Subgroups — C₂×C₉×#896 #13152394

Order 1728.

1058 conjugacy classes of subgroups.

The subgroup lattice has 432 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	C₂²×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₉×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#896	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#896	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×C₂²⋊Q₈	—	3	1	no	maximal
11	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
15	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	—	2	4	no	—
19	C₂×C₄×D₃×C₉	C₂²	1	4	yes	—
20	C₂×C₉×Dic₆	—	2	4	no	—
21	C₂×C₉×Dic₆	C₂²	1	4	yes	complemented
22	C₃×C₉×C₄⋊C₄	C₂²	1	4	yes	complemented
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
25	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
26	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
27	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
28	C₂²×C₃×Dic₆	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃²×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
32	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₃×#896	C₂×C₃	1	8	yes	—
35	C₂²×Q₈×C₉	—	3	1	no	—
36	C₂³×C₄×C₉	—	3	1	no	—
37	C₉×C₂²⋊Q₈	—	3	8	no	—
38	C₂×C₉×C₄⋊C₄	—	2	1	no	—
39	C₂×C₉×C₄⋊C₄	—	3	1	no	—
40	C₂×C₉×C₄⋊C₄	—	3	1	no	—
41	C₂×C₉×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
42	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
43	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
44	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
45	C₂²×D₃×C₉	—	2	2	no	—
46	C₂²×D₃×C₉	—	2	2	no	—
47	C₂²×D₃×C₉	Q₈	1	4	yes	complemented
48	C₂²×D₃×C₉	C₂³	1	2	yes	—
49	C₂×C₃×C₄×C₉	—	2	2	no	—
50	C₂×C₃×C₄×C₉	—	2	2	no	—
51	C₂×C₃×C₄×C₉	—	2	2	no	—
52	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
53	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
54	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
55	C₂×C₉×Dic₃	—	2	2	no	—
56	C₂×C₉×Dic₃	—	2	2	no	—
57	C₂×C₉×Dic₃	D₄	1	4	yes	—
58	C₂×C₉×Dic₃	C₂³	1	2	yes	—
59	C₂×C₉×Dic₃	C₂³	1	2	yes	—
60	C₂×C₉×Dic₃	C₂³	1	2	yes	—
61	C₄×D₃×C₉	—	2	8	no	—
62	C₉×Dic₆	—	2	8	no	—
63	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
64	C₂×#896	C₉	1	1	yes	characteristic, direct product factor
65	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
70	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	—	2	4	no	—
73	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
74	C₂×C₃×Dic₆	—	2	4	no	—
75	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
76	C₂⁴×C₉	—	3	1	no	—
77	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
78	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
79	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
80	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
81	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
82	C₂×Q₈×C₉	—	3	4	no	—
83	C₂×Q₈×C₉	—	6	4	no	—
84	C₂²×C₄×C₉	—	2	1	no	—
85	C₂²×C₄×C₉	—	2	1	no	—
86	C₂²×C₄×C₉	—	2	1	no	—
87	C₂²×C₄×C₉	—	3	1	no	—
88	C₂²×C₄×C₉	—	3	1	no	—
89	C₂²×C₄×C₉	—	3	1	no	—
90	C₂²×C₄×C₉	—	3	4	no	—
91	C₂²×C₄×C₉	—	6	4	no	—
92	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
93	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
95	C₉×C₄⋊C₄	—	2	4	no	—
96	C₉×C₄⋊C₄	—	3	4	no	—
97	C₉×C₄⋊C₄	—	3	4	no	—
98	C₉×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
99	C₉×C₂²⋊C₄	—	3	4	no	—
100	C₉×C₂²⋊C₄	—	3	4	no	—
101	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
102	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
103	C₂²×C₃×C₉	#41	1	2	yes	—
104	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
105	C₂×D₃×C₉	—	2	8	no	—
106	C₂×D₃×C₉	—	2	2	no	—
107	C₂×D₃×C₉	—	2	2	no	—
108	C₂×D₃×C₉	C₂×Q₈	1	4	yes	complemented
109	C₃×C₄×C₉	—	2	2	no	—
110	C₃×C₄×C₉	—	2	2	no	—
111	C₃×C₄×C₉	—	2	2	no	—
112	C₉×Dic₃	—	2	2	no	—
113	C₉×Dic₃	—	2	2	no	—
114	C₉×Dic₃	C₂×D₄	1	4	yes	—
115	C₂²×C₃×Q₈	—	3	1	no	—
116	C₂³×C₃×C₄	—	3	1	no	—
117	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic
118	C₂²×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
119	C₃×C₂²⋊Q₈	—	3	8	no	—
120	C₂×C₃×C₄⋊C₄	—	2	1	no	—
121	C₂×C₃×C₄⋊C₄	—	3	1	no	—
122	C₂×C₃×C₄⋊C₄	—	3	1	no	—
123	C₂×C₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
124	C₂×C₃×C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
125	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
126	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
127	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
128	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic
129	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
130	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
131	#896	C₂×C₉	1	8	yes	direct product factor
132	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
133	C₂²×C₃×D₃	—	2	2	no	—
134	C₂²×C₃×D₃	—	2	2	no	—
135	C₂²×C₃×D₃	C₃×Q₈	1	4	yes	—
136	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	—	2	2	no	—
139	C₂×C₃²×C₄	—	2	2	no	—
140	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
141	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
142	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
143	C₂×C₃×Dic₃	—	2	2	no	—
144	C₂×C₃×Dic₃	—	2	2	no	—
145	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
146	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
147	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
148	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
149	C₃×C₄×D₃	—	2	8	no	—
150	C₃×Dic₆	—	2	8	no	—
151	C₂³×C₉	—	2	1	no	—
152	C₂³×C₉	—	3	4	no	—
153	C₂³×C₉	—	3	2	no	—
154	C₂³×C₉	—	6	2	no	—
155	C₂³×C₉	—	6	2	no	—
156	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
157	Q₈×C₉	—	6	8	no	—
158	C₂×C₄×C₉	—	2	4	no	—
159	C₂×C₄×C₉	—	2	2	no	—
160	C₂×C₄×C₉	—	2	2	no	—
161	C₂×C₄×C₉	—	2	2	no	—
162	C₂×C₄×C₉	—	2	2	no	—
163	C₂×C₄×C₉	—	2	2	no	—
164	C₂×C₄×C₉	—	2	2	no	—
165	C₂×C₄×C₉	—	3	4	no	—
166	C₂×C₄×C₉	—	3	2	no	—
167	C₂×C₄×C₉	—	3	2	no	—
168	C₂×C₄×C₉	—	3	2	no	—
169	C₂×C₄×C₉	—	4	2	no	—
170	C₂×C₄×C₉	—	4	2	no	—
171	C₂×C₄×C₉	—	6	8	no	—
172	C₂×C₄×C₉	—	6	2	no	—
173	C₂×C₄×C₉	—	6	2	no	—
174	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
175	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
176	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
177	C₂×C₂²⋊Q₈	—	3	1	no	Sylow
178	C₂×C₃×C₉	C₂²⋊Q₈	1	4	yes	complemented
179	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
182	D₃×C₉	—	2	4	no	—
183	C₂⁴×C₃	—	3	1	no	—
184	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
185	C₂×C₃×Q₈	—	3	4	no	—
186	C₂×C₃×Q₈	—	6	4	no	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	—	3	1	no	—
191	C₂²×C₃×C₄	—	3	1	no	—
192	C₂²×C₃×C₄	—	3	1	no	—
193	C₂²×C₃×C₄	—	3	4	no	—
194	C₂²×C₃×C₄	—	6	4	no	—
195	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
201	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
202	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
203	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
204	C₂×C₄×D₃	—	2	4	no	—
205	C₂×C₄×D₃	C₂²×C₉	1	4	yes	—
206	C₂×Dic₆	—	2	4	no	—
207	C₂×Dic₆	C₂²×C₉	1	4	yes	complemented
208	C₃×C₄⋊C₄	—	2	4	no	—
209	C₃×C₄⋊C₄	—	3	4	no	—
210	C₃×C₄⋊C₄	—	3	4	no	—
211	C₃×C₄⋊C₄	C₂²×C₉	1	4	yes	complemented
212	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
213	C₃×C₂²⋊C₄	—	3	4	no	—
214	C₃×C₂²⋊C₄	—	3	4	no	—
215	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
216	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
217	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
218	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
219	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
220	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
221	C₂²×C₃²	C₃×#41	1	2	yes	—
222	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
223	C₂×C₃×D₃	—	2	8	no	—
224	C₂×C₃×D₃	—	2	2	no	—
225	C₂×C₃×D₃	—	2	2	no	—
226	C₂×C₃×D₃	C₂×C₃×Q₈	1	4	yes	—
227	C₃²×C₄	—	2	2	no	—
228	C₃²×C₄	—	2	2	no	—
229	C₃²×C₄	—	2	2	no	—
230	C₃×Dic₃	—	2	2	no	—
231	C₃×Dic₃	—	2	2	no	—
232	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
233	C₂²×C₉	—	2	1	no	—
234	C₂²×C₉	—	2	2	no	—
235	C₂²×C₉	—	2	2	no	—
236	C₂²×C₉	—	2	2	no	—
237	C₂²×C₉	—	3	4	no	—
238	C₂²×C₉	—	6	8	no	—
239	C₂²×C₉	—	6	2	no	—
240	C₂²×C₉	—	6	2	no	—
241	C₂²×C₉	#235	1	2	yes	—
242	C₂²×C₉	D₃×D₄	1	2	yes	—
243	C₂²×C₉	D₃×Q₈	1	2	yes	—
244	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
245	C₄×C₉	—	2	4	no	—
246	C₄×C₉	—	2	2	no	—
247	C₄×C₉	—	2	2	no	—
248	C₄×C₉	—	2	2	no	—
249	C₄×C₉	—	3	4	no	—
250	C₄×C₉	—	4	2	no	—
251	C₄×C₉	—	4	2	no	—
252	C₄×C₉	—	6	2	no	—
253	C₄×C₉	—	6	2	no	—
254	C₂²×Q₈	—	3	1	no	—
255	C₂³×C₄	—	3	1	no	—
256	C₂²⋊Q₈	—	3	8	no	—
257	C₂×C₄⋊C₄	—	3	1	no	—
258	C₂×C₄⋊C₄	—	3	1	no	—
259	C₂×C₄⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
260	C₂×C₂²⋊C₄	—	3	1	no	—
261	C₂×C₂²⋊C₄	—	3	1	no	—
262	C₃×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	3	2	no	—
265	C₂³×C₃	—	3	4	no	—
266	C₂³×C₃	—	6	2	no	—
267	C₂³×C₃	—	6	2	no	—
268	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
269	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
270	C₂²×D₃	—	2	2	no	—
271	C₂²×D₃	—	2	2	no	—
272	C₂²×D₃	Q₈×C₉	1	4	yes	complemented
273	C₂²×D₃	C₂³×C₉	1	2	yes	—
274	C₃×Q₈	—	6	8	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	2	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	3	2	no	—
286	C₂×C₃×C₄	—	3	4	no	—
287	C₂×C₃×C₄	—	3	2	no	—
288	C₂×C₃×C₄	—	3	2	no	—
289	C₂×C₃×C₄	—	4	2	no	—
290	C₂×C₃×C₄	—	4	2	no	—
291	C₂×C₃×C₄	—	6	8	no	—
292	C₂×C₃×C₄	—	6	2	no	—
293	C₂×C₃×C₄	—	6	2	no	—
294	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
295	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
296	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
297	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
298	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
299	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
300	C₂×Dic₃	—	2	2	no	—
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	D₄×C₉	1	4	yes	—
303	C₂×Dic₃	C₂³×C₉	1	2	yes	—
304	C₂×Dic₃	C₂³×C₉	1	2	yes	—
305	C₂×Dic₃	C₂³×C₉	1	2	yes	—
306	C₄×D₃	—	2	8	no	—
307	Dic₆	—	2	8	no	—
308	C₂×C₃²	C₃×C₂²⋊Q₈	1	4	yes	—
309	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
311	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
312	C₃×D₃	—	2	4	no	—
313	C₂×C₉	—	2	4	no	—
314	C₂×C₉	—	2	1	no	—
315	C₂×C₉	—	2	1	no	—
316	C₂×C₉	—	2	1	no	—
317	C₂×C₉	—	6	4	no	—
318	C₂×C₉	#896	1	4	yes	direct product factor
319	C₂×C₉	C₂×#235	1	1	yes	characteristic
320	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
321	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
322	C₂⁴	—	3	1	no	—
323	C₂×Q₈	—	3	4	no	—
324	C₂×Q₈	—	6	4	no	—
325	C₂²×C₄	—	3	1	no	—
326	C₂²×C₄	—	3	1	no	—
327	C₂²×C₄	—	3	1	no	—
328	C₂²×C₄	—	3	4	no	—
329	C₂²×C₄	—	6	4	no	—
330	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
333	C₄⋊C₄	—	3	4	no	—
334	C₄⋊C₄	—	3	4	no	—
335	C₄⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
336	C₂²⋊C₄	—	3	4	no	—
337	C₂²⋊C₄	—	3	4	no	—
338	C₂²×C₃	—	2	1	no	—
339	C₂²×C₃	—	2	2	no	—
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	2	2	no	—
342	C₂²×C₃	—	3	4	no	—
343	C₂²×C₃	—	6	8	no	—
344	C₂²×C₃	—	6	2	no	—
345	C₂²×C₃	—	6	2	no	—
346	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
347	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	—
348	C₂²×C₃	C₉×#41	1	2	yes	—
349	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
350	C₂²×C₃	C₃×#235	1	2	yes	—
351	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
352	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
353	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
354	C₂×D₃	—	2	8	no	—
355	C₂×D₃	—	2	2	no	—
356	C₂×D₃	—	2	2	no	—
357	C₂×D₃	C₂×Q₈×C₉	1	4	yes	complemented
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	3	4	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	—	6	2	no	—
369	C₃×C₄	—	6	2	no	—
370	Dic₃	—	2	2	no	—
371	Dic₃	—	2	2	no	—
372	Dic₃	C₂×D₄×C₉	1	4	yes	—
373	C₃²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
374	C₉	—	2	1	no	—
375	C₉	C₂×#896	1	1	yes	characteristic, direct product factor
376	C₂³	—	3	2	no	—
377	C₂³	—	3	4	no	—
378	C₂³	—	6	2	no	—
379	C₂³	—	6	2	no	—
380	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
381	Q₈	—	6	8	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	3	2	no	—
386	C₂×C₄	—	3	4	no	—
387	C₂×C₄	—	3	2	no	—
388	C₂×C₄	—	3	2	no	—
389	C₂×C₄	—	6	8	no	—
390	C₂×C₄	—	6	2	no	—
391	C₂×C₄	—	6	2	no	—
392	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
393	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
394	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	2	4	no	—
399	C₂×C₃	—	6	4	no	—
400	C₂×C₃	C₉×C₂²⋊Q₈	1	4	yes	complemented
401	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
402	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
403	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
404	C₂×C₃	C₃×#896	1	4	yes	—
405	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
406	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
407	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
408	D₃	—	2	4	no	—
409	C₂²	—	3	4	no	—
410	C₂²	—	6	2	no	—
411	C₂²	—	6	2	no	—
412	C₂²	—	6	8	no	—
413	C₂²	C₉×#235	1	2	yes	—
414	C₂²	D₃×D₄×C₉	1	2	yes	—
415	C₂²	D₃×Q₈×C₉	1	2	yes	—
416	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	3	4	no	—
421	C₄	—	6	2	no	—
422	C₄	—	6	2	no	—
423	C₃	—	2	1	no	—
424	C₃	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic, complemented
425	C₃	C₂×C₃×#896	1	1	yes	characteristic
426	C₂	—	6	4	no	—
427	C₂	C₉×#896	1	4	yes	direct product factor
428	C₂	C₂×C₉×#235	1	1	yes	characteristic
429	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
430	C₂	C₂×D₃×Q₈×C₉	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	C₂³×C₃×D₃	C₂²×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₉×C₂²⋊Q₈
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
2. C₂²×C₉×Dic₆	C₂	semidirect
3. C₂×C₃×C₉×C₄⋊C₄	C₂	semidirect
6. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
7. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
8. C₉×#896	C₂	direct (N × H)
21. C₂×C₉×Dic₆	C₂²	semidirect
22. C₃×C₉×C₄⋊C₄	C₂²	semidirect
25. C₉×Dic₃⋊C₄	C₂²	semidirect
26. C₉×Dic₃⋊C₄	C₂²	semidirect
41. C₂×C₉×C₄⋊C₄	D₃	semidirect
47. C₂²×D₃×C₉	Q₈	semidirect
64. C₂×#896	C₉	direct (N × H)
98. C₉×C₄⋊C₄	C₂×D₃	semidirect
108. C₂×D₃×C₉	C₂×Q₈	semidirect
118. C₂²×Dic₆	C₂×C₉	semidirect
123. C₂×C₃×C₄⋊C₄	C₂×C₉	semidirect
129. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
130. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
131. #896	C₂×C₉	direct (N × H)
178. C₂×C₃×C₉	C₂²⋊Q₈	semidirect
207. C₂×Dic₆	C₂²×C₉	semidirect
211. C₃×C₄⋊C₄	C₂²×C₉	semidirect
217. Dic₃⋊C₄	C₂²×C₉	semidirect
218. Dic₃⋊C₄	C₂²×C₉	semidirect
259. C₂×C₄⋊C₄	D₃×C₉	semidirect
262. C₃×C₉	C₂×C₂²⋊Q₈	semidirect
272. C₂²×D₃	Q₈×C₉	semidirect
318. C₂×C₉	#896	direct (N × H)
335. C₄⋊C₄	C₂×D₃×C₉	semidirect
357. C₂×D₃	C₂×Q₈×C₉	semidirect
375. C₉	C₂×#896	direct (N × H)
400. C₂×C₃	C₉×C₂²⋊Q₈	semidirect
424. C₃	C₂×C₉×C₂²⋊Q₈	semidirect
427. C₂	C₉×#896	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×C₄×D₃×C₉	2
C₂²×C₉×Dic₆	2
C₂×C₃×C₉×C₄⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#896	2
C₂×C₃×#896	3
C₂×C₉×C₂²⋊Q₈	3

Subgroups — C2×C9×#896 #13152394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#896 #13152394