Subgroups — #11801140

Order 1152.

852 conjugacy classes of subgroups.

The subgroup lattice has 267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₉	C₂	1	1	yes	maximal, characteristic
2	#10588892	C₂	1	2	yes	maximal
3	#10588891	C₂	1	2	yes	maximal
4	C₄×#3676	C₂	1	2	yes	maximal
5	#10588617	C₂	1	2	yes	maximal, complemented
6	#10588616	C₂	1	2	yes	maximal, complemented
7	C₄×C₄⋊Dic₉	C₂	1	2	yes	maximal, complemented
8	#10588612	C₂	1	2	yes	maximal, complemented
9	#82060	—	3	1	no	maximal
10	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₉	C₄	1	8	yes	complemented
14	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
16	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
18	C₂×#3676	C₂²	1	4	yes	—
19	C₂×C₄⋊Dic₉	C₂²	1	4	yes	—
20	C₂×C₄×Dic₉	C₂²	1	4	yes	—
21	C₉⋊#95	C₂²	1	4	yes	—
22	C₉⋊#95	C₂²	1	4	yes	—
23	C₉⋊#95	C₂²	1	4	yes	—
24	C₉⋊#95	C₂²	1	4	yes	—
25	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic
26	#5212	—	3	2	no	—
27	#5211	—	3	2	no	—
28	C₄×#217	—	3	2	no	—
29	#4937	—	3	2	no	—
30	#4936	—	3	2	no	—
31	C₄×C₄⋊Dic₃	—	3	2	no	—
32	#4932	—	3	2	no	—
33	C₂⁴×C₉	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₉	—	2	4	no	—
35	C₂²×C₄×C₉	—	2	4	no	—
36	C₂²×C₄×C₉	—	2	4	no	—
37	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
38	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
39	C₂²×C₄×C₉	C₂×C₄	1	4	yes	—
40	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
46	C₂²×Dic₉	C₂³	1	8	yes	—
47	C₄²×C₉	C₂×C₄	1	4	yes	—
48	C₄²×C₉	C₂×C₄	1	4	yes	—
49	C₄²×C₉	C₂×C₄	1	4	yes	—
50	C₄²×C₉	C₂×C₄	1	4	yes	—
51	#3676	—	2	8	no	—
52	C₄⋊Dic₉	—	2	8	no	—
53	C₄×Dic₉	—	2	8	no	—
54	#2283	—	9	1	no	Sylow
55	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
56	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
57	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
58	C₂×C₃×C₄²	Dic₃	1	8	yes	—
59	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
60	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
63	C₂×#217	—	3	4	no	—
64	C₂×C₄⋊Dic₃	—	3	4	no	—
65	C₂×C₄×Dic₃	—	3	4	no	—
66	C₃⋊#95	—	3	4	no	—
67	C₃⋊#95	—	3	4	no	—
68	C₃⋊#95	—	3	4	no	—
69	C₃⋊#95	—	3	4	no	—
70	C₂³×C₉	—	2	2	no	—
71	C₂³×C₉	—	2	2	no	—
72	C₂³×C₉	C₂²×C₄	1	2	yes	—
73	C₂³×C₉	#41	1	4	yes	—
74	C₂³×C₉	C₂⁴	1	1	yes	characteristic
75	C₂×C₄×C₉	—	2	8	no	—
76	C₂×C₄×C₉	—	2	2	no	—
77	C₂×C₄×C₉	—	2	2	no	—
78	C₂×C₄×C₉	—	2	2	no	—
79	C₂×C₄×C₉	—	2	2	no	—
80	C₂×C₄×C₉	—	2	8	no	—
81	C₂×C₄×C₉	—	2	8	no	—
82	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
83	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
84	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
85	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
86	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
87	C₂×C₄×C₉	C₂²×C₄	1	2	yes	—
88	C₂×C₄×C₉	#41	1	4	yes	—
89	C₂×C₄×C₉	#41	1	4	yes	—
90	C₂×Dic₉	—	2	8	no	—
91	C₂×Dic₉	—	2	8	no	—
92	C₂×Dic₉	—	2	8	no	—
93	C₂²×C₄²	D₉	1	1	yes	characteristic
94	#383	—	9	2	no	—
95	#382	—	9	2	no	—
96	#381	—	9	2	no	—
97	#380	—	9	2	no	—
98	C₄×C₄⋊C₄	—	9	2	no	—
99	C₄×C₂²⋊C₄	—	9	2	no	—
100	#376	—	9	2	no	—
101	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
102	C₂²×C₃×C₄	—	2	4	no	—
103	C₂²×C₃×C₄	—	2	4	no	—
104	C₂²×C₃×C₄	—	2	4	no	—
105	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
106	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
107	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
108	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
110	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
111	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
112	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
113	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
114	C₂²×Dic₃	—	3	8	no	—
115	C₃×C₄²	C₂×Dic₃	1	4	yes	—
116	C₃×C₄²	C₂×Dic₃	1	4	yes	—
117	C₃×C₄²	C₂×Dic₃	1	4	yes	—
118	C₃×C₄²	C₂×Dic₃	1	4	yes	—
119	#217	—	6	8	no	—
120	C₄⋊Dic₃	—	6	8	no	—
121	C₄×Dic₃	—	6	8	no	—
122	C₂²×C₉	—	2	2	no	—
123	C₂²×C₉	—	2	2	no	—
124	C₂²×C₉	—	2	8	no	—
125	C₂²×C₉	#117	1	4	yes	—
126	C₂²×C₉	C₂³×C₄	1	1	yes	characteristic
127	C₂²×C₉	C₂×#41	1	2	yes	—
128	C₂²×C₉	C₂×#41	1	2	yes	—
129	C₂²×C₉	C₂×#41	1	2	yes	—
130	C₄×C₉	—	2	2	no	—
131	C₄×C₉	—	2	2	no	—
132	C₄×C₉	—	2	2	no	—
133	C₄×C₉	—	2	2	no	—
134	C₄×C₉	#117	1	4	yes	—
135	C₄×C₉	#117	1	4	yes	—
136	Dic₉	—	4	8	no	—
137	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
138	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
139	C₂³×C₄	C₂×D₉	1	1	yes	characteristic
140	C₂×C₄⋊C₄	—	9	4	no	—
141	C₂×C₂²⋊C₄	—	9	4	no	—
142	C₂×C₄²	—	9	4	no	—
143	C₂×C₄²	Dic₉	1	8	yes	complemented
144	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
145	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
146	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
147	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
148	#95	—	9	4	no	—
149	#95	—	9	4	no	—
150	#95	—	9	4	no	—
151	#95	—	9	4	no	—
152	C₂³×C₃	—	2	2	no	—
153	C₂³×C₃	—	2	2	no	—
154	C₂³×C₃	#235	1	4	yes	—
155	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
156	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
157	C₂×C₃×C₄	—	2	8	no	—
158	C₂×C₃×C₄	—	2	2	no	—
159	C₂×C₃×C₄	—	2	2	no	—
160	C₂×C₃×C₄	—	2	2	no	—
161	C₂×C₃×C₄	—	2	2	no	—
162	C₂×C₃×C₄	—	2	8	no	—
163	C₂×C₃×C₄	—	2	8	no	—
164	C₂×C₃×C₄	#235	1	4	yes	—
165	C₂×C₃×C₄	#235	1	4	yes	—
166	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
167	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
168	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
169	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
170	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
171	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
172	C₂×Dic₃	—	6	8	no	—
173	C₂×Dic₃	—	6	8	no	—
174	C₂×Dic₃	—	6	8	no	—
175	C₂×C₉	—	2	4	no	—
176	C₂×C₉	C₂×#117	1	1	yes	characteristic
177	C₂×C₉	C₂×#117	1	1	yes	characteristic
178	C₂×C₉	C₂×#117	1	1	yes	characteristic
179	C₂×C₉	#529	1	4	yes	—
180	C₂⁴	C₂²×D₉	1	1	yes	characteristic
181	C₂²×C₄	—	2	4	no	—
182	C₂²×C₄	—	2	4	no	—
183	C₂²×C₄	—	2	4	no	—
184	C₂²×C₄	—	9	8	no	—
185	C₂²×C₄	C₂×Dic₉	1	4	yes	—
186	C₂²×C₄	C₂×Dic₉	1	4	yes	—
187	C₂²×C₄	C₂×Dic₉	1	4	yes	—
188	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
189	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
190	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
191	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
192	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
193	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
194	C₄⋊C₄	—	18	8	no	—
195	C₂²⋊C₄	—	18	8	no	—
196	C₄²	—	18	8	no	—
197	C₄²	C₂×Dic₉	1	4	yes	—
198	C₄²	C₂×Dic₉	1	4	yes	—
199	C₄²	C₂×Dic₉	1	4	yes	—
200	C₄²	C₂×Dic₉	1	4	yes	—
201	C₂²×C₃	—	2	8	no	—
202	C₂²×C₃	—	2	2	no	—
203	C₂²×C₃	—	2	2	no	—
204	C₂²×C₃	#926	1	4	yes	—
205	C₂²×C₃	C₂×#235	1	2	yes	—
206	C₂²×C₃	C₂×#235	1	2	yes	—
207	C₂²×C₃	C₂×#235	1	2	yes	—
208	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
209	C₃×C₄	—	2	2	no	—
210	C₃×C₄	—	2	2	no	—
211	C₃×C₄	—	2	2	no	—
212	C₃×C₄	—	2	2	no	—
213	C₃×C₄	#926	1	4	yes	—
214	C₃×C₄	#926	1	4	yes	—
215	Dic₃	—	12	8	no	—
216	C₉	#2283	1	1	yes	characteristic, complemented, Sylow
217	C₂³	—	2	2	no	—
218	C₂³	—	2	2	no	—
219	C₂³	#3697	1	4	yes	—
220	C₂³	C₂²×Dic₉	1	2	yes	—
221	C₂³	C₂³×D₉	1	1	yes	characteristic
222	C₂×C₄	—	2	8	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	8	no	—
228	C₂×C₄	—	2	8	no	—
229	C₂×C₄	—	18	8	no	—
230	C₂×C₄	—	18	8	no	—
231	C₂×C₄	—	18	8	no	—
232	C₂×C₄	#3697	1	4	yes	—
233	C₂×C₄	#3697	1	4	yes	—
234	C₂×C₄	C₂²×Dic₉	1	2	yes	—
235	C₂×C₄	C₂²×Dic₉	1	2	yes	—
236	C₂×C₄	C₂²×Dic₉	1	2	yes	—
237	C₂×C₄	C₂²×Dic₉	1	2	yes	—
238	C₂×C₄	C₂²×Dic₉	1	2	yes	—
239	C₂×C₄	C₂²×Dic₉	1	2	yes	—
240	C₂×C₃	—	2	4	no	—
241	C₂×C₃	#5479	1	4	yes	—
242	C₂×C₃	C₂×#926	1	1	yes	characteristic
243	C₂×C₃	C₂×#926	1	1	yes	characteristic
244	C₂×C₃	C₂×#926	1	1	yes	characteristic
245	C₂²	—	2	8	no	—
246	C₂²	—	2	2	no	—
247	C₂²	—	2	2	no	—
248	C₂²	#63488	1	4	yes	—
249	C₂²	C₂×#3697	1	2	yes	—
250	C₂²	C₂×#3697	1	2	yes	—
251	C₂²	C₂×#3697	1	2	yes	—
252	C₂²	C₂³×Dic₉	1	1	yes	characteristic
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	2	no	—
257	C₄	—	36	8	no	—
258	C₄	#63488	1	4	yes	—
259	C₄	#63488	1	4	yes	—
260	C₃	#82060	1	1	yes	characteristic
261	C₂	—	2	4	no	—
262	C₂	#10589581	1	4	yes	—
263	C₂	C₂×#63488	1	1	yes	characteristic
264	C₂	C₂×#63488	1	1	yes	characteristic
265	C₂	C₂×#63488	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₉
commutator	C₂²×C₉	C₂³×C₄
Frattini, socle	C₂³×C₃	C₂³×D₃
Fitting	C₂²×C₄²×C₉	C₂
prime radical	C₂⁴×C₃	C₂²×D₃
cosocle	C₂³×C₉	C₂⁴
hypercenter	C₂²×C₄²	D₉
hypocenter	C₉	#2283
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
5. #10588617	C₂	semidirect
6. #10588616	C₂	semidirect
7. C₄×C₄⋊Dic₉	C₂	semidirect
8. #10588612	C₂	semidirect
13. C₂×C₄²×C₉	C₄	semidirect
143. C₂×C₄²	Dic₉	semidirect
216. C₉	#2283	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₉	2
#10588892	2
#10588891	2
C₄×#3676	2
#10588617	2
#10588616	2
C₄×C₄⋊Dic₉	2
#10588612	2
#82060	3