Subgroups — C₉×#3251 #11767972

Order 1152.

588 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#478	C₂	1	2	yes	maximal, complemented
4	C₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#474	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#469	C₂	1	2	yes	maximal, complemented
7	C₉×#468	C₂	1	2	yes	maximal, complemented
8	C₉×#463	C₂	1	2	yes	maximal, complemented
9	C₉×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3251	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	—	2	1	no	—
14	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₉×D₈	C₂²	1	2	yes	—
16	C₂×C₉×M₁₆	C₂²	1	2	yes	—
17	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₉×#127	C₂²	1	1	yes	characteristic
19	C₉×#126	—	2	1	no	—
20	C₉×#125	C₂²	1	1	yes	characteristic
21	C₉×#124	—	2	1	no	—
22	C₉×#124	C₂²	1	1	yes	characteristic
23	C₉×#123	—	2	1	no	—
24	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₉×#121	—	2	1	no	—
26	C₉×#121	C₂²	1	1	yes	characteristic
27	C₉×#121	C₂²	1	2	yes	—
28	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
29	C₄×D₄×C₉	—	2	1	no	—
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₉	C₂²	1	2	yes	—
33	C₉×#117	—	2	1	no	—
34	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
35	C₉×#107	C₂²	1	2	yes	—
36	C₉×#106	C₂²	1	2	yes	—
37	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₉×C₄⋊C₈	C₂²	1	2	yes	—
40	C₉×#103	C₂²	1	2	yes	—
41	C₉×#102	C₂²	1	2	yes	—
42	C₉×#102	C₂²	1	2	yes	—
43	C₉×#102	C₂²	1	2	yes	—
44	C₃×#532	C₂×C₃	1	1	yes	characteristic
45	C₃×#529	C₂×C₃	1	1	yes	characteristic
46	C₃×#478	C₂×C₃	1	2	yes	—
47	C₃×#475	C₂×C₃	1	1	yes	characteristic
48	C₃×#474	C₂×C₃	1	1	yes	characteristic
49	C₃×#469	C₂×C₃	1	2	yes	—
50	C₃×#468	C₂×C₃	1	2	yes	—
51	C₃×#463	C₂×C₃	1	2	yes	—
52	C₃×#460	C₂×C₃	1	1	yes	characteristic
53	C₃×#459	C₂×C₃	1	1	yes	characteristic
54	C₃×#423	C₂×C₃	1	1	yes	characteristic
55	C₉×#41	—	4	4	no	—
56	C₂×Q₈×C₉	—	2	1	no	—
57	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
58	C₂×D₄×C₉	—	2	1	no	—
59	C₂×D₄×C₉	—	2	2	no	—
60	C₂×D₄×C₉	—	2	1	no	—
61	C₂×D₄×C₉	—	2	1	no	—
62	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₉	C₂³	1	2	yes	—
64	C₂²×C₄×C₉	—	2	1	no	—
65	C₂²×C₄×C₉	—	2	2	no	—
66	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
67	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
68	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₉×SD₁₆	—	4	2	no	—
70	C₉×D₈	—	4	2	no	—
71	C₉×M₁₆	—	4	2	no	—
72	C₂×C₈×C₉	C₂³	1	2	yes	—
73	C₂×C₈×C₉	C₂³	1	2	yes	—
74	C₉×C₄⋊C₄	—	2	1	no	—
75	C₉×C₄⋊C₄	—	2	1	no	—
76	C₉×C₄⋊C₄	—	2	1	no	—
77	C₉×C₄⋊C₄	—	2	1	no	—
78	C₉×C₄⋊C₄	—	2	1	no	—
79	C₉×C₄⋊C₄	C₂³	1	2	yes	—
80	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₉×C₂²⋊C₄	—	2	1	no	—
83	C₉×C₂²⋊C₄	—	2	1	no	—
84	C₉×C₂²⋊C₄	—	2	1	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₉×C₂²⋊C₄	—	2	1	no	—
87	C₉×C₂²⋊C₄	—	2	2	no	—
88	C₉×C₂²⋊C₄	—	2	1	no	—
89	C₄²×C₉	—	2	1	no	—
90	C₄²×C₉	D₄	1	1	yes	characteristic
91	C₄²×C₉	D₄	1	1	yes	characteristic
92	C₄²×C₉	C₂³	1	1	yes	characteristic
93	C₄²×C₉	C₂³	1	1	yes	characteristic
94	#3251	C₉	1	1	yes	characteristic, direct product factor, Sylow
95	C₂×C₃×#41	—	2	1	no	—
96	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
97	C₂×C₃×D₈	C₂²×C₃	1	2	yes	—
98	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
99	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₃×#127	C₂²×C₃	1	1	yes	characteristic
101	C₃×#126	—	2	1	no	—
102	C₃×#125	C₂²×C₃	1	1	yes	characteristic
103	C₃×#124	—	2	1	no	—
104	C₃×#124	C₂²×C₃	1	1	yes	characteristic
105	C₃×#123	—	2	1	no	—
106	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×#121	—	2	1	no	—
108	C₃×#121	C₂²×C₃	1	2	yes	—
109	C₃×#121	C₂²×C₃	1	1	yes	characteristic
110	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
111	C₃×C₄×D₄	—	2	1	no	—
112	C₃×C₄×D₄	—	2	1	no	—
113	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
114	C₃×C₄×D₄	C₂²×C₃	1	2	yes	—
115	C₃×#117	—	2	1	no	—
116	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
117	C₃×#107	C₂²×C₃	1	2	yes	—
118	C₃×#106	C₂²×C₃	1	2	yes	—
119	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
122	C₃×#103	C₂²×C₃	1	2	yes	—
123	C₃×#102	C₂²×C₃	1	2	yes	—
124	C₃×#102	C₂²×C₃	1	2	yes	—
125	C₃×#102	C₂²×C₃	1	2	yes	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	—	2	2	no	—
128	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
129	Q₈×C₉	—	2	1	no	—
130	Q₈×C₉	—	2	1	no	—
131	Q₈×C₉	—	4	2	no	—
132	D₄×C₉	—	2	1	no	—
133	D₄×C₉	—	2	2	no	—
134	D₄×C₉	—	2	1	no	—
135	D₄×C₉	—	2	2	no	—
136	D₄×C₉	—	4	2	no	—
137	D₄×C₉	—	4	2	no	—
138	D₄×C₉	—	4	4	no	—
139	D₄×C₉	—	4	2	no	—
140	C₂×C₄×C₉	—	2	2	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	2	1	no	—
146	C₂×C₄×C₉	—	2	2	no	—
147	C₂×C₄×C₉	—	4	1	no	—
148	C₂×C₄×C₉	—	4	4	no	—
149	C₂×C₄×C₉	—	4	2	no	—
150	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
156	C₈×C₉	—	2	2	no	—
157	C₈×C₉	—	2	2	no	—
158	#532	C₂×C₉	1	1	yes	characteristic, complemented
159	#529	C₂×C₉	1	1	yes	characteristic, complemented
160	#478	C₂×C₉	1	2	yes	complemented
161	#475	C₂×C₉	1	1	yes	characteristic, complemented
162	#474	C₂×C₉	1	1	yes	characteristic, complemented
163	#469	C₂×C₉	1	2	yes	complemented
164	#468	C₂×C₉	1	2	yes	complemented
165	#463	C₂×C₉	1	2	yes	complemented
166	#460	C₂×C₉	1	1	yes	characteristic, complemented
167	#459	C₂×C₉	1	1	yes	characteristic, complemented
168	#423	C₂×C₉	1	1	yes	characteristic, complemented
169	C₃×#41	—	4	4	no	—
170	C₂×C₃×Q₈	—	2	1	no	—
171	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	—	2	2	no	—
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	—	2	1	no	—
176	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	2	no	—
180	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
181	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₃×SD₁₆	—	4	2	no	—
184	C₃×D₈	—	4	2	no	—
185	C₃×M₁₆	—	4	2	no	—
186	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
187	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	—	2	1	no	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
194	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
195	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
196	C₃×C₂²⋊C₄	—	2	1	no	—
197	C₃×C₂²⋊C₄	—	2	1	no	—
198	C₃×C₂²⋊C₄	—	2	1	no	—
199	C₃×C₂²⋊C₄	—	2	2	no	—
200	C₃×C₂²⋊C₄	—	2	1	no	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	—	2	1	no	—
203	C₃×C₄²	—	2	1	no	—
204	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
205	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
206	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
207	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₉	—	2	1	no	—
209	C₂²×C₉	—	2	1	no	—
210	C₂²×C₉	—	2	1	no	—
211	C₂²×C₉	—	4	1	no	—
212	C₂²×C₉	—	4	2	no	—
213	C₂²×C₉	—	4	2	no	—
214	C₂²×C₉	—	4	1	no	—
215	C₂²×C₉	—	4	2	no	—
216	C₂²×C₉	—	4	1	no	—
217	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
218	C₄×C₉	—	2	1	no	—
219	C₄×C₉	—	2	1	no	—
220	C₄×C₉	—	2	1	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	4	1	no	—
223	C₄×C₉	—	4	1	no	—
224	C₄×C₉	—	4	2	no	—
225	C₄×C₉	—	4	1	no	—
226	C₄×C₉	AGL(1,ℤ/8)	1	2	yes	—
227	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
228	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
229	C₂×#41	—	2	1	no	—
230	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
231	C₂×D₈	C₂²×C₉	1	2	yes	—
232	C₂×M₁₆	C₂²×C₉	1	2	yes	—
233	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
234	#127	C₂²×C₉	1	1	yes	characteristic
235	#126	—	2	1	no	—
236	#125	C₂²×C₉	1	1	yes	characteristic
237	#124	—	2	1	no	—
238	#124	C₂²×C₉	1	1	yes	characteristic
239	#123	—	2	1	no	—
240	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
241	#121	—	2	1	no	—
242	#121	C₂²×C₉	1	1	yes	characteristic
243	#121	C₂²×C₉	1	2	yes	—
244	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
248	C₄×D₄	C₂²×C₉	1	2	yes	—
249	#117	—	2	1	no	—
250	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
251	#107	C₂²×C₉	1	2	yes	—
252	#106	C₂²×C₉	1	2	yes	—
253	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
254	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
255	C₄⋊C₈	C₂²×C₉	1	2	yes	—
256	#103	C₂²×C₉	1	2	yes	—
257	#102	C₂²×C₉	1	2	yes	—
258	#102	C₂²×C₉	1	2	yes	—
259	#102	C₂²×C₉	1	2	yes	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	2	no	—
262	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
263	C₃×Q₈	—	2	1	no	—
264	C₃×Q₈	—	2	1	no	—
265	C₃×Q₈	—	4	2	no	—
266	C₃×D₄	—	2	1	no	—
267	C₃×D₄	—	2	2	no	—
268	C₃×D₄	—	2	1	no	—
269	C₃×D₄	—	2	2	no	—
270	C₃×D₄	—	4	2	no	—
271	C₃×D₄	—	4	2	no	—
272	C₃×D₄	—	4	4	no	—
273	C₃×D₄	—	4	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	4	4	no	—
283	C₂×C₃×C₄	—	4	2	no	—
284	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
290	C₃×C₈	—	2	2	no	—
291	C₃×C₈	—	2	2	no	—
292	C₂×C₉	—	4	1	no	—
293	C₂×C₉	—	8	2	no	—
294	C₂×C₉	—	8	1	no	—
295	C₂×C₉	#537	1	1	yes	characteristic
296	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂×C₉	#575	1	1	yes	characteristic
298	#41	—	4	4	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
306	C₂×D₄	C₂³×C₉	1	2	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
310	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
311	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
312	SD₁₆	—	4	2	no	—
313	D₈	—	4	2	no	—
314	M₁₆	—	4	2	no	—
315	C₂×C₈	C₂³×C₉	1	2	yes	—
316	C₂×C₈	C₂³×C₉	1	2	yes	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
323	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
324	C₄⋊C₄	C₂³×C₉	1	2	yes	—
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	D₄×C₉	1	1	yes	characteristic
334	C₄²	D₄×C₉	1	1	yes	characteristic
335	C₄²	C₂³×C₉	1	1	yes	characteristic
336	C₄²	C₂³×C₉	1	1	yes	characteristic
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	1	no	—
340	C₂²×C₃	—	4	2	no	—
341	C₂²×C₃	—	4	1	no	—
342	C₂²×C₃	—	4	2	no	—
343	C₂²×C₃	—	4	1	no	—
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	—	4	2	no	—
346	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	—	4	1	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	—	4	1	no	—
355	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
356	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
357	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
358	C₉	#3251	1	1	yes	characteristic, direct product factor, Sylow
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
362	Q₈	—	2	1	no	—
363	Q₈	—	2	1	no	—
364	Q₈	—	4	2	no	—
365	D₄	—	2	1	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	1	no	—
368	D₄	—	2	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
384	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
385	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
387	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
388	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
389	C₈	—	2	2	no	—
390	C₈	—	2	2	no	—
391	C₂×C₃	—	4	1	no	—
392	C₂×C₃	—	8	2	no	—
393	C₂×C₃	—	8	1	no	—
394	C₂×C₃	C₃×#537	1	1	yes	characteristic
395	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂×C₃	C₃×#575	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	1	no	—
406	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	C₉×AGL(1,ℤ/8)	1	2	yes	—
416	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
417	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
418	C₃	C₃×#3251	1	1	yes	characteristic
419	C₂	—	4	1	no	—
420	C₂	—	8	2	no	—
421	C₂	—	8	1	no	—
422	C₂	C₉×#537	1	1	yes	characteristic
423	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
424	C₂	C₉×#575	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×#3251	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#532	C₂	semidirect
2. C₉×#529	C₂	semidirect
3. C₉×#478	C₂	semidirect
4. C₉×#475	C₂	semidirect
5. C₉×#474	C₂	semidirect
6. C₉×#469	C₂	semidirect
7. C₉×#468	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#460	C₂	semidirect
10. C₉×#459	C₂	semidirect
11. C₉×#423	C₂	semidirect
94. #3251	C₉	direct (N × H)
158. #532	C₂×C₉	semidirect
159. #529	C₂×C₉	semidirect
160. #478	C₂×C₉	semidirect
161. #475	C₂×C₉	semidirect
162. #474	C₂×C₉	semidirect
163. #469	C₂×C₉	semidirect
164. #468	C₂×C₉	semidirect
165. #463	C₂×C₉	semidirect
166. #460	C₂×C₉	semidirect
167. #459	C₂×C₉	semidirect
168. #423	C₂×C₉	semidirect
358. C₉	#3251	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×#532	2
C₉×#529	2
C₉×#478	2
C₉×#475	2
C₉×#474	2
C₉×#469	2
C₉×#468	2
C₉×#463	2
C₉×#460	2
C₉×#459	2
C₉×#423	2
C₃×#3251	3

Subgroups — C9×#3251 #11767972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3251 #11767972