Subgroups — #11858864

Order 1152.

588 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic
2	#10588887	C₂	1	2	yes	maximal
3	#10588678	C₂	1	8	yes	maximal, complemented
4	#10588604	C₂	1	2	yes	maximal, complemented
5	C₄×#3667	C₂	1	2	yes	maximal, complemented
6	#82209	—	3	1	no	maximal
7	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₉×#117	C₄	1	4	yes	—
9	C₉×#117	C₂²	1	4	yes	—
10	C₂×C₉×C₄⋊C₄	C₄	1	2	yes	—
11	C₂×C₉×C₂²⋊C₄	C₄	1	2	yes	—
12	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
14	C₂×#3667	C₂²	1	4	yes	—
15	#63389	C₂²	1	8	yes	—
16	C₄⋊(C₉⋊C₈)	C₂²	1	8	yes	complemented
17	#63362	C₂²	1	4	yes	complemented
18	C₄×C₉⋊C₈	C₂²	1	4	yes	complemented
19	C₂×C₃×#117	D₃	1	1	yes	characteristic
20	#5207	—	3	2	no	—
21	#5000	—	3	8	no	—
22	#4924	—	3	2	no	—
23	C₄×#208	—	3	2	no	—
24	C₂⁴×C₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×C₉	—	2	4	no	—
26	C₂²×C₄×C₉	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
28	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₉	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₉	C₂³	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₉×C₄⋊C₄	C₂×C₄	1	8	yes	—
33	C₉×C₂²⋊C₄	C₂×C₄	1	8	yes	—
34	C₄²×C₉	C₂×C₄	1	2	yes	—
35	C₄²×C₉	C₂×C₄	1	2	yes	—
36	C₄²×C₉	C₂³	1	2	yes	—
37	C₄²×C₉	C₂³	1	2	yes	—
38	#3667	—	2	8	no	—
39	C₂×C₉⋊C₈	C₂³	1	8	yes	—
40	#2921	—	9	1	no	Sylow
41	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
42	C₃×#117	Dic₃	1	4	yes	—
43	C₃×#117	C₂×D₃	1	4	yes	—
44	C₂×C₃×C₄⋊C₄	Dic₃	1	2	yes	—
45	C₂×C₃×C₂²⋊C₄	Dic₃	1	2	yes	—
46	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
47	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
48	C₂×#208	—	3	4	no	—
49	#830	—	3	8	no	—
50	C₄⋊(C₃⋊C₈)	—	3	8	no	—
51	#803	—	3	4	no	—
52	C₄×C₃⋊C₈	—	3	4	no	—
53	C₂³×C₉	—	2	2	no	—
54	C₂³×C₉	—	4	2	no	—
55	C₂³×C₉	C₂²×C₄	1	2	yes	—
56	C₂³×C₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₉	—	2	2	no	—
58	C₂×C₄×C₉	—	2	4	no	—
59	C₂×C₄×C₉	—	2	4	no	—
60	C₂×C₄×C₉	—	4	2	no	—
61	C₂×C₄×C₉	—	4	2	no	—
62	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
63	C₂×C₄×C₉	C₂²×C₄	1	4	yes	—
64	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
65	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₉	#41	1	4	yes	—
67	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
68	C₉⋊C₈	—	2	8	no	—
69	C₂×#117	D₉	1	1	yes	characteristic
70	#433	—	9	8	no	—
71	#423	—	9	2	no	—
72	#407	—	9	2	no	—
73	C₄×M₁₆	—	9	2	no	—
74	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
75	C₂²×C₃×C₄	—	2	4	no	—
76	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
77	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
78	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
79	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
80	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
81	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
82	C₃×C₄⋊C₄	C₂×Dic₃	1	8	yes	—
83	C₃×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
84	C₃×C₄²	C₂×Dic₃	1	2	yes	—
85	C₃×C₄²	C₂×Dic₃	1	2	yes	—
86	C₃×C₄²	C₂²×D₃	1	2	yes	—
87	C₃×C₄²	C₂²×D₃	1	2	yes	—
88	#208	—	6	8	no	—
89	C₂×C₃⋊C₈	—	3	8	no	—
90	C₂²×C₉	—	2	2	no	—
91	C₂²×C₉	—	2	2	no	—
92	C₂²×C₉	—	2	4	no	—
93	C₂²×C₉	—	4	4	no	—
94	C₂²×C₉	#117	1	2	yes	—
95	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
96	C₄×C₉	—	2	2	no	—
97	C₄×C₉	—	2	4	no	—
98	C₄×C₉	—	2	4	no	—
99	C₄×C₉	#117	1	2	yes	—
100	C₄×C₉	C₂×#41	1	2	yes	—
101	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
102	C₂×M₁₆	—	9	4	no	—
103	#117	Dic₉	1	4	yes	—
104	#117	C₂×D₉	1	4	yes	—
105	C₂×C₄⋊C₄	Dic₉	1	2	yes	—
106	C₂×C₂²⋊C₄	Dic₉	1	2	yes	—
107	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
108	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
109	C₄⋊C₈	—	9	8	no	—
110	C₂²⋊C₈	—	9	8	no	—
111	#97	—	9	4	no	—
112	C₄×C₈	—	9	4	no	—
113	C₂³×C₃	—	2	2	no	—
114	C₂³×C₃	—	4	2	no	—
115	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
116	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
117	C₂×C₃×C₄	—	2	2	no	—
118	C₂×C₃×C₄	—	2	4	no	—
119	C₂×C₃×C₄	—	2	4	no	—
120	C₂×C₃×C₄	—	4	2	no	—
121	C₂×C₃×C₄	—	4	2	no	—
122	C₂×C₃×C₄	#235	1	4	yes	—
123	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
124	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
125	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
126	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
127	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
128	C₃⋊C₈	—	6	8	no	—
129	C₂×C₉	—	2	2	no	—
130	C₂×C₉	—	4	2	no	—
131	C₂×C₉	C₂×#117	1	1	yes	characteristic
132	C₂×C₉	#568	1	2	yes	—
133	C₂⁴	C₂×Dic₉	1	1	yes	characteristic
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	C₂×Dic₉	1	1	yes	characteristic
136	C₂²×C₄	C₂×Dic₉	1	2	yes	—
137	C₂²×C₄	C₂×Dic₉	1	2	yes	—
138	C₂²×C₄	C₂×Dic₉	1	2	yes	—
139	C₂²×C₄	C₂²×D₉	1	2	yes	—
140	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
141	M₁₆	—	18	8	no	—
142	C₂×C₈	—	9	8	no	—
143	C₄⋊C₄	C₂×Dic₉	1	8	yes	—
144	C₂²⋊C₄	C₂×Dic₉	1	8	yes	—
145	C₄²	C₂×Dic₉	1	2	yes	—
146	C₄²	C₂×Dic₉	1	2	yes	—
147	C₄²	C₂²×D₉	1	2	yes	—
148	C₄²	C₂²×D₉	1	2	yes	—
149	C₂²×C₃	—	2	2	no	—
150	C₂²×C₃	—	2	2	no	—
151	C₂²×C₃	—	2	4	no	—
152	C₂²×C₃	—	4	4	no	—
153	C₂²×C₃	#926	1	2	yes	—
154	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
155	C₃×C₄	—	2	2	no	—
156	C₃×C₄	—	2	4	no	—
157	C₃×C₄	—	2	4	no	—
158	C₃×C₄	#926	1	2	yes	—
159	C₃×C₄	C₂×#235	1	2	yes	—
160	C₉	#2921	1	1	yes	characteristic, complemented, Sylow
161	C₂³	—	2	2	no	—
162	C₂³	—	4	2	no	—
163	C₂³	C₂²×Dic₉	1	2	yes	—
164	C₂³	C₂²×Dic₉	1	1	yes	characteristic
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	4	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	—	4	2	no	—
169	C₂×C₄	—	4	2	no	—
170	C₂×C₄	#3697	1	4	yes	—
171	C₂×C₄	C₂²×Dic₉	1	4	yes	—
172	C₂×C₄	C₂²×Dic₉	1	4	yes	—
173	C₂×C₄	C₂²×Dic₉	1	2	yes	—
174	C₂×C₄	C₂²×Dic₉	1	1	yes	characteristic
175	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
176	C₈	—	18	8	no	—
177	C₂×C₃	—	2	2	no	—
178	C₂×C₃	—	4	2	no	—
179	C₂×C₃	C₂×#926	1	1	yes	characteristic
180	C₂×C₃	#5819	1	2	yes	—
181	C₂²	—	2	2	no	—
182	C₂²	—	2	2	no	—
183	C₂²	—	2	4	no	—
184	C₂²	—	4	4	no	—
185	C₂²	#63488	1	2	yes	—
186	C₂²	C₂³×Dic₉	1	1	yes	characteristic
187	C₄	—	2	2	no	—
188	C₄	—	2	4	no	—
189	C₄	—	2	4	no	—
190	C₄	#63488	1	2	yes	—
191	C₄	C₂×#3697	1	2	yes	—
192	C₃	#82209	1	1	yes	characteristic
193	C₂	—	2	2	no	—
194	C₂	—	4	2	no	—
195	C₂	C₂×#63488	1	1	yes	characteristic
196	C₂	#10589921	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×#117	C₂
socle	C₂²×C₃	C₂³×Dic₃
prime radical	C₂⁴×C₃	C₂×Dic₃
cosocle	C₂×C₄×C₉	C₂⁴
hypercenter	C₂×#117	D₉
hypocenter	C₉	#2921
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
3. #10588678	C₂	semidirect
4. #10588604	C₂	semidirect
5. C₄×#3667	C₂	semidirect
16. C₄⋊(C₉⋊C₈)	C₂²	semidirect
17. #63362	C₂²	semidirect
18. C₄×C₉⋊C₈	C₂²	semidirect
160. C₉	#2921	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#117	2
#10588887	2
#10588678	2
#10588604	2
C₄×#3667	2
#82209	3