Subgroups — C₉×#5522 #13152496

Order 1728.

1006 conjugacy classes of subgroups.

The subgroup lattice has 382 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	C₃×C₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#893	C₂	1	2	yes	maximal, complemented
5	C₉×#887	C₂	1	2	yes	maximal, complemented
6	C₉×#67⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₉×#872	C₂	1	2	yes	maximal, complemented
8	C₄²×D₃×C₉	C₂	1	2	yes	maximal, complemented
9	C₃×#5522	C₃	1	1	yes	maximal, characteristic
10	C₄×C₉×#41	—	3	1	no	maximal
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#67	C₂²	1	2	yes	—
13	C₂²×C₉×Dic₃	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×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₃×C₄²×C₉	C₂²	1	2	yes	—
22	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
23	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
24	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
25	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
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	C₃²×#117	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
31	C₃×#893	C₂×C₃	1	2	yes	—
32	C₃×#887	C₂×C₃	1	2	yes	—
33	C₃×#67⋊C₄	C₂×C₃	1	4	yes	—
34	C₃×#872	C₂×C₃	1	2	yes	—
35	C₃×C₄²×D₃	C₂×C₃	1	2	yes	—
36	C₂×C₉×#41	—	3	1	no	—
37	C₄×Q₈×C₉	—	3	2	no	—
38	C₄×D₄×C₉	—	3	2	no	—
39	C₄×D₄×C₉	—	3	4	no	—
40	C₉×#117	—	2	1	no	—
41	C₉×#117	—	3	2	no	—
42	C₉×#117	D₃	1	1	yes	characteristic, complemented
43	C₂×C₄²×C₉	—	3	1	no	—
44	C₂×C₄²×C₉	—	3	2	no	—
45	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
46	C₂²×D₃×C₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
48	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₉×#67	C₂×C₄	1	8	yes	complemented
52	C₂×C₉×Dic₃	—	2	4	no	—
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	—	2	8	no	—
58	C₄×D₃×C₉	C₂×C₄	1	8	yes	complemented
59	C₉×Dic₆	C₂×C₄	1	4	yes	complemented
60	C₃×C₄×#41	—	3	1	no	—
61	#5522	C₉	1	1	yes	characteristic, direct product factor
62	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
64	C₂²×C₃×Dic₃	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×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
72	C₃²×C₄²	C₂²×C₃	1	2	yes	—
73	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
74	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
75	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
76	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
77	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
78	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
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	—	3	2	no	—
85	C₂²×C₄×C₉	—	3	2	no	—
86	C₂²×C₄×C₉	—	3	4	no	—
87	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	3	4	no	—
90	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
91	C₉×C₂²⋊C₄	—	2	2	no	—
92	C₉×C₂²⋊C₄	—	3	4	no	—
93	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
94	C₄²×C₉	—	2	2	no	—
95	C₄²×C₉	—	3	4	no	—
96	C₄²×C₉	—	3	2	no	—
97	C₄²×C₉	—	3	1	no	—
98	C₄²×C₉	—	3	1	no	—
99	C₄²×C₉	C₂×D₃	1	2	yes	—
100	C₂²×C₃×C₉	—	2	2	no	—
101	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
102	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
103	C₂×D₃×C₉	—	2	4	no	—
104	C₂×D₃×C₉	C₂²×C₄	1	4	yes	—
105	C₃×C₄×C₉	—	2	4	no	—
106	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
107	C₃×C₄×C₉	C₂²×C₄	1	2	yes	—
108	C₉×Dic₃	—	2	2	no	—
109	C₉×Dic₃	C₂²×C₄	1	4	yes	—
110	C₉×Dic₃	#41	1	4	yes	complemented
111	C₂×C₃×#41	—	3	1	no	—
112	C₂×#235	C₂×C₉	1	1	yes	characteristic
113	C₃×C₄×Q₈	—	3	2	no	—
114	C₃×C₄×D₄	—	3	2	no	—
115	C₃×C₄×D₄	—	3	4	no	—
116	C₃×#117	—	2	1	no	—
117	C₃×#117	—	3	2	no	—
118	C₃×#117	C₂×C₉	1	1	yes	characteristic, complemented
119	C₃×#117	C₃×D₃	1	1	yes	characteristic
120	C₂×C₃×C₄²	—	3	1	no	—
121	C₂×C₃×C₄²	—	3	2	no	—
122	C₂×C₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
123	#893	C₂×C₉	1	2	yes	complemented
124	#887	C₂×C₉	1	2	yes	complemented
125	#67⋊C₄	C₂×C₉	1	4	yes	complemented
126	#872	C₂×C₉	1	2	yes	complemented
127	C₄²×D₃	C₂×C₉	1	2	yes	complemented
128	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
129	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
130	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
131	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
132	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
134	C₃×#67	C₂×C₃×C₄	1	8	yes	—
135	C₂×C₃×Dic₃	—	2	4	no	—
136	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
137	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
138	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
139	C₃×D₁₂	C₂×C₃×C₄	1	4	yes	—
140	C₃×C₄×D₃	—	2	8	no	—
141	C₃×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
142	C₃×Dic₆	C₂×C₃×C₄	1	4	yes	—
143	C₂³×C₉	—	2	1	no	—
144	C₂³×C₉	—	3	2	no	—
145	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
146	Q₈×C₉	—	3	4	no	—
147	D₄×C₉	—	3	8	no	—
148	D₄×C₉	—	3	4	no	—
149	C₂×C₄×C₉	—	2	4	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	4	no	—
153	C₂×C₄×C₉	—	3	2	no	—
154	C₂×C₄×C₉	—	3	2	no	—
155	C₂×C₄×C₉	—	3	8	no	—
156	C₂×C₄×C₉	—	3	2	no	—
157	C₂×C₄×C₉	—	6	8	no	—
158	C₂×C₄×C₉	—	6	4	no	—
159	C₂×C₄×C₉	C₄×D₃	1	4	yes	complemented
160	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
161	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
162	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
163	C₄×#41	—	3	1	no	Sylow
164	C₂×C₃×C₉	—	2	2	no	—
165	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₃×C₉	C₂×#41	1	2	yes	—
167	D₃×C₉	—	2	4	no	—
168	C₃×#41	—	3	8	no	—
169	C₂×C₃×Q₈	—	3	1	no	—
170	C₂×C₃×D₄	—	3	2	no	—
171	C₂×C₃×D₄	—	3	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	3	2	no	—
174	C₂²×C₃×C₄	—	3	2	no	—
175	C₂²×C₃×C₄	—	3	4	no	—
176	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
178	C₂×#67	C₂²×C₉	1	2	yes	—
179	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
180	#235	C₄×C₉	1	8	yes	complemented
181	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
182	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
183	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
184	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₄⋊C₄	—	3	4	no	—
187	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
188	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	3	4	no	—
191	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
193	C₃×C₄²	—	2	2	no	—
194	C₃×C₄²	—	3	1	no	—
195	C₃×C₄²	—	3	1	no	—
196	C₃×C₄²	—	3	4	no	—
197	C₃×C₄²	—	3	2	no	—
198	C₃×C₄²	C₂²×C₉	1	2	yes	—
199	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
200	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
201	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
202	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
203	C₄×Dic₃	C₂²×C₉	1	4	yes	—
204	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
205	C₄×Dic₃	C₂²×C₉	1	2	yes	—
206	C₂²×C₃²	—	2	2	no	—
207	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
208	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
209	C₂×C₃×D₃	—	2	4	no	—
210	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
211	C₃²×C₄	—	2	4	no	—
212	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
213	C₃²×C₄	C₂²×C₃×C₄	1	2	yes	—
214	C₃×Dic₃	—	2	2	no	—
215	C₃×Dic₃	C₂²×C₃×C₄	1	4	yes	—
216	C₃×Dic₃	C₃×#41	1	4	yes	—
217	C₂²×C₉	—	2	2	no	—
218	C₂²×C₉	—	2	1	no	—
219	C₂²×C₉	—	2	2	no	—
220	C₂²×C₉	—	3	4	no	—
221	C₂²×C₉	—	4	2	no	—
222	C₂²×C₉	—	6	4	no	—
223	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
224	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
225	C₄×C₉	—	2	4	no	—
226	C₄×C₉	—	2	2	no	—
227	C₄×C₉	—	2	2	no	—
228	C₄×C₉	—	3	4	no	—
229	C₄×C₉	—	3	4	no	—
230	C₄×C₉	—	4	4	no	—
231	C₄×C₉	—	6	2	no	—
232	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
233	C₄×C₉	C₂×C₄×D₃	1	2	yes	—
234	C₂×#41	—	3	1	no	—
235	C₄×Q₈	—	3	2	no	—
236	C₄×D₄	—	3	2	no	—
237	C₄×D₄	—	3	4	no	—
238	#117	—	3	2	no	—
239	#117	D₃×C₉	1	1	yes	characteristic, complemented
240	C₂×C₄²	—	3	1	no	—
241	C₂×C₄²	—	3	2	no	—
242	C₃×C₉	C₄×#41	1	1	yes	characteristic, complemented, Sylow
243	C₂³×C₃	—	2	1	no	—
244	C₂³×C₃	—	3	2	no	—
245	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
246	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
247	C₂²×D₃	C₂³×C₉	1	2	yes	—
248	C₃×Q₈	—	3	4	no	—
249	C₃×D₄	—	3	8	no	—
250	C₃×D₄	—	3	4	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	3	2	no	—
256	C₂×C₃×C₄	—	3	2	no	—
257	C₂×C₃×C₄	—	3	8	no	—
258	C₂×C₃×C₄	—	3	2	no	—
259	C₂×C₃×C₄	—	6	8	no	—
260	C₂×C₃×C₄	—	6	4	no	—
261	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
262	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
263	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
265	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
269	#67	C₂×C₄×C₉	1	8	yes	complemented
270	C₂×Dic₃	—	2	4	no	—
271	C₂×Dic₃	C₂³×C₉	1	2	yes	—
272	C₂×Dic₃	C₂³×C₉	1	2	yes	—
273	C₂×Dic₃	C₂³×C₉	1	2	yes	—
274	D₁₂	C₂×C₄×C₉	1	4	yes	complemented
275	C₄×D₃	—	2	8	no	—
276	C₄×D₃	C₂×C₄×C₉	1	8	yes	complemented
277	Dic₆	C₂×C₄×C₉	1	4	yes	complemented
278	C₂×C₃²	—	2	2	no	—
279	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
280	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
281	C₃×D₃	—	2	4	no	—
282	C₂×C₉	—	2	2	no	—
283	C₂×C₉	—	2	1	no	—
284	C₂×C₉	—	2	2	no	—
285	C₂×C₉	—	4	2	no	—
286	C₂×C₉	—	6	4	no	—
287	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
288	C₂×C₉	D₃×#41	1	2	yes	—
289	#41	—	3	8	no	—
290	C₂×Q₈	—	3	1	no	—
291	C₂×D₄	—	3	2	no	—
292	C₂×D₄	—	3	1	no	—
293	C₂²×C₄	—	3	2	no	—
294	C₂²×C₄	—	3	2	no	—
295	C₂²×C₄	—	3	4	no	—
296	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
297	C₄⋊C₄	—	3	4	no	—
298	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
299	C₂²⋊C₄	—	3	4	no	—
300	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
301	C₄²	—	3	1	no	—
302	C₄²	—	3	1	no	—
303	C₄²	—	3	4	no	—
304	C₄²	—	3	2	no	—
305	C₄²	C₂×D₃×C₉	1	2	yes	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	3	4	no	—
311	C₂²×C₃	—	4	2	no	—
312	C₂²×C₃	—	6	4	no	—
313	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
314	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
315	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
316	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
317	C₂×D₃	—	2	4	no	—
318	C₂×D₃	C₂²×C₄×C₉	1	4	yes	—
319	C₃×C₄	—	2	4	no	—
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	3	4	no	—
324	C₃×C₄	—	3	4	no	—
325	C₃×C₄	—	4	4	no	—
326	C₃×C₄	—	6	2	no	—
327	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
328	C₃×C₄	C₂²×C₄×C₉	1	2	yes	—
329	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
330	C₃×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
331	Dic₃	—	2	2	no	—
332	Dic₃	C₂²×C₄×C₉	1	4	yes	—
333	Dic₃	C₉×#41	1	4	yes	complemented
334	C₃²	C₃×C₄×#41	1	1	yes	characteristic
335	C₉	—	2	1	no	—
336	C₉	#5522	1	1	yes	characteristic, direct product factor
337	C₂³	—	3	2	no	—
338	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
339	Q₈	—	3	4	no	—
340	D₄	—	3	8	no	—
341	D₄	—	3	4	no	—
342	C₂×C₄	—	3	2	no	—
343	C₂×C₄	—	3	2	no	—
344	C₂×C₄	—	3	8	no	—
345	C₂×C₄	—	3	2	no	—
346	C₂×C₄	—	6	8	no	—
347	C₂×C₄	—	6	4	no	—
348	C₂×C₄	C₄×D₃×C₉	1	4	yes	complemented
349	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
350	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	2	2	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	4	2	no	—
357	C₂×C₃	—	6	4	no	—
358	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
359	C₂×C₃	C₂×C₉×#41	1	2	yes	—
360	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
361	C₂×C₃	C₃×D₃×#41	1	2	yes	—
362	D₃	—	2	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	3	4	no	—
365	C₂²	—	6	4	no	—
366	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
367	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
368	C₄	—	2	4	no	—
369	C₄	—	3	4	no	—
370	C₄	—	3	4	no	—
371	C₄	—	6	2	no	—
372	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
373	C₄	C₂×C₄×D₃×C₉	1	2	yes	—
374	C₃	—	2	1	no	—
375	C₃	C₄×C₉×#41	1	1	yes	characteristic, complemented
376	C₃	C₃×#5522	1	1	yes	characteristic
377	C₂	—	2	2	no	—
378	C₂	—	6	4	no	—
379	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
380	C₂	D₃×C₉×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#117	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×#235	C₂×C₃
hypercenter	C₉×#117	D₃
hypocenter	C₃	C₄×C₉×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₉×#117

Complements

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

N	H ≅ G/N	type
2. C₃×C₉×#117	C₂	semidirect
3. C₂×C₄×C₉×Dic₃	C₂	semidirect
4. C₉×#893	C₂	semidirect
5. C₉×#887	C₂	semidirect
6. C₉×#67⋊C₄	C₂	semidirect
7. C₉×#872	C₂	semidirect
8. C₄²×D₃×C₉	C₂	semidirect
14. C₉×#235	C₄	semidirect
42. C₉×#117	D₃	semidirect
47. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
51. 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. #5522	C₉	direct (N × H)
110. C₉×Dic₃	#41	semidirect
118. C₃×#117	C₂×C₉	semidirect
122. C₂×C₄×Dic₃	C₂×C₉	semidirect
123. #893	C₂×C₉	semidirect
124. #887	C₂×C₉	semidirect
125. #67⋊C₄	C₂×C₉	semidirect
126. #872	C₂×C₉	semidirect
127. C₄²×D₃	C₂×C₉	semidirect
159. C₂×C₄×C₉	C₄×D₃	semidirect
180. #235	C₄×C₉	semidirect
239. #117	D₃×C₉	semidirect
242. C₃×C₉	C₄×#41	semidirect
261. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
269. #67	C₂×C₄×C₉	semidirect
274. D₁₂	C₂×C₄×C₉	semidirect
276. C₄×D₃	C₂×C₄×C₉	semidirect
277. Dic₆	C₂×C₄×C₉	semidirect
333. Dic₃	C₉×#41	semidirect
336. C₉	#5522	direct (N × H)
348. C₂×C₄	C₄×D₃×C₉	semidirect
375. C₃	C₄×C₉×#41	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
C₃×C₉×#117	2
C₂×C₄×C₉×Dic₃	2
C₉×#893	2
C₉×#887	2
C₉×#67⋊C₄	2
C₉×#872	2
C₄²×D₃×C₉	2
C₃×#5522	3
C₄×C₉×#41	3

Subgroups — C9×#5522 #13152496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5522 #13152496