₁	#2255	semidirect
182. C₁₆	C₂×Dic₂₂	semidirect
183. C₁₁	C₂×#2255	semidirect
215. C₂	#13070902	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×#10622295	2
C₂×#10622296	2
#13070902	2
C₂×#10622143	2
C₂×#10622142	2
C₂×C₁₁×#346	2
C₂×#2255	11

Subgroups — C2×#13070902 #14909270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070902 #14909270