Subgroups — C₉×Dic₃×C₂²⋊C₄ #13142463

Order 1728.

906 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₉×Dic₃	C₂	1	2	yes	maximal, complemented
5	C₉×C₃⋊#95	C₂	1	2	yes	maximal, complemented
6	C₃×Dic₃×C₂²⋊C₄	C₃	1	1	yes	maximal, characteristic
7	C₄×C₉×C₂²⋊C₄	—	3	1	no	maximal
8	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
10	C₂²×C₉×Dic₃	—	2	4	no	—
11	C₂²×C₉×Dic₃	C₄	1	4	yes	complemented
12	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
14	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
15	C₃×C₉×C₂²⋊C₄	C₄	1	4	yes	complemented
16	C₉×#217	C₄	1	4	yes	complemented
17	C₄×C₉×Dic₃	—	2	4	no	—
18	C₂³×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
19	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
20	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×C₄×Dic₃	C₂×C₃	1	2	yes	—
22	C₂³×C₄×C₉	—	3	1	no	—
23	C₃×C₃⋊#95	C₂×C₃	1	2	yes	—
24	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
25	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
26	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic
27	C₂×C₄²×C₉	—	3	2	no	—
28	C₉×#95	—	3	2	no	—
29	C₂³×C₃×C₉	—	2	2	no	—
30	C₂³×C₃×C₉	—	2	2	no	—
31	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
32	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
33	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
34	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₄×C₉	—	2	2	no	—
36	C₂×C₃×C₄×C₉	—	2	2	no	—
37	C₂×C₃×C₄×C₉	C₂×C₄	1	4	yes	complemented
38	C₂×C₉×Dic₃	—	2	2	no	—
39	C₂×C₉×Dic₃	—	2	2	no	—
40	C₂×C₉×Dic₃	—	2	2	no	—
41	C₂×C₉×Dic₃	—	2	8	no	—
42	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
43	C₂×C₉×Dic₃	C₂×C₄	1	2	yes	—
44	C₂×C₉×Dic₃	C₂×C₄	1	4	yes	complemented
45	C₂×C₉×Dic₃	D₄	1	4	yes	—
46	C₃×C₄×C₂²⋊C₄	—	3	1	no	—
47	Dic₃×C₂²⋊C₄	C₉	1	1	yes	characteristic, direct product factor
48	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
49	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
50	C₂²×C₃×Dic₃	—	2	4	no	—
51	C₂²×C₃×Dic₃	C₃×C₄	1	4	yes	—
52	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
53	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
54	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
55	C₂⁴×C₉	—	2	1	no	—
56	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
57	C₃²×C₂²⋊C₄	C₃×C₄	1	4	yes	—
58	C₃×#217	C₃×C₄	1	4	yes	—
59	C₃×C₄×Dic₃	—	2	4	no	—
60	C₂²×C₄×C₉	—	2	2	no	—
61	C₂²×C₄×C₉	—	3	1	no	—
62	C₂²×C₄×C₉	—	3	4	no	—
63	C₂²×C₄×C₉	—	3	2	no	—
64	C₂²×C₄×C₉	—	3	1	no	—
65	C₂²×C₄×C₉	—	6	4	no	—
66	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
67	C₉×C₂²⋊C₄	—	2	4	no	—
68	C₉×C₂²⋊C₄	—	3	4	no	—
69	C₉×C₂²⋊C₄	Dic₃	1	4	yes	direct product factor
70	C₄²×C₉	—	6	4	no	—
71	C₂²×C₃×C₉	—	2	2	no	—
72	C₂²×C₃×C₉	—	2	2	no	—
73	C₂²×C₃×C₉	—	2	4	no	—
74	C₂²×C₃×C₉	—	2	4	no	—
75	C₂²×C₃×C₉	C₄²	1	4	yes	complemented
76	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
80	C₂²×C₃×C₉	#41	1	2	yes	—
81	C₃×C₄×C₉	—	2	4	no	—
82	C₉×Dic₃	—	2	2	no	—
83	C₉×Dic₃	—	2	4	no	—
84	C₉×Dic₃	C₂²⋊C₄	1	4	yes	direct product factor
85	C₂³×C₃×C₄	—	3	1	no	—
86	C₂³×Dic₃	C₂×C₉	1	1	yes	characteristic
87	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
89	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
90	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
91	C₂×C₃×C₄²	—	3	2	no	—
92	C₂×#217	C₂×C₉	1	1	yes	characteristic
93	C₂×C₄×Dic₃	C₂×C₉	1	2	yes	complemented
94	C₃×#95	—	3	2	no	—
95	C₃⋊#95	C₂×C₉	1	2	yes	complemented
96	C₂³×C₃²	—	2	2	no	—
97	C₂³×C₃²	—	2	2	no	—
98	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
99	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
100	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
101	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
102	C₂×C₃²×C₄	—	2	2	no	—
103	C₂×C₃²×C₄	—	2	2	no	—
104	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
105	C₂×C₃×Dic₃	—	2	2	no	—
106	C₂×C₃×Dic₃	—	2	2	no	—
107	C₂×C₃×Dic₃	—	2	2	no	—
108	C₂×C₃×Dic₃	—	2	8	no	—
109	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
110	C₂×C₃×Dic₃	C₂×C₃×C₄	1	2	yes	—
111	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
112	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
113	C₂³×C₉	—	2	2	no	—
114	C₂³×C₉	—	2	2	no	—
115	C₂³×C₉	—	2	2	no	—
116	C₂³×C₉	—	2	2	no	—
117	C₂³×C₉	—	2	2	no	—
118	C₂³×C₉	—	2	1	no	—
119	C₂³×C₉	—	4	2	no	—
120	C₂³×C₉	—	4	2	no	—
121	C₂³×C₉	C₄×D₃	1	2	yes	—
122	C₂³×C₉	C₄×D₃	1	2	yes	—
123	C₂³×C₉	C₂×Dic₃	1	2	yes	—
124	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
125	C₂×C₄×C₉	—	2	2	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	4	no	—
128	C₂×C₄×C₉	—	3	2	no	—
129	C₂×C₄×C₉	—	3	4	no	—
130	C₂×C₄×C₉	—	3	2	no	—
131	C₂×C₄×C₉	—	3	4	no	—
132	C₂×C₄×C₉	—	4	2	no	—
133	C₂×C₄×C₉	—	4	2	no	—
134	C₂×C₄×C₉	—	6	8	no	—
135	C₂×C₄×C₉	—	6	2	no	—
136	C₂×C₄×C₉	—	6	2	no	—
137	C₂×C₄×C₉	—	6	2	no	—
138	C₂×C₄×C₉	C₂×Dic₃	1	4	yes	complemented
139	C₄×C₂²⋊C₄	—	3	1	no	Sylow
140	C₂×C₃×C₉	—	2	4	no	—
141	C₂×C₃×C₉	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₃×C₉	#117	1	1	yes	characteristic
144	C₂×C₃×C₉	C₄×D₄	1	2	yes	—
145	C₂×C₃×C₉	C₄×D₄	1	2	yes	—
146	C₂⁴×C₃	—	2	1	no	—
147	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
148	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
149	C₂²×C₃×C₄	—	2	2	no	—
150	C₂²×C₃×C₄	—	3	1	no	—
151	C₂²×C₃×C₄	—	3	4	no	—
152	C₂²×C₃×C₄	—	3	1	no	—
153	C₂²×C₃×C₄	—	3	2	no	—
154	C₂²×C₃×C₄	—	6	4	no	—
155	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
156	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
157	C₂²×Dic₃	—	2	4	no	—
158	C₂²×Dic₃	C₄×C₉	1	4	yes	complemented
159	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
160	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
161	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
162	C₃×C₂²⋊C₄	—	2	4	no	—
163	C₃×C₂²⋊C₄	—	3	4	no	—
164	C₃×C₂²⋊C₄	C₄×C₉	1	4	yes	complemented
165	C₃×C₂²⋊C₄	C₃×Dic₃	1	4	yes	—
166	C₃×C₄²	—	6	4	no	—
167	#217	C₄×C₉	1	4	yes	complemented
168	C₄×Dic₃	—	2	4	no	—
169	C₂²×C₃²	—	2	2	no	—
170	C₂²×C₃²	—	2	2	no	—
171	C₂²×C₃²	—	2	4	no	—
172	C₂²×C₃²	—	2	4	no	—
173	C₂²×C₃²	C₃×C₄²	1	4	yes	—
174	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
175	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
176	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
177	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
178	C₂²×C₃²	C₃×#41	1	2	yes	—
179	C₃²×C₄	—	2	4	no	—
180	C₃×Dic₃	—	2	2	no	—
181	C₃×Dic₃	—	2	4	no	—
182	C₃×Dic₃	C₃×C₂²⋊C₄	1	4	yes	—
183	C₂²×C₉	—	2	2	no	—
184	C₂²×C₉	—	2	2	no	—
185	C₂²×C₉	—	2	4	no	—
186	C₂²×C₉	—	2	4	no	—
187	C₂²×C₉	—	2	4	no	—
188	C₂²×C₉	—	2	1	no	—
189	C₂²×C₉	—	2	1	no	—
190	C₂²×C₉	—	2	2	no	—
191	C₂²×C₉	—	2	2	no	—
192	C₂²×C₉	—	2	1	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	—	4	2	no	—
195	C₂²×C₉	—	4	4	no	—
196	C₂²×C₉	—	4	4	no	—
197	C₂²×C₉	C₄×Dic₃	1	4	yes	complemented
198	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
199	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
200	C₂²×C₉	D₃×D₄	1	2	yes	—
201	C₂²×C₉	#237	1	2	yes	—
202	C₂²×C₉	C₂²×Dic₃	1	1	yes	characteristic
203	C₄×C₉	—	2	4	no	—
204	C₄×C₉	—	3	4	no	—
205	C₄×C₉	—	4	4	no	—
206	C₄×C₉	—	6	2	no	—
207	C₄×C₉	—	6	4	no	—
208	C₂³×C₄	—	3	1	no	—
209	C₂×C₂²⋊C₄	—	3	1	no	—
210	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic
211	C₂×C₄²	—	3	2	no	—
212	#95	—	3	2	no	—
213	C₃×C₉	C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	2	no	—
216	C₂³×C₃	—	2	2	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	2	no	—
219	C₂³×C₃	—	2	2	no	—
220	C₂³×C₃	—	2	2	no	—
221	C₂³×C₃	—	2	1	no	—
222	C₂³×C₃	—	4	2	no	—
223	C₂³×C₃	—	4	2	no	—
224	C₂³×C₃	C₂×C₄×C₉	1	2	yes	—
225	C₂³×C₃	C₂×C₄×C₉	1	2	yes	—
226	C₂³×C₃	C₂×C₄×C₉	1	2	yes	—
227	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
228	C₂³×C₃	C₃×C₄×D₃	1	2	yes	—
229	C₂³×C₃	C₃×C₄×D₃	1	2	yes	—
230	C₂³×C₃	C₂×C₃×Dic₃	1	2	yes	—
231	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	3	2	no	—
238	C₂×C₃×C₄	—	3	4	no	—
239	C₂×C₃×C₄	—	3	4	no	—
240	C₂×C₃×C₄	—	3	2	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	6	8	no	—
244	C₂×C₃×C₄	—	6	2	no	—
245	C₂×C₃×C₄	—	6	2	no	—
246	C₂×C₃×C₄	—	6	2	no	—
247	C₂×C₃×C₄	C₂×C₄×C₉	1	4	yes	complemented
248	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
249	C₂×Dic₃	—	2	2	no	—
250	C₂×Dic₃	—	2	2	no	—
251	C₂×Dic₃	—	2	2	no	—
252	C₂×Dic₃	—	2	8	no	—
253	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
254	C₂×Dic₃	C₂×C₄×C₉	1	2	yes	—
255	C₂×Dic₃	C₂×C₄×C₉	1	4	yes	complemented
256	C₂×Dic₃	D₄×C₉	1	4	yes	—
257	C₂×C₃²	—	2	4	no	—
258	C₂×C₃²	C₂×C₃×C₄²	1	1	yes	characteristic
259	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₃²	C₃×#117	1	1	yes	characteristic
261	C₂×C₃²	C₃×C₄×D₄	1	2	yes	—
262	C₂×C₃²	C₃×C₄×D₄	1	2	yes	—
263	C₂×C₉	—	2	4	no	—
264	C₂×C₉	—	2	1	no	—
265	C₂×C₉	—	2	1	no	—
266	C₂×C₉	—	2	2	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	—	2	2	no	—
269	C₂×C₉	—	4	4	no	—
270	C₂×C₉	#877	1	1	yes	characteristic
271	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₉	#67⋊C₄	1	2	yes	—
273	C₂×C₉	C₂×C₄×Dic₃	1	1	yes	characteristic
274	C₂×C₉	D₄×Dic₃	1	2	yes	—
275	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
276	C₂²×C₄	—	3	1	no	—
277	C₂²×C₄	—	3	4	no	—
278	C₂²×C₄	—	3	1	no	—
279	C₂²×C₄	—	3	2	no	—
280	C₂²×C₄	—	6	4	no	—
281	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
282	C₂²⋊C₄	—	3	4	no	—
283	C₂²⋊C₄	C₉×Dic₃	1	4	yes	direct product factor
284	C₄²	—	6	4	no	—
285	C₂²×C₃	—	2	2	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	4	no	—
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	2	1	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	4	no	—
299	C₂²×C₃	—	4	4	no	—
300	C₂²×C₃	—	4	2	no	—
301	C₂²×C₃	—	4	2	no	—
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	C₄²×C₉	1	4	yes	complemented
304	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
305	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
306	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
307	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
308	C₂²×C₃	C₉×#41	1	2	yes	—
309	C₂²×C₃	C₃×C₄×Dic₃	1	4	yes	—
310	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
311	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
312	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
313	C₂²×C₃	C₃×#237	1	2	yes	—
314	C₂²×C₃	C₂²×C₃×Dic₃	1	1	yes	characteristic
315	C₃×C₄	—	2	4	no	—
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	—	3	4	no	—
318	C₃×C₄	—	4	4	no	—
319	C₃×C₄	—	6	2	no	—
320	C₃×C₄	—	6	4	no	—
321	Dic₃	—	2	2	no	—
322	Dic₃	—	2	4	no	—
323	Dic₃	C₉×C₂²⋊C₄	1	4	yes	direct product factor
324	C₃²	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
325	C₉	—	2	1	no	—
326	C₉	Dic₃×C₂²⋊C₄	1	1	yes	characteristic, direct product factor
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	C₄×D₃×C₉	1	2	yes	—
330	C₂³	C₄×D₃×C₉	1	2	yes	—
331	C₂³	C₂×C₉×Dic₃	1	2	yes	—
332	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	3	2	no	—
336	C₂×C₄	—	3	4	no	—
337	C₂×C₄	—	3	4	no	—
338	C₂×C₄	—	3	2	no	—
339	C₂×C₄	—	6	8	no	—
340	C₂×C₄	—	6	2	no	—
341	C₂×C₄	—	6	2	no	—
342	C₂×C₄	—	6	2	no	—
343	C₂×C₄	C₂×C₉×Dic₃	1	4	yes	complemented
344	C₂×C₃	—	2	4	no	—
345	C₂×C₃	—	2	4	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	2	no	—
351	C₂×C₃	—	4	4	no	—
352	C₂×C₃	C₂×C₄²×C₉	1	1	yes	characteristic
353	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
354	C₂×C₃	C₉×#117	1	1	yes	characteristic
355	C₂×C₃	C₄×D₄×C₉	1	2	yes	—
356	C₂×C₃	C₄×D₄×C₉	1	2	yes	—
357	C₂×C₃	C₃×#877	1	1	yes	characteristic
358	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
359	C₂×C₃	C₃×#67⋊C₄	1	2	yes	—
360	C₂×C₃	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
361	C₂×C₃	C₃×D₄×Dic₃	1	2	yes	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	C₄×C₉×Dic₃	1	4	yes	complemented
367	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
368	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
369	C₂²	D₃×D₄×C₉	1	2	yes	—
370	C₂²	C₉×#237	1	2	yes	—
371	C₂²	C₂²×C₉×Dic₃	1	1	yes	characteristic
372	C₄	—	2	4	no	—
373	C₄	—	3	4	no	—
374	C₄	—	6	2	no	—
375	C₄	—	6	4	no	—
376	C₃	—	2	1	no	—
377	C₃	C₄×C₉×C₂²⋊C₄	1	1	yes	characteristic, complemented
378	C₃	C₃×Dic₃×C₂²⋊C₄	1	1	yes	characteristic
379	C₂	—	2	4	no	—
380	C₂	C₉×#877	1	1	yes	characteristic
381	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
382	C₂	C₉×#67⋊C₄	1	2	yes	—
383	C₂	C₂×C₄×C₉×Dic₃	1	1	yes	characteristic
384	C₂	D₄×C₉×Dic₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂×C₃	C₂×C₄²×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂⁴×C₃²	C₂²×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₄×C₉×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₂×C₄×C₉×Dic₃	C₂	semidirect
5. C₉×C₃⋊#95	C₂	semidirect
11. C₂²×C₉×Dic₃	C₄	semidirect
15. C₃×C₉×C₂²⋊C₄	C₄	semidirect
16. C₉×#217	C₄	semidirect
37. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
44. C₂×C₉×Dic₃	C₂×C₄	semidirect
47. Dic₃×C₂²⋊C₄	C₉	direct (N × H)
69. C₉×C₂²⋊C₄	Dic₃	direct (N × H)
75. C₂²×C₃×C₉	C₄²	semidirect
84. C₉×Dic₃	C₂²⋊C₄	direct (N × H)
93. C₂×C₄×Dic₃	C₂×C₉	semidirect
95. C₃⋊#95	C₂×C₉	semidirect
138. C₂×C₄×C₉	C₂×Dic₃	semidirect
158. C₂²×Dic₃	C₄×C₉	semidirect
164. C₃×C₂²⋊C₄	C₄×C₉	semidirect
167. #217	C₄×C₉	semidirect
197. C₂²×C₉	C₄×Dic₃	semidirect
213. C₃×C₉	C₄×C₂²⋊C₄	semidirect
247. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
255. C₂×Dic₃	C₂×C₄×C₉	semidirect
283. C₂²⋊C₄	C₉×Dic₃	direct (N × H)
303. C₂²×C₃	C₄²×C₉	semidirect
323. Dic₃	C₉×C₂²⋊C₄	direct (N × H)
326. C₉	Dic₃×C₂²⋊C₄	direct (N × H)
343. C₂×C₄	C₂×C₉×Dic₃	semidirect
366. C₂²	C₄×C₉×Dic₃	semidirect
377. C₃	C₄×C₉×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₉×Dic₃	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₂×C₄×C₉×Dic₃	2
C₉×C₃⋊#95	2
C₃×Dic₃×C₂²⋊C₄	3
C₄×C₉×C₂²⋊C₄	3

Subgroups — C9×Dic3×C22⋊C4 #13142463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₃×C₂²⋊C₄ #13142463