Subgroups — C₉×#4770 #13141753

Order 1728.

620 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#832	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#809	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4770	C₃	1	1	yes	maximal, characteristic
9	C₉×#418	—	3	1	no	maximal
10	C₂³×D₃×C₉	—	2	1	no	—
11	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#67	—	2	1	no	—
13	D₃×D₄×C₉	—	2	2	no	—
14	D₃×D₄×C₉	C₄	1	4	yes	complemented
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
19	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
20	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
21	C₄×C₉×Dic₃	—	2	1	no	—
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
23	C₉×ΓL(1,𝔽₂₅)	—	2	2	no	—
24	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
26	C₃×#892	C₂×C₃	1	1	yes	characteristic
27	C₂²×D₄×C₉	—	3	1	no	—
28	C₃²×#102	C₂×C₃	1	1	yes	characteristic
29	C₃×#832	C₂×C₃	1	1	yes	characteristic
30	C₃×#821	C₂×C₃	1	1	yes	characteristic
31	C₃×#809	C₂×C₃	1	1	yes	characteristic
32	C₂×C₉×M₁₆	—	3	1	no	—
33	C₉×#117	—	3	1	no	—
34	C₉×#102	—	2	1	no	—
35	C₉×#102	—	3	1	no	—
36	C₉×#102	—	3	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₉×#102	D₃	1	1	yes	characteristic, complemented
39	C₂³×C₃×C₉	—	2	1	no	—
40	C₂²×D₃×C₉	—	2	1	no	—
41	C₂²×D₃×C₉	—	2	4	no	—
42	C₂²×D₃×C₉	—	4	2	no	—
43	C₂²×D₃×C₉	—	4	2	no	—
44	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
45	C₃×D₄×C₉	—	2	1	no	—
46	C₃×D₄×C₉	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×C₉	—	2	1	no	—
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₉×#67	—	2	4	no	—
50	C₂×C₉×Dic₃	—	2	1	no	—
51	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
52	C₉×D₁₂	—	2	1	no	—
53	C₉×D₁₂	C₂×C₄	1	2	yes	—
54	C₄×D₃×C₉	C₂×C₄	1	2	yes	—
55	C₄×D₃×C₉	D₄	1	2	yes	—
56	C₃×C₈×C₉	—	2	1	no	—
57	C₉×C₃⋊C₈	—	2	1	no	—
58	C₃×#418	—	3	1	no	—
59	#4770	C₉	1	1	yes	characteristic, direct product factor
60	C₂³×C₃×D₃	—	2	1	no	—
61	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₃×#67	—	2	1	no	—
63	C₃×D₃×D₄	—	2	2	no	—
64	C₃×D₃×D₄	C₃×C₄	1	4	yes	—
65	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
67	C₂⁴×C₉	—	6	1	no	—
68	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
69	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
71	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₃×C₄×Dic₃	—	2	1	no	—
73	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
74	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
75	C₂×D₄×C₉	—	2	1	no	—
76	C₂×D₄×C₉	—	3	4	no	—
77	C₂×D₄×C₉	—	3	1	no	—
78	C₂×D₄×C₉	—	6	2	no	—
79	C₂×D₄×C₉	—	6	1	no	—
80	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₄×C₉	—	3	1	no	—
82	C₉×M₁₆	—	6	2	no	—
83	C₂×C₈×C₉	—	2	1	no	—
84	C₂×C₈×C₉	—	3	1	no	—
85	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
86	C₉×C₄⋊C₄	—	2	1	no	—
87	C₉×C₄⋊C₄	—	3	1	no	—
88	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
89	C₉×C₂²⋊C₄	—	6	1	no	—
90	C₄²×C₉	—	6	1	no	—
91	C₂²×C₃×C₉	—	2	2	no	—
92	C₂²×C₃×C₉	—	4	1	no	—
93	C₂²×C₃×C₉	—	4	1	no	—
94	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
95	C₂×D₃×C₉	—	2	1	no	—
96	C₂×D₃×C₉	—	2	1	no	—
97	C₂×D₃×C₉	—	2	2	no	—
98	C₂×D₃×C₉	—	4	8	no	—
99	C₂×D₃×C₉	—	4	1	no	—
100	C₂×D₃×C₉	—	4	1	no	—
101	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
102	C₃×C₄×C₉	—	4	1	no	—
103	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
104	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
105	C₉×Dic₃	—	4	1	no	—
106	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₃×D₄	—	3	1	no	—
108	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic
109	C₂×C₃×M₁₆	—	3	1	no	—
110	C₃×#117	—	3	1	no	—
111	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic, complemented
112	#892	C₂×C₉	1	1	yes	characteristic, complemented
113	C₃×#102	—	2	1	no	—
114	C₃×#102	—	3	1	no	—
115	C₃×#102	—	3	1	no	—
116	C₃×#102	—	3	1	no	—
117	C₃×#102	C₂×C₉	1	1	yes	characteristic, complemented
118	C₃×#102	C₃×D₃	1	1	yes	characteristic
119	#832	C₂×C₉	1	1	yes	characteristic, complemented
120	#821	C₂×C₉	1	1	yes	characteristic, complemented
121	#809	C₂×C₉	1	1	yes	characteristic, complemented
122	C₂³×C₃²	—	2	1	no	—
123	C₂²×C₃×D₃	—	2	1	no	—
124	C₂²×C₃×D₃	—	2	4	no	—
125	C₂²×C₃×D₃	—	4	2	no	—
126	C₂²×C₃×D₃	—	4	2	no	—
127	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
128	C₃²×D₄	—	2	1	no	—
129	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
130	C₂×C₃²×C₄	—	2	1	no	—
131	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
132	C₃×#67	—	2	4	no	—
133	C₂×C₃×Dic₃	—	2	1	no	—
134	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
135	C₃×D₁₂	—	2	1	no	—
136	C₃×D₁₂	C₂×C₃×C₄	1	2	yes	—
137	C₃×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
138	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
139	C₂³×C₉	—	2	1	no	—
140	C₂³×C₉	—	3	1	no	—
141	C₂³×C₉	—	4	1	no	—
142	C₂³×C₉	—	6	4	no	—
143	C₂³×C₉	—	6	1	no	—
144	C₂³×C₉	—	12	2	no	—
145	C₂³×C₉	—	12	2	no	—
146	C₃²×C₈	—	2	1	no	—
147	C₃×C₃⋊C₈	—	2	1	no	—
148	D₄×C₉	—	2	1	no	—
149	D₄×C₉	—	2	2	no	—
150	D₄×C₉	—	3	2	no	—
151	D₄×C₉	—	4	1	no	—
152	D₄×C₉	—	6	4	no	—
153	D₄×C₉	—	6	1	no	—
154	D₄×C₉	C₄×D₃	1	2	yes	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	3	1	no	—
158	C₂×C₄×C₉	—	3	2	no	—
159	C₂×C₄×C₉	—	3	2	no	—
160	C₂×C₄×C₉	—	4	1	no	—
161	C₂×C₄×C₉	—	6	1	no	—
162	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
163	C₈×C₉	—	2	1	no	—
164	C₈×C₉	—	4	1	no	—
165	C₈×C₉	—	6	1	no	—
166	#418	—	3	1	no	Sylow
167	C₂×C₃×C₉	—	4	2	no	—
168	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	D₃×C₉	—	2	2	no	—
172	D₃×C₉	—	4	2	no	—
173	C₂⁴×C₃	—	6	1	no	—
174	C₂³×D₃	—	2	1	no	—
175	C₂×C₃×D₄	—	2	1	no	—
176	C₂×C₃×D₄	—	3	4	no	—
177	C₂×C₃×D₄	—	3	1	no	—
178	C₂×C₃×D₄	—	6	2	no	—
179	C₂×C₃×D₄	—	6	1	no	—
180	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
181	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	3	1	no	—
183	C₂×#67	—	2	1	no	—
184	D₃×D₄	—	2	2	no	—
185	D₃×D₄	C₄×C₉	1	4	yes	complemented
186	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
187	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
188	C₃×M₁₆	—	6	2	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	3	1	no	—
191	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
192	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	—	3	1	no	—
195	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
196	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
197	C₃×C₂²⋊C₄	—	6	1	no	—
198	C₃×C₄²	—	6	1	no	—
199	(C₂×D₃)⋊C₄	—	2	1	no	—
200	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
201	C₄×Dic₃	—	2	1	no	—
202	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
203	ΓL(1,𝔽₂₅)	—	2	2	no	—
204	C₂²×C₃²	—	2	2	no	—
205	C₂²×C₃²	—	4	1	no	—
206	C₂²×C₃²	—	4	1	no	—
207	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂×C₃×D₃	—	2	1	no	—
209	C₂×C₃×D₃	—	2	1	no	—
210	C₂×C₃×D₃	—	2	2	no	—
211	C₂×C₃×D₃	—	4	8	no	—
212	C₂×C₃×D₃	—	4	1	no	—
213	C₂×C₃×D₃	—	4	1	no	—
214	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
215	C₃²×C₄	—	4	1	no	—
216	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
218	C₃×Dic₃	—	4	1	no	—
219	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
220	C₂²×C₉	—	2	2	no	—
221	C₂²×C₉	—	2	1	no	—
222	C₂²×C₉	—	3	2	no	—
223	C₂²×C₉	—	4	2	no	—
224	C₂²×C₉	—	4	1	no	—
225	C₂²×C₉	—	4	1	no	—
226	C₂²×C₉	—	6	1	no	—
227	C₂²×C₉	—	6	1	no	—
228	C₂²×C₉	—	6	2	no	—
229	C₂²×C₉	—	8	1	no	—
230	C₂²×C₉	—	8	1	no	—
231	C₂²×C₉	—	12	8	no	—
232	C₂²×C₉	—	12	1	no	—
233	C₂²×C₉	—	12	1	no	—
234	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
235	C₄×C₉	—	2	1	no	—
236	C₄×C₉	—	2	1	no	—
237	C₄×C₉	—	3	2	no	—
238	C₄×C₉	—	4	1	no	—
239	C₄×C₉	—	8	1	no	—
240	C₄×C₉	—	12	1	no	—
241	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
242	C₄×C₉	D₃×D₄	1	1	yes	characteristic
243	C₂²×D₄	—	3	1	no	—
244	C₂×M₁₆	—	3	1	no	—
245	#117	—	3	1	no	—
246	#102	—	3	1	no	—
247	#102	—	3	1	no	—
248	#102	—	3	1	no	—
249	#102	D₃×C₉	1	1	yes	characteristic, complemented
250	C₃×C₉	#418	1	1	yes	characteristic, complemented, Sylow
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	3	1	no	—
254	C₂³×C₃	—	4	1	no	—
255	C₂³×C₃	—	6	4	no	—
256	C₂³×C₃	—	6	1	no	—
257	C₂³×C₃	—	12	2	no	—
258	C₂³×C₃	—	12	2	no	—
259	C₂²×D₃	—	2	1	no	—
260	C₂²×D₃	—	2	4	no	—
261	C₂²×D₃	—	4	2	no	—
262	C₂²×D₃	—	4	2	no	—
263	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
264	C₃×D₄	—	2	1	no	—
265	C₃×D₄	—	2	1	no	—
266	C₃×D₄	—	2	2	no	—
267	C₃×D₄	—	3	2	no	—
268	C₃×D₄	—	4	1	no	—
269	C₃×D₄	—	6	4	no	—
270	C₃×D₄	—	6	1	no	—
271	C₃×D₄	C₂×C₄×C₉	1	2	yes	—
272	C₃×D₄	C₃×C₄×D₃	1	2	yes	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	3	1	no	—
277	C₂×C₃×C₄	—	3	2	no	—
278	C₂×C₃×C₄	—	3	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	—	6	1	no	—
281	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
283	#67	—	2	4	no	—
284	C₂×Dic₃	—	2	1	no	—
285	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
286	D₁₂	—	2	1	no	—
287	D₁₂	C₂×C₄×C₉	1	2	yes	—
288	C₄×D₃	C₂×C₄×C₉	1	2	yes	—
289	C₄×D₃	D₄×C₉	1	2	yes	—
290	C₃×C₈	—	2	1	no	—
291	C₃×C₈	—	2	1	no	—
292	C₃×C₈	—	4	1	no	—
293	C₃×C₈	—	6	1	no	—
294	C₃⋊C₈	—	2	1	no	—
295	C₂×C₃²	—	4	2	no	—
296	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₃×D₃	—	2	2	no	—
300	C₃×D₃	—	4	2	no	—
301	C₂×C₉	—	2	1	no	—
302	C₂×C₉	—	2	1	no	—
303	C₂×C₉	—	2	1	no	—
304	C₂×C₉	—	4	2	no	—
305	C₂×C₉	—	6	2	no	—
306	C₂×C₉	—	8	2	no	—
307	C₂×C₉	—	12	2	no	—
308	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₉	#911	1	1	yes	characteristic
310	C₂×C₉	#914	1	1	yes	characteristic
311	C₂⁴	—	6	1	no	—
312	C₂×D₄	—	3	4	no	—
313	C₂×D₄	—	3	1	no	—
314	C₂×D₄	—	6	2	no	—
315	C₂×D₄	—	6	1	no	—
316	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
317	C₂²×C₄	—	3	1	no	—
318	M₁₆	—	6	2	no	—
319	C₂×C₈	—	3	1	no	—
320	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
321	C₄⋊C₄	—	3	1	no	—
322	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
323	C₂²⋊C₄	—	6	1	no	—
324	C₄²	—	6	1	no	—
325	C₂²×C₃	—	2	2	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	3	2	no	—
329	C₂²×C₃	—	4	2	no	—
330	C₂²×C₃	—	4	1	no	—
331	C₂²×C₃	—	4	1	no	—
332	C₂²×C₃	—	4	1	no	—
333	C₂²×C₃	—	4	1	no	—
334	C₂²×C₃	—	6	1	no	—
335	C₂²×C₃	—	6	1	no	—
336	C₂²×C₃	—	6	2	no	—
337	C₂²×C₃	—	8	1	no	—
338	C₂²×C₃	—	8	1	no	—
339	C₂²×C₃	—	12	8	no	—
340	C₂²×C₃	—	12	1	no	—
341	C₂²×C₃	—	12	1	no	—
342	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
343	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
344	C₂×D₃	—	2	1	no	—
345	C₂×D₃	—	2	1	no	—
346	C₂×D₃	—	2	2	no	—
347	C₂×D₃	—	4	8	no	—
348	C₂×D₃	—	4	1	no	—
349	C₂×D₃	—	4	1	no	—
350	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	3	2	no	—
354	C₃×C₄	—	4	1	no	—
355	C₃×C₄	—	4	1	no	—
356	C₃×C₄	—	8	1	no	—
357	C₃×C₄	—	12	1	no	—
358	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
359	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
360	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
361	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
362	Dic₃	—	4	1	no	—
363	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
364	C₃²	C₃×#418	1	1	yes	characteristic
365	C₉	—	2	1	no	—
366	C₉	#4770	1	1	yes	characteristic, direct product factor
367	C₂³	—	2	1	no	—
368	C₂³	—	3	1	no	—
369	C₂³	—	6	4	no	—
370	C₂³	—	6	1	no	—
371	C₂³	—	12	2	no	—
372	C₂³	—	12	2	no	—
373	D₄	—	2	1	no	—
374	D₄	—	3	2	no	—
375	D₄	—	6	4	no	—
376	D₄	—	6	1	no	—
377	D₄	C₄×D₃×C₉	1	2	yes	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	3	1	no	—
380	C₂×C₄	—	3	2	no	—
381	C₂×C₄	—	3	2	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
384	C₈	—	2	1	no	—
385	C₈	—	6	1	no	—
386	C₂×C₃	—	2	1	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	4	2	no	—
390	C₂×C₃	—	4	2	no	—
391	C₂×C₃	—	6	2	no	—
392	C₂×C₃	—	8	2	no	—
393	C₂×C₃	—	12	2	no	—
394	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
395	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
397	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
398	C₂×C₃	C₃×#911	1	1	yes	characteristic
399	C₂×C₃	C₃×#914	1	1	yes	characteristic
400	D₃	—	2	2	no	—
401	D₃	—	4	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	3	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	6	1	no	—
407	C₂²	—	6	1	no	—
408	C₂²	—	6	2	no	—
409	C₂²	—	12	8	no	—
410	C₂²	—	12	1	no	—
411	C₂²	—	12	1	no	—
412	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
413	C₄	—	3	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	12	1	no	—
416	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
417	C₄	D₃×D₄×C₉	1	1	yes	characteristic
418	C₃	—	2	1	no	—
419	C₃	C₉×#418	1	1	yes	characteristic, complemented
420	C₃	C₃×#4770	1	1	yes	characteristic
421	C₂	—	4	2	no	—
422	C₂	—	6	2	no	—
423	C₂	—	12	2	no	—
424	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
425	C₂	C₉×#911	1	1	yes	characteristic
426	C₂	C₉×#914	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#102	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×D₃×D₄	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#102	D₃
hypocenter	C₃	C₉×#418
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#102

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₉×#892	C₂	semidirect
4. C₃×C₉×#102	C₂	semidirect
5. C₉×#832	C₂	semidirect
6. C₉×#821	C₂	semidirect
7. C₉×#809	C₂	semidirect
14. D₃×D₄×C₉	C₄	semidirect
17. C₂×C₃×C₈×C₉	C₂²	semidirect
18. C₃×C₉×C₄⋊C₄	C₂²	semidirect
20. C₉×C₄⋊Dic₃	C₂²	semidirect
22. C₂×C₉×C₃⋊C₈	C₂²	semidirect
38. C₉×#102	D₃	semidirect
59. #4770	C₉	direct (N × H)
85. C₂×C₈×C₉	C₂×D₃	semidirect
88. C₉×C₄⋊C₄	C₂×D₃	semidirect
111. C₂×ΓL(1,𝔽₂₅)	C₂×C₉	semidirect
112. #892	C₂×C₉	semidirect
117. C₃×#102	C₂×C₉	semidirect
119. #832	C₂×C₉	semidirect
120. #821	C₂×C₉	semidirect
121. #809	C₂×C₉	semidirect
185. D₃×D₄	C₄×C₉	semidirect
191. C₂×C₃×C₈	C₂²×C₉	semidirect
195. C₃×C₄⋊C₄	C₂²×C₉	semidirect
200. C₄⋊Dic₃	C₂²×C₉	semidirect
202. C₂×C₃⋊C₈	C₂²×C₉	semidirect
249. #102	D₃×C₉	semidirect
250. C₃×C₉	#418	semidirect
320. C₂×C₈	C₂×D₃×C₉	semidirect
322. C₄⋊C₄	C₂×D₃×C₉	semidirect
366. C₉	#4770	direct (N × H)
419. C₃	C₉×#418	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₃×D₄×C₉	2
C₂×C₉×ΓL(1,𝔽₂₅)	2
C₉×#892	2
C₃×C₉×#102	2
C₉×#832	2
C₉×#821	2
C₉×#809	2
C₃×#4770	3
C₉×#418	3

Subgroups — C9×#4770 #13141753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4770 #13141753