Subgroups — C₄×C₉×(C₂×D₃)⋊C₄ #13142403

Order 1728.

882 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄²×C₉	C₂	semidirect
4. C₂×C₄×C₉×Dic₃	C₂	semidirect
5. C₉×C₃⋊#95	C₂	semidirect
15. C₂×C₄×D₃×C₉	C₄	semidirect
17. C₉×(C₂×D₃)⋊C₄	C₄	direct (N × H)
28. C₂×C₄²×C₉	D₃	semidirect
39. C₂×C₃×C₄×C₉	C₂×C₄	semidirect
47. C₂×C₉×Dic₃	C₂×C₄	semidirect
50. C₄×(C₂×D₃)⋊C₄	C₉	direct (N × H)
85. C₂×D₃×C₉	C₄²	semidirect
87. C₃×C₄×C₉	C₂²⋊C₄	semidirect
95. C₂×C₃×C₄²	C₂×C₉	semidirect
98. C₂×C₄×Dic₃	C₂×C₉	semidirect
100. C₃⋊#95	C₂×C₉	semidirect
143. C₂×C₄×C₉	C₄×D₃	semidirect
170. C₂×C₄×D₃	C₄×C₉	semidirect
176. (C₂×D₃)⋊C₄	C₄×C₉	direct (N × H)
212. C₄×C₉	(C₂×D₃)⋊C₄	direct (N × H)
216. C₂×C₄²	D₃×C₉	semidirect
218. C₃×C₉	C₄×C₂²⋊C₄	semidirect
250. C₂×C₃×C₄	C₂×C₄×C₉	semidirect
262. C₂×Dic₃	C₂×C₄×C₉	semidirect
316. C₂×D₃	C₄²×C₉	semidirect
323. C₃×C₄	C₉×C₂²⋊C₄	semidirect
329. C₉	C₄×(C₂×D₃)⋊C₄	direct (N × H)
346. C₂×C₄	C₄×D₃×C₉	semidirect
379. C₄	C₉×(C₂×D₃)⋊C₄	direct (N × H)
381. 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
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₄²×C₉	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₄×C₉×Dic₃	2
C₉×C₃⋊#95	2
C₃×C₄×(C₂×D₃)⋊C₄	3
C₄×C₉×C₂²⋊C₄	3

Subgroups — C4×C9×(C2×D3)⋊C4 #13142403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×(C₂×D₃)⋊C₄ #13142403