Subgroups — C₄×#10622150 #14668600

Order 2816.

418 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622150	C₂	1	4	yes	maximal
2	C₄×#66876	C₂	1	1	yes	maximal, characteristic
3	C₄×#66879	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×#66879	C₄	1	2	yes	—
8	C₂×#66879	C₂²	1	2	yes	—
9	C₂×#66876	C₂²	1	2	yes	—
10	C₄²×Dic₁₁	C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
12	C₁₁×#346	C₄	1	2	yes	complemented
13	C₄×C₁₁×C₁₆	C₄	1	2	yes	complemented
14	#10622150	C₄	1	16	yes	direct product factor
15	#10622099	C₄	1	2	yes	complemented
16	C₄×C₁₁⋊C₁₆	C₄	1	2	yes	complemented
17	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₁	—	2	2	no	—
21	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
22	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
23	C₁₁×M₃₂	C₂×C₄	1	8	yes	—
24	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
25	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	#66879	—	2	4	no	—
30	#66879	C₂×C₄	1	8	yes	—
31	#66876	C₂×C₄	1	8	yes	—
32	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
33	C₄×C₁₁⋊C₈	—	2	2	no	—
34	C₄×#347	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
37	C₂²×Dic₁₁	—	2	2	no	—
38	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
40	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
41	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
43	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₄²×C₁₁	C₄²	1	1	yes	characteristic
45	C₄²×C₁₁	C₄²	1	1	yes	characteristic
46	C₄²×C₁₁	M₁₆	1	2	yes	—
47	C₄×Dic₁₁	—	2	2	no	—
48	C₄×Dic₁₁	—	4	4	no	—
49	C₄×Dic₁₁	C₄²	1	4	yes	—
50	C₂×C₁₁⋊C₈	—	2	2	no	—
51	C₂×C₁₁⋊C₈	—	2	2	no	—
52	C₂×C₁₁⋊C₈	C₄²	1	4	yes	—
53	C₁₁×C₁₆	C₄²	1	8	yes	complemented
54	C₁₁⋊C₁₆	C₄²	1	8	yes	complemented
55	C₂×#347	—	11	4	no	—
56	C₄×M₃₂	—	11	1	no	—
57	C₄×M₃₂	D₁₁	1	1	yes	characteristic
58	C₄×#97	—	11	1	no	—
59	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
60	C₂×C₄×C₁₁	—	2	4	no	—
61	C₂×C₄×C₁₁	#97	1	2	yes	—
62	C₂×C₄×C₁₁	#97	1	2	yes	—
63	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
64	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
66	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
67	C₂×Dic₁₁	—	2	4	no	—
68	C₂×Dic₁₁	—	4	4	no	—
69	C₈×C₁₁	#97	1	2	yes	—
70	C₈×C₁₁	#97	1	2	yes	—
71	C₈×C₁₁	C₂×C₄²	1	2	yes	—
72	C₈×C₁₁	C₂×C₄²	1	2	yes	—
73	C₁₁⋊C₈	—	2	4	no	—
74	C₂×M₃₂	—	11	2	no	—
75	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
76	C₂×#97	—	11	2	no	—
77	C₂×#97	—	11	2	no	—
78	C₂×C₄×C₈	—	11	1	no	—
79	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
80	C₄³	—	11	1	no	—
81	#347	—	11	16	no	—
82	#346	—	11	2	no	—
83	#346	Dic₁₁	1	2	yes	complemented
84	C₄×C₁₆	—	11	2	no	—
85	C₄×C₁₆	Dic₁₁	1	2	yes	complemented
86	C₂²×C₁₁	—	2	2	no	—
87	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
88	C₂²×C₁₁	C₄×M₁₆	1	2	yes	—
89	C₄×C₁₁	—	2	2	no	—
90	C₄×C₁₁	#347	1	4	yes	complemented
91	C₄×C₁₁	C₄³	1	1	yes	characteristic
92	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
93	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
94	Dic₁₁	—	4	4	no	—
95	C₂²×C₈	—	11	2	no	—
96	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
97	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
98	C₂×C₄²	—	11	2	no	—
99	C₂×C₄²	—	22	2	no	—
100	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
101	M₃₂	—	11	8	no	—
102	M₃₂	C₄×D₁₁	1	8	yes	—
103	C₂×C₁₆	—	11	4	no	—
104	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	—
105	#97	—	11	8	no	—
106	#97	—	22	4	no	—
107	C₄×C₈	—	22	2	no	—
108	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
109	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
110	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
111	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
112	C₂×C₁₁	—	2	2	no	—
113	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
114	C₂×C₁₁	C₂×#347	1	2	yes	—
115	C₂²×C₄	—	22	2	no	—
116	C₂²×C₄	#4313	1	2	yes	—
117	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
118	C₂×C₈	—	11	4	no	—
119	C₂×C₈	—	22	2	no	—
120	C₂×C₈	—	22	2	no	—
121	C₂×C₈	#4313	1	4	yes	—
122	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
123	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
124	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
125	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
126	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
127	C₄²	—	11	4	no	—
128	C₄²	—	22	2	no	—
129	C₄²	—	44	4	no	—
130	C₄²	#4313	1	2	yes	—
131	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
132	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
133	C₁₆	—	11	8	no	—
134	C₁₆	C₄×Dic₁₁	1	8	yes	complemented
135	C₁₁	C₄×#347	1	1	yes	characteristic, complemented, Sylow
136	C₂³	C₂×#4313	1	1	yes	characteristic
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	22	4	no	—
139	C₂×C₄	—	44	4	no	—
140	C₂×C₄	#66879	1	2	yes	—
141	C₂×C₄	#66879	1	2	yes	—
142	C₂×C₄	C₄²×D₁₁	1	2	yes	—
143	C₂×C₄	C₂×#4313	1	1	yes	characteristic
144	C₂×C₄	C₂×#4313	1	2	yes	—
145	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
146	C₈	—	22	4	no	—
147	C₈	#66879	1	2	yes	—
148	C₈	#66879	1	2	yes	—
149	C₈	C₄²×D₁₁	1	2	yes	—
150	C₈	C₂×C₄×Dic₁₁	1	2	yes	—
151	C₂²	—	2	2	no	—
152	C₂²	C₄×#4313	1	2	yes	—
153	C₂²	C₂×#66879	1	1	yes	characteristic
154	C₄	—	2	2	no	—
155	C₄	—	44	4	no	—
156	C₄	#10622150	1	4	yes	direct product factor
157	C₄	C₄×#4313	1	2	yes	—
158	C₄	C₄²×Dic₁₁	1	1	yes	characteristic
159	C₄	C₂×#66879	1	1	yes	characteristic
160	C₂	—	2	2	no	—
161	C₂	C₄×#66879	1	1	yes	characteristic
162	C₂	C₂×#10622150	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₁₁
commutator	C₄×C₁₁	C₄³
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×M₃₂	C₂
socle	C₂²×C₁₁	C₂×#97
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₄×M₃₂	D₁₁
hypocenter	C₁₁	C₄×#347
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
12. C₁₁×#346	C₄	semidirect
13. C₄×C₁₁×C₁₆	C₄	semidirect
14. #10622150	C₄	direct (N × H)
15. #10622099	C₄	semidirect
16. C₄×C₁₁⋊C₁₆	C₄	semidirect
53. C₁₁×C₁₆	C₄²	semidirect
54. C₁₁⋊C₁₆	C₄²	semidirect
83. #346	Dic₁₁	semidirect
85. C₄×C₁₆	Dic₁₁	semidirect
90. C₄×C₁₁	#347	semidirect
134. C₁₆	C₄×Dic₁₁	semidirect
135. C₁₁	C₄×#347	semidirect
156. C₄	#10622150	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×#10622150	2
C₄×#66876	2
C₄×#66879	2
C₄×C₁₁×M₃₂	2
C₄×#347	11

Subgroups — C4×#10622150 #14668600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10622150 #14668600