Subgroups — C₉×#5525 #13152499

Order 1728.

1078 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#895	C₂	1	4	yes	maximal, complemented
5	C₉×#882	C₂	1	4	yes	maximal, complemented
6	C₉×#875	C₂	1	2	yes	maximal, complemented
7	C₉×#874	C₂	1	2	yes	maximal, complemented
8	C₃×#5525	C₃	1	1	yes	maximal, characteristic
9	C₉×#535	—	3	1	no	maximal
10	C₂³×D₃×C₉	C₂²	1	2	yes	—
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#67	C₂²	1	2	yes	—
13	C₉×#235	—	2	4	no	—
14	C₂×C₉×D₁₂	—	2	4	no	—
15	C₂×C₉×D₁₂	C₂²	1	2	yes	—
16	C₂×C₉×D₁₂	C₂²	1	2	yes	—
17	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₉×D₁₂	C₂²	1	8	yes	complemented
19	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
20	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃×C₄²×C₉	C₂²	1	2	yes	complemented
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
25	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
26	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
27	C₃²×#117	C₂×C₃	1	1	yes	characteristic
28	C₃×#895	C₂×C₃	1	4	yes	—
29	C₃×#882	C₂×C₃	1	4	yes	—
30	C₃×#875	C₂×C₃	1	2	yes	—
31	C₃×#874	C₂×C₃	1	2	yes	—
32	C₂×C₉×#41	—	3	1	no	—
33	C₂²×D₄×C₉	—	3	1	no	—
34	C₉×#127	—	3	2	no	—
35	C₉×#124	—	3	2	no	—
36	C₉×#121	—	3	4	no	—
37	C₉×#120	—	3	4	no	—
38	C₉×#117	—	2	1	no	—
39	C₉×#117	D₃	1	1	yes	characteristic, complemented
40	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
41	C₂²×D₃×C₉	—	2	4	no	—
42	C₂²×D₃×C₉	—	4	4	no	—
43	C₂²×D₃×C₉	C₂³	1	4	yes	—
44	C₂²×D₃×C₉	C₂³	1	2	yes	—
45	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₉×#67	—	2	4	no	—
50	C₂×C₉×Dic₃	C₂³	1	2	yes	—
51	C₉×D₁₂	—	2	4	no	—
52	C₉×D₁₂	—	2	4	no	—
53	C₉×D₁₂	—	2	2	no	—
54	C₉×D₁₂	—	4	8	no	—
55	C₄×D₃×C₉	—	2	4	no	—
56	C₉×Dic₆	—	2	2	no	—
57	C₃×#535	—	3	1	no	—
58	#5525	C₉	1	1	yes	characteristic, direct product factor
59	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
60	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
62	C₃×#235	—	2	4	no	—
63	C₂×C₃×D₁₂	—	2	4	no	—
64	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
65	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
66	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
69	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
70	C₂⁴×C₉	—	3	2	no	—
71	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
73	C₃²×C₄²	C₂²×C₃	1	2	yes	—
74	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
75	C₉×#41	—	6	4	no	—
76	C₂×Q₈×C₉	—	3	1	no	—
77	C₂×D₄×C₉	—	3	2	no	—
78	C₂×D₄×C₉	—	3	2	no	—
79	C₂×D₄×C₉	—	3	2	no	—
80	C₂×D₄×C₉	—	3	1	no	—
81	C₂×D₄×C₉	—	3	8	no	—
82	C₂×D₄×C₉	—	6	4	no	—
83	C₂²×C₄×C₉	—	2	1	no	—
84	C₂²×C₄×C₉	—	3	2	no	—
85	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
86	C₉×C₄⋊C₄	—	2	2	no	—
87	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
88	C₉×C₂²⋊C₄	—	2	2	no	—
89	C₉×C₂²⋊C₄	—	3	8	no	—
90	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
91	C₄²×C₉	—	2	2	no	—
92	C₄²×C₉	C₂×D₃	1	2	yes	complemented
93	C₂²×C₃×C₉	—	2	2	no	—
94	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
95	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
96	C₂×D₃×C₉	—	2	2	no	—
97	C₂×D₃×C₉	—	2	4	no	—
98	C₂×D₃×C₉	—	2	4	no	—
99	C₂×D₃×C₉	—	2	8	no	—
100	C₂×D₃×C₉	—	4	8	no	—
101	C₃×C₄×C₉	—	2	4	no	—
102	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
103	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
104	C₉×Dic₃	—	2	2	no	—
105	C₂×C₃×#41	—	3	1	no	—
106	C₂²×C₃×D₄	—	3	1	no	—
107	C₂×#235	C₂×C₉	1	1	yes	characteristic, complemented
108	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
109	C₃×#127	—	3	2	no	—
110	C₃×#124	—	3	2	no	—
111	C₃×#121	—	3	4	no	—
112	C₃×#120	—	3	4	no	—
113	C₃×#117	—	2	1	no	—
114	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
115	C₃×#117	C₃×D₃	1	1	yes	characteristic
116	#895	C₂×C₉	1	4	yes	complemented
117	#882	C₂×C₉	1	4	yes	complemented
118	#875	C₂×C₉	1	2	yes	complemented
119	#874	C₂×C₉	1	2	yes	complemented
120	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
121	C₂²×C₃×D₃	—	2	4	no	—
122	C₂²×C₃×D₃	—	4	4	no	—
123	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
124	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
125	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
126	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
129	C₃×#67	—	2	4	no	—
130	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
131	C₃×D₁₂	—	2	4	no	—
132	C₃×D₁₂	—	2	4	no	—
133	C₃×D₁₂	—	2	2	no	—
134	C₃×D₁₂	—	4	8	no	—
135	C₃×C₄×D₃	—	2	4	no	—
136	C₃×Dic₆	—	2	2	no	—
137	C₂³×C₉	—	2	1	no	—
138	C₂³×C₉	—	3	4	no	—
139	C₂³×C₉	—	3	2	no	—
140	C₂³×C₉	—	6	4	no	—
141	C₂³×C₉	—	12	4	no	—
142	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
143	Q₈×C₉	—	6	2	no	—
144	D₄×C₉	—	6	4	no	—
145	D₄×C₉	—	6	4	no	—
146	D₄×C₉	—	6	4	no	—
147	D₄×C₉	—	6	2	no	—
148	D₄×C₉	—	12	8	no	—
149	C₂×C₄×C₉	—	2	4	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	4	no	—
153	C₂×C₄×C₉	—	3	2	no	—
154	C₂×C₄×C₉	—	6	4	no	—
155	C₂×C₄×C₉	D₁₂	1	4	yes	complemented
156	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
157	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
158	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
159	#535	—	3	1	no	Sylow
160	C₂×C₃×C₉	—	2	2	no	—
161	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
163	D₃×C₉	—	4	2	no	—
164	D₃×C₉	—	4	4	no	—
165	C₂⁴×C₃	—	3	2	no	—
166	C₂³×D₃	C₂²×C₉	1	2	yes	—
167	C₃×#41	—	6	4	no	—
168	C₂×C₃×Q₈	—	3	1	no	—
169	C₂×C₃×D₄	—	3	2	no	—
170	C₂×C₃×D₄	—	3	2	no	—
171	C₂×C₃×D₄	—	3	2	no	—
172	C₂×C₃×D₄	—	3	1	no	—
173	C₂×C₃×D₄	—	3	8	no	—
174	C₂×C₃×D₄	—	6	4	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	3	2	no	—
177	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
179	C₂×#67	C₂²×C₉	1	2	yes	—
180	#235	—	2	4	no	—
181	C₂×D₁₂	—	2	4	no	—
182	C₂×D₁₂	C₂²×C₉	1	2	yes	—
183	C₂×D₁₂	C₂²×C₉	1	2	yes	—
184	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
185	C₂×D₁₂	C₂²×C₉	1	8	yes	complemented
186	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
187	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
190	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
191	C₃×C₂²⋊C₄	—	2	2	no	—
192	C₃×C₂²⋊C₄	—	3	8	no	—
193	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
195	C₃×C₄²	—	2	2	no	—
196	C₃×C₄²	C₂²×C₉	1	2	yes	complemented
197	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
198	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	complemented
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
201	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
202	C₂×C₃×D₃	—	2	2	no	—
203	C₂×C₃×D₃	—	2	4	no	—
204	C₂×C₃×D₃	—	2	4	no	—
205	C₂×C₃×D₃	—	2	8	no	—
206	C₂×C₃×D₃	—	4	8	no	—
207	C₃²×C₄	—	2	4	no	—
208	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
209	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
210	C₃×Dic₃	—	2	2	no	—
211	C₂²×C₉	—	2	2	no	—
212	C₂²×C₉	—	2	1	no	—
213	C₂²×C₉	—	2	2	no	—
214	C₂²×C₉	—	4	2	no	—
215	C₂²×C₉	—	6	2	no	—
216	C₂²×C₉	—	6	4	no	—
217	C₂²×C₉	—	6	4	no	—
218	C₂²×C₉	—	6	8	no	—
219	C₂²×C₉	—	12	8	no	—
220	C₂²×C₉	C₂×D₁₂	1	2	yes	—
221	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
222	C₄×C₉	—	2	4	no	—
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	2	2	no	—
225	C₄×C₉	—	4	4	no	—
226	C₄×C₉	—	6	2	no	—
227	C₄×C₉	C₂×D₁₂	1	2	yes	—
228	C₄×C₉	C₂×D₁₂	1	2	yes	—
229	C₂×#41	—	3	1	no	—
230	C₂²×D₄	—	3	1	no	—
231	#127	—	3	2	no	—
232	#124	—	3	2	no	—
233	#121	—	3	4	no	—
234	#120	—	3	4	no	—
235	#117	D₃×C₉	1	1	yes	characteristic, complemented
236	C₃×C₉	#535	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	3	4	no	—
239	C₂³×C₃	—	3	2	no	—
240	C₂³×C₃	—	6	4	no	—
241	C₂³×C₃	—	12	4	no	—
242	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
243	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
244	C₂²×D₃	—	2	4	no	—
245	C₂²×D₃	—	4	4	no	—
246	C₂²×D₃	C₂³×C₉	1	4	yes	—
247	C₂²×D₃	C₂³×C₉	1	2	yes	—
248	C₃×Q₈	—	6	2	no	—
249	C₃×D₄	—	6	4	no	—
250	C₃×D₄	—	6	4	no	—
251	C₃×D₄	—	6	4	no	—
252	C₃×D₄	—	6	2	no	—
253	C₃×D₄	—	12	8	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	3	2	no	—
259	C₂×C₃×C₄	—	6	4	no	—
260	C₂×C₃×C₄	D₄×C₉	1	4	yes	complemented
261	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
262	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
264	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
265	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
268	#67	—	2	4	no	—
269	C₂×Dic₃	C₂³×C₉	1	2	yes	—
270	D₁₂	—	2	4	no	—
271	D₁₂	—	2	4	no	—
272	D₁₂	—	2	2	no	—
273	D₁₂	—	4	8	no	—
274	C₄×D₃	—	2	4	no	—
275	Dic₆	—	2	2	no	—
276	C₂×C₃²	—	2	2	no	—
277	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
278	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
279	C₃×D₃	—	4	2	no	—
280	C₃×D₃	—	4	4	no	—
281	C₂×C₉	—	2	2	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	—	2	2	no	—
284	C₂×C₉	—	4	2	no	—
285	C₂×C₉	—	12	2	no	—
286	C₂×C₉	—	12	4	no	—
287	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
288	C₂×C₉	#1009	1	2	yes	—
289	C₂⁴	—	3	2	no	—
290	#41	—	6	4	no	—
291	C₂×Q₈	—	3	1	no	—
292	C₂×D₄	—	3	2	no	—
293	C₂×D₄	—	3	2	no	—
294	C₂×D₄	—	3	2	no	—
295	C₂×D₄	—	3	1	no	—
296	C₂×D₄	—	3	8	no	—
297	C₂×D₄	—	6	4	no	—
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
300	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
301	C₂²⋊C₄	—	3	8	no	—
302	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
303	C₄²	C₂×D₃×C₉	1	2	yes	complemented
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	6	2	no	—
310	C₂²×C₃	—	6	4	no	—
311	C₂²×C₃	—	6	4	no	—
312	C₂²×C₃	—	6	8	no	—
313	C₂²×C₃	—	12	8	no	—
314	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
315	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
316	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
317	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
318	C₂×D₃	—	2	2	no	—
319	C₂×D₃	—	2	4	no	—
320	C₂×D₃	—	2	4	no	—
321	C₂×D₃	—	2	8	no	—
322	C₂×D₃	—	4	8	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	2	2	no	—
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	4	4	no	—
328	C₃×C₄	—	6	2	no	—
329	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
330	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
331	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
332	C₃×C₄	C₂×C₃×D₁₂	1	2	yes	—
333	Dic₃	—	2	2	no	—
334	C₃²	C₃×#535	1	1	yes	characteristic
335	C₉	—	2	1	no	—
336	C₉	#5525	1	1	yes	characteristic, direct product factor
337	C₂³	—	3	4	no	—
338	C₂³	—	3	2	no	—
339	C₂³	—	6	4	no	—
340	C₂³	—	12	4	no	—
341	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
342	Q₈	—	6	2	no	—
343	D₄	—	6	4	no	—
344	D₄	—	6	4	no	—
345	D₄	—	6	4	no	—
346	D₄	—	6	2	no	—
347	D₄	—	12	8	no	—
348	C₂×C₄	—	3	2	no	—
349	C₂×C₄	—	6	4	no	—
350	C₂×C₄	C₉×D₁₂	1	4	yes	complemented
351	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
352	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
354	C₂×C₃	—	2	2	no	—
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	4	2	no	—
359	C₂×C₃	—	12	4	no	—
360	C₂×C₃	—	12	2	no	—
361	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
362	C₂×C₃	C₉×H(5,𝔽₂)	1	2	yes	—
363	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
364	C₂×C₃	C₃×#1009	1	2	yes	—
365	D₃	—	4	4	no	—
366	D₃	—	4	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	6	2	no	—
369	C₂²	—	6	4	no	—
370	C₂²	—	6	4	no	—
371	C₂²	—	6	8	no	—
372	C₂²	—	12	8	no	—
373	C₂²	C₂×C₉×D₁₂	1	2	yes	—
374	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
375	C₄	—	2	4	no	—
376	C₄	—	6	2	no	—
377	C₄	C₂×C₉×D₁₂	1	2	yes	—
378	C₄	C₂×C₉×D₁₂	1	2	yes	—
379	C₃	—	2	1	no	—
380	C₃	C₉×#535	1	1	yes	characteristic, complemented
381	C₃	C₃×#5525	1	1	yes	characteristic
382	C₂	—	2	2	no	—
383	C₂	—	12	4	no	—
384	C₂	—	12	2	no	—
385	C₂	C₂²×C₉×D₁₂	1	1	yes	characteristic
386	C₂	C₉×#1009	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5525	C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₉×#535
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#235	C₂	semidirect
2. C₂²×C₉×D₁₂	C₂	semidirect
3. C₃×C₉×#117	C₂	semidirect
4. C₉×#895	C₂	semidirect
5. C₉×#882	C₂	semidirect
6. C₉×#875	C₂	semidirect
7. C₉×#874	C₂	semidirect
17. C₂×C₉×D₁₂	C₂²	semidirect
18. C₂×C₉×D₁₂	C₂²	semidirect
19. C₂×C₄×D₃×C₉	C₂²	semidirect
20. C₂×C₉×Dic₆	C₂²	semidirect
21. C₃×C₉×C₄⋊C₄	C₂²	semidirect
23. C₃×C₄²×C₉	C₂²	semidirect
24. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
39. C₉×#117	D₃	semidirect
45. C₂×C₃×C₄×C₉	D₄	semidirect
58. #5525	C₉	direct (N × H)
87. C₉×C₄⋊C₄	C₂×D₃	semidirect
92. C₄²×C₉	C₂×D₃	semidirect
107. C₂×#235	C₂×C₉	semidirect
108. C₂²×D₁₂	C₂×C₉	semidirect
114. C₃×#117	C₂×C₉	semidirect
116. #895	C₂×C₉	semidirect
117. #882	C₂×C₉	semidirect
118. #875	C₂×C₉	semidirect
119. #874	C₂×C₉	semidirect
155. C₂×C₄×C₉	D₁₂	semidirect
184. C₂×D₁₂	C₂²×C₉	semidirect
185. C₂×D₁₂	C₂²×C₉	semidirect
186. C₂×C₄×D₃	C₂²×C₉	semidirect
187. C₂×Dic₆	C₂²×C₉	semidirect
189. C₃×C₄⋊C₄	C₂²×C₉	semidirect
196. C₃×C₄²	C₂²×C₉	semidirect
198. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
235. #117	D₃×C₉	semidirect
236. C₃×C₉	#535	semidirect
260. C₂×C₃×C₄	D₄×C₉	semidirect
300. C₄⋊C₄	C₂×D₃×C₉	semidirect
303. C₄²	C₂×D₃×C₉	semidirect
336. C₉	#5525	direct (N × H)
350. C₂×C₄	C₉×D₁₂	semidirect
380. C₃	C₉×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#235	2
C₂²×C₉×D₁₂	2
C₃×C₉×#117	2
C₉×#895	2
C₉×#882	2
C₉×#875	2
C₉×#874	2
C₃×#5525	3
C₉×#535	3

Subgroups — C9×#5525 #13152499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5525 #13152499