Subgroups — C₉×#3198 #11767919

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3198	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic
18	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
23	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
24	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
26	C₉×#127	—	2	1	no	—
27	C₉×#124	—	2	1	no	—
28	C₉×C₂²⋊Q₈	—	2	1	no	—
29	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₉×#121	—	2	1	no	—
32	C₉×#121	—	2	1	no	—
33	C₉×#121	—	2	1	no	—
34	C₉×#121	C₂²	1	1	yes	characteristic
35	C₉×#121	C₂²	1	1	yes	characteristic
36	C₉×#121	C₂²	1	1	yes	characteristic
37	C₉×#121	C₂²	1	1	yes	characteristic
38	C₉×#121	C₂²	1	1	yes	characteristic
39	C₉×#121	C₂²	1	1	yes	characteristic, complemented
40	C₉×#120	—	2	1	no	—
41	C₉×#120	—	2	1	no	—
42	C₉×#117	C₂²	1	1	yes	characteristic
43	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₉×#107	C₂²	1	1	yes	characteristic, complemented
45	C₉×#107	C₂²	1	1	yes	characteristic, complemented
46	C₉×#106	C₂²	1	1	yes	characteristic, complemented
47	C₉×#106	C₂²	1	1	yes	characteristic, complemented
48	C₉×#103	C₂²	1	1	yes	characteristic, complemented
49	C₉×#103	C₂²	1	1	yes	characteristic, complemented
50	C₉×#102	C₂²	1	1	yes	characteristic
51	C₉×#102	C₂²	1	1	yes	characteristic
52	C₉×#102	C₂²	1	1	yes	characteristic
53	C₉×#102	C₂²	1	1	yes	characteristic
54	C₉×#102	C₂²	1	1	yes	characteristic, complemented
55	C₉×#102	C₂²	1	1	yes	characteristic, complemented
56	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×#537	C₂×C₃	1	1	yes	characteristic
61	C₃×#535	C₂×C₃	1	1	yes	characteristic
62	C₃×#485	C₂×C₃	1	1	yes	characteristic
63	C₃×#482	C₂×C₃	1	1	yes	characteristic
64	C₃×#481	C₂×C₃	1	1	yes	characteristic
65	C₃×#480	C₂×C₃	1	1	yes	characteristic
66	C₃×#469	C₂×C₃	1	1	yes	characteristic
67	C₃×#468	C₂×C₃	1	1	yes	characteristic
68	C₃×#466	C₂×C₃	1	1	yes	characteristic
69	C₃×#465	C₂×C₃	1	1	yes	characteristic
70	C₃×#450	C₂×C₃	1	1	yes	characteristic
71	C₃×#449	C₂×C₃	1	1	yes	characteristic
72	C₃×#449	C₂×C₃	1	1	yes	characteristic
73	C₃×#447	C₂×C₃	1	1	yes	characteristic
74	C₃×#408	C₂×C₃	1	1	yes	characteristic
75	C₂⁴×C₉	—	2	1	no	—
76	C₉×#41	—	4	1	no	—
77	C₉×#41	—	4	1	no	—
78	C₉×#41	—	4	1	no	—
79	C₉×#41	—	4	1	no	—
80	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
81	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₉	—	2	1	no	—
83	C₂×D₄×C₉	—	2	1	no	—
84	C₂×D₄×C₉	—	2	1	no	—
85	C₂×D₄×C₉	—	2	1	no	—
86	C₂×D₄×C₉	—	2	1	no	—
87	C₂×D₄×C₉	—	2	1	no	—
88	C₂×D₄×C₉	—	2	1	no	—
89	C₂×D₄×C₉	—	2	1	no	—
90	C₂×D₄×C₉	—	4	1	no	—
91	C₂×D₄×C₉	—	4	1	no	—
92	C₂×D₄×C₉	D₄	1	1	yes	characteristic
93	C₂×D₄×C₉	D₄	1	1	yes	characteristic
94	C₂×D₄×C₉	D₄	1	1	yes	characteristic
95	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
96	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
97	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₉	—	2	1	no	—
99	C₂²×C₄×C₉	—	2	1	no	—
100	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₉×SD₁₆	—	4	1	no	—
104	C₉×SD₁₆	—	4	1	no	—
105	C₉×D₈	—	4	1	no	—
106	C₉×D₈	—	4	1	no	—
107	C₉×M₁₆	—	4	1	no	—
108	C₂×C₈×C₉	—	4	1	no	—
109	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
110	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
113	C₉×C₄⋊C₄	—	2	1	no	—
114	C₉×C₄⋊C₄	—	2	1	no	—
115	C₉×C₄⋊C₄	—	2	1	no	—
116	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₉×C₂²⋊C₄	—	2	1	no	—
121	C₉×C₂²⋊C₄	—	2	1	no	—
122	C₉×C₂²⋊C₄	—	2	1	no	—
123	C₉×C₂²⋊C₄	—	2	1	no	—
124	C₉×C₂²⋊C₄	—	2	1	no	—
125	C₉×C₂²⋊C₄	—	2	1	no	—
126	C₉×C₂²⋊C₄	—	2	1	no	—
127	C₉×C₂²⋊C₄	—	2	1	no	—
128	C₉×C₂²⋊C₄	—	2	1	no	—
129	C₄²×C₉	—	2	1	no	—
130	#3198	C₉	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
133	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
139	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
140	C₃×#127	—	2	1	no	—
141	C₃×#124	—	2	1	no	—
142	C₃×C₂²⋊Q₈	—	2	1	no	—
143	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
144	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
145	C₃×#121	—	2	1	no	—
146	C₃×#121	—	2	1	no	—
147	C₃×#121	—	2	1	no	—
148	C₃×#121	C₂²×C₃	1	1	yes	characteristic
149	C₃×#121	C₂²×C₃	1	1	yes	characteristic
150	C₃×#121	C₂²×C₃	1	1	yes	characteristic
151	C₃×#121	C₂²×C₃	1	1	yes	characteristic
152	C₃×#121	C₂²×C₃	1	1	yes	characteristic
153	C₃×#121	C₂²×C₃	1	1	yes	characteristic
154	C₃×#120	—	2	1	no	—
155	C₃×#120	—	2	1	no	—
156	C₃×#117	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₃×#107	C₂²×C₃	1	1	yes	characteristic
159	C₃×#107	C₂²×C₃	1	1	yes	characteristic
160	C₃×#106	C₂²×C₃	1	1	yes	characteristic
161	C₃×#106	C₂²×C₃	1	1	yes	characteristic
162	C₃×#103	C₂²×C₃	1	1	yes	characteristic
163	C₃×#103	C₂²×C₃	1	1	yes	characteristic
164	C₃×#102	C₂²×C₃	1	1	yes	characteristic
165	C₃×#102	C₂²×C₃	1	1	yes	characteristic
166	C₃×#102	C₂²×C₃	1	1	yes	characteristic
167	C₃×#102	C₂²×C₃	1	1	yes	characteristic
168	C₃×#102	C₂²×C₃	1	1	yes	characteristic
169	C₃×#102	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
172	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
173	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
174	C₂³×C₉	—	2	1	no	—
175	C₂³×C₉	—	2	1	no	—
176	C₂³×C₉	—	2	1	no	—
177	C₂³×C₉	—	4	2	no	—
178	C₂³×C₉	—	8	1	no	—
179	C₂³×C₉	—	8	1	no	—
180	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
182	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
183	Q₈×C₉	—	2	1	no	—
184	Q₈×C₉	—	2	1	no	—
185	Q₈×C₉	—	4	1	no	—
186	D₄×C₉	—	2	1	no	—
187	D₄×C₉	—	2	1	no	—
188	D₄×C₉	—	2	1	no	—
189	D₄×C₉	—	2	1	no	—
190	D₄×C₉	—	2	1	no	—
191	D₄×C₉	—	2	1	no	—
192	D₄×C₉	—	4	1	no	—
193	D₄×C₉	—	4	1	no	—
194	D₄×C₉	—	4	1	no	—
195	D₄×C₉	—	4	2	no	—
196	D₄×C₉	—	4	2	no	—
197	D₄×C₉	—	8	1	no	—
198	D₄×C₉	—	8	1	no	—
199	D₄×C₉	—	8	1	no	—
200	D₄×C₉	—	8	1	no	—
201	D₄×C₉	—	8	1	no	—
202	D₄×C₉	—	8	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	1	no	—
205	C₂×C₄×C₉	—	2	1	no	—
206	C₂×C₄×C₉	—	2	1	no	—
207	C₂×C₄×C₉	—	2	1	no	—
208	C₂×C₄×C₉	—	2	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	4	2	no	—
215	C₂×C₄×C₉	—	8	1	no	—
216	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
217	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
218	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
219	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
220	C₈×C₉	—	2	1	no	—
221	C₈×C₉	—	2	1	no	—
222	C₈×C₉	—	2	1	no	—
223	C₈×C₉	—	2	1	no	—
224	#537	C₂×C₉	1	1	yes	characteristic, complemented
225	#535	C₂×C₉	1	1	yes	characteristic, complemented
226	#485	C₂×C₉	1	1	yes	characteristic, complemented
227	#482	C₂×C₉	1	1	yes	characteristic, complemented
228	#481	C₂×C₉	1	1	yes	characteristic, complemented
229	#480	C₂×C₉	1	1	yes	characteristic, complemented
230	#469	C₂×C₉	1	1	yes	characteristic, complemented
231	#468	C₂×C₉	1	1	yes	characteristic, complemented
232	#466	C₂×C₉	1	1	yes	characteristic, complemented
233	#465	C₂×C₉	1	1	yes	characteristic, complemented
234	#450	C₂×C₉	1	1	yes	characteristic, complemented
235	#449	C₂×C₉	1	1	yes	characteristic, complemented
236	#449	C₂×C₉	1	1	yes	characteristic, complemented
237	#447	C₂×C₉	1	1	yes	characteristic, complemented
238	#408	C₂×C₉	1	1	yes	characteristic, complemented
239	C₂⁴×C₃	—	2	1	no	—
240	C₃×#41	—	4	1	no	—
241	C₃×#41	—	4	1	no	—
242	C₃×#41	—	4	1	no	—
243	C₃×#41	—	4	1	no	—
244	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
245	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
246	C₂×C₃×D₄	—	2	1	no	—
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	—	2	1	no	—
249	C₂×C₃×D₄	—	2	1	no	—
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	—	2	1	no	—
252	C₂×C₃×D₄	—	2	1	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×C₃×D₄	—	4	1	no	—
255	C₂×C₃×D₄	—	4	1	no	—
256	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
257	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
258	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
259	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	—	2	1	no	—
264	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
267	C₃×SD₁₆	—	4	1	no	—
268	C₃×SD₁₆	—	4	1	no	—
269	C₃×D₈	—	4	1	no	—
270	C₃×D₈	—	4	1	no	—
271	C₃×M₁₆	—	4	1	no	—
272	C₂×C₃×C₈	—	4	1	no	—
273	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
277	C₃×C₄⋊C₄	—	2	1	no	—
278	C₃×C₄⋊C₄	—	2	1	no	—
279	C₃×C₄⋊C₄	—	2	1	no	—
280	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
281	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
283	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
284	C₃×C₂²⋊C₄	—	2	1	no	—
285	C₃×C₂²⋊C₄	—	2	1	no	—
286	C₃×C₂²⋊C₄	—	2	1	no	—
287	C₃×C₂²⋊C₄	—	2	1	no	—
288	C₃×C₂²⋊C₄	—	2	1	no	—
289	C₃×C₂²⋊C₄	—	2	1	no	—
290	C₃×C₂²⋊C₄	—	2	1	no	—
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	2	1	no	—
293	C₃×C₄²	—	2	1	no	—
294	C₂²×C₉	—	2	1	no	—
295	C₂²×C₉	—	2	1	no	—
296	C₂²×C₉	—	2	1	no	—
297	C₂²×C₉	—	2	1	no	—
298	C₂²×C₉	—	2	1	no	—
299	C₂²×C₉	—	2	1	no	—
300	C₂²×C₉	—	2	1	no	—
301	C₂²×C₉	—	2	1	no	—
302	C₂²×C₉	—	2	1	no	—
303	C₂²×C₉	—	4	1	no	—
304	C₂²×C₉	—	4	1	no	—
305	C₂²×C₉	—	4	1	no	—
306	C₂²×C₉	—	4	1	no	—
307	C₂²×C₉	—	4	1	no	—
308	C₂²×C₉	—	4	1	no	—
309	C₂²×C₉	—	4	1	no	—
310	C₂²×C₉	—	4	1	no	—
311	C₂²×C₉	—	4	1	no	—
312	C₂²×C₉	—	8	4	no	—
313	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
314	C₄×C₉	—	2	1	no	—
315	C₄×C₉	—	2	1	no	—
316	C₄×C₉	—	2	1	no	—
317	C₄×C₉	—	4	1	no	—
318	C₄×C₉	—	4	1	no	—
319	C₄×C₉	—	4	1	no	—
320	C₄×C₉	—	4	1	no	—
321	C₄×C₉	—	4	1	no	—
322	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
323	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×#41	C₂²×C₉	1	1	yes	characteristic
325	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
326	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
327	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
328	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
329	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
330	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
331	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
332	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
333	#127	—	2	1	no	—
334	#124	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
337	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	C₂²×C₉	1	1	yes	characteristic
342	#121	C₂²×C₉	1	1	yes	characteristic
343	#121	C₂²×C₉	1	1	yes	characteristic
344	#121	C₂²×C₉	1	1	yes	characteristic
345	#121	C₂²×C₉	1	1	yes	characteristic
346	#121	C₂²×C₉	1	1	yes	characteristic, complemented
347	#120	—	2	1	no	—
348	#120	—	2	1	no	—
349	#117	C₂²×C₉	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
351	#107	C₂²×C₉	1	1	yes	characteristic, complemented
352	#107	C₂²×C₉	1	1	yes	characteristic, complemented
353	#106	C₂²×C₉	1	1	yes	characteristic, complemented
354	#106	C₂²×C₉	1	1	yes	characteristic, complemented
355	#103	C₂²×C₉	1	1	yes	characteristic, complemented
356	#103	C₂²×C₉	1	1	yes	characteristic, complemented
357	#102	C₂²×C₉	1	1	yes	characteristic
358	#102	C₂²×C₉	1	1	yes	characteristic
359	#102	C₂²×C₉	1	1	yes	characteristic
360	#102	C₂²×C₉	1	1	yes	characteristic
361	#102	C₂²×C₉	1	1	yes	characteristic, complemented
362	#102	C₂²×C₉	1	1	yes	characteristic, complemented
363	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
364	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
365	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
366	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
367	C₂³×C₃	—	2	1	no	—
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	—	2	1	no	—
370	C₂³×C₃	—	4	2	no	—
371	C₂³×C₃	—	8	1	no	—
372	C₂³×C₃	—	8	1	no	—
373	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
374	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
375	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
376	C₃×Q₈	—	2	1	no	—
377	C₃×Q₈	—	2	1	no	—
378	C₃×Q₈	—	4	1	no	—
379	C₃×D₄	—	2	1	no	—
380	C₃×D₄	—	2	1	no	—
381	C₃×D₄	—	2	1	no	—
382	C₃×D₄	—	2	1	no	—
383	C₃×D₄	—	2	1	no	—
384	C₃×D₄	—	2	1	no	—
385	C₃×D₄	—	4	1	no	—
386	C₃×D₄	—	4	1	no	—
387	C₃×D₄	—	4	1	no	—
388	C₃×D₄	—	4	2	no	—
389	C₃×D₄	—	4	2	no	—
390	C₃×D₄	—	8	1	no	—
391	C₃×D₄	—	8	1	no	—
392	C₃×D₄	—	8	1	no	—
393	C₃×D₄	—	8	1	no	—
394	C₃×D₄	—	8	1	no	—
395	C₃×D₄	—	8	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	4	2	no	—
408	C₂×C₃×C₄	—	8	1	no	—
409	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
413	C₃×C₈	—	2	1	no	—
414	C₃×C₈	—	2	1	no	—
415	C₃×C₈	—	2	1	no	—
416	C₃×C₈	—	2	1	no	—
417	C₂×C₉	—	4	1	no	—
418	C₂×C₉	—	4	1	no	—
419	C₂×C₉	—	4	1	no	—
420	C₂×C₉	—	8	1	no	—
421	C₂×C₉	—	8	1	no	—
422	C₂×C₉	—	8	1	no	—
423	C₂×C₉	#534	1	1	yes	characteristic
424	C₂×C₉	#576	1	1	yes	characteristic
425	C₂×C₉	#577	1	1	yes	characteristic
426	C₂⁴	—	2	1	no	—
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	1	no	—
430	#41	—	4	1	no	—
431	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
432	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	D₄×C₉	1	1	yes	characteristic
444	C₂×D₄	D₄×C₉	1	1	yes	characteristic
445	C₂×D₄	D₄×C₉	1	1	yes	characteristic
446	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
447	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
448	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
452	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
453	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
454	SD₁₆	—	4	1	no	—
455	SD₁₆	—	4	1	no	—
456	D₈	—	4	1	no	—
457	D₈	—	4	1	no	—
458	M₁₆	—	4	1	no	—
459	C₂×C₈	—	4	1	no	—
460	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
461	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
462	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
463	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
468	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	2	1	no	—
486	C₂²×C₃	—	2	1	no	—
487	C₂²×C₃	—	2	1	no	—
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	1	no	—
496	C₂²×C₃	—	4	1	no	—
497	C₂²×C₃	—	4	1	no	—
498	C₂²×C₃	—	4	1	no	—
499	C₂²×C₃	—	8	4	no	—
500	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	4	1	no	—
505	C₃×C₄	—	4	1	no	—
506	C₃×C₄	—	4	1	no	—
507	C₃×C₄	—	4	1	no	—
508	C₃×C₄	—	4	1	no	—
509	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
510	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
511	C₉	#3198	1	1	yes	characteristic, direct product factor, Sylow
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	8	1	no	—
517	C₂³	—	8	1	no	—
518	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
519	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
520	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	4	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	1	no	—
537	D₄	—	8	1	no	—
538	D₄	—	8	1	no	—
539	D₄	—	8	1	no	—
540	D₄	—	8	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	8	1	no	—
554	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
555	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
556	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
557	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₂×C₃	—	4	1	no	—
563	C₂×C₃	—	4	1	no	—
564	C₂×C₃	—	4	1	no	—
565	C₂×C₃	—	8	1	no	—
566	C₂×C₃	—	8	1	no	—
567	C₂×C₃	—	8	1	no	—
568	C₂×C₃	C₃×#534	1	1	yes	characteristic
569	C₂×C₃	C₃×#576	1	1	yes	characteristic
570	C₂×C₃	C₃×#577	1	1	yes	characteristic
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	8	4	no	—
590	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
600	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
601	C₃	C₃×#3198	1	1	yes	characteristic
602	C₂	—	4	1	no	—
603	C₂	—	4	1	no	—
604	C₂	—	4	1	no	—
605	C₂	—	8	1	no	—
606	C₂	—	8	1	no	—
607	C₂	—	8	1	no	—
608	C₂	C₉×#534	1	1	yes	characteristic
609	C₂	C₉×#576	1	1	yes	characteristic
610	C₂	C₉×#577	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#3198	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#537	C₂	semidirect
2. C₉×#535	C₂	semidirect
3. C₉×#485	C₂	semidirect
4. C₉×#482	C₂	semidirect
5. C₉×#481	C₂	semidirect
6. C₉×#480	C₂	semidirect
7. C₉×#469	C₂	semidirect
8. C₉×#468	C₂	semidirect
9. C₉×#466	C₂	semidirect
10. C₉×#465	C₂	semidirect
11. C₉×#450	C₂	semidirect
12. C₉×#449	C₂	semidirect
13. C₉×#449	C₂	semidirect
14. C₉×#447	C₂	semidirect
15. C₉×#408	C₂	semidirect
18. C₂×C₉×#41	C₂²	semidirect
24. C₂×C₉×M₁₆	C₂²	semidirect
25. C₂²×C₈×C₉	C₂²	semidirect
30. C₉×C₂²⋊Q₈	C₂²	semidirect
39. C₉×#121	C₂²	semidirect
43. C₂×C₉×C₄⋊C₄	C₂²	semidirect
44. C₉×#107	C₂²	semidirect
45. C₉×#107	C₂²	semidirect
46. C₉×#106	C₂²	semidirect
47. C₉×#106	C₂²	semidirect
48. C₉×#103	C₂²	semidirect
49. C₉×#103	C₂²	semidirect
54. C₉×#102	C₂²	semidirect
55. C₉×#102	C₂²	semidirect
58. C₉×C₂²⋊C₈	C₂²	semidirect
59. C₉×C₂²⋊C₈	C₂²	semidirect
130. #3198	C₉	direct (N × H)
224. #537	C₂×C₉	semidirect
225. #535	C₂×C₉	semidirect
226. #485	C₂×C₉	semidirect
227. #482	C₂×C₉	semidirect
228. #481	C₂×C₉	semidirect
229. #480	C₂×C₉	semidirect
230. #469	C₂×C₉	semidirect
231. #468	C₂×C₉	semidirect
232. #466	C₂×C₉	semidirect
233. #465	C₂×C₉	semidirect
234. #450	C₂×C₉	semidirect
235. #449	C₂×C₉	semidirect
236. #449	C₂×C₉	semidirect
237. #447	C₂×C₉	semidirect
238. #408	C₂×C₉	semidirect
325. C₂×#41	C₂²×C₉	semidirect
331. C₂×M₁₆	C₂²×C₉	semidirect
332. C₂²×C₈	C₂²×C₉	semidirect
337. C₂²⋊Q₈	C₂²×C₉	semidirect
346. #121	C₂²×C₉	semidirect
350. C₂×C₄⋊C₄	C₂²×C₉	semidirect
351. #107	C₂²×C₉	semidirect
352. #107	C₂²×C₉	semidirect
353. #106	C₂²×C₉	semidirect
354. #106	C₂²×C₉	semidirect
355. #103	C₂²×C₉	semidirect
356. #103	C₂²×C₉	semidirect
361. #102	C₂²×C₉	semidirect
362. #102	C₂²×C₉	semidirect
365. C₂²⋊C₈	C₂²×C₉	semidirect
366. C₂²⋊C₈	C₂²×C₉	semidirect
511. C₉	#3198	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×#537	2
C₉×#535	2
C₉×#485	2
C₉×#482	2
C₉×#481	2
C₉×#480	2
C₉×#469	2
C₉×#468	2
C₉×#466	2
C₉×#465	2
C₉×#450	2
C₉×#449	2
C₉×#447	2
C₉×#408	2
C₃×#3198	3

Subgroups — C9×#3198 #11767919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3198 #11767919