Subgroups — C₉×#3224 #11767945

Order 1152.

612 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#450	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×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3224	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
25	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
26	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
27	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₉×#127	C₂²	1	1	yes	characteristic
29	C₉×#127	C₂²	1	1	yes	characteristic
30	C₉×#126	—	2	1	no	—
31	C₉×#124	—	2	1	no	—
32	C₉×#124	C₂²	1	1	yes	characteristic
33	C₉×#124	C₂²	1	1	yes	characteristic
34	C₉×#124	C₂²	1	1	yes	characteristic, complemented
35	C₉×#123	—	2	1	no	—
36	C₉×C₂²⋊Q₈	—	2	1	no	—
37	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₉×#121	—	2	1	no	—
39	C₉×#121	—	2	1	no	—
40	C₉×#121	C₂²	1	1	yes	characteristic
41	C₉×#120	—	2	1	no	—
42	C₉×#120	—	2	1	no	—
43	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
44	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
45	C₉×#117	C₂²	1	1	yes	characteristic
46	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₉×C₄⋊C₈	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×#97	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
60	C₃×#542	C₂×C₃	1	1	yes	characteristic
61	C₃×#535	C₂×C₃	1	1	yes	characteristic
62	C₃×#496	C₂×C₃	1	1	yes	characteristic
63	C₃×#495	C₂×C₃	1	1	yes	characteristic
64	C₃×#489	C₂×C₃	1	1	yes	characteristic
65	C₃×#486	C₂×C₃	1	1	yes	characteristic
66	C₃×#464	C₂×C₃	1	1	yes	characteristic
67	C₃×#463	C₂×C₃	1	1	yes	characteristic
68	C₃×#460	C₂×C₃	1	1	yes	characteristic
69	C₃×#459	C₂×C₃	1	1	yes	characteristic
70	C₃×#452	C₂×C₃	1	1	yes	characteristic
71	C₃×#450	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×#433	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	C₂×Q₈×C₉	—	2	1	no	—
79	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
80	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
81	C₂×D₄×C₉	—	2	1	no	—
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	—	4	1	no	—
89	C₂×D₄×C₉	—	4	1	no	—
90	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
91	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
92	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
93	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₉	—	2	1	no	—
95	C₂²×C₄×C₉	—	2	1	no	—
96	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₉×Q₁₆	—	4	1	no	—
98	C₉×SD₁₆	—	4	1	no	—
99	C₉×SD₁₆	—	4	1	no	—
100	C₉×SD₁₆	—	4	1	no	—
101	C₉×SD₁₆	—	4	1	no	—
102	C₉×D₈	—	4	1	no	—
103	C₉×D₈	—	4	1	no	—
104	C₉×D₈	—	4	1	no	—
105	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	—	2	1	no	—
112	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₉×C₂²⋊C₄	—	2	1	no	—
117	C₉×C₂²⋊C₄	—	2	1	no	—
118	C₉×C₂²⋊C₄	—	2	1	no	—
119	C₉×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
126	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₄²×C₉	—	2	1	no	—
128	C₄²×C₉	C₂³	1	1	yes	characteristic
129	C₄²×C₉	C₂³	1	1	yes	characteristic
130	#3224	C₉	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×Q₁₆	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×SD₁₆	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
141	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
142	C₃×#127	C₂²×C₃	1	1	yes	characteristic
143	C₃×#127	C₂²×C₃	1	1	yes	characteristic
144	C₃×#126	—	2	1	no	—
145	C₃×#124	—	2	1	no	—
146	C₃×#124	C₂²×C₃	1	1	yes	characteristic
147	C₃×#124	C₂²×C₃	1	1	yes	characteristic
148	C₃×#124	C₂²×C₃	1	1	yes	characteristic
149	C₃×#123	—	2	1	no	—
150	C₃×C₂²⋊Q₈	—	2	1	no	—
151	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₃×#121	—	2	1	no	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	C₂²×C₃	1	1	yes	characteristic
155	C₃×#120	—	2	1	no	—
156	C₃×#120	—	2	1	no	—
157	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₃×#117	C₂²×C₃	1	1	yes	characteristic
160	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
161	C₃×C₄⋊C₈	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×#97	C₂²×C₃	1	1	yes	characteristic
173	C₃×C₄×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	—	2	1	no	—
178	C₂³×C₉	—	4	2	no	—
179	C₂³×C₉	—	8	1	no	—
180	C₂³×C₉	—	8	1	no	—
181	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
182	Q₈×C₉	—	2	1	no	—
183	Q₈×C₉	—	2	1	no	—
184	Q₈×C₉	—	2	1	no	—
185	Q₈×C₉	—	2	1	no	—
186	Q₈×C₉	—	8	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	—	2	1	no	—
193	D₄×C₉	—	2	1	no	—
194	D₄×C₉	—	2	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	C₂×C₄×C₉	—	2	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	—	4	2	no	—
209	C₂×C₄×C₉	—	8	1	no	—
210	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
211	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
212	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
213	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
214	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
215	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
216	C₈×C₉	—	2	1	no	—
217	C₈×C₉	—	2	1	no	—
218	C₈×C₉	—	2	1	no	—
219	C₈×C₉	—	2	1	no	—
220	#542	C₂×C₉	1	1	yes	characteristic, complemented
221	#535	C₂×C₉	1	1	yes	characteristic, complemented
222	#496	C₂×C₉	1	1	yes	characteristic, complemented
223	#495	C₂×C₉	1	1	yes	characteristic, complemented
224	#489	C₂×C₉	1	1	yes	characteristic, complemented
225	#486	C₂×C₉	1	1	yes	characteristic, complemented
226	#464	C₂×C₉	1	1	yes	characteristic, complemented
227	#463	C₂×C₉	1	1	yes	characteristic, complemented
228	#460	C₂×C₉	1	1	yes	characteristic, complemented
229	#459	C₂×C₉	1	1	yes	characteristic, complemented
230	#452	C₂×C₉	1	1	yes	characteristic, complemented
231	#450	C₂×C₉	1	1	yes	characteristic, complemented
232	#449	C₂×C₉	1	1	yes	characteristic, complemented
233	#447	C₂×C₉	1	1	yes	characteristic, complemented
234	#433	C₂×C₉	1	1	yes	characteristic, complemented
235	C₂⁴×C₃	—	2	1	no	—
236	C₃×#41	—	4	1	no	—
237	C₃×#41	—	4	1	no	—
238	C₂×C₃×Q₈	—	2	1	no	—
239	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
240	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₃×D₄	—	2	1	no	—
242	C₂×C₃×D₄	—	2	1	no	—
243	C₂×C₃×D₄	—	2	1	no	—
244	C₂×C₃×D₄	—	2	1	no	—
245	C₂×C₃×D₄	—	2	1	no	—
246	C₂×C₃×D₄	—	2	1	no	—
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	—	4	1	no	—
249	C₂×C₃×D₄	—	4	1	no	—
250	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
251	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
252	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₃×C₄	—	2	1	no	—
255	C₂²×C₃×C₄	—	2	1	no	—
256	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
257	C₃×Q₁₆	—	4	1	no	—
258	C₃×SD₁₆	—	4	1	no	—
259	C₃×SD₁₆	—	4	1	no	—
260	C₃×SD₁₆	—	4	1	no	—
261	C₃×SD₁₆	—	4	1	no	—
262	C₃×D₈	—	4	1	no	—
263	C₃×D₈	—	4	1	no	—
264	C₃×D₈	—	4	1	no	—
265	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
267	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
269	C₃×C₄⋊C₄	—	2	1	no	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
273	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
275	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	—	2	1	no	—
277	C₃×C₂²⋊C₄	—	2	1	no	—
278	C₃×C₂²⋊C₄	—	2	1	no	—
279	C₃×C₂²⋊C₄	—	2	1	no	—
280	C₃×C₂²⋊C₄	—	2	1	no	—
281	C₃×C₂²⋊C₄	—	2	1	no	—
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×C₂²⋊C₄	—	2	1	no	—
285	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
286	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
287	C₃×C₄²	—	2	1	no	—
288	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
289	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₉	—	2	1	no	—
291	C₂²×C₉	—	2	1	no	—
292	C₂²×C₉	—	2	1	no	—
293	C₂²×C₉	—	4	1	no	—
294	C₂²×C₉	—	4	1	no	—
295	C₂²×C₉	—	4	1	no	—
296	C₂²×C₉	—	4	1	no	—
297	C₂²×C₉	—	4	1	no	—
298	C₂²×C₉	—	4	1	no	—
299	C₂²×C₉	—	4	1	no	—
300	C₂²×C₉	—	4	1	no	—
301	C₂²×C₉	—	4	1	no	—
302	C₂²×C₉	—	4	1	no	—
303	C₂²×C₉	—	4	1	no	—
304	C₂²×C₉	—	4	1	no	—
305	C₂²×C₉	—	8	4	no	—
306	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
307	C₄×C₉	—	2	1	no	—
308	C₄×C₉	—	2	1	no	—
309	C₄×C₉	—	2	1	no	—
310	C₄×C₉	—	2	1	no	—
311	C₄×C₉	—	2	1	no	—
312	C₄×C₉	—	4	1	no	—
313	C₄×C₉	—	4	1	no	—
314	C₄×C₉	—	4	1	no	—
315	C₄×C₉	—	4	1	no	—
316	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
317	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×#41	C₂²×C₉	1	1	yes	characteristic
319	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
320	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
321	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
322	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
323	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
324	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
325	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
326	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
327	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
328	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
329	#127	C₂²×C₉	1	1	yes	characteristic
330	#127	C₂²×C₉	1	1	yes	characteristic
331	#126	—	2	1	no	—
332	#124	—	2	1	no	—
333	#124	C₂²×C₉	1	1	yes	characteristic
334	#124	C₂²×C₉	1	1	yes	characteristic
335	#124	C₂²×C₉	1	1	yes	characteristic, complemented
336	#123	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
339	#121	—	2	1	no	—
340	#121	—	2	1	no	—
341	#121	C₂²×C₉	1	1	yes	characteristic
342	#120	—	2	1	no	—
343	#120	—	2	1	no	—
344	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
345	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
346	#117	C₂²×C₉	1	1	yes	characteristic
347	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
348	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
349	#103	C₂²×C₉	1	1	yes	characteristic, complemented
350	#103	C₂²×C₉	1	1	yes	characteristic, complemented
351	#102	C₂²×C₉	1	1	yes	characteristic
352	#102	C₂²×C₉	1	1	yes	characteristic
353	#102	C₂²×C₉	1	1	yes	characteristic
354	#102	C₂²×C₉	1	1	yes	characteristic
355	#102	C₂²×C₉	1	1	yes	characteristic, complemented
356	#102	C₂²×C₉	1	1	yes	characteristic, complemented
357	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
358	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
359	#97	C₂²×C₉	1	1	yes	characteristic, complemented
360	C₄×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	1	no	—
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	2	1	no	—
365	C₂³×C₃	—	4	2	no	—
366	C₂³×C₃	—	8	1	no	—
367	C₂³×C₃	—	8	1	no	—
368	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
369	C₃×Q₈	—	2	1	no	—
370	C₃×Q₈	—	2	1	no	—
371	C₃×Q₈	—	2	1	no	—
372	C₃×Q₈	—	2	1	no	—
373	C₃×Q₈	—	8	1	no	—
374	C₃×D₄	—	2	1	no	—
375	C₃×D₄	—	2	1	no	—
376	C₃×D₄	—	2	1	no	—
377	C₃×D₄	—	2	1	no	—
378	C₃×D₄	—	2	1	no	—
379	C₃×D₄	—	2	1	no	—
380	C₃×D₄	—	2	1	no	—
381	C₃×D₄	—	2	1	no	—
382	C₃×D₄	—	4	2	no	—
383	C₃×D₄	—	4	2	no	—
384	C₃×D₄	—	8	1	no	—
385	C₃×D₄	—	8	1	no	—
386	C₃×D₄	—	8	1	no	—
387	C₃×D₄	—	8	1	no	—
388	C₃×D₄	—	8	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	4	2	no	—
396	C₂×C₃×C₄	—	8	1	no	—
397	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
403	C₃×C₈	—	2	1	no	—
404	C₃×C₈	—	2	1	no	—
405	C₃×C₈	—	2	1	no	—
406	C₃×C₈	—	2	1	no	—
407	C₂×C₉	—	4	1	no	—
408	C₂×C₉	—	8	1	no	—
409	C₂×C₉	—	8	1	no	—
410	C₂×C₉	—	8	1	no	—
411	C₂×C₉	—	8	1	no	—
412	C₂×C₉	#535	1	1	yes	characteristic
413	C₂×C₉	#576	1	1	yes	characteristic
414	C₂×C₉	#577	1	1	yes	characteristic
415	C₂⁴	—	2	1	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
420	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
431	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
432	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
433	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
437	Q₁₆	—	4	1	no	—
438	SD₁₆	—	4	1	no	—
439	SD₁₆	—	4	1	no	—
440	SD₁₆	—	4	1	no	—
441	SD₁₆	—	4	1	no	—
442	D₈	—	4	1	no	—
443	D₈	—	4	1	no	—
444	D₈	—	4	1	no	—
445	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
446	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
447	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
448	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
453	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
454	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
455	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
466	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
467	C₄²	—	2	1	no	—
468	C₄²	C₂³×C₉	1	1	yes	characteristic
469	C₄²	C₂³×C₉	1	1	yes	characteristic
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	—	4	1	no	—
475	C₂²×C₃	—	4	1	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	1	no	—
479	C₂²×C₃	—	4	1	no	—
480	C₂²×C₃	—	4	1	no	—
481	C₂²×C₃	—	4	1	no	—
482	C₂²×C₃	—	4	1	no	—
483	C₂²×C₃	—	4	1	no	—
484	C₂²×C₃	—	4	1	no	—
485	C₂²×C₃	—	8	4	no	—
486	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
487	C₃×C₄	—	2	1	no	—
488	C₃×C₄	—	2	1	no	—
489	C₃×C₄	—	2	1	no	—
490	C₃×C₄	—	2	1	no	—
491	C₃×C₄	—	2	1	no	—
492	C₃×C₄	—	4	1	no	—
493	C₃×C₄	—	4	1	no	—
494	C₃×C₄	—	4	1	no	—
495	C₃×C₄	—	4	1	no	—
496	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
497	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
498	C₉	#3224	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	8	1	no	—
505	C₂³	—	8	1	no	—
506	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	8	1	no	—
512	D₄	—	2	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	2	1	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	8	1	no	—
523	D₄	—	8	1	no	—
524	D₄	—	8	1	no	—
525	D₄	—	8	1	no	—
526	D₄	—	8	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	8	1	no	—
535	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
536	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
537	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
538	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
539	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
540	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₂×C₃	—	4	1	no	—
546	C₂×C₃	—	8	1	no	—
547	C₂×C₃	—	8	1	no	—
548	C₂×C₃	—	8	1	no	—
549	C₂×C₃	—	8	1	no	—
550	C₂×C₃	C₃×#535	1	1	yes	characteristic
551	C₂×C₃	C₃×#576	1	1	yes	characteristic
552	C₂×C₃	C₃×#577	1	1	yes	characteristic
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	8	4	no	—
569	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
580	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
581	C₃	C₃×#3224	1	1	yes	characteristic
582	C₂	—	4	1	no	—
583	C₂	—	8	1	no	—
584	C₂	—	8	1	no	—
585	C₂	—	8	1	no	—
586	C₂	—	8	1	no	—
587	C₂	C₉×#535	1	1	yes	characteristic
588	C₂	C₉×#576	1	1	yes	characteristic
589	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×#3224	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#542	C₂	semidirect
2. C₉×#535	C₂	semidirect
3. C₉×#496	C₂	semidirect
4. C₉×#495	C₂	semidirect
5. C₉×#489	C₂	semidirect
6. C₉×#486	C₂	semidirect
7. C₉×#464	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#460	C₂	semidirect
10. C₉×#459	C₂	semidirect
11. C₉×#452	C₂	semidirect
12. C₉×#450	C₂	semidirect
13. C₉×#449	C₂	semidirect
14. C₉×#447	C₂	semidirect
15. C₉×#433	C₂	semidirect
19. C₂×C₉×Q₁₆	C₂²	semidirect
22. C₂×C₉×SD₁₆	C₂²	semidirect
23. C₂×C₉×SD₁₆	C₂²	semidirect
26. C₂×C₉×D₈	C₂²	semidirect
27. C₉×C₄⋊Q₈	C₂²	semidirect
34. C₉×#124	C₂²	semidirect
43. C₄×Q₈×C₉	C₂²	semidirect
44. C₄×D₄×C₉	C₂²	semidirect
46. C₉×C₄⋊C₈	C₂²	semidirect
47. C₉×C₄⋊C₈	C₂²	semidirect
48. C₉×#103	C₂²	semidirect
49. C₉×#103	C₂²	semidirect
54. C₉×#102	C₂²	semidirect
55. C₉×#102	C₂²	semidirect
58. C₉×#97	C₂²	semidirect
59. C₄×C₈×C₉	C₂²	semidirect
130. #3224	C₉	direct (N × H)
220. #542	C₂×C₉	semidirect
221. #535	C₂×C₉	semidirect
222. #496	C₂×C₉	semidirect
223. #495	C₂×C₉	semidirect
224. #489	C₂×C₉	semidirect
225. #486	C₂×C₉	semidirect
226. #464	C₂×C₉	semidirect
227. #463	C₂×C₉	semidirect
228. #460	C₂×C₉	semidirect
229. #459	C₂×C₉	semidirect
230. #452	C₂×C₉	semidirect
231. #450	C₂×C₉	semidirect
232. #449	C₂×C₉	semidirect
233. #447	C₂×C₉	semidirect
234. #433	C₂×C₉	semidirect
320. C₂×Q₁₆	C₂²×C₉	semidirect
323. C₂×SD₁₆	C₂²×C₉	semidirect
324. C₂×SD₁₆	C₂²×C₉	semidirect
327. C₂×D₈	C₂²×C₉	semidirect
328. C₄⋊Q₈	C₂²×C₉	semidirect
335. #124	C₂²×C₉	semidirect
344. C₄×Q₈	C₂²×C₉	semidirect
345. C₄×D₄	C₂²×C₉	semidirect
347. C₄⋊C₈	C₂²×C₉	semidirect
348. C₄⋊C₈	C₂²×C₉	semidirect
349. #103	C₂²×C₉	semidirect
350. #103	C₂²×C₉	semidirect
355. #102	C₂²×C₉	semidirect
356. #102	C₂²×C₉	semidirect
359. #97	C₂²×C₉	semidirect
360. C₄×C₈	C₂²×C₉	semidirect
498. C₉	#3224	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×#542	2
C₉×#535	2
C₉×#496	2
C₉×#495	2
C₉×#489	2
C₉×#486	2
C₉×#464	2
C₉×#463	2
C₉×#460	2
C₉×#459	2
C₉×#452	2
C₉×#450	2
C₉×#449	2
C₉×#447	2
C₉×#433	2
C₃×#3224	3

Subgroups — C9×#3224 #11767945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3224 #11767945