Subgroups — C₉×#2402 #11767123

Order 1152.

600 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#400	C₂	1	4	yes	maximal
2	C₉×#398	C₂	1	4	yes	maximal
3	C₄×C₉×C₄⋊C₄	C₂	1	4	yes	maximal
4	C₄×C₉×C₄⋊C₄	C₂	1	2	yes	maximal
5	C₉×#376	C₂	1	1	yes	maximal, characteristic
6	C₃×#2402	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
9	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×C₄²×C₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₉×#95	C₂²	1	4	yes	—
14	C₉×#95	C₂²	1	2	yes	—
15	C₉×#95	C₂²	1	4	yes	—
16	C₉×#95	C₂²	1	4	yes	—
17	C₉×#95	C₂²	1	2	yes	—
18	C₃×#400	C₂×C₃	1	4	yes	—
19	C₃×#398	C₂×C₃	1	4	yes	—
20	C₃×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	—
21	C₃×C₄×C₄⋊C₄	C₂×C₃	1	4	yes	—
22	C₃×#376	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₄×C₉	C₂³	1	4	yes	—
24	C₂²×C₄×C₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₉	C₂³	1	4	yes	—
27	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
28	C₉×C₄⋊C₄	—	2	8	no	—
29	C₉×C₄⋊C₄	—	2	8	no	—
30	C₉×C₄⋊C₄	—	2	8	no	—
31	C₄²×C₉	—	2	8	no	—
32	C₄²×C₉	—	2	4	no	—
33	C₄²×C₉	Q₈	1	4	yes	—
34	#2402	C₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
36	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
37	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
38	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
39	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
40	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₃×#95	C₂²×C₃	1	4	yes	—
42	C₃×#95	C₂²×C₃	1	2	yes	—
43	C₃×#95	C₂²×C₃	1	4	yes	—
44	C₃×#95	C₂²×C₃	1	4	yes	—
45	C₃×#95	C₂²×C₃	1	2	yes	—
46	C₂³×C₉	C₂⁴	1	1	yes	characteristic
47	C₂×C₄×C₉	—	2	4	no	—
48	C₂×C₄×C₉	—	2	4	no	—
49	C₂×C₄×C₉	—	2	4	no	—
50	C₂×C₄×C₉	—	2	4	no	—
51	C₂×C₄×C₉	—	2	4	no	—
52	C₂×C₄×C₉	—	2	4	no	—
53	C₂×C₄×C₉	—	2	4	no	—
54	C₂×C₄×C₉	—	2	4	no	—
55	C₂×C₄×C₉	—	2	4	no	—
56	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
57	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
58	C₂×C₄×C₉	#41	1	8	yes	—
59	C₂×C₄×C₉	#41	1	4	yes	—
60	#400	C₂×C₉	1	4	yes	—
61	#398	C₂×C₉	1	4	yes	—
62	C₄×C₄⋊C₄	C₂×C₉	1	2	yes	—
63	C₄×C₄⋊C₄	C₂×C₉	1	4	yes	—
64	#376	C₂×C₉	1	1	yes	characteristic
65	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
66	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
67	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
68	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
69	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
70	C₃×C₄⋊C₄	—	2	8	no	—
71	C₃×C₄⋊C₄	—	2	8	no	—
72	C₃×C₄⋊C₄	—	2	8	no	—
73	C₃×C₄²	—	2	8	no	—
74	C₃×C₄²	—	2	4	no	—
75	C₃×C₄²	C₃×Q₈	1	4	yes	—
76	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
77	C₂²×C₉	C₂×#41	1	2	yes	—
78	C₂²×C₉	C₂×#41	1	4	yes	—
79	C₄×C₉	—	2	8	no	—
80	C₄×C₉	—	2	4	no	—
81	C₄×C₉	—	4	4	no	—
82	C₄×C₉	—	4	4	no	—
83	C₄×C₉	#125	1	4	yes	—
84	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
85	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
86	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
87	C₂×C₄²	C₂²×C₉	1	2	yes	—
88	C₂×C₄²	C₂²×C₉	1	4	yes	—
89	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
90	#95	C₂²×C₉	1	4	yes	—
91	#95	C₂²×C₉	1	2	yes	—
92	#95	C₂²×C₉	1	4	yes	—
93	#95	C₂²×C₉	1	4	yes	—
94	#95	C₂²×C₉	1	2	yes	—
95	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
96	C₂×C₃×C₄	—	2	4	no	—
97	C₂×C₃×C₄	—	2	4	no	—
98	C₂×C₃×C₄	—	2	4	no	—
99	C₂×C₃×C₄	—	2	4	no	—
100	C₂×C₃×C₄	—	2	4	no	—
101	C₂×C₃×C₄	—	2	4	no	—
102	C₂×C₃×C₄	—	2	4	no	—
103	C₂×C₃×C₄	—	2	4	no	—
104	C₂×C₃×C₄	—	2	4	no	—
105	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
106	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
107	C₂×C₃×C₄	C₃×#41	1	8	yes	—
108	C₂×C₃×C₄	C₃×#41	1	4	yes	—
109	C₂×C₉	C₂×#125	1	1	yes	characteristic
110	C₂×C₉	#529	1	4	yes	—
111	C₂×C₉	#533	1	2	yes	—
112	C₂²×C₄	C₂³×C₉	1	4	yes	—
113	C₂²×C₄	C₂³×C₉	1	4	yes	—
114	C₂²×C₄	C₂³×C₉	1	2	yes	—
115	C₂²×C₄	C₂³×C₉	1	4	yes	—
116	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
117	C₄⋊C₄	—	2	8	no	—
118	C₄⋊C₄	—	2	8	no	—
119	C₄⋊C₄	—	2	8	no	—
120	C₄²	—	2	8	no	—
121	C₄²	—	2	4	no	—
122	C₄²	Q₈×C₉	1	4	yes	—
123	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
124	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
125	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
126	C₃×C₄	—	2	8	no	—
127	C₃×C₄	—	2	4	no	—
128	C₃×C₄	—	4	4	no	—
129	C₃×C₄	—	4	4	no	—
130	C₃×C₄	C₃×#125	1	4	yes	—
131	C₉	#2402	1	1	yes	characteristic, direct product factor, Sylow
132	C₂³	C₂⁴×C₉	1	1	yes	characteristic
133	C₂×C₄	—	2	4	no	—
134	C₂×C₄	—	2	4	no	—
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	—	2	4	no	—
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	2	4	no	—
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	2	4	no	—
141	C₂×C₄	—	2	4	no	—
142	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
143	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
144	C₂×C₄	C₉×#41	1	8	yes	—
145	C₂×C₄	C₉×#41	1	4	yes	—
146	C₂×C₃	C₂×C₃×#125	1	1	yes	characteristic
147	C₂×C₃	C₃×#529	1	4	yes	—
148	C₂×C₃	C₃×#533	1	2	yes	—
149	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
150	C₂²	C₂×C₉×#41	1	2	yes	—
151	C₂²	C₂×C₉×#41	1	4	yes	—
152	C₄	—	2	8	no	—
153	C₄	—	2	4	no	—
154	C₄	—	4	4	no	—
155	C₄	—	4	4	no	—
156	C₄	C₉×#125	1	4	yes	—
157	C₃	C₃×#2402	1	1	yes	characteristic
158	C₂	C₂×C₉×#125	1	1	yes	characteristic
159	C₂	C₉×#529	1	4	yes	—
160	C₂	C₉×#533	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
34. #2402	C₉	direct (N × H)
131. C₉	#2402	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#400	2
C₉×#398	2
C₄×C₉×C₄⋊C₄	2
C₉×#376	2
C₃×#2402	3

Subgroups — C9×#2402 #11767123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2402 #11767123