Subgroups — C₉×#5735 #13153316

Order 1728.

656 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	1	yes	maximal, characteristic
3	C₉×#946	C₂	1	2	yes	maximal, complemented
4	C₉×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#898	C₂	1	2	yes	maximal, complemented
6	C₉×#896	C₂	1	2	yes	maximal, complemented
7	C₉×#894	C₂	1	2	yes	maximal
8	C₉×#889	C₂	1	2	yes	maximal, complemented
9	C₉×#876	C₂	1	2	yes	maximal, complemented
10	C₃×#5735	C₃	1	1	yes	maximal, characteristic
11	C₉×#563	—	3	1	no	maximal
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
14	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
16	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
17	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
22	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
26	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
27	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
28	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
29	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
30	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
31	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
32	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
33	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
34	C₃×#947	C₂×C₃	1	1	yes	characteristic
35	C₃×#946	C₂×C₃	1	2	yes	—
36	C₃×#944	C₂×C₃	1	1	yes	characteristic
37	C₃×#898	C₂×C₃	1	2	yes	—
38	C₃×#896	C₂×C₃	1	2	yes	—
39	C₃×#894	C₂×C₃	1	2	yes	—
40	C₃×#889	C₂×C₃	1	2	yes	—
41	C₃×#876	C₂×C₃	1	2	yes	—
42	C₉×C₄⋊Q₈	—	2	1	no	—
43	C₉×C₄⋊Q₈	—	3	1	no	—
44	C₉×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
45	C₉×#126	—	3	2	no	—
46	C₉×#126	—	3	2	no	—
47	C₉×#125	—	3	2	no	—
48	C₉×#124	—	3	1	no	—
49	C₉×#123	—	3	2	no	—
50	C₉×C₂²⋊Q₈	—	3	2	no	—
51	C₉×C₂²⋊Q₈	—	3	2	no	—
52	C₂²×D₃×C₉	C₂³	1	2	yes	—
53	C₃×Q₈×C₉	—	4	1	no	—
54	C₃×Q₈×C₉	—	4	1	no	—
55	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
57	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
60	C₂×C₉×Dic₃	C₂³	1	2	yes	—
61	C₂×C₉×Dic₃	C₂³	1	2	yes	—
62	C₂×C₉×Dic₃	C₂³	1	2	yes	—
63	C₉×D₁₂	—	4	1	no	—
64	C₄×D₃×C₉	—	4	2	no	—
65	C₉×Dic₆	—	4	1	no	—
66	C₃×#563	—	3	1	no	—
67	#5735	C₉	1	1	yes	characteristic, direct product factor
68	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
72	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
74	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
75	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
76	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
77	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
78	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
79	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
80	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
81	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
82	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
83	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
85	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
86	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
87	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
88	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
89	C₂×Q₈×C₉	—	2	1	no	—
90	C₂×Q₈×C₉	—	2	1	no	—
91	C₂×Q₈×C₉	—	3	1	no	—
92	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
93	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
94	C₂×D₄×C₉	—	3	1	no	—
95	C₂²×C₄×C₉	—	3	2	no	—
96	C₉×C₄⋊C₄	—	2	2	no	—
97	C₉×C₄⋊C₄	—	2	2	no	—
98	C₉×C₄⋊C₄	—	3	2	no	—
99	C₉×C₄⋊C₄	—	3	2	no	—
100	C₉×C₄⋊C₄	—	3	2	no	—
101	C₉×C₄⋊C₄	—	3	2	no	—
102	C₉×C₄⋊C₄	—	3	2	no	—
103	C₉×C₄⋊C₄	—	3	2	no	—
104	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
105	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
106	C₉×C₂²⋊C₄	—	3	2	no	—
107	C₉×C₂²⋊C₄	—	3	2	no	—
108	C₉×C₂²⋊C₄	—	3	2	no	—
109	C₉×C₂²⋊C₄	—	3	2	no	—
110	C₉×C₂²⋊C₄	—	3	2	no	—
111	C₄²×C₉	—	2	1	no	—
112	C₄²×C₉	—	3	1	no	—
113	C₄²×C₉	—	3	1	no	—
114	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
115	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
116	C₂×D₃×C₉	—	2	2	no	—
117	C₂×D₃×C₉	—	2	4	no	—
118	C₃×C₄×C₉	—	2	1	no	—
119	C₃×C₄×C₉	—	2	1	no	—
120	C₃×C₄×C₉	—	2	2	no	—
121	C₃×C₄×C₉	—	2	1	no	—
122	C₃×C₄×C₉	—	2	2	no	—
123	C₉×Dic₃	—	2	2	no	—
124	C₉×Dic₃	—	2	2	no	—
125	C₉×Dic₃	—	2	2	no	—
126	C₃×C₄⋊Q₈	—	2	1	no	—
127	C₃×C₄⋊Q₈	—	3	1	no	—
128	C₃×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
129	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
130	C₃×#126	—	3	2	no	—
131	C₃×#126	—	3	2	no	—
132	C₃×#125	—	3	2	no	—
133	C₃×#124	—	3	1	no	—
134	C₃×#123	—	3	2	no	—
135	C₃×C₂²⋊Q₈	—	3	2	no	—
136	C₃×C₂²⋊Q₈	—	3	2	no	—
137	#947	C₂×C₉	1	1	yes	characteristic
138	#946	C₂×C₉	1	2	yes	complemented
139	#944	C₂×C₉	1	1	yes	characteristic, complemented
140	#898	C₂×C₉	1	2	yes	complemented
141	#896	C₂×C₉	1	2	yes	complemented
142	#894	C₂×C₉	1	2	yes	—
143	#889	C₂×C₉	1	2	yes	complemented
144	#876	C₂×C₉	1	2	yes	complemented
145	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
146	C₃²×Q₈	—	4	1	no	—
147	C₃²×Q₈	—	4	1	no	—
148	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
150	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
151	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
153	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
154	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
155	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
156	C₃×D₁₂	—	4	1	no	—
157	C₃×C₄×D₃	—	4	2	no	—
158	C₃×Dic₆	—	4	1	no	—
159	C₂³×C₉	—	3	2	no	—
160	Q₈×C₉	—	4	1	no	—
161	Q₈×C₉	—	4	1	no	—
162	Q₈×C₉	—	4	2	no	—
163	Q₈×C₉	—	4	2	no	—
164	Q₈×C₉	—	12	1	no	—
165	D₄×C₉	—	12	1	no	—
166	C₂×C₄×C₉	—	2	2	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	2	no	—
171	C₂×C₄×C₉	—	3	2	no	—
172	C₂×C₄×C₉	—	3	2	no	—
173	C₂×C₄×C₉	—	3	2	no	—
174	C₂×C₄×C₉	—	12	2	no	—
175	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
176	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
178	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
180	#563	—	3	1	no	Sylow
181	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₃×C₉	2₋¹⁺⁴	1	2	yes	—
183	D₃×C₉	—	4	2	no	—
184	C₂×C₃×Q₈	—	2	1	no	—
185	C₂×C₃×Q₈	—	2	1	no	—
186	C₂×C₃×Q₈	—	3	1	no	—
187	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
188	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
189	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
190	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
191	C₂×C₃×D₄	—	3	1	no	—
192	C₂²×C₃×C₄	—	3	2	no	—
193	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
194	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
195	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
196	C₃×C₄⋊C₄	—	2	2	no	—
197	C₃×C₄⋊C₄	—	2	2	no	—
198	C₃×C₄⋊C₄	—	3	2	no	—
199	C₃×C₄⋊C₄	—	3	2	no	—
200	C₃×C₄⋊C₄	—	3	2	no	—
201	C₃×C₄⋊C₄	—	3	2	no	—
202	C₃×C₄⋊C₄	—	3	2	no	—
203	C₃×C₄⋊C₄	—	3	2	no	—
204	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
205	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
206	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
207	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
208	C₃×C₂²⋊C₄	—	3	2	no	—
209	C₃×C₂²⋊C₄	—	3	2	no	—
210	C₃×C₂²⋊C₄	—	3	2	no	—
211	C₃×C₂²⋊C₄	—	3	2	no	—
212	C₃×C₂²⋊C₄	—	3	2	no	—
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	—	3	1	no	—
215	C₃×C₄²	—	3	1	no	—
216	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
217	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
218	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
219	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
220	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
221	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
222	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
223	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
224	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
225	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
226	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
227	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
228	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
229	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
230	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
231	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
232	C₂×C₃×D₃	—	2	2	no	—
233	C₂×C₃×D₃	—	2	4	no	—
234	C₃²×C₄	—	2	1	no	—
235	C₃²×C₄	—	2	2	no	—
236	C₃²×C₄	—	2	1	no	—
237	C₃²×C₄	—	2	2	no	—
238	C₃²×C₄	—	2	1	no	—
239	C₃×Dic₃	—	2	2	no	—
240	C₃×Dic₃	—	2	2	no	—
241	C₃×Dic₃	—	2	2	no	—
242	C₂²×C₉	—	2	1	no	—
243	C₂²×C₉	—	6	2	no	—
244	C₂²×C₉	—	6	4	no	—
245	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
246	C₄×C₉	—	2	4	no	—
247	C₄×C₉	—	2	2	no	—
248	C₄×C₉	—	2	2	no	—
249	C₄×C₉	—	2	1	no	—
250	C₄×C₉	—	2	1	no	—
251	C₄×C₉	—	2	1	no	—
252	C₄×C₉	—	2	2	no	—
253	C₄×C₉	—	4	2	no	—
254	C₄×C₉	—	4	1	no	—
255	C₄×C₉	—	4	1	no	—
256	C₄×C₉	—	6	2	no	—
257	C₄×C₉	—	6	2	no	—
258	C₄×C₉	—	6	2	no	—
259	C₄⋊Q₈	—	3	1	no	—
260	C₄⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
261	#126	—	3	2	no	—
262	#126	—	3	2	no	—
263	#125	—	3	2	no	—
264	#124	—	3	1	no	—
265	#123	—	3	2	no	—
266	C₂²⋊Q₈	—	3	2	no	—
267	C₂²⋊Q₈	—	3	2	no	—
268	C₃×C₉	#563	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₃	—	3	2	no	—
270	C₂²×D₃	C₂³×C₉	1	2	yes	—
271	C₃×Q₈	—	4	1	no	—
272	C₃×Q₈	—	4	1	no	—
273	C₃×Q₈	—	4	1	no	—
274	C₃×Q₈	—	4	1	no	—
275	C₃×Q₈	—	4	2	no	—
276	C₃×Q₈	—	4	2	no	—
277	C₃×Q₈	—	12	1	no	—
278	C₃×D₄	—	12	1	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	3	2	no	—
285	C₂×C₃×C₄	—	3	2	no	—
286	C₂×C₃×C₄	—	3	2	no	—
287	C₂×C₃×C₄	—	12	2	no	—
288	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
291	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
293	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
296	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
298	C₂×Dic₃	C₂³×C₉	1	2	yes	—
299	C₂×Dic₃	C₂³×C₉	1	2	yes	—
300	C₂×Dic₃	C₂³×C₉	1	2	yes	—
301	D₁₂	—	4	1	no	—
302	C₄×D₃	—	4	2	no	—
303	Dic₆	—	4	1	no	—
304	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×C₃²	C₃×2₋¹⁺⁴	1	2	yes	—
306	C₃×D₃	—	4	2	no	—
307	C₂×C₉	—	2	1	no	—
308	C₂×C₉	—	2	2	no	—
309	C₂×C₉	—	12	2	no	—
310	C₂×C₉	#1004	1	1	yes	characteristic
311	C₂×C₉	#1007	1	2	yes	—
312	C₂×Q₈	—	3	1	no	—
313	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
314	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
315	C₂×D₄	—	3	1	no	—
316	C₂²×C₄	—	3	2	no	—
317	C₄⋊C₄	—	3	2	no	—
318	C₄⋊C₄	—	3	2	no	—
319	C₄⋊C₄	—	3	2	no	—
320	C₄⋊C₄	—	3	2	no	—
321	C₄⋊C₄	—	3	2	no	—
322	C₄⋊C₄	—	3	2	no	—
323	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
324	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
325	C₂²⋊C₄	—	3	2	no	—
326	C₂²⋊C₄	—	3	2	no	—
327	C₂²⋊C₄	—	3	2	no	—
328	C₂²⋊C₄	—	3	2	no	—
329	C₂²⋊C₄	—	3	2	no	—
330	C₄²	—	3	1	no	—
331	C₄²	—	3	1	no	—
332	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	6	2	no	—
335	C₂²×C₃	—	6	4	no	—
336	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
337	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
338	C₂×D₃	—	2	2	no	—
339	C₂×D₃	—	2	4	no	—
340	C₃×C₄	—	2	2	no	—
341	C₃×C₄	—	2	4	no	—
342	C₃×C₄	—	2	2	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	2	2	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	—	4	1	no	—
355	C₃×C₄	—	6	2	no	—
356	C₃×C₄	—	6	2	no	—
357	C₃×C₄	—	6	2	no	—
358	Dic₃	—	2	2	no	—
359	Dic₃	—	2	2	no	—
360	Dic₃	—	2	2	no	—
361	C₃²	C₃×#563	1	1	yes	characteristic
362	C₉	—	2	1	no	—
363	C₉	#5735	1	1	yes	characteristic, direct product factor
364	C₂³	—	3	2	no	—
365	Q₈	—	4	1	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	12	1	no	—
368	D₄	—	12	1	no	—
369	C₂×C₄	—	3	2	no	—
370	C₂×C₄	—	3	2	no	—
371	C₂×C₄	—	3	2	no	—
372	C₂×C₄	—	12	2	no	—
373	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
376	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	2	no	—
380	C₂×C₃	—	12	2	no	—
381	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₃	C₉×2₋¹⁺⁴	1	2	yes	—
383	C₂×C₃	C₃×#1004	1	1	yes	characteristic
384	C₂×C₃	C₃×#1007	1	2	yes	—
385	D₃	—	4	2	no	—
386	C₂²	—	6	2	no	—
387	C₂²	—	6	4	no	—
388	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	6	2	no	—
395	C₄	—	6	2	no	—
396	C₄	—	6	2	no	—
397	C₃	—	2	1	no	—
398	C₃	C₉×#563	1	1	yes	characteristic, complemented
399	C₃	C₃×#5735	1	1	yes	characteristic
400	C₂	—	12	2	no	—
401	C₂	C₉×#1004	1	1	yes	characteristic
402	C₂	C₉×#1007	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₉×C₄⋊Q₈	D₃
hypocenter	C₃	C₉×#563
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₄⋊Q₈	C₂	semidirect
3. C₉×#946	C₂	semidirect
4. C₉×#944	C₂	semidirect
5. C₉×#898	C₂	semidirect
6. C₉×#896	C₂	semidirect
8. C₉×#889	C₂	semidirect
9. C₉×#876	C₂	semidirect
44. C₉×C₄⋊Q₈	D₃	semidirect
67. #5735	C₉	direct (N × H)
128. C₃×C₄⋊Q₈	C₂×C₉	semidirect
138. #946	C₂×C₉	semidirect
139. #944	C₂×C₉	semidirect
140. #898	C₂×C₉	semidirect
141. #896	C₂×C₉	semidirect
143. #889	C₂×C₉	semidirect
144. #876	C₂×C₉	semidirect
260. C₄⋊Q₈	D₃×C₉	semidirect
268. C₃×C₉	#563	semidirect
363. C₉	#5735	direct (N × H)
398. C₃	C₉×#563	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₄⋊Q₈	2
C₉×#947	2
C₉×#946	2
C₉×#944	2
C₉×#898	2
C₉×#896	2
C₉×#894	2
C₉×#889	2
C₉×#876	2
C₃×#5735	3
C₉×#563	3

Subgroups — C9×#5735 #13153316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5735 #13153316