Subgroups — C₂×C₉×#895 #13152418

Order 1728.

1370 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₉×#895	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#895	C₃	1	1	yes	maximal, characteristic
8	C₂×C₉×#121	—	3	1	no	maximal
9	C₂³×D₃×C₉	C₂²	1	2	yes	—
10	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₉×D₁₂	—	2	8	no	—
15	C₂×C₉×D₁₂	—	2	4	no	—
16	C₂×C₉×D₁₂	C₂²	1	8	yes	complemented
17	C₂×C₉×D₁₂	C₂²	1	4	yes	complemented
18	C₂×C₄×D₃×C₉	—	2	4	no	—
19	C₂×C₄×D₃×C₉	C₂²	1	4	yes	complemented
20	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
22	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₃×D₁₂	C₂×C₃	1	2	yes	—
24	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
25	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
27	C₃×#895	C₂×C₃	1	8	yes	—
28	C₂²×D₄×C₉	—	3	2	no	—
29	C₂²×D₄×C₉	—	3	1	no	—
30	C₂³×C₄×C₉	—	3	1	no	—
31	C₉×#121	—	3	8	no	—
32	C₂×C₉×C₄⋊C₄	—	2	1	no	—
33	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
34	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
35	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
36	C₂²×D₃×C₉	—	2	2	no	—
37	C₂²×D₃×C₉	—	2	2	no	—
38	C₂²×D₃×C₉	—	2	4	no	—
39	C₂²×D₃×C₉	—	2	4	no	—
40	C₂²×D₃×C₉	—	2	4	no	—
41	C₂²×D₃×C₉	D₄	1	4	yes	complemented
42	C₂²×D₃×C₉	C₂³	1	4	yes	—
43	C₂²×D₃×C₉	C₂³	1	2	yes	—
44	C₂×C₃×C₄×C₉	—	2	4	no	—
45	C₂×C₃×C₄×C₉	D₄	1	4	yes	complemented
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
48	C₂×C₉×Dic₃	—	2	2	no	—
49	C₂×C₉×Dic₃	C₂³	1	2	yes	—
50	C₉×D₁₂	—	2	16	no	—
51	C₉×D₁₂	—	2	8	no	—
52	C₄×D₃×C₉	—	2	8	no	—
53	C₂×C₃×#121	—	3	1	no	—
54	C₂×#895	C₉	1	1	yes	characteristic, direct product factor
55	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
56	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
58	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
59	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃×D₁₂	—	2	8	no	—
61	C₂×C₃×D₁₂	—	2	4	no	—
62	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
63	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
64	C₂×C₃×C₄×D₃	—	2	4	no	—
65	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
66	C₂⁴×C₉	—	3	1	no	—
67	C₂⁴×C₉	—	3	2	no	—
68	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
69	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
70	C₂×D₄×C₉	—	3	8	no	—
71	C₂×D₄×C₉	—	3	4	no	—
72	C₂×D₄×C₉	—	6	8	no	—
73	C₂×D₄×C₉	—	6	4	no	—
74	C₂²×C₄×C₉	—	2	1	no	—
75	C₂²×C₄×C₉	—	2	2	no	—
76	C₂²×C₄×C₉	—	3	1	no	—
77	C₂²×C₄×C₉	—	3	4	no	—
78	C₂²×C₄×C₉	—	6	4	no	—
79	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
80	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
81	C₉×C₄⋊C₄	—	2	4	no	—
82	C₉×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
83	C₉×C₂²⋊C₄	—	3	8	no	—
84	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
85	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
86	C₂²×C₃×C₉	#41	1	2	yes	—
87	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
88	C₂×D₃×C₉	—	2	8	no	—
89	C₂×D₃×C₉	—	2	2	no	—
90	C₂×D₃×C₉	—	2	2	no	—
91	C₂×D₃×C₉	—	2	4	no	—
92	C₂×D₃×C₉	—	2	4	no	—
93	C₂×D₃×C₉	—	2	4	no	—
94	C₂×D₃×C₉	—	4	8	no	—
95	C₂×D₃×C₉	C₂×D₄	1	4	yes	complemented
96	C₃×C₄×C₉	—	2	4	no	—
97	C₃×C₄×C₉	C₂×D₄	1	4	yes	complemented
98	C₉×Dic₃	—	2	2	no	—
99	C₂²×C₃×D₄	—	3	2	no	—
100	C₂²×C₃×D₄	—	3	1	no	—
101	C₂³×C₃×C₄	—	3	1	no	—
102	C₂²×D₁₂	C₂×C₉	1	2	yes	complemented
103	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
104	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic, complemented
105	C₃×#121	—	3	8	no	—
106	C₂×C₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
108	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
109	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
110	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	complemented
111	#895	C₂×C₉	1	8	yes	direct product factor
112	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
113	C₂²×C₃×D₃	—	2	2	no	—
114	C₂²×C₃×D₃	—	2	2	no	—
115	C₂²×C₃×D₃	—	2	4	no	—
116	C₂²×C₃×D₃	—	2	4	no	—
117	C₂²×C₃×D₃	—	2	4	no	—
118	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
119	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
120	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
123	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
124	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
125	C₂×C₃×Dic₃	—	2	2	no	—
126	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
127	C₃×D₁₂	—	2	16	no	—
128	C₃×D₁₂	—	2	8	no	—
129	C₃×C₄×D₃	—	2	8	no	—
130	C₂³×C₉	—	2	1	no	—
131	C₂³×C₉	—	3	4	no	—
132	C₂³×C₉	—	3	2	no	—
133	C₂³×C₉	—	3	4	no	—
134	C₂³×C₉	—	6	2	no	—
135	C₂³×C₉	—	6	2	no	—
136	C₂³×C₉	—	6	4	no	—
137	C₂³×C₉	—	6	4	no	—
138	C₂³×C₉	—	6	4	no	—
139	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
140	D₄×C₉	—	6	16	no	—
141	D₄×C₉	—	6	8	no	—
142	C₂×C₄×C₉	—	2	4	no	—
143	C₂×C₄×C₉	—	2	4	no	—
144	C₂×C₄×C₉	—	2	2	no	—
145	C₂×C₄×C₉	—	2	4	no	—
146	C₂×C₄×C₉	—	3	2	no	—
147	C₂×C₄×C₉	—	4	4	no	—
148	C₂×C₄×C₉	—	6	2	no	—
149	C₂×C₄×C₉	—	6	8	no	—
150	C₂×C₄×C₉	D₁₂	1	4	yes	complemented
151	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
152	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
153	C₂×#121	—	3	1	no	Sylow
154	C₂×C₃×C₉	#121	1	4	yes	complemented
155	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
158	D₃×C₉	—	2	4	no	—
159	D₃×C₉	—	4	4	no	—
160	C₂⁴×C₃	—	3	1	no	—
161	C₂⁴×C₃	—	3	2	no	—
162	C₂³×D₃	C₂²×C₉	1	2	yes	—
163	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
164	C₂×C₃×D₄	—	3	8	no	—
165	C₂×C₃×D₄	—	3	4	no	—
166	C₂×C₃×D₄	—	6	8	no	—
167	C₂×C₃×D₄	—	6	4	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	2	no	—
170	C₂²×C₃×C₄	—	3	1	no	—
171	C₂²×C₃×C₄	—	3	4	no	—
172	C₂²×C₃×C₄	—	6	4	no	—
173	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
174	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
176	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
177	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
178	C₂×D₁₂	—	2	8	no	—
179	C₂×D₁₂	—	2	4	no	—
180	C₂×D₁₂	C₂²×C₉	1	8	yes	complemented
181	C₂×D₁₂	C₂²×C₉	1	4	yes	complemented
182	C₂×C₄×D₃	—	2	4	no	—
183	C₂×C₄×D₃	C₂²×C₉	1	4	yes	complemented
184	C₃×C₄⋊C₄	—	2	4	no	—
185	C₃×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
186	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
187	C₃×C₂²⋊C₄	—	3	8	no	—
188	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	complemented
189	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
190	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
191	C₂²×C₃²	C₃×#41	1	2	yes	—
192	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
193	C₂×C₃×D₃	—	2	8	no	—
194	C₂×C₃×D₃	—	2	2	no	—
195	C₂×C₃×D₃	—	2	2	no	—
196	C₂×C₃×D₃	—	2	4	no	—
197	C₂×C₃×D₃	—	2	4	no	—
198	C₂×C₃×D₃	—	2	4	no	—
199	C₂×C₃×D₃	—	4	8	no	—
200	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
201	C₃²×C₄	—	2	4	no	—
202	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
203	C₃×Dic₃	—	2	2	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	2	2	no	—
206	C₂²×C₉	—	2	2	no	—
207	C₂²×C₉	—	2	2	no	—
208	C₂²×C₉	—	3	4	no	—
209	C₂²×C₉	—	6	8	no	—
210	C₂²×C₉	—	6	2	no	—
211	C₂²×C₉	—	6	2	no	—
212	C₂²×C₉	—	6	4	no	—
213	C₂²×C₉	—	6	4	no	—
214	C₂²×C₉	—	6	4	no	—
215	C₂²×C₉	—	12	8	no	—
216	C₂²×C₉	C₂×D₁₂	1	2	yes	—
217	C₂²×C₉	D₃×D₄	1	2	yes	—
218	C₂²×C₉	#239	1	2	yes	—
219	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
220	C₄×C₉	—	2	4	no	—
221	C₄×C₉	—	2	4	no	—
222	C₄×C₉	—	4	4	no	—
223	C₄×C₉	—	6	2	no	—
224	C₄×C₉	C₂×D₁₂	1	4	yes	complemented
225	C₂²×D₄	—	3	2	no	—
226	C₂²×D₄	—	3	1	no	—
227	C₂³×C₄	—	3	1	no	—
228	#121	—	3	8	no	—
229	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
230	C₂×C₂²⋊C₄	—	3	2	no	—
231	C₃×C₉	C₂×#121	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₃	—	2	1	no	—
233	C₂³×C₃	—	3	2	no	—
234	C₂³×C₃	—	3	4	no	—
235	C₂³×C₃	—	3	4	no	—
236	C₂³×C₃	—	6	2	no	—
237	C₂³×C₃	—	6	2	no	—
238	C₂³×C₃	—	6	4	no	—
239	C₂³×C₃	—	6	4	no	—
240	C₂³×C₃	—	6	4	no	—
241	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
242	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
243	C₂²×D₃	—	2	2	no	—
244	C₂²×D₃	—	2	2	no	—
245	C₂²×D₃	—	2	4	no	—
246	C₂²×D₃	—	2	4	no	—
247	C₂²×D₃	—	2	4	no	—
248	C₂²×D₃	D₄×C₉	1	4	yes	complemented
249	C₂²×D₃	C₂³×C₉	1	4	yes	—
250	C₂²×D₃	C₂³×C₉	1	2	yes	—
251	C₃×D₄	—	6	16	no	—
252	C₃×D₄	—	6	8	no	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	3	2	no	—
259	C₂×C₃×C₄	—	4	4	no	—
260	C₂×C₃×C₄	—	6	2	no	—
261	C₂×C₃×C₄	—	6	8	no	—
262	C₂×C₃×C₄	D₄×C₉	1	4	yes	complemented
263	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
264	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
265	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
266	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
268	C₂×Dic₃	—	2	2	no	—
269	C₂×Dic₃	C₂³×C₉	1	2	yes	—
270	D₁₂	—	2	16	no	—
271	D₁₂	—	2	8	no	—
272	C₄×D₃	—	2	8	no	—
273	C₂×C₃²	C₃×#121	1	4	yes	—
274	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
275	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
276	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
277	C₃×D₃	—	2	4	no	—
278	C₃×D₃	—	4	4	no	—
279	C₂×C₉	—	2	4	no	—
280	C₂×C₉	—	2	1	no	—
281	C₂×C₉	—	2	1	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	—	6	4	no	—
284	C₂×C₉	—	12	4	no	—
285	C₂×C₉	#895	1	4	yes	direct product factor
286	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
287	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
288	C₂×C₉	C₂×#239	1	1	yes	characteristic
289	C₂⁴	—	3	1	no	—
290	C₂⁴	—	3	2	no	—
291	C₂×D₄	—	3	8	no	—
292	C₂×D₄	—	3	4	no	—
293	C₂×D₄	—	6	8	no	—
294	C₂×D₄	—	6	4	no	—
295	C₂²×C₄	—	3	1	no	—
296	C₂²×C₄	—	3	4	no	—
297	C₂²×C₄	—	6	4	no	—
298	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
299	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
300	C₄⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
301	C₂²⋊C₄	—	3	8	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	3	4	no	—
307	C₂²×C₃	—	6	8	no	—
308	C₂²×C₃	—	6	2	no	—
309	C₂²×C₃	—	6	2	no	—
310	C₂²×C₃	—	6	4	no	—
311	C₂²×C₃	—	6	4	no	—
312	C₂²×C₃	—	6	4	no	—
313	C₂²×C₃	—	12	8	no	—
314	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
315	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
316	C₂²×C₃	C₉×#41	1	2	yes	—
317	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
318	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
319	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
320	C₂²×C₃	C₃×#239	1	2	yes	—
321	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
322	C₂×D₃	—	2	8	no	—
323	C₂×D₃	—	2	2	no	—
324	C₂×D₃	—	2	2	no	—
325	C₂×D₃	—	2	4	no	—
326	C₂×D₃	—	2	4	no	—
327	C₂×D₃	—	2	4	no	—
328	C₂×D₃	—	4	8	no	—
329	C₂×D₃	C₂×D₄×C₉	1	4	yes	complemented
330	C₃×C₄	—	2	4	no	—
331	C₃×C₄	—	2	4	no	—
332	C₃×C₄	—	2	4	no	—
333	C₃×C₄	—	4	4	no	—
334	C₃×C₄	—	6	2	no	—
335	C₃×C₄	C₂×D₄×C₉	1	4	yes	complemented
336	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
337	Dic₃	—	2	2	no	—
338	C₃²	C₂×C₃×#121	1	1	yes	characteristic
339	C₉	—	2	1	no	—
340	C₉	C₂×#895	1	1	yes	characteristic, direct product factor
341	C₂³	—	3	2	no	—
342	C₂³	—	3	4	no	—
343	C₂³	—	3	4	no	—
344	C₂³	—	6	2	no	—
345	C₂³	—	6	2	no	—
346	C₂³	—	6	4	no	—
347	C₂³	—	6	4	no	—
348	C₂³	—	6	4	no	—
349	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
350	D₄	—	6	16	no	—
351	D₄	—	6	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	3	2	no	—
354	C₂×C₄	—	6	2	no	—
355	C₂×C₄	—	6	8	no	—
356	C₂×C₄	C₉×D₁₂	1	4	yes	complemented
357	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
358	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	4	no	—
363	C₂×C₃	—	6	4	no	—
364	C₂×C₃	—	12	4	no	—
365	C₂×C₃	C₉×#121	1	4	yes	complemented
366	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
367	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
368	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
369	C₂×C₃	C₃×#895	1	4	yes	—
370	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
371	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
372	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
373	D₃	—	2	4	no	—
374	D₃	—	4	4	no	—
375	C₂²	—	3	4	no	—
376	C₂²	—	6	2	no	—
377	C₂²	—	6	2	no	—
378	C₂²	—	6	8	no	—
379	C₂²	—	6	4	no	—
380	C₂²	—	6	4	no	—
381	C₂²	—	6	4	no	—
382	C₂²	—	12	8	no	—
383	C₂²	C₂×C₉×D₁₂	1	2	yes	—
384	C₂²	D₃×D₄×C₉	1	2	yes	—
385	C₂²	C₉×#239	1	2	yes	—
386	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
387	C₄	—	2	4	no	—
388	C₄	—	6	2	no	—
389	C₄	C₂×C₉×D₁₂	1	4	yes	complemented
390	C₃	—	2	1	no	—
391	C₃	C₂×C₉×#121	1	1	yes	characteristic, complemented
392	C₃	C₂×C₃×#895	1	1	yes	characteristic
393	C₂	—	6	4	no	—
394	C₂	—	12	4	no	—
395	C₂	C₉×#895	1	4	yes	direct product factor
396	C₂	C₂²×C₉×D₁₂	1	1	yes	characteristic
397	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
398	C₂	C₂×C₉×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₄⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂×C₃×#895	C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#121
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×D₁₂	C₂	semidirect
2. C₂²×C₉×D₁₂	C₂	semidirect
3. C₂²×C₄×D₃×C₉	C₂	semidirect
4. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
5. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₉×#895	C₂	direct (N × H)
16. C₂×C₉×D₁₂	C₂²	semidirect
17. C₂×C₉×D₁₂	C₂²	semidirect
19. C₂×C₄×D₃×C₉	C₂²	semidirect
20. C₃×C₉×C₄⋊C₄	C₂²	semidirect
21. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
33. C₂×C₉×C₄⋊C₄	D₃	semidirect
41. C₂²×D₃×C₉	D₄	semidirect
45. C₂×C₃×C₄×C₉	D₄	semidirect
54. C₂×#895	C₉	direct (N × H)
82. C₉×C₄⋊C₄	C₂×D₃	semidirect
95. C₂×D₃×C₉	C₂×D₄	semidirect
97. C₃×C₄×C₉	C₂×D₄	semidirect
102. C₂²×D₁₂	C₂×C₉	semidirect
103. C₂²×D₁₂	C₂×C₉	semidirect
104. C₂²×C₄×D₃	C₂×C₉	semidirect
107. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
110. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
111. #895	C₂×C₉	direct (N × H)
150. C₂×C₄×C₉	D₁₂	semidirect
154. C₂×C₃×C₉	#121	semidirect
180. C₂×D₁₂	C₂²×C₉	semidirect
181. C₂×D₁₂	C₂²×C₉	semidirect
183. C₂×C₄×D₃	C₂²×C₉	semidirect
185. C₃×C₄⋊C₄	C₂²×C₉	semidirect
188. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
224. C₄×C₉	C₂×D₁₂	semidirect
229. C₂×C₄⋊C₄	D₃×C₉	semidirect
231. C₃×C₉	C₂×#121	semidirect
248. C₂²×D₃	D₄×C₉	semidirect
262. C₂×C₃×C₄	D₄×C₉	semidirect
285. C₂×C₉	#895	direct (N × H)
300. C₄⋊C₄	C₂×D₃×C₉	semidirect
329. C₂×D₃	C₂×D₄×C₉	semidirect
335. C₃×C₄	C₂×D₄×C₉	semidirect
340. C₉	C₂×#895	direct (N × H)
356. C₂×C₄	C₉×D₁₂	semidirect
365. C₂×C₃	C₉×#121	semidirect
389. C₄	C₂×C₉×D₁₂	semidirect
391. C₃	C₂×C₉×#121	semidirect
395. C₂	C₉×#895	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×D₁₂	2
C₂²×C₄×D₃×C₉	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×#895	2
C₂×C₃×#895	3
C₂×C₉×#121	3

Subgroups — C2×C9×#895 #13152418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#895 #13152418