Subgroups — C₂×D₃×C₉×C₂²⋊C₄ #13152344

Order 1728.

2154 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	C₂⁴×D₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₃×C₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	D₃×C₉×C₂²⋊C₄	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×D₃×C₂²⋊C₄	C₃	1	1	yes	maximal, characteristic
8	C₂²×C₉×C₂²⋊C₄	—	3	1	no	maximal
9	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
10	C₂³×D₃×C₉	—	2	8	no	—
11	C₂³×D₃×C₉	C₄	1	8	yes	complemented
12	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
13	C₂³×D₃×C₉	C₂²	1	4	yes	—
14	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	complemented
16	C₂²×C₉×Dic₃	C₂²	1	2	yes	complemented
17	C₂×C₄×D₃×C₉	—	2	8	no	—
18	C₂×C₄×D₃×C₉	C₂²	1	8	yes	complemented
19	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
20	C₉×#217	C₂²	1	4	yes	complemented
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
22	C₂⁴×C₃×D₃	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₃	C₂×C₃	1	2	yes	—
24	C₂⁵×C₉	—	3	1	no	—
25	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
28	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	8	yes	—
29	C₂³×C₄×C₉	—	3	2	no	—
30	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
31	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
32	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
33	C₂×C₉×C₂²⋊C₄	—	3	8	no	—
34	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, direct product factor
35	C₂³×C₃×C₉	—	2	4	no	—
36	C₂³×C₃×C₉	C₂×C₄	1	4	yes	complemented
37	C₂³×C₃×C₉	C₂³	1	2	yes	—
38	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
39	C₂²×D₃×C₉	—	2	4	no	—
40	C₂²×D₃×C₉	—	2	32	no	—
41	C₂²×D₃×C₉	—	2	16	no	—
42	C₂²×D₃×C₉	C₂×C₄	1	4	yes	—
43	C₂²×D₃×C₉	C₂×C₄	1	16	yes	complemented
44	C₂²×D₃×C₉	C₂×C₄	1	4	yes	complemented
45	C₂²×D₃×C₉	D₄	1	8	yes	—
46	C₂²×D₃×C₉	C₂³	1	2	yes	—
47	C₂²×D₃×C₉	C₂³	1	2	yes	—
48	C₂×C₃×C₄×C₉	—	2	4	no	—
49	C₂×C₃×C₄×C₉	C₂³	1	4	yes	complemented
50	C₂×C₉×Dic₃	—	2	4	no	—
51	C₂×C₉×Dic₃	C₂³	1	4	yes	complemented
52	C₄×D₃×C₉	—	2	16	no	—
53	C₂²×C₃×C₂²⋊C₄	—	3	1	no	—
54	C₂×D₃×C₂²⋊C₄	C₉	1	1	yes	characteristic, direct product factor
55	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
56	C₂³×C₃×D₃	—	2	8	no	—
57	C₂³×C₃×D₃	C₃×C₄	1	8	yes	—
58	C₂³×C₃×D₃	C₂²×C₃	1	4	yes	—
59	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
60	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
62	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
63	C₂×C₃×C₄×D₃	—	2	8	no	—
64	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	—
65	C₂⁴×C₉	—	2	1	no	—
66	C₂⁴×C₉	—	3	1	no	—
67	C₂⁴×C₉	—	3	8	no	—
68	C₂⁴×C₉	—	3	4	no	—
69	C₂⁴×C₉	—	3	1	no	—
70	C₂⁴×C₉	—	6	8	no	—
71	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
72	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
73	C₃×#217	C₂²×C₃	1	4	yes	—
74	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
75	C₂²×C₄×C₉	—	2	2	no	—
76	C₂²×C₄×C₉	—	3	2	no	—
77	C₂²×C₄×C₉	—	3	8	no	—
78	C₂²×C₄×C₉	—	6	8	no	—
79	C₂²×C₄×C₉	C₂×D₃	1	2	yes	complemented
80	C₉×C₂²⋊C₄	—	2	4	no	—
81	C₉×C₂²⋊C₄	—	3	4	no	—
82	C₉×C₂²⋊C₄	—	3	8	no	—
83	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	direct product factor
84	C₂²×C₃×C₉	—	2	8	no	—
85	C₂²×C₃×C₉	—	2	4	no	—
86	C₂²×C₃×C₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₃×C₉	C₂²×C₄	1	4	yes	complemented
88	C₂²×C₃×C₉	C₂×D₄	1	4	yes	—
89	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
90	C₂×D₃×C₉	—	2	8	no	—
91	C₂×D₃×C₉	—	2	4	no	—
92	C₂×D₃×C₉	—	2	32	no	—
93	C₂×D₃×C₉	C₂²⋊C₄	1	16	yes	direct product factor
94	C₂×D₃×C₉	C₂²×C₄	1	4	yes	—
95	C₂×D₃×C₉	C₂²×C₄	1	4	yes	complemented
96	C₂×D₃×C₉	C₂×D₄	1	8	yes	—
97	C₃×C₄×C₉	—	2	4	no	—
98	C₉×Dic₃	—	2	4	no	—
99	C₂⁵×C₃	—	3	1	no	—
100	C₂⁴×D₃	C₂×C₉	1	1	yes	characteristic
101	C₂³×C₃×C₄	—	3	2	no	—
102	C₂²×C₄×D₃	C₂×C₉	1	2	yes	complemented
103	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
105	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
106	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
107	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
108	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
109	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
110	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	complemented
111	D₃×C₂²⋊C₄	C₂×C₉	1	8	yes	direct product factor
112	C₂³×C₃²	—	2	4	no	—
113	C₂³×C₃²	C₂×C₃×C₄	1	4	yes	—
114	C₂³×C₃²	C₂³×C₃	1	2	yes	—
115	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
116	C₂²×C₃×D₃	—	2	4	no	—
117	C₂²×C₃×D₃	—	2	32	no	—
118	C₂²×C₃×D₃	—	2	16	no	—
119	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
120	C₂²×C₃×D₃	C₂×C₃×C₄	1	16	yes	—
121	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
122	C₂²×C₃×D₃	C₃×D₄	1	8	yes	—
123	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
124	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
125	C₂×C₃²×C₄	—	2	4	no	—
126	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
127	C₂×C₃×Dic₃	—	2	4	no	—
128	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
129	C₃×C₄×D₃	—	2	16	no	—
130	C₂³×C₉	—	2	4	no	—
131	C₂³×C₉	—	2	4	no	—
132	C₂³×C₉	—	2	1	no	—
133	C₂³×C₉	—	2	2	no	—
134	C₂³×C₉	—	3	4	no	—
135	C₂³×C₉	—	3	8	no	—
136	C₂³×C₉	—	3	2	no	—
137	C₂³×C₉	—	3	4	no	—
138	C₂³×C₉	—	3	16	no	—
139	C₂³×C₉	—	3	2	no	—
140	C₂³×C₉	—	4	4	no	—
141	C₂³×C₉	—	6	32	no	—
142	C₂³×C₉	—	6	16	no	—
143	C₂³×C₉	—	6	4	no	—
144	C₂³×C₉	C₄×D₃	1	4	yes	complemented
145	C₂³×C₉	C₂²×D₃	1	2	yes	—
146	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₄×C₉	—	2	4	no	—
148	C₂×C₄×C₉	—	2	4	no	—
149	C₂×C₄×C₉	—	3	4	no	—
150	C₂×C₄×C₉	—	4	4	no	—
151	C₂×C₄×C₉	—	6	16	no	—
152	C₂×C₄×C₉	—	6	4	no	—
153	C₂×C₄×C₉	C₂²×D₃	1	4	yes	complemented
154	C₂²×C₂²⋊C₄	—	3	1	no	Sylow
155	C₂×C₃×C₉	—	2	4	no	—
156	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	4	yes	complemented
157	C₂×C₃×C₉	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₃×C₉	C₂²×D₄	1	2	yes	—
159	D₃×C₉	—	2	4	no	—
160	D₃×C₉	C₂×C₂²⋊C₄	1	8	yes	direct product factor
161	C₂⁴×C₃	—	2	1	no	—
162	C₂⁴×C₃	—	3	1	no	—
163	C₂⁴×C₃	—	3	8	no	—
164	C₂⁴×C₃	—	3	4	no	—
165	C₂⁴×C₃	—	3	1	no	—
166	C₂⁴×C₃	—	6	8	no	—
167	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
168	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
169	C₂³×D₃	—	2	8	no	—
170	C₂³×D₃	C₄×C₉	1	8	yes	complemented
171	C₂³×D₃	C₂²×C₉	1	4	yes	—
172	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
173	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
174	C₂²×C₃×C₄	—	2	2	no	—
175	C₂²×C₃×C₄	—	3	2	no	—
176	C₂²×C₃×C₄	—	3	8	no	—
177	C₂²×C₃×C₄	—	6	8	no	—
178	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	complemented
179	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
180	C₂²×Dic₃	C₂²×C₉	1	2	yes	complemented
181	C₂×C₄×D₃	—	2	8	no	—
182	C₂×C₄×D₃	C₂²×C₉	1	8	yes	complemented
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₂²⋊C₄	—	3	4	no	—
185	C₃×C₂²⋊C₄	—	3	8	no	—
186	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
187	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
188	#217	C₂²×C₉	1	4	yes	complemented
189	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	complemented
190	C₂²×C₃²	—	2	8	no	—
191	C₂²×C₃²	—	2	4	no	—
192	C₂²×C₃²	C₂²×C₃×C₄	1	2	yes	—
193	C₂²×C₃²	C₂²×C₃×C₄	1	4	yes	—
194	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
195	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
196	C₂×C₃×D₃	—	2	8	no	—
197	C₂×C₃×D₃	—	2	4	no	—
198	C₂×C₃×D₃	—	2	32	no	—
199	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	16	yes	—
200	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
201	C₂×C₃×D₃	C₂²×C₃×C₄	1	4	yes	—
202	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
203	C₃²×C₄	—	2	4	no	—
204	C₃×Dic₃	—	2	4	no	—
205	C₂²×C₉	—	2	8	no	—
206	C₂²×C₉	—	2	4	no	—
207	C₂²×C₉	—	2	1	no	—
208	C₂²×C₉	—	2	2	no	—
209	C₂²×C₉	—	2	4	no	—
210	C₂²×C₉	—	2	4	no	—
211	C₂²×C₉	—	3	16	no	—
212	C₂²×C₉	—	3	4	no	—
213	C₂²×C₉	—	3	8	no	—
214	C₂²×C₉	—	3	4	no	—
215	C₂²×C₉	—	4	8	no	—
216	C₂²×C₉	—	4	4	no	—
217	C₂²×C₉	—	6	32	no	—
218	C₂²×C₉	—	6	8	no	—
219	C₂²×C₉	—	6	4	no	—
220	C₂²×C₉	C₂×C₄×D₃	1	2	yes	—
221	C₂²×C₉	C₂×C₄×D₃	1	4	yes	complemented
222	C₂²×C₉	D₃×D₄	1	4	yes	—
223	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
224	C₄×C₉	—	2	4	no	—
225	C₄×C₉	—	4	4	no	—
226	C₄×C₉	—	6	4	no	—
227	C₂⁵	—	3	1	no	—
228	C₂³×C₄	—	3	2	no	—
229	C₂×C₂²⋊C₄	—	3	1	no	—
230	C₂×C₂²⋊C₄	—	3	2	no	—
231	C₂×C₂²⋊C₄	—	3	8	no	—
232	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, direct product factor
233	C₃×C₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	2	4	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	2	4	no	—
237	C₂³×C₃	—	2	1	no	—
238	C₂³×C₃	—	2	2	no	—
239	C₂³×C₃	—	3	2	no	—
240	C₂³×C₃	—	3	4	no	—
241	C₂³×C₃	—	3	8	no	—
242	C₂³×C₃	—	3	2	no	—
243	C₂³×C₃	—	3	4	no	—
244	C₂³×C₃	—	3	16	no	—
245	C₂³×C₃	—	4	4	no	—
246	C₂³×C₃	—	6	32	no	—
247	C₂³×C₃	—	6	16	no	—
248	C₂³×C₃	—	6	4	no	—
249	C₂³×C₃	C₂×C₄×C₉	1	4	yes	complemented
250	C₂³×C₃	C₂³×C₉	1	2	yes	—
251	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
252	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
253	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
254	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
255	C₂²×D₃	—	2	4	no	—
256	C₂²×D₃	—	2	32	no	—
257	C₂²×D₃	—	2	16	no	—
258	C₂²×D₃	C₂×C₄×C₉	1	4	yes	—
259	C₂²×D₃	C₂×C₄×C₉	1	16	yes	complemented
260	C₂²×D₃	C₂×C₄×C₉	1	4	yes	complemented
261	C₂²×D₃	D₄×C₉	1	8	yes	—
262	C₂²×D₃	C₂³×C₉	1	2	yes	—
263	C₂²×D₃	C₂³×C₉	1	2	yes	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	3	4	no	—
268	C₂×C₃×C₄	—	4	4	no	—
269	C₂×C₃×C₄	—	6	16	no	—
270	C₂×C₃×C₄	—	6	4	no	—
271	C₂×C₃×C₄	C₂³×C₉	1	4	yes	complemented
272	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
273	C₂×Dic₃	—	2	4	no	—
274	C₂×Dic₃	C₂³×C₉	1	4	yes	complemented
275	C₄×D₃	—	2	16	no	—
276	C₂×C₃²	—	2	4	no	—
277	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	4	yes	—
278	C₂×C₃²	C₂³×C₃×C₄	1	1	yes	characteristic
279	C₂×C₃²	C₂²×C₃×D₄	1	2	yes	—
280	C₃×D₃	—	2	4	no	—
281	C₃×D₃	C₂×C₃×C₂²⋊C₄	1	8	yes	—
282	C₂×C₉	—	2	4	no	—
283	C₂×C₉	—	2	4	no	—
284	C₂×C₉	—	2	1	no	—
285	C₂×C₉	—	2	2	no	—
286	C₂×C₉	—	3	8	no	—
287	C₂×C₉	—	4	4	no	—
288	C₂×C₉	—	6	4	no	—
289	C₂×C₉	D₃×C₂²⋊C₄	1	4	yes	direct product factor
290	C₂×C₉	C₂²×C₄×D₃	1	1	yes	characteristic
291	C₂×C₉	C₂×D₃×D₄	1	2	yes	—
292	C₂⁴	—	3	1	no	—
293	C₂⁴	—	3	8	no	—
294	C₂⁴	—	3	4	no	—
295	C₂⁴	—	3	1	no	—
296	C₂⁴	—	6	8	no	—
297	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	—	3	8	no	—
300	C₂²×C₄	—	6	8	no	—
301	C₂²×C₄	C₂×D₃×C₉	1	2	yes	complemented
302	C₂²⋊C₄	—	3	4	no	—
303	C₂²⋊C₄	—	3	8	no	—
304	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	direct product factor
305	C₂²×C₃	—	2	8	no	—
306	C₂²×C₃	—	2	8	no	—
307	C₂²×C₃	—	2	4	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	2	no	—
311	C₂²×C₃	—	2	4	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	3	16	no	—
314	C₂²×C₃	—	3	4	no	—
315	C₂²×C₃	—	3	8	no	—
316	C₂²×C₃	—	3	4	no	—
317	C₂²×C₃	—	4	4	no	—
318	C₂²×C₃	—	4	8	no	—
319	C₂²×C₃	—	6	32	no	—
320	C₂²×C₃	—	6	8	no	—
321	C₂²×C₃	—	6	4	no	—
322	C₂²×C₃	C₂²×C₄×C₉	1	2	yes	—
323	C₂²×C₃	C₂²×C₄×C₉	1	4	yes	complemented
324	C₂²×C₃	C₂×D₄×C₉	1	4	yes	—
325	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
326	C₂²×C₃	C₂×C₃×C₄×D₃	1	2	yes	—
327	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
328	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
329	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
330	C₂×D₃	—	2	8	no	—
331	C₂×D₃	—	2	4	no	—
332	C₂×D₃	—	2	32	no	—
333	C₂×D₃	C₉×C₂²⋊C₄	1	16	yes	direct product factor
334	C₂×D₃	C₂²×C₄×C₉	1	4	yes	—
335	C₂×D₃	C₂²×C₄×C₉	1	4	yes	complemented
336	C₂×D₃	C₂×D₄×C₉	1	8	yes	—
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	2	4	no	—
339	C₃×C₄	—	4	4	no	—
340	C₃×C₄	—	6	4	no	—
341	Dic₃	—	2	4	no	—
342	C₃²	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
343	C₉	—	2	1	no	—
344	C₉	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic, direct product factor
345	C₂³	—	2	4	no	—
346	C₂³	—	3	2	no	—
347	C₂³	—	3	4	no	—
348	C₂³	—	3	8	no	—
349	C₂³	—	3	2	no	—
350	C₂³	—	3	4	no	—
351	C₂³	—	3	16	no	—
352	C₂³	—	6	16	no	—
353	C₂³	—	6	32	no	—
354	C₂³	—	6	4	no	—
355	C₂³	C₄×D₃×C₉	1	4	yes	complemented
356	C₂³	C₂²×D₃×C₉	1	2	yes	—
357	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	3	4	no	—
360	C₂×C₄	—	6	16	no	—
361	C₂×C₄	—	6	4	no	—
362	C₂×C₄	C₂²×D₃×C₉	1	4	yes	complemented
363	C₂×C₃	—	2	4	no	—
364	C₂×C₃	—	2	4	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	2	4	no	—
368	C₂×C₃	—	3	8	no	—
369	C₂×C₃	—	4	4	no	—
370	C₂×C₃	—	6	4	no	—
371	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	4	yes	complemented
372	C₂×C₃	C₂³×C₄×C₉	1	1	yes	characteristic
373	C₂×C₃	C₂²×D₄×C₉	1	2	yes	—
374	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	4	yes	—
375	C₂×C₃	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
376	C₂×C₃	C₂×C₃×D₃×D₄	1	2	yes	—
377	D₃	—	2	4	no	—
378	D₃	C₂×C₉×C₂²⋊C₄	1	8	yes	direct product factor
379	C₂²	—	2	4	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	3	4	no	—
382	C₂²	—	3	8	no	—
383	C₂²	—	3	16	no	—
384	C₂²	—	3	4	no	—
385	C₂²	—	6	32	no	—
386	C₂²	—	6	4	no	—
387	C₂²	—	6	8	no	—
388	C₂²	C₂×C₄×D₃×C₉	1	2	yes	—
389	C₂²	C₂×C₄×D₃×C₉	1	4	yes	complemented
390	C₂²	D₃×D₄×C₉	1	4	yes	—
391	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
392	C₄	—	2	4	no	—
393	C₄	—	6	4	no	—
394	C₃	—	2	1	no	—
395	C₃	C₂²×C₉×C₂²⋊C₄	1	1	yes	characteristic, complemented
396	C₃	C₂×C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
397	C₂	—	2	4	no	—
398	C₂	—	3	8	no	—
399	C₂	—	6	4	no	—
400	C₂	D₃×C₉×C₂²⋊C₄	1	4	yes	direct product factor
401	C₂	C₂²×C₄×D₃×C₉	1	1	yes	characteristic
402	C₂	C₂×D₃×D₄×C₉	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂×C₃	C₂³×C₄×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂⁴×C₃×D₃	C₂×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂²×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
2. C₂²×C₄×D₃×C₉	C₂	semidirect
3. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
4. C₂×C₉×#217	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. D₃×C₉×C₂²⋊C₄	C₂	direct (N × H)
11. C₂³×D₃×C₉	C₄	semidirect
15. C₂²×C₃×C₄×C₉	C₂²	semidirect
16. C₂²×C₉×Dic₃	C₂²	semidirect
18. C₂×C₄×D₃×C₉	C₂²	semidirect
19. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
20. C₉×#217	C₂²	semidirect
21. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₂×C₉×C₂²⋊C₄	D₃	direct (N × H)
36. C₂³×C₃×C₉	C₂×C₄	semidirect
43. C₂²×D₃×C₉	C₂×C₄	semidirect
44. C₂²×D₃×C₉	C₂×C₄	semidirect
49. C₂×C₃×C₄×C₉	C₂³	semidirect
51. C₂×C₉×Dic₃	C₂³	semidirect
54. C₂×D₃×C₂²⋊C₄	C₉	direct (N × H)
79. C₂²×C₄×C₉	C₂×D₃	semidirect
83. C₉×C₂²⋊C₄	C₂×D₃	direct (N × H)
87. C₂²×C₃×C₉	C₂²×C₄	semidirect
93. C₂×D₃×C₉	C₂²⋊C₄	direct (N × H)
95. C₂×D₃×C₉	C₂²×C₄	semidirect
102. C₂²×C₄×D₃	C₂×C₉	semidirect
107. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
109. C₂×#217	C₂×C₉	semidirect
110. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
111. D₃×C₂²⋊C₄	C₂×C₉	direct (N × H)
144. C₂³×C₉	C₄×D₃	semidirect
153. C₂×C₄×C₉	C₂²×D₃	semidirect
156. C₂×C₃×C₉	C₂×C₂²⋊C₄	semidirect
160. D₃×C₉	C₂×C₂²⋊C₄	direct (N × H)
170. C₂³×D₃	C₄×C₉	semidirect
178. C₂²×C₃×C₄	C₂²×C₉	semidirect
180. C₂²×Dic₃	C₂²×C₉	semidirect
182. C₂×C₄×D₃	C₂²×C₉	semidirect
186. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
188. #217	C₂²×C₉	semidirect
189. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
221. C₂²×C₉	C₂×C₄×D₃	semidirect
232. C₂×C₂²⋊C₄	D₃×C₉	direct (N × H)
233. C₃×C₉	C₂²×C₂²⋊C₄	semidirect
249. C₂³×C₃	C₂×C₄×C₉	semidirect
259. C₂²×D₃	C₂×C₄×C₉	semidirect
260. C₂²×D₃	C₂×C₄×C₉	semidirect
271. C₂×C₃×C₄	C₂³×C₉	semidirect
274. C₂×Dic₃	C₂³×C₉	semidirect
289. C₂×C₉	D₃×C₂²⋊C₄	direct (N × H)
301. C₂²×C₄	C₂×D₃×C₉	semidirect
304. C₂²⋊C₄	C₂×D₃×C₉	direct (N × H)
323. C₂²×C₃	C₂²×C₄×C₉	semidirect
333. C₂×D₃	C₉×C₂²⋊C₄	direct (N × H)
335. C₂×D₃	C₂²×C₄×C₉	semidirect
344. C₉	C₂×D₃×C₂²⋊C₄	direct (N × H)
355. C₂³	C₄×D₃×C₉	semidirect
362. C₂×C₄	C₂²×D₃×C₉	semidirect
371. C₂×C₃	C₂×C₉×C₂²⋊C₄	semidirect
378. D₃	C₂×C₉×C₂²⋊C₄	direct (N × H)
389. C₂²	C₂×C₄×D₃×C₉	semidirect
395. C₃	C₂²×C₉×C₂²⋊C₄	semidirect
400. C₂	D₃×C₉×C₂²⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃×C₉	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₂×C₉×(C₂×D₃)⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₂×C₃×D₃×C₂²⋊C₄	3
C₂²×C₉×C₂²⋊C₄	3

Subgroups — C2×D3×C9×C22⋊C4 #13152344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₉×C₂²⋊C₄ #13152344