Subgroups — C₂×#13070895 #14909255

Order 2816.

494 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622296	C₂	1	2	yes	maximal
2	#13070895	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10622143	C₂	1	2	yes	maximal
4	C₂×#10622142	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×#66923	—	2	2	no	—
7	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×#66882	C₂²	1	4	yes	—
11	C₂×#66881	—	2	2	no	—
12	#10622296	—	2	4	no	—
13	#10622296	C₂²	1	8	yes	—
14	C₄×C₁₁×C₁₆	C₂²	1	4	yes	—
15	#10622143	C₂²	1	8	yes	—
16	#10622142	C₂²	1	8	yes	—
17	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₁	—	2	4	no	—
21	C₂×Dic₁₁⋊C₄	—	4	4	no	—
22	#66923	—	2	8	no	—
23	#66923	—	4	4	no	—
24	C₂×C₁₁×C₁₆	Q₈	1	4	yes	—
25	C₂×C₁₁×C₁₆	Q₈	1	4	yes	—
26	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
27	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
28	C₄×C₈×C₁₁	D₄	1	2	yes	—
29	C₄×C₈×C₁₁	C₂³	1	2	yes	—
30	#66882	—	2	4	no	—
31	#66882	C₂³	1	8	yes	—
32	#66881	—	2	8	no	—
33	C₂×#2253	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	D₈	1	2	yes	—
35	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₁₁	—	4	4	no	—
37	C₂×C₈×C₁₁	Q₁₆	1	4	yes	—
38	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
40	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
41	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
42	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
43	C₄²×C₁₁	D₈	1	2	yes	—
44	C₄²×C₁₁	C₂×D₄	1	2	yes	—
45	C₄⋊Dic₁₁	—	2	8	no	—
46	C₄⋊Dic₁₁	—	4	4	no	—
47	Dic₁₁⋊C₄	—	4	16	no	—
48	C₁₁×C₁₆	C₂×Q₈	1	4	yes	—
49	C₁₁×C₁₆	C₂×Q₈	1	4	yes	—
50	C₂×#499	—	11	2	no	—
51	#2253	—	11	8	no	—
52	C₂×#367	—	11	2	no	—
53	C₂×#366	—	11	2	no	—
54	C₂×C₄×C₁₆	D₁₁	1	1	yes	characteristic
55	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
56	C₂×C₄×C₁₁	—	2	4	no	—
57	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
58	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
59	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
60	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
61	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
62	C₂×Dic₁₁	—	4	8	no	—
63	C₂×Dic₁₁	—	8	8	no	—
64	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
65	C₈×C₁₁	C₂×Q₁₆	1	4	yes	—
66	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
67	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
68	C₂×#125	—	22	2	no	—
69	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
70	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
71	#499	—	11	8	no	—
72	#499	—	22	4	no	—
73	C₂×#107	—	11	4	no	—
74	C₂×#106	—	22	2	no	—
75	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
76	#367	—	11	8	no	—
77	#366	—	11	8	no	—
78	C₄×C₁₆	C₂×D₁₁	1	4	yes	—
79	C₂²×C₁₁	#500	1	2	yes	—
80	C₂²×C₁₁	#508	1	4	yes	—
81	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
82	C₄×C₁₁	—	2	4	no	—
83	C₄×C₁₁	#500	1	2	yes	—
84	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
85	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
86	Dic₁₁	—	8	8	no	—
87	C₂²×C₈	D₄₄	1	1	yes	characteristic
88	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
89	#125	—	22	8	no	—
90	#125	—	44	4	no	—
91	C₂×C₄⋊C₄	—	22	4	no	—
92	C₂×C₄⋊C₄	—	44	4	no	—
93	C₂×C₄²	D₄₄	1	1	yes	characteristic
94	C₂×C₁₆	Dic₂₂	1	4	yes	—
95	C₂×C₁₆	Dic₂₂	1	4	yes	—
96	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
97	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
98	#107	—	11	8	no	—
99	#107	—	22	4	no	—
100	#106	—	22	8	no	—
101	C₄×C₈	D₄₄	1	2	yes	—
102	C₄×C₈	C₂²×D₁₁	1	2	yes	—
103	C₂×C₁₁	#2253	1	4	yes	complemented
104	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
105	C₂×C₁₁	C₂×#508	1	2	yes	—
106	C₂²×C₄	—	44	4	no	—
107	C₂²×C₄	D₈₈	1	2	yes	—
108	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
109	C₂×C₈	Dic₄₄	1	4	yes	—
110	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
111	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
112	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
113	C₂×C₈	C₂×D₄₄	1	2	yes	—
114	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
115	C₄⋊C₄	—	22	8	no	—
116	C₄⋊C₄	—	44	4	no	—
117	C₄⋊C₄	—	44	16	no	—
118	C₄²	D₈₈	1	2	yes	—
119	C₄²	C₂×D₄₄	1	2	yes	—
120	C₁₆	C₂×Dic₂₂	1	4	yes	—
121	C₁₆	C₂×Dic₂₂	1	4	yes	—
122	C₁₁	C₂×#2253	1	1	yes	characteristic, complemented, Sylow
123	C₂³	C₂×D₈₈	1	1	yes	characteristic
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	44	8	no	—
126	C₂×C₄	—	88	8	no	—
127	C₂×C₄	#66922	1	2	yes	—
128	C₂×C₄	C₂×D₈₈	1	4	yes	—
129	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
130	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
131	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
132	C₈	#66922	1	2	yes	—
133	C₈	C₂×Dic₄₄	1	4	yes	—
134	C₈	C₂²×Dic₂₂	1	1	yes	characteristic
135	C₈	C₂²×Dic₂₂	1	1	yes	characteristic
136	C₂²	#10622295	1	2	yes	—
137	C₂²	#10622517	1	4	yes	—
138	C₂²	C₂²×D₈₈	1	1	yes	characteristic
139	C₄	—	2	4	no	—
140	C₄	—	88	8	no	—
141	C₄	#10622295	1	2	yes	—
142	C₄	C₂×#66922	1	1	yes	characteristic
143	C₄	C₂²×Dic₄₄	1	1	yes	characteristic
144	C₂	#13070895	1	4	yes	direct product factor
145	C₂	C₂×#10622295	1	1	yes	characteristic
146	C₂	C₂×#10622517	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₄×C₁₁×C₁₆	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	C₂×C₄×C₁₆	D₁₁
hypocenter	C₁₁	C₂×#2253
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13070895	C₂	direct (N × H)
103. C₂×C₁₁	#2253	semidirect
122. C₁₁	C₂×#2253	semidirect
144. C₂	#13070895	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×#10622296	2
#13070895	2
C₂×#10622143	2
C₂×#10622142	2
C₂×C₄×C₁₁×C₁₆	2
C₂×#2253	11

Subgroups — C2×#13070895 #14909255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070895 #14909255