Subgroups — C₉×#3485 #11768206

Order 1152.

2340 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#547	C₂	1	8	yes	maximal, complemented
4	C₉×#546	C₂	1	8	yes	maximal, complemented
5	C₉×#536	C₂	1	2	yes	maximal, complemented
6	C₉×#534	C₂	1	4	yes	maximal, complemented
7	C₉×#525	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×#123	C₂	1	4	yes	maximal, complemented
9	C₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3485	C₃	1	1	yes	maximal, characteristic
11	C₉×H(5,𝔽₂)	—	2	8	no	—
12	C₂×C₉×#41	—	2	8	no	—
13	C₂×C₉×#41	C₂²	1	2	yes	—
14	C₂×C₉×#41	C₂²	1	8	yes	complemented
15	C₂×C₉×#41	C₂²	1	4	yes	complemented
16	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄×C₉	C₂²	1	4	yes	—
18	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₉	C₂²	1	2	yes	complemented
20	C₂²×D₄×C₉	C₂²	1	4	yes	complemented
21	C₂³×C₄×C₉	C₂²	1	2	yes	complemented
22	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
23	C₉×C₄⋊Q₈	C₂²	1	4	yes	complemented
24	C₉×#124	C₂²	1	4	yes	complemented
25	C₉×#123	C₂²	1	4	yes	complemented
26	C₉×#123	C₂²	1	8	yes	complemented
27	C₉×#123	C₂²	1	16	yes	complemented
28	C₉×#123	C₂²	1	8	yes	complemented
29	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
30	C₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
31	C₉×#121	C₂²	1	4	yes	complemented
32	C₉×#121	C₂²	1	16	yes	complemented
33	C₉×#120	C₂²	1	4	yes	complemented
34	C₉×#120	C₂²	1	8	yes	complemented
35	C₄×D₄×C₉	C₂²	1	8	yes	complemented
36	C₄×D₄×C₉	C₂²	1	8	yes	complemented
37	C₉×#117	C₂²	1	2	yes	complemented
38	C₂×C₉×C₄⋊C₄	C₂²	1	8	yes	complemented
39	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
40	C₂×C₉×C₂²⋊C₄	C₂²	1	8	yes	complemented
41	C₂×C₃×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic
42	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic
43	C₃×#547	C₂×C₃	1	8	yes	—
44	C₃×#546	C₂×C₃	1	8	yes	—
45	C₃×#536	C₂×C₃	1	2	yes	—
46	C₃×#534	C₂×C₃	1	4	yes	—
47	C₃×#525	C₂×C₃	1	2	yes	—
48	C₂×C₃×#123	C₂×C₃	1	4	yes	—
49	C₃×#518	C₂×C₃	1	1	yes	characteristic
50	C₂⁴×C₉	C₂³	1	4	yes	—
51	C₂⁴×C₉	C₂³	1	1	yes	characteristic
52	C₂⁴×C₉	C₂³	1	2	yes	—
53	C₉×#41	—	2	32	no	—
54	C₉×#41	—	2	16	no	—
55	C₉×#41	—	2	8	no	—
56	C₂×Q₈×C₉	—	2	4	no	—
57	C₂×Q₈×C₉	C₂³	1	4	yes	—
58	C₂×Q₈×C₉	C₂³	1	2	yes	—
59	C₂×D₄×C₉	—	2	16	no	—
60	C₂×D₄×C₉	—	2	8	no	—
61	C₂×D₄×C₉	—	2	16	no	—
62	C₂×D₄×C₉	D₄	1	8	yes	complemented
63	C₂×D₄×C₉	C₂³	1	8	yes	—
64	C₂×D₄×C₉	C₂³	1	4	yes	—
65	C₂×D₄×C₉	C₂³	1	8	yes	—
66	C₂×D₄×C₉	C₂³	1	2	yes	—
67	C₂×D₄×C₉	C₂³	1	8	yes	—
68	C₂×D₄×C₉	C₂³	1	4	yes	—
69	C₂²×C₄×C₉	—	2	8	no	—
70	C₂²×C₄×C₉	—	2	4	no	—
71	C₂²×C₄×C₉	C₂³	1	8	yes	—
72	C₂²×C₄×C₉	C₂³	1	4	yes	—
73	C₂²×C₄×C₉	C₂³	1	4	yes	—
74	C₂²×C₄×C₉	C₂³	1	4	yes	—
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	C₂³	1	2	yes	—
77	C₂²×C₄×C₉	C₂³	1	8	yes	—
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₉×C₄⋊C₄	C₂³	1	8	yes	—
80	C₉×C₄⋊C₄	C₂³	1	16	yes	—
81	C₉×C₄⋊C₄	C₂³	1	4	yes	—
82	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₉×C₂²⋊C₄	C₂³	1	16	yes	—
86	C₉×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₄²×C₉	C₂³	1	4	yes	—
88	#3485	C₉	1	1	yes	characteristic, direct product factor, Sylow
89	C₃×H(5,𝔽₂)	—	2	8	no	—
90	C₂×C₃×#41	—	2	8	no	—
91	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
92	C₂×C₃×#41	C₂²×C₃	1	8	yes	—
93	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
94	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
96	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
98	C₂²×C₃×D₄	C₂²×C₃	1	4	yes	—
99	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
100	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
101	C₃×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
102	C₃×#124	C₂²×C₃	1	4	yes	—
103	C₃×#123	C₂²×C₃	1	4	yes	—
104	C₃×#123	C₂²×C₃	1	8	yes	—
105	C₃×#123	C₂²×C₃	1	16	yes	—
106	C₃×#123	C₂²×C₃	1	8	yes	—
107	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
108	C₃×C₂²⋊Q₈	C₂²×C₃	1	8	yes	—
109	C₃×#121	C₂²×C₃	1	4	yes	—
110	C₃×#121	C₂²×C₃	1	16	yes	—
111	C₃×#120	C₂²×C₃	1	4	yes	—
112	C₃×#120	C₂²×C₃	1	8	yes	—
113	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
114	C₃×C₄×D₄	C₂²×C₃	1	8	yes	—
115	C₃×#117	C₂²×C₃	1	2	yes	—
116	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	8	yes	—
117	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
118	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	8	yes	—
119	C₂³×C₉	—	2	2	no	—
120	C₂³×C₉	—	2	8	no	—
121	C₂³×C₉	—	4	4	no	—
122	C₂³×C₉	—	4	2	no	—
123	C₂³×C₉	—	4	8	no	—
124	C₂³×C₉	C₂×D₄	1	8	yes	—
125	C₂³×C₉	C₂⁴	1	4	yes	—
126	C₂³×C₉	C₂⁴	1	2	yes	—
127	C₂³×C₉	C₂⁴	1	1	yes	characteristic
128	C₂³×C₉	C₂⁴	1	4	yes	—
129	Q₈×C₉	—	2	8	no	—
130	Q₈×C₉	—	2	4	no	—
131	D₄×C₉	—	2	8	no	—
132	D₄×C₉	—	2	16	no	—
133	D₄×C₉	—	2	16	no	—
134	D₄×C₉	—	2	4	no	—
135	D₄×C₉	—	4	8	no	—
136	D₄×C₉	C₂×D₄	1	16	yes	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	2	4	no	—
139	C₂×C₄×C₉	—	2	16	no	—
140	C₂×C₄×C₉	—	2	8	no	—
141	C₂×C₄×C₉	—	2	8	no	—
142	C₂×C₄×C₉	—	2	8	no	—
143	C₂×C₄×C₉	—	4	8	no	—
144	C₂×C₄×C₉	C₂×D₄	1	4	yes	—
145	C₂×C₄×C₉	C₂⁴	1	8	yes	—
146	C₂×C₄×C₉	C₂⁴	1	2	yes	—
147	C₂×C₄×C₉	C₂⁴	1	4	yes	—
148	C₂×C₄×C₉	C₂⁴	1	4	yes	—
149	C₂×C₄×C₉	C₂⁴	1	2	yes	—
150	C₂×H(5,𝔽₂)	C₂×C₉	1	1	yes	characteristic, complemented
151	C₂²×#41	C₂×C₉	1	1	yes	characteristic, complemented
152	#547	C₂×C₉	1	8	yes	complemented
153	#546	C₂×C₉	1	8	yes	complemented
154	#536	C₂×C₉	1	2	yes	complemented
155	#534	C₂×C₉	1	4	yes	complemented
156	#525	C₂×C₉	1	2	yes	complemented
157	C₂×#123	C₂×C₉	1	4	yes	complemented
158	#518	C₂×C₉	1	1	yes	characteristic, complemented
159	C₂⁴×C₃	C₂³×C₃	1	4	yes	—
160	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
161	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
162	C₃×#41	—	2	32	no	—
163	C₃×#41	—	2	16	no	—
164	C₃×#41	—	2	8	no	—
165	C₂×C₃×Q₈	—	2	4	no	—
166	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
167	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
168	C₂×C₃×D₄	—	2	8	no	—
169	C₂×C₃×D₄	—	2	16	no	—
170	C₂×C₃×D₄	—	2	16	no	—
171	C₂×C₃×D₄	C₃×D₄	1	8	yes	—
172	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
173	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
174	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
175	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
176	C₂×C₃×D₄	C₂³×C₃	1	8	yes	—
177	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
178	C₂²×C₃×C₄	—	2	8	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
181	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
182	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
183	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₃	1	8	yes	—
187	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
188	C₃×C₄⋊C₄	C₂³×C₃	1	8	yes	—
189	C₃×C₄⋊C₄	C₂³×C₃	1	16	yes	—
190	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
191	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
192	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
193	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
194	C₃×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
195	C₃×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
196	C₃×C₄²	C₂³×C₃	1	4	yes	—
197	C₂²×C₉	—	2	8	no	—
198	C₂²×C₉	—	2	2	no	—
199	C₂²×C₉	—	2	2	no	—
200	C₂²×C₉	—	2	4	no	—
201	C₂²×C₉	—	2	4	no	—
202	C₂²×C₉	—	2	8	no	—
203	C₂²×C₉	—	4	8	no	—
204	C₂²×C₉	—	4	4	no	—
205	C₂²×C₉	—	8	8	no	—
206	C₂²×C₉	C₂²×D₄	1	2	yes	—
207	C₂²×C₉	C₂²×D₄	1	8	yes	—
208	C₂²×C₉	C₂⁵	1	1	yes	characteristic
209	C₄×C₉	—	2	2	no	—
210	C₄×C₉	—	2	4	no	—
211	C₄×C₉	—	2	4	no	—
212	C₄×C₉	—	2	8	no	—
213	C₄×C₉	C₂²×D₄	1	4	yes	—
214	H(5,𝔽₂)	—	2	8	no	—
215	C₂×#41	—	2	8	no	—
216	C₂×#41	C₂²×C₉	1	2	yes	—
217	C₂×#41	C₂²×C₉	1	8	yes	complemented
218	C₂×#41	C₂²×C₉	1	4	yes	complemented
219	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
220	C₂²×D₄	C₂²×C₉	1	4	yes	—
221	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
222	C₂²×D₄	C₂²×C₉	1	2	yes	complemented
223	C₂²×D₄	C₂²×C₉	1	4	yes	complemented
224	C₂³×C₄	C₂²×C₉	1	2	yes	complemented
225	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
226	C₄⋊Q₈	C₂²×C₉	1	4	yes	complemented
227	#124	C₂²×C₉	1	4	yes	complemented
228	#123	C₂²×C₉	1	4	yes	complemented
229	#123	C₂²×C₉	1	8	yes	complemented
230	#123	C₂²×C₉	1	16	yes	complemented
231	#123	C₂²×C₉	1	8	yes	complemented
232	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
233	C₂²⋊Q₈	C₂²×C₉	1	8	yes	complemented
234	#121	C₂²×C₉	1	4	yes	complemented
235	#121	C₂²×C₉	1	16	yes	complemented
236	#120	C₂²×C₉	1	4	yes	complemented
237	#120	C₂²×C₉	1	8	yes	complemented
238	C₄×D₄	C₂²×C₉	1	8	yes	complemented
239	C₄×D₄	C₂²×C₉	1	8	yes	complemented
240	#117	C₂²×C₉	1	2	yes	complemented
241	C₂×C₄⋊C₄	C₂²×C₉	1	8	yes	complemented
242	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
243	C₂×C₂²⋊C₄	C₂²×C₉	1	8	yes	complemented
244	C₂³×C₃	—	2	2	no	—
245	C₂³×C₃	—	2	8	no	—
246	C₂³×C₃	—	4	4	no	—
247	C₂³×C₃	—	4	2	no	—
248	C₂³×C₃	—	4	8	no	—
249	C₂³×C₃	C₂×C₃×D₄	1	8	yes	—
250	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
251	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
252	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
253	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
254	C₃×Q₈	—	2	8	no	—
255	C₃×Q₈	—	2	4	no	—
256	C₃×D₄	—	2	8	no	—
257	C₃×D₄	—	2	16	no	—
258	C₃×D₄	—	2	16	no	—
259	C₃×D₄	—	2	4	no	—
260	C₃×D₄	—	4	8	no	—
261	C₃×D₄	C₂×C₃×D₄	1	16	yes	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	16	no	—
265	C₂×C₃×C₄	—	2	8	no	—
266	C₂×C₃×C₄	—	2	8	no	—
267	C₂×C₃×C₄	—	2	8	no	—
268	C₂×C₃×C₄	—	4	8	no	—
269	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
270	C₂×C₃×C₄	C₂⁴×C₃	1	8	yes	—
271	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
272	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
273	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
274	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
275	C₂×C₉	—	2	2	no	—
276	C₂×C₉	—	2	8	no	—
277	C₂×C₉	—	4	2	no	—
278	C₂×C₉	—	4	4	no	—
279	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
280	C₂×C₉	#585	1	2	yes	—
281	C₂⁴	C₂³×C₉	1	4	yes	—
282	C₂⁴	C₂³×C₉	1	1	yes	characteristic
283	C₂⁴	C₂³×C₉	1	2	yes	—
284	#41	—	2	32	no	—
285	#41	—	2	16	no	—
286	#41	—	2	8	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	C₂³×C₉	1	4	yes	—
289	C₂×Q₈	C₂³×C₉	1	2	yes	—
290	C₂×D₄	—	2	16	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	16	no	—
293	C₂×D₄	D₄×C₉	1	8	yes	complemented
294	C₂×D₄	C₂³×C₉	1	8	yes	—
295	C₂×D₄	C₂³×C₉	1	4	yes	—
296	C₂×D₄	C₂³×C₉	1	8	yes	—
297	C₂×D₄	C₂³×C₉	1	2	yes	—
298	C₂×D₄	C₂³×C₉	1	8	yes	—
299	C₂×D₄	C₂³×C₉	1	4	yes	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	C₂³×C₉	1	8	yes	—
303	C₂²×C₄	C₂³×C₉	1	4	yes	—
304	C₂²×C₄	C₂³×C₉	1	4	yes	—
305	C₂²×C₄	C₂³×C₉	1	4	yes	—
306	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
307	C₂²×C₄	C₂³×C₉	1	2	yes	—
308	C₂²×C₄	C₂³×C₉	1	8	yes	—
309	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
310	C₄⋊C₄	C₂³×C₉	1	8	yes	—
311	C₄⋊C₄	C₂³×C₉	1	16	yes	—
312	C₄⋊C₄	C₂³×C₉	1	4	yes	—
313	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
314	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
315	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
316	C₂²⋊C₄	C₂³×C₉	1	16	yes	—
317	C₂²⋊C₄	C₂³×C₉	1	8	yes	—
318	C₄²	C₂³×C₉	1	4	yes	—
319	C₂²×C₃	—	2	8	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	4	no	—
323	C₂²×C₃	—	2	4	no	—
324	C₂²×C₃	—	2	8	no	—
325	C₂²×C₃	—	4	8	no	—
326	C₂²×C₃	—	4	4	no	—
327	C₂²×C₃	—	8	8	no	—
328	C₂²×C₃	C₂²×C₃×D₄	1	2	yes	—
329	C₂²×C₃	C₂²×C₃×D₄	1	8	yes	—
330	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
331	C₃×C₄	—	2	2	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	8	no	—
335	C₃×C₄	C₂²×C₃×D₄	1	4	yes	—
336	C₉	#3485	1	1	yes	characteristic, direct product factor, Sylow
337	C₂³	—	2	2	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	8	no	—
342	C₂³	C₂×D₄×C₉	1	8	yes	—
343	C₂³	C₂⁴×C₉	1	4	yes	—
344	C₂³	C₂⁴×C₉	1	2	yes	—
345	C₂³	C₂⁴×C₉	1	1	yes	characteristic
346	C₂³	C₂⁴×C₉	1	4	yes	—
347	Q₈	—	2	8	no	—
348	Q₈	—	2	4	no	—
349	D₄	—	2	8	no	—
350	D₄	—	2	16	no	—
351	D₄	—	2	16	no	—
352	D₄	—	2	4	no	—
353	D₄	—	4	8	no	—
354	D₄	C₂×D₄×C₉	1	16	yes	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	16	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	C₂×D₄×C₉	1	4	yes	—
363	C₂×C₄	C₂⁴×C₉	1	8	yes	—
364	C₂×C₄	C₂⁴×C₉	1	2	yes	—
365	C₂×C₄	C₂⁴×C₉	1	4	yes	—
366	C₂×C₄	C₂⁴×C₉	1	4	yes	—
367	C₂×C₄	C₂⁴×C₉	1	2	yes	—
368	C₂×C₃	—	2	2	no	—
369	C₂×C₃	—	2	8	no	—
370	C₂×C₃	—	4	2	no	—
371	C₂×C₃	—	4	4	no	—
372	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
373	C₂×C₃	C₃×#585	1	2	yes	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	8	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	8	no	—
383	C₂²	C₂²×D₄×C₉	1	2	yes	—
384	C₂²	C₂²×D₄×C₉	1	8	yes	—
385	C₂²	C₂⁵×C₉	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	4	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	8	no	—
390	C₄	C₂²×D₄×C₉	1	4	yes	—
391	C₃	C₃×#3485	1	1	yes	characteristic
392	C₂	—	2	2	no	—
393	C₂	—	2	8	no	—
394	C₂	—	4	2	no	—
395	C₂	—	4	4	no	—
396	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
397	C₂	C₉×#585	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂⁵
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3485	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×H(5,𝔽₂)	C₂	semidirect
2. C₂²×C₉×#41	C₂	semidirect
3. C₉×#547	C₂	semidirect
4. C₉×#546	C₂	semidirect
5. C₉×#536	C₂	semidirect
6. C₉×#534	C₂	semidirect
7. C₉×#525	C₂	semidirect
8. C₂×C₉×#123	C₂	semidirect
9. C₉×#518	C₂	semidirect
14. C₂×C₉×#41	C₂²	semidirect
15. C₂×C₉×#41	C₂²	semidirect
16. C₂²×Q₈×C₉	C₂²	semidirect
19. C₂²×D₄×C₉	C₂²	semidirect
20. C₂²×D₄×C₉	C₂²	semidirect
21. C₂³×C₄×C₉	C₂²	semidirect
22. C₂³×C₄×C₉	C₂²	semidirect
23. C₉×C₄⋊Q₈	C₂²	semidirect
24. C₉×#124	C₂²	semidirect
25. C₉×#123	C₂²	semidirect
26. C₉×#123	C₂²	semidirect
27. C₉×#123	C₂²	semidirect
28. C₉×#123	C₂²	semidirect
29. C₉×C₂²⋊Q₈	C₂²	semidirect
30. C₉×C₂²⋊Q₈	C₂²	semidirect
31. C₉×#121	C₂²	semidirect
32. C₉×#121	C₂²	semidirect
33. C₉×#120	C₂²	semidirect
34. C₉×#120	C₂²	semidirect
35. C₄×D₄×C₉	C₂²	semidirect
36. C₄×D₄×C₉	C₂²	semidirect
37. C₉×#117	C₂²	semidirect
38. C₂×C₉×C₄⋊C₄	C₂²	semidirect
39. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
40. C₂×C₉×C₂²⋊C₄	C₂²	semidirect
62. C₂×D₄×C₉	D₄	semidirect
88. #3485	C₉	direct (N × H)
150. C₂×H(5,𝔽₂)	C₂×C₉	semidirect
151. C₂²×#41	C₂×C₉	semidirect
152. #547	C₂×C₉	semidirect
153. #546	C₂×C₉	semidirect
154. #536	C₂×C₉	semidirect
155. #534	C₂×C₉	semidirect
156. #525	C₂×C₉	semidirect
157. C₂×#123	C₂×C₉	semidirect
158. #518	C₂×C₉	semidirect
217. C₂×#41	C₂²×C₉	semidirect
218. C₂×#41	C₂²×C₉	semidirect
219. C₂²×Q₈	C₂²×C₉	semidirect
222. C₂²×D₄	C₂²×C₉	semidirect
223. C₂²×D₄	C₂²×C₉	semidirect
224. C₂³×C₄	C₂²×C₉	semidirect
225. C₂³×C₄	C₂²×C₉	semidirect
226. C₄⋊Q₈	C₂²×C₉	semidirect
227. #124	C₂²×C₉	semidirect
228. #123	C₂²×C₉	semidirect
229. #123	C₂²×C₉	semidirect
230. #123	C₂²×C₉	semidirect
231. #123	C₂²×C₉	semidirect
232. C₂²⋊Q₈	C₂²×C₉	semidirect
233. C₂²⋊Q₈	C₂²×C₉	semidirect
234. #121	C₂²×C₉	semidirect
235. #121	C₂²×C₉	semidirect
236. #120	C₂²×C₉	semidirect
237. #120	C₂²×C₉	semidirect
238. C₄×D₄	C₂²×C₉	semidirect
239. C₄×D₄	C₂²×C₉	semidirect
240. #117	C₂²×C₉	semidirect
241. C₂×C₄⋊C₄	C₂²×C₉	semidirect
242. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
243. C₂×C₂²⋊C₄	C₂²×C₉	semidirect
293. C₂×D₄	D₄×C₉	semidirect
336. C₉	#3485	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×H(5,𝔽₂)	2
C₂²×C₉×#41	2
C₉×#547	2
C₉×#546	2
C₉×#536	2
C₉×#534	2
C₉×#525	2
C₂×C₉×#123	2
C₉×#518	2
C₃×#3485	3

Subgroups — C9×#3485 #11768206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3485 #11768206