Subgroups — C₄×#63371 #11795852

Order 1152.

294 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#63371	C₂	1	2	yes	maximal
3	#10588138	C₂	1	2	yes	maximal, complemented
4	C₄×C₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄×#812	—	3	1	no	maximal
6	C₂²×C₈×C₉	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₉	C₄	1	1	yes	characteristic
9	C₄×C₈×C₉	C₄	1	1	yes	characteristic
10	C₄×C₈×C₉	C₄	1	1	yes	characteristic
11	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
13	#63371	C₄	1	8	yes	direct product factor
14	C₂×C₉⋊C₁₆	C₂²	1	4	yes	—
15	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
16	C₂×#812	—	3	2	no	—
17	#4461	—	3	2	no	—
18	C₄×C₃⋊C₁₆	—	3	2	no	—
19	C₂²×C₄×C₉	C₈	1	2	yes	—
20	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₉	C₈	1	4	yes	—
22	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₉	C₂×C₄	1	4	yes	—
24	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
27	C₄²×C₉	C₈	1	2	yes	—
28	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
30	C₉⋊C₁₆	C₂×C₄	1	8	yes	complemented
31	C₄×M₃₂	—	9	1	no	Sylow
32	C₂²×C₃×C₈	Dic₃	1	1	yes	characteristic
33	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
34	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
35	C₃×C₄×C₈	Dic₃	1	1	yes	characteristic
36	C₃×C₄×C₈	Dic₃	1	1	yes	characteristic
37	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
38	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
39	#812	—	3	8	no	—
40	C₂×C₃⋊C₁₆	—	3	4	no	—
41	C₂³×C₉	C₂×C₈	1	1	yes	characteristic
42	C₂×C₄×C₉	—	2	4	no	—
43	C₂×C₄×C₉	C₄²	1	2	yes	—
44	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
45	C₂×C₄×C₉	C₂×C₈	1	1	yes	characteristic
46	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
47	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
48	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
49	C₈×C₉	C₄²	1	2	yes	—
50	C₈×C₉	C₂×C₈	1	2	yes	—
51	C₈×C₉	C₂×C₈	1	2	yes	—
52	C₈×C₉	C₂²×C₄	1	2	yes	—
53	C₂×M₃₂	—	9	2	no	—
54	C₂×C₄×C₈	D₉	1	1	yes	characteristic
55	#346	—	9	2	no	—
56	C₄×C₁₆	—	9	2	no	—
57	C₂²×C₃×C₄	C₃⋊C₈	1	2	yes	—
58	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
59	C₂×C₃×C₈	C₃⋊C₈	1	4	yes	—
60	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
61	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
62	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
63	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
64	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
65	C₃×C₄²	C₃⋊C₈	1	2	yes	—
66	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
67	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
68	C₃⋊C₁₆	—	3	8	no	—
69	C₂²×C₉	—	2	2	no	—
70	C₂²×C₉	C₄×C₈	1	2	yes	—
71	C₂²×C₉	C₂²×C₈	1	1	yes	characteristic
72	C₄×C₉	—	2	2	no	—
73	C₄×C₉	C₄×C₈	1	2	yes	—
74	C₄×C₉	M₃₂	1	4	yes	complemented
75	C₄×C₉	C₂×C₄²	1	1	yes	characteristic
76	C₄×C₉	C₂²×C₈	1	1	yes	characteristic
77	C₂²×C₈	Dic₉	1	1	yes	characteristic
78	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
79	C₂×C₄²	Dic₉	1	1	yes	characteristic
80	M₃₂	—	9	8	no	—
81	C₂×C₁₆	—	9	4	no	—
82	C₄×C₈	Dic₉	1	1	yes	characteristic
83	C₄×C₈	Dic₉	1	1	yes	characteristic
84	C₄×C₈	C₂×D₉	1	1	yes	characteristic
85	C₄×C₈	C₂×D₉	1	1	yes	characteristic
86	C₂³×C₃	C₂×C₃⋊C₈	1	1	yes	characteristic
87	C₂×C₃×C₄	—	2	4	no	—
88	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
89	C₂×C₃×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
90	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
91	C₂×C₃×C₄	C₂×C₃⋊C₈	1	2	yes	—
92	C₂×C₃×C₄	C₄×Dic₃	1	2	yes	—
93	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
94	C₃×C₈	C₂×C₃⋊C₈	1	2	yes	—
95	C₃×C₈	C₂×C₃⋊C₈	1	2	yes	—
96	C₃×C₈	C₄×Dic₃	1	2	yes	—
97	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
98	C₂×C₉	—	2	2	no	—
99	C₂×C₉	C₂×C₄×C₈	1	1	yes	characteristic
100	C₂×C₉	C₂×M₃₂	1	2	yes	—
101	C₂²×C₄	C₉⋊C₈	1	2	yes	—
102	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
103	C₂×C₈	C₉⋊C₈	1	4	yes	—
104	C₂×C₈	C₄×D₉	1	4	yes	—
105	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
106	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
107	C₂×C₈	C₂×Dic₉	1	1	yes	characteristic
108	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
109	C₄²	C₉⋊C₈	1	2	yes	—
110	C₄²	C₂×Dic₉	1	1	yes	characteristic
111	C₄²	C₂×Dic₉	1	1	yes	characteristic
112	C₁₆	—	9	8	no	—
113	C₂²×C₃	—	2	2	no	—
114	C₂²×C₃	C₄×C₃⋊C₈	1	2	yes	—
115	C₂²×C₃	C₂²×C₃⋊C₈	1	1	yes	characteristic
116	C₃×C₄	—	2	2	no	—
117	C₃×C₄	C₄×C₃⋊C₈	1	2	yes	—
118	C₃×C₄	#812	1	4	yes	—
119	C₃×C₄	C₂²×C₃⋊C₈	1	1	yes	characteristic
120	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
121	C₉	C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
122	C₂³	C₂×C₉⋊C₈	1	1	yes	characteristic
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	C₂×C₉⋊C₈	1	2	yes	—
125	C₂×C₄	C₂×C₉⋊C₈	1	1	yes	characteristic
126	C₂×C₄	C₂×C₉⋊C₈	1	2	yes	—
127	C₂×C₄	C₂×C₉⋊C₈	1	2	yes	—
128	C₂×C₄	C₄×Dic₉	1	2	yes	—
129	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
130	C₈	C₂×C₉⋊C₈	1	2	yes	—
131	C₈	C₂×C₉⋊C₈	1	2	yes	—
132	C₈	C₄×Dic₉	1	2	yes	—
133	C₈	C₂×C₄×D₉	1	2	yes	—
134	C₂×C₃	—	2	2	no	—
135	C₂×C₃	C₂×C₄×C₃⋊C₈	1	1	yes	characteristic
136	C₂×C₃	C₂×#812	1	2	yes	—
137	C₂²	—	2	2	no	—
138	C₂²	C₄×C₉⋊C₈	1	2	yes	—
139	C₂²	C₂²×C₉⋊C₈	1	1	yes	characteristic
140	C₄	—	2	2	no	—
141	C₄	C₄×C₉⋊C₈	1	2	yes	—
142	C₄	#63371	1	4	yes	direct product factor
143	C₄	C₂²×C₉⋊C₈	1	1	yes	characteristic
144	C₄	C₂×C₄×Dic₉	1	1	yes	characteristic
145	C₃	C₄×#812	1	1	yes	characteristic
146	C₂	—	2	2	no	—
147	C₂	C₂×C₄×C₉⋊C₈	1	1	yes	characteristic
148	C₂	C₂×#63371	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×D₉
commutator	C₂×C₉	C₂×C₄×C₈
Frattini	C₂×C₃×C₈	C₂²×D₃
Fitting	C₂×C₄×C₈×C₉	C₂
socle	C₂²×C₃	C₂²×C₃⋊C₈
prime radical	C₂³×C₃	C₂×C₃⋊C₈
cosocle	C₂×C₈×C₉	C₂³
hypercenter	C₂×C₄×C₈	D₉
hypocenter	C₉	C₄×M₃₂
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #10588138	C₂	semidirect
4. C₄×C₉⋊C₁₆	C₂	semidirect
13. #63371	C₄	direct (N × H)
30. C₉⋊C₁₆	C₂×C₄	semidirect
74. C₄×C₉	M₃₂	semidirect
121. C₉	C₄×M₃₂	semidirect
142. C₄	#63371	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×C₄×C₈×C₉	2
C₂×#63371	2
#10588138	2
C₄×C₉⋊C₁₆	2
C₄×#812	3

Subgroups — C4×#63371 #11795852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#63371 #11795852