Subgroups — C₉×#2512 #11767233

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#126	C₂	1	2	yes	maximal, complemented
2	C₉×#397	C₂	1	2	yes	maximal, complemented
3	C₉×#396	C₂	1	2	yes	maximal, complemented
4	C₉×#390	C₂	1	1	yes	maximal, characteristic
5	C₉×#390	C₂	1	1	yes	maximal, characteristic
6	C₉×#390	C₂	1	1	yes	maximal, characteristic
7	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#388	C₂	1	2	yes	maximal, complemented
9	C₉×#384	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2512	C₃	1	1	yes	maximal, characteristic
13	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
14	C₉×#126	—	2	8	no	—
15	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₉	C₂²	1	2	yes	—
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₉×#95	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	2	yes	—
35	C₉×#95	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	2	yes	—
37	C₂×C₃×#126	C₂×C₃	1	2	yes	—
38	C₃×#397	C₂×C₃	1	2	yes	—
39	C₃×#396	C₂×C₃	1	2	yes	—
40	C₃×#390	C₂×C₃	1	1	yes	characteristic
41	C₃×#390	C₂×C₃	1	1	yes	characteristic
42	C₃×#390	C₂×C₃	1	1	yes	characteristic
43	C₃×#389	C₂×C₃	1	1	yes	characteristic
44	C₃×#388	C₂×C₃	1	2	yes	—
45	C₃×#384	C₂×C₃	1	1	yes	characteristic
46	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
48	C₂⁴×C₉	C₂³	1	2	yes	—
49	C₂×D₄×C₉	—	2	2	no	—
50	C₂×D₄×C₉	—	2	2	no	—
51	C₂×D₄×C₉	—	2	2	no	—
52	C₂²×C₄×C₉	C₂³	1	2	yes	—
53	C₂²×C₄×C₉	C₂³	1	2	yes	—
54	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
55	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₂²×C₄×C₉	C₂³	1	2	yes	—
57	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
62	C₉×C₄⋊C₄	—	2	4	no	—
63	C₉×C₄⋊C₄	—	2	4	no	—
64	C₉×C₄⋊C₄	—	2	2	no	—
65	C₉×C₄⋊C₄	—	2	2	no	—
66	C₉×C₄⋊C₄	—	2	2	no	—
67	C₉×C₄⋊C₄	—	2	2	no	—
68	C₉×C₄⋊C₄	—	4	2	no	—
69	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
70	C₉×C₂²⋊C₄	—	2	4	no	—
71	C₉×C₂²⋊C₄	—	2	4	no	—
72	C₉×C₂²⋊C₄	—	2	4	no	—
73	C₉×C₂²⋊C₄	—	2	4	no	—
74	C₉×C₂²⋊C₄	—	4	2	no	—
75	C₉×C₂²⋊C₄	—	4	2	no	—
76	C₄²×C₉	—	2	4	no	—
77	C₄²×C₉	—	2	2	no	—
78	C₄²×C₉	—	2	2	no	—
79	C₄²×C₉	—	2	2	no	—
80	#2512	C₉	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₃×#126	—	2	8	no	—
83	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
95	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
100	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
101	C₃×#95	C₂²×C₃	1	1	yes	characteristic
102	C₃×#95	C₂²×C₃	1	2	yes	—
103	C₃×#95	C₂²×C₃	1	1	yes	characteristic
104	C₃×#95	C₂²×C₃	1	2	yes	—
105	C₂³×C₉	—	2	2	no	—
106	C₂³×C₉	—	2	2	no	—
107	C₂³×C₉	—	2	2	no	—
108	C₂³×C₉	—	2	2	no	—
109	C₂³×C₉	—	2	2	no	—
110	C₂³×C₉	—	2	2	no	—
111	C₂³×C₉	—	2	2	no	—
112	C₂³×C₉	C₂⁴	1	1	yes	characteristic
113	D₄×C₉	—	4	4	no	—
114	C₂×C₄×C₉	—	2	1	no	—
115	C₂×C₄×C₉	—	2	1	no	—
116	C₂×C₄×C₉	—	2	1	no	—
117	C₂×C₄×C₉	—	2	1	no	—
118	C₂×C₄×C₉	—	2	1	no	—
119	C₂×C₄×C₉	—	2	1	no	—
120	C₂×C₄×C₉	—	2	1	no	—
121	C₂×C₄×C₉	—	2	1	no	—
122	C₂×C₄×C₉	—	2	2	no	—
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	2	2	no	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	1	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	2	2	no	—
129	C₂×C₄×C₉	—	2	2	no	—
130	C₂×C₄×C₉	—	2	2	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	1	no	—
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
139	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₉	#41	1	2	yes	—
141	C₂×C₄×C₉	#41	1	2	yes	—
142	C₂×C₄×C₉	#41	1	2	yes	—
143	C₂×C₄×C₉	#41	1	2	yes	—
144	C₂×#126	C₂×C₉	1	2	yes	complemented
145	#397	C₂×C₉	1	2	yes	complemented
146	#396	C₂×C₉	1	2	yes	complemented
147	#390	C₂×C₉	1	1	yes	characteristic
148	#390	C₂×C₉	1	1	yes	characteristic
149	#390	C₂×C₉	1	1	yes	characteristic
150	#389	C₂×C₉	1	1	yes	characteristic, complemented
151	#388	C₂×C₉	1	2	yes	complemented
152	#384	C₂×C₉	1	1	yes	characteristic, complemented
153	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
154	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
155	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
156	C₂×C₃×D₄	—	2	2	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
162	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
163	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
164	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	—	4	2	no	—
176	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
177	C₃×C₂²⋊C₄	—	2	4	no	—
178	C₃×C₂²⋊C₄	—	2	4	no	—
179	C₃×C₂²⋊C₄	—	2	4	no	—
180	C₃×C₂²⋊C₄	—	2	4	no	—
181	C₃×C₂²⋊C₄	—	4	2	no	—
182	C₃×C₂²⋊C₄	—	4	2	no	—
183	C₃×C₄²	—	2	4	no	—
184	C₃×C₄²	—	2	2	no	—
185	C₃×C₄²	—	2	2	no	—
186	C₃×C₄²	—	2	2	no	—
187	C₂²×C₉	—	4	2	no	—
188	C₂²×C₉	—	4	2	no	—
189	C₂²×C₉	—	4	2	no	—
190	C₂²×C₉	—	4	2	no	—
191	C₂²×C₉	—	4	2	no	—
192	C₂²×C₉	—	4	2	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
195	C₂²×C₉	C₂×#41	1	1	yes	characteristic
196	C₂²×C₉	C₂×#41	1	1	yes	characteristic
197	C₂²×C₉	C₂×#41	1	1	yes	characteristic
198	C₂²×C₉	C₂×#41	1	1	yes	characteristic
199	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
201	C₄×C₉	—	2	2	no	—
202	C₄×C₉	—	2	2	no	—
203	C₄×C₉	—	2	2	no	—
204	C₄×C₉	—	2	2	no	—
205	C₄×C₉	—	4	2	no	—
206	C₄×C₉	—	4	1	no	—
207	C₄×C₉	—	4	2	no	—
208	C₄×C₉	—	4	2	no	—
209	C₄×C₉	—	4	1	no	—
210	C₄×C₉	#126	1	4	yes	complemented
211	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
212	#126	—	2	8	no	—
213	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
214	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
215	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
220	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
221	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
227	C₂×C₄²	C₂²×C₉	1	2	yes	—
228	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
229	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
230	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
231	#95	C₂²×C₉	1	1	yes	characteristic
232	#95	C₂²×C₉	1	2	yes	—
233	#95	C₂²×C₉	1	1	yes	characteristic
234	#95	C₂²×C₉	1	2	yes	—
235	C₂³×C₃	—	2	2	no	—
236	C₂³×C₃	—	2	2	no	—
237	C₂³×C₃	—	2	2	no	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	2	2	no	—
240	C₂³×C₃	—	2	2	no	—
241	C₂³×C₃	—	2	2	no	—
242	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
243	C₃×D₄	—	4	4	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
268	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
269	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
270	C₂×C₃×C₄	C₃×#41	1	2	yes	—
271	C₂×C₃×C₄	C₃×#41	1	2	yes	—
272	C₂×C₃×C₄	C₃×#41	1	2	yes	—
273	C₂×C₃×C₄	C₃×#41	1	2	yes	—
274	C₂×C₉	—	8	2	no	—
275	C₂×C₉	C₂×#126	1	1	yes	characteristic
276	C₂×C₉	#532	1	1	yes	characteristic
277	C₂×C₉	#542	1	1	yes	characteristic
278	C₂×C₉	#547	1	1	yes	characteristic
279	C₂×C₉	#550	1	1	yes	characteristic
280	C₂×C₉	#553	1	1	yes	characteristic
281	C₂×C₉	#556	1	1	yes	characteristic
282	C₂⁴	C₂³×C₉	1	2	yes	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
287	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
288	C₂²×C₄	C₂³×C₉	1	2	yes	—
289	C₂²×C₄	C₂³×C₉	1	2	yes	—
290	C₂²×C₄	C₂³×C₉	1	2	yes	—
291	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
294	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
295	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₂²×C₃	—	4	2	no	—
315	C₂²×C₃	—	4	2	no	—
316	C₂²×C₃	—	4	2	no	—
317	C₂²×C₃	—	4	2	no	—
318	C₂²×C₃	—	4	2	no	—
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
323	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
324	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
325	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
326	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	4	2	no	—
333	C₃×C₄	—	4	1	no	—
334	C₃×C₄	—	4	2	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	—	4	1	no	—
337	C₃×C₄	C₃×#126	1	4	yes	—
338	C₉	#2512	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	C₂⁴×C₉	1	1	yes	characteristic
347	D₄	—	4	4	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
372	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
373	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
374	C₂×C₄	C₉×#41	1	2	yes	—
375	C₂×C₄	C₉×#41	1	2	yes	—
376	C₂×C₄	C₉×#41	1	2	yes	—
377	C₂×C₄	C₉×#41	1	2	yes	—
378	C₂×C₃	—	8	2	no	—
379	C₂×C₃	C₂×C₃×#126	1	1	yes	characteristic
380	C₂×C₃	C₃×#532	1	1	yes	characteristic
381	C₂×C₃	C₃×#542	1	1	yes	characteristic
382	C₂×C₃	C₃×#547	1	1	yes	characteristic
383	C₂×C₃	C₃×#550	1	1	yes	characteristic
384	C₂×C₃	C₃×#553	1	1	yes	characteristic
385	C₂×C₃	C₃×#556	1	1	yes	characteristic
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
394	C₂²	C₂×C₉×#41	1	1	yes	characteristic
395	C₂²	C₂×C₉×#41	1	1	yes	characteristic
396	C₂²	C₂×C₉×#41	1	1	yes	characteristic
397	C₂²	C₂×C₉×#41	1	1	yes	characteristic
398	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	1	no	—
409	C₄	C₉×#126	1	4	yes	complemented
410	C₃	C₃×#2512	1	1	yes	characteristic
411	C₂	—	8	2	no	—
412	C₂	C₂×C₉×#126	1	1	yes	characteristic
413	C₂	C₉×#532	1	1	yes	characteristic
414	C₂	C₉×#542	1	1	yes	characteristic
415	C₂	C₉×#547	1	1	yes	characteristic
416	C₂	C₉×#550	1	1	yes	characteristic
417	C₂	C₉×#553	1	1	yes	characteristic
418	C₂	C₉×#556	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂²×C₃×D₄	C₂²×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#126	C₂	semidirect
2. C₉×#397	C₂	semidirect
3. C₉×#396	C₂	semidirect
7. C₉×#389	C₂	semidirect
8. C₉×#388	C₂	semidirect
9. C₉×#384	C₂	semidirect
10. C₄×C₉×C₄⋊C₄	C₂	semidirect
11. C₄×C₉×C₄⋊C₄	C₂	semidirect
69. C₉×C₄⋊C₄	D₄	semidirect
80. #2512	C₉	direct (N × H)
144. C₂×#126	C₂×C₉	semidirect
145. #397	C₂×C₉	semidirect
146. #396	C₂×C₉	semidirect
150. #389	C₂×C₉	semidirect
151. #388	C₂×C₉	semidirect
152. #384	C₂×C₉	semidirect
153. C₄×C₄⋊C₄	C₂×C₉	semidirect
154. C₄×C₄⋊C₄	C₂×C₉	semidirect
210. C₄×C₉	#126	semidirect
303. C₄⋊C₄	D₄×C₉	semidirect
338. C₉	#2512	direct (N × H)
409. C₄	C₉×#126	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#126	2
C₉×#397	2
C₉×#396	2
C₉×#390	2
C₉×#389	2
C₉×#388	2
C₉×#384	2
C₄×C₉×C₄⋊C₄	2
C₃×#2512	3

Subgroups — C9×#2512 #11767233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2512 #11767233