Subgroups — C₂×#13070889 #14909248

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 200 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	#13070889	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10622127	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
7	C₂×#66922	—	2	1	no	—
8	C₁₁×#500	—	2	2	no	—
9	C₁₁×#500	C₂²	1	4	yes	—
10	C₂×C₁₁×#107	—	2	1	no	—
11	C₂×C₁₁×#107	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×#66882	—	2	1	no	—
14	C₂×#66882	C₂²	1	2	yes	—
15	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
16	#10622295	—	2	2	no	—
17	#10622295	C₂²	1	4	yes	—
18	#10622127	C₂²	1	16	yes	—
19	C₄×C₁₁⋊C₁₆	C₂²	1	4	yes	—
20	C₂²×Q₈×C₁₁	—	4	1	no	—
21	C₂²×Dic₂₂	—	4	1	no	—
22	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	C₁₁×C₄⋊Q₈	—	2	4	no	—
25	C₁₁×C₄⋊Q₈	—	4	2	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	C₂×C₄⋊Dic₁₁	—	2	2	no	—
30	C₂×C₄⋊Dic₁₁	—	4	1	no	—
31	#66922	—	2	4	no	—
32	#66922	—	4	2	no	—
33	C₁₁×#107	—	2	2	no	—
34	C₁₁×#107	—	2	4	no	—
35	C₁₁×#107	C₂³	1	4	yes	—
36	C₄×C₈×C₁₁	D₄	1	2	yes	—
37	C₄×C₈×C₁₁	C₂³	1	2	yes	—
38	#66882	—	2	2	no	—
39	#66882	—	2	4	no	—
40	#66882	C₂³	1	4	yes	—
41	C₂×C₁₁⋊C₁₆	Q₈	1	8	yes	complemented
42	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
43	C₂×#2252	—	11	1	no	maximal, Sylow
44	C₂×Q₈×C₁₁	—	4	4	no	—
45	C₂×Q₈×C₁₁	—	8	4	no	—
46	C₂²×C₄×C₁₁	—	4	2	no	—
47	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₁	—	4	2	no	—
51	C₂×Dic₂₂	—	4	4	no	—
52	C₂×Dic₂₂	—	8	4	no	—
53	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
54	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
57	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	—	2	4	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	4	4	no	—
61	C₄²×C₁₁	D₈	1	2	yes	—
62	C₄²×C₁₁	C₂×D₄	1	2	yes	—
63	C₄⋊Dic₁₁	—	2	4	no	—
64	C₄⋊Dic₁₁	—	4	4	no	—
65	C₄⋊Dic₁₁	—	4	2	no	—
66	C₁₁⋊C₁₆	C₂×Q₈	1	8	yes	complemented
67	C₂×#500	—	11	1	no	—
68	C₂×#500	D₁₁	1	1	yes	characteristic
69	#2252	—	11	8	no	—
70	C₂×#366	—	11	4	no	—
71	C₂×C₄×C₁₆	—	11	1	no	—
72	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
73	Q₈×C₁₁	—	8	8	no	—
74	C₂×C₄×C₁₁	—	4	4	no	—
75	C₂×C₄×C₁₁	—	8	4	no	—
76	C₂×C₄×C₁₁	D₁₆	1	4	yes	—
77	C₂×C₄×C₁₁	Q₃₂	1	4	yes	—
78	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
79	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
81	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
82	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
83	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
84	C₂×Dic₁₁	—	4	4	no	—
85	C₂×Dic₁₁	—	8	4	no	—
86	Dic₂₂	—	8	8	no	—
87	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
88	C₈×C₁₁	C₂×Q₁₆	1	4	yes	—
89	C₈×C₁₁	C₂²×Q₈	1	2	yes	—
90	C₂×C₄⋊Q₈	—	2	1	no	—
91	C₂×C₄⋊Q₈	—	22	1	no	—
92	C₂²×C₁₆	—	11	2	no	—
93	#500	—	2	2	no	—
94	#500	—	11	4	no	—
95	#500	—	22	2	no	—
96	#500	C₂×D₁₁	1	4	yes	—
97	C₂×#107	—	2	1	no	—
98	C₂×#107	—	11	2	no	—
99	C₂×#107	—	22	1	no	—
100	C₂×#107	C₂×D₁₁	1	2	yes	—
101	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
102	#366	—	11	16	no	—
103	C₄×C₁₆	—	11	4	no	—
104	C₂²×C₁₁	#500	1	2	yes	—
105	C₂²×C₁₁	C₂×D₁₆	1	2	yes	—
106	C₂²×C₁₁	C₂×Q₃₂	1	2	yes	—
107	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
108	C₄×C₁₁	—	8	4	no	—
109	C₄×C₁₁	#500	1	2	yes	—
110	C₄×C₁₁	C₂×D₁₆	1	4	yes	—
111	C₄×C₁₁	C₂×Q₃₂	1	4	yes	—
112	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
113	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
114	Dic₁₁	—	8	4	no	—
115	C₂²×Q₈	—	4	1	no	—
116	C₂²×Q₈	—	44	1	no	—
117	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
118	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
119	C₄⋊Q₈	—	2	4	no	—
120	C₄⋊Q₈	—	4	2	no	—
121	C₄⋊Q₈	—	22	4	no	—
122	C₄⋊Q₈	—	44	2	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄⋊C₄	—	4	1	no	—
125	C₂×C₄⋊C₄	—	22	2	no	—
126	C₂×C₄⋊C₄	—	44	1	no	—
127	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
128	C₂×C₁₆	—	11	8	no	—
129	C₂×C₁₆	—	11	4	no	—
130	#107	—	2	4	no	—
131	#107	—	2	2	no	—
132	#107	—	11	4	no	—
133	#107	—	22	2	no	—
134	#107	—	22	4	no	—
135	#107	C₂²×D₁₁	1	4	yes	—
136	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
137	C₄×C₈	C₂²×D₁₁	1	2	yes	—
138	C₂×C₁₁	#2252	1	4	yes	complemented
139	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
140	C₂×C₁₁	C₂²×D₁₆	1	1	yes	characteristic
141	C₂×C₁₁	C₂²×Q₃₂	1	1	yes	characteristic
142	C₂×Q₈	—	4	4	no	—
143	C₂×Q₈	—	8	4	no	—
144	C₂×Q₈	—	44	4	no	—
145	C₂×Q₈	—	88	4	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	44	2	no	—
148	C₂²×C₄	#4323	1	1	yes	characteristic
149	C₂²×C₄	#4323	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
151	C₂×C₈	#4326	1	4	yes	—
152	C₂×C₈	Q₈×D₁₁	1	4	yes	—
153	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
154	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
155	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	4	no	—
159	C₄⋊C₄	—	22	4	no	—
160	C₄⋊C₄	—	44	2	no	—
161	C₄⋊C₄	—	44	4	no	—
162	C₄²	#4323	1	2	yes	—
163	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
164	C₁₆	—	11	8	no	—
165	C₁₁	C₂×#2252	1	1	yes	characteristic, complemented, Sylow
166	C₂³	C₂×#4323	1	1	yes	characteristic
167	Q₈	—	8	8	no	—
168	Q₈	—	88	8	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	8	4	no	—
171	C₂×C₄	—	44	4	no	—
172	C₂×C₄	—	88	4	no	—
173	C₂×C₄	#66890	1	4	yes	—
174	C₂×C₄	#66893	1	4	yes	—
175	C₂×C₄	C₂×#4323	1	2	yes	—
176	C₂×C₄	C₂×#4323	1	2	yes	—
177	C₂×C₄	C₂×#4323	1	1	yes	characteristic
178	C₂×C₄	C₂×#4326	1	2	yes	—
179	C₂×C₄	#66997	1	2	yes	—
180	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
181	C₈	C₂×#4326	1	4	yes	—
182	C₈	#66997	1	2	yes	—
183	C₈	C₂×Q₈×D₁₁	1	2	yes	—
184	C₂²	#10622691	1	2	yes	—
185	C₂²	C₂×#66890	1	2	yes	—
186	C₂²	C₂×#66893	1	2	yes	—
187	C₂²	C₂²×#4323	1	1	yes	characteristic
188	C₄	—	8	4	no	—
189	C₄	—	88	4	no	—
190	C₄	#10622691	1	2	yes	—
191	C₄	C₂×#66890	1	4	yes	—
192	C₄	C₂×#66893	1	4	yes	—
193	C₄	C₂²×#4326	1	1	yes	characteristic
194	C₄	C₂×#66997	1	1	yes	characteristic
195	C₂	#13070889	1	4	yes	direct product factor
196	C₂	C₂×#10622691	1	1	yes	characteristic
197	C₂	C₂²×#66890	1	1	yes	characteristic
198	C₂	C₂²×#66893	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#4323
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#500	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	C₂×#500	D₁₁
hypocenter	C₁₁	C₂×#2252
LCS	G ▷ C₂×C₈×C₁₁ ▷ 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
2. #13070889	C₂	direct (N × H)
41. C₂×C₁₁⋊C₁₆	Q₈	semidirect
66. C₁₁⋊C₁₆	C₂×Q₈	semidirect
138. C₂×C₁₁	#2252	semidirect
165. C₁₁	C₂×#2252	semidirect
195. C₂	#13070889	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
#13070889	2
C₂×#10622127	2
C₂×C₄×C₁₁⋊C₁₆	2
C₂×C₁₁×#500	2
C₂×#2252	11

Subgroups — C2×#13070889 #14909248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070889 #14909248