Subgroups — C₉×#3475 #11768196

Order 1152.

1698 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#553	C₂	1	2	yes	maximal, complemented
5	C₉×#552	C₂	1	2	yes	maximal, complemented
6	C₉×#552	C₂	1	2	yes	maximal, complemented
7	C₉×#551	C₂	1	4	yes	maximal, complemented
8	C₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#546	C₂	1	2	yes	maximal, complemented
10	C₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#529	C₂	1	4	yes	maximal, complemented
12	C₉×#529	C₂	1	2	yes	maximal, complemented
13	C₉×#525	C₂	1	2	yes	maximal, complemented
14	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×#41	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₉×#117	C₂	1	2	yes	maximal, complemented
18	C₃×#3475	C₃	1	1	yes	maximal, characteristic
19	C₂×C₉×#41	C₂²	1	1	yes	characteristic
20	C₂×C₉×#41	C₂²	1	2	yes	—
21	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₉	C₂²	1	2	yes	—
23	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₉×#126	C₂²	1	4	yes	complemented
26	C₉×#126	C₂²	1	4	yes	complemented
27	C₉×#126	C₂²	1	4	yes	complemented
28	C₉×#125	C₂²	1	4	yes	complemented
29	C₉×#125	C₂²	1	2	yes	complemented
30	C₉×#125	C₂²	1	2	yes	complemented
31	C₉×#124	C₂²	1	2	yes	—
32	C₉×#124	C₂²	1	4	yes	complemented
33	C₉×#123	C₂²	1	4	yes	—
34	C₉×#123	C₂²	1	4	yes	—
35	C₉×#123	C₂²	1	4	yes	complemented
36	C₉×#123	C₂²	1	4	yes	complemented
37	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
40	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
41	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
42	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₉×#121	C₂²	1	4	yes	—
44	C₉×#121	C₂²	1	2	yes	—
45	C₉×#121	C₂²	1	2	yes	complemented
46	C₉×#121	C₂²	1	2	yes	complemented
47	C₉×#120	C₂²	1	4	yes	—
48	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
49	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
50	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
51	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
52	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₉	C₂²	1	2	yes	—
55	C₄×D₄×C₉	C₂²	1	2	yes	—
56	C₄×D₄×C₉	C₂²	1	2	yes	—
57	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
58	C₄×D₄×C₉	C₂²	1	2	yes	—
59	C₄×D₄×C₉	C₂²	1	2	yes	—
60	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
61	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
62	C₄×D₄×C₉	C₂²	1	4	yes	complemented
63	C₄×D₄×C₉	C₂²	1	4	yes	complemented
64	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₄×C₉	C₂²	1	4	yes	complemented
66	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
67	C₉×#117	C₂²	1	2	yes	—
68	C₉×#117	C₂²	1	4	yes	—
69	C₉×#117	C₂²	1	1	yes	characteristic
70	C₉×#117	C₂²	1	4	yes	complemented
71	C₉×#117	C₂²	1	2	yes	complemented
72	C₉×#117	C₂²	1	4	yes	complemented
73	C₉×#117	C₂²	1	2	yes	complemented
74	C₉×#117	C₂²	1	2	yes	complemented
75	C₉×#117	C₂²	1	2	yes	complemented
76	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
78	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
79	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
82	C₂×C₄²×C₉	C₂²	1	4	yes	complemented
83	C₂×C₄²×C₉	C₂²	1	2	yes	complemented
84	C₃×#556	C₂×C₃	1	1	yes	characteristic
85	C₃×#555	C₂×C₃	1	1	yes	characteristic
86	C₃×#554	C₂×C₃	1	1	yes	characteristic
87	C₃×#553	C₂×C₃	1	2	yes	—
88	C₃×#552	C₂×C₃	1	2	yes	—
89	C₃×#552	C₂×C₃	1	2	yes	—
90	C₃×#551	C₂×C₃	1	4	yes	—
91	C₃×#547	C₂×C₃	1	1	yes	characteristic
92	C₃×#546	C₂×C₃	1	2	yes	—
93	C₃×#533	C₂×C₃	1	1	yes	characteristic
94	C₃×#529	C₂×C₃	1	4	yes	—
95	C₃×#529	C₂×C₃	1	2	yes	—
96	C₃×#525	C₂×C₃	1	2	yes	—
97	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
98	C₃×C₄×#41	C₂×C₃	1	2	yes	—
99	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
100	C₂×C₃×#117	C₂×C₃	1	2	yes	—
101	C₂⁴×C₉	C₂³	1	2	yes	—
102	C₉×#41	—	2	8	no	—
103	C₉×#41	—	2	4	no	—
104	C₂×Q₈×C₉	C₂³	1	2	yes	—
105	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
106	C₂×Q₈×C₉	C₂³	1	2	yes	—
107	C₂×D₄×C₉	—	2	4	no	—
108	C₂×D₄×C₉	C₂³	1	2	yes	—
109	C₂×D₄×C₉	C₂³	1	2	yes	—
110	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₉	C₂³	1	4	yes	—
112	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₉	C₂³	1	4	yes	—
114	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₉	—	2	8	no	—
116	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₉	C₂³	1	4	yes	—
118	C₂²×C₄×C₉	C₂³	1	2	yes	—
119	C₂²×C₄×C₉	C₂³	1	2	yes	—
120	C₂²×C₄×C₉	C₂³	1	2	yes	—
121	C₂²×C₄×C₉	C₂³	1	2	yes	—
122	C₂²×C₄×C₉	C₂³	1	2	yes	—
123	C₂²×C₄×C₉	C₂³	1	2	yes	—
124	C₂²×C₄×C₉	C₂³	1	2	yes	—
125	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₉	C₂³	1	4	yes	—
127	C₂²×C₄×C₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
129	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₉×C₄⋊C₄	C₂³	1	2	yes	—
132	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
134	C₉×C₄⋊C₄	C₂³	1	2	yes	—
135	C₉×C₄⋊C₄	C₂³	1	2	yes	—
136	C₉×C₄⋊C₄	C₂³	1	4	yes	—
137	C₉×C₄⋊C₄	C₂³	1	4	yes	—
138	C₉×C₄⋊C₄	C₂³	1	2	yes	—
139	C₉×C₄⋊C₄	C₂³	1	2	yes	—
140	C₉×C₄⋊C₄	C₂³	1	2	yes	—
141	C₉×C₄⋊C₄	C₂³	1	4	yes	—
142	C₉×C₄⋊C₄	C₂³	1	4	yes	—
143	C₉×C₄⋊C₄	C₂³	1	4	yes	—
144	C₉×C₄⋊C₄	C₂³	1	4	yes	—
145	C₉×C₄⋊C₄	C₂³	1	2	yes	—
146	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₄²×C₉	C₂³	1	1	yes	characteristic
161	C₄²×C₉	C₂³	1	1	yes	characteristic
162	C₄²×C₉	C₂³	1	4	yes	—
163	C₄²×C₉	C₂³	1	4	yes	—
164	C₄²×C₉	C₂³	1	2	yes	—
165	C₄²×C₉	C₂³	1	2	yes	—
166	C₄²×C₉	C₂³	1	1	yes	characteristic
167	C₄²×C₉	C₂³	1	1	yes	characteristic
168	C₄²×C₉	C₂³	1	2	yes	—
169	C₄²×C₉	C₂³	1	4	yes	—
170	#3475	C₉	1	1	yes	characteristic, direct product factor, Sylow
171	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
173	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
174	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
175	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
176	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
177	C₃×#126	C₂²×C₃	1	4	yes	—
178	C₃×#126	C₂²×C₃	1	4	yes	—
179	C₃×#126	C₂²×C₃	1	4	yes	—
180	C₃×#125	C₂²×C₃	1	4	yes	—
181	C₃×#125	C₂²×C₃	1	2	yes	—
182	C₃×#125	C₂²×C₃	1	2	yes	—
183	C₃×#124	C₂²×C₃	1	2	yes	—
184	C₃×#124	C₂²×C₃	1	4	yes	—
185	C₃×#123	C₂²×C₃	1	4	yes	—
186	C₃×#123	C₂²×C₃	1	4	yes	—
187	C₃×#123	C₂²×C₃	1	4	yes	—
188	C₃×#123	C₂²×C₃	1	4	yes	—
189	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
190	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
191	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
192	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
193	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
194	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
195	C₃×#121	C₂²×C₃	1	4	yes	—
196	C₃×#121	C₂²×C₃	1	2	yes	—
197	C₃×#121	C₂²×C₃	1	2	yes	—
198	C₃×#121	C₂²×C₃	1	2	yes	—
199	C₃×#120	C₂²×C₃	1	4	yes	—
200	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
201	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
202	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
203	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
204	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
205	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
206	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
207	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
208	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
209	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
210	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
211	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
212	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
213	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
214	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
215	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
216	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
217	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
218	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
219	C₃×#117	C₂²×C₃	1	1	yes	characteristic
220	C₃×#117	C₂²×C₃	1	2	yes	—
221	C₃×#117	C₂²×C₃	1	4	yes	—
222	C₃×#117	C₂²×C₃	1	4	yes	—
223	C₃×#117	C₂²×C₃	1	2	yes	—
224	C₃×#117	C₂²×C₃	1	2	yes	—
225	C₃×#117	C₂²×C₃	1	2	yes	—
226	C₃×#117	C₂²×C₃	1	4	yes	—
227	C₃×#117	C₂²×C₃	1	2	yes	—
228	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
230	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
231	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
233	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
234	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
235	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
236	C₂³×C₉	—	2	4	no	—
237	C₂³×C₉	—	2	4	no	—
238	C₂³×C₉	—	4	2	no	—
239	C₂³×C₉	C₂⁴	1	2	yes	—
240	C₂³×C₉	C₂⁴	1	2	yes	—
241	C₂³×C₉	C₂⁴	1	1	yes	characteristic
242	C₂³×C₉	C₂⁴	1	2	yes	—
243	Q₈×C₉	—	2	2	no	—
244	Q₈×C₉	—	2	4	no	—
245	Q₈×C₉	—	4	2	no	—
246	D₄×C₉	—	2	4	no	—
247	D₄×C₉	—	2	4	no	—
248	D₄×C₉	—	2	8	no	—
249	D₄×C₉	—	2	2	no	—
250	D₄×C₉	—	2	2	no	—
251	D₄×C₉	—	4	4	no	—
252	D₄×C₉	#41	1	4	yes	complemented
253	C₂×C₄×C₉	—	2	4	no	—
254	C₂×C₄×C₉	—	2	8	no	—
255	C₂×C₄×C₉	—	2	4	no	—
256	C₂×C₄×C₉	—	2	4	no	—
257	C₂×C₄×C₉	—	2	4	no	—
258	C₂×C₄×C₉	—	2	4	no	—
259	C₂×C₄×C₉	—	2	2	no	—
260	C₂×C₄×C₉	—	2	4	no	—
261	C₂×C₄×C₉	—	2	4	no	—
262	C₂×C₄×C₉	—	4	2	no	—
263	C₂×C₄×C₉	—	4	4	no	—
264	C₂×C₄×C₉	—	4	1	no	—
265	C₂×C₄×C₉	#41	1	4	yes	complemented
266	C₂×C₄×C₉	C₂⁴	1	2	yes	—
267	C₂×C₄×C₉	C₂⁴	1	2	yes	—
268	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×C₉	C₂⁴	1	2	yes	—
270	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₉	C₂⁴	1	4	yes	—
272	C₂×C₄×C₉	C₂⁴	1	2	yes	—
273	C₂×C₄×C₉	C₂⁴	1	4	yes	—
274	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₉	C₂⁴	1	2	yes	—
276	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
279	#556	C₂×C₉	1	1	yes	characteristic, complemented
280	#555	C₂×C₉	1	1	yes	characteristic, complemented
281	#554	C₂×C₉	1	1	yes	characteristic, complemented
282	#553	C₂×C₉	1	2	yes	complemented
283	#552	C₂×C₉	1	2	yes	complemented
284	#552	C₂×C₉	1	2	yes	complemented
285	#551	C₂×C₉	1	4	yes	complemented
286	#547	C₂×C₉	1	1	yes	characteristic, complemented
287	#546	C₂×C₉	1	2	yes	complemented
288	#533	C₂×C₉	1	1	yes	characteristic, complemented
289	#529	C₂×C₉	1	4	yes	complemented
290	#529	C₂×C₉	1	2	yes	complemented
291	#525	C₂×C₉	1	2	yes	complemented
292	C₄×#41	C₂×C₉	1	1	yes	characteristic, complemented
293	C₄×#41	C₂×C₉	1	2	yes	complemented
294	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic, complemented
295	C₂×#117	C₂×C₉	1	2	yes	complemented
296	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
297	C₃×#41	—	2	8	no	—
298	C₃×#41	—	2	4	no	—
299	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
301	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
304	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
305	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
306	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
307	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
309	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
310	C₂²×C₃×C₄	—	2	8	no	—
311	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
312	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
313	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
314	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
315	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
316	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
317	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
318	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
319	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
320	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
321	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
322	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
323	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
324	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
325	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
326	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
327	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
328	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
329	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
330	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
331	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
332	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
333	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
334	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
335	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
336	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
337	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
338	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
339	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
340	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
341	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
342	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
343	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
344	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
345	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
346	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
347	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
348	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
349	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
350	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
352	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
353	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
354	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
355	C₃×C₄²	C₂³×C₃	1	2	yes	—
356	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
357	C₃×C₄²	C₂³×C₃	1	4	yes	—
358	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
359	C₃×C₄²	C₂³×C₃	1	4	yes	—
360	C₃×C₄²	C₂³×C₃	1	4	yes	—
361	C₃×C₄²	C₂³×C₃	1	2	yes	—
362	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
363	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
364	C₃×C₄²	C₂³×C₃	1	2	yes	—
365	C₂²×C₉	—	2	2	no	—
366	C₂²×C₉	—	2	1	no	—
367	C₂²×C₉	—	2	2	no	—
368	C₂²×C₉	—	2	1	no	—
369	C₂²×C₉	—	2	2	no	—
370	C₂²×C₉	—	2	2	no	—
371	C₂²×C₉	—	2	2	no	—
372	C₂²×C₉	—	2	2	no	—
373	C₂²×C₉	—	2	2	no	—
374	C₂²×C₉	—	2	2	no	—
375	C₂²×C₉	—	4	8	no	—
376	C₂²×C₉	C₂×#41	1	2	yes	—
377	C₂²×C₉	C₂×#41	1	4	yes	—
378	C₂²×C₉	C₂⁵	1	1	yes	characteristic
379	C₄×C₉	—	2	2	no	—
380	C₄×C₉	—	2	2	no	—
381	C₄×C₉	—	2	2	no	—
382	C₄×C₉	—	2	1	no	—
383	C₄×C₉	—	2	4	no	—
384	C₄×C₉	—	2	2	no	—
385	C₄×C₉	—	2	1	no	—
386	C₄×C₉	—	2	2	no	—
387	C₄×C₉	—	2	4	no	—
388	C₄×C₉	—	2	1	no	—
389	C₄×C₉	C₂×#41	1	2	yes	—
390	C₄×C₉	C₂×#41	1	2	yes	—
391	C₄×C₉	C₂×#41	1	2	yes	—
392	C₂×#41	C₂²×C₉	1	1	yes	characteristic
393	C₂×#41	C₂²×C₉	1	2	yes	—
394	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
395	C₂³×C₄	C₂²×C₉	1	2	yes	—
396	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
397	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
398	#126	C₂²×C₉	1	4	yes	complemented
399	#126	C₂²×C₉	1	4	yes	complemented
400	#126	C₂²×C₉	1	4	yes	complemented
401	#125	C₂²×C₉	1	4	yes	complemented
402	#125	C₂²×C₉	1	2	yes	complemented
403	#125	C₂²×C₉	1	2	yes	complemented
404	#124	C₂²×C₉	1	2	yes	—
405	#124	C₂²×C₉	1	4	yes	complemented
406	#123	C₂²×C₉	1	4	yes	—
407	#123	C₂²×C₉	1	4	yes	—
408	#123	C₂²×C₉	1	4	yes	complemented
409	#123	C₂²×C₉	1	4	yes	complemented
410	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
411	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
412	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
413	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
414	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
415	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
416	#121	C₂²×C₉	1	4	yes	—
417	#121	C₂²×C₉	1	2	yes	—
418	#121	C₂²×C₉	1	2	yes	complemented
419	#121	C₂²×C₉	1	2	yes	complemented
420	#120	C₂²×C₉	1	4	yes	—
421	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
422	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
423	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
424	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
425	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
426	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
427	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
428	C₄×D₄	C₂²×C₉	1	2	yes	—
429	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
430	C₄×D₄	C₂²×C₉	1	2	yes	—
431	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
432	C₄×D₄	C₂²×C₉	1	2	yes	—
433	C₄×D₄	C₂²×C₉	1	2	yes	—
434	C₄×D₄	C₂²×C₉	1	2	yes	—
435	C₄×D₄	C₂²×C₉	1	4	yes	complemented
436	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
437	C₄×D₄	C₂²×C₉	1	4	yes	complemented
438	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
439	C₄×D₄	C₂²×C₉	1	4	yes	complemented
440	#117	C₂²×C₉	1	1	yes	characteristic
441	#117	C₂²×C₉	1	2	yes	—
442	#117	C₂²×C₉	1	4	yes	—
443	#117	C₂²×C₉	1	4	yes	complemented
444	#117	C₂²×C₉	1	2	yes	complemented
445	#117	C₂²×C₉	1	2	yes	complemented
446	#117	C₂²×C₉	1	2	yes	complemented
447	#117	C₂²×C₉	1	4	yes	complemented
448	#117	C₂²×C₉	1	2	yes	complemented
449	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
451	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
452	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
454	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
455	C₂×C₄²	C₂²×C₉	1	4	yes	complemented
456	C₂×C₄²	C₂²×C₉	1	2	yes	complemented
457	C₂³×C₃	—	2	4	no	—
458	C₂³×C₃	—	2	4	no	—
459	C₂³×C₃	—	4	2	no	—
460	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
461	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
462	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
463	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
464	C₃×Q₈	—	2	2	no	—
465	C₃×Q₈	—	2	4	no	—
466	C₃×Q₈	—	4	2	no	—
467	C₃×D₄	—	2	4	no	—
468	C₃×D₄	—	2	4	no	—
469	C₃×D₄	—	2	8	no	—
470	C₃×D₄	—	2	2	no	—
471	C₃×D₄	—	2	2	no	—
472	C₃×D₄	—	4	4	no	—
473	C₃×D₄	C₃×#41	1	4	yes	—
474	C₂×C₃×C₄	—	2	4	no	—
475	C₂×C₃×C₄	—	2	8	no	—
476	C₂×C₃×C₄	—	2	4	no	—
477	C₂×C₃×C₄	—	2	4	no	—
478	C₂×C₃×C₄	—	2	4	no	—
479	C₂×C₃×C₄	—	2	4	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	4	no	—
482	C₂×C₃×C₄	—	2	4	no	—
483	C₂×C₃×C₄	—	4	2	no	—
484	C₂×C₃×C₄	—	4	4	no	—
485	C₂×C₃×C₄	—	4	1	no	—
486	C₂×C₃×C₄	C₃×#41	1	4	yes	—
487	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
488	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
489	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
490	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
492	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
493	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
494	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
495	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
497	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
498	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
499	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
500	C₂×C₉	—	2	2	no	—
501	C₂×C₉	—	2	4	no	—
502	C₂×C₉	—	4	2	no	—
503	C₂×C₉	—	4	2	no	—
504	C₂×C₉	C₂²×#41	1	1	yes	characteristic
505	C₂×C₉	C₂²×#41	1	1	yes	characteristic
506	C₂×C₉	#585	1	1	yes	characteristic
507	C₂⁴	C₂³×C₉	1	2	yes	—
508	#41	—	2	8	no	—
509	#41	—	2	4	no	—
510	C₂×Q₈	C₂³×C₉	1	2	yes	—
511	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
512	C₂×Q₈	C₂³×C₉	1	2	yes	—
513	C₂×D₄	—	2	4	no	—
514	C₂×D₄	C₂³×C₉	1	2	yes	—
515	C₂×D₄	C₂³×C₉	1	2	yes	—
516	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
517	C₂×D₄	C₂³×C₉	1	4	yes	—
518	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
519	C₂×D₄	C₂³×C₉	1	4	yes	—
520	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
521	C₂²×C₄	—	2	8	no	—
522	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
523	C₂²×C₄	C₂³×C₉	1	2	yes	—
524	C₂²×C₄	C₂³×C₉	1	4	yes	—
525	C₂²×C₄	C₂³×C₉	1	2	yes	—
526	C₂²×C₄	C₂³×C₉	1	2	yes	—
527	C₂²×C₄	C₂³×C₉	1	2	yes	—
528	C₂²×C₄	C₂³×C₉	1	2	yes	—
529	C₂²×C₄	C₂³×C₉	1	2	yes	—
530	C₂²×C₄	C₂³×C₉	1	2	yes	—
531	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
532	C₂²×C₄	C₂³×C₉	1	4	yes	—
533	C₂²×C₄	C₂³×C₉	1	2	yes	—
534	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
537	C₄⋊C₄	C₂³×C₉	1	2	yes	—
538	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
539	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
540	C₄⋊C₄	C₂³×C₉	1	2	yes	—
541	C₄⋊C₄	C₂³×C₉	1	2	yes	—
542	C₄⋊C₄	C₂³×C₉	1	4	yes	—
543	C₄⋊C₄	C₂³×C₉	1	4	yes	—
544	C₄⋊C₄	C₂³×C₉	1	2	yes	—
545	C₄⋊C₄	C₂³×C₉	1	2	yes	—
546	C₄⋊C₄	C₂³×C₉	1	2	yes	—
547	C₄⋊C₄	C₂³×C₉	1	4	yes	—
548	C₄⋊C₄	C₂³×C₉	1	4	yes	—
549	C₄⋊C₄	C₂³×C₉	1	4	yes	—
550	C₄⋊C₄	C₂³×C₉	1	4	yes	—
551	C₄⋊C₄	C₂³×C₉	1	2	yes	—
552	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
553	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
554	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
555	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
556	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
557	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
558	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
559	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
560	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
561	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
562	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
563	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
564	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
565	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
566	C₄²	C₂³×C₉	1	1	yes	characteristic
567	C₄²	C₂³×C₉	1	1	yes	characteristic
568	C₄²	C₂³×C₉	1	1	yes	characteristic
569	C₄²	C₂³×C₉	1	1	yes	characteristic
570	C₄²	C₂³×C₉	1	2	yes	—
571	C₄²	C₂³×C₉	1	4	yes	—
572	C₄²	C₂³×C₉	1	4	yes	—
573	C₄²	C₂³×C₉	1	4	yes	—
574	C₄²	C₂³×C₉	1	2	yes	—
575	C₄²	C₂³×C₉	1	2	yes	—
576	C₂²×C₃	—	2	2	no	—
577	C₂²×C₃	—	2	1	no	—
578	C₂²×C₃	—	2	2	no	—
579	C₂²×C₃	—	2	1	no	—
580	C₂²×C₃	—	2	2	no	—
581	C₂²×C₃	—	2	2	no	—
582	C₂²×C₃	—	2	2	no	—
583	C₂²×C₃	—	2	2	no	—
584	C₂²×C₃	—	2	2	no	—
585	C₂²×C₃	—	2	2	no	—
586	C₂²×C₃	—	4	8	no	—
587	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
588	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
589	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
590	C₃×C₄	—	2	2	no	—
591	C₃×C₄	—	2	2	no	—
592	C₃×C₄	—	2	2	no	—
593	C₃×C₄	—	2	1	no	—
594	C₃×C₄	—	2	4	no	—
595	C₃×C₄	—	2	2	no	—
596	C₃×C₄	—	2	1	no	—
597	C₃×C₄	—	2	2	no	—
598	C₃×C₄	—	2	4	no	—
599	C₃×C₄	—	2	1	no	—
600	C₃×C₄	C₂×C₃×#41	1	2	yes	—
601	C₃×C₄	C₂×C₃×#41	1	2	yes	—
602	C₃×C₄	C₂×C₃×#41	1	2	yes	—
603	C₉	#3475	1	1	yes	characteristic, direct product factor, Sylow
604	C₂³	—	2	4	no	—
605	C₂³	—	2	4	no	—
606	C₂³	—	4	2	no	—
607	C₂³	C₂⁴×C₉	1	2	yes	—
608	C₂³	C₂⁴×C₉	1	2	yes	—
609	C₂³	C₂⁴×C₉	1	1	yes	characteristic
610	C₂³	C₂⁴×C₉	1	2	yes	—
611	Q₈	—	2	2	no	—
612	Q₈	—	2	4	no	—
613	Q₈	—	4	2	no	—
614	D₄	—	2	4	no	—
615	D₄	—	2	4	no	—
616	D₄	—	2	8	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	2	no	—
619	D₄	—	4	4	no	—
620	D₄	C₉×#41	1	4	yes	complemented
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	—	4	4	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	C₉×#41	1	4	yes	complemented
634	C₂×C₄	C₂⁴×C₉	1	2	yes	—
635	C₂×C₄	C₂⁴×C₉	1	2	yes	—
636	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
637	C₂×C₄	C₂⁴×C₉	1	2	yes	—
638	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
639	C₂×C₄	C₂⁴×C₉	1	4	yes	—
640	C₂×C₄	C₂⁴×C₉	1	2	yes	—
641	C₂×C₄	C₂⁴×C₉	1	4	yes	—
642	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
643	C₂×C₄	C₂⁴×C₉	1	2	yes	—
644	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
645	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
646	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
647	C₂×C₃	—	2	2	no	—
648	C₂×C₃	—	2	4	no	—
649	C₂×C₃	—	4	2	no	—
650	C₂×C₃	—	4	2	no	—
651	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
652	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
653	C₂×C₃	C₃×#585	1	1	yes	characteristic
654	C₂²	—	2	2	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	4	8	no	—
665	C₂²	C₂×C₉×#41	1	2	yes	—
666	C₂²	C₂×C₉×#41	1	4	yes	—
667	C₂²	C₂⁵×C₉	1	1	yes	characteristic
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	2	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	4	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	4	no	—
677	C₄	—	2	1	no	—
678	C₄	C₂×C₉×#41	1	2	yes	—
679	C₄	C₂×C₉×#41	1	2	yes	—
680	C₄	C₂×C₉×#41	1	2	yes	—
681	C₃	C₃×#3475	1	1	yes	characteristic
682	C₂	—	2	2	no	—
683	C₂	—	2	4	no	—
684	C₂	—	4	2	no	—
685	C₂	—	4	2	no	—
686	C₂	C₂²×C₉×#41	1	1	yes	characteristic
687	C₂	C₂²×C₉×#41	1	1	yes	characteristic
688	C₂	C₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂⁴
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3475	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#556	C₂	semidirect
2. C₉×#555	C₂	semidirect
3. C₉×#554	C₂	semidirect
4. C₉×#553	C₂	semidirect
5. C₉×#552	C₂	semidirect
6. C₉×#552	C₂	semidirect
7. C₉×#551	C₂	semidirect
8. C₉×#547	C₂	semidirect
9. C₉×#546	C₂	semidirect
10. C₉×#533	C₂	semidirect
11. C₉×#529	C₂	semidirect
12. C₉×#529	C₂	semidirect
13. C₉×#525	C₂	semidirect
14. C₄×C₉×#41	C₂	semidirect
15. C₄×C₉×#41	C₂	semidirect
16. C₂×C₄×D₄×C₉	C₂	semidirect
17. C₂×C₉×#117	C₂	semidirect
23. C₉×C₄⋊Q₈	C₂²	semidirect
24. C₉×C₄⋊Q₈	C₂²	semidirect
25. C₉×#126	C₂²	semidirect
26. C₉×#126	C₂²	semidirect
27. C₉×#126	C₂²	semidirect
28. C₉×#125	C₂²	semidirect
29. C₉×#125	C₂²	semidirect
30. C₉×#125	C₂²	semidirect
32. C₉×#124	C₂²	semidirect
35. C₉×#123	C₂²	semidirect
36. C₉×#123	C₂²	semidirect
39. C₉×C₂²⋊Q₈	C₂²	semidirect
40. C₉×C₂²⋊Q₈	C₂²	semidirect
41. C₉×C₂²⋊Q₈	C₂²	semidirect
42. C₉×C₂²⋊Q₈	C₂²	semidirect
45. C₉×#121	C₂²	semidirect
46. C₉×#121	C₂²	semidirect
48. C₄×Q₈×C₉	C₂²	semidirect
49. C₄×Q₈×C₉	C₂²	semidirect
50. C₄×Q₈×C₉	C₂²	semidirect
51. C₄×Q₈×C₉	C₂²	semidirect
52. C₄×Q₈×C₉	C₂²	semidirect
62. C₄×D₄×C₉	C₂²	semidirect
63. C₄×D₄×C₉	C₂²	semidirect
64. C₄×D₄×C₉	C₂²	semidirect
65. C₄×D₄×C₉	C₂²	semidirect
66. C₄×D₄×C₉	C₂²	semidirect
70. C₉×#117	C₂²	semidirect
71. C₉×#117	C₂²	semidirect
72. C₉×#117	C₂²	semidirect
73. C₉×#117	C₂²	semidirect
74. C₉×#117	C₂²	semidirect
75. C₉×#117	C₂²	semidirect
77. C₂×C₉×C₄⋊C₄	C₂²	semidirect
78. C₂×C₉×C₄⋊C₄	C₂²	semidirect
82. C₂×C₄²×C₉	C₂²	semidirect
83. C₂×C₄²×C₉	C₂²	semidirect
170. #3475	C₉	direct (N × H)
252. D₄×C₉	#41	semidirect
265. C₂×C₄×C₉	#41	semidirect
279. #556	C₂×C₉	semidirect
280. #555	C₂×C₉	semidirect
281. #554	C₂×C₉	semidirect
282. #553	C₂×C₉	semidirect
283. #552	C₂×C₉	semidirect
284. #552	C₂×C₉	semidirect
285. #551	C₂×C₉	semidirect
286. #547	C₂×C₉	semidirect
287. #546	C₂×C₉	semidirect
288. #533	C₂×C₉	semidirect
289. #529	C₂×C₉	semidirect
290. #529	C₂×C₉	semidirect
291. #525	C₂×C₉	semidirect
292. C₄×#41	C₂×C₉	semidirect
293. C₄×#41	C₂×C₉	semidirect
294. C₂×C₄×D₄	C₂×C₉	semidirect
295. C₂×#117	C₂×C₉	semidirect
396. C₄⋊Q₈	C₂²×C₉	semidirect
397. C₄⋊Q₈	C₂²×C₉	semidirect
398. #126	C₂²×C₉	semidirect
399. #126	C₂²×C₉	semidirect
400. #126	C₂²×C₉	semidirect
401. #125	C₂²×C₉	semidirect
402. #125	C₂²×C₉	semidirect
403. #125	C₂²×C₉	semidirect
405. #124	C₂²×C₉	semidirect
408. #123	C₂²×C₉	semidirect
409. #123	C₂²×C₉	semidirect
412. C₂²⋊Q₈	C₂²×C₉	semidirect
413. C₂²⋊Q₈	C₂²×C₉	semidirect
414. C₂²⋊Q₈	C₂²×C₉	semidirect
415. C₂²⋊Q₈	C₂²×C₉	semidirect
418. #121	C₂²×C₉	semidirect
419. #121	C₂²×C₉	semidirect
421. C₄×Q₈	C₂²×C₉	semidirect
422. C₄×Q₈	C₂²×C₉	semidirect
423. C₄×Q₈	C₂²×C₉	semidirect
424. C₄×Q₈	C₂²×C₉	semidirect
425. C₄×Q₈	C₂²×C₉	semidirect
435. C₄×D₄	C₂²×C₉	semidirect
436. C₄×D₄	C₂²×C₉	semidirect
437. C₄×D₄	C₂²×C₉	semidirect
438. C₄×D₄	C₂²×C₉	semidirect
439. C₄×D₄	C₂²×C₉	semidirect
443. #117	C₂²×C₉	semidirect
444. #117	C₂²×C₉	semidirect
445. #117	C₂²×C₉	semidirect
446. #117	C₂²×C₉	semidirect
447. #117	C₂²×C₉	semidirect
448. #117	C₂²×C₉	semidirect
450. C₂×C₄⋊C₄	C₂²×C₉	semidirect
451. C₂×C₄⋊C₄	C₂²×C₉	semidirect
455. C₂×C₄²	C₂²×C₉	semidirect
456. C₂×C₄²	C₂²×C₉	semidirect
603. C₉	#3475	direct (N × H)
620. D₄	C₉×#41	semidirect
633. C₂×C₄	C₉×#41	semidirect

Maximal subgroups

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

subgroup	index
C₉×#556	2
C₉×#555	2
C₉×#554	2
C₉×#553	2
C₉×#552	2
C₉×#551	2
C₉×#547	2
C₉×#546	2
C₉×#533	2
C₉×#529	2
C₉×#525	2
C₄×C₉×#41	2
C₂×C₄×D₄×C₉	2
C₂×C₉×#117	2
C₃×#3475	3

Subgroups — C9×#3475 #11768196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3475 #11768196