Subgroups — #11785995

Order 1152.

258 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	C₉×#427	C₂	1	1	yes	maximal, characteristic
2	#10588782	C₂	1	1	yes	maximal, characteristic
3	C₂×#63372	C₂	1	1	yes	maximal, characteristic
4	#10588210	C₂	1	2	yes	maximal
5	#10588209	C₂	1	2	yes	maximal
6	#70657	—	3	1	no	maximal
7	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₉×#117	C₂²	1	2	yes	—
9	#63488	C₂²	1	1	yes	characteristic
10	C₂×#3667	C₂²	1	2	yes	—
11	C₂×#3667	C₂²	1	1	yes	characteristic
12	C₉×#107	—	2	1	no	—
13	C₉×#106	—	2	1	no	—
14	#63375	C₄	1	2	yes	complemented
15	C₈×Dic₉	C₄	1	2	yes	complemented
16	#63372	—	2	1	no	—
17	#63372	—	2	1	no	—
18	C₃×#427	D₃	1	1	yes	characteristic
19	C₂×#819	—	3	1	no	—
20	#5101	—	3	1	no	—
21	#4533	—	3	2	no	—
22	#4531	—	3	2	no	—
23	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₉	D₄	1	1	yes	characteristic
27	C₂×C₈×C₉	D₄	1	1	yes	characteristic
28	C₂×C₈×C₉	Q₈	1	1	yes	characteristic
29	C₂×C₈×C₉	Q₈	1	1	yes	characteristic
30	C₉×C₄⋊C₄	—	2	2	no	—
31	C₉×C₂²⋊C₄	—	2	2	no	—
32	C₄²×C₉	—	2	2	no	—
33	#3676	—	2	1	no	—
34	C₄⋊Dic₉	—	2	1	no	—
35	C₄×Dic₉	C₂×C₄	1	2	yes	—
36	#3667	—	2	1	no	—
37	#3667	—	2	1	no	—
38	#3667	—	2	2	no	—
39	#3667	—	2	2	no	—
40	C₂×C₉⋊C₈	—	2	2	no	—
41	C₂×C₉⋊C₈	C₂×C₄	1	2	yes	—
42	#1833	—	9	1	no	Sylow
43	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
44	C₃×#117	C₂×D₃	1	2	yes	—
45	#926	—	3	1	no	—
46	C₂×#208	—	3	1	no	—
47	C₂×#208	—	3	2	no	—
48	C₃×#107	—	2	1	no	—
49	C₃×#106	—	2	1	no	—
50	#819	—	6	1	no	—
51	#819	—	6	1	no	—
52	#815	—	3	2	no	—
53	C₈×Dic₃	—	3	2	no	—
54	C₂³×C₉	#41	1	1	yes	characteristic
55	C₂×C₄×C₉	—	4	2	no	—
56	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₄×C₉	#41	1	1	yes	characteristic
60	C₂×C₄×C₉	#41	1	1	yes	characteristic
61	C₂×C₄×C₉	#41	1	1	yes	characteristic
62	C₂×Dic₉	—	2	2	no	—
63	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
64	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
65	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
66	C₈×C₉	C₄⋊C₄	1	1	yes	characteristic
67	C₉⋊C₈	—	2	2	no	—
68	C₉⋊C₈	—	4	2	no	—
69	C₂×#108	—	9	1	no	—
70	#427	D₉	1	1	yes	characteristic
71	#405	—	9	1	no	—
72	#344	—	9	2	no	—
73	H(3,ℤ/4)	—	9	2	no	—
74	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
75	C₂×C₃×C₈	Dic₆	1	1	yes	characteristic
76	C₂×C₃×C₈	Dic₆	1	1	yes	characteristic
77	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
78	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
79	C₂×C₃×C₈	#67	1	1	yes	characteristic
80	C₂×C₃×C₈	#67	1	1	yes	characteristic
81	C₃×C₄⋊C₄	—	2	2	no	—
82	C₃×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₄²	—	2	2	no	—
84	#217	—	6	1	no	—
85	C₄⋊Dic₃	—	6	1	no	—
86	C₄×Dic₃	—	3	2	no	—
87	#208	—	6	1	no	—
88	#208	—	6	1	no	—
89	#208	—	6	2	no	—
90	#208	—	6	2	no	—
91	C₂×C₃⋊C₈	—	3	2	no	—
92	C₂×C₃⋊C₈	—	6	2	no	—
93	C₂²×C₉	—	4	1	no	—
94	C₂²×C₉	#117	1	1	yes	characteristic
95	C₂²×C₉	#124	1	1	yes	characteristic
96	C₂²×C₉	#125	1	1	yes	characteristic
97	C₄×C₉	—	8	2	no	—
98	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₄×C₉	#117	1	1	yes	characteristic
100	C₄×C₉	#124	1	1	yes	characteristic
101	C₄×C₉	#125	1	1	yes	characteristic
102	Dic₉	—	4	2	no	—
103	C₂×M₁₆	—	9	1	no	—
104	C₂×M₁₆	—	9	2	no	—
105	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
106	#117	—	9	1	no	—
107	#117	C₂×D₉	1	2	yes	—
108	#108	—	18	1	no	—
109	#108	—	18	1	no	—
110	#107	—	2	1	no	—
111	#106	—	2	1	no	—
112	#97	—	9	2	no	—
113	C₄×C₈	—	9	2	no	—
114	C₂³×C₃	#237	1	1	yes	characteristic
115	C₂×C₃×C₄	—	4	2	no	—
116	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
117	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
118	C₂×C₃×C₄	#237	1	1	yes	characteristic
119	C₂×C₃×C₄	#239	1	1	yes	characteristic
120	C₂×C₃×C₄	#239	1	1	yes	characteristic
121	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
122	C₂×Dic₃	—	6	2	no	—
123	C₃×C₈	Dic₃⋊C₄	1	1	yes	characteristic
124	C₃×C₈	Dic₃⋊C₄	1	1	yes	characteristic
125	C₃×C₈	Dic₃⋊C₄	1	1	yes	characteristic
126	C₃×C₈	Dic₃⋊C₄	1	1	yes	characteristic
127	C₃⋊C₈	—	6	2	no	—
128	C₃⋊C₈	—	12	2	no	—
129	C₂×C₉	—	2	1	no	—
130	C₂×C₉	—	2	1	no	—
131	C₂×C₉	—	2	1	no	—
132	C₂×C₉	#382	1	1	yes	characteristic
133	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
134	M₁₆	—	18	1	no	—
135	M₁₆	—	18	1	no	—
136	M₁₆	—	18	2	no	—
137	M₁₆	—	18	2	no	—
138	C₂×C₈	—	9	2	no	—
139	C₂×C₈	—	18	2	no	—
140	C₂×C₈	Dic₁₈	1	1	yes	characteristic
141	C₂×C₈	Dic₁₈	1	1	yes	characteristic
142	C₂×C₈	C₄×D₉	1	1	yes	characteristic
143	C₂×C₈	C₄×D₉	1	1	yes	characteristic
144	C₂×C₈	#611	1	1	yes	characteristic
145	C₂×C₈	#611	1	1	yes	characteristic
146	C₄⋊C₄	—	2	2	no	—
147	C₄⋊C₄	—	18	1	no	—
148	C₂²⋊C₄	—	2	2	no	—
149	C₂²⋊C₄	—	18	1	no	—
150	C₄²	—	2	2	no	—
151	C₄²	—	9	2	no	—
152	C₂²×C₃	—	4	1	no	—
153	C₂²×C₃	#890	1	1	yes	characteristic
154	C₂²×C₃	#892	1	1	yes	characteristic
155	C₂²×C₃	#936	1	1	yes	characteristic
156	C₃×C₄	—	8	2	no	—
157	C₃×C₄	#890	1	1	yes	characteristic
158	C₃×C₄	#892	1	1	yes	characteristic
159	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
160	C₃×C₄	#947	1	1	yes	characteristic
161	Dic₃	—	12	2	no	—
162	C₉	#1833	1	1	yes	characteristic, complemented, Sylow
163	C₂³	#3699	1	1	yes	characteristic
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	—	18	2	no	—
166	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
167	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
168	C₂×C₄	#3699	1	1	yes	characteristic
169	C₂×C₄	#3701	1	1	yes	characteristic
170	C₂×C₄	#3701	1	1	yes	characteristic
171	C₂×C₄	C₂×#611	1	1	yes	characteristic
172	C₈	—	18	2	no	—
173	C₈	—	36	2	no	—
174	C₈	Dic₉⋊C₄	1	1	yes	characteristic
175	C₈	Dic₉⋊C₄	1	1	yes	characteristic
176	C₈	Dic₉⋊C₄	1	1	yes	characteristic
177	C₈	Dic₉⋊C₄	1	1	yes	characteristic
178	C₂×C₃	—	2	1	no	—
179	C₂×C₃	—	2	1	no	—
180	C₂×C₃	—	2	1	no	—
181	C₂×C₃	#4977	1	1	yes	characteristic
182	C₂²	—	4	1	no	—
183	C₂²	#63452	1	1	yes	characteristic
184	C₂²	#63454	1	1	yes	characteristic
185	C₂²	#63498	1	1	yes	characteristic
186	C₄	—	8	2	no	—
187	C₄	—	36	2	no	—
188	C₄	#63452	1	1	yes	characteristic
189	C₄	#63454	1	1	yes	characteristic
190	C₄	C₂×Dic₉⋊C₄	1	1	yes	characteristic
191	C₄	#63509	1	1	yes	characteristic
192	C₃	#70657	1	1	yes	characteristic
193	C₂	—	2	1	no	—
194	C₂	—	2	1	no	—
195	C₂	—	2	1	no	—
196	C₂	#10588657	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#63454
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#427	C₂
socle	C₂×C₃	#4977
prime radical	C₂³×C₃	#237
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#427	D₉
hypocenter	C₉	#1833
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #427

Complements

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

N	H ≅ G/N	type
14. #63375	C₄	semidirect
15. C₈×Dic₉	C₄	semidirect
162. C₉	#1833	semidirect

Maximal subgroups

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

subgroup	index
C₉×#427	2
#10588782	2
C₂×#63372	2
#10588210	2
#10588209	2
#70657	3