Subgroups — C₈×C₉×#67 #13143101

Order 1728.

478 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic
3	C₂×D₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#830	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₈×#67	C₃	1	1	yes	maximal, characteristic
9	C₈×D₄×C₉	—	3	1	no	maximal
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×#67	C₄	1	1	yes	characteristic
12	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₈×C₉	—	2	2	no	—
14	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
16	C₉×#217	C₄	1	1	yes	characteristic
17	C₉×(C₂×D₃)⋊C₄	C₄	1	1	yes	characteristic
18	C₉×Dic₃⋊C₄	C₄	1	1	yes	characteristic
19	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	D₃×C₈×C₉	—	2	2	no	—
23	C₂²×C₃²×C₈	C₂×C₃	1	1	yes	characteristic
24	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
26	C₃×#830	C₂×C₃	1	1	yes	characteristic
27	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
28	C₃×Dic₃⋊C₈	C₂×C₃	1	1	yes	characteristic
29	C₃×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic
30	C₂²×C₈×C₉	—	2	1	no	—
31	C₂²×C₈×C₉	—	3	1	no	—
32	C₂²×C₈×C₉	D₃	1	1	yes	characteristic, complemented
33	C₄×D₄×C₉	—	3	1	no	—
34	C₉×C₄⋊C₈	—	3	1	no	—
35	C₉×C₂²⋊C₈	—	3	1	no	—
36	C₉×C₂²⋊C₈	—	3	1	no	—
37	C₄×C₈×C₉	—	3	1	no	—
38	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×C₉	—	2	1	no	—
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
44	C₉×#67	C₈	1	4	yes	direct product factor
45	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₄×D₃×C₉	—	2	1	no	—
49	C₄×D₃×C₉	—	2	1	no	—
50	C₃×C₈×C₉	—	2	1	no	—
51	C₃×C₈×C₉	D₄	1	2	yes	complemented
52	C₉×C₃⋊C₈	—	2	1	no	—
53	C₉×C₃⋊C₈	—	2	1	no	—
54	C₃×C₈×D₄	—	3	1	no	—
55	C₈×#67	C₉	1	1	yes	characteristic, direct product factor
56	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₃×#67	C₃×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃²×C₈	—	2	2	no	—
60	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
62	C₃×#217	C₃×C₄	1	1	yes	characteristic
63	C₃×(C₂×D₃)⋊C₄	C₃×C₄	1	1	yes	characteristic
64	C₃×Dic₃⋊C₄	C₃×C₄	1	1	yes	characteristic
65	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
68	C₃×D₃×C₈	—	2	2	no	—
69	C₂×D₄×C₉	—	3	1	no	—
70	C₂²×C₄×C₉	—	2	1	no	—
71	C₂²×C₄×C₉	—	3	1	no	—
72	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
73	C₂×C₈×C₉	—	2	4	no	—
74	C₂×C₈×C₉	—	2	1	no	—
75	C₂×C₈×C₉	—	2	1	no	—
76	C₂×C₈×C₉	—	2	2	no	—
77	C₂×C₈×C₉	—	3	1	no	—
78	C₂×C₈×C₉	—	3	1	no	—
79	C₂×C₈×C₉	—	6	2	no	—
80	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
81	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
82	C₉×C₄⋊C₄	—	3	1	no	—
83	C₉×C₂²⋊C₄	—	3	1	no	—
84	C₉×C₂²⋊C₄	—	3	1	no	—
85	C₄²×C₉	—	3	1	no	—
86	C₂²×C₃×C₉	—	2	1	no	—
87	C₂²×C₃×C₉	—	2	1	no	—
88	C₂²×C₃×C₉	C₂×C₈	1	2	yes	complemented
89	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
90	C₂×D₃×C₉	—	2	1	no	—
91	C₂×D₃×C₉	—	2	1	no	—
92	C₂×D₃×C₉	C₂×C₈	1	2	yes	complemented
93	C₃×C₄×C₉	—	2	1	no	—
94	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
95	C₃×C₄×C₉	#41	1	1	yes	characteristic
96	C₉×Dic₃	—	2	1	no	—
97	C₉×Dic₃	—	2	1	no	—
98	C₉×Dic₃	C₂×C₈	1	2	yes	complemented
99	C₂²×C₃×C₈	—	2	1	no	—
100	C₂²×C₃×C₈	—	3	1	no	—
101	C₂²×C₃×C₈	C₂×C₉	1	1	yes	characteristic, complemented
102	C₂²×C₃×C₈	C₃×D₃	1	1	yes	characteristic
103	C₃×C₄×D₄	—	3	1	no	—
104	C₄×#67	C₂×C₉	1	1	yes	characteristic
105	C₂×D₃×C₈	C₂×C₉	1	1	yes	characteristic, complemented
106	C₃×C₄⋊C₈	—	3	1	no	—
107	C₃×C₂²⋊C₈	—	3	1	no	—
108	C₃×C₂²⋊C₈	—	3	1	no	—
109	C₃×C₄×C₈	—	3	1	no	—
110	#830	C₂×C₉	1	1	yes	characteristic, complemented
111	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
112	Dic₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
113	C₈×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
114	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
115	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	—	2	1	no	—
118	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
120	C₃×#67	C₃×C₈	1	4	yes	—
121	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
124	C₃×C₄×D₃	—	2	1	no	—
125	C₃×C₄×D₃	—	2	1	no	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	—	3	1	no	—
128	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
129	C₃²×C₈	—	2	1	no	—
130	C₃²×C₈	C₃×D₄	1	2	yes	—
131	C₃×C₃⋊C₈	—	2	1	no	—
132	C₃×C₃⋊C₈	—	2	1	no	—
133	D₄×C₉	—	3	4	no	—
134	C₂×C₄×C₉	—	2	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	1	no	—
140	C₂×C₄×C₉	—	3	1	no	—
141	C₂×C₄×C₉	—	3	1	no	—
142	C₂×C₄×C₉	—	3	1	no	—
143	C₂×C₄×C₉	—	6	1	no	—
144	C₂×C₄×C₉	—	6	1	no	—
145	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
146	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
147	C₈×C₉	—	2	2	no	—
148	C₈×C₉	—	2	1	no	—
149	C₈×C₉	—	2	2	no	—
150	C₈×C₉	—	6	1	no	—
151	C₈×C₉	—	6	1	no	—
152	C₈×C₉	#67	1	2	yes	direct product factor
153	C₈×D₄	—	3	1	no	Sylow
154	C₂×C₃×C₉	—	2	2	no	—
155	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₃×C₉	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₃×C₉	#131	1	1	yes	characteristic
158	D₃×C₉	—	2	2	no	—
159	C₂×C₃×D₄	—	3	1	no	—
160	C₂²×C₃×C₄	—	2	1	no	—
161	C₂²×C₃×C₄	—	3	1	no	—
162	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
164	C₂×#67	C₄×C₉	1	1	yes	characteristic
165	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
166	C₂×C₃×C₈	—	2	4	no	—
167	C₂×C₃×C₈	—	2	2	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	1	no	—
171	C₂×C₃×C₈	—	3	1	no	—
172	C₂×C₃×C₈	—	3	1	no	—
173	C₂×C₃×C₈	—	6	2	no	—
174	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
176	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
178	C₃×C₄⋊C₄	—	3	1	no	—
179	C₃×C₂²⋊C₄	—	3	1	no	—
180	C₃×C₂²⋊C₄	—	3	1	no	—
181	C₃×C₄²	—	3	1	no	—
182	#217	C₄×C₉	1	1	yes	characteristic
183	(C₂×D₃)⋊C₄	C₄×C₉	1	1	yes	characteristic
184	Dic₃⋊C₄	C₄×C₉	1	1	yes	characteristic
185	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
186	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
187	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
188	D₃×C₈	—	2	2	no	—
189	C₂²×C₃²	—	2	1	no	—
190	C₂²×C₃²	—	2	1	no	—
191	C₂²×C₃²	C₂×C₃×C₈	1	2	yes	—
192	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
193	C₂×C₃×D₃	—	2	1	no	—
194	C₂×C₃×D₃	—	2	1	no	—
195	C₂×C₃×D₃	C₂×C₃×C₈	1	2	yes	—
196	C₃²×C₄	—	2	1	no	—
197	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
198	C₃²×C₄	C₃×#41	1	1	yes	characteristic
199	C₃×Dic₃	—	2	1	no	—
200	C₃×Dic₃	—	2	1	no	—
201	C₃×Dic₃	C₂×C₃×C₈	1	2	yes	—
202	C₂²×C₉	—	2	2	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	2	1	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	3	2	no	—
209	C₂²×C₉	—	6	1	no	—
210	C₂²×C₉	—	6	1	no	—
211	C₂²×C₉	D₃×C₈	1	2	yes	complemented
212	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
213	C₄×C₉	—	2	2	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	1	no	—
216	C₄×C₉	—	2	1	no	—
217	C₄×C₉	—	3	2	no	—
218	C₄×C₉	—	6	1	no	—
219	C₄×C₉	—	6	1	no	—
220	C₄×C₉	#235	1	1	yes	characteristic
221	C₄×C₉	C₂×#67	1	1	yes	characteristic
222	C₂²×C₈	—	3	1	no	—
223	C₂²×C₈	D₃×C₉	1	1	yes	characteristic, complemented
224	C₄×D₄	—	3	1	no	—
225	C₄⋊C₈	—	3	1	no	—
226	C₂²⋊C₈	—	3	1	no	—
227	C₂²⋊C₈	—	3	1	no	—
228	C₄×C₈	—	3	1	no	—
229	C₃×C₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₃	—	2	1	no	—
231	C₂³×C₃	—	3	1	no	—
232	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic
233	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
234	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
235	C₃×D₄	—	3	4	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	3	1	no	—
245	C₂×C₃×C₄	—	3	1	no	—
246	C₂×C₃×C₄	—	3	1	no	—
247	C₂×C₃×C₄	—	6	1	no	—
248	C₂×C₃×C₄	—	6	1	no	—
249	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
251	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
253	#67	C₈×C₉	1	4	yes	direct product factor
254	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
255	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
256	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
257	C₄×D₃	—	2	1	no	—
258	C₄×D₃	—	2	1	no	—
259	C₃×C₈	—	2	2	no	—
260	C₃×C₈	—	2	1	no	—
261	C₃×C₈	—	2	1	no	—
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	6	1	no	—
264	C₃×C₈	—	6	1	no	—
265	C₃×C₈	D₄×C₉	1	2	yes	complemented
266	C₃×C₈	C₃×#67	1	2	yes	—
267	C₃⋊C₈	—	2	1	no	—
268	C₃⋊C₈	—	2	1	no	—
269	C₂×C₃²	—	2	2	no	—
270	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
271	C₂×C₃²	C₂²×C₃×C₈	1	1	yes	characteristic
272	C₂×C₃²	C₃×#131	1	1	yes	characteristic
273	C₃×D₃	—	2	2	no	—
274	C₂×C₉	—	2	4	no	—
275	C₂×C₉	—	2	2	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	—	2	1	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	—	6	2	no	—
280	C₂×C₉	C₂×D₃×C₈	1	1	yes	characteristic
281	C₂×C₉	#901	1	1	yes	characteristic
282	C₂×C₉	C₄×#67	1	1	yes	characteristic
283	C₂×D₄	—	3	1	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	3	1	no	—
288	C₂×C₈	—	3	1	no	—
289	C₂×C₈	—	6	2	no	—
290	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
291	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
292	C₄⋊C₄	—	3	1	no	—
293	C₂²⋊C₄	—	3	1	no	—
294	C₂²⋊C₄	—	3	1	no	—
295	C₄²	—	3	1	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	3	2	no	—
305	C₂²×C₃	—	6	1	no	—
306	C₂²×C₃	—	6	1	no	—
307	C₂²×C₃	C₂×C₈×C₉	1	2	yes	complemented
308	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
309	C₂²×C₃	C₃×D₃×C₈	1	2	yes	—
310	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
311	C₂×D₃	—	2	1	no	—
312	C₂×D₃	—	2	1	no	—
313	C₂×D₃	C₂×C₈×C₉	1	2	yes	complemented
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	2	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	3	2	no	—
320	C₃×C₄	—	6	1	no	—
321	C₃×C₄	—	6	1	no	—
322	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
323	C₃×C₄	C₉×#41	1	1	yes	characteristic
324	C₃×C₄	C₃×#235	1	1	yes	characteristic
325	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
326	Dic₃	—	2	1	no	—
327	Dic₃	—	2	1	no	—
328	Dic₃	C₂×C₈×C₉	1	2	yes	complemented
329	C₃²	C₃×C₈×D₄	1	1	yes	characteristic
330	C₉	—	2	1	no	—
331	C₉	C₈×#67	1	1	yes	characteristic, direct product factor
332	C₂³	—	3	1	no	—
333	C₂³	C₄×D₃×C₉	1	1	yes	characteristic
334	D₄	—	3	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	3	1	no	—
338	C₂×C₄	—	3	1	no	—
339	C₂×C₄	—	3	1	no	—
340	C₂×C₄	—	6	1	no	—
341	C₂×C₄	—	6	1	no	—
342	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
344	C₈	—	2	1	no	—
345	C₈	—	6	1	no	—
346	C₈	—	6	1	no	—
347	C₈	C₉×#67	1	2	yes	direct product factor
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	6	2	no	—
355	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
356	C₂×C₃	C₂²×C₈×C₉	1	1	yes	characteristic
357	C₂×C₃	C₉×#131	1	1	yes	characteristic
358	C₂×C₃	C₂×C₃×D₃×C₈	1	1	yes	characteristic
359	C₂×C₃	C₃×#901	1	1	yes	characteristic
360	C₂×C₃	C₃×C₄×#67	1	1	yes	characteristic
361	D₃	—	2	2	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	3	2	no	—
365	C₂²	—	6	1	no	—
366	C₂²	—	6	1	no	—
367	C₂²	D₃×C₈×C₉	1	2	yes	complemented
368	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	3	2	no	—
371	C₄	—	6	1	no	—
372	C₄	—	6	1	no	—
373	C₄	C₉×#235	1	1	yes	characteristic
374	C₄	C₂×C₉×#67	1	1	yes	characteristic
375	C₃	—	2	1	no	—
376	C₃	C₈×D₄×C₉	1	1	yes	characteristic, complemented
377	C₃	C₃×C₈×#67	1	1	yes	characteristic
378	C₂	—	2	2	no	—
379	C₂	—	6	2	no	—
380	C₂	C₂×D₃×C₈×C₉	1	1	yes	characteristic
381	C₂	C₉×#901	1	1	yes	characteristic
382	C₂	C₄×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₉	C₂×D₃
commutator	C₂×C₃	C₂²×C₈×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂²×C₃×C₈×C₉	C₂
socle	C₂²×C₃²	C₂²×C₃×C₄
prime radical	C₂×C₃×#67	C₃×C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂²×C₈×C₉	D₃
hypocenter	C₃	C₈×D₄×C₉
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₈×C₉ ◁ C₂²×C₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₈×C₉	C₂	semidirect
3. C₂×D₃×C₈×C₉	C₂	semidirect
4. C₉×#830	C₂	semidirect
5. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
6. C₉×Dic₃⋊C₈	C₂	semidirect
7. C₈×C₉×Dic₃	C₂	semidirect
32. C₂²×C₈×C₉	D₃	semidirect
44. C₉×#67	C₈	direct (N × H)
51. C₃×C₈×C₉	D₄	semidirect
55. C₈×#67	C₉	direct (N × H)
88. C₂²×C₃×C₉	C₂×C₈	semidirect
92. C₂×D₃×C₉	C₂×C₈	semidirect
98. C₉×Dic₃	C₂×C₈	semidirect
101. C₂²×C₃×C₈	C₂×C₉	semidirect
105. C₂×D₃×C₈	C₂×C₉	semidirect
110. #830	C₂×C₉	semidirect
111. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
112. Dic₃⋊C₈	C₂×C₉	semidirect
113. C₈×Dic₃	C₂×C₉	semidirect
152. C₈×C₉	#67	direct (N × H)
211. C₂²×C₉	D₃×C₈	semidirect
223. C₂²×C₈	D₃×C₉	semidirect
229. C₃×C₉	C₈×D₄	semidirect
253. #67	C₈×C₉	direct (N × H)
265. C₃×C₈	D₄×C₉	semidirect
307. C₂²×C₃	C₂×C₈×C₉	semidirect
313. C₂×D₃	C₂×C₈×C₉	semidirect
328. Dic₃	C₂×C₈×C₉	semidirect
331. C₉	C₈×#67	direct (N × H)
347. C₈	C₉×#67	direct (N × H)
367. C₂²	D₃×C₈×C₉	semidirect
376. C₃	C₈×D₄×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₈×C₉	2
C₄×C₉×#67	2
C₂×D₃×C₈×C₉	2
C₉×#830	2
C₉×(C₂×D₃)⋊C₈	2
C₉×Dic₃⋊C₈	2
C₈×C₉×Dic₃	2
C₃×C₈×#67	3
C₈×D₄×C₉	3

Subgroups — C8×C9×#67 #13143101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₉×#67 #13143101