Subgroups — C₂×#13066684 #14665335

Order 2816.

222 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622101	C₂	1	2	yes	maximal
2	#13066684	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₁₁×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×#66876	—	2	2	no	—
8	C₁₁×#346	C₄	1	2	yes	—
9	C₁₁×#346	C₂²	1	2	yes	—
10	#10622101	—	2	2	no	—
11	#10622101	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
15	C₂×C₁₁×C₁₆	—	2	1	no	—
16	C₂×C₁₁×C₁₆	—	2	1	no	—
17	C₂×C₁₁×C₁₆	C₈	1	2	yes	—
18	C₂×C₁₁×C₁₆	C₈	1	2	yes	—
19	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
24	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
25	#66876	—	2	4	no	—
26	#66876	—	4	2	no	—
27	C₂×C₁₁⋊C₁₆	—	4	2	no	—
28	C₂×#1369	—	11	1	no	maximal, Sylow
29	C₂²×C₄×C₁₁	—	2	1	no	—
30	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
36	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
38	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
39	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
41	C₄²×C₁₁	—	2	1	no	—
42	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
43	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
44	C₁₁×C₁₆	—	2	2	no	—
45	C₁₁×C₁₆	C₂×C₈	1	4	yes	—
46	C₁₁⋊C₁₆	—	4	4	no	—
47	C₂×#364	—	11	2	no	—
48	C₂×#346	D₁₁	1	1	yes	characteristic
49	#1369	—	11	4	no	—
50	C₂³×C₁₁	#108	1	1	yes	characteristic
51	C₂×C₄×C₁₁	—	2	1	no	—
52	C₂×C₄×C₁₁	—	2	1	no	—
53	C₂×C₄×C₁₁	—	4	2	no	—
54	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
57	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
58	C₂×C₄×C₁₁	#108	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
60	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
61	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
62	C₈×C₁₁	#106	1	2	yes	—
63	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
64	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
65	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
66	C₂×M₃₂	—	22	2	no	—
67	C₂²×C₁₆	Dic₁₁	1	1	yes	characteristic
68	C₂²×C₁₆	Dic₁₁	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
70	#364	—	11	4	no	—
71	#364	—	22	2	no	—
72	#346	Dic₁₁	1	2	yes	—
73	#346	C₂×D₁₁	1	2	yes	—
74	C₂²×C₁₁	—	2	2	no	—
75	C₂²×C₁₁	#334	1	1	yes	characteristic
76	C₂²×C₁₁	#334	1	1	yes	characteristic
77	C₂²×C₁₁	C₂×#108	1	1	yes	characteristic
78	C₄×C₁₁	—	4	1	no	—
79	C₄×C₁₁	—	4	1	no	—
80	C₄×C₁₁	#334	1	1	yes	characteristic
81	C₄×C₁₁	#334	1	1	yes	characteristic
82	C₄×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
83	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
84	C₂²×C₈	D₄₄	1	1	yes	characteristic
85	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
86	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
87	M₃₂	—	22	4	no	—
88	M₃₂	—	44	2	no	—
89	C₂×C₁₆	—	2	1	no	—
90	C₂×C₁₆	—	2	1	no	—
91	C₂×C₁₆	—	44	2	no	—
92	C₂×C₁₆	C₁₁⋊C₈	1	2	yes	—
93	C₂×C₁₆	C₁₁⋊C₈	1	2	yes	—
94	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
95	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
96	C₄×C₈	Dic₂₂	1	1	yes	characteristic
97	C₄×C₈	D₄₄	1	1	yes	characteristic
98	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
99	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
100	C₂×C₁₁	—	2	1	no	—
101	C₂×C₁₁	—	2	1	no	—
102	C₂×C₁₁	#1369	1	2	yes	complemented
103	C₂×C₁₁	C₂×#334	1	1	yes	characteristic
104	C₂²×C₄	—	2	1	no	—
105	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
106	C₂×C₈	#4314	1	2	yes	—
107	C₂×C₈	#4314	1	2	yes	—
108	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
109	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
110	C₂×C₈	#4318	1	1	yes	characteristic
111	C₂×C₈	#4318	1	1	yes	characteristic
112	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
113	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
114	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
115	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
116	C₄²	—	2	1	no	—
117	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
118	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
119	C₁₆	—	2	2	no	—
120	C₁₆	—	44	4	no	—
121	C₁₆	C₂×C₁₁⋊C₈	1	4	yes	—
122	C₁₁	C₂×#1369	1	1	yes	characteristic, complemented, Sylow
123	C₂³	#66883	1	1	yes	characteristic
124	C₂×C₄	—	2	1	no	—
125	C₂×C₄	—	2	1	no	—
126	C₂×C₄	—	4	2	no	—
127	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
128	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
129	C₂×C₄	#66881	1	1	yes	characteristic
130	C₂×C₄	#66881	1	1	yes	characteristic
131	C₂×C₄	#66883	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
133	C₈	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
134	C₈	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
135	C₈	#66881	1	2	yes	—
136	C₈	C₂×#4314	1	2	yes	—
137	C₈	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
138	C₈	C₂×#4318	1	1	yes	characteristic
139	C₂²	—	2	2	no	—
140	C₂²	#10622095	1	1	yes	characteristic
141	C₂²	#10622095	1	1	yes	characteristic
142	C₂²	C₂×#66883	1	1	yes	characteristic
143	C₄	—	4	1	no	—
144	C₄	—	4	1	no	—
145	C₄	#10622095	1	1	yes	characteristic
146	C₄	#10622095	1	1	yes	characteristic
147	C₄	C₂×C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
148	C₄	C₂×#66881	1	1	yes	characteristic
149	C₂	—	2	1	no	—
150	C₂	—	2	1	no	—
151	C₂	#13066684	1	2	yes	direct product factor
152	C₂	C₂×#10622095	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#66881
commutator	C₈×C₁₁	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle	C₂²×C₁₁	#334
prime radical	C₂³×C₁₁	#108
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	C₂×#1369
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. #13066684	C₂	direct (N × H)
102. C₂×C₁₁	#1369	semidirect
122. C₁₁	C₂×#1369	semidirect
151. C₂	#13066684	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×#10622101	2
#13066684	2
C₂×C₁₁×#346	2
C₂×#1369	11

Subgroups — C2×#13066684 #14665335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066684 #14665335