Subgroups — C₉×#3494 #11768215

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#555	C₂	1	2	yes	maximal, complemented
2	C₉×#553	C₂	1	2	yes	maximal, complemented
3	C₉×#553	C₂	1	2	yes	maximal, complemented
4	C₉×#551	C₂	1	4	yes	maximal, complemented
5	C₉×#547	C₂	1	2	yes	maximal, complemented
6	C₉×#546	C₂	1	4	yes	maximal, complemented
7	C₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#542	C₂	1	2	yes	maximal, complemented
9	C₉×#540	C₂	1	2	yes	maximal, complemented
10	C₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#532	C₂	1	2	yes	maximal, complemented
12	C₉×#529	C₂	1	2	yes	maximal, complemented
13	C₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
16	C₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3494	C₃	1	1	yes	maximal, characteristic
19	C₂×C₉×#41	C₂²	1	1	yes	characteristic
20	C₂×C₉×#41	C₂²	1	4	yes	complemented
21	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₉	C₂²	1	2	yes	—
23	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
24	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₉×#127	C₂²	1	2	yes	complemented
27	C₉×#126	C₂²	1	4	yes	complemented
28	C₉×#126	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	complemented
32	C₉×#124	C₂²	1	4	yes	complemented
33	C₉×#124	C₂²	1	4	yes	complemented
34	C₉×#123	C₂²	1	2	yes	—
35	C₉×#123	C₂²	1	4	yes	complemented
36	C₉×#123	C₂²	1	4	yes	complemented
37	C₉×#123	C₂²	1	4	yes	complemented
38	C₉×#123	C₂²	1	4	yes	complemented
39	C₉×C₂²⋊Q₈	C₂²	1	4	yes	—
40	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₉×#121	C₂²	1	2	yes	—
44	C₉×#121	C₂²	1	2	yes	—
45	C₉×#121	C₂²	1	2	yes	—
46	C₉×#121	C₂²	1	2	yes	—
47	C₉×#121	C₂²	1	1	yes	characteristic, complemented
48	C₉×#121	C₂²	1	1	yes	characteristic, complemented
49	C₉×#121	C₂²	1	4	yes	complemented
50	C₉×#121	C₂²	1	2	yes	complemented
51	C₉×#121	C₂²	1	2	yes	complemented
52	C₉×#121	C₂²	1	4	yes	complemented
53	C₉×#121	C₂²	1	4	yes	complemented
54	C₉×#120	C₂²	1	2	yes	—
55	C₉×#120	C₂²	1	4	yes	—
56	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
57	C₄×D₄×C₉	C₂²	1	4	yes	—
58	C₄×D₄×C₉	C₂²	1	2	yes	complemented
59	C₄×D₄×C₉	C₂²	1	2	yes	complemented
60	C₄×D₄×C₉	C₂²	1	2	yes	complemented
61	C₄×D₄×C₉	C₂²	1	2	yes	complemented
62	C₄×D₄×C₉	C₂²	1	4	yes	complemented
63	C₄×D₄×C₉	C₂²	1	2	yes	complemented
64	C₄×D₄×C₉	C₂²	1	4	yes	complemented
65	C₄×D₄×C₉	C₂²	1	2	yes	complemented
66	C₄×D₄×C₉	C₂²	1	2	yes	complemented
67	C₉×#117	C₂²	1	1	yes	characteristic
68	C₉×#117	C₂²	1	1	yes	characteristic
69	C₉×#117	C₂²	1	1	yes	characteristic
70	C₉×#117	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
75	C₉×#117	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
79	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
81	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
83	C₂×C₄²×C₉	C₂²	1	2	yes	complemented
84	C₃×#555	C₂×C₃	1	2	yes	—
85	C₃×#553	C₂×C₃	1	2	yes	—
86	C₃×#553	C₂×C₃	1	2	yes	—
87	C₃×#551	C₂×C₃	1	4	yes	—
88	C₃×#547	C₂×C₃	1	2	yes	—
89	C₃×#546	C₂×C₃	1	4	yes	—
90	C₃×#544	C₂×C₃	1	1	yes	characteristic
91	C₃×#542	C₂×C₃	1	2	yes	—
92	C₃×#540	C₂×C₃	1	2	yes	—
93	C₃×#535	C₂×C₃	1	1	yes	characteristic
94	C₃×#532	C₂×C₃	1	2	yes	—
95	C₃×#529	C₂×C₃	1	2	yes	—
96	C₃×#525	C₂×C₃	1	1	yes	characteristic
97	C₂×C₃×#121	C₂×C₃	1	1	yes	characteristic
98	C₃×#520	C₂×C₃	1	1	yes	characteristic
99	C₃×#518	C₂×C₃	1	1	yes	characteristic
100	C₂×C₃×#117	C₂×C₃	1	1	yes	characteristic
101	C₂⁴×C₉	C₂³	1	1	yes	characteristic
102	C₂⁴×C₉	C₂³	1	2	yes	—
103	C₉×#41	—	2	4	no	—
104	C₉×#41	—	4	8	no	—
105	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
106	C₂×Q₈×C₉	C₂³	1	4	yes	—
107	C₂×D₄×C₉	—	2	4	no	—
108	C₂×D₄×C₉	—	4	4	no	—
109	C₂×D₄×C₉	C₂³	1	2	yes	—
110	C₂×D₄×C₉	C₂³	1	2	yes	—
111	C₂×D₄×C₉	C₂³	1	2	yes	—
112	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₉	C₂³	1	2	yes	—
114	C₂×D₄×C₉	C₂³	1	4	yes	—
115	C₂×D₄×C₉	C₂³	1	2	yes	—
116	C₂×D₄×C₉	C₂³	1	4	yes	—
117	C₂×D₄×C₉	C₂³	1	4	yes	—
118	C₂×D₄×C₉	C₂³	1	4	yes	—
119	C₂²×C₄×C₉	—	2	4	no	—
120	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₉	C₂³	1	2	yes	—
122	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₉	C₂³	1	2	yes	—
125	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₉	C₂³	1	2	yes	—
129	C₂²×C₄×C₉	C₂³	1	4	yes	—
130	C₂²×C₄×C₉	C₂³	1	4	yes	—
131	C₂²×C₄×C₉	C₂³	1	4	yes	—
132	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
133	C₉×C₄⋊C₄	C₂³	1	2	yes	—
134	C₉×C₄⋊C₄	C₂³	1	2	yes	—
135	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
143	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₉×C₄⋊C₄	C₂³	1	2	yes	—
145	C₉×C₄⋊C₄	C₂³	1	4	yes	—
146	C₉×C₄⋊C₄	C₂³	1	4	yes	—
147	C₉×C₄⋊C₄	C₂³	1	4	yes	—
148	C₉×C₄⋊C₄	C₂³	1	2	yes	—
149	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₉×C₂²⋊C₄	C₂³	1	2	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	4	yes	—
156	C₉×C₂²⋊C₄	C₂³	1	4	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	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
163	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₄²×C₉	C₂³	1	2	yes	—
166	C₄²×C₉	C₂³	1	2	yes	—
167	C₄²×C₉	C₂³	1	2	yes	—
168	C₄²×C₉	C₂³	1	2	yes	—
169	C₄²×C₉	C₂³	1	2	yes	—
170	C₄²×C₉	C₂³	1	4	yes	—
171	#3494	C₉	1	1	yes	characteristic, direct product factor, Sylow
172	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₃×#41	C₂²×C₃	1	4	yes	—
174	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
175	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
176	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
177	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
178	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
179	C₃×#127	C₂²×C₃	1	2	yes	—
180	C₃×#126	C₂²×C₃	1	4	yes	—
181	C₃×#126	C₂²×C₃	1	4	yes	—
182	C₃×#125	C₂²×C₃	1	2	yes	—
183	C₃×#125	C₂²×C₃	1	2	yes	—
184	C₃×#124	C₂²×C₃	1	2	yes	—
185	C₃×#124	C₂²×C₃	1	4	yes	—
186	C₃×#124	C₂²×C₃	1	4	yes	—
187	C₃×#123	C₂²×C₃	1	2	yes	—
188	C₃×#123	C₂²×C₃	1	4	yes	—
189	C₃×#123	C₂²×C₃	1	4	yes	—
190	C₃×#123	C₂²×C₃	1	4	yes	—
191	C₃×#123	C₂²×C₃	1	4	yes	—
192	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
193	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
194	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
195	C₃×C₂²⋊Q₈	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×#121	C₂²×C₃	1	2	yes	—
200	C₃×#121	C₂²×C₃	1	1	yes	characteristic
201	C₃×#121	C₂²×C₃	1	1	yes	characteristic
202	C₃×#121	C₂²×C₃	1	4	yes	—
203	C₃×#121	C₂²×C₃	1	2	yes	—
204	C₃×#121	C₂²×C₃	1	2	yes	—
205	C₃×#121	C₂²×C₃	1	4	yes	—
206	C₃×#121	C₂²×C₃	1	4	yes	—
207	C₃×#120	C₂²×C₃	1	2	yes	—
208	C₃×#120	C₂²×C₃	1	4	yes	—
209	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
210	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
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	2	yes	—
215	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
216	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
217	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
218	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
219	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
220	C₃×#117	C₂²×C₃	1	1	yes	characteristic
221	C₃×#117	C₂²×C₃	1	1	yes	characteristic
222	C₃×#117	C₂²×C₃	1	2	yes	—
223	C₃×#117	C₂²×C₃	1	1	yes	characteristic
224	C₃×#117	C₂²×C₃	1	2	yes	—
225	C₃×#117	C₂²×C₃	1	1	yes	characteristic
226	C₃×#117	C₂²×C₃	1	1	yes	characteristic
227	C₃×#117	C₂²×C₃	1	2	yes	—
228	C₃×#117	C₂²×C₃	1	4	yes	—
229	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
231	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
232	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
234	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
235	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
236	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
237	C₂³×C₉	—	2	2	no	—
238	C₂³×C₉	—	2	2	no	—
239	C₂³×C₉	—	2	4	no	—
240	C₂³×C₉	—	4	1	no	—
241	C₂³×C₉	—	4	2	no	—
242	C₂³×C₉	—	4	2	no	—
243	C₂³×C₉	C₂⁴	1	1	yes	characteristic
244	C₂³×C₉	C₂⁴	1	4	yes	—
245	C₂³×C₉	C₂⁴	1	2	yes	—
246	C₂³×C₉	C₂⁴	1	1	yes	characteristic
247	C₂³×C₉	C₂⁴	1	1	yes	characteristic
248	Q₈×C₉	—	2	2	no	—
249	Q₈×C₉	—	4	4	no	—
250	D₄×C₉	—	2	4	no	—
251	D₄×C₉	—	2	8	no	—
252	D₄×C₉	—	2	4	no	—
253	D₄×C₉	—	2	4	no	—
254	D₄×C₉	—	2	4	no	—
255	D₄×C₉	—	2	2	no	—
256	D₄×C₉	—	4	4	no	—
257	D₄×C₉	—	4	2	no	—
258	D₄×C₉	—	4	4	no	—
259	D₄×C₉	—	4	4	no	—
260	C₂×C₄×C₉	—	2	2	no	—
261	C₂×C₄×C₉	—	2	4	no	—
262	C₂×C₄×C₉	—	2	2	no	—
263	C₂×C₄×C₉	—	2	2	no	—
264	C₂×C₄×C₉	—	2	2	no	—
265	C₂×C₄×C₉	—	2	2	no	—
266	C₂×C₄×C₉	—	2	4	no	—
267	C₂×C₄×C₉	—	4	4	no	—
268	C₂×C₄×C₉	—	4	2	no	—
269	C₂×C₄×C₉	—	4	2	no	—
270	C₂×C₄×C₉	—	4	4	no	—
271	C₂×C₄×C₉	—	4	4	no	—
272	C₂×C₄×C₉	#41	1	4	yes	complemented
273	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₉	C₂⁴	1	2	yes	—
276	C₂×C₄×C₉	C₂⁴	1	2	yes	—
277	C₂×C₄×C₉	C₂⁴	1	2	yes	—
278	C₂×C₄×C₉	C₂⁴	1	2	yes	—
279	C₂×C₄×C₉	C₂⁴	1	2	yes	—
280	C₂×C₄×C₉	C₂⁴	1	2	yes	—
281	C₂×C₄×C₉	C₂⁴	1	4	yes	—
282	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
285	#555	C₂×C₉	1	2	yes	complemented
286	#553	C₂×C₉	1	2	yes	complemented
287	#553	C₂×C₉	1	2	yes	complemented
288	#551	C₂×C₉	1	4	yes	complemented
289	#547	C₂×C₉	1	2	yes	complemented
290	#546	C₂×C₉	1	4	yes	complemented
291	#544	C₂×C₉	1	1	yes	characteristic, complemented
292	#542	C₂×C₉	1	2	yes	complemented
293	#540	C₂×C₉	1	2	yes	complemented
294	#535	C₂×C₉	1	1	yes	characteristic, complemented
295	#532	C₂×C₉	1	2	yes	complemented
296	#529	C₂×C₉	1	2	yes	complemented
297	#525	C₂×C₉	1	1	yes	characteristic, complemented
298	C₂×#121	C₂×C₉	1	1	yes	characteristic, complemented
299	#520	C₂×C₉	1	1	yes	characteristic, complemented
300	#518	C₂×C₉	1	1	yes	characteristic, complemented
301	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
302	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
303	C₂⁴×C₃	C₂³×C₃	1	2	yes	—
304	C₃×#41	—	2	4	no	—
305	C₃×#41	—	4	8	no	—
306	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
308	C₂×C₃×D₄	—	2	4	no	—
309	C₂×C₃×D₄	—	4	4	no	—
310	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
311	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
312	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
313	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
314	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
315	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
316	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
317	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
318	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
319	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
320	C₂²×C₃×C₄	—	2	4	no	—
321	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
322	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
323	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
326	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
329	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
330	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
331	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
332	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
333	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
334	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
335	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
336	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
337	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
338	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
339	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
340	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
341	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
342	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
343	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
344	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
345	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
346	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
347	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
348	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
349	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
350	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
352	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
353	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
354	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
355	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
356	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
357	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
358	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
359	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
360	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
361	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
362	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
363	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
364	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
365	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
366	C₃×C₄²	C₂³×C₃	1	2	yes	—
367	C₃×C₄²	C₂³×C₃	1	2	yes	—
368	C₃×C₄²	C₂³×C₃	1	2	yes	—
369	C₃×C₄²	C₂³×C₃	1	2	yes	—
370	C₃×C₄²	C₂³×C₃	1	4	yes	—
371	C₃×C₄²	C₂³×C₃	1	2	yes	—
372	C₂²×C₉	—	2	1	no	—
373	C₂²×C₉	—	2	1	no	—
374	C₂²×C₉	—	2	1	no	—
375	C₂²×C₉	—	2	1	no	—
376	C₂²×C₉	—	2	1	no	—
377	C₂²×C₉	—	2	2	no	—
378	C₂²×C₉	—	2	4	no	—
379	C₂²×C₉	—	2	2	no	—
380	C₂²×C₉	—	2	4	no	—
381	C₂²×C₉	—	2	1	no	—
382	C₂²×C₉	—	2	4	no	—
383	C₂²×C₉	—	2	2	no	—
384	C₂²×C₉	—	2	1	no	—
385	C₂²×C₉	—	4	4	no	—
386	C₂²×C₉	—	8	4	no	—
387	C₂²×C₉	C₂×#41	1	2	yes	—
388	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
389	C₂²×C₉	C₂⁵	1	1	yes	characteristic
390	C₄×C₉	—	2	1	no	—
391	C₄×C₉	—	2	1	no	—
392	C₄×C₉	—	2	2	no	—
393	C₄×C₉	—	2	2	no	—
394	C₄×C₉	—	2	2	no	—
395	C₄×C₉	—	2	4	no	—
396	C₄×C₉	—	2	2	no	—
397	C₄×C₉	—	2	2	no	—
398	C₄×C₉	—	2	2	no	—
399	C₄×C₉	—	2	2	no	—
400	C₄×C₉	C₂×#41	1	2	yes	—
401	C₄×C₉	C₂×#41	1	2	yes	—
402	C₂×#41	C₂²×C₉	1	1	yes	characteristic
403	C₂×#41	C₂²×C₉	1	4	yes	complemented
404	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
405	C₂²×D₄	C₂²×C₉	1	2	yes	—
406	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
407	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
408	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
409	#127	C₂²×C₉	1	2	yes	complemented
410	#126	C₂²×C₉	1	4	yes	complemented
411	#126	C₂²×C₉	1	4	yes	complemented
412	#125	C₂²×C₉	1	2	yes	complemented
413	#125	C₂²×C₉	1	2	yes	complemented
414	#124	C₂²×C₉	1	2	yes	complemented
415	#124	C₂²×C₉	1	4	yes	complemented
416	#124	C₂²×C₉	1	4	yes	complemented
417	#123	C₂²×C₉	1	2	yes	—
418	#123	C₂²×C₉	1	4	yes	complemented
419	#123	C₂²×C₉	1	4	yes	complemented
420	#123	C₂²×C₉	1	4	yes	complemented
421	#123	C₂²×C₉	1	4	yes	complemented
422	C₂²⋊Q₈	C₂²×C₉	1	4	yes	—
423	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
424	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
425	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
426	#121	C₂²×C₉	1	2	yes	—
427	#121	C₂²×C₉	1	2	yes	—
428	#121	C₂²×C₉	1	2	yes	—
429	#121	C₂²×C₉	1	2	yes	—
430	#121	C₂²×C₉	1	1	yes	characteristic, complemented
431	#121	C₂²×C₉	1	1	yes	characteristic, complemented
432	#121	C₂²×C₉	1	4	yes	complemented
433	#121	C₂²×C₉	1	2	yes	complemented
434	#121	C₂²×C₉	1	2	yes	complemented
435	#121	C₂²×C₉	1	4	yes	complemented
436	#121	C₂²×C₉	1	4	yes	complemented
437	#120	C₂²×C₉	1	2	yes	—
438	#120	C₂²×C₉	1	4	yes	—
439	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
440	C₄×D₄	C₂²×C₉	1	4	yes	—
441	C₄×D₄	C₂²×C₉	1	2	yes	complemented
442	C₄×D₄	C₂²×C₉	1	2	yes	complemented
443	C₄×D₄	C₂²×C₉	1	2	yes	complemented
444	C₄×D₄	C₂²×C₉	1	2	yes	complemented
445	C₄×D₄	C₂²×C₉	1	2	yes	complemented
446	C₄×D₄	C₂²×C₉	1	2	yes	complemented
447	C₄×D₄	C₂²×C₉	1	2	yes	complemented
448	C₄×D₄	C₂²×C₉	1	4	yes	complemented
449	C₄×D₄	C₂²×C₉	1	4	yes	complemented
450	#117	C₂²×C₉	1	1	yes	characteristic
451	#117	C₂²×C₉	1	1	yes	characteristic
452	#117	C₂²×C₉	1	2	yes	—
453	#117	C₂²×C₉	1	1	yes	characteristic
454	#117	C₂²×C₉	1	2	yes	complemented
455	#117	C₂²×C₉	1	1	yes	characteristic, complemented
456	#117	C₂²×C₉	1	1	yes	characteristic, complemented
457	#117	C₂²×C₉	1	2	yes	complemented
458	#117	C₂²×C₉	1	4	yes	complemented
459	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
461	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
462	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
463	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
465	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
466	C₂×C₄²	C₂²×C₉	1	2	yes	complemented
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	2	no	—
469	C₂³×C₃	—	2	4	no	—
470	C₂³×C₃	—	4	1	no	—
471	C₂³×C₃	—	4	2	no	—
472	C₂³×C₃	—	4	2	no	—
473	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
474	C₂³×C₃	C₂⁴×C₃	1	4	yes	—
475	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
476	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
477	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
478	C₃×Q₈	—	2	2	no	—
479	C₃×Q₈	—	4	4	no	—
480	C₃×D₄	—	2	4	no	—
481	C₃×D₄	—	2	8	no	—
482	C₃×D₄	—	2	4	no	—
483	C₃×D₄	—	2	4	no	—
484	C₃×D₄	—	2	4	no	—
485	C₃×D₄	—	2	2	no	—
486	C₃×D₄	—	4	4	no	—
487	C₃×D₄	—	4	2	no	—
488	C₃×D₄	—	4	4	no	—
489	C₃×D₄	—	4	4	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	4	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	2	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	4	4	no	—
498	C₂×C₃×C₄	—	4	2	no	—
499	C₂×C₃×C₄	—	4	2	no	—
500	C₂×C₃×C₄	—	4	4	no	—
501	C₂×C₃×C₄	—	4	4	no	—
502	C₂×C₃×C₄	C₃×#41	1	4	yes	—
503	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
505	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
506	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
507	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
508	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
509	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
510	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
511	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
512	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
514	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
515	C₂×C₉	—	2	2	no	—
516	C₂×C₉	—	2	2	no	—
517	C₂×C₉	—	4	2	no	—
518	C₂×C₉	—	4	1	no	—
519	C₂×C₉	—	4	4	no	—
520	C₂×C₉	C₂²×#41	1	1	yes	characteristic
521	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂×C₉	#585	1	1	yes	characteristic
523	C₂⁴	C₂³×C₉	1	1	yes	characteristic
524	C₂⁴	C₂³×C₉	1	2	yes	—
525	#41	—	2	4	no	—
526	#41	—	4	8	no	—
527	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
528	C₂×Q₈	C₂³×C₉	1	4	yes	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	4	4	no	—
531	C₂×D₄	C₂³×C₉	1	2	yes	—
532	C₂×D₄	C₂³×C₉	1	2	yes	—
533	C₂×D₄	C₂³×C₉	1	2	yes	—
534	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
535	C₂×D₄	C₂³×C₉	1	2	yes	—
536	C₂×D₄	C₂³×C₉	1	4	yes	—
537	C₂×D₄	C₂³×C₉	1	2	yes	—
538	C₂×D₄	C₂³×C₉	1	4	yes	—
539	C₂×D₄	C₂³×C₉	1	4	yes	—
540	C₂×D₄	C₂³×C₉	1	4	yes	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
543	C₂²×C₄	C₂³×C₉	1	2	yes	—
544	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
545	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
546	C₂²×C₄	C₂³×C₉	1	2	yes	—
547	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
548	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
549	C₂²×C₄	C₂³×C₉	1	2	yes	—
550	C₂²×C₄	C₂³×C₉	1	2	yes	—
551	C₂²×C₄	C₂³×C₉	1	4	yes	—
552	C₂²×C₄	C₂³×C₉	1	4	yes	—
553	C₂²×C₄	C₂³×C₉	1	4	yes	—
554	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
555	C₄⋊C₄	C₂³×C₉	1	2	yes	—
556	C₄⋊C₄	C₂³×C₉	1	2	yes	—
557	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
558	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
559	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
560	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
561	C₄⋊C₄	C₂³×C₉	1	2	yes	—
562	C₄⋊C₄	C₂³×C₉	1	2	yes	—
563	C₄⋊C₄	C₂³×C₉	1	4	yes	—
564	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
565	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
566	C₄⋊C₄	C₂³×C₉	1	2	yes	—
567	C₄⋊C₄	C₂³×C₉	1	4	yes	—
568	C₄⋊C₄	C₂³×C₉	1	4	yes	—
569	C₄⋊C₄	C₂³×C₉	1	4	yes	—
570	C₄⋊C₄	C₂³×C₉	1	2	yes	—
571	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
572	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
573	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
574	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
575	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
576	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
577	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
578	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
579	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
580	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
581	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
582	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
583	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
584	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
585	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
586	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
587	C₄²	C₂³×C₉	1	2	yes	—
588	C₄²	C₂³×C₉	1	2	yes	—
589	C₄²	C₂³×C₉	1	2	yes	—
590	C₄²	C₂³×C₉	1	2	yes	—
591	C₄²	C₂³×C₉	1	2	yes	—
592	C₄²	C₂³×C₉	1	4	yes	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	2	1	no	—
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	2	no	—
599	C₂²×C₃	—	2	4	no	—
600	C₂²×C₃	—	2	2	no	—
601	C₂²×C₃	—	2	4	no	—
602	C₂²×C₃	—	2	1	no	—
603	C₂²×C₃	—	2	4	no	—
604	C₂²×C₃	—	2	2	no	—
605	C₂²×C₃	—	2	1	no	—
606	C₂²×C₃	—	4	4	no	—
607	C₂²×C₃	—	8	4	no	—
608	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
609	C₂²×C₃	C₃×H(5,𝔽₂)	1	2	yes	—
610	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
611	C₃×C₄	—	2	1	no	—
612	C₃×C₄	—	2	1	no	—
613	C₃×C₄	—	2	2	no	—
614	C₃×C₄	—	2	2	no	—
615	C₃×C₄	—	2	2	no	—
616	C₃×C₄	—	2	4	no	—
617	C₃×C₄	—	2	2	no	—
618	C₃×C₄	—	2	2	no	—
619	C₃×C₄	—	2	2	no	—
620	C₃×C₄	—	2	2	no	—
621	C₃×C₄	C₂×C₃×#41	1	2	yes	—
622	C₃×C₄	C₂×C₃×#41	1	2	yes	—
623	C₉	#3494	1	1	yes	characteristic, direct product factor, Sylow
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	2	no	—
630	C₂³	C₂⁴×C₉	1	1	yes	characteristic
631	C₂³	C₂⁴×C₉	1	4	yes	—
632	C₂³	C₂⁴×C₉	1	2	yes	—
633	C₂³	C₂⁴×C₉	1	1	yes	characteristic
634	C₂³	C₂⁴×C₉	1	1	yes	characteristic
635	Q₈	—	2	2	no	—
636	Q₈	—	4	4	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	8	no	—
639	D₄	—	2	4	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	4	no	—
642	D₄	—	2	2	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	4	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	C₉×#41	1	4	yes	complemented
660	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
661	C₂×C₄	C₂⁴×C₉	1	2	yes	—
662	C₂×C₄	C₂⁴×C₉	1	2	yes	—
663	C₂×C₄	C₂⁴×C₉	1	2	yes	—
664	C₂×C₄	C₂⁴×C₉	1	2	yes	—
665	C₂×C₄	C₂⁴×C₉	1	2	yes	—
666	C₂×C₄	C₂⁴×C₉	1	2	yes	—
667	C₂×C₄	C₂⁴×C₉	1	2	yes	—
668	C₂×C₄	C₂⁴×C₉	1	4	yes	—
669	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
670	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
671	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
672	C₂×C₃	—	2	2	no	—
673	C₂×C₃	—	2	2	no	—
674	C₂×C₃	—	4	1	no	—
675	C₂×C₃	—	4	4	no	—
676	C₂×C₃	—	4	2	no	—
677	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
678	C₂×C₃	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
679	C₂×C₃	C₃×#585	1	1	yes	characteristic
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	4	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	8	4	no	—
695	C₂²	C₂×C₉×#41	1	2	yes	—
696	C₂²	C₉×H(5,𝔽₂)	1	2	yes	—
697	C₂²	C₂⁵×C₉	1	1	yes	characteristic
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	2	4	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	C₂×C₉×#41	1	2	yes	—
709	C₄	C₂×C₉×#41	1	2	yes	—
710	C₃	C₃×#3494	1	1	yes	characteristic
711	C₂	—	2	2	no	—
712	C₂	—	2	2	no	—
713	C₂	—	4	1	no	—
714	C₂	—	4	4	no	—
715	C₂	—	4	2	no	—
716	C₂	C₂²×C₉×#41	1	1	yes	characteristic
717	C₂	C₂×C₉×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂	C₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂⁵
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3494	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. C₉×#555	C₂	semidirect
2. C₉×#553	C₂	semidirect
3. C₉×#553	C₂	semidirect
4. C₉×#551	C₂	semidirect
5. C₉×#547	C₂	semidirect
6. C₉×#546	C₂	semidirect
7. C₉×#544	C₂	semidirect
8. C₉×#542	C₂	semidirect
9. C₉×#540	C₂	semidirect
10. C₉×#535	C₂	semidirect
11. C₉×#532	C₂	semidirect
12. C₉×#529	C₂	semidirect
13. C₉×#525	C₂	semidirect
14. C₂×C₉×#121	C₂	semidirect
15. C₉×#520	C₂	semidirect
16. C₉×#518	C₂	semidirect
17. C₂×C₉×#117	C₂	semidirect
20. C₂×C₉×#41	C₂²	semidirect
24. C₉×C₄⋊Q₈	C₂²	semidirect
25. C₉×C₄⋊Q₈	C₂²	semidirect
26. C₉×#127	C₂²	semidirect
27. C₉×#126	C₂²	semidirect
28. C₉×#126	C₂²	semidirect
29. C₉×#125	C₂²	semidirect
30. C₉×#125	C₂²	semidirect
31. C₉×#124	C₂²	semidirect
32. C₉×#124	C₂²	semidirect
33. C₉×#124	C₂²	semidirect
35. C₉×#123	C₂²	semidirect
36. C₉×#123	C₂²	semidirect
37. C₉×#123	C₂²	semidirect
38. C₉×#123	C₂²	semidirect
40. C₉×C₂²⋊Q₈	C₂²	semidirect
41. C₉×C₂²⋊Q₈	C₂²	semidirect
42. C₉×C₂²⋊Q₈	C₂²	semidirect
47. C₉×#121	C₂²	semidirect
48. C₉×#121	C₂²	semidirect
49. C₉×#121	C₂²	semidirect
50. C₉×#121	C₂²	semidirect
51. C₉×#121	C₂²	semidirect
52. C₉×#121	C₂²	semidirect
53. C₉×#121	C₂²	semidirect
56. C₄×Q₈×C₉	C₂²	semidirect
58. C₄×D₄×C₉	C₂²	semidirect
59. C₄×D₄×C₉	C₂²	semidirect
60. C₄×D₄×C₉	C₂²	semidirect
61. C₄×D₄×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
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
79. C₂×C₉×C₄⋊C₄	C₂²	semidirect
83. C₂×C₄²×C₉	C₂²	semidirect
171. #3494	C₉	direct (N × H)
272. C₂×C₄×C₉	#41	semidirect
285. #555	C₂×C₉	semidirect
286. #553	C₂×C₉	semidirect
287. #553	C₂×C₉	semidirect
288. #551	C₂×C₉	semidirect
289. #547	C₂×C₉	semidirect
290. #546	C₂×C₉	semidirect
291. #544	C₂×C₉	semidirect
292. #542	C₂×C₉	semidirect
293. #540	C₂×C₉	semidirect
294. #535	C₂×C₉	semidirect
295. #532	C₂×C₉	semidirect
296. #529	C₂×C₉	semidirect
297. #525	C₂×C₉	semidirect
298. C₂×#121	C₂×C₉	semidirect
299. #520	C₂×C₉	semidirect
300. #518	C₂×C₉	semidirect
301. C₂×#117	C₂×C₉	semidirect
403. C₂×#41	C₂²×C₉	semidirect
407. C₄⋊Q₈	C₂²×C₉	semidirect
408. C₄⋊Q₈	C₂²×C₉	semidirect
409. #127	C₂²×C₉	semidirect
410. #126	C₂²×C₉	semidirect
411. #126	C₂²×C₉	semidirect
412. #125	C₂²×C₉	semidirect
413. #125	C₂²×C₉	semidirect
414. #124	C₂²×C₉	semidirect
415. #124	C₂²×C₉	semidirect
416. #124	C₂²×C₉	semidirect
418. #123	C₂²×C₉	semidirect
419. #123	C₂²×C₉	semidirect
420. #123	C₂²×C₉	semidirect
421. #123	C₂²×C₉	semidirect
423. C₂²⋊Q₈	C₂²×C₉	semidirect
424. C₂²⋊Q₈	C₂²×C₉	semidirect
425. C₂²⋊Q₈	C₂²×C₉	semidirect
430. #121	C₂²×C₉	semidirect
431. #121	C₂²×C₉	semidirect
432. #121	C₂²×C₉	semidirect
433. #121	C₂²×C₉	semidirect
434. #121	C₂²×C₉	semidirect
435. #121	C₂²×C₉	semidirect
436. #121	C₂²×C₉	semidirect
439. C₄×Q₈	C₂²×C₉	semidirect
441. C₄×D₄	C₂²×C₉	semidirect
442. C₄×D₄	C₂²×C₉	semidirect
443. C₄×D₄	C₂²×C₉	semidirect
444. C₄×D₄	C₂²×C₉	semidirect
445. C₄×D₄	C₂²×C₉	semidirect
446. C₄×D₄	C₂²×C₉	semidirect
447. C₄×D₄	C₂²×C₉	semidirect
448. C₄×D₄	C₂²×C₉	semidirect
449. C₄×D₄	C₂²×C₉	semidirect
454. #117	C₂²×C₉	semidirect
455. #117	C₂²×C₉	semidirect
456. #117	C₂²×C₉	semidirect
457. #117	C₂²×C₉	semidirect
458. #117	C₂²×C₉	semidirect
460. C₂×C₄⋊C₄	C₂²×C₉	semidirect
461. C₂×C₄⋊C₄	C₂²×C₉	semidirect
462. C₂×C₄⋊C₄	C₂²×C₉	semidirect
466. C₂×C₄²	C₂²×C₉	semidirect
623. C₉	#3494	direct (N × H)
659. 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×#555	2
C₉×#553	2
C₉×#551	2
C₉×#547	2
C₉×#546	2
C₉×#544	2
C₉×#542	2
C₉×#540	2
C₉×#535	2
C₉×#532	2
C₉×#529	2
C₉×#525	2
C₂×C₉×#121	2
C₉×#520	2
C₉×#518	2
C₂×C₉×#117	2
C₃×#3494	3

Subgroups — C9×#3494 #11768215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3494 #11768215