Subgroups — D₃×C₉×C₂²⋊Q₈ #13152925

Order 1728.

1040 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₃×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#896	C₂	1	2	yes	maximal, complemented
8	D₃×C₉×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×C₉×C₂²⋊C₄	C₂	1	2	yes	maximal
11	C₉×#878	C₂	1	2	yes	maximal, complemented
12	C₃×D₃×C₂²⋊Q₈	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×C₂²⋊Q₈	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
18	D₃×Q₈×C₉	—	2	4	no	—
19	C₂×C₄×D₃×C₉	—	2	4	no	—
20	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
24	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₉×Dic₆	C₂²	1	2	yes	complemented
28	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₉×#217	C₂²	1	2	yes	—
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
35	C₉×C₄⋊Dic₃	C₂²	1	2	yes	complemented
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
38	C₉×Dic₃⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₃×D₃×Q₈	C₂×C₃	1	1	yes	characteristic
40	C₂²×C₃×C₄×D₃	C₂×C₃	1	1	yes	characteristic
41	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
42	C₃×#946	C₂×C₃	1	1	yes	characteristic
43	C₃×#924	C₂×C₃	1	1	yes	characteristic
44	C₃×#897	C₂×C₃	1	1	yes	characteristic
45	C₃×#896	C₂×C₃	1	2	yes	—
46	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
47	C₃×D₃×C₄⋊C₄	C₂×C₃	1	2	yes	—
48	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	2	yes	—
49	C₃×#878	C₂×C₃	1	2	yes	—
50	C₂²×Q₈×C₉	—	3	1	no	—
51	C₂³×C₄×C₉	—	3	1	no	—
52	C₉×C₂²⋊Q₈	—	2	1	no	—
53	C₉×C₂²⋊Q₈	—	3	1	no	—
54	C₉×C₂²⋊Q₈	—	3	1	no	—
55	C₉×C₂²⋊Q₈	—	3	2	no	—
56	C₉×C₂²⋊Q₈	—	3	1	no	—
57	C₉×C₂²⋊Q₈	—	3	2	no	—
58	C₉×C₂²⋊Q₈	D₃	1	1	yes	characteristic, direct product factor
59	C₂×C₉×C₄⋊C₄	—	3	1	no	—
60	C₂×C₉×C₄⋊C₄	—	3	2	no	—
61	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
62	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₉	—	2	2	no	—
64	C₂²×D₃×C₉	—	2	2	no	—
65	C₂²×D₃×C₉	Q₈	1	4	yes	complemented
66	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
67	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
68	C₃×Q₈×C₉	—	2	2	no	—
69	C₂×C₃×C₄×C₉	—	2	2	no	—
70	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
71	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
73	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
74	C₂×C₉×Dic₃	—	2	2	no	—
75	C₂×C₉×Dic₃	C₂³	1	2	yes	—
76	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₉×Dic₃	C₂³	1	2	yes	—
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₄×D₃×C₉	—	2	2	no	—
80	C₄×D₃×C₉	—	2	4	no	—
81	C₄×D₃×C₉	—	2	4	no	—
82	C₄×D₃×C₉	—	2	2	no	—
83	C₄×D₃×C₉	—	2	2	no	—
84	C₄×D₃×C₉	D₄	1	4	yes	—
85	C₉×Dic₆	—	2	2	no	—
86	C₉×Dic₆	—	2	4	no	—
87	C₂×C₃×C₂²⋊Q₈	—	3	1	no	—
88	D₃×C₂²⋊Q₈	C₉	1	1	yes	characteristic, direct product factor
89	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₃×D₃×Q₈	—	2	4	no	—
94	C₂×C₃×C₄×D₃	—	2	4	no	—
95	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
96	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
97	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
102	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
103	C₂⁴×C₉	—	3	1	no	—
104	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
105	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
107	C₃×#217	C₂²×C₃	1	2	yes	—
108	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
109	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
110	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
111	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
112	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
113	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
114	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
115	C₂×Q₈×C₉	—	2	1	no	—
116	C₂×Q₈×C₉	—	3	2	no	—
117	C₂×Q₈×C₉	—	3	1	no	—
118	C₂×Q₈×C₉	—	6	4	no	—
119	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
120	C₂²×C₄×C₉	—	2	1	no	—
121	C₂²×C₄×C₉	—	3	1	no	—
122	C₂²×C₄×C₉	—	3	1	no	—
123	C₂²×C₄×C₉	—	3	2	no	—
124	C₂²×C₄×C₉	—	3	2	no	—
125	C₂²×C₄×C₉	—	3	1	no	—
126	C₂²×C₄×C₉	—	3	1	no	—
127	C₂²×C₄×C₉	—	3	1	no	—
128	C₂²×C₄×C₉	—	6	4	no	—
129	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
130	C₉×C₄⋊C₄	—	2	1	no	—
131	C₉×C₄⋊C₄	—	2	2	no	—
132	C₉×C₄⋊C₄	—	3	2	no	—
133	C₉×C₄⋊C₄	—	3	2	no	—
134	C₉×C₄⋊C₄	—	3	2	no	—
135	C₉×C₄⋊C₄	—	3	1	no	—
136	C₉×C₄⋊C₄	—	3	2	no	—
137	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
138	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
139	C₉×C₂²⋊C₄	—	2	2	no	—
140	C₉×C₂²⋊C₄	—	3	2	no	—
141	C₉×C₂²⋊C₄	—	3	2	no	—
142	C₉×C₂²⋊C₄	—	3	2	no	—
143	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
144	C₂²×C₃×C₉	—	2	1	no	—
145	C₂²×C₃×C₉	—	2	1	no	—
146	C₂²×C₃×C₉	C₂×Q₈	1	2	yes	complemented
147	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
148	C₂×D₃×C₉	—	2	1	no	—
149	C₂×D₃×C₉	—	2	1	no	—
150	C₂×D₃×C₉	—	2	8	no	—
151	C₂×D₃×C₉	C₂×D₄	1	2	yes	—
152	C₂×D₃×C₉	C₂×Q₈	1	2	yes	—
153	C₂×D₃×C₉	C₂×Q₈	1	2	yes	complemented
154	C₂×D₃×C₉	#41	1	2	yes	—
155	C₃×C₄×C₉	—	2	2	no	—
156	C₃×C₄×C₉	—	2	1	no	—
157	C₃×C₄×C₉	—	2	2	no	—
158	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
159	C₉×Dic₃	—	2	2	no	—
160	C₉×Dic₃	—	2	1	no	—
161	C₉×Dic₃	—	2	2	no	—
162	C₉×Dic₃	C₂×D₄	1	2	yes	—
163	C₂²×C₃×Q₈	—	3	1	no	—
164	C₂³×C₃×C₄	—	3	1	no	—
165	C₂×D₃×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
166	C₂²×C₄×D₃	C₂×C₉	1	1	yes	characteristic
167	C₃×C₂²⋊Q₈	—	2	1	no	—
168	C₃×C₂²⋊Q₈	—	3	1	no	—
169	C₃×C₂²⋊Q₈	—	3	1	no	—
170	C₃×C₂²⋊Q₈	—	3	2	no	—
171	C₃×C₂²⋊Q₈	—	3	1	no	—
172	C₃×C₂²⋊Q₈	—	3	2	no	—
173	C₃×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
174	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	—	3	1	no	—
176	C₂×C₃×C₄⋊C₄	—	3	2	no	—
177	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
178	#946	C₂×C₉	1	1	yes	characteristic, complemented
179	#924	C₂×C₉	1	1	yes	characteristic, complemented
180	#897	C₂×C₉	1	1	yes	characteristic, complemented
181	#896	C₂×C₉	1	2	yes	complemented
182	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
183	D₃×C₄⋊C₄	C₂×C₉	1	2	yes	complemented
184	D₃×C₂²⋊C₄	C₂×C₉	1	2	yes	—
185	#878	C₂×C₉	1	2	yes	complemented
186	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
187	C₂²×C₃×D₃	—	2	2	no	—
188	C₂²×C₃×D₃	—	2	2	no	—
189	C₂²×C₃×D₃	C₃×Q₈	1	4	yes	—
190	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
191	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
192	C₃²×Q₈	—	2	2	no	—
193	C₂×C₃²×C₄	—	2	2	no	—
194	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
196	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
197	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₃×Dic₃	—	2	2	no	—
199	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
200	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
202	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
203	C₃×C₄×D₃	—	2	2	no	—
204	C₃×C₄×D₃	—	2	4	no	—
205	C₃×C₄×D₃	—	2	4	no	—
206	C₃×C₄×D₃	—	2	2	no	—
207	C₃×C₄×D₃	—	2	2	no	—
208	C₃×C₄×D₃	C₃×D₄	1	4	yes	—
209	C₃×Dic₆	—	2	2	no	—
210	C₃×Dic₆	—	2	4	no	—
211	C₂³×C₉	—	2	1	no	—
212	C₂³×C₉	—	3	1	no	—
213	C₂³×C₉	—	3	4	no	—
214	C₂³×C₉	—	3	1	no	—
215	C₂³×C₉	—	6	2	no	—
216	C₂³×C₉	—	6	2	no	—
217	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
218	Q₈×C₉	—	2	2	no	—
219	Q₈×C₉	—	4	2	no	—
220	Q₈×C₉	—	6	4	no	—
221	Q₈×C₉	—	6	2	no	—
222	C₂×C₄×C₉	—	2	2	no	—
223	C₂×C₄×C₉	—	2	1	no	—
224	C₂×C₄×C₉	—	2	2	no	—
225	C₂×C₄×C₉	—	2	2	no	—
226	C₂×C₄×C₉	—	2	1	no	—
227	C₂×C₄×C₉	—	3	1	no	—
228	C₂×C₄×C₉	—	3	4	no	—
229	C₂×C₄×C₉	—	3	2	no	—
230	C₂×C₄×C₉	—	3	2	no	—
231	C₂×C₄×C₉	—	3	1	no	—
232	C₂×C₄×C₉	—	4	2	no	—
233	C₂×C₄×C₉	—	6	2	no	—
234	C₂×C₄×C₉	—	6	4	no	—
235	C₂×C₄×C₉	—	6	2	no	—
236	C₂×C₄×C₉	—	6	4	no	—
237	C₂×C₄×C₉	—	6	2	no	—
238	C₂×C₄×C₉	—	6	2	no	—
239	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
240	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
241	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
242	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
243	C₂×C₂²⋊Q₈	—	3	1	no	Sylow
244	C₂×C₃×C₉	—	2	2	no	—
245	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
247	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
248	D₃×C₉	—	2	2	no	—
249	D₃×C₉	C₂²⋊Q₈	1	4	yes	direct product factor
250	C₂⁴×C₃	—	3	1	no	—
251	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
252	C₂×C₃×Q₈	—	2	1	no	—
253	C₂×C₃×Q₈	—	3	2	no	—
254	C₂×C₃×Q₈	—	3	1	no	—
255	C₂×C₃×Q₈	—	6	4	no	—
256	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
257	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
258	C₂²×C₃×C₄	—	2	1	no	—
259	C₂²×C₃×C₄	—	3	1	no	—
260	C₂²×C₃×C₄	—	3	1	no	—
261	C₂²×C₃×C₄	—	3	2	no	—
262	C₂²×C₃×C₄	—	3	2	no	—
263	C₂²×C₃×C₄	—	3	1	no	—
264	C₂²×C₃×C₄	—	3	1	no	—
265	C₂²×C₃×C₄	—	3	1	no	—
266	C₂²×C₃×C₄	—	6	4	no	—
267	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
269	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
270	D₃×Q₈	—	2	4	no	—
271	C₂×C₄×D₃	—	2	4	no	—
272	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
273	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
274	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
275	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
276	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
277	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
278	C₂×Dic₆	C₂²×C₉	1	2	yes	complemented
279	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
280	C₃×C₄⋊C₄	—	2	1	no	—
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	—	3	2	no	—
283	C₃×C₄⋊C₄	—	3	2	no	—
284	C₃×C₄⋊C₄	—	3	2	no	—
285	C₃×C₄⋊C₄	—	3	1	no	—
286	C₃×C₄⋊C₄	—	3	2	no	—
287	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	complemented
288	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
289	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
290	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
291	C₃×C₂²⋊C₄	—	2	2	no	—
292	C₃×C₂²⋊C₄	—	3	2	no	—
293	C₃×C₂²⋊C₄	—	3	2	no	—
294	C₃×C₂²⋊C₄	—	3	2	no	—
295	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
296	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
297	#217	C₂²×C₉	1	2	yes	—
298	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
299	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
300	C₄⋊Dic₃	C₂²×C₉	1	2	yes	complemented
301	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
302	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
303	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
304	Dic₃⋊C₄	C₂²×C₉	1	2	yes	complemented
305	C₂²×C₃²	—	2	1	no	—
306	C₂²×C₃²	—	2	1	no	—
307	C₂²×C₃²	C₂×C₃×Q₈	1	2	yes	—
308	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
309	C₂×C₃×D₃	—	2	1	no	—
310	C₂×C₃×D₃	—	2	1	no	—
311	C₂×C₃×D₃	—	2	8	no	—
312	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
313	C₂×C₃×D₃	C₂×C₃×Q₈	1	2	yes	—
314	C₂×C₃×D₃	C₂×C₃×Q₈	1	2	yes	—
315	C₂×C₃×D₃	C₃×#41	1	2	yes	—
316	C₃²×C₄	—	2	2	no	—
317	C₃²×C₄	—	2	1	no	—
318	C₃²×C₄	—	2	2	no	—
319	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
320	C₃×Dic₃	—	2	2	no	—
321	C₃×Dic₃	—	2	1	no	—
322	C₃×Dic₃	—	2	2	no	—
323	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
324	C₂²×C₉	—	2	1	no	—
325	C₂²×C₉	—	2	1	no	—
326	C₂²×C₉	—	2	1	no	—
327	C₂²×C₉	—	2	2	no	—
328	C₂²×C₉	—	3	2	no	—
329	C₂²×C₉	—	3	2	no	—
330	C₂²×C₉	—	3	2	no	—
331	C₂²×C₉	—	3	2	no	—
332	C₂²×C₉	—	4	1	no	—
333	C₂²×C₉	—	4	1	no	—
334	C₂²×C₉	—	6	8	no	—
335	C₂²×C₉	—	6	1	no	—
336	C₂²×C₉	—	6	1	no	—
337	C₂²×C₉	D₃×Q₈	1	2	yes	complemented
338	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
339	C₄×C₉	—	2	1	no	—
340	C₄×C₉	—	2	2	no	—
341	C₄×C₉	—	2	2	no	—
342	C₄×C₉	—	2	2	no	—
343	C₄×C₉	—	3	2	no	—
344	C₄×C₉	—	4	2	no	—
345	C₄×C₉	—	4	1	no	—
346	C₄×C₉	—	4	2	no	—
347	C₄×C₉	—	6	1	no	—
348	C₄×C₉	—	6	2	no	—
349	C₄×C₉	—	6	2	no	—
350	C₄×C₉	D₃×D₄	1	2	yes	—
351	C₂²×Q₈	—	3	1	no	—
352	C₂³×C₄	—	3	1	no	—
353	C₂²⋊Q₈	—	3	1	no	—
354	C₂²⋊Q₈	—	3	1	no	—
355	C₂²⋊Q₈	—	3	2	no	—
356	C₂²⋊Q₈	—	3	1	no	—
357	C₂²⋊Q₈	—	3	2	no	—
358	C₂²⋊Q₈	D₃×C₉	1	1	yes	characteristic, direct product factor
359	C₂×C₄⋊C₄	—	3	1	no	—
360	C₂×C₄⋊C₄	—	3	2	no	—
361	C₂×C₂²⋊C₄	—	3	2	no	—
362	C₃×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	—	3	1	no	—
365	C₂³×C₃	—	3	1	no	—
366	C₂³×C₃	—	3	4	no	—
367	C₂³×C₃	—	6	2	no	—
368	C₂³×C₃	—	6	2	no	—
369	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
370	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
371	C₂²×D₃	—	2	2	no	—
372	C₂²×D₃	—	2	2	no	—
373	C₂²×D₃	Q₈×C₉	1	4	yes	complemented
374	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
375	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
376	C₃×Q₈	—	2	2	no	—
377	C₃×Q₈	—	2	2	no	—
378	C₃×Q₈	—	4	2	no	—
379	C₃×Q₈	—	6	4	no	—
380	C₃×Q₈	—	6	2	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	3	1	no	—
388	C₂×C₃×C₄	—	3	4	no	—
389	C₂×C₃×C₄	—	3	2	no	—
390	C₂×C₃×C₄	—	3	2	no	—
391	C₂×C₃×C₄	—	3	1	no	—
392	C₂×C₃×C₄	—	4	2	no	—
393	C₂×C₃×C₄	—	6	2	no	—
394	C₂×C₃×C₄	—	6	4	no	—
395	C₂×C₃×C₄	—	6	2	no	—
396	C₂×C₃×C₄	—	6	4	no	—
397	C₂×C₃×C₄	—	6	2	no	—
398	C₂×C₃×C₄	—	6	2	no	—
399	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
401	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
402	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
404	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
405	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
407	C₂×Dic₃	—	2	2	no	—
408	C₂×Dic₃	C₂³×C₉	1	2	yes	—
409	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
410	C₂×Dic₃	C₂³×C₉	1	2	yes	—
411	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
412	C₄×D₃	—	2	2	no	—
413	C₄×D₃	—	2	4	no	—
414	C₄×D₃	—	2	4	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	D₄×C₉	1	4	yes	—
418	Dic₆	—	2	2	no	—
419	Dic₆	—	2	4	no	—
420	C₂×C₃²	—	2	2	no	—
421	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
422	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
423	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
424	C₃×D₃	—	2	2	no	—
425	C₃×D₃	C₃×C₂²⋊Q₈	1	4	yes	—
426	C₂×C₉	—	2	2	no	—
427	C₂×C₉	—	2	1	no	—
428	C₂×C₉	—	2	1	no	—
429	C₂×C₉	—	2	1	no	—
430	C₂×C₉	—	3	4	no	—
431	C₂×C₉	—	4	2	no	—
432	C₂×C₉	—	6	2	no	—
433	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
434	C₂×C₉	C₂×D₃×Q₈	1	1	yes	characteristic
435	C₂×C₉	D₃×#41	1	1	yes	characteristic
436	C₂⁴	—	3	1	no	—
437	C₂×Q₈	—	3	2	no	—
438	C₂×Q₈	—	3	1	no	—
439	C₂×Q₈	—	6	4	no	—
440	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	—	3	1	no	—
443	C₂²×C₄	—	3	2	no	—
444	C₂²×C₄	—	3	2	no	—
445	C₂²×C₄	—	3	1	no	—
446	C₂²×C₄	—	3	1	no	—
447	C₂²×C₄	—	3	1	no	—
448	C₂²×C₄	—	6	4	no	—
449	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
450	C₄⋊C₄	—	3	2	no	—
451	C₄⋊C₄	—	3	2	no	—
452	C₄⋊C₄	—	3	2	no	—
453	C₄⋊C₄	—	3	1	no	—
454	C₄⋊C₄	—	3	2	no	—
455	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
456	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
457	C₂²⋊C₄	—	3	2	no	—
458	C₂²⋊C₄	—	3	2	no	—
459	C₂²⋊C₄	—	3	2	no	—
460	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	1	no	—
466	C₂²×C₃	—	2	2	no	—
467	C₂²×C₃	—	3	2	no	—
468	C₂²×C₃	—	3	2	no	—
469	C₂²×C₃	—	3	2	no	—
470	C₂²×C₃	—	3	2	no	—
471	C₂²×C₃	—	4	1	no	—
472	C₂²×C₃	—	4	1	no	—
473	C₂²×C₃	—	6	8	no	—
474	C₂²×C₃	—	6	1	no	—
475	C₂²×C₃	—	6	1	no	—
476	C₂²×C₃	C₂×Q₈×C₉	1	2	yes	complemented
477	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
478	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
479	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
480	C₂×D₃	—	2	1	no	—
481	C₂×D₃	—	2	1	no	—
482	C₂×D₃	—	2	8	no	—
483	C₂×D₃	C₂×D₄×C₉	1	2	yes	—
484	C₂×D₃	C₂×Q₈×C₉	1	2	yes	—
485	C₂×D₃	C₂×Q₈×C₉	1	2	yes	complemented
486	C₂×D₃	C₉×#41	1	2	yes	—
487	C₃×C₄	—	2	1	no	—
488	C₃×C₄	—	2	2	no	—
489	C₃×C₄	—	2	2	no	—
490	C₃×C₄	—	2	2	no	—
491	C₃×C₄	—	2	1	no	—
492	C₃×C₄	—	2	2	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	3	2	no	—
495	C₃×C₄	—	4	1	no	—
496	C₃×C₄	—	4	2	no	—
497	C₃×C₄	—	4	2	no	—
498	C₃×C₄	—	6	1	no	—
499	C₃×C₄	—	6	2	no	—
500	C₃×C₄	—	6	2	no	—
501	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
502	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
503	Dic₃	—	2	2	no	—
504	Dic₃	—	2	1	no	—
505	Dic₃	—	2	2	no	—
506	Dic₃	C₂×D₄×C₉	1	2	yes	—
507	C₃²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
508	C₉	—	2	1	no	—
509	C₉	D₃×C₂²⋊Q₈	1	1	yes	characteristic, direct product factor
510	C₂³	—	3	1	no	—
511	C₂³	—	3	1	no	—
512	C₂³	—	3	4	no	—
513	C₂³	—	6	2	no	—
514	C₂³	—	6	2	no	—
515	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	6	4	no	—
518	Q₈	—	6	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	3	1	no	—
521	C₂×C₄	—	3	4	no	—
522	C₂×C₄	—	3	2	no	—
523	C₂×C₄	—	3	2	no	—
524	C₂×C₄	—	3	1	no	—
525	C₂×C₄	—	6	2	no	—
526	C₂×C₄	—	6	2	no	—
527	C₂×C₄	—	6	4	no	—
528	C₂×C₄	—	6	4	no	—
529	C₂×C₄	—	6	2	no	—
530	C₂×C₄	—	6	2	no	—
531	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
532	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
533	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
535	C₂×C₃	—	2	2	no	—
536	C₂×C₃	—	2	2	no	—
537	C₂×C₃	—	2	1	no	—
538	C₂×C₃	—	2	1	no	—
539	C₂×C₃	—	2	1	no	—
540	C₂×C₃	—	3	4	no	—
541	C₂×C₃	—	4	2	no	—
542	C₂×C₃	—	6	2	no	—
543	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
544	C₂×C₃	C₂²×Q₈×C₉	1	1	yes	characteristic
545	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
546	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
547	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
548	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
549	D₃	—	2	2	no	—
550	D₃	C₉×C₂²⋊Q₈	1	4	yes	direct product factor
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	3	2	no	—
554	C₂²	—	3	2	no	—
555	C₂²	—	3	2	no	—
556	C₂²	—	3	2	no	—
557	C₂²	—	6	8	no	—
558	C₂²	—	6	1	no	—
559	C₂²	—	6	1	no	—
560	C₂²	D₃×Q₈×C₉	1	2	yes	complemented
561	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	2	no	—
565	C₄	—	3	2	no	—
566	C₄	—	6	1	no	—
567	C₄	—	6	2	no	—
568	C₄	—	6	2	no	—
569	C₄	D₃×D₄×C₉	1	2	yes	—
570	C₃	—	2	1	no	—
571	C₃	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic, complemented
572	C₃	C₃×D₃×C₂²⋊Q₈	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	3	4	no	—
575	C₂	—	6	2	no	—
576	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
577	C₂	C₂×D₃×Q₈×C₉	1	1	yes	characteristic
578	C₂	D₃×C₉×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₂²⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂³×C₃×D₃	C₂²×C₃
hypercenter	C₉×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₉×C₂²⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×Q₈×C₉	C₂	semidirect
3. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₉×#946	C₂	semidirect
5. C₉×#924	C₂	semidirect
6. C₉×#897	C₂	semidirect
7. C₉×#896	C₂	semidirect
8. D₃×C₉×C₄⋊C₄	C₂	semidirect
9. D₃×C₉×C₄⋊C₄	C₂	semidirect
11. C₉×#878	C₂	semidirect
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
26. C₂×C₉×Dic₆	C₂²	semidirect
27. C₂×C₉×Dic₆	C₂²	semidirect
28. C₃×C₉×C₄⋊C₄	C₂²	semidirect
29. C₃×C₉×C₄⋊C₄	C₂²	semidirect
34. C₉×C₄⋊Dic₃	C₂²	semidirect
35. C₉×C₄⋊Dic₃	C₂²	semidirect
36. C₉×Dic₃⋊C₄	C₂²	semidirect
37. C₉×Dic₃⋊C₄	C₂²	semidirect
38. C₉×Dic₃⋊C₄	C₂²	semidirect
58. C₉×C₂²⋊Q₈	D₃	direct (N × H)
65. C₂²×D₃×C₉	Q₈	semidirect
88. D₃×C₂²⋊Q₈	C₉	direct (N × H)
119. C₂×Q₈×C₉	C₂×D₃	semidirect
137. C₉×C₄⋊C₄	C₂×D₃	semidirect
138. C₉×C₄⋊C₄	C₂×D₃	semidirect
146. C₂²×C₃×C₉	C₂×Q₈	semidirect
153. C₂×D₃×C₉	C₂×Q₈	semidirect
165. C₂×D₃×Q₈	C₂×C₉	semidirect
173. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
178. #946	C₂×C₉	semidirect
179. #924	C₂×C₉	semidirect
180. #897	C₂×C₉	semidirect
181. #896	C₂×C₉	semidirect
182. D₃×C₄⋊C₄	C₂×C₉	semidirect
183. D₃×C₄⋊C₄	C₂×C₉	semidirect
185. #878	C₂×C₉	semidirect
249. D₃×C₉	C₂²⋊Q₈	direct (N × H)
256. C₂×C₃×Q₈	C₂²×C₉	semidirect
278. C₂×Dic₆	C₂²×C₉	semidirect
279. C₂×Dic₆	C₂²×C₉	semidirect
287. C₃×C₄⋊C₄	C₂²×C₉	semidirect
288. C₃×C₄⋊C₄	C₂²×C₉	semidirect
300. C₄⋊Dic₃	C₂²×C₉	semidirect
301. C₄⋊Dic₃	C₂²×C₉	semidirect
302. Dic₃⋊C₄	C₂²×C₉	semidirect
303. Dic₃⋊C₄	C₂²×C₉	semidirect
304. Dic₃⋊C₄	C₂²×C₉	semidirect
337. C₂²×C₉	D₃×Q₈	semidirect
358. C₂²⋊Q₈	D₃×C₉	direct (N × H)
362. C₃×C₉	C₂×C₂²⋊Q₈	semidirect
373. C₂²×D₃	Q₈×C₉	semidirect
440. C₂×Q₈	C₂×D₃×C₉	semidirect
455. C₄⋊C₄	C₂×D₃×C₉	semidirect
456. C₄⋊C₄	C₂×D₃×C₉	semidirect
476. C₂²×C₃	C₂×Q₈×C₉	semidirect
485. C₂×D₃	C₂×Q₈×C₉	semidirect
509. C₉	D₃×C₂²⋊Q₈	direct (N × H)
550. D₃	C₉×C₂²⋊Q₈	direct (N × H)
560. C₂²	D₃×Q₈×C₉	semidirect
571. C₃	C₂×C₉×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×Q₈×C₉	2
C₂²×C₄×D₃×C₉	2
C₃×C₉×C₂²⋊Q₈	2
C₉×#946	2
C₉×#924	2
C₉×#897	2
C₉×#896	2
D₃×C₉×C₄⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₉×#878	2
C₃×D₃×C₂²⋊Q₈	3
C₂×C₉×C₂²⋊Q₈	3

Subgroups — D3×C9×C22⋊Q8 #13152925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×C₂²⋊Q₈ #13152925