Subgroups — C₉×#5504 #13152416

Order 1728.

974 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₉×#67	C₂	1	4	yes	maximal, complemented
4	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#893	C₂	1	2	yes	maximal, complemented
6	C₉×#892	C₂	1	2	yes	maximal, complemented
7	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₉×#887	C₂	1	2	yes	maximal, complemented
9	C₃×#5504	C₃	1	1	yes	maximal, characteristic
10	C₉×#520	—	3	1	no	maximal
11	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₉×#67	C₂²	1	2	yes	—
14	C₉×#235	C₄	1	8	yes	complemented
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
18	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
21	C₉×#217	C₂²	1	2	yes	—
22	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
23	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
24	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₄×C₉×Dic₃	C₂²	1	2	yes	—
27	C₄×C₉×Dic₃	C₂²	1	4	yes	—
28	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₃×C₄×#67	C₂×C₃	1	4	yes	—
31	C₃×#926	C₂×C₃	1	1	yes	characteristic
32	C₃×#893	C₂×C₃	1	2	yes	—
33	C₃×#892	C₂×C₃	1	2	yes	—
34	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
35	C₃×#887	C₂×C₃	1	2	yes	—
36	C₂×C₉×#41	—	3	1	no	—
37	C₄×Q₈×C₉	—	3	2	no	—
38	C₄×D₄×C₉	—	3	4	no	—
39	C₄×D₄×C₉	—	3	2	no	—
40	C₉×#117	—	3	1	no	—
41	C₉×#117	—	3	2	no	—
42	C₂×C₉×C₄⋊C₄	—	2	1	no	—
43	C₂×C₉×C₄⋊C₄	—	3	2	no	—
44	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×D₃×C₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	—	4	2	no	—
48	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
52	C₉×#67	C₂×C₄	1	8	yes	complemented
53	C₂×C₉×Dic₃	C₂³	1	2	yes	—
54	C₂×C₉×Dic₃	C₂³	1	2	yes	—
55	C₂×C₉×Dic₃	C₂³	1	2	yes	—
56	C₉×D₁₂	C₂×C₄	1	4	yes	complemented
57	C₄×D₃×C₉	—	4	4	no	—
58	C₄×D₃×C₉	C₂×C₄	1	8	yes	complemented
59	C₉×Dic₆	C₂×C₄	1	4	yes	complemented
60	C₃×#520	—	3	1	no	—
61	#5504	C₉	1	1	yes	characteristic, direct product factor
62	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
63	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
65	C₃×#235	C₃×C₄	1	8	yes	—
66	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
68	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
69	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
70	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
71	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₃×#217	C₂²×C₃	1	2	yes	—
73	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
74	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
75	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
76	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
77	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
78	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
79	C₉×#41	—	3	8	no	—
80	C₂×Q₈×C₉	—	3	1	no	—
81	C₂×D₄×C₉	—	3	2	no	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂²×C₄×C₉	—	2	1	no	—
84	C₂²×C₄×C₉	—	2	2	no	—
85	C₂²×C₄×C₉	—	3	2	no	—
86	C₂²×C₄×C₉	—	3	4	no	—
87	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
88	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
89	C₉×C₄⋊C₄	—	2	2	no	—
90	C₉×C₄⋊C₄	—	2	2	no	—
91	C₉×C₄⋊C₄	—	3	1	no	—
92	C₉×C₄⋊C₄	—	3	4	no	—
93	C₉×C₄⋊C₄	—	3	1	no	—
94	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
95	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
96	C₉×C₂²⋊C₄	—	3	2	no	—
97	C₉×C₂²⋊C₄	—	3	4	no	—
98	C₄²×C₉	—	3	4	no	—
99	C₄²×C₉	—	3	2	no	—
100	C₂²×C₃×C₉	—	2	1	no	—
101	C₂²×C₃×C₉	—	2	1	no	—
102	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
104	C₂×D₃×C₉	—	2	2	no	—
105	C₂×D₃×C₉	—	2	2	no	—
106	C₂×D₃×C₉	C₂²×C₄	1	4	yes	—
107	C₃×C₄×C₉	—	2	4	no	—
108	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
109	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
110	C₉×Dic₃	—	2	2	no	—
111	C₉×Dic₃	—	2	2	no	—
112	C₉×Dic₃	C₂²×C₄	1	4	yes	—
113	C₂×C₃×#41	—	3	1	no	—
114	C₂×#235	C₂×C₉	1	1	yes	characteristic
115	C₃×C₄×Q₈	—	3	2	no	—
116	C₃×C₄×D₄	—	3	4	no	—
117	C₃×C₄×D₄	—	3	2	no	—
118	C₃×#117	—	3	1	no	—
119	C₃×#117	—	3	2	no	—
120	C₂×C₃×C₄⋊C₄	—	2	1	no	—
121	C₂×C₃×C₄⋊C₄	—	3	2	no	—
122	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
123	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
124	C₄×#67	C₂×C₉	1	4	yes	complemented
125	#926	C₂×C₉	1	1	yes	characteristic, complemented
126	#893	C₂×C₉	1	2	yes	complemented
127	#892	C₂×C₉	1	2	yes	complemented
128	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
129	#887	C₂×C₉	1	2	yes	complemented
130	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
131	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
132	C₂×C₃²×C₄	—	4	2	no	—
133	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
134	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
135	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
137	C₃×#67	C₂×C₃×C₄	1	8	yes	—
138	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
139	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
140	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
141	C₃×D₁₂	C₂×C₃×C₄	1	4	yes	—
142	C₃×C₄×D₃	—	4	4	no	—
143	C₃×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
144	C₃×Dic₆	C₂×C₃×C₄	1	4	yes	—
145	C₂³×C₉	—	2	1	no	—
146	C₂³×C₉	—	3	2	no	—
147	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
148	Q₈×C₉	—	3	4	no	—
149	D₄×C₉	—	3	8	no	—
150	D₄×C₉	—	3	4	no	—
151	C₂×C₄×C₉	—	2	4	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	4	no	—
155	C₂×C₄×C₉	—	3	2	no	—
156	C₂×C₄×C₉	—	3	8	no	—
157	C₂×C₄×C₉	—	3	2	no	—
158	C₂×C₄×C₉	—	3	2	no	—
159	C₂×C₄×C₉	—	4	2	no	—
160	C₂×C₄×C₉	—	4	4	no	—
161	C₂×C₄×C₉	—	12	4	no	—
162	C₂×C₄×C₉	C₄×D₃	1	4	yes	complemented
163	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
164	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
166	#520	—	3	1	no	Sylow
167	C₂×C₃×C₉	—	2	2	no	—
168	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
171	D₃×C₉	—	2	4	no	—
172	C₃×#41	—	3	8	no	—
173	C₂×C₃×Q₈	—	3	1	no	—
174	C₂×C₃×D₄	—	3	2	no	—
175	C₂×C₃×D₄	—	3	1	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	2	2	no	—
178	C₂²×C₃×C₄	—	3	2	no	—
179	C₂²×C₃×C₄	—	3	4	no	—
180	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
181	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
183	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
184	C₂×#67	C₂²×C₉	1	2	yes	—
185	#235	C₄×C₉	1	8	yes	complemented
186	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
187	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
188	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
189	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	3	4	no	—
193	C₃×C₄⋊C₄	—	3	1	no	—
194	C₃×C₄⋊C₄	—	3	1	no	—
195	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
196	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
197	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
198	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
199	C₃×C₂²⋊C₄	—	3	2	no	—
200	C₃×C₂²⋊C₄	—	3	4	no	—
201	C₃×C₄²	—	3	4	no	—
202	C₃×C₄²	—	3	2	no	—
203	#217	C₂²×C₉	1	2	yes	—
204	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
205	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
206	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
207	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
208	C₄×Dic₃	C₂²×C₉	1	4	yes	—
209	C₄×Dic₃	C₂²×C₉	1	2	yes	—
210	C₂²×C₃²	—	2	1	no	—
211	C₂²×C₃²	—	2	1	no	—
212	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
213	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
214	C₂×C₃×D₃	—	2	2	no	—
215	C₂×C₃×D₃	—	2	2	no	—
216	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
217	C₃²×C₄	—	2	4	no	—
218	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
219	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
220	C₃×Dic₃	—	2	2	no	—
221	C₃×Dic₃	—	2	2	no	—
222	C₃×Dic₃	C₂²×C₃×C₄	1	4	yes	—
223	C₂²×C₉	—	2	2	no	—
224	C₂²×C₉	—	2	2	no	—
225	C₂²×C₉	—	2	1	no	—
226	C₂²×C₉	—	2	1	no	—
227	C₂²×C₉	—	2	1	no	—
228	C₂²×C₉	—	2	2	no	—
229	C₂²×C₉	—	3	4	no	—
230	C₂²×C₉	—	6	2	no	—
231	C₂²×C₉	—	6	2	no	—
232	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
233	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
234	C₄×C₉	—	2	4	no	—
235	C₄×C₉	—	2	2	no	—
236	C₄×C₉	—	2	2	no	—
237	C₄×C₉	—	3	4	no	—
238	C₄×C₉	—	4	4	no	—
239	C₄×C₉	—	6	2	no	—
240	C₄×C₉	—	6	2	no	—
241	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
242	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
243	C₂×#41	—	3	1	no	—
244	C₄×Q₈	—	3	2	no	—
245	C₄×D₄	—	3	4	no	—
246	C₄×D₄	—	3	2	no	—
247	#117	—	3	1	no	—
248	#117	—	3	2	no	—
249	C₂×C₄⋊C₄	—	3	2	no	—
250	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
251	C₃×C₉	#520	1	1	yes	characteristic, complemented, Sylow
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	—	3	2	no	—
254	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
255	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
256	C₂²×D₃	C₂³×C₉	1	2	yes	—
257	C₃×Q₈	—	3	4	no	—
258	C₃×D₄	—	3	8	no	—
259	C₃×D₄	—	3	4	no	—
260	C₂×C₃×C₄	—	2	4	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	3	2	no	—
265	C₂×C₃×C₄	—	3	8	no	—
266	C₂×C₃×C₄	—	3	2	no	—
267	C₂×C₃×C₄	—	3	2	no	—
268	C₂×C₃×C₄	—	4	2	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	4	no	—
271	C₂×C₃×C₄	—	12	4	no	—
272	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
273	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
274	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
276	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
278	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
280	#67	C₂×C₄×C₉	1	8	yes	complemented
281	C₂×Dic₃	C₂³×C₉	1	2	yes	—
282	C₂×Dic₃	C₂³×C₉	1	2	yes	—
283	C₂×Dic₃	C₂³×C₉	1	2	yes	—
284	D₁₂	C₂×C₄×C₉	1	4	yes	complemented
285	C₄×D₃	—	4	4	no	—
286	C₄×D₃	C₂×C₄×C₉	1	8	yes	complemented
287	Dic₆	C₂×C₄×C₉	1	4	yes	complemented
288	C₂×C₃²	—	2	2	no	—
289	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
290	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
292	C₃×D₃	—	2	4	no	—
293	C₂×C₉	—	2	4	no	—
294	C₂×C₉	—	2	2	no	—
295	C₂×C₉	—	2	1	no	—
296	C₂×C₉	—	2	1	no	—
297	C₂×C₉	—	2	1	no	—
298	C₂×C₉	—	6	4	no	—
299	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
300	C₂×C₉	#1004	1	1	yes	characteristic
301	C₂×C₉	#1007	1	1	yes	characteristic
302	#41	—	3	8	no	—
303	C₂×Q₈	—	3	1	no	—
304	C₂×D₄	—	3	2	no	—
305	C₂×D₄	—	3	1	no	—
306	C₂²×C₄	—	3	2	no	—
307	C₂²×C₄	—	3	4	no	—
308	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
309	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
310	C₄⋊C₄	—	3	1	no	—
311	C₄⋊C₄	—	3	4	no	—
312	C₄⋊C₄	—	3	1	no	—
313	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
314	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
315	C₂²⋊C₄	—	3	2	no	—
316	C₂²⋊C₄	—	3	4	no	—
317	C₄²	—	3	4	no	—
318	C₄²	—	3	2	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	2	2	no	—
327	C₂²×C₃	—	3	4	no	—
328	C₂²×C₃	—	6	2	no	—
329	C₂²×C₃	—	6	2	no	—
330	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
331	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
332	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
333	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
334	C₂×D₃	—	2	2	no	—
335	C₂×D₃	—	2	2	no	—
336	C₂×D₃	C₂²×C₄×C₉	1	4	yes	—
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	2	2	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	3	4	no	—
342	C₃×C₄	—	4	4	no	—
343	C₃×C₄	—	6	2	no	—
344	C₃×C₄	—	6	2	no	—
345	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
346	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
347	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
348	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
349	Dic₃	—	2	2	no	—
350	Dic₃	—	2	2	no	—
351	Dic₃	C₂²×C₄×C₉	1	4	yes	—
352	C₃²	C₃×#520	1	1	yes	characteristic
353	C₉	—	2	1	no	—
354	C₉	#5504	1	1	yes	characteristic, direct product factor
355	C₂³	—	3	2	no	—
356	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
357	Q₈	—	3	4	no	—
358	D₄	—	3	8	no	—
359	D₄	—	3	4	no	—
360	C₂×C₄	—	3	2	no	—
361	C₂×C₄	—	3	8	no	—
362	C₂×C₄	—	3	2	no	—
363	C₂×C₄	—	3	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	12	4	no	—
366	C₂×C₄	C₄×D₃×C₉	1	4	yes	complemented
367	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
368	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
370	C₂×C₃	—	2	4	no	—
371	C₂×C₃	—	2	2	no	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	1	no	—
376	C₂×C₃	—	6	4	no	—
377	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
378	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
380	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
381	C₂×C₃	C₃×#1004	1	1	yes	characteristic
382	C₂×C₃	C₃×#1007	1	1	yes	characteristic
383	D₃	—	2	4	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	3	4	no	—
387	C₂²	—	6	2	no	—
388	C₂²	—	6	2	no	—
389	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
390	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	3	4	no	—
393	C₄	—	6	2	no	—
394	C₄	—	6	2	no	—
395	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
396	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
397	C₃	—	2	1	no	—
398	C₃	C₉×#520	1	1	yes	characteristic, complemented
399	C₃	C₃×#5504	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	6	4	no	—
402	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
403	C₂	C₉×#1004	1	1	yes	characteristic
404	C₂	C₉×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#235	C₂×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₉×#520
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
3. C₄×C₉×#67	C₂	semidirect
4. C₉×#926	C₂	semidirect
5. C₉×#893	C₂	semidirect
6. C₉×#892	C₂	semidirect
7. D₃×C₉×C₄⋊C₄	C₂	semidirect
8. C₉×#887	C₂	semidirect
14. C₉×#235	C₄	semidirect
44. C₂×C₉×C₄⋊C₄	D₃	semidirect
48. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
52. C₉×#67	C₂×C₄	semidirect
56. C₉×D₁₂	C₂×C₄	semidirect
58. C₄×D₃×C₉	C₂×C₄	semidirect
59. C₉×Dic₆	C₂×C₄	semidirect
61. #5504	C₉	direct (N × H)
122. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
124. C₄×#67	C₂×C₉	semidirect
125. #926	C₂×C₉	semidirect
126. #893	C₂×C₉	semidirect
127. #892	C₂×C₉	semidirect
128. D₃×C₄⋊C₄	C₂×C₉	semidirect
129. #887	C₂×C₉	semidirect
162. C₂×C₄×C₉	C₄×D₃	semidirect
185. #235	C₄×C₉	semidirect
250. C₂×C₄⋊C₄	D₃×C₉	semidirect
251. C₃×C₉	#520	semidirect
272. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
280. #67	C₂×C₄×C₉	semidirect
284. D₁₂	C₂×C₄×C₉	semidirect
286. C₄×D₃	C₂×C₄×C₉	semidirect
287. Dic₆	C₂×C₄×C₉	semidirect
354. C₉	#5504	direct (N × H)
366. C₂×C₄	C₄×D₃×C₉	semidirect
398. C₃	C₉×#520	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#235	2
C₂×C₃×C₉×C₄⋊C₄	2
C₄×C₉×#67	2
C₉×#926	2
C₉×#893	2
C₉×#892	2
D₃×C₉×C₄⋊C₄	2
C₉×#887	2
C₃×#5504	3
C₉×#520	3

Subgroups — C9×#5504 #13152416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5504 #13152416