Subgroups — C₉×#2571 #11767292

Order 1152.

570 conjugacy classes of subgroups.

The subgroup lattice has 177 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×#389	C₂	1	4	yes	maximal
3	C₉×#384	C₂	1	1	yes	maximal, characteristic
4	C₉×#382	C₂	1	4	yes	maximal
5	C₄×C₉×C₄⋊C₄	C₂	1	2	yes	maximal
6	C₃×#2571	C₃	1	1	yes	maximal, characteristic
7	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
8	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
9	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
10	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₉×C₄⋊C₄	C₂²	1	4	yes	—
12	C₂×C₄²×C₉	C₂²	1	4	yes	—
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₉×#95	C₂²	1	4	yes	—
15	C₉×#95	C₂²	1	4	yes	—
16	C₉×#95	C₂²	1	8	yes	—
17	C₃×#400	C₂×C₃	1	4	yes	—
18	C₃×#389	C₂×C₃	1	4	yes	—
19	C₃×#384	C₂×C₃	1	1	yes	characteristic
20	C₃×#382	C₂×C₃	1	4	yes	—
21	C₃×C₄×C₄⋊C₄	C₂×C₃	1	2	yes	—
22	C₂²×C₄×C₉	C₂³	1	4	yes	—
23	C₂²×C₄×C₉	C₂³	1	4	yes	—
24	C₂²×C₄×C₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₉	C₂³	1	2	yes	—
27	C₉×C₄⋊C₄	—	2	4	no	—
28	C₉×C₄⋊C₄	—	2	4	no	—
29	C₉×C₄⋊C₄	—	2	8	no	—
30	C₉×C₄⋊C₄	—	4	2	no	—
31	C₉×C₄⋊C₄	—	4	4	no	—
32	C₄²×C₉	—	2	8	no	—
33	C₄²×C₉	Q₈	1	4	yes	—
34	#2571	C₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
36	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
37	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
38	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
39	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
40	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
41	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
42	C₃×#95	C₂²×C₃	1	4	yes	—
43	C₃×#95	C₂²×C₃	1	4	yes	—
44	C₃×#95	C₂²×C₃	1	8	yes	—
45	C₂³×C₉	C₂⁴	1	1	yes	characteristic
46	C₂×C₄×C₉	—	2	1	no	—
47	C₂×C₄×C₉	—	2	1	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	8	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	2	yes	—
57	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
58	C₂×C₄×C₉	#41	1	4	yes	—
59	C₂×C₄×C₉	#41	1	4	yes	—
60	#400	C₂×C₉	1	4	yes	—
61	#389	C₂×C₉	1	4	yes	—
62	#384	C₂×C₉	1	1	yes	characteristic
63	#382	C₂×C₉	1	4	yes	—
64	C₄×C₄⋊C₄	C₂×C₉	1	2	yes	—
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	4	yes	—
68	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
69	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
70	C₃×C₄⋊C₄	—	2	4	no	—
71	C₃×C₄⋊C₄	—	2	4	no	—
72	C₃×C₄⋊C₄	—	2	8	no	—
73	C₃×C₄⋊C₄	—	4	2	no	—
74	C₃×C₄⋊C₄	—	4	4	no	—
75	C₃×C₄²	—	2	8	no	—
76	C₃×C₄²	C₃×Q₈	1	4	yes	—
77	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
78	C₂²×C₉	C₂×#41	1	2	yes	—
79	C₂²×C₉	C₂×#41	1	2	yes	—
80	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
81	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
82	C₄×C₉	—	2	2	no	—
83	C₄×C₉	—	4	4	no	—
84	C₄×C₉	—	4	4	no	—
85	C₄×C₉	—	4	4	no	—
86	C₄×C₉	#125	1	8	yes	—
87	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
88	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
89	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
90	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
91	C₂×C₄⋊C₄	C₂²×C₉	1	4	yes	—
92	C₂×C₄²	C₂²×C₉	1	4	yes	—
93	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
94	#95	C₂²×C₉	1	4	yes	—
95	#95	C₂²×C₉	1	4	yes	—
96	#95	C₂²×C₉	1	8	yes	—
97	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄	—	2	1	no	—
99	C₂×C₃×C₄	—	2	1	no	—
100	C₂×C₃×C₄	—	2	4	no	—
101	C₂×C₃×C₄	—	2	4	no	—
102	C₂×C₃×C₄	—	2	8	no	—
103	C₂×C₃×C₄	—	2	4	no	—
104	C₂×C₃×C₄	—	2	4	no	—
105	C₂×C₃×C₄	—	2	4	no	—
106	C₂×C₃×C₄	—	2	4	no	—
107	C₂×C₃×C₄	—	2	4	no	—
108	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
109	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
110	C₂×C₃×C₄	C₃×#41	1	4	yes	—
111	C₂×C₃×C₄	C₃×#41	1	4	yes	—
112	C₂×C₉	C₂×#125	1	2	yes	—
113	C₂×C₉	#544	1	1	yes	characteristic
114	C₂×C₉	#555	1	1	yes	characteristic
115	C₂×C₉	#556	1	2	yes	—
116	C₂×C₉	#559	1	1	yes	characteristic
117	C₂²×C₄	C₂³×C₉	1	4	yes	—
118	C₂²×C₄	C₂³×C₉	1	4	yes	—
119	C₂²×C₄	C₂³×C₉	1	4	yes	—
120	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
121	C₂²×C₄	C₂³×C₉	1	2	yes	—
122	C₄⋊C₄	—	2	4	no	—
123	C₄⋊C₄	—	2	4	no	—
124	C₄⋊C₄	—	2	8	no	—
125	C₄⋊C₄	—	4	2	no	—
126	C₄⋊C₄	—	4	4	no	—
127	C₄²	—	2	8	no	—
128	C₄²	Q₈×C₉	1	4	yes	—
129	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
130	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
131	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
132	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
133	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
134	C₃×C₄	—	2	2	no	—
135	C₃×C₄	—	4	4	no	—
136	C₃×C₄	—	4	4	no	—
137	C₃×C₄	—	4	4	no	—
138	C₃×C₄	C₃×#125	1	8	yes	—
139	C₉	#2571	1	1	yes	characteristic, direct product factor, Sylow
140	C₂³	C₂⁴×C₉	1	1	yes	characteristic
141	C₂×C₄	—	2	1	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	4	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	2	4	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	2	8	no	—
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
152	C₂×C₄	C₂×Q₈×C₉	1	4	yes	—
153	C₂×C₄	C₉×#41	1	4	yes	—
154	C₂×C₄	C₉×#41	1	4	yes	—
155	C₂×C₃	C₂×C₃×#125	1	2	yes	—
156	C₂×C₃	C₃×#544	1	1	yes	characteristic
157	C₂×C₃	C₃×#555	1	1	yes	characteristic
158	C₂×C₃	C₃×#556	1	2	yes	—
159	C₂×C₃	C₃×#559	1	1	yes	characteristic
160	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
161	C₂²	C₂×C₉×#41	1	2	yes	—
162	C₂²	C₂×C₉×#41	1	2	yes	—
163	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
164	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
165	C₄	—	2	2	no	—
166	C₄	—	4	4	no	—
167	C₄	—	4	4	no	—
168	C₄	—	4	4	no	—
169	C₄	C₉×#125	1	8	yes	—
170	C₃	C₃×#2571	1	1	yes	characteristic
171	C₂	C₂×C₉×#125	1	2	yes	—
172	C₂	C₉×#544	1	1	yes	characteristic
173	C₂	C₉×#555	1	1	yes	characteristic
174	C₂	C₉×#556	1	2	yes	—
175	C₂	C₉×#559	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
34. #2571	C₉	direct (N × H)
139. C₉	#2571	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×#389	2
C₉×#384	2
C₉×#382	2
C₄×C₉×C₄⋊C₄	2
C₃×#2571	3

Subgroups — C9×#2571 #11767292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2571 #11767292