Subgroups — C₄×C₉×#127 #11767027

Order 1152.

1386 conjugacy classes of subgroups.

The subgroup lattice has 171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄×C₉	C₂	1	6	yes	maximal, complemented
3	C₉×#390	C₂	1	6	yes	maximal, complemented
4	C₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄³×C₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₄×#127	C₃	1	1	yes	maximal, characteristic
7	C₂²×D₄×C₉	C₂²	1	6	yes	—
8	C₂³×C₄×C₉	C₂²	1	4	yes	—
9	C₉×#127	C₄	1	8	yes	direct product factor
10	C₄×D₄×C₉	—	2	24	no	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	6	yes	—
12	C₂×C₉×C₂²⋊C₄	C₂²	1	12	yes	—
13	C₂×C₄²×C₉	C₂²	1	3	yes	—
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₉	C₂²	1	3	yes	—
16	C₂×C₃×#127	C₂×C₃	1	1	yes	characteristic
17	C₂×C₃×C₄×D₄	C₂×C₃	1	6	yes	—
18	C₃×#390	C₂×C₃	1	6	yes	—
19	C₃×#384	C₂×C₃	1	1	yes	characteristic
20	C₃×C₄³	C₂×C₃	1	1	yes	characteristic
21	C₂⁴×C₉	C₂³	1	4	yes	—
22	C₂×D₄×C₉	—	2	12	no	—
23	C₂×D₄×C₉	—	2	12	no	—
24	C₂×D₄×C₉	C₂×C₄	1	24	yes	complemented
25	C₂²×C₄×C₉	—	2	24	no	—
26	C₂²×C₄×C₉	C₂³	1	4	yes	—
27	C₂²×C₄×C₉	C₂³	1	3	yes	—
28	C₂²×C₄×C₉	C₂³	1	3	yes	—
29	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₉×C₄⋊C₄	—	2	12	no	—
31	C₉×C₂²⋊C₄	—	2	24	no	—
32	C₄²×C₉	—	2	6	no	—
33	C₄²×C₉	C₂×C₄	1	4	yes	complemented
34	C₄²×C₉	D₄	1	12	yes	complemented
35	C₄×#127	C₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₃×D₄	C₂²×C₃	1	6	yes	—
37	C₂³×C₃×C₄	C₂²×C₃	1	4	yes	—
38	C₃×#127	C₃×C₄	1	8	yes	—
39	C₃×C₄×D₄	—	2	24	no	—
40	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	6	yes	—
41	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	12	yes	—
42	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	—
43	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
44	C₂×C₃×C₄²	C₂²×C₃	1	3	yes	—
45	C₂³×C₉	—	2	12	no	—
46	C₂³×C₉	—	2	12	no	—
47	C₂³×C₉	C₂²×C₄	1	8	yes	—
48	C₂³×C₉	C₂⁴	1	1	yes	characteristic
49	D₄×C₉	—	2	48	no	—
50	C₂×C₄×C₉	—	2	6	no	—
51	C₂×C₄×C₉	—	2	12	no	—
52	C₂×C₄×C₉	—	4	16	no	—
53	C₂×C₄×C₉	C₂²×C₄	1	6	yes	—
54	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
55	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
56	C₂×C₄×C₉	C₂×D₄	1	6	yes	—
57	C₂×C₄×C₉	#41	1	6	yes	—
58	C₂×#127	C₂×C₉	1	1	yes	characteristic
59	C₂×C₄×D₄	C₂×C₉	1	6	yes	complemented
60	#390	C₂×C₉	1	6	yes	complemented
61	#384	C₂×C₉	1	1	yes	characteristic, complemented
62	C₄³	C₂×C₉	1	1	yes	characteristic, complemented
63	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
64	C₂×C₃×D₄	—	2	12	no	—
65	C₂×C₃×D₄	—	2	12	no	—
66	C₂×C₃×D₄	C₂×C₃×C₄	1	24	yes	—
67	C₂²×C₃×C₄	—	2	24	no	—
68	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
69	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
70	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
71	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
72	C₃×C₄⋊C₄	—	2	12	no	—
73	C₃×C₂²⋊C₄	—	2	24	no	—
74	C₃×C₄²	—	2	6	no	—
75	C₃×C₄²	C₂×C₃×C₄	1	4	yes	—
76	C₃×C₄²	C₃×D₄	1	12	yes	—
77	C₂²×C₉	—	2	24	no	—
78	C₂²×C₉	—	4	4	no	—
79	C₂²×C₉	—	4	12	no	—
80	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
81	C₂²×C₉	C₂²×D₄	1	3	yes	—
82	C₂²×C₉	C₂×#41	1	3	yes	—
83	C₄×C₉	—	2	6	no	—
84	C₄×C₉	—	4	4	no	—
85	C₄×C₉	C₄×D₄	1	12	yes	complemented
86	C₄×C₉	#127	1	4	yes	direct product factor
87	C₂²×D₄	C₂²×C₉	1	6	yes	—
88	C₂³×C₄	C₂²×C₉	1	4	yes	—
89	#127	C₄×C₉	1	8	yes	direct product factor
90	C₄×D₄	—	2	24	no	—
91	C₂×C₄⋊C₄	C₂²×C₉	1	6	yes	—
92	C₂×C₂²⋊C₄	C₂²×C₉	1	12	yes	—
93	C₂×C₄²	C₂²×C₉	1	3	yes	—
94	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
95	C₂×C₄²	C₂²×C₉	1	3	yes	—
96	C₂³×C₃	—	2	12	no	—
97	C₂³×C₃	—	2	12	no	—
98	C₂³×C₃	C₂²×C₃×C₄	1	8	yes	—
99	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
100	C₃×D₄	—	2	48	no	—
101	C₂×C₃×C₄	—	2	6	no	—
102	C₂×C₃×C₄	—	2	12	no	—
103	C₂×C₃×C₄	—	4	16	no	—
104	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
105	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
106	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
107	C₂×C₃×C₄	C₂×C₃×D₄	1	6	yes	—
108	C₂×C₃×C₄	C₃×#41	1	6	yes	—
109	C₂×C₉	—	4	8	no	—
110	C₂×C₉	C₂×C₄×D₄	1	3	yes	—
111	C₂×C₉	C₂×#127	1	1	yes	characteristic
112	C₂×C₉	#532	1	3	yes	—
113	C₂⁴	C₂³×C₉	1	4	yes	—
114	C₂×D₄	—	2	12	no	—
115	C₂×D₄	—	2	12	no	—
116	C₂×D₄	C₂×C₄×C₉	1	24	yes	complemented
117	C₂²×C₄	—	2	24	no	—
118	C₂²×C₄	C₂³×C₉	1	4	yes	—
119	C₂²×C₄	C₂³×C₉	1	3	yes	—
120	C₂²×C₄	C₂³×C₉	1	3	yes	—
121	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
122	C₄⋊C₄	—	2	12	no	—
123	C₂²⋊C₄	—	2	24	no	—
124	C₄²	—	2	6	no	—
125	C₄²	C₂×C₄×C₉	1	4	yes	complemented
126	C₄²	D₄×C₉	1	12	yes	complemented
127	C₂²×C₃	—	2	24	no	—
128	C₂²×C₃	—	4	4	no	—
129	C₂²×C₃	—	4	12	no	—
130	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
131	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
132	C₂²×C₃	C₂×C₃×#41	1	3	yes	—
133	C₃×C₄	—	2	6	no	—
134	C₃×C₄	—	4	4	no	—
135	C₃×C₄	C₃×C₄×D₄	1	12	yes	—
136	C₃×C₄	C₃×#127	1	4	yes	—
137	C₉	C₄×#127	1	1	yes	characteristic, direct product factor, Sylow
138	C₂³	—	2	12	no	—
139	C₂³	—	2	12	no	—
140	C₂³	C₂²×C₄×C₉	1	8	yes	—
141	C₂³	C₂⁴×C₉	1	1	yes	characteristic
142	D₄	—	2	48	no	—
143	C₂×C₄	—	2	6	no	—
144	C₂×C₄	—	2	12	no	—
145	C₂×C₄	—	4	16	no	—
146	C₂×C₄	C₂²×C₄×C₉	1	6	yes	—
147	C₂×C₄	C₂×D₄×C₉	1	6	yes	—
148	C₂×C₄	C₂×D₄×C₉	1	6	yes	—
149	C₂×C₄	C₂×D₄×C₉	1	6	yes	—
150	C₂×C₄	C₉×#41	1	6	yes	—
151	C₂×C₃	—	4	8	no	—
152	C₂×C₃	C₂×C₃×C₄×D₄	1	3	yes	—
153	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
154	C₂×C₃	C₃×#532	1	3	yes	—
155	C₂²	—	2	24	no	—
156	C₂²	—	4	4	no	—
157	C₂²	—	4	12	no	—
158	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
159	C₂²	C₂²×D₄×C₉	1	3	yes	—
160	C₂²	C₂×C₉×#41	1	3	yes	—
161	C₄	—	2	6	no	—
162	C₄	—	4	4	no	—
163	C₄	C₄×D₄×C₉	1	12	yes	complemented
164	C₄	C₉×#127	1	4	yes	direct product factor
165	C₃	C₃×C₄×#127	1	1	yes	characteristic
166	C₂	—	4	8	no	—
167	C₂	C₂×C₄×D₄×C₉	1	3	yes	—
168	C₂	C₂×C₉×#127	1	1	yes	characteristic
169	C₂	C₉×#532	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#127	C₂×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄×C₉	C₂	semidirect
3. C₉×#390	C₂	semidirect
4. C₉×#384	C₂	semidirect
5. C₄³×C₉	C₂	semidirect
9. C₉×#127	C₄	direct (N × H)
24. C₂×D₄×C₉	C₂×C₄	semidirect
33. C₄²×C₉	C₂×C₄	semidirect
34. C₄²×C₉	D₄	semidirect
35. C₄×#127	C₉	direct (N × H)
59. C₂×C₄×D₄	C₂×C₉	semidirect
60. #390	C₂×C₉	semidirect
61. #384	C₂×C₉	semidirect
62. C₄³	C₂×C₉	semidirect
85. C₄×C₉	C₄×D₄	semidirect
86. C₄×C₉	#127	direct (N × H)
89. #127	C₄×C₉	direct (N × H)
116. C₂×D₄	C₂×C₄×C₉	semidirect
125. C₄²	C₂×C₄×C₉	semidirect
126. C₄²	D₄×C₉	semidirect
137. C₉	C₄×#127	direct (N × H)
163. C₄	C₄×D₄×C₉	semidirect
164. C₄	C₉×#127	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×C₉×#127	2
C₂×C₄×D₄×C₉	2
C₉×#390	2
C₉×#384	2
C₄³×C₉	2
C₃×C₄×#127	3

Subgroups — C4×C9×#127 #11767027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×#127 #11767027