Subgroups — C₂×C₉×#878 #13152329

Order 1728.

1098 conjugacy classes of subgroups.

The subgroup lattice has 444 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	C₂²×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic
5	C₂×C₉×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
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×#878	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₃×#878	C₃	1	1	yes	maximal, characteristic
10	C₂×C₉×C₂²⋊Q₈	—	3	1	no	maximal
11	C₂⁴×C₃×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×C₉×Dic₃	—	2	4	no	—
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	C₂²×C₉×Dic₃	C₂²	1	4	yes	—
19	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₉×Dic₆	—	2	4	no	—
21	C₂×C₉×Dic₆	C₂²	1	4	yes	complemented
22	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	—
23	C₉×#217	C₂²	1	4	yes	—
24	C₉×C₄⋊Dic₃	C₂²	1	4	yes	complemented
25	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
26	C₉×Dic₃⋊C₄	C₂²	1	4	yes	complemented
27	C₂³×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
28	C₂²×C₃×Dic₆	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
30	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
31	C₂×C₃×C₄⋊Dic₃	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×#878	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	—	3	1	no	—
39	C₂×C₉×C₄⋊C₄	—	3	1	no	—
40	C₂×C₉×C₄⋊C₄	—	3	1	no	—
41	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
42	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
43	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic
44	C₂³×C₃×C₉	—	2	2	no	—
45	C₂³×C₃×C₉	—	2	2	no	—
46	C₂³×C₃×C₉	Q₈	1	4	yes	complemented
47	C₂³×C₃×C₉	C₂³	1	2	yes	—
48	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×C₉	—	2	2	no	—
50	C₂×C₃×C₄×C₉	—	2	2	no	—
51	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
52	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
53	C₂×C₉×Dic₃	—	2	2	no	—
54	C₂×C₉×Dic₃	—	2	2	no	—
55	C₂×C₉×Dic₃	—	2	2	no	—
56	C₂×C₉×Dic₃	—	2	8	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	C₂×C₉×Dic₃	C₂³	1	2	yes	—
62	C₉×Dic₆	—	2	8	no	—
63	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
64	C₂×#878	C₉	1	1	yes	characteristic, direct product factor
65	C₂⁴×C₃²	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×C₃×Dic₃	—	2	4	no	—
69	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
70	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×Dic₆	—	2	4	no	—
75	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
76	C₂⁴×C₉	—	2	1	no	—
77	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
78	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
79	C₃×#217	C₂²×C₃	1	4	yes	—
80	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
81	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
82	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
83	C₂×Q₈×C₉	—	3	4	no	—
84	C₂×Q₈×C₉	—	6	4	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	4	no	—
89	C₂²×C₄×C₉	—	3	1	no	—
90	C₂²×C₄×C₉	—	3	1	no	—
91	C₂²×C₄×C₉	—	3	1	no	—
92	C₂²×C₄×C₉	—	6	4	no	—
93	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
95	C₉×C₄⋊C₄	—	3	4	no	—
96	C₉×C₄⋊C₄	—	3	4	no	—
97	C₉×C₄⋊C₄	—	3	4	no	—
98	C₉×C₂²⋊C₄	—	2	4	no	—
99	C₉×C₂²⋊C₄	—	3	4	no	—
100	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	—
101	C₂²×C₃×C₉	—	2	8	no	—
102	C₂²×C₃×C₉	—	2	2	no	—
103	C₂²×C₃×C₉	—	2	2	no	—
104	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
105	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	—
106	C₂²×C₃×C₉	C₂×Q₈	1	4	yes	complemented
107	C₂²×C₃×C₉	#41	1	2	yes	—
108	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
109	C₃×C₄×C₉	—	2	2	no	—
110	C₃×C₄×C₉	—	2	2	no	—
111	C₉×Dic₃	—	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	C₂³×Dic₃	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	—	3	1	no	—
121	C₂×C₃×C₄⋊C₄	—	3	1	no	—
122	C₂×C₃×C₄⋊C₄	—	3	1	no	—
123	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
125	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
126	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
127	C₂×#217	C₂×C₉	1	1	yes	characteristic
128	C₂×C₄⋊Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
129	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
130	C₂×Dic₃⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
131	#878	C₂×C₉	1	8	yes	direct product factor
132	C₂³×C₃²	—	2	2	no	—
133	C₂³×C₃²	—	2	2	no	—
134	C₂³×C₃²	C₃×Q₈	1	4	yes	—
135	C₂³×C₃²	C₂³×C₃	1	2	yes	—
136	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	—	2	2	no	—
139	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
140	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
141	C₂×C₃×Dic₃	—	2	2	no	—
142	C₂×C₃×Dic₃	—	2	2	no	—
143	C₂×C₃×Dic₃	—	2	2	no	—
144	C₂×C₃×Dic₃	—	2	8	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	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
150	C₃×Dic₆	—	2	8	no	—
151	C₂³×C₉	—	2	2	no	—
152	C₂³×C₉	—	2	2	no	—
153	C₂³×C₉	—	2	4	no	—
154	C₂³×C₉	—	2	1	no	—
155	C₂³×C₉	—	2	2	no	—
156	C₂³×C₉	—	4	2	no	—
157	C₂³×C₉	—	4	2	no	—
158	C₂³×C₉	Dic₆	1	4	yes	complemented
159	C₂³×C₉	C₂²×D₃	1	2	yes	—
160	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
161	Q₈×C₉	—	6	8	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	—	2	2	no	—
166	C₂×C₄×C₉	—	3	4	no	—
167	C₂×C₄×C₉	—	3	2	no	—
168	C₂×C₄×C₉	—	3	2	no	—
169	C₂×C₄×C₉	—	3	2	no	—
170	C₂×C₄×C₉	—	3	2	no	—
171	C₂×C₄×C₉	—	4	2	no	—
172	C₂×C₄×C₉	—	4	2	no	—
173	C₂×C₄×C₉	—	6	8	no	—
174	C₂×C₄×C₉	—	6	2	no	—
175	C₂×C₄×C₉	—	6	2	no	—
176	C₂×C₄×C₉	—	6	2	no	—
177	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
178	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
179	C₂×C₂²⋊Q₈	—	3	1	no	Sylow
180	C₂×C₃×C₉	—	2	4	no	—
181	C₂×C₃×C₉	C₂²⋊Q₈	1	4	yes	complemented
182	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
185	C₂⁴×C₃	—	2	1	no	—
186	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
187	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
188	C₂×C₃×Q₈	—	3	4	no	—
189	C₂×C₃×Q₈	—	6	4	no	—
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂²×C₃×C₄	—	3	1	no	—
193	C₂²×C₃×C₄	—	3	1	no	—
194	C₂²×C₃×C₄	—	3	1	no	—
195	C₂²×C₃×C₄	—	3	1	no	—
196	C₂²×C₃×C₄	—	3	4	no	—
197	C₂²×C₃×C₄	—	6	4	no	—
198	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
202	C₂²×Dic₃	—	2	4	no	—
203	C₂²×Dic₃	C₂²×C₉	1	4	yes	—
204	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
205	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
206	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
207	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
208	C₂×Dic₆	—	2	4	no	—
209	C₂×Dic₆	C₂²×C₉	1	4	yes	complemented
210	C₃×C₄⋊C₄	—	3	4	no	—
211	C₃×C₄⋊C₄	—	3	4	no	—
212	C₃×C₄⋊C₄	—	3	4	no	—
213	C₃×C₂²⋊C₄	—	2	4	no	—
214	C₃×C₂²⋊C₄	—	3	4	no	—
215	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	—
216	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
217	#217	C₂²×C₉	1	4	yes	—
218	C₄⋊Dic₃	C₂²×C₉	1	4	yes	complemented
219	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
220	Dic₃⋊C₄	C₂²×C₉	1	4	yes	complemented
221	C₂²×C₃²	—	2	8	no	—
222	C₂²×C₃²	—	2	2	no	—
223	C₂²×C₃²	—	2	2	no	—
224	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
225	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
226	C₂²×C₃²	C₂×C₃×Q₈	1	4	yes	—
227	C₂²×C₃²	C₃×#41	1	2	yes	—
228	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
229	C₃²×C₄	—	2	2	no	—
230	C₃²×C₄	—	2	2	no	—
231	C₃×Dic₃	—	2	2	no	—
232	C₃×Dic₃	—	2	2	no	—
233	C₃×Dic₃	—	2	2	no	—
234	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
235	C₂²×C₉	—	2	8	no	—
236	C₂²×C₉	—	2	2	no	—
237	C₂²×C₉	—	2	2	no	—
238	C₂²×C₉	—	2	1	no	—
239	C₂²×C₉	—	2	2	no	—
240	C₂²×C₉	—	2	4	no	—
241	C₂²×C₉	—	2	2	no	—
242	C₂²×C₉	—	2	2	no	—
243	C₂²×C₉	—	4	8	no	—
244	C₂²×C₉	—	4	2	no	—
245	C₂²×C₉	—	4	2	no	—
246	C₂²×C₉	C₂×Dic₆	1	2	yes	—
247	C₂²×C₉	C₂×Dic₆	1	4	yes	complemented
248	C₂²×C₉	D₃×D₄	1	2	yes	—
249	C₂²×C₉	#237	1	2	yes	—
250	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
251	C₄×C₉	—	2	2	no	—
252	C₄×C₉	—	2	2	no	—
253	C₄×C₉	—	3	4	no	—
254	C₄×C₉	—	4	2	no	—
255	C₄×C₉	—	4	2	no	—
256	C₄×C₉	—	6	2	no	—
257	C₄×C₉	—	6	2	no	—
258	C₄×C₉	—	6	2	no	—
259	C₂²×Q₈	—	3	1	no	—
260	C₂³×C₄	—	3	1	no	—
261	C₂²⋊Q₈	—	3	8	no	—
262	C₂×C₄⋊C₄	—	3	1	no	—
263	C₂×C₄⋊C₄	—	3	1	no	—
264	C₂×C₄⋊C₄	—	3	1	no	—
265	C₂×C₂²⋊C₄	—	3	1	no	—
266	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic
267	C₃×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	2	2	no	—
270	C₂³×C₃	—	2	2	no	—
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	4	no	—
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	4	2	no	—
276	C₂³×C₃	—	4	2	no	—
277	C₂³×C₃	Q₈×C₉	1	4	yes	complemented
278	C₂³×C₃	C₂³×C₉	1	2	yes	—
279	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
280	C₂³×C₃	C₃×Dic₆	1	4	yes	—
281	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
282	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
283	C₃×Q₈	—	6	8	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	3	2	no	—
291	C₂×C₃×C₄	—	3	4	no	—
292	C₂×C₃×C₄	—	3	2	no	—
293	C₂×C₃×C₄	—	3	2	no	—
294	C₂×C₃×C₄	—	3	2	no	—
295	C₂×C₃×C₄	—	4	2	no	—
296	C₂×C₃×C₄	—	4	2	no	—
297	C₂×C₃×C₄	—	6	8	no	—
298	C₂×C₃×C₄	—	6	2	no	—
299	C₂×C₃×C₄	—	6	2	no	—
300	C₂×C₃×C₄	—	6	2	no	—
301	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
302	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
303	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
304	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
305	C₂×Dic₃	—	2	2	no	—
306	C₂×Dic₃	—	2	2	no	—
307	C₂×Dic₃	—	2	2	no	—
308	C₂×Dic₃	—	2	8	no	—
309	C₂×Dic₃	D₄×C₉	1	4	yes	—
310	C₂×Dic₃	C₂³×C₉	1	2	yes	—
311	C₂×Dic₃	C₂³×C₉	1	2	yes	—
312	C₂×Dic₃	C₂³×C₉	1	2	yes	—
313	C₂×Dic₃	C₂³×C₉	1	2	yes	—
314	Dic₆	—	2	8	no	—
315	C₂×C₃²	—	2	4	no	—
316	C₂×C₃²	C₃×C₂²⋊Q₈	1	4	yes	—
317	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
318	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
319	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
320	C₂×C₉	—	2	4	no	—
321	C₂×C₉	—	2	4	no	—
322	C₂×C₉	—	2	1	no	—
323	C₂×C₉	—	2	1	no	—
324	C₂×C₉	—	2	1	no	—
325	C₂×C₉	—	4	4	no	—
326	C₂×C₉	#878	1	4	yes	direct product factor
327	C₂×C₉	C₂²×Dic₆	1	1	yes	characteristic
328	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
329	C₂×C₉	C₂×#237	1	1	yes	characteristic
330	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
331	C₂×Q₈	—	3	4	no	—
332	C₂×Q₈	—	6	4	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	3	1	no	—
335	C₂²×C₄	—	3	1	no	—
336	C₂²×C₄	—	3	1	no	—
337	C₂²×C₄	—	3	4	no	—
338	C₂²×C₄	—	6	4	no	—
339	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
341	C₄⋊C₄	—	3	4	no	—
342	C₄⋊C₄	—	3	4	no	—
343	C₄⋊C₄	—	3	4	no	—
344	C₂²⋊C₄	—	3	4	no	—
345	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	—
346	C₂²×C₃	—	2	8	no	—
347	C₂²×C₃	—	2	8	no	—
348	C₂²×C₃	—	2	2	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	2	2	no	—
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	4	2	no	—
359	C₂²×C₃	—	4	8	no	—
360	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
361	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	—
362	C₂²×C₃	C₂×Q₈×C₉	1	4	yes	complemented
363	C₂²×C₃	C₉×#41	1	2	yes	—
364	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
365	C₂²×C₃	C₂×C₃×Dic₆	1	2	yes	—
366	C₂²×C₃	C₂×C₃×Dic₆	1	4	yes	—
367	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
368	C₂²×C₃	C₃×#237	1	2	yes	—
369	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	2	2	no	—
372	C₃×C₄	—	2	2	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	—	3	4	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	—	4	2	no	—
377	C₃×C₄	—	6	2	no	—
378	C₃×C₄	—	6	2	no	—
379	C₃×C₄	—	6	2	no	—
380	Dic₃	—	2	2	no	—
381	Dic₃	—	2	2	no	—
382	Dic₃	—	2	2	no	—
383	Dic₃	C₂×D₄×C₉	1	4	yes	—
384	C₃²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
385	C₉	—	2	1	no	—
386	C₉	C₂×#878	1	1	yes	characteristic, direct product factor
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	C₉×Dic₆	1	4	yes	complemented
390	C₂³	C₂²×D₃×C₉	1	2	yes	—
391	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
392	Q₈	—	6	8	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	3	2	no	—
396	C₂×C₄	—	3	4	no	—
397	C₂×C₄	—	3	2	no	—
398	C₂×C₄	—	3	2	no	—
399	C₂×C₄	—	3	2	no	—
400	C₂×C₄	—	6	8	no	—
401	C₂×C₄	—	6	2	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	6	2	no	—
404	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
405	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
406	C₂×C₃	—	2	4	no	—
407	C₂×C₃	—	2	4	no	—
408	C₂×C₃	—	2	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	2	4	no	—
412	C₂×C₃	—	4	4	no	—
413	C₂×C₃	C₉×C₂²⋊Q₈	1	4	yes	complemented
414	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
415	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
416	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
417	C₂×C₃	C₃×#878	1	4	yes	—
418	C₂×C₃	C₂²×C₃×Dic₆	1	1	yes	characteristic
419	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
420	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	8	no	—
424	C₂²	C₂×C₉×Dic₆	1	2	yes	—
425	C₂²	C₂×C₉×Dic₆	1	4	yes	complemented
426	C₂²	D₃×D₄×C₉	1	2	yes	—
427	C₂²	C₉×#237	1	2	yes	—
428	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	3	4	no	—
432	C₄	—	6	2	no	—
433	C₄	—	6	2	no	—
434	C₄	—	6	2	no	—
435	C₃	—	2	1	no	—
436	C₃	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic, complemented
437	C₃	C₂×C₃×#878	1	1	yes	characteristic
438	C₂	—	2	4	no	—
439	C₂	C₉×#878	1	4	yes	direct product factor
440	C₂	C₂²×C₉×Dic₆	1	1	yes	characteristic
441	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
442	C₂	C₂×C₉×#237	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×C₂²⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂⁴×C₃²	C₂²×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₉×C₂²⋊Q₈
LCS	G ▷ C₂²×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×C₉×Dic₆	C₂	semidirect
5. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
6. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
7. C₂×C₉×Dic₃⋊C₄	C₂	semidirect
8. C₉×#878	C₂	direct (N × H)
21. C₂×C₉×Dic₆	C₂²	semidirect
24. C₉×C₄⋊Dic₃	C₂²	semidirect
25. C₉×Dic₃⋊C₄	C₂²	semidirect
26. C₉×Dic₃⋊C₄	C₂²	semidirect
46. C₂³×C₃×C₉	Q₈	semidirect
64. C₂×#878	C₉	direct (N × H)
106. C₂²×C₃×C₉	C₂×Q₈	semidirect
118. C₂²×Dic₆	C₂×C₉	semidirect
128. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
129. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
130. C₂×Dic₃⋊C₄	C₂×C₉	semidirect
131. #878	C₂×C₉	direct (N × H)
158. C₂³×C₉	Dic₆	semidirect
181. C₂×C₃×C₉	C₂²⋊Q₈	semidirect
209. C₂×Dic₆	C₂²×C₉	semidirect
218. C₄⋊Dic₃	C₂²×C₉	semidirect
219. Dic₃⋊C₄	C₂²×C₉	semidirect
220. Dic₃⋊C₄	C₂²×C₉	semidirect
247. C₂²×C₉	C₂×Dic₆	semidirect
267. C₃×C₉	C₂×C₂²⋊Q₈	semidirect
277. C₂³×C₃	Q₈×C₉	semidirect
326. C₂×C₉	#878	direct (N × H)
362. C₂²×C₃	C₂×Q₈×C₉	semidirect
386. C₉	C₂×#878	direct (N × H)
389. C₂³	C₉×Dic₆	semidirect
413. C₂×C₃	C₉×C₂²⋊Q₈	semidirect
425. C₂²	C₂×C₉×Dic₆	semidirect
436. C₃	C₂×C₉×C₂²⋊Q₈	semidirect
439. C₂	C₉×#878	direct (N × H)

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
C₂²×C₉×Dic₆	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×#217	2
C₂×C₉×C₄⋊Dic₃	2
C₂×C₉×Dic₃⋊C₄	2
C₉×#878	2
C₂×C₃×#878	3
C₂×C₉×C₂²⋊Q₈	3

Subgroups — C2×C9×#878 #13152329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#878 #13152329