Subgroups — C₉×#3257 #11767978

Order 1152.

537 conjugacy classes of subgroups.

The subgroup lattice has 537 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×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#474	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×#463	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3257	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
23	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₉×#127	C₂²	1	1	yes	characteristic
25	C₉×#126	—	2	1	no	—
26	C₉×#125	C₂²	1	1	yes	characteristic
27	C₉×#124	—	2	1	no	—
28	C₉×#124	C₂²	1	1	yes	characteristic
29	C₉×#123	—	2	1	no	—
30	C₉×#123	—	2	1	no	—
31	C₉×#123	—	2	1	no	—
32	C₉×C₂²⋊Q₈	—	2	1	no	—
33	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₉×#121	—	2	1	no	—
35	C₉×#121	—	2	1	no	—
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	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
40	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
41	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
42	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
43	C₉×#117	C₂²	1	1	yes	characteristic
44	C₉×#107	C₂²	1	1	yes	characteristic
45	C₉×#107	C₂²	1	1	yes	characteristic
46	C₉×#106	C₂²	1	1	yes	characteristic
47	C₉×#106	C₂²	1	1	yes	characteristic
48	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₉×#103	C₂²	1	1	yes	characteristic
53	C₉×#103	C₂²	1	1	yes	characteristic
54	C₉×#102	C₂²	1	1	yes	characteristic
55	C₉×#102	C₂²	1	1	yes	characteristic
56	C₉×#102	C₂²	1	1	yes	characteristic
57	C₉×#102	C₂²	1	1	yes	characteristic
58	C₉×#102	C₂²	1	1	yes	characteristic
59	C₉×#102	C₂²	1	1	yes	characteristic
60	C₃×#542	C₂×C₃	1	1	yes	characteristic
61	C₃×#540	C₂×C₃	1	1	yes	characteristic
62	C₃×#479	C₂×C₃	1	1	yes	characteristic
63	C₃×#478	C₂×C₃	1	1	yes	characteristic
64	C₃×#476	C₂×C₃	1	1	yes	characteristic
65	C₃×#474	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×#463	C₂×C₃	1	1	yes	characteristic
71	C₃×#463	C₂×C₃	1	1	yes	characteristic
72	C₃×#460	C₂×C₃	1	1	yes	characteristic
73	C₃×#459	C₂×C₃	1	1	yes	characteristic
74	C₃×#424	C₂×C₃	1	1	yes	characteristic
75	C₂×Q₈×C₉	—	2	1	no	—
76	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₉	—	2	1	no	—
78	C₂×D₄×C₉	—	2	1	no	—
79	C₂×D₄×C₉	—	2	1	no	—
80	C₂×D₄×C₉	—	2	1	no	—
81	C₂×D₄×C₉	—	2	1	no	—
82	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₉	—	2	1	no	—
86	C₂²×C₄×C₉	—	2	1	no	—
87	C₂²×C₄×C₉	—	2	1	no	—
88	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₉×SD₁₆	—	4	1	no	—
90	C₉×SD₁₆	—	4	1	no	—
91	C₉×D₈	—	4	1	no	—
92	C₉×D₈	—	4	1	no	—
93	C₉×M₁₆	—	4	1	no	—
94	C₂×C₈×C₉	—	4	1	no	—
95	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
96	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
97	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
99	C₉×C₄⋊C₄	—	2	1	no	—
100	C₉×C₄⋊C₄	—	2	1	no	—
101	C₉×C₄⋊C₄	—	2	1	no	—
102	C₉×C₄⋊C₄	—	2	1	no	—
103	C₉×C₄⋊C₄	—	2	1	no	—
104	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₉×C₂²⋊C₄	—	2	1	no	—
111	C₉×C₂²⋊C₄	—	2	1	no	—
112	C₉×C₂²⋊C₄	—	2	1	no	—
113	C₉×C₂²⋊C₄	—	2	1	no	—
114	C₉×C₂²⋊C₄	—	2	1	no	—
115	C₉×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
120	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₄²×C₉	—	2	1	no	—
122	C₄²×C₉	C₂³	1	1	yes	characteristic
123	C₄²×C₉	C₂³	1	1	yes	characteristic
124	#3257	C₉	1	1	yes	characteristic, direct product factor, Sylow
125	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
131	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
132	C₃×#127	C₂²×C₃	1	1	yes	characteristic
133	C₃×#126	—	2	1	no	—
134	C₃×#125	C₂²×C₃	1	1	yes	characteristic
135	C₃×#124	—	2	1	no	—
136	C₃×#124	C₂²×C₃	1	1	yes	characteristic
137	C₃×#123	—	2	1	no	—
138	C₃×#123	—	2	1	no	—
139	C₃×#123	—	2	1	no	—
140	C₃×C₂²⋊Q₈	—	2	1	no	—
141	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
142	C₃×#121	—	2	1	no	—
143	C₃×#121	—	2	1	no	—
144	C₃×#121	C₂²×C₃	1	1	yes	characteristic
145	C₃×#121	C₂²×C₃	1	1	yes	characteristic
146	C₃×#121	C₂²×C₃	1	1	yes	characteristic
147	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
148	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
149	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
150	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
151	C₃×#117	C₂²×C₃	1	1	yes	characteristic
152	C₃×#107	C₂²×C₃	1	1	yes	characteristic
153	C₃×#107	C₂²×C₃	1	1	yes	characteristic
154	C₃×#106	C₂²×C₃	1	1	yes	characteristic
155	C₃×#106	C₂²×C₃	1	1	yes	characteristic
156	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
157	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
158	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
159	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
160	C₃×#103	C₂²×C₃	1	1	yes	characteristic
161	C₃×#103	C₂²×C₃	1	1	yes	characteristic
162	C₃×#102	C₂²×C₃	1	1	yes	characteristic
163	C₃×#102	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	C₂³×C₉	—	2	1	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	—	2	1	no	—
171	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
172	Q₈×C₉	—	2	1	no	—
173	Q₈×C₉	—	2	1	no	—
174	Q₈×C₉	—	8	1	no	—
175	D₄×C₉	—	2	1	no	—
176	D₄×C₉	—	2	1	no	—
177	D₄×C₉	—	2	1	no	—
178	D₄×C₉	—	2	1	no	—
179	D₄×C₉	—	2	1	no	—
180	D₄×C₉	—	2	1	no	—
181	D₄×C₉	—	8	1	no	—
182	D₄×C₉	—	8	1	no	—
183	D₄×C₉	—	8	1	no	—
184	D₄×C₉	—	8	1	no	—
185	D₄×C₉	—	8	1	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	1	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	8	1	no	—
194	C₂×C₄×C₉	—	8	1	no	—
195	C₂×C₄×C₉	—	8	1	no	—
196	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
202	C₈×C₉	—	2	1	no	—
203	C₈×C₉	—	2	1	no	—
204	C₈×C₉	—	2	1	no	—
205	C₈×C₉	—	2	1	no	—
206	#542	C₂×C₉	1	1	yes	characteristic, complemented
207	#540	C₂×C₉	1	1	yes	characteristic, complemented
208	#479	C₂×C₉	1	1	yes	characteristic, complemented
209	#478	C₂×C₉	1	1	yes	characteristic, complemented
210	#476	C₂×C₉	1	1	yes	characteristic, complemented
211	#474	C₂×C₉	1	1	yes	characteristic, complemented
212	#469	C₂×C₉	1	1	yes	characteristic, complemented
213	#468	C₂×C₉	1	1	yes	characteristic, complemented
214	#466	C₂×C₉	1	1	yes	characteristic, complemented
215	#465	C₂×C₉	1	1	yes	characteristic, complemented
216	#463	C₂×C₉	1	1	yes	characteristic, complemented
217	#463	C₂×C₉	1	1	yes	characteristic, complemented
218	#460	C₂×C₉	1	1	yes	characteristic, complemented
219	#459	C₂×C₉	1	1	yes	characteristic, complemented
220	#424	C₂×C₉	1	1	yes	characteristic, complemented
221	C₂×C₃×Q₈	—	2	1	no	—
222	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₃×D₄	—	2	1	no	—
224	C₂×C₃×D₄	—	2	1	no	—
225	C₂×C₃×D₄	—	2	1	no	—
226	C₂×C₃×D₄	—	2	1	no	—
227	C₂×C₃×D₄	—	2	1	no	—
228	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
229	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	2	1	no	—
233	C₂²×C₃×C₄	—	2	1	no	—
234	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
235	C₃×SD₁₆	—	4	1	no	—
236	C₃×SD₁₆	—	4	1	no	—
237	C₃×D₈	—	4	1	no	—
238	C₃×D₈	—	4	1	no	—
239	C₃×M₁₆	—	4	1	no	—
240	C₂×C₃×C₈	—	4	1	no	—
241	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
245	C₃×C₄⋊C₄	—	2	1	no	—
246	C₃×C₄⋊C₄	—	2	1	no	—
247	C₃×C₄⋊C₄	—	2	1	no	—
248	C₃×C₄⋊C₄	—	2	1	no	—
249	C₃×C₄⋊C₄	—	2	1	no	—
250	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
251	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
252	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
253	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
254	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
255	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
256	C₃×C₂²⋊C₄	—	2	1	no	—
257	C₃×C₂²⋊C₄	—	2	1	no	—
258	C₃×C₂²⋊C₄	—	2	1	no	—
259	C₃×C₂²⋊C₄	—	2	1	no	—
260	C₃×C₂²⋊C₄	—	2	1	no	—
261	C₃×C₂²⋊C₄	—	2	1	no	—
262	C₃×C₂²⋊C₄	—	2	1	no	—
263	C₃×C₂²⋊C₄	—	2	1	no	—
264	C₃×C₂²⋊C₄	—	2	1	no	—
265	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
266	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
267	C₃×C₄²	—	2	1	no	—
268	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
269	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
270	C₂²×C₉	—	2	1	no	—
271	C₂²×C₉	—	2	1	no	—
272	C₂²×C₉	—	2	1	no	—
273	C₂²×C₉	—	4	1	no	—
274	C₂²×C₉	—	4	1	no	—
275	C₂²×C₉	—	4	1	no	—
276	C₂²×C₉	—	4	1	no	—
277	C₂²×C₉	—	4	1	no	—
278	C₂²×C₉	—	4	1	no	—
279	C₂²×C₉	—	4	1	no	—
280	C₂²×C₉	—	4	1	no	—
281	C₂²×C₉	—	4	1	no	—
282	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
283	C₄×C₉	—	2	1	no	—
284	C₄×C₉	—	2	1	no	—
285	C₄×C₉	—	2	1	no	—
286	C₄×C₉	—	2	1	no	—
287	C₄×C₉	—	2	1	no	—
288	C₄×C₉	—	4	1	no	—
289	C₄×C₉	—	4	1	no	—
290	C₄×C₉	—	4	1	no	—
291	C₄×C₉	—	4	1	no	—
292	C₄×C₉	—	4	1	no	—
293	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
294	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
296	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
297	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
298	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
299	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
300	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
301	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
302	#127	C₂²×C₉	1	1	yes	characteristic
303	#126	—	2	1	no	—
304	#125	C₂²×C₉	1	1	yes	characteristic
305	#124	—	2	1	no	—
306	#124	C₂²×C₉	1	1	yes	characteristic
307	#123	—	2	1	no	—
308	#123	—	2	1	no	—
309	#123	—	2	1	no	—
310	C₂²⋊Q₈	—	2	1	no	—
311	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
312	#121	—	2	1	no	—
313	#121	—	2	1	no	—
314	#121	C₂²×C₉	1	1	yes	characteristic
315	#121	C₂²×C₉	1	1	yes	characteristic
316	#121	C₂²×C₉	1	1	yes	characteristic
317	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
318	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
319	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
320	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
321	#117	C₂²×C₉	1	1	yes	characteristic
322	#107	C₂²×C₉	1	1	yes	characteristic
323	#107	C₂²×C₉	1	1	yes	characteristic
324	#106	C₂²×C₉	1	1	yes	characteristic
325	#106	C₂²×C₉	1	1	yes	characteristic
326	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
327	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
328	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
329	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
330	#103	C₂²×C₉	1	1	yes	characteristic
331	#103	C₂²×C₉	1	1	yes	characteristic
332	#102	C₂²×C₉	1	1	yes	characteristic
333	#102	C₂²×C₉	1	1	yes	characteristic
334	#102	C₂²×C₉	1	1	yes	characteristic
335	#102	C₂²×C₉	1	1	yes	characteristic
336	#102	C₂²×C₉	1	1	yes	characteristic
337	#102	C₂²×C₉	1	1	yes	characteristic
338	C₂³×C₃	—	2	1	no	—
339	C₂³×C₃	—	2	1	no	—
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
342	C₃×Q₈	—	2	1	no	—
343	C₃×Q₈	—	2	1	no	—
344	C₃×Q₈	—	8	1	no	—
345	C₃×D₄	—	2	1	no	—
346	C₃×D₄	—	2	1	no	—
347	C₃×D₄	—	2	1	no	—
348	C₃×D₄	—	2	1	no	—
349	C₃×D₄	—	2	1	no	—
350	C₃×D₄	—	2	1	no	—
351	C₃×D₄	—	8	1	no	—
352	C₃×D₄	—	8	1	no	—
353	C₃×D₄	—	8	1	no	—
354	C₃×D₄	—	8	1	no	—
355	C₃×D₄	—	8	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	8	1	no	—
364	C₂×C₃×C₄	—	8	1	no	—
365	C₂×C₃×C₄	—	8	1	no	—
366	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
372	C₃×C₈	—	2	1	no	—
373	C₃×C₈	—	2	1	no	—
374	C₃×C₈	—	2	1	no	—
375	C₃×C₈	—	2	1	no	—
376	C₂×C₉	—	4	1	no	—
377	C₂×C₉	—	8	1	no	—
378	C₂×C₉	—	8	1	no	—
379	C₂×C₉	—	8	1	no	—
380	C₂×C₉	#537	1	1	yes	characteristic
381	C₂×C₉	#576	1	1	yes	characteristic
382	C₂×C₉	#577	1	1	yes	characteristic
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
391	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
392	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
397	SD₁₆	—	4	1	no	—
398	SD₁₆	—	4	1	no	—
399	D₈	—	4	1	no	—
400	D₈	—	4	1	no	—
401	M₁₆	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
404	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
405	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
406	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
413	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
414	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
415	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
416	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
417	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
428	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
429	C₄²	—	2	1	no	—
430	C₄²	C₂³×C₉	1	1	yes	characteristic
431	C₄²	C₂³×C₉	1	1	yes	characteristic
432	C₂²×C₃	—	2	1	no	—
433	C₂²×C₃	—	2	1	no	—
434	C₂²×C₃	—	2	1	no	—
435	C₂²×C₃	—	4	1	no	—
436	C₂²×C₃	—	4	1	no	—
437	C₂²×C₃	—	4	1	no	—
438	C₂²×C₃	—	4	1	no	—
439	C₂²×C₃	—	4	1	no	—
440	C₂²×C₃	—	4	1	no	—
441	C₂²×C₃	—	4	1	no	—
442	C₂²×C₃	—	4	1	no	—
443	C₂²×C₃	—	4	1	no	—
444	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
445	C₃×C₄	—	2	1	no	—
446	C₃×C₄	—	2	1	no	—
447	C₃×C₄	—	2	1	no	—
448	C₃×C₄	—	2	1	no	—
449	C₃×C₄	—	2	1	no	—
450	C₃×C₄	—	4	1	no	—
451	C₃×C₄	—	4	1	no	—
452	C₃×C₄	—	4	1	no	—
453	C₃×C₄	—	4	1	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
456	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
457	C₉	#3257	1	1	yes	characteristic, direct product factor, Sylow
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
462	Q₈	—	2	1	no	—
463	Q₈	—	2	1	no	—
464	Q₈	—	8	1	no	—
465	D₄	—	2	1	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	8	1	no	—
472	D₄	—	8	1	no	—
473	D₄	—	8	1	no	—
474	D₄	—	8	1	no	—
475	D₄	—	8	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	8	1	no	—
484	C₂×C₄	—	8	1	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
489	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
491	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
492	C₈	—	2	1	no	—
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	2	1	no	—
496	C₂×C₃	—	4	1	no	—
497	C₂×C₃	—	8	1	no	—
498	C₂×C₃	—	8	1	no	—
499	C₂×C₃	—	8	1	no	—
500	C₂×C₃	C₃×#537	1	1	yes	characteristic
501	C₂×C₃	C₃×#576	1	1	yes	characteristic
502	C₂×C₃	C₃×#577	1	1	yes	characteristic
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	1	no	—
515	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
516	C₄	—	2	1	no	—
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
527	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
528	C₃	C₃×#3257	1	1	yes	characteristic
529	C₂	—	4	1	no	—
530	C₂	—	8	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	8	1	no	—
533	C₂	C₉×#537	1	1	yes	characteristic
534	C₂	C₉×#576	1	1	yes	characteristic
535	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×#3257	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×#540	C₂	semidirect
3. C₉×#479	C₂	semidirect
4. C₉×#478	C₂	semidirect
5. C₉×#476	C₂	semidirect
6. C₉×#474	C₂	semidirect
7. C₉×#469	C₂	semidirect
8. C₉×#468	C₂	semidirect
9. C₉×#466	C₂	semidirect
10. C₉×#465	C₂	semidirect
11. C₉×#463	C₂	semidirect
12. C₉×#463	C₂	semidirect
13. C₉×#460	C₂	semidirect
14. C₉×#459	C₂	semidirect
15. C₉×#424	C₂	semidirect
124. #3257	C₉	direct (N × H)
206. #542	C₂×C₉	semidirect
207. #540	C₂×C₉	semidirect
208. #479	C₂×C₉	semidirect
209. #478	C₂×C₉	semidirect
210. #476	C₂×C₉	semidirect
211. #474	C₂×C₉	semidirect
212. #469	C₂×C₉	semidirect
213. #468	C₂×C₉	semidirect
214. #466	C₂×C₉	semidirect
215. #465	C₂×C₉	semidirect
216. #463	C₂×C₉	semidirect
217. #463	C₂×C₉	semidirect
218. #460	C₂×C₉	semidirect
219. #459	C₂×C₉	semidirect
220. #424	C₂×C₉	semidirect
457. C₉	#3257	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×#540	2
C₉×#479	2
C₉×#478	2
C₉×#476	2
C₉×#474	2
C₉×#469	2
C₉×#468	2
C₉×#466	2
C₉×#465	2
C₉×#463	2
C₉×#460	2
C₉×#459	2
C₉×#424	2
C₃×#3257	3

Subgroups — C9×#3257 #11767978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3257 #11767978