Subgroups — C₂×C₉×#535 #11768167

Order 1152.

2844 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#535	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₉×#127	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×#124	C₂	1	2	yes	maximal, complemented
6	C₂×C₉×#121	C₂	1	4	yes	maximal, complemented
7	C₂×C₉×#120	C₂	1	4	yes	maximal, complemented
8	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#535	C₃	1	1	yes	maximal, characteristic
10	C₂⁵×C₉	C₂²	1	2	yes	—
11	C₂×C₉×#41	—	2	8	no	—
12	C₂×C₉×#41	C₂²	1	8	yes	complemented
13	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
14	C₂²×D₄×C₉	—	2	8	no	—
15	C₂²×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×D₄×C₉	C₂²	1	2	yes	—
17	C₂²×D₄×C₉	C₂²	1	2	yes	—
18	C₂²×D₄×C₉	C₂²	1	8	yes	complemented
19	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×C₉	C₂²	1	8	yes	complemented
21	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
23	C₉×#127	C₂²	1	16	yes	complemented
24	C₉×#124	C₂²	1	16	yes	complemented
25	C₉×#121	C₂²	1	32	yes	complemented
26	C₉×#120	C₂²	1	32	yes	complemented
27	C₉×#117	C₂²	1	8	yes	complemented
28	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
31	C₂×C₄²×C₉	C₂²	1	2	yes	complemented
32	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic
33	C₂³×C₃×D₄	C₂×C₃	1	1	yes	characteristic
34	C₃×#535	C₂×C₃	1	16	yes	—
35	C₂×C₃×#127	C₂×C₃	1	2	yes	—
36	C₂×C₃×#124	C₂×C₃	1	2	yes	—
37	C₂×C₃×#121	C₂×C₃	1	4	yes	—
38	C₂×C₃×#120	C₂×C₃	1	4	yes	—
39	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
40	C₂⁴×C₉	—	2	8	no	—
41	C₂⁴×C₉	—	4	8	no	—
42	C₂⁴×C₉	C₂³	1	4	yes	—
43	C₂⁴×C₉	C₂³	1	2	yes	—
44	C₂⁴×C₉	C₂³	1	1	yes	characteristic
45	C₂⁴×C₉	C₂³	1	8	yes	—
46	C₉×#41	—	2	32	no	—
47	C₂×Q₈×C₉	—	2	4	no	—
48	C₂×Q₈×C₉	C₂³	1	4	yes	complemented
49	C₂×D₄×C₉	—	2	8	no	—
50	C₂×D₄×C₉	—	2	8	no	—
51	C₂×D₄×C₉	—	2	8	no	—
52	C₂×D₄×C₉	—	2	4	no	—
53	C₂×D₄×C₉	—	2	32	no	—
54	C₂×D₄×C₉	—	4	16	no	—
55	C₂×D₄×C₉	C₂³	1	8	yes	—
56	C₂×D₄×C₉	C₂³	1	8	yes	—
57	C₂×D₄×C₉	C₂³	1	8	yes	—
58	C₂×D₄×C₉	C₂³	1	4	yes	complemented
59	C₂×D₄×C₉	C₂³	1	32	yes	complemented
60	C₂²×C₄×C₉	—	2	8	no	—
61	C₂²×C₄×C₉	D₄	1	8	yes	complemented
62	C₂²×C₄×C₉	C₂³	1	4	yes	—
63	C₂²×C₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₉	C₂³	1	4	yes	—
67	C₂²×C₄×C₉	C₂³	1	8	yes	complemented
68	C₉×C₄⋊C₄	C₂³	1	8	yes	complemented
69	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
70	C₉×C₂²⋊C₄	C₂³	1	32	yes	complemented
71	C₄²×C₉	C₂³	1	8	yes	complemented
72	C₂×#535	C₉	1	1	yes	characteristic, direct product factor, Sylow
73	C₂⁵×C₃	C₂²×C₃	1	2	yes	—
74	C₂×C₃×#41	—	2	8	no	—
75	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
76	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₃×D₄	—	2	8	no	—
78	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
79	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
80	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
81	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
82	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃×D₄	C₂²×C₃	1	8	yes	—
84	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
86	C₃×#127	C₂²×C₃	1	16	yes	—
87	C₃×#124	C₂²×C₃	1	16	yes	—
88	C₃×#121	C₂²×C₃	1	32	yes	—
89	C₃×#120	C₂²×C₃	1	32	yes	—
90	C₃×#117	C₂²×C₃	1	8	yes	—
91	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
94	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
95	C₂³×C₉	—	2	4	no	—
96	C₂³×C₉	—	2	4	no	—
97	C₂³×C₉	—	2	16	no	—
98	C₂³×C₉	—	2	8	no	—
99	C₂³×C₉	—	2	8	no	—
100	C₂³×C₉	—	2	16	no	—
101	C₂³×C₉	—	4	16	no	—
102	C₂³×C₉	—	4	32	no	—
103	C₂³×C₉	C₂×D₄	1	4	yes	—
104	C₂³×C₉	C₂⁴	1	8	yes	—
105	C₂³×C₉	C₂⁴	1	4	yes	—
106	C₂³×C₉	C₂⁴	1	2	yes	—
107	C₂³×C₉	C₂⁴	1	1	yes	characteristic
108	Q₈×C₉	—	2	8	no	—
109	D₄×C₉	—	2	16	no	—
110	D₄×C₉	—	2	16	no	—
111	D₄×C₉	—	2	16	no	—
112	D₄×C₉	—	2	8	no	—
113	D₄×C₉	—	4	32	no	—
114	C₂×C₄×C₉	—	2	4	no	—
115	C₂×C₄×C₉	—	2	8	no	—
116	C₂×C₄×C₉	—	2	16	no	—
117	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
118	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
119	C₂×C₄×C₉	C₂×D₄	1	16	yes	complemented
120	C₂×C₄×C₉	C₂⁴	1	8	yes	—
121	C₂×C₄×C₉	C₂⁴	1	4	yes	—
122	C₂×C₄×C₉	C₂⁴	1	2	yes	—
123	C₂×C₄×C₉	C₂⁴	1	2	yes	—
124	C₂²×#41	C₂×C₉	1	1	yes	characteristic, complemented
125	C₂³×D₄	C₂×C₉	1	1	yes	characteristic, complemented
126	#535	C₂×C₉	1	16	yes	direct product factor
127	C₂×#127	C₂×C₉	1	2	yes	complemented
128	C₂×#124	C₂×C₉	1	2	yes	complemented
129	C₂×#121	C₂×C₉	1	4	yes	complemented
130	C₂×#120	C₂×C₉	1	4	yes	complemented
131	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
132	C₂⁴×C₃	—	2	8	no	—
133	C₂⁴×C₃	—	4	8	no	—
134	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
135	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
136	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
137	C₂⁴×C₃	C₂³×C₃	1	8	yes	—
138	C₃×#41	—	2	32	no	—
139	C₂×C₃×Q₈	—	2	4	no	—
140	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
141	C₂×C₃×D₄	—	2	8	no	—
142	C₂×C₃×D₄	—	2	8	no	—
143	C₂×C₃×D₄	—	2	8	no	—
144	C₂×C₃×D₄	—	2	32	no	—
145	C₂×C₃×D₄	—	2	4	no	—
146	C₂×C₃×D₄	—	4	16	no	—
147	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
148	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
149	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
150	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
151	C₂×C₃×D₄	C₂³×C₃	1	32	yes	—
152	C₂²×C₃×C₄	—	2	8	no	—
153	C₂²×C₃×C₄	C₃×D₄	1	8	yes	—
154	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
155	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
156	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
159	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
160	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
161	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
162	C₃×C₂²⋊C₄	C₂³×C₃	1	32	yes	—
163	C₃×C₄²	C₂³×C₃	1	8	yes	—
164	C₂²×C₉	—	2	8	no	—
165	C₂²×C₉	—	2	4	no	—
166	C₂²×C₉	—	2	4	no	—
167	C₂²×C₉	—	2	8	no	—
168	C₂²×C₉	—	2	8	no	—
169	C₂²×C₉	—	2	16	no	—
170	C₂²×C₉	—	4	32	no	—
171	C₂²×C₉	—	4	8	no	—
172	C₂²×C₉	—	4	16	no	—
173	C₂²×C₉	C₂²×D₄	1	4	yes	—
174	C₂²×C₉	C₂²×D₄	1	2	yes	—
175	C₂²×C₉	H(5,𝔽₂)	1	4	yes	—
176	C₂²×C₉	C₂⁵	1	1	yes	characteristic
177	C₄×C₉	—	2	4	no	—
178	C₄×C₉	—	2	8	no	—
179	C₄×C₉	C₂²×D₄	1	4	yes	—
180	C₄×C₉	C₂²×D₄	1	4	yes	—
181	C₂⁵	C₂²×C₉	1	2	yes	—
182	C₂×#41	—	2	8	no	—
183	C₂×#41	C₂²×C₉	1	8	yes	complemented
184	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
185	C₂²×D₄	—	2	8	no	—
186	C₂²×D₄	C₂²×C₉	1	2	yes	—
187	C₂²×D₄	C₂²×C₉	1	2	yes	—
188	C₂²×D₄	C₂²×C₉	1	2	yes	—
189	C₂²×D₄	C₂²×C₉	1	8	yes	complemented
190	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
191	C₂²×D₄	C₂²×C₉	1	8	yes	complemented
192	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
193	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
194	#127	C₂²×C₉	1	16	yes	complemented
195	#124	C₂²×C₉	1	16	yes	complemented
196	#121	C₂²×C₉	1	32	yes	complemented
197	#120	C₂²×C₉	1	32	yes	complemented
198	#117	C₂²×C₉	1	8	yes	complemented
199	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
200	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
201	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
202	C₂×C₄²	C₂²×C₉	1	2	yes	complemented
203	C₂³×C₃	—	2	4	no	—
204	C₂³×C₃	—	2	4	no	—
205	C₂³×C₃	—	2	16	no	—
206	C₂³×C₃	—	2	8	no	—
207	C₂³×C₃	—	2	8	no	—
208	C₂³×C₃	—	2	16	no	—
209	C₂³×C₃	—	4	16	no	—
210	C₂³×C₃	—	4	32	no	—
211	C₂³×C₃	C₂×C₃×D₄	1	4	yes	—
212	C₂³×C₃	C₂⁴×C₃	1	8	yes	—
213	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
214	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
215	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
216	C₃×Q₈	—	2	8	no	—
217	C₃×D₄	—	2	16	no	—
218	C₃×D₄	—	2	16	no	—
219	C₃×D₄	—	2	16	no	—
220	C₃×D₄	—	2	8	no	—
221	C₃×D₄	—	4	32	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	8	no	—
224	C₂×C₃×C₄	—	2	16	no	—
225	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
226	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
227	C₂×C₃×C₄	C₂×C₃×D₄	1	16	yes	—
228	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
229	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
230	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
231	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
232	C₂×C₉	—	2	4	no	—
233	C₂×C₉	—	4	4	no	—
234	C₂×C₉	—	4	8	no	—
235	C₂×C₉	#535	1	4	yes	direct product factor
236	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
237	C₂×C₉	C₂×H(5,𝔽₂)	1	2	yes	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	4	8	no	—
240	C₂⁴	C₂³×C₉	1	4	yes	—
241	C₂⁴	C₂³×C₉	1	2	yes	—
242	C₂⁴	C₂³×C₉	1	1	yes	characteristic
243	C₂⁴	C₂³×C₉	1	8	yes	—
244	#41	—	2	32	no	—
245	C₂×Q₈	—	2	4	no	—
246	C₂×Q₈	C₂³×C₉	1	4	yes	complemented
247	C₂×D₄	—	2	8	no	—
248	C₂×D₄	—	2	8	no	—
249	C₂×D₄	—	2	8	no	—
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	32	no	—
252	C₂×D₄	—	4	16	no	—
253	C₂×D₄	C₂³×C₉	1	8	yes	—
254	C₂×D₄	C₂³×C₉	1	8	yes	—
255	C₂×D₄	C₂³×C₉	1	8	yes	—
256	C₂×D₄	C₂³×C₉	1	4	yes	complemented
257	C₂×D₄	C₂³×C₉	1	32	yes	complemented
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	D₄×C₉	1	8	yes	complemented
260	C₂²×C₄	C₂³×C₉	1	4	yes	—
261	C₂²×C₄	C₂³×C₉	1	2	yes	—
262	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₉	1	4	yes	—
265	C₂²×C₄	C₂³×C₉	1	8	yes	complemented
266	C₄⋊C₄	C₂³×C₉	1	8	yes	complemented
267	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
268	C₂²⋊C₄	C₂³×C₉	1	32	yes	complemented
269	C₄²	C₂³×C₉	1	8	yes	complemented
270	C₂²×C₃	—	2	4	no	—
271	C₂²×C₃	—	2	8	no	—
272	C₂²×C₃	—	2	4	no	—
273	C₂²×C₃	—	2	8	no	—
274	C₂²×C₃	—	2	8	no	—
275	C₂²×C₃	—	2	16	no	—
276	C₂²×C₃	—	4	32	no	—
277	C₂²×C₃	—	4	16	no	—
278	C₂²×C₃	—	4	8	no	—
279	C₂²×C₃	C₂²×C₃×D₄	1	4	yes	—
280	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
281	C₂²×C₃	C₃×H(5,𝔽₂)	1	4	yes	—
282	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
283	C₃×C₄	—	2	4	no	—
284	C₃×C₄	—	2	8	no	—
285	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
286	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
287	C₉	C₂×#535	1	1	yes	characteristic, direct product factor, Sylow
288	C₂³	—	2	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	16	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	8	no	—
293	C₂³	—	2	16	no	—
294	C₂³	—	4	16	no	—
295	C₂³	—	4	32	no	—
296	C₂³	C₂×D₄×C₉	1	4	yes	—
297	C₂³	C₂⁴×C₉	1	8	yes	—
298	C₂³	C₂⁴×C₉	1	4	yes	—
299	C₂³	C₂⁴×C₉	1	2	yes	—
300	C₂³	C₂⁴×C₉	1	1	yes	characteristic
301	Q₈	—	2	8	no	—
302	D₄	—	2	16	no	—
303	D₄	—	2	16	no	—
304	D₄	—	2	16	no	—
305	D₄	—	2	8	no	—
306	D₄	—	4	32	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	16	no	—
310	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
311	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
312	C₂×C₄	C₂×D₄×C₉	1	16	yes	complemented
313	C₂×C₄	C₂⁴×C₉	1	8	yes	—
314	C₂×C₄	C₂⁴×C₉	1	4	yes	—
315	C₂×C₄	C₂⁴×C₉	1	2	yes	—
316	C₂×C₄	C₂⁴×C₉	1	2	yes	—
317	C₂×C₃	—	2	4	no	—
318	C₂×C₃	—	4	8	no	—
319	C₂×C₃	—	4	4	no	—
320	C₂×C₃	C₃×#535	1	4	yes	—
321	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
322	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	4	no	—
326	C₂²	—	2	8	no	—
327	C₂²	—	2	8	no	—
328	C₂²	—	2	16	no	—
329	C₂²	—	4	32	no	—
330	C₂²	—	4	16	no	—
331	C₂²	—	4	8	no	—
332	C₂²	C₂²×D₄×C₉	1	4	yes	—
333	C₂²	C₂²×D₄×C₉	1	2	yes	—
334	C₂²	C₉×H(5,𝔽₂)	1	4	yes	—
335	C₂²	C₂⁵×C₉	1	1	yes	characteristic
336	C₄	—	2	4	no	—
337	C₄	—	2	8	no	—
338	C₄	C₂²×D₄×C₉	1	4	yes	—
339	C₄	C₂²×D₄×C₉	1	4	yes	—
340	C₃	C₂×C₃×#535	1	1	yes	characteristic
341	C₂	—	2	4	no	—
342	C₂	—	4	8	no	—
343	C₂	—	4	4	no	—
344	C₂	C₉×#535	1	4	yes	direct product factor
345	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
346	C₂	C₂×C₉×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, cosocle	C₂²×C₃	C₂⁵×C₃
socle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂×C₃×#535	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×#41	C₂	semidirect
2. C₂³×D₄×C₉	C₂	semidirect
3. C₉×#535	C₂	direct (N × H)
4. C₂×C₉×#127	C₂	semidirect
5. C₂×C₉×#124	C₂	semidirect
6. C₂×C₉×#121	C₂	semidirect
7. C₂×C₉×#120	C₂	semidirect
8. C₂×C₉×#117	C₂	semidirect
12. C₂×C₉×#41	C₂²	semidirect
13. C₂²×Q₈×C₉	C₂²	semidirect
18. C₂²×D₄×C₉	C₂²	semidirect
19. C₂²×D₄×C₉	C₂²	semidirect
20. C₂²×D₄×C₉	C₂²	semidirect
22. C₂³×C₄×C₉	C₂²	semidirect
23. C₉×#127	C₂²	semidirect
24. C₉×#124	C₂²	semidirect
25. C₉×#121	C₂²	semidirect
26. C₉×#120	C₂²	semidirect
27. C₉×#117	C₂²	semidirect
28. C₂×C₉×C₄⋊C₄	C₂²	semidirect
30. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
31. C₂×C₄²×C₉	C₂²	semidirect
48. C₂×Q₈×C₉	C₂³	semidirect
58. C₂×D₄×C₉	C₂³	semidirect
59. C₂×D₄×C₉	C₂³	semidirect
61. C₂²×C₄×C₉	D₄	semidirect
67. C₂²×C₄×C₉	C₂³	semidirect
68. C₉×C₄⋊C₄	C₂³	semidirect
70. C₉×C₂²⋊C₄	C₂³	semidirect
71. C₄²×C₉	C₂³	semidirect
72. C₂×#535	C₉	direct (N × H)
119. C₂×C₄×C₉	C₂×D₄	semidirect
124. C₂²×#41	C₂×C₉	semidirect
125. C₂³×D₄	C₂×C₉	semidirect
126. #535	C₂×C₉	direct (N × H)
127. C₂×#127	C₂×C₉	semidirect
128. C₂×#124	C₂×C₉	semidirect
129. C₂×#121	C₂×C₉	semidirect
130. C₂×#120	C₂×C₉	semidirect
131. C₂×#117	C₂×C₉	semidirect
183. C₂×#41	C₂²×C₉	semidirect
184. C₂²×Q₈	C₂²×C₉	semidirect
189. C₂²×D₄	C₂²×C₉	semidirect
190. C₂²×D₄	C₂²×C₉	semidirect
191. C₂²×D₄	C₂²×C₉	semidirect
193. C₂³×C₄	C₂²×C₉	semidirect
194. #127	C₂²×C₉	semidirect
195. #124	C₂²×C₉	semidirect
196. #121	C₂²×C₉	semidirect
197. #120	C₂²×C₉	semidirect
198. #117	C₂²×C₉	semidirect
199. C₂×C₄⋊C₄	C₂²×C₉	semidirect
201. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
202. C₂×C₄²	C₂²×C₉	semidirect
235. C₂×C₉	#535	direct (N × H)
246. C₂×Q₈	C₂³×C₉	semidirect
256. C₂×D₄	C₂³×C₉	semidirect
257. C₂×D₄	C₂³×C₉	semidirect
259. C₂²×C₄	D₄×C₉	semidirect
265. C₂²×C₄	C₂³×C₉	semidirect
266. C₄⋊C₄	C₂³×C₉	semidirect
268. C₂²⋊C₄	C₂³×C₉	semidirect
269. C₄²	C₂³×C₉	semidirect
287. C₉	C₂×#535	direct (N × H)
312. C₂×C₄	C₂×D₄×C₉	semidirect
344. C₂	C₉×#535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×#41	2
C₂³×D₄×C₉	2
C₉×#535	2
C₂×C₉×#127	2
C₂×C₉×#124	2
C₂×C₉×#121	2
C₂×C₉×#120	2
C₂×C₉×#117	2
C₂×C₃×#535	3

Subgroups — C2×C9×#535 #11768167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#535 #11768167