Subgroups — #11790487

Order 1152.

294 conjugacy classes of subgroups.

The subgroup lattice has 207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#405	C₂	1	1	yes	maximal, characteristic
2	C₂×#63378	C₂	1	1	yes	maximal, characteristic
3	C₂×#63372	C₂	1	1	yes	maximal, characteristic
4	#10588679	C₂	1	2	yes	maximal
5	#10588234	C₂	1	2	yes	maximal
6	#69894	—	3	1	no	maximal
7	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
11	C₂×#3667	C₂²	1	2	yes	—
12	C₉×#97	—	2	1	no	—
13	C₄×C₈×C₉	—	2	1	no	—
14	#63378	—	2	1	no	—
15	#63378	—	2	1	no	—
16	#63372	C₄	1	4	yes	complemented
17	#63367	—	2	2	no	—
18	#63366	—	2	2	no	—
19	C₃×#405	D₃	1	1	yes	characteristic
20	C₂×#819	—	3	1	no	—
21	C₂×#818	—	3	1	no	—
22	#4995	—	3	2	no	—
23	#4554	—	3	2	no	—
24	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
25	C₂²×Dic₉	—	2	2	no	—
26	C₉×M₁₆	—	2	1	no	—
27	C₉×M₁₆	Q₈	1	2	yes	—
28	C₂×C₈×C₉	—	2	1	no	—
29	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₉	D₄	1	1	yes	characteristic
31	C₂×C₈×C₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₉	Q₈	1	2	yes	—
33	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
34	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
35	C₉×C₂²⋊C₄	—	2	1	no	—
36	C₄²×C₉	—	2	1	no	—
37	C₄⋊Dic₉	—	2	2	no	—
38	C₄⋊Dic₉	—	2	2	no	—
39	#3667	—	2	2	no	—
40	#3667	C₂×C₄	1	4	yes	—
41	C₂×C₉⋊C₈	—	2	2	no	—
42	#1952	—	9	1	no	Sylow
43	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
44	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
45	C₃×#117	C₂×D₃	1	1	yes	characteristic
46	C₂×C₄⋊Dic₃	—	3	2	no	—
47	C₂×#208	—	3	2	no	—
48	C₃×#97	—	2	1	no	—
49	C₃×C₄×C₈	—	2	1	no	—
50	#819	—	3	4	no	—
51	#818	—	6	1	no	—
52	#818	—	6	1	no	—
53	#808	—	6	2	no	—
54	#807	—	6	2	no	—
55	C₂³×C₉	#41	1	1	yes	characteristic
56	C₂×C₄×C₉	—	2	1	no	—
57	C₂×C₄×C₉	—	2	1	no	—
58	C₂×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
62	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₄×C₉	#41	1	1	yes	characteristic
64	C₂×Dic₉	—	4	2	no	—
65	C₂×Dic₉	—	8	2	no	—
66	C₈×C₉	—	2	2	no	—
67	C₈×C₉	C₄⋊C₄	1	2	yes	—
68	C₈×C₉	C₄⋊C₄	1	2	yes	—
69	C₉⋊C₈	—	2	4	no	—
70	C₂×#108	—	9	1	no	—
71	#428	—	9	2	no	—
72	C₂×#107	—	9	1	no	—
73	#405	D₉	1	1	yes	characteristic
74	#343	—	9	2	no	—
75	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
76	C₂²×Dic₃	—	6	2	no	—
77	C₃×M₁₆	—	2	1	no	—
78	C₃×M₁₆	Dic₆	1	2	yes	—
79	C₂×C₃×C₈	—	2	1	no	—
80	C₂×C₃×C₈	Dic₆	1	2	yes	—
81	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
82	C₂×C₃×C₈	#67	1	1	yes	characteristic
83	C₂×C₃×C₈	#67	1	1	yes	characteristic
84	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
85	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
86	C₃×C₂²⋊C₄	—	2	1	no	—
87	C₃×C₄²	—	2	1	no	—
88	C₄⋊Dic₃	—	6	2	no	—
89	C₄⋊Dic₃	—	6	2	no	—
90	#208	—	3	4	no	—
91	#208	—	6	2	no	—
92	C₂×C₃⋊C₈	—	6	2	no	—
93	C₂²×C₉	—	2	1	no	—
94	C₂²×C₉	—	2	1	no	—
95	C₂²×C₉	C₄×Q₈	1	1	yes	characteristic
96	C₂²×C₉	#121	1	1	yes	characteristic
97	C₂²×C₉	#125	1	1	yes	characteristic
98	C₄×C₉	—	4	1	no	—
99	C₄×C₉	—	4	1	no	—
100	C₄×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₄×C₉	C₄×D₄	1	1	yes	characteristic
102	C₄×C₉	C₂²⋊Q₈	1	1	yes	characteristic
103	C₄×C₉	C₄⋊Q₈	1	1	yes	characteristic
104	Dic₉	—	8	2	no	—
105	C₂×M₁₆	—	9	2	no	—
106	C₂×M₁₆	C₂×D₉	1	1	yes	characteristic
107	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
108	#117	C₂×D₉	1	1	yes	characteristic
109	C₂×C₄⋊C₄	—	9	2	no	—
110	#108	—	9	4	no	—
111	#107	—	18	1	no	—
112	#107	—	18	1	no	—
113	#107	—	18	2	no	—
114	#106	—	18	2	no	—
115	#97	—	2	1	no	—
116	C₄×C₈	—	2	1	no	—
117	C₂³×C₃	#235	1	1	yes	characteristic
118	C₂×C₃×C₄	—	2	1	no	—
119	C₂×C₃×C₄	—	2	1	no	—
120	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
121	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
122	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
123	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
124	C₂×C₃×C₄	#235	1	1	yes	characteristic
125	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
126	C₂×Dic₃	—	12	2	no	—
127	C₂×Dic₃	—	24	2	no	—
128	C₃×C₈	—	2	2	no	—
129	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
130	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
131	C₃⋊C₈	—	6	4	no	—
132	C₂×C₉	—	2	1	no	—
133	C₂×C₉	—	2	1	no	—
134	C₂×C₉	#389	1	1	yes	characteristic
135	C₂×C₉	#472	1	1	yes	characteristic
136	C₂×C₉	#473	1	1	yes	characteristic
137	C₂²×C₄	—	18	2	no	—
138	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
139	M₁₆	—	2	1	no	—
140	M₁₆	—	9	4	no	—
141	M₁₆	—	18	2	no	—
142	M₁₆	Dic₁₈	1	2	yes	—
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	18	2	no	—
145	C₂×C₈	Dic₁₈	1	2	yes	—
146	C₂×C₈	C₄×D₉	1	2	yes	—
147	C₂×C₈	#611	1	1	yes	characteristic
148	C₂×C₈	#611	1	1	yes	characteristic
149	C₄⋊C₄	—	18	2	no	—
150	C₄⋊C₄	—	18	2	no	—
151	C₄⋊C₄	D₃₆	1	1	yes	characteristic
152	C₄⋊C₄	D₃₆	1	1	yes	characteristic
153	C₂²⋊C₄	—	2	1	no	—
154	C₄²	—	2	1	no	—
155	C₂²×C₃	—	2	1	no	—
156	C₂²×C₃	—	2	1	no	—
157	C₂²×C₃	C₄×Dic₆	1	1	yes	characteristic
158	C₂²×C₃	#870	1	1	yes	characteristic
159	C₂²×C₃	#930	1	1	yes	characteristic
160	C₃×C₄	—	4	1	no	—
161	C₃×C₄	—	4	1	no	—
162	C₃×C₄	#869	1	1	yes	characteristic
163	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
164	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
165	C₃×C₄	#924	1	1	yes	characteristic
166	Dic₃	—	24	2	no	—
167	C₉	#1952	1	1	yes	characteristic, complemented, Sylow
168	C₂³	#3697	1	1	yes	characteristic
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	36	2	no	—
172	C₂×C₄	—	72	2	no	—
173	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
174	C₂×C₄	C₂×Dic₁₈	1	1	yes	characteristic
175	C₂×C₄	C₂×C₄×D₉	1	1	yes	characteristic
176	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
177	C₂×C₄	#3697	1	1	yes	characteristic
178	C₂×C₄	C₂×#611	1	1	yes	characteristic
179	C₈	—	2	2	no	—
180	C₈	—	18	4	no	—
181	C₈	Dic₉⋊C₄	1	2	yes	—
182	C₈	Dic₉⋊C₄	1	2	yes	—
183	C₂×C₃	—	2	1	no	—
184	C₂×C₃	—	2	1	no	—
185	C₂×C₃	#4928	1	1	yes	characteristic
186	C₂×C₃	#5142	1	1	yes	characteristic
187	C₂×C₃	#5143	1	1	yes	characteristic
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	C₄×Dic₁₈	1	1	yes	characteristic
191	C₂²	#63432	1	1	yes	characteristic
192	C₂²	#63492	1	1	yes	characteristic
193	C₄	—	4	1	no	—
194	C₄	—	4	1	no	—
195	C₄	—	72	2	no	—
196	C₄	#63431	1	1	yes	characteristic
197	C₄	C₄×D₃₆	1	1	yes	characteristic
198	C₄	C₂×Dic₉⋊C₄	1	1	yes	characteristic
199	C₄	#63486	1	1	yes	characteristic
200	C₃	#69894	1	1	yes	characteristic
201	C₂	—	2	1	no	—
202	C₂	—	2	1	no	—
203	C₂	#10588608	1	1	yes	characteristic
204	C₂	#10588821	1	1	yes	characteristic
205	C₂	#10588823	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63492
commutator	C₂×C₄×C₉	C₂²×C₄
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#405	C₂
socle	C₂²×C₃	#930
prime radical	C₂³×C₃	#235
cosocle	C₂²×C₄×C₉	C₂³
hypercenter	#405	D₉
hypocenter	C₉	#1952
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
16. #63372	C₄	semidirect
167. C₉	#1952	semidirect

Maximal subgroups

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

subgroup	index
C₉×#405	2
C₂×#63378	2
C₂×#63372	2
#10588679	2
#10588234	2
#69894	3