Subgroups — C₉×#2987 #11767708

Order 1152.

471 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	C₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₉×#446	C₂	1	8	yes	maximal, complemented
3	C₉×#433	C₂	1	4	yes	maximal
4	C₉×#432	C₂	1	2	yes	maximal
5	C₃×#2987	C₃	1	1	yes	maximal, characteristic
6	C₉×C₄⋊Q₈	C₄	1	2	yes	—
7	C₉×#125	C₄	1	2	yes	—
8	C₉×C₂²⋊Q₈	C₄	1	4	yes	—
9	C₄×Q₈×C₉	C₂²	1	4	yes	—
10	C₉×#117	C₂²	1	2	yes	—
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₉×C₄⋊C₈	C₂²	1	4	yes	—
13	C₉×C₄⋊C₈	C₂²	1	8	yes	—
14	C₉×C₂²⋊C₈	C₂²	1	4	yes	—
15	C₉×#97	C₂²	1	4	yes	—
16	C₉×#97	C₂²	1	4	yes	—
17	C₄×C₈×C₉	C₂²	1	4	yes	—
18	C₃×#533	C₂×C₃	1	1	yes	characteristic
19	C₃×#446	C₂×C₃	1	8	yes	—
20	C₃×#433	C₂×C₃	1	4	yes	—
21	C₃×#432	C₂×C₃	1	2	yes	—
22	C₂×Q₈×C₉	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₉	C₂³	1	8	yes	—
26	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
27	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
28	C₉×C₄⋊C₄	C₂×C₄	1	4	yes	—
29	C₉×C₂²⋊C₄	C₂×C₄	1	4	yes	—
30	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
32	C₄²×C₉	C₂³	1	2	yes	—
33	C₄²×C₉	C₂³	1	4	yes	—
34	#2987	C₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₃×C₄⋊Q₈	C₃×C₄	1	2	yes	—
36	C₃×#125	C₃×C₄	1	2	yes	—
37	C₃×C₂²⋊Q₈	C₃×C₄	1	4	yes	—
38	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
39	C₃×#117	C₂²×C₃	1	2	yes	—
40	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
42	C₃×C₄⋊C₈	C₂²×C₃	1	8	yes	—
43	C₃×C₂²⋊C₈	C₂²×C₃	1	4	yes	—
44	C₃×#97	C₂²×C₃	1	4	yes	—
45	C₃×#97	C₂²×C₃	1	4	yes	—
46	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
47	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
48	Q₈×C₉	—	4	4	no	—
49	C₂×C₄×C₉	—	2	2	no	—
50	C₂×C₄×C₉	—	4	2	no	—
51	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
53	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
54	C₂×C₄×C₉	C₂²×C₄	1	8	yes	—
55	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
56	C₈×C₉	—	2	8	no	—
57	#533	C₂×C₉	1	1	yes	characteristic
58	#446	C₂×C₉	1	8	yes	complemented
59	#433	C₂×C₉	1	4	yes	—
60	#432	C₂×C₉	1	2	yes	—
61	C₂×C₃×Q₈	C₂×C₃×C₄	1	4	yes	—
62	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
63	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
64	C₂×C₃×C₈	C₂³×C₃	1	8	yes	—
65	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
66	C₃×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
67	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
68	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
69	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
70	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
71	C₃×C₄²	C₂³×C₃	1	4	yes	—
72	C₃×C₄²	C₂³×C₃	1	2	yes	—
73	C₂²×C₉	—	2	1	no	—
74	C₂²×C₉	—	2	2	no	—
75	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
76	C₄×C₉	—	2	1	no	—
77	C₄×C₉	—	2	2	no	—
78	C₄×C₉	—	2	2	no	—
79	C₄×C₉	—	2	8	no	—
80	C₄×C₉	2₋¹⁺⁴	1	2	yes	—
81	C₄⋊Q₈	C₄×C₉	1	2	yes	—
82	#125	C₄×C₉	1	2	yes	—
83	C₂²⋊Q₈	C₄×C₉	1	4	yes	—
84	C₄×Q₈	C₂²×C₉	1	4	yes	—
85	#117	C₂²×C₉	1	2	yes	—
86	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
87	C₄⋊C₈	C₂²×C₉	1	4	yes	—
88	C₄⋊C₈	C₂²×C₉	1	8	yes	—
89	C₂²⋊C₈	C₂²×C₉	1	4	yes	—
90	#97	C₂²×C₉	1	4	yes	—
91	#97	C₂²×C₉	1	4	yes	—
92	C₄×C₈	C₂²×C₉	1	4	yes	—
93	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
94	C₃×Q₈	—	4	4	no	—
95	C₂×C₃×C₄	—	2	2	no	—
96	C₂×C₃×C₄	—	4	2	no	—
97	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
98	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
99	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
100	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
101	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
102	C₃×C₈	—	2	8	no	—
103	C₂×C₉	—	4	1	no	—
104	C₂×C₉	#519	1	1	yes	characteristic
105	C₂×C₉	#568	1	2	yes	—
106	C₂×Q₈	C₂×C₄×C₉	1	4	yes	—
107	C₂²×C₄	C₂×C₄×C₉	1	2	yes	—
108	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
109	C₂×C₈	C₂³×C₉	1	8	yes	—
110	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
111	C₄⋊C₄	C₂×C₄×C₉	1	8	yes	—
112	C₄⋊C₄	C₂×C₄×C₉	1	4	yes	—
113	C₂²⋊C₄	C₂×C₄×C₉	1	4	yes	—
114	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
115	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
116	C₄²	C₂³×C₉	1	4	yes	—
117	C₄²	C₂³×C₉	1	2	yes	—
118	C₂²×C₃	—	2	2	no	—
119	C₂²×C₃	—	2	1	no	—
120	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
121	C₃×C₄	—	2	2	no	—
122	C₃×C₄	—	2	2	no	—
123	C₃×C₄	—	2	8	no	—
124	C₃×C₄	—	2	1	no	—
125	C₃×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
126	C₉	#2987	1	1	yes	characteristic, direct product factor, Sylow
127	C₂³	C₂²×C₄×C₉	1	1	yes	characteristic
128	Q₈	—	4	4	no	—
129	C₂×C₄	—	2	2	no	—
130	C₂×C₄	—	4	2	no	—
131	C₂×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
132	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
133	C₂×C₄	C₂²×C₄×C₉	1	2	yes	—
134	C₂×C₄	C₂²×C₄×C₉	1	8	yes	—
135	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
136	C₈	—	2	8	no	—
137	C₂×C₃	—	4	1	no	—
138	C₂×C₃	C₃×#519	1	1	yes	characteristic
139	C₂×C₃	C₃×#568	1	2	yes	—
140	C₂²	—	2	2	no	—
141	C₂²	—	2	1	no	—
142	C₂²	C₂³×C₄×C₉	1	1	yes	characteristic
143	C₄	—	2	2	no	—
144	C₄	—	2	2	no	—
145	C₄	—	2	8	no	—
146	C₄	—	2	1	no	—
147	C₄	C₉×2₋¹⁺⁴	1	2	yes	—
148	C₃	C₃×#2987	1	1	yes	characteristic
149	C₂	—	4	1	no	—
150	C₂	C₉×#519	1	1	yes	characteristic
151	C₂	C₉×#568	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₉×#446	C₂	semidirect
34. #2987	C₉	direct (N × H)
58. #446	C₂×C₉	semidirect
126. C₉	#2987	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×#533	2
C₉×#446	2
C₉×#433	2
C₉×#432	2
C₃×#2987	3

Subgroups — C9×#2987 #11767708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2987 #11767708