Subgroups — C₉×#4886 #13142206

Order 1728.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#204	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#895	C₂	1	1	yes	maximal, characteristic
5	C₃×C₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4886	C₃	1	1	yes	maximal, characteristic
9	C₉×#468	—	3	1	no	maximal
10	C₂×C₉×D₁₂	—	2	1	no	—
11	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
18	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₉×C₄⋊Dic₃	—	2	1	no	—
20	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₉×#204	—	2	2	no	—
22	C₉×ΓL(1,𝔽₂₅)	—	2	2	no	—
23	C₂×C₃×#204	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
25	C₃×#897	C₂×C₃	1	1	yes	characteristic
26	C₃×#895	C₂×C₃	1	1	yes	characteristic
27	C₃²×#107	C₂×C₃	1	1	yes	characteristic
28	C₃×#810	C₂×C₃	1	1	yes	characteristic
29	C₃×#809	C₂×C₃	1	1	yes	characteristic
30	C₂×C₉×SD₁₆	—	3	1	no	—
31	C₂×C₉×M₁₆	—	3	1	no	—
32	C₉×C₂²⋊Q₈	—	3	1	no	—
33	C₉×#121	—	3	1	no	—
34	C₉×#107	—	2	1	no	—
35	C₉×#107	D₃	1	1	yes	characteristic, complemented
36	C₉×#103	—	3	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₂²×D₃×C₉	—	2	1	no	—
39	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
43	C₂×C₉×Dic₃	—	2	1	no	—
44	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
45	C₉×D₁₂	—	2	1	no	—
46	C₉×D₁₂	—	2	1	no	—
47	C₉×D₁₂	—	4	2	no	—
48	C₄×D₃×C₉	—	2	1	no	—
49	C₄×D₃×C₉	—	2	1	no	—
50	C₉×Dic₆	—	2	1	no	—
51	C₉×Dic₆	—	2	1	no	—
52	C₃×C₈×C₉	D₄	1	2	yes	complemented
53	C₉×C₃⋊C₈	—	2	1	no	—
54	C₃×#468	—	3	1	no	—
55	#4886	C₉	1	1	yes	characteristic, direct product factor
56	C₂×C₃×D₁₂	—	2	1	no	—
57	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
61	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
62	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
63	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
64	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
65	C₃×C₄⋊Dic₃	—	2	1	no	—
66	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
67	C₃×#204	—	2	2	no	—
68	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
69	C₂×Q₈×C₉	—	3	1	no	—
70	C₂×D₄×C₉	—	3	1	no	—
71	C₂×D₄×C₉	—	6	1	no	—
72	C₂²×C₄×C₉	—	3	1	no	—
73	C₉×SD₁₆	—	6	2	no	—
74	C₉×M₁₆	—	6	2	no	—
75	C₂×C₈×C₉	—	2	1	no	—
76	C₂×C₈×C₉	—	3	1	no	—
77	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
78	C₉×C₄⋊C₄	—	2	1	no	—
79	C₉×C₄⋊C₄	—	2	1	no	—
80	C₉×C₄⋊C₄	—	6	1	no	—
81	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
83	C₉×C₂²⋊C₄	—	6	1	no	—
84	C₉×C₂²⋊C₄	—	6	1	no	—
85	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
86	C₂×D₃×C₉	—	2	1	no	—
87	C₂×D₃×C₉	—	2	1	no	—
88	C₂×D₃×C₉	—	2	1	no	—
89	C₂×D₃×C₉	—	4	1	no	—
90	C₂×D₃×C₉	—	4	1	no	—
91	C₂×D₃×C₉	—	4	1	no	—
92	C₃×C₄×C₉	—	4	1	no	—
93	C₃×C₄×C₉	—	4	1	no	—
94	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
95	C₃×C₄×C₉	#41	1	1	yes	characteristic
96	C₉×Dic₃	—	2	1	no	—
97	C₉×Dic₃	—	4	1	no	—
98	C₂×C₃×SD₁₆	—	3	1	no	—
99	C₂×C₃×M₁₆	—	3	1	no	—
100	C₃×C₂²⋊Q₈	—	3	1	no	—
101	C₃×#121	—	3	1	no	—
102	C₂×#204	C₂×C₉	1	1	yes	characteristic, complemented
103	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic, complemented
104	#897	C₂×C₉	1	1	yes	characteristic, complemented
105	#895	C₂×C₉	1	1	yes	characteristic
106	C₃×#107	—	2	1	no	—
107	C₃×#107	C₂×C₉	1	1	yes	characteristic, complemented
108	C₃×#107	C₃×D₃	1	1	yes	characteristic
109	C₃×#103	—	3	1	no	—
110	C₃×#102	—	3	1	no	—
111	#810	C₂×C₉	1	1	yes	characteristic, complemented
112	#809	C₂×C₉	1	1	yes	characteristic, complemented
113	C₂²×C₃×D₃	—	2	1	no	—
114	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
118	C₂×C₃×Dic₃	—	2	1	no	—
119	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
120	C₃×D₁₂	—	2	1	no	—
121	C₃×D₁₂	—	2	1	no	—
122	C₃×D₁₂	—	4	2	no	—
123	C₃×C₄×D₃	—	2	1	no	—
124	C₃×C₄×D₃	—	2	1	no	—
125	C₃×Dic₆	—	2	1	no	—
126	C₃×Dic₆	—	2	1	no	—
127	C₂³×C₉	—	3	1	no	—
128	C₂³×C₉	—	6	1	no	—
129	C₃²×C₈	C₃×D₄	1	2	yes	—
130	C₃×C₃⋊C₈	—	2	1	no	—
131	Q₈×C₉	—	6	1	no	—
132	Q₈×C₉	—	6	1	no	—
133	D₄×C₉	—	6	1	no	—
134	D₄×C₉	—	6	1	no	—
135	D₄×C₉	—	12	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	3	1	no	—
140	C₂×C₄×C₉	—	4	1	no	—
141	C₂×C₄×C₉	—	4	1	no	—
142	C₂×C₄×C₉	—	6	1	no	—
143	C₂×C₄×C₉	—	6	1	no	—
144	C₂×C₄×C₉	—	6	1	no	—
145	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
146	C₈×C₉	—	2	2	no	—
147	C₈×C₉	—	6	1	no	—
148	C₈×C₉	D₁₂	1	2	yes	complemented
149	#468	—	3	1	no	Sylow
150	C₂×C₃×C₉	#121	1	1	yes	characteristic
151	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₃×C₉	#137	1	1	yes	characteristic
153	D₃×C₉	—	4	1	no	—
154	D₃×C₉	—	8	1	no	—
155	C₂×C₃×Q₈	—	3	1	no	—
156	C₂×C₃×D₄	—	3	1	no	—
157	C₂×C₃×D₄	—	6	1	no	—
158	C₂²×C₃×C₄	—	3	1	no	—
159	C₂×D₁₂	—	2	1	no	—
160	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
161	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
162	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
163	C₃×SD₁₆	—	6	2	no	—
164	C₃×M₁₆	—	6	2	no	—
165	C₂×C₃×C₈	—	2	1	no	—
166	C₂×C₃×C₈	—	3	1	no	—
167	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
169	C₃×C₄⋊C₄	—	2	1	no	—
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	—	6	1	no	—
172	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
173	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
174	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
176	C₃×C₂²⋊C₄	—	6	1	no	—
177	C₃×C₂²⋊C₄	—	6	1	no	—
178	(C₂×D₃)⋊C₄	—	2	1	no	—
179	(C₂×D₃)⋊C₄	—	2	1	no	—
180	C₄⋊Dic₃	—	2	1	no	—
181	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
182	#204	—	2	2	no	—
183	ΓL(1,𝔽₂₅)	—	2	2	no	—
184	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂×C₃×D₃	—	2	1	no	—
186	C₂×C₃×D₃	—	2	1	no	—
187	C₂×C₃×D₃	—	2	1	no	—
188	C₂×C₃×D₃	—	4	1	no	—
189	C₂×C₃×D₃	—	4	1	no	—
190	C₂×C₃×D₃	—	4	1	no	—
191	C₃²×C₄	—	4	1	no	—
192	C₃²×C₄	—	4	1	no	—
193	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
194	C₃²×C₄	C₃×#41	1	1	yes	characteristic
195	C₃×Dic₃	—	2	1	no	—
196	C₃×Dic₃	—	4	1	no	—
197	C₂²×C₉	—	2	1	no	—
198	C₂²×C₉	—	6	1	no	—
199	C₂²×C₉	—	6	1	no	—
200	C₂²×C₉	—	6	1	no	—
201	C₂²×C₉	—	12	1	no	—
202	C₂²×C₉	—	12	1	no	—
203	C₂²×C₉	—	12	1	no	—
204	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
205	C₄×C₉	—	2	1	no	—
206	C₄×C₉	—	2	1	no	—
207	C₄×C₉	—	4	1	no	—
208	C₄×C₉	—	4	1	no	—
209	C₄×C₉	—	6	1	no	—
210	C₄×C₉	—	8	1	no	—
211	C₄×C₉	—	8	1	no	—
212	C₄×C₉	—	12	1	no	—
213	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
214	C₄×C₉	#239	1	1	yes	characteristic
215	C₂×SD₁₆	—	3	1	no	—
216	C₂×M₁₆	—	3	1	no	—
217	C₂²⋊Q₈	—	3	1	no	—
218	#121	—	3	1	no	—
219	#107	D₃×C₉	1	1	yes	characteristic, complemented
220	#103	—	3	1	no	—
221	#102	—	3	1	no	—
222	C₃×C₉	#468	1	1	yes	characteristic, complemented, Sylow
223	C₂³×C₃	—	3	1	no	—
224	C₂³×C₃	—	6	1	no	—
225	C₂²×D₃	—	2	1	no	—
226	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
227	C₃×Q₈	—	6	1	no	—
228	C₃×Q₈	—	6	1	no	—
229	C₃×D₄	—	6	1	no	—
230	C₃×D₄	—	6	1	no	—
231	C₃×D₄	—	12	2	no	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	3	1	no	—
238	C₂×C₃×C₄	—	4	1	no	—
239	C₂×C₃×C₄	—	4	1	no	—
240	C₂×C₃×C₄	—	6	1	no	—
241	C₂×C₃×C₄	—	6	1	no	—
242	C₂×C₃×C₄	—	6	1	no	—
243	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
245	C₂×Dic₃	—	2	1	no	—
246	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
247	D₁₂	—	2	1	no	—
248	D₁₂	—	2	1	no	—
249	D₁₂	—	4	2	no	—
250	C₄×D₃	—	2	1	no	—
251	C₄×D₃	—	2	1	no	—
252	Dic₆	—	2	1	no	—
253	Dic₆	—	2	1	no	—
254	C₃×C₈	—	2	2	no	—
255	C₃×C₈	—	6	1	no	—
256	C₃×C₈	D₄×C₉	1	2	yes	complemented
257	C₃×C₈	C₃×D₁₂	1	2	yes	—
258	C₃⋊C₈	—	2	1	no	—
259	C₂×C₃²	C₃×#121	1	1	yes	characteristic
260	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂×C₃²	C₃×#137	1	1	yes	characteristic
262	C₃×D₃	—	4	1	no	—
263	C₃×D₃	—	8	1	no	—
264	C₂×C₉	—	2	1	no	—
265	C₂×C₉	—	2	1	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	12	1	no	—
268	C₂×C₉	—	24	1	no	—
269	C₂×C₉	#895	1	1	yes	characteristic
270	C₂×C₉	#911	1	1	yes	characteristic
271	C₂×C₉	#918	1	1	yes	characteristic
272	C₂×Q₈	—	3	1	no	—
273	C₂×D₄	—	3	1	no	—
274	C₂×D₄	—	6	1	no	—
275	C₂²×C₄	—	3	1	no	—
276	SD₁₆	—	6	2	no	—
277	M₁₆	—	6	2	no	—
278	C₂×C₈	—	3	1	no	—
279	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
280	C₄⋊C₄	—	6	1	no	—
281	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
282	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
283	C₂²⋊C₄	—	6	1	no	—
284	C₂²⋊C₄	—	6	1	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	6	1	no	—
287	C₂²×C₃	—	6	1	no	—
288	C₂²×C₃	—	6	1	no	—
289	C₂²×C₃	—	12	1	no	—
290	C₂²×C₃	—	12	1	no	—
291	C₂²×C₃	—	12	1	no	—
292	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
293	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
294	C₂×D₃	—	2	1	no	—
295	C₂×D₃	—	2	1	no	—
296	C₂×D₃	—	2	1	no	—
297	C₂×D₃	—	4	1	no	—
298	C₂×D₃	—	4	1	no	—
299	C₂×D₃	—	4	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	4	1	no	—
303	C₃×C₄	—	4	1	no	—
304	C₃×C₄	—	4	1	no	—
305	C₃×C₄	—	4	1	no	—
306	C₃×C₄	—	6	1	no	—
307	C₃×C₄	—	8	1	no	—
308	C₃×C₄	—	8	1	no	—
309	C₃×C₄	—	12	1	no	—
310	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
311	C₃×C₄	C₉×#41	1	1	yes	characteristic
312	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
313	C₃×C₄	C₃×#239	1	1	yes	characteristic
314	Dic₃	—	2	1	no	—
315	Dic₃	—	4	1	no	—
316	C₃²	C₃×#468	1	1	yes	characteristic
317	C₉	—	2	1	no	—
318	C₉	#4886	1	1	yes	characteristic, direct product factor
319	C₂³	—	3	1	no	—
320	C₂³	—	6	1	no	—
321	Q₈	—	6	1	no	—
322	Q₈	—	6	1	no	—
323	D₄	—	6	1	no	—
324	D₄	—	6	1	no	—
325	D₄	—	12	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	3	1	no	—
329	C₂×C₄	—	6	1	no	—
330	C₂×C₄	—	6	1	no	—
331	C₂×C₄	—	6	1	no	—
332	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
333	C₈	—	6	1	no	—
334	C₈	C₉×D₁₂	1	2	yes	complemented
335	C₂×C₃	—	2	1	no	—
336	C₂×C₃	—	2	1	no	—
337	C₂×C₃	—	2	1	no	—
338	C₂×C₃	—	12	1	no	—
339	C₂×C₃	—	24	1	no	—
340	C₂×C₃	C₉×#121	1	1	yes	characteristic
341	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₃	C₉×#137	1	1	yes	characteristic
343	C₂×C₃	C₃×#895	1	1	yes	characteristic
344	C₂×C₃	C₃×#911	1	1	yes	characteristic
345	C₂×C₃	C₃×#918	1	1	yes	characteristic
346	D₃	—	4	1	no	—
347	D₃	—	8	1	no	—
348	C₂²	—	6	1	no	—
349	C₂²	—	6	1	no	—
350	C₂²	—	6	1	no	—
351	C₂²	—	12	1	no	—
352	C₂²	—	12	1	no	—
353	C₂²	—	12	1	no	—
354	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
355	C₄	—	4	1	no	—
356	C₄	—	4	1	no	—
357	C₄	—	6	1	no	—
358	C₄	—	12	1	no	—
359	C₄	C₂×C₉×D₁₂	1	1	yes	characteristic
360	C₄	C₉×#239	1	1	yes	characteristic
361	C₃	—	2	1	no	—
362	C₃	C₉×#468	1	1	yes	characteristic, complemented
363	C₃	C₃×#4886	1	1	yes	characteristic
364	C₂	—	12	1	no	—
365	C₂	—	24	1	no	—
366	C₂	C₉×#895	1	1	yes	characteristic
367	C₂	C₉×#911	1	1	yes	characteristic
368	C₂	C₉×#918	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#107	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₃×#895	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#107	D₃
hypocenter	C₃	C₉×#468
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#107

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#204	C₂	semidirect
2. C₂×C₉×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₉×#897	C₂	semidirect
5. C₃×C₉×#107	C₂	semidirect
6. C₉×#810	C₂	semidirect
7. C₉×#809	C₂	semidirect
35. C₉×#107	D₃	semidirect
52. C₃×C₈×C₉	D₄	semidirect
55. #4886	C₉	direct (N × H)
102. C₂×#204	C₂×C₉	semidirect
103. C₂×ΓL(1,𝔽₂₅)	C₂×C₉	semidirect
104. #897	C₂×C₉	semidirect
107. C₃×#107	C₂×C₉	semidirect
111. #810	C₂×C₉	semidirect
112. #809	C₂×C₉	semidirect
148. C₈×C₉	D₁₂	semidirect
219. #107	D₃×C₉	semidirect
222. C₃×C₉	#468	semidirect
256. C₃×C₈	D₄×C₉	semidirect
318. C₉	#4886	direct (N × H)
334. C₈	C₉×D₁₂	semidirect
362. C₃	C₉×#468	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#204	2
C₂×C₉×ΓL(1,𝔽₂₅)	2
C₉×#897	2
C₉×#895	2
C₃×C₉×#107	2
C₉×#810	2
C₉×#809	2
C₃×#4886	3
C₉×#468	3

Subgroups — C9×#4886 #13142206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4886 #13142206