Subgroups — C₂²×#63375 #11857117

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₉	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#63375	C₂	1	12	yes	maximal, direct product factor
5	C₂²×#815	—	3	1	no	maximal
6	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₂³×Dic₉	C₄	1	2	yes	—
8	C₂²×C₈×C₉	C₄	1	8	yes	complemented
9	C₂²×C₈×C₉	C₂²	1	6	yes	—
10	C₂×C₄×Dic₉	C₄	1	6	yes	—
11	C₂×C₄×Dic₉	C₂²	1	6	yes	—
12	C₂²×C₉⋊C₈	C₄	1	8	yes	complemented
13	C₂²×C₉⋊C₈	C₂²	1	6	yes	—
14	#63375	C₂²	1	16	yes	direct product factor
15	C₂³×C₃×C₈	D₃	1	1	yes	characteristic
16	C₂²×C₄×Dic₃	—	3	1	no	—
17	C₂³×C₃⋊C₈	—	3	1	no	—
18	C₂×#815	—	3	12	no	—
19	C₂⁴×C₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₉	C₂×C₄	1	3	yes	—
21	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
22	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₉	C₂³	1	3	yes	—
24	C₂²×Dic₉	—	2	8	no	—
25	C₂²×Dic₉	C₂×C₄	1	12	yes	—
26	C₂×C₈×C₉	C₂×C₄	1	24	yes	complemented
27	C₂×C₈×C₉	C₂³	1	4	yes	—
28	C₄×Dic₉	C₂×C₄	1	12	yes	—
29	C₄×Dic₉	C₂³	1	4	yes	—
30	C₂×C₉⋊C₈	C₂×C₄	1	24	yes	complemented
31	C₂×C₉⋊C₈	C₂³	1	4	yes	—
32	C₂²×#97	—	9	1	no	Sylow
33	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
34	C₂³×Dic₃	—	3	2	no	—
35	C₂²×C₃×C₈	Dic₃	1	8	yes	—
36	C₂²×C₃×C₈	C₂×D₃	1	6	yes	—
37	C₂×C₄×Dic₃	—	3	6	no	—
38	C₂×C₄×Dic₃	—	3	6	no	—
39	C₂²×C₃⋊C₈	—	3	8	no	—
40	C₂²×C₃⋊C₈	—	3	6	no	—
41	#815	—	3	16	no	—
42	C₂³×C₉	C₄²	1	4	yes	—
43	C₂³×C₉	M₁₆	1	8	yes	—
44	C₂³×C₉	C₂²×C₄	1	3	yes	—
45	C₂×C₄×C₉	C₄²	1	12	yes	—
46	C₂×C₄×C₉	C₂²×C₄	1	3	yes	—
47	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
48	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
49	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₉	—	2	24	no	—
51	C₂×Dic₉	C₂²×C₄	1	8	yes	—
52	C₈×C₉	C₂²×C₄	1	8	yes	complemented
53	C₉⋊C₈	C₂²×C₄	1	8	yes	complemented
54	C₂³×C₈	—	9	1	no	—
55	C₂³×C₈	D₉	1	1	yes	characteristic
56	C₂²×C₄²	—	9	1	no	—
57	C₂×#97	—	9	12	no	—
58	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
59	C₂²×C₃×C₄	C₄×D₃	1	3	yes	—
60	C₂²×C₃×C₄	C₄×D₃	1	4	yes	—
61	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
62	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
63	C₂²×Dic₃	—	3	12	no	—
64	C₂²×Dic₃	—	6	8	no	—
65	C₂×C₃×C₈	C₂×Dic₃	1	24	yes	—
66	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
67	C₄×Dic₃	—	3	12	no	—
68	C₄×Dic₃	—	3	4	no	—
69	C₂×C₃⋊C₈	—	3	24	no	—
70	C₂×C₃⋊C₈	—	3	4	no	—
71	C₂²×C₉	#97	1	16	yes	complemented
72	C₂²×C₉	C₂×C₄²	1	6	yes	—
73	C₂²×C₉	C₂×M₁₆	1	12	yes	—
74	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
75	C₄×C₉	C₂×C₄²	1	6	yes	—
76	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
77	C₄×C₉	C₂³×C₄	1	1	yes	characteristic
78	Dic₉	—	2	8	no	—
79	C₂³×C₄	—	9	2	no	—
80	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
81	C₂²×C₈	—	9	8	no	—
82	C₂²×C₈	—	9	6	no	—
83	C₂²×C₈	Dic₉	1	8	yes	complemented
84	C₂²×C₈	C₂×D₉	1	6	yes	—
85	C₂×C₄²	—	9	6	no	—
86	C₂×C₄²	—	9	6	no	—
87	#97	—	9	16	no	—
88	C₂³×C₃	ΓL(1,𝔽₂₅)	1	8	yes	—
89	C₂³×C₃	C₄×Dic₃	1	4	yes	—
90	C₂³×C₃	C₂×C₄×D₃	1	3	yes	—
91	C₂×C₃×C₄	C₄×Dic₃	1	12	yes	—
92	C₂×C₃×C₄	C₂×C₄×D₃	1	3	yes	—
93	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
94	C₂×C₃×C₄	C₂²×Dic₃	1	6	yes	—
95	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
96	C₂×Dic₃	—	3	8	no	—
97	C₂×Dic₃	—	6	24	no	—
98	C₃×C₈	C₂²×Dic₃	1	8	yes	—
99	C₃⋊C₈	—	3	8	no	—
100	C₂×C₉	C₂×#97	1	12	yes	complemented
101	C₂×C₉	C₂²×C₄²	1	1	yes	characteristic
102	C₂×C₉	C₂²×M₁₆	1	2	yes	—
103	C₂⁴	C₄×D₉	1	1	yes	characteristic
104	C₂²×C₄	—	9	12	no	—
105	C₂²×C₄	—	18	8	no	—
106	C₂²×C₄	C₄×D₉	1	3	yes	—
107	C₂²×C₄	C₄×D₉	1	4	yes	—
108	C₂²×C₄	C₂×Dic₉	1	4	yes	—
109	C₂²×C₄	C₂²×D₉	1	3	yes	—
110	C₂×C₈	—	9	24	no	—
111	C₂×C₈	—	9	4	no	—
112	C₂×C₈	C₂×Dic₉	1	24	yes	complemented
113	C₂×C₈	C₂²×D₉	1	4	yes	—
114	C₄²	—	9	12	no	—
115	C₄²	—	9	4	no	—
116	C₂²×C₃	#815	1	16	yes	—
117	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	12	yes	—
118	C₂²×C₃	C₂×C₄×Dic₃	1	6	yes	—
119	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
120	C₃×C₄	C₂×C₄×Dic₃	1	6	yes	—
121	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
122	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
123	Dic₃	—	6	8	no	—
124	C₉	C₂²×#97	1	1	yes	characteristic, complemented, Sylow
125	C₂³	#3663	1	8	yes	—
126	C₂³	C₄×Dic₉	1	4	yes	—
127	C₂³	C₂×C₄×D₉	1	3	yes	—
128	C₂×C₄	—	9	8	no	—
129	C₂×C₄	—	18	24	no	—
130	C₂×C₄	C₄×Dic₉	1	12	yes	—
131	C₂×C₄	C₂×C₄×D₉	1	6	yes	—
132	C₂×C₄	C₂×C₄×D₉	1	3	yes	—
133	C₂×C₄	C₂²×Dic₉	1	6	yes	—
134	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
135	C₈	—	9	8	no	—
136	C₈	C₂²×Dic₉	1	8	yes	complemented
137	C₂×C₃	C₂×#815	1	12	yes	—
138	C₂×C₃	C₂²×ΓL(1,𝔽₂₅)	1	2	yes	—
139	C₂×C₃	C₂²×C₄×Dic₃	1	1	yes	characteristic
140	C₂²	#63375	1	16	yes	direct product factor
141	C₂²	C₂×#3663	1	12	yes	—
142	C₂²	C₂×C₄×Dic₉	1	6	yes	—
143	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
144	C₄	—	18	8	no	—
145	C₄	C₂×C₄×Dic₉	1	6	yes	—
146	C₄	C₂²×C₄×D₉	1	1	yes	characteristic
147	C₄	C₂³×Dic₉	1	1	yes	characteristic
148	C₃	C₂²×#815	1	1	yes	characteristic
149	C₂	C₂×#63375	1	12	yes	direct product factor
150	C₂	C₂²×#3663	1	2	yes	—
151	C₂	C₂²×C₄×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×D₉
commutator	C₂×C₉	C₂²×C₄²
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂³×C₈×C₉	C₂
socle, prime radical	C₂⁴×C₃	C₄×D₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂³×C₈	D₉
hypocenter	C₉	C₂²×#97
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
4. C₂×#63375	C₂	direct (N × H)
8. C₂²×C₈×C₉	C₄	semidirect
12. C₂²×C₉⋊C₈	C₄	semidirect
14. #63375	C₂²	direct (N × H)
26. C₂×C₈×C₉	C₂×C₄	semidirect
30. C₂×C₉⋊C₈	C₂×C₄	semidirect
52. C₈×C₉	C₂²×C₄	semidirect
53. C₉⋊C₈	C₂²×C₄	semidirect
71. C₂²×C₉	#97	semidirect
83. C₂²×C₈	Dic₉	semidirect
100. C₂×C₉	C₂×#97	semidirect
112. C₂×C₈	C₂×Dic₉	semidirect
124. C₉	C₂²×#97	semidirect
136. C₈	C₂²×Dic₉	semidirect
140. C₂²	#63375	direct (N × H)
149. C₂	C₂×#63375	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈×C₉	2
C₂²×C₄×Dic₉	2
C₂³×C₉⋊C₈	2
C₂×#63375	2
C₂²×#815	3

Subgroups — C22×#63375 #11857117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#63375 #11857117