Subgroups — #11861321

Order 1152.

546 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10589572	C₂	1	1	yes	maximal, characteristic
2	C₉×#423	C₂	1	1	yes	maximal, characteristic
3	#10588803	C₂	1	2	yes	maximal
4	#10588797	C₂	1	2	yes	maximal
5	C₂×C₄×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#10588509	C₂	1	4	yes	maximal, complemented
7	#10588508	C₂	1	4	yes	maximal, complemented
8	#79044	—	3	1	no	maximal
9	C₂×C₉×M₁₆	C₂²	1	2	yes	—
10	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
11	#63488	C₂²	1	2	yes	—
12	#63486	C₄	1	4	yes	—
13	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	#63432	C₄	1	2	yes	—
16	#63431	C₄	1	2	yes	—
17	C₄×Dic₁₈	C₂²	1	4	yes	—
18	C₉×C₄⋊C₈	C₂²	1	4	yes	—
19	#63375	C₂²	1	4	yes	—
20	Dic₉⋊C₈	C₂²	1	8	yes	—
21	C₈×Dic₉	C₂²	1	4	yes	—
22	C₄×C₉⋊C₈	C₂²	1	2	yes	—
23	C₄×C₉⋊C₈	C₂²	1	2	yes	—
24	#5470	—	3	1	no	—
25	C₃×#423	D₃	1	1	yes	characteristic
26	#5122	—	3	2	no	—
27	#5119	—	3	2	no	—
28	C₂×C₄×C₃⋊C₈	—	3	1	no	—
29	#4831	—	3	4	no	—
30	#4830	—	3	4	no	—
31	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
32	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
33	C₂×Dic₁₈	C₂×C₄	1	4	yes	—
34	C₉×M₁₆	—	2	4	no	—
35	C₂×C₈×C₉	C₂³	1	4	yes	—
36	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
37	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
38	C₄²×C₉	C₂³	1	2	yes	—
39	#3676	C₂×C₄	1	4	yes	—
40	C₄⋊Dic₉	C₂×C₄	1	4	yes	—
41	C₄⋊Dic₉	C₂×C₄	1	4	yes	—
42	Dic₉⋊C₄	C₂×C₄	1	8	yes	—
43	C₄×Dic₉	C₂³	1	4	yes	—
44	C₂×C₉⋊C₈	—	2	2	no	—
45	C₂×C₉⋊C₈	Q₈	1	4	yes	complemented
46	C₂×C₉⋊C₈	C₂³	1	2	yes	—
47	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×C₉⋊C₈	C₂³	1	1	yes	characteristic
49	#2960	—	9	1	no	Sylow
50	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
51	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
52	#926	—	3	2	no	—
53	#924	—	3	4	no	—
54	C₂²×C₃⋊C₈	—	3	1	no	—
55	C₂²×C₃⋊C₈	—	3	1	no	—
56	#870	—	3	2	no	—
57	#869	—	3	2	no	—
58	C₄×Dic₆	—	3	4	no	—
59	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	—
60	#815	—	3	4	no	—
61	Dic₃⋊C₈	—	3	8	no	—
62	C₈×Dic₃	—	3	4	no	—
63	C₄×C₃⋊C₈	—	3	2	no	—
64	C₄×C₃⋊C₈	—	3	2	no	—
65	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₉	—	2	4	no	—
67	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
68	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
71	C₂×C₄×C₉	#41	1	2	yes	—
72	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
73	C₂×Dic₉	C₂²×C₄	1	8	yes	—
74	Dic₁₈	—	2	8	no	—
75	C₈×C₉	—	2	4	no	—
76	C₉⋊C₈	—	2	2	no	—
77	C₉⋊C₈	C₂×Q₈	1	2	yes	—
78	C₉⋊C₈	C₂×Q₈	1	2	yes	—
79	#533	—	9	1	no	—
80	#446	—	9	4	no	—
81	C₈×Q₈	—	9	4	no	—
82	#424	—	9	2	no	—
83	#423	D₉	1	1	yes	characteristic
84	#405	—	9	2	no	—
85	C₂×C₄×C₈	—	9	1	no	—
86	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
87	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
88	C₂×Dic₆	—	3	4	no	—
89	C₃×M₁₆	—	2	4	no	—
90	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
91	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
92	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
93	C₃×C₄²	C₂²×D₃	1	2	yes	—
94	#217	—	3	4	no	—
95	C₄⋊Dic₃	—	3	4	no	—
96	C₄⋊Dic₃	—	3	4	no	—
97	Dic₃⋊C₄	—	3	8	no	—
98	C₄×Dic₃	—	3	4	no	—
99	C₂×C₃⋊C₈	—	3	4	no	—
100	C₂×C₃⋊C₈	—	3	1	no	—
101	C₂×C₃⋊C₈	—	3	1	no	—
102	C₂×C₃⋊C₈	—	3	2	no	—
103	C₂×C₃⋊C₈	—	6	2	no	—
104	C₂²×C₉	—	2	2	no	—
105	C₂²×C₉	C₄×Q₈	1	2	yes	—
106	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
107	C₄×C₉	—	2	2	no	—
108	C₄×C₉	C₄×Q₈	1	2	yes	—
109	C₄×C₉	#131	1	4	yes	—
110	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
111	C₄×C₉	C₂×#41	1	1	yes	characteristic
112	Dic₉	—	2	8	no	—
113	C₂×M₁₆	C₂×D₉	1	2	yes	—
114	C₂²×C₈	—	9	1	no	—
115	C₂²×C₈	—	9	1	no	—
116	C₄⋊Q₈	—	9	2	no	—
117	#125	—	9	2	no	—
118	C₂²⋊Q₈	—	9	4	no	—
119	C₄×Q₈	—	9	4	no	—
120	#117	—	9	2	no	—
121	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
122	C₄⋊C₈	—	9	8	no	—
123	C₄⋊C₈	C₂×D₉	1	4	yes	—
124	#97	—	9	4	no	—
125	C₄×C₈	—	9	4	no	—
126	C₄×C₈	—	9	2	no	—
127	C₄×C₈	—	9	2	no	—
128	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
129	C₂×C₃×C₄	—	2	4	no	—
130	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
131	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
132	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
133	C₂×C₃×C₄	#237	1	2	yes	—
134	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
135	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
136	C₂×Dic₃	—	3	8	no	—
137	Dic₆	—	6	8	no	—
138	C₃×C₈	—	2	4	no	—
139	C₃⋊C₈	—	3	2	no	—
140	C₃⋊C₈	—	3	2	no	—
141	C₃⋊C₈	—	6	2	no	—
142	C₂×C₉	—	2	2	no	—
143	C₂×C₉	C₂×C₄×Q₈	1	1	yes	characteristic
144	C₂×C₉	C₂×#131	1	2	yes	—
145	C₂×Q₈	—	9	4	no	—
146	C₂²×C₄	C₄×D₉	1	2	yes	—
147	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
148	M₁₆	—	2	4	no	—
149	C₂×C₈	—	9	4	no	—
150	C₂×C₈	—	9	1	no	—
151	C₂×C₈	—	9	1	no	—
152	C₂×C₈	—	9	2	no	—
153	C₂×C₈	—	18	2	no	—
154	C₂×C₈	C₂²×D₉	1	4	yes	—
155	C₄⋊C₄	—	9	4	no	—
156	C₄⋊C₄	—	9	8	no	—
157	C₄⋊C₄	—	9	4	no	—
158	C₂²⋊C₄	—	9	4	no	—
159	C₄²	—	9	4	no	—
160	C₄²	C₄×D₉	1	1	yes	characteristic
161	C₄²	C₄×D₉	1	1	yes	characteristic
162	C₄²	C₂²×D₉	1	2	yes	—
163	C₂²×C₃	—	2	2	no	—
164	C₂²×C₃	#887	1	2	yes	—
165	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
166	C₃×C₄	—	2	2	no	—
167	C₃×C₄	#887	1	2	yes	—
168	C₃×C₄	#907	1	4	yes	—
169	C₃×C₄	C₂×#237	1	1	yes	characteristic
170	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
171	Dic₃	—	6	8	no	—
172	C₉	#2960	1	1	yes	characteristic, complemented, Sylow
173	C₂³	C₂×C₄×D₉	1	1	yes	characteristic
174	Q₈	—	18	8	no	—
175	C₂×C₄	—	2	4	no	—
176	C₂×C₄	—	9	8	no	—
177	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
178	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
179	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
180	C₂×C₄	#3699	1	2	yes	—
181	C₂×C₄	Q₈×D₉	1	2	yes	—
182	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
183	C₈	—	2	4	no	—
184	C₈	—	9	2	no	—
185	C₈	—	9	2	no	—
186	C₈	—	18	2	no	—
187	C₂×C₃	—	2	2	no	—
188	C₂×C₃	C₂×#887	1	1	yes	characteristic
189	C₂×C₃	C₂×#907	1	2	yes	—
190	C₂²	—	2	2	no	—
191	C₂²	#63449	1	2	yes	—
192	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	18	8	no	—
195	C₄	#63449	1	2	yes	—
196	C₄	#63469	1	4	yes	—
197	C₄	C₂×#3699	1	1	yes	characteristic
198	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
199	C₃	#79044	1	1	yes	characteristic
200	C₂	—	2	2	no	—
201	C₂	C₂×#63449	1	1	yes	characteristic
202	C₂	C₂×#63469	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₉×#423	C₂
socle	C₂²×C₃	C₂²×C₄×D₃
prime radical	C₂³×C₃	C₂×C₄×D₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	#423	D₉
hypocenter	C₉	#2960
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
6. #10588509	C₂	semidirect
7. #10588508	C₂	semidirect
45. C₂×C₉⋊C₈	Q₈	semidirect
172. C₉	#2960	semidirect

Maximal subgroups

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

subgroup	index
#10589572	2
C₉×#423	2
#10588803	2
#10588797	2
C₂×C₄×C₉⋊C₈	2
#10588509	2
#10588508	2
#79044	3