Subgroups — C₉×#3252 #11767973

Order 1152.

522 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#529	C₂	1	1	yes	maximal, characteristic
3	C₉×#479	C₂	1	2	yes	maximal, complemented
4	C₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#470	C₂	1	2	yes	maximal, complemented
7	C₉×#468	C₂	1	2	yes	maximal
8	C₉×#464	C₂	1	2	yes	maximal, complemented
9	C₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3252	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₉×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₉×M₁₆	C₂²	1	2	yes	—
16	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₉×#126	—	2	1	no	—
19	C₉×#125	—	2	1	no	—
20	C₉×#125	C₂²	1	1	yes	characteristic
21	C₉×#124	C₂²	1	1	yes	characteristic
22	C₉×#123	—	2	1	no	—
23	C₉×C₂²⋊Q₈	—	2	1	no	—
24	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₉×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₉×#121	C₂²	1	1	yes	characteristic
27	C₄×Q₈×C₉	—	2	1	no	—
28	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₉	C₂²	1	2	yes	—
30	C₄×D₄×C₉	—	2	1	no	—
31	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
32	C₉×#117	—	2	1	no	—
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×#103	C₂²	1	2	yes	—
42	C₉×#103	C₂²	1	2	yes	—
43	C₉×#102	C₂²	1	2	yes	—
44	C₃×#533	C₂×C₃	1	1	yes	characteristic
45	C₃×#529	C₂×C₃	1	1	yes	characteristic
46	C₃×#479	C₂×C₃	1	2	yes	—
47	C₃×#477	C₂×C₃	1	1	yes	characteristic
48	C₃×#476	C₂×C₃	1	1	yes	characteristic
49	C₃×#470	C₂×C₃	1	2	yes	—
50	C₃×#468	C₂×C₃	1	2	yes	—
51	C₃×#464	C₂×C₃	1	2	yes	—
52	C₃×#462	C₂×C₃	1	1	yes	characteristic
53	C₃×#461	C₂×C₃	1	1	yes	characteristic
54	C₃×#423	C₂×C₃	1	1	yes	characteristic
55	C₂×Q₈×C₉	—	2	1	no	—
56	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
57	C₂×Q₈×C₉	C₂³	1	2	yes	—
58	C₂×D₄×C₉	—	2	1	no	—
59	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
60	C₂²×C₄×C₉	—	2	1	no	—
61	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
62	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
63	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
64	C₉×Q₁₆	—	4	2	no	—
65	C₉×SD₁₆	—	4	2	no	—
66	C₉×M₁₆	—	4	2	no	—
67	C₂×C₈×C₉	C₂³	1	2	yes	—
68	C₂×C₈×C₉	C₂³	1	2	yes	—
69	C₉×C₄⋊C₄	—	2	1	no	—
70	C₉×C₄⋊C₄	—	2	1	no	—
71	C₉×C₄⋊C₄	—	2	1	no	—
72	C₉×C₄⋊C₄	—	2	1	no	—
73	C₉×C₄⋊C₄	—	2	1	no	—
74	C₉×C₄⋊C₄	—	2	1	no	—
75	C₉×C₄⋊C₄	—	2	2	no	—
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	—	2	1	no	—
78	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₉×C₄⋊C₄	C₂³	1	2	yes	—
81	C₉×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
86	C₉×C₂²⋊C₄	—	2	1	no	—
87	C₄²×C₉	—	2	1	no	—
88	C₄²×C₉	—	2	2	no	—
89	C₄²×C₉	D₄	1	1	yes	characteristic
90	C₄²×C₉	D₄	1	1	yes	characteristic
91	C₄²×C₉	C₂³	1	1	yes	characteristic
92	C₄²×C₉	C₂³	1	1	yes	characteristic
93	#3252	C₉	1	1	yes	characteristic, direct product factor, Sylow
94	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	—
95	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
96	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
97	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
99	C₃×#126	—	2	1	no	—
100	C₃×#125	—	2	1	no	—
101	C₃×#125	C₂²×C₃	1	1	yes	characteristic
102	C₃×#124	C₂²×C₃	1	1	yes	characteristic
103	C₃×#123	—	2	1	no	—
104	C₃×C₂²⋊Q₈	—	2	1	no	—
105	C₃×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
106	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×#121	C₂²×C₃	1	1	yes	characteristic
108	C₃×C₄×Q₈	—	2	1	no	—
109	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
111	C₃×C₄×D₄	—	2	1	no	—
112	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
113	C₃×#117	—	2	1	no	—
114	C₃×#117	—	2	1	no	—
115	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
116	C₃×#107	C₂²×C₃	1	2	yes	—
117	C₃×#106	C₂²×C₃	1	2	yes	—
118	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
119	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
121	C₃×#103	C₂²×C₃	1	2	yes	—
122	C₃×#103	C₂²×C₃	1	2	yes	—
123	C₃×#103	C₂²×C₃	1	2	yes	—
124	C₃×#102	C₂²×C₃	1	2	yes	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
127	Q₈×C₉	—	2	2	no	—
128	Q₈×C₉	—	2	1	no	—
129	Q₈×C₉	—	2	1	no	—
130	Q₈×C₉	—	2	2	no	—
131	Q₈×C₉	—	4	2	no	—
132	D₄×C₉	—	2	1	no	—
133	D₄×C₉	—	2	1	no	—
134	D₄×C₉	—	4	2	no	—
135	C₂×C₄×C₉	—	2	2	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	2	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	4	1	no	—
144	C₂×C₄×C₉	—	4	2	no	—
145	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
151	C₈×C₉	—	2	2	no	—
152	C₈×C₉	—	2	2	no	—
153	#533	C₂×C₉	1	1	yes	characteristic, complemented
154	#529	C₂×C₉	1	1	yes	characteristic
155	#479	C₂×C₉	1	2	yes	complemented
156	#477	C₂×C₉	1	1	yes	characteristic, complemented
157	#476	C₂×C₉	1	1	yes	characteristic, complemented
158	#470	C₂×C₉	1	2	yes	complemented
159	#468	C₂×C₉	1	2	yes	—
160	#464	C₂×C₉	1	2	yes	complemented
161	#462	C₂×C₉	1	1	yes	characteristic, complemented
162	#461	C₂×C₉	1	1	yes	characteristic, complemented
163	#423	C₂×C₉	1	1	yes	characteristic, complemented
164	C₂×C₃×Q₈	—	2	1	no	—
165	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₃×Q₁₆	—	4	2	no	—
174	C₃×SD₁₆	—	4	2	no	—
175	C₃×M₁₆	—	4	2	no	—
176	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
177	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
178	C₃×C₄⋊C₄	—	2	1	no	—
179	C₃×C₄⋊C₄	—	2	1	no	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
188	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
189	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₂²⋊C₄	—	2	1	no	—
192	C₃×C₂²⋊C₄	—	2	1	no	—
193	C₃×C₂²⋊C₄	—	2	1	no	—
194	C₃×C₂²⋊C₄	—	2	1	no	—
195	C₃×C₂²⋊C₄	—	2	1	no	—
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	—	2	2	no	—
198	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
199	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
200	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
201	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₉	—	2	1	no	—
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	4	1	no	—
206	C₂²×C₉	—	4	1	no	—
207	C₂²×C₉	—	4	1	no	—
208	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₉	—	2	1	no	—
210	C₄×C₉	—	2	1	no	—
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	—	2	1	no	—
213	C₄×C₉	—	4	1	no	—
214	C₄×C₉	—	4	2	no	—
215	C₄×C₉	—	4	1	no	—
216	C₄×C₉	—	4	1	no	—
217	C₄×C₉	—	4	2	no	—
218	C₄×C₉	#137	1	2	yes	—
219	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
220	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×Q₁₆	C₂²×C₉	1	2	yes	—
222	C₂×SD₁₆	C₂²×C₉	1	2	yes	—
223	C₂×M₁₆	C₂²×C₉	1	2	yes	—
224	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
225	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
226	#126	—	2	1	no	—
227	#125	—	2	1	no	—
228	#125	C₂²×C₉	1	1	yes	characteristic
229	#124	C₂²×C₉	1	1	yes	characteristic
230	#123	—	2	1	no	—
231	C₂²⋊Q₈	—	2	1	no	—
232	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
233	C₂²⋊Q₈	C₂²×C₉	1	2	yes	—
234	#121	C₂²×C₉	1	1	yes	characteristic
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
237	C₄×Q₈	C₂²×C₉	1	2	yes	—
238	C₄×D₄	—	2	1	no	—
239	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
240	#117	—	2	1	no	—
241	#117	—	2	1	no	—
242	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
243	#107	C₂²×C₉	1	2	yes	—
244	#106	C₂²×C₉	1	2	yes	—
245	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
246	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
247	C₄⋊C₈	C₂²×C₉	1	2	yes	—
248	#103	C₂²×C₉	1	2	yes	—
249	#103	C₂²×C₉	1	2	yes	—
250	#103	C₂²×C₉	1	2	yes	—
251	#102	C₂²×C₉	1	2	yes	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	—	2	1	no	—
256	C₃×Q₈	—	2	1	no	—
257	C₃×Q₈	—	2	2	no	—
258	C₃×Q₈	—	4	2	no	—
259	C₃×D₄	—	2	1	no	—
260	C₃×D₄	—	2	1	no	—
261	C₃×D₄	—	4	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
278	C₃×C₈	—	2	2	no	—
279	C₃×C₈	—	2	2	no	—
280	C₂×C₉	—	4	1	no	—
281	C₂×C₉	—	8	1	no	—
282	C₂×C₉	#537	1	1	yes	characteristic
283	C₂×C₉	C₂×#137	1	1	yes	characteristic
284	C₂×C₉	#575	1	1	yes	characteristic
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
287	C₂×Q₈	C₂³×C₉	1	2	yes	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
292	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
293	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
294	Q₁₆	—	4	2	no	—
295	SD₁₆	—	4	2	no	—
296	M₁₆	—	4	2	no	—
297	C₂×C₈	C₂³×C₉	1	2	yes	—
298	C₂×C₈	C₂³×C₉	1	2	yes	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	C₂³×C₉	1	2	yes	—
309	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
310	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	2	1	no	—
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	2	no	—
319	C₄²	D₄×C₉	1	1	yes	characteristic
320	C₄²	D₄×C₉	1	1	yes	characteristic
321	C₄²	C₂³×C₉	1	1	yes	characteristic
322	C₄²	C₂³×C₉	1	1	yes	characteristic
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	4	1	no	—
327	C₂²×C₃	—	4	1	no	—
328	C₂²×C₃	—	4	1	no	—
329	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	4	1	no	—
335	C₃×C₄	—	4	1	no	—
336	C₃×C₄	—	4	2	no	—
337	C₃×C₄	—	4	1	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	C₃×#137	1	2	yes	—
340	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
341	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
342	C₉	#3252	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	2	1	no	—
344	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	2	no	—
350	D₄	—	2	1	no	—
351	D₄	—	2	1	no	—
352	D₄	—	4	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
364	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
365	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
366	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
367	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
368	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
369	C₈	—	2	2	no	—
370	C₈	—	2	2	no	—
371	C₂×C₃	—	4	1	no	—
372	C₂×C₃	—	8	1	no	—
373	C₂×C₃	C₃×#537	1	1	yes	characteristic
374	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
375	C₂×C₃	C₃×#575	1	1	yes	characteristic
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	2	no	—
392	C₄	C₉×#137	1	2	yes	—
393	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
394	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
395	C₃	C₃×#3252	1	1	yes	characteristic
396	C₂	—	4	1	no	—
397	C₂	—	8	1	no	—
398	C₂	C₉×#537	1	1	yes	characteristic
399	C₂	C₂×C₉×#137	1	1	yes	characteristic
400	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×#121	C₂²×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×#533	C₂	semidirect
3. C₉×#479	C₂	semidirect
4. C₉×#477	C₂	semidirect
5. C₉×#476	C₂	semidirect
6. C₉×#470	C₂	semidirect
8. C₉×#464	C₂	semidirect
9. C₉×#462	C₂	semidirect
10. C₉×#461	C₂	semidirect
11. C₉×#423	C₂	semidirect
93. #3252	C₉	direct (N × H)
153. #533	C₂×C₉	semidirect
155. #479	C₂×C₉	semidirect
156. #477	C₂×C₉	semidirect
157. #476	C₂×C₉	semidirect
158. #470	C₂×C₉	semidirect
160. #464	C₂×C₉	semidirect
161. #462	C₂×C₉	semidirect
162. #461	C₂×C₉	semidirect
163. #423	C₂×C₉	semidirect
342. C₉	#3252	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×#533	2
C₉×#529	2
C₉×#479	2
C₉×#477	2
C₉×#476	2
C₉×#470	2
C₉×#468	2
C₉×#464	2
C₉×#462	2
C₉×#461	2
C₉×#423	2
C₃×#3252	3

Subgroups — C9×#3252 #11767973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3252 #11767973