Subgroups — C₉×#3495 #11768216

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 678 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	2	yes	maximal, complemented
2	C₉×#554	C₂	1	2	yes	maximal, complemented
3	C₉×#552	C₂	1	4	yes	maximal, complemented
4	C₉×#552	C₂	1	2	yes	maximal, complemented
5	C₉×#552	C₂	1	2	yes	maximal, complemented
6	C₉×#551	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×#541	C₂	1	2	yes	maximal, complemented
10	C₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#533	C₂	1	2	yes	maximal, complemented
12	C₉×#529	C₂	1	2	yes	maximal, complemented
13	C₉×#525	C₂	1	1	yes	maximal, characteristic
14	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
16	C₉×#519	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#3495	C₃	1	1	yes	maximal, characteristic
19	C₂×C₉×#41	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
22	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₉×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₉×#126	C₂²	1	4	yes	—
26	C₉×#126	C₂²	1	4	yes	—
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	4	yes	complemented
31	C₉×#125	C₂²	1	4	yes	complemented
32	C₉×#125	C₂²	1	4	yes	complemented
33	C₉×#125	C₂²	1	2	yes	complemented
34	C₉×#124	C₂²	1	4	yes	—
35	C₉×#124	C₂²	1	2	yes	complemented
36	C₉×#123	C₂²	1	2	yes	—
37	C₉×#123	C₂²	1	4	yes	—
38	C₉×#123	C₂²	1	4	yes	—
39	C₉×#123	C₂²	1	4	yes	—
40	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
41	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
45	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₉×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₉×C₂²⋊Q₈	C₂²	1	4	yes	—
48	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
49	C₉×C₂²⋊Q₈	C₂²	1	2	yes	complemented
50	C₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
51	C₉×#121	C₂²	1	1	yes	characteristic
52	C₉×#121	C₂²	1	1	yes	characteristic
53	C₉×#120	C₂²	1	2	yes	—
54	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
55	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
56	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
57	C₄×Q₈×C₉	C₂²	1	4	yes	complemented
58	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
59	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
60	C₄×D₄×C₉	C₂²	1	4	yes	—
61	C₄×D₄×C₉	C₂²	1	2	yes	—
62	C₄×D₄×C₉	C₂²	1	2	yes	—
63	C₄×D₄×C₉	C₂²	1	4	yes	—
64	C₄×D₄×C₉	C₂²	1	2	yes	complemented
65	C₉×#117	C₂²	1	1	yes	characteristic
66	C₉×#117	C₂²	1	1	yes	characteristic
67	C₉×#117	C₂²	1	4	yes	—
68	C₉×#117	C₂²	1	1	yes	characteristic
69	C₉×#117	C₂²	1	2	yes	—
70	C₉×#117	C₂²	1	4	yes	—
71	C₉×#117	C₂²	1	1	yes	characteristic
72	C₉×#117	C₂²	1	2	yes	—
73	C₉×#117	C₂²	1	1	yes	characteristic
74	C₉×#117	C₂²	1	2	yes	complemented
75	C₉×#117	C₂²	1	4	yes	complemented
76	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
78	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
79	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
80	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₂×C₄²×C₉	C₂²	1	2	yes	—
84	C₃×#556	C₂×C₃	1	2	yes	—
85	C₃×#554	C₂×C₃	1	2	yes	—
86	C₃×#552	C₂×C₃	1	2	yes	—
87	C₃×#552	C₂×C₃	1	4	yes	—
88	C₃×#552	C₂×C₃	1	2	yes	—
89	C₃×#551	C₂×C₃	1	4	yes	—
90	C₃×#544	C₂×C₃	1	1	yes	characteristic
91	C₃×#542	C₂×C₃	1	2	yes	—
92	C₃×#541	C₂×C₃	1	2	yes	—
93	C₃×#536	C₂×C₃	1	1	yes	characteristic
94	C₃×#533	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×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
98	C₃×#520	C₂×C₃	1	1	yes	characteristic
99	C₃×#519	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	C₉×#41	—	2	4	no	—
103	C₂×Q₈×C₉	—	2	4	no	—
104	C₂×Q₈×C₉	C₂³	1	2	yes	—
105	C₂×Q₈×C₉	C₂³	1	2	yes	—
106	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₉	C₂³	1	4	yes	—
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	2	yes	—
112	C₂²×C₄×C₉	—	2	4	no	—
113	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₉	C₂³	1	2	yes	—
115	C₂²×C₄×C₉	C₂³	1	2	yes	—
116	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₉	C₂³	1	2	yes	—
119	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₉	C₂³	1	2	yes	—
122	C₂²×C₄×C₉	C₂³	1	2	yes	—
123	C₂²×C₄×C₉	C₂³	1	4	yes	—
124	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
125	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₉×C₄⋊C₄	C₂³	1	2	yes	—
127	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₉×C₄⋊C₄	C₂³	1	2	yes	—
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	4	yes	—
133	C₉×C₄⋊C₄	C₂³	1	2	yes	—
134	C₉×C₄⋊C₄	C₂³	1	4	yes	—
135	C₉×C₄⋊C₄	C₂³	1	4	yes	—
136	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₉×C₄⋊C₄	C₂³	1	4	yes	—
139	C₉×C₄⋊C₄	C₂³	1	4	yes	—
140	C₉×C₄⋊C₄	C₂³	1	4	yes	—
141	C₉×C₄⋊C₄	C₂³	1	4	yes	—
142	C₉×C₄⋊C₄	C₂³	1	4	yes	—
143	C₉×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₉×C₂²⋊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	4	yes	—
152	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
153	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₉×C₂²⋊C₄	C₂³	1	4	yes	—
161	C₄²×C₉	C₂³	1	2	yes	—
162	C₄²×C₉	C₂³	1	2	yes	—
163	C₄²×C₉	C₂³	1	2	yes	—
164	C₄²×C₉	C₂³	1	2	yes	—
165	C₄²×C₉	C₂³	1	4	yes	—
166	C₄²×C₉	C₂³	1	4	yes	—
167	C₄²×C₉	C₂³	1	4	yes	—
168	C₄²×C₉	C₂³	1	2	yes	—
169	#3495	C₉	1	1	yes	characteristic, direct product factor, Sylow
170	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
172	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
173	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
174	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
175	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
176	C₃×#126	C₂²×C₃	1	4	yes	—
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	2	yes	—
181	C₃×#125	C₂²×C₃	1	4	yes	—
182	C₃×#125	C₂²×C₃	1	4	yes	—
183	C₃×#125	C₂²×C₃	1	4	yes	—
184	C₃×#125	C₂²×C₃	1	2	yes	—
185	C₃×#124	C₂²×C₃	1	4	yes	—
186	C₃×#124	C₂²×C₃	1	2	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×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	2	yes	—
195	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
196	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
197	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
198	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
199	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
200	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
201	C₃×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
202	C₃×#121	C₂²×C₃	1	1	yes	characteristic
203	C₃×#121	C₂²×C₃	1	1	yes	characteristic
204	C₃×#120	C₂²×C₃	1	2	yes	—
205	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
206	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
207	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
208	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
209	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
210	C₃×C₄×Q₈	C₂²×C₃	1	4	yes	—
211	C₃×C₄×D₄	C₂²×C₃	1	4	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	2	yes	—
216	C₃×#117	C₂²×C₃	1	1	yes	characteristic
217	C₃×#117	C₂²×C₃	1	1	yes	characteristic
218	C₃×#117	C₂²×C₃	1	2	yes	—
219	C₃×#117	C₂²×C₃	1	1	yes	characteristic
220	C₃×#117	C₂²×C₃	1	2	yes	—
221	C₃×#117	C₂²×C₃	1	1	yes	characteristic
222	C₃×#117	C₂²×C₃	1	1	yes	characteristic
223	C₃×#117	C₂²×C₃	1	4	yes	—
224	C₃×#117	C₂²×C₃	1	4	yes	—
225	C₃×#117	C₂²×C₃	1	2	yes	—
226	C₃×#117	C₂²×C₃	1	4	yes	—
227	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
228	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
229	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
230	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
231	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
232	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
233	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
234	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
235	C₂³×C₉	—	2	2	no	—
236	C₂³×C₉	—	2	2	no	—
237	C₂³×C₉	—	4	1	no	—
238	C₂³×C₉	C₂⁴	1	1	yes	characteristic
239	C₂³×C₉	C₂⁴	1	2	yes	—
240	C₂³×C₉	C₂⁴	1	1	yes	characteristic
241	C₂³×C₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₉	—	2	4	no	—
243	Q₈×C₉	—	2	4	no	—
244	Q₈×C₉	—	2	2	no	—
245	Q₈×C₉	—	4	4	no	—
246	D₄×C₉	—	2	4	no	—
247	D₄×C₉	—	2	4	no	—
248	D₄×C₉	—	2	2	no	—
249	D₄×C₉	—	4	2	no	—
250	C₂×C₄×C₉	—	2	2	no	—
251	C₂×C₄×C₉	—	2	4	no	—
252	C₂×C₄×C₉	—	2	4	no	—
253	C₂×C₄×C₉	—	2	2	no	—
254	C₂×C₄×C₉	—	2	2	no	—
255	C₂×C₄×C₉	—	2	2	no	—
256	C₂×C₄×C₉	—	2	2	no	—
257	C₂×C₄×C₉	—	2	4	no	—
258	C₂×C₄×C₉	—	4	4	no	—
259	C₂×C₄×C₉	—	4	2	no	—
260	C₂×C₄×C₉	—	4	2	no	—
261	C₂×C₄×C₉	#41	1	4	yes	—
262	C₂×C₄×C₉	C₂⁴	1	2	yes	—
263	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₉	C₂⁴	1	2	yes	—
265	C₂×C₄×C₉	C₂⁴	1	2	yes	—
266	C₂×C₄×C₉	C₂⁴	1	2	yes	—
267	C₂×C₄×C₉	C₂⁴	1	2	yes	—
268	C₂×C₄×C₉	C₂⁴	1	4	yes	—
269	C₂×C₄×C₉	C₂⁴	1	2	yes	—
270	C₂×C₄×C₉	C₂⁴	1	2	yes	—
271	C₂×C₄×C₉	C₂⁴	1	4	yes	—
272	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
275	#556	C₂×C₉	1	2	yes	complemented
276	#554	C₂×C₉	1	2	yes	complemented
277	#552	C₂×C₉	1	2	yes	complemented
278	#552	C₂×C₉	1	4	yes	complemented
279	#552	C₂×C₉	1	2	yes	complemented
280	#551	C₂×C₉	1	4	yes	complemented
281	#544	C₂×C₉	1	1	yes	characteristic, complemented
282	#542	C₂×C₉	1	2	yes	complemented
283	#541	C₂×C₉	1	2	yes	complemented
284	#536	C₂×C₉	1	1	yes	characteristic, complemented
285	#533	C₂×C₉	1	2	yes	complemented
286	#529	C₂×C₉	1	2	yes	complemented
287	#525	C₂×C₉	1	1	yes	characteristic
288	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
289	#520	C₂×C₉	1	1	yes	characteristic, complemented
290	#519	C₂×C₉	1	1	yes	characteristic, complemented
291	C₂×#117	C₂×C₉	1	1	yes	characteristic, complemented
292	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
293	C₃×#41	—	2	4	no	—
294	C₂×C₃×Q₈	—	2	4	no	—
295	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
296	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
297	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₃×Q₈	C₂³×C₃	1	4	yes	—
299	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
300	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
301	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
303	C₂²×C₃×C₄	—	2	4	no	—
304	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
306	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
307	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
308	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
310	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
313	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
314	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
315	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
316	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
317	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
318	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
319	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
320	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
321	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
322	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
323	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
324	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
325	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
326	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
327	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
328	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	4	yes	—
332	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
333	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
334	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
335	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
336	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
337	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
338	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
339	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
340	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
341	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
342	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
343	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
344	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
345	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
346	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
347	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
348	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
349	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
350	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₃×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
352	C₃×C₄²	C₂³×C₃	1	2	yes	—
353	C₃×C₄²	C₂³×C₃	1	2	yes	—
354	C₃×C₄²	C₂³×C₃	1	2	yes	—
355	C₃×C₄²	C₂³×C₃	1	2	yes	—
356	C₃×C₄²	C₂³×C₃	1	4	yes	—
357	C₃×C₄²	C₂³×C₃	1	4	yes	—
358	C₃×C₄²	C₂³×C₃	1	4	yes	—
359	C₃×C₄²	C₂³×C₃	1	2	yes	—
360	C₂²×C₉	—	2	1	no	—
361	C₂²×C₉	—	2	1	no	—
362	C₂²×C₉	—	2	1	no	—
363	C₂²×C₉	—	2	1	no	—
364	C₂²×C₉	—	2	1	no	—
365	C₂²×C₉	—	2	2	no	—
366	C₂²×C₉	—	2	2	no	—
367	C₂²×C₉	—	2	1	no	—
368	C₂²×C₉	—	2	2	no	—
369	C₂²×C₉	—	2	1	no	—
370	C₂²×C₉	—	4	4	no	—
371	C₂²×C₉	C₂×#41	1	2	yes	—
372	C₂²×C₉	2₋¹⁺⁴	1	2	yes	—
373	C₂²×C₉	C₂⁵	1	1	yes	characteristic
374	C₄×C₉	—	2	1	no	—
375	C₄×C₉	—	2	1	no	—
376	C₄×C₉	—	2	2	no	—
377	C₄×C₉	—	2	4	no	—
378	C₄×C₉	—	2	2	no	—
379	C₄×C₉	—	2	2	no	—
380	C₄×C₉	—	2	2	no	—
381	C₄×C₉	—	2	2	no	—
382	C₄×C₉	—	2	4	no	—
383	C₄×C₉	—	2	2	no	—
384	C₄×C₉	—	2	2	no	—
385	C₄×C₉	C₂×#41	1	2	yes	—
386	C₄×C₉	C₂×#41	1	2	yes	—
387	C₂×#41	C₂²×C₉	1	1	yes	characteristic
388	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
389	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
390	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
391	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
392	C₄⋊Q₈	C₂²×C₉	1	2	yes	complemented
393	#126	C₂²×C₉	1	4	yes	—
394	#126	C₂²×C₉	1	4	yes	—
395	#126	C₂²×C₉	1	4	yes	complemented
396	#126	C₂²×C₉	1	4	yes	complemented
397	#125	C₂²×C₉	1	2	yes	complemented
398	#125	C₂²×C₉	1	4	yes	complemented
399	#125	C₂²×C₉	1	4	yes	complemented
400	#125	C₂²×C₉	1	4	yes	complemented
401	#125	C₂²×C₉	1	2	yes	complemented
402	#124	C₂²×C₉	1	4	yes	—
403	#124	C₂²×C₉	1	2	yes	complemented
404	#123	C₂²×C₉	1	2	yes	—
405	#123	C₂²×C₉	1	4	yes	—
406	#123	C₂²×C₉	1	4	yes	—
407	#123	C₂²×C₉	1	4	yes	—
408	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
409	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
410	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
411	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
412	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
413	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
414	C₂²⋊Q₈	C₂²×C₉	1	4	yes	—
415	C₂²⋊Q₈	C₂²×C₉	1	4	yes	—
416	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
417	C₂²⋊Q₈	C₂²×C₉	1	2	yes	complemented
418	C₂²⋊Q₈	C₂²×C₉	1	4	yes	complemented
419	#121	C₂²×C₉	1	1	yes	characteristic
420	#121	C₂²×C₉	1	1	yes	characteristic
421	#120	C₂²×C₉	1	2	yes	—
422	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
423	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
424	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
425	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
426	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
427	C₄×Q₈	C₂²×C₉	1	4	yes	complemented
428	C₄×D₄	C₂²×C₉	1	4	yes	—
429	C₄×D₄	C₂²×C₉	1	2	yes	—
430	C₄×D₄	C₂²×C₉	1	2	yes	—
431	C₄×D₄	C₂²×C₉	1	4	yes	—
432	C₄×D₄	C₂²×C₉	1	2	yes	complemented
433	#117	C₂²×C₉	1	1	yes	characteristic
434	#117	C₂²×C₉	1	1	yes	characteristic
435	#117	C₂²×C₉	1	2	yes	—
436	#117	C₂²×C₉	1	1	yes	characteristic
437	#117	C₂²×C₉	1	2	yes	—
438	#117	C₂²×C₉	1	1	yes	characteristic
439	#117	C₂²×C₉	1	1	yes	characteristic
440	#117	C₂²×C₉	1	4	yes	—
441	#117	C₂²×C₉	1	4	yes	—
442	#117	C₂²×C₉	1	2	yes	complemented
443	#117	C₂²×C₉	1	4	yes	complemented
444	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	—
448	C₂×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
449	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
451	C₂×C₄²	C₂²×C₉	1	2	yes	—
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	—	2	2	no	—
454	C₂³×C₃	—	4	1	no	—
455	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
456	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
457	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
458	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
459	C₃×Q₈	—	2	4	no	—
460	C₃×Q₈	—	2	4	no	—
461	C₃×Q₈	—	2	2	no	—
462	C₃×Q₈	—	4	4	no	—
463	C₃×D₄	—	2	4	no	—
464	C₃×D₄	—	2	4	no	—
465	C₃×D₄	—	2	2	no	—
466	C₃×D₄	—	4	2	no	—
467	C₂×C₃×C₄	—	2	2	no	—
468	C₂×C₃×C₄	—	2	4	no	—
469	C₂×C₃×C₄	—	2	4	no	—
470	C₂×C₃×C₄	—	2	2	no	—
471	C₂×C₃×C₄	—	2	2	no	—
472	C₂×C₃×C₄	—	2	2	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	2	4	no	—
475	C₂×C₃×C₄	—	4	4	no	—
476	C₂×C₃×C₄	—	4	2	no	—
477	C₂×C₃×C₄	—	4	2	no	—
478	C₂×C₃×C₄	C₃×#41	1	4	yes	—
479	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
480	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
482	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
483	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
484	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
485	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
486	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
487	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
488	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
489	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
492	C₂×C₉	—	2	2	no	—
493	C₂×C₉	—	2	2	no	—
494	C₂×C₉	—	4	2	no	—
495	C₂×C₉	—	4	1	no	—
496	C₂×C₉	C₂²×#41	1	1	yes	characteristic
497	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
498	C₂×C₉	#585	1	1	yes	characteristic
499	C₂⁴	C₂³×C₉	1	1	yes	characteristic
500	#41	—	2	4	no	—
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	C₂³×C₉	1	2	yes	—
503	C₂×Q₈	C₂³×C₉	1	2	yes	—
504	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
505	C₂×Q₈	C₂³×C₉	1	4	yes	—
506	C₂×D₄	C₂³×C₉	1	2	yes	—
507	C₂×D₄	C₂³×C₉	1	2	yes	—
508	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
509	C₂×D₄	C₂³×C₉	1	2	yes	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
512	C₂²×C₄	C₂³×C₉	1	2	yes	—
513	C₂²×C₄	C₂³×C₉	1	2	yes	—
514	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
515	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
516	C₂²×C₄	C₂³×C₉	1	2	yes	—
517	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
518	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
519	C₂²×C₄	C₂³×C₉	1	2	yes	—
520	C₂²×C₄	C₂³×C₉	1	2	yes	—
521	C₂²×C₄	C₂³×C₉	1	4	yes	—
522	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂³×C₉	1	2	yes	—
525	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂³×C₉	1	2	yes	—
527	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂³×C₉	1	2	yes	—
530	C₄⋊C₄	C₂³×C₉	1	4	yes	—
531	C₄⋊C₄	C₂³×C₉	1	2	yes	—
532	C₄⋊C₄	C₂³×C₉	1	4	yes	—
533	C₄⋊C₄	C₂³×C₉	1	4	yes	—
534	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂³×C₉	1	4	yes	—
537	C₄⋊C₄	C₂³×C₉	1	4	yes	—
538	C₄⋊C₄	C₂³×C₉	1	4	yes	—
539	C₄⋊C₄	C₂³×C₉	1	4	yes	—
540	C₄⋊C₄	C₂³×C₉	1	4	yes	—
541	C₄⋊C₄	C₂³×C₉	1	2	yes	—
542	C₄⋊C₄	C₂³×C₉	1	2	yes	—
543	C₄⋊C₄	C₂³×C₉	1	4	yes	—
544	C₄⋊C₄	C₂³×C₉	1	4	yes	—
545	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
546	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
547	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
548	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
549	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
550	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
551	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
552	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
553	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
554	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
555	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
556	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
557	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
558	C₂²⋊C₄	C₂³×C₉	1	4	yes	—
559	C₄²	C₂³×C₉	1	2	yes	—
560	C₄²	C₂³×C₉	1	2	yes	—
561	C₄²	C₂³×C₉	1	2	yes	—
562	C₄²	C₂³×C₉	1	2	yes	—
563	C₄²	C₂³×C₉	1	4	yes	—
564	C₄²	C₂³×C₉	1	4	yes	—
565	C₄²	C₂³×C₉	1	4	yes	—
566	C₄²	C₂³×C₉	1	2	yes	—
567	C₂²×C₃	—	2	1	no	—
568	C₂²×C₃	—	2	1	no	—
569	C₂²×C₃	—	2	1	no	—
570	C₂²×C₃	—	2	1	no	—
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	2	2	no	—
573	C₂²×C₃	—	2	2	no	—
574	C₂²×C₃	—	2	1	no	—
575	C₂²×C₃	—	2	2	no	—
576	C₂²×C₃	—	2	1	no	—
577	C₂²×C₃	—	4	4	no	—
578	C₂²×C₃	C₂×C₃×#41	1	2	yes	—
579	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
580	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	1	no	—
583	C₃×C₄	—	2	2	no	—
584	C₃×C₄	—	2	4	no	—
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	2	no	—
587	C₃×C₄	—	2	2	no	—
588	C₃×C₄	—	2	2	no	—
589	C₃×C₄	—	2	4	no	—
590	C₃×C₄	—	2	2	no	—
591	C₃×C₄	—	2	2	no	—
592	C₃×C₄	C₂×C₃×#41	1	2	yes	—
593	C₃×C₄	C₂×C₃×#41	1	2	yes	—
594	C₉	#3495	1	1	yes	characteristic, direct product factor, Sylow
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	4	1	no	—
598	C₂³	C₂⁴×C₉	1	1	yes	characteristic
599	C₂³	C₂⁴×C₉	1	2	yes	—
600	C₂³	C₂⁴×C₉	1	1	yes	characteristic
601	C₂³	C₂⁴×C₉	1	1	yes	characteristic
602	Q₈	—	2	4	no	—
603	Q₈	—	2	4	no	—
604	Q₈	—	2	2	no	—
605	Q₈	—	4	4	no	—
606	D₄	—	2	4	no	—
607	D₄	—	2	4	no	—
608	D₄	—	2	2	no	—
609	D₄	—	4	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	C₉×#41	1	4	yes	—
622	C₂×C₄	C₂⁴×C₉	1	2	yes	—
623	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
624	C₂×C₄	C₂⁴×C₉	1	2	yes	—
625	C₂×C₄	C₂⁴×C₉	1	2	yes	—
626	C₂×C₄	C₂⁴×C₉	1	2	yes	—
627	C₂×C₄	C₂⁴×C₉	1	2	yes	—
628	C₂×C₄	C₂⁴×C₉	1	4	yes	—
629	C₂×C₄	C₂⁴×C₉	1	2	yes	—
630	C₂×C₄	C₂⁴×C₉	1	2	yes	—
631	C₂×C₄	C₂⁴×C₉	1	4	yes	—
632	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
633	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
634	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
635	C₂×C₃	—	2	2	no	—
636	C₂×C₃	—	2	2	no	—
637	C₂×C₃	—	4	1	no	—
638	C₂×C₃	—	4	2	no	—
639	C₂×C₃	C₂²×C₃×#41	1	1	yes	characteristic
640	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
641	C₂×C₃	C₃×#585	1	1	yes	characteristic
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	4	4	no	—
653	C₂²	C₂×C₉×#41	1	2	yes	—
654	C₂²	C₉×2₋¹⁺⁴	1	2	yes	—
655	C₂²	C₂⁵×C₉	1	1	yes	characteristic
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	4	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	C₂×C₉×#41	1	2	yes	—
668	C₄	C₂×C₉×#41	1	2	yes	—
669	C₃	C₃×#3495	1	1	yes	characteristic
670	C₂	—	2	2	no	—
671	C₂	—	2	2	no	—
672	C₂	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	C₂²×C₉×#41	1	1	yes	characteristic
675	C₂	C₂×C₉×2₋¹⁺⁴	1	1	yes	characteristic
676	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×#525	C₂×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×#556	C₂	semidirect
2. C₉×#554	C₂	semidirect
3. C₉×#552	C₂	semidirect
4. C₉×#552	C₂	semidirect
5. C₉×#552	C₂	semidirect
6. C₉×#551	C₂	semidirect
7. C₉×#544	C₂	semidirect
8. C₉×#542	C₂	semidirect
9. C₉×#541	C₂	semidirect
10. C₉×#536	C₂	semidirect
11. C₉×#533	C₂	semidirect
12. C₉×#529	C₂	semidirect
14. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
15. C₉×#520	C₂	semidirect
16. C₉×#519	C₂	semidirect
17. C₂×C₉×#117	C₂	semidirect
22. C₉×C₄⋊Q₈	C₂²	semidirect
23. C₉×C₄⋊Q₈	C₂²	semidirect
24. C₉×C₄⋊Q₈	C₂²	semidirect
27. C₉×#126	C₂²	semidirect
28. C₉×#126	C₂²	semidirect
29. C₉×#125	C₂²	semidirect
30. C₉×#125	C₂²	semidirect
31. C₉×#125	C₂²	semidirect
32. C₉×#125	C₂²	semidirect
33. C₉×#125	C₂²	semidirect
35. C₉×#124	C₂²	semidirect
48. C₉×C₂²⋊Q₈	C₂²	semidirect
49. C₉×C₂²⋊Q₈	C₂²	semidirect
50. C₉×C₂²⋊Q₈	C₂²	semidirect
54. C₄×Q₈×C₉	C₂²	semidirect
55. C₄×Q₈×C₉	C₂²	semidirect
56. C₄×Q₈×C₉	C₂²	semidirect
57. C₄×Q₈×C₉	C₂²	semidirect
58. C₄×Q₈×C₉	C₂²	semidirect
59. C₄×Q₈×C₉	C₂²	semidirect
64. C₄×D₄×C₉	C₂²	semidirect
74. C₉×#117	C₂²	semidirect
75. C₉×#117	C₂²	semidirect
80. C₂×C₉×C₄⋊C₄	C₂²	semidirect
169. #3495	C₉	direct (N × H)
275. #556	C₂×C₉	semidirect
276. #554	C₂×C₉	semidirect
277. #552	C₂×C₉	semidirect
278. #552	C₂×C₉	semidirect
279. #552	C₂×C₉	semidirect
280. #551	C₂×C₉	semidirect
281. #544	C₂×C₉	semidirect
282. #542	C₂×C₉	semidirect
283. #541	C₂×C₉	semidirect
284. #536	C₂×C₉	semidirect
285. #533	C₂×C₉	semidirect
286. #529	C₂×C₉	semidirect
288. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
289. #520	C₂×C₉	semidirect
290. #519	C₂×C₉	semidirect
291. C₂×#117	C₂×C₉	semidirect
390. C₄⋊Q₈	C₂²×C₉	semidirect
391. C₄⋊Q₈	C₂²×C₉	semidirect
392. C₄⋊Q₈	C₂²×C₉	semidirect
395. #126	C₂²×C₉	semidirect
396. #126	C₂²×C₉	semidirect
397. #125	C₂²×C₉	semidirect
398. #125	C₂²×C₉	semidirect
399. #125	C₂²×C₉	semidirect
400. #125	C₂²×C₉	semidirect
401. #125	C₂²×C₉	semidirect
403. #124	C₂²×C₉	semidirect
416. C₂²⋊Q₈	C₂²×C₉	semidirect
417. C₂²⋊Q₈	C₂²×C₉	semidirect
418. C₂²⋊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
426. C₄×Q₈	C₂²×C₉	semidirect
427. C₄×Q₈	C₂²×C₉	semidirect
432. C₄×D₄	C₂²×C₉	semidirect
442. #117	C₂²×C₉	semidirect
443. #117	C₂²×C₉	semidirect
448. C₂×C₄⋊C₄	C₂²×C₉	semidirect
594. C₉	#3495	direct (N × H)

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×#554	2
C₉×#552	2
C₉×#551	2
C₉×#544	2
C₉×#542	2
C₉×#541	2
C₉×#536	2
C₉×#533	2
C₉×#529	2
C₉×#525	2
C₂×C₉×C₂²⋊Q₈	2
C₉×#520	2
C₉×#519	2
C₂×C₉×#117	2
C₃×#3495	3

Subgroups — C9×#3495 #11768216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3495 #11768216