Subgroups — C₂×#13068768 #14754152

Order 2816.

1470 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₁₁⋊C₈)	C₂	1	6	yes	maximal
2	#13068768	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄³×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄²×C₁₁	C₄	1	3	yes	—
5	C₂²×C₄²×C₁₁	C₄	1	1	yes	characteristic
6	C₂²×C₄²×C₁₁	C₂²	1	3	yes	—
7	C₂³×C₁₁⋊C₈	C₂²	1	4	yes	—
8	C₄³×C₁₁	C₄	1	4	yes	—
9	C₄³×C₁₁	C₂²	1	4	yes	—
10	C₂×C₄⋊(C₁₁⋊C₈)	—	2	24	no	—
11	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	24	yes	—
12	C₂³×C₄×C₁₁	C₂×C₄	1	3	yes	—
13	C₂³×C₄×C₁₁	C₂×C₄	1	3	yes	—
14	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₁	—	2	12	no	—
16	C₂×C₄²×C₁₁	C₈	1	8	yes	complemented
17	C₂×C₄²×C₁₁	C₂×C₄	1	12	yes	—
18	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
19	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₁	D₄	1	12	yes	—
21	C₂×C₄²×C₁₁	Q₈	1	12	yes	—
22	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
23	C₂²×C₁₁⋊C₈	—	2	24	no	—
24	C₂²×C₁₁⋊C₈	C₂³	1	8	yes	—
25	C₄⋊(C₁₁⋊C₈)	—	2	48	no	—
26	C₂×#1842	—	11	1	no	maximal, Sylow
27	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₁	—	2	12	no	—
29	C₂²×C₄×C₁₁	C₄⋊C₄	1	12	yes	—
30	C₂²×C₄×C₁₁	C₄⋊C₄	1	12	yes	—
31	C₂²×C₄×C₁₁	C₂×C₈	1	12	yes	—
32	C₂²×C₄×C₁₁	M₁₆	1	12	yes	—
33	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
34	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
36	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
37	C₂²×C₄×C₁₁	C₂×Q₈	1	6	yes	—
38	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
39	C₄²×C₁₁	—	2	24	no	—
40	C₄²×C₁₁	C₄⋊C₄	1	24	yes	—
41	C₄²×C₁₁	C₂×C₈	1	16	yes	complemented
42	C₄²×C₁₁	C₂×D₄	1	12	yes	—
43	C₄²×C₁₁	C₂×Q₈	1	12	yes	—
44	C₂×C₁₁⋊C₈	—	2	24	no	—
45	C₂×C₁₁⋊C₈	—	4	16	no	—
46	C₂²×C₄⋊C₈	—	11	6	no	—
47	C₂×C₄³	D₁₁	1	1	yes	characteristic
48	#1842	—	11	8	no	—
49	C₂³×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
50	C₂³×C₁₁	C₂²×C₈	1	2	yes	—
51	C₂³×C₁₁	C₂×M₁₆	1	6	yes	—
52	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₁	—	2	12	no	—
54	C₂×C₄×C₁₁	—	2	24	no	—
55	C₂×C₄×C₁₁	C₄⋊C₈	1	48	yes	complemented
56	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	12	yes	—
57	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
58	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	12	yes	—
59	C₂×C₄×C₁₁	#127	1	4	yes	—
60	C₂×C₄×C₁₁	C₄⋊Q₈	1	12	yes	—
61	C₂×C₄×C₁₁	C₂²×C₈	1	12	yes	—
62	C₂×C₄×C₁₁	C₂×M₁₆	1	12	yes	—
63	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
64	C₂×C₄×C₁₁	C₂²×Q₈	1	3	yes	—
65	C₁₁⋊C₈	—	4	8	no	—
66	C₂³×C₈	—	11	4	no	—
67	C₂²×C₄²	Dic₁₁	1	3	yes	—
68	C₂²×C₄²	Dic₁₁	1	1	yes	characteristic
69	C₂²×C₄²	C₂×D₁₁	1	3	yes	—
70	C₂×C₄⋊C₈	—	11	24	no	—
71	C₂×C₄⋊C₈	—	22	24	no	—
72	C₄³	Dic₁₁	1	4	yes	—
73	C₄³	C₂×D₁₁	1	4	yes	—
74	C₂²×C₁₁	#384	1	4	yes	—
75	C₂²×C₁₁	C₂×C₄⋊C₈	1	12	yes	—
76	C₂²×C₁₁	#423	1	12	yes	—
77	C₂²×C₁₁	C₂²×C₄⋊C₄	1	3	yes	—
78	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
79	C₂²×C₁₁	C₂²×M₁₆	1	3	yes	—
80	C₄×C₁₁	—	2	12	no	—
81	C₄×C₁₁	#384	1	4	yes	—
82	C₄×C₁₁	C₂×C₄⋊C₈	1	24	yes	complemented
83	C₄×C₁₁	C₂×#127	1	1	yes	characteristic
84	C₄×C₁₁	C₂×C₄⋊Q₈	1	3	yes	—
85	C₂³×C₄	C₂×Dic₁₁	1	3	yes	—
86	C₂³×C₄	C₂×Dic₁₁	1	3	yes	—
87	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
88	C₂²×C₈	—	11	8	no	—
89	C₂²×C₈	—	22	24	no	—
90	C₂×C₄²	—	2	12	no	—
91	C₂×C₄²	C₁₁⋊C₈	1	8	yes	complemented
92	C₂×C₄²	Dic₂₂	1	12	yes	—
93	C₂×C₄²	D₄₄	1	12	yes	—
94	C₂×C₄²	C₂×Dic₁₁	1	12	yes	—
95	C₂×C₄²	C₂×Dic₁₁	1	4	yes	—
96	C₂×C₄²	C₂×Dic₁₁	1	6	yes	—
97	C₂×C₄²	C₂²×D₁₁	1	6	yes	—
98	C₄⋊C₈	—	22	48	no	—
99	C₂×C₁₁	#1842	1	8	yes	complemented
100	C₂×C₁₁	C₂×#384	1	1	yes	characteristic
101	C₂×C₁₁	C₂²×C₄⋊C₈	1	3	yes	—
102	C₂×C₁₁	C₂×#423	1	3	yes	—
103	C₂⁴	C₂²×Dic₁₁	1	1	yes	characteristic
104	C₂²×C₄	—	2	12	no	—
105	C₂²×C₄	C₂×C₁₁⋊C₈	1	12	yes	—
106	C₂²×C₄	#4318	1	12	yes	—
107	C₂²×C₄	C₄⋊Dic₁₁	1	12	yes	—
108	C₂²×C₄	C₄⋊Dic₁₁	1	12	yes	—
109	C₂²×C₄	C₂×Dic₂₂	1	6	yes	—
110	C₂²×C₄	C₂×D₄₄	1	6	yes	—
111	C₂²×C₄	C₂²×Dic₁₁	1	6	yes	—
112	C₂²×C₄	C₂²×Dic₁₁	1	6	yes	—
113	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
114	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
115	C₂×C₈	—	22	24	no	—
116	C₂×C₈	—	44	16	no	—
117	C₄²	—	2	24	no	—
118	C₄²	C₂×C₁₁⋊C₈	1	16	yes	complemented
119	C₄²	C₄⋊Dic₁₁	1	24	yes	—
120	C₄²	C₂×Dic₂₂	1	12	yes	—
121	C₄²	C₂×D₄₄	1	12	yes	—
122	C₁₁	C₂×#1842	1	1	yes	characteristic, complemented, Sylow
123	C₂³	C₂²×C₁₁⋊C₈	1	2	yes	—
124	C₂³	C₂×#4318	1	6	yes	—
125	C₂³	C₂×C₄⋊Dic₁₁	1	6	yes	—
126	C₂³	C₂³×Dic₁₁	1	1	yes	characteristic
127	C₂×C₄	—	2	24	no	—
128	C₂×C₄	—	2	12	no	—
129	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	48	yes	complemented
130	C₂×C₄	#66922	1	12	yes	—
131	C₂×C₄	#66927	1	4	yes	—
132	C₂×C₄	C₂²×C₁₁⋊C₈	1	12	yes	—
133	C₂×C₄	C₂×#4318	1	12	yes	—
134	C₂×C₄	C₂×C₄⋊Dic₁₁	1	12	yes	—
135	C₂×C₄	C₂×C₄⋊Dic₁₁	1	12	yes	—
136	C₂×C₄	C₂×C₄⋊Dic₁₁	1	6	yes	—
137	C₂×C₄	C₂²×Dic₂₂	1	3	yes	—
138	C₂×C₄	C₂²×D₄₄	1	3	yes	—
139	C₈	—	44	8	no	—
140	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	12	yes	—
141	C₂²	#10622537	1	12	yes	—
142	C₂²	#10622548	1	4	yes	—
143	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
144	C₂²	C₂²×#4318	1	3	yes	—
145	C₂²	C₂²×C₄⋊Dic₁₁	1	3	yes	—
146	C₄	—	2	12	no	—
147	C₄	C₂×C₄⋊(C₁₁⋊C₈)	1	24	yes	complemented
148	C₄	#10622548	1	4	yes	—
149	C₄	C₂×#66922	1	3	yes	—
150	C₄	C₂×#66927	1	1	yes	characteristic
151	C₂	#13068768	1	8	yes	direct product factor
152	C₂	C₂×#10622548	1	1	yes	characteristic
153	C₂	C₂²×C₄⋊(C₁₁⋊C₈)	1	3	yes	—
154	C₂	C₂×#10622537	1	3	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₁
commutator	C₂²×C₁₁	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₂×C₄³×C₁₁	C₂
socle, prime radical	C₂⁴×C₁₁	C₂²×C₄
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	C₂×C₄³	D₁₁
hypocenter	C₁₁	C₂×#1842
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
2. #13068768	C₂	direct (N × H)
16. C₂×C₄²×C₁₁	C₈	semidirect
41. C₄²×C₁₁	C₂×C₈	semidirect
55. C₂×C₄×C₁₁	C₄⋊C₈	semidirect
82. C₄×C₁₁	C₂×C₄⋊C₈	semidirect
91. C₂×C₄²	C₁₁⋊C₈	semidirect
99. C₂×C₁₁	#1842	semidirect
118. C₄²	C₂×C₁₁⋊C₈	semidirect
122. C₁₁	C₂×#1842	semidirect
129. C₂×C₄	C₄⋊(C₁₁⋊C₈)	semidirect
147. C₄	C₂×C₄⋊(C₁₁⋊C₈)	semidirect
151. C₂	#13068768	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄⋊(C₁₁⋊C₈)	2
#13068768	2
C₂×C₄³×C₁₁	2
C₂×#1842	11

Subgroups — C2×#13068768 #14754152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13068768 #14754152