Subgroups — #11861333

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	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	#10588783	C₂	1	2	yes	maximal
4	#10588782	C₂	1	2	yes	maximal
5	#10588604	C₂	1	1	yes	maximal, characteristic
6	#10588359	C₂	1	4	yes	maximal, complemented
7	C₈×Dic₁₈	C₂	1	4	yes	maximal, complemented
8	#78445	—	3	1	no	maximal
9	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	#63488	C₂²	1	2	yes	—
13	#63486	C₄	1	4	yes	—
14	C₂×#3667	C₂²	1	2	yes	—
15	#63432	C₄	1	2	yes	—
16	#63431	C₄	1	2	yes	—
17	C₄×Dic₁₈	C₂²	1	4	yes	—
18	C₄×C₈×C₉	C₂²	1	2	yes	—
19	C₄×C₈×C₉	C₂²	1	2	yes	—
20	#63375	C₂²	1	4	yes	—
21	Dic₉⋊C₈	C₂²	1	8	yes	—
22	C₈×Dic₉	C₂²	1	4	yes	—
23	C₄⋊(C₉⋊C₈)	C₂²	1	4	yes	—
24	#5470	—	3	1	no	—
25	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
26	#5102	—	3	2	no	—
27	#5101	—	3	2	no	—
28	#4924	—	3	1	no	—
29	#4679	—	3	4	no	—
30	C₈×Dic₆	—	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	C₂×C₈×C₉	—	2	2	no	—
35	C₂×C₈×C₉	Q₈	1	4	yes	complemented
36	C₂×C₈×C₉	C₂³	1	2	yes	—
37	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
38	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
39	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
40	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
41	C₄²×C₉	C₂³	1	2	yes	—
42	#3676	C₂×C₄	1	4	yes	—
43	C₄⋊Dic₉	C₂×C₄	1	4	yes	—
44	C₄⋊Dic₉	C₂×C₄	1	4	yes	—
45	Dic₉⋊C₄	C₂×C₄	1	8	yes	—
46	C₄×Dic₉	C₂³	1	4	yes	—
47	#3667	—	2	4	no	—
48	C₂×C₉⋊C₈	C₂³	1	4	yes	—
49	#2960	—	9	1	no	Sylow
50	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
51	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
52	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
53	#926	—	3	2	no	—
54	#924	—	3	4	no	—
55	C₂×#208	—	3	2	no	—
56	#870	—	3	2	no	—
57	#869	—	3	2	no	—
58	C₄×Dic₆	—	3	4	no	—
59	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
60	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
61	#815	—	3	4	no	—
62	Dic₃⋊C₈	—	3	8	no	—
63	C₈×Dic₃	—	3	4	no	—
64	C₄⋊(C₃⋊C₈)	—	3	4	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	2	no	—
76	C₈×C₉	C₂×Q₈	1	2	yes	—
77	C₈×C₉	C₂×Q₈	1	2	yes	—
78	C₉⋊C₈	—	2	4	no	—
79	#533	—	9	1	no	—
80	#446	—	9	4	no	—
81	C₈×Q₈	—	9	4	no	—
82	#424	—	9	2	no	—
83	#423	—	9	1	no	—
84	#405	—	9	2	no	—
85	C₂×C₄×C₈	D₉	1	1	yes	characteristic
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	C₂×C₃×C₈	—	2	2	no	—
90	C₂×C₃×C₈	Dic₆	1	4	yes	—
91	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
92	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
93	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
94	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
95	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
96	C₃×C₄²	C₂²×D₃	1	2	yes	—
97	#217	—	3	4	no	—
98	C₄⋊Dic₃	—	3	4	no	—
99	C₄⋊Dic₃	—	3	4	no	—
100	Dic₃⋊C₄	—	3	8	no	—
101	C₄×Dic₃	—	3	4	no	—
102	#208	—	6	4	no	—
103	C₂×C₃⋊C₈	—	3	4	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	—	9	2	no	—
114	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
115	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
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	—	9	4	no	—
124	#97	—	9	4	no	—
125	C₄×C₈	—	9	4	no	—
126	C₄×C₈	C₂×D₉	1	2	yes	—
127	C₄×C₈	C₂×D₉	1	2	yes	—
128	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
129	C₂×C₃×C₄	—	2	4	no	—
130	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
131	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
132	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
133	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
134	C₂×C₃×C₄	#235	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	2	no	—
139	C₃×C₈	C₂×Dic₆	1	2	yes	—
140	C₃×C₈	C₂×Dic₆	1	2	yes	—
141	C₃⋊C₈	—	6	4	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	—	18	4	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	9	4	no	—
151	C₂×C₈	Dic₁₈	1	4	yes	complemented
152	C₂×C₈	C₂²×D₉	1	2	yes	—
153	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
154	C₂×C₈	C₂²×D₉	1	1	yes	characteristic
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	C₄×Dic₆	1	2	yes	—
165	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
166	C₃×C₄	—	2	2	no	—
167	C₃×C₄	C₄×Dic₆	1	2	yes	—
168	C₃×C₄	#901	1	4	yes	—
169	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
170	C₃×C₄	C₂×#235	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×Dic₁₈	1	2	yes	—
178	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
179	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
180	C₂×C₄	C₂×C₄×D₉	1	2	yes	—
181	C₂×C₄	#3697	1	2	yes	—
182	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
183	C₈	—	2	2	no	—
184	C₈	—	18	4	no	—
185	C₈	C₂×Dic₁₈	1	2	yes	—
186	C₈	C₂×Dic₁₈	1	2	yes	—
187	C₂×C₃	—	2	2	no	—
188	C₂×C₃	C₂×C₄×Dic₆	1	1	yes	characteristic
189	C₂×C₃	C₂×#901	1	2	yes	—
190	C₂²	—	2	2	no	—
191	C₂²	C₄×Dic₁₈	1	2	yes	—
192	C₂²	C₂²×C₄×D₉	1	1	yes	characteristic
193	C₄	—	2	2	no	—
194	C₄	—	18	8	no	—
195	C₄	C₄×Dic₁₈	1	2	yes	—
196	C₄	#63464	1	4	yes	—
197	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
198	C₄	C₂×#3697	1	1	yes	characteristic
199	C₃	#78445	1	1	yes	characteristic
200	C₂	—	2	2	no	—
201	C₂	C₂×C₄×Dic₁₈	1	1	yes	characteristic
202	C₂	C₂×#63464	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂²×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₄×C₈×C₉	C₂
socle	C₂²×C₃	C₂²×C₄×D₃
prime radical	C₂³×C₃	C₂×C₄×D₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂×C₄×C₈	D₉
hypocenter	C₉	#2960
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
6. #10588359	C₂	semidirect
7. C₈×Dic₁₈	C₂	semidirect
35. C₂×C₈×C₉	Q₈	semidirect
151. C₂×C₈	Dic₁₈	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
C₂×C₄×C₈×C₉	2
#10588783	2
#10588782	2
#10588604	2
#10588359	2
C₈×Dic₁₈	2
#78445	3