Subgroups — C₂×C₃×#63480 #13153456

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3701	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Q₈×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3675	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3674	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63480	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#3664	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3663	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#918	—	3	1	no	maximal
10	C₂×#63480	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
13	C₃×#3701	—	2	2	no	—
14	C₃×#3701	C₂²	1	4	yes	—
15	C₃×Q₈×D₉	—	2	2	no	—
16	C₃×Q₈×D₉	C₂²	1	4	yes	complemented
17	C₂×C₃×D₃₆	—	2	1	no	—
18	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₉	—	2	1	no	—
20	C₂×C₃×C₄×D₉	—	2	1	no	—
21	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic
22	C₂×C₃×Dic₁₈	—	2	1	no	—
23	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
24	C₃×C₉×Q₁₆	C₂²	1	4	yes	complemented
25	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
26	C₃×#3675	C₂²	1	4	yes	complemented
27	C₃×#3674	C₂²	1	4	yes	complemented
28	C₂×C₃×C₉⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×#3664	C₂²	1	4	yes	complemented
30	C₃×#3663	C₂²	1	4	yes	complemented
31	C₂×C₃×#239	—	3	1	no	—
32	C₂×C₃×D₃×Q₈	—	3	1	no	—
33	C₂×C₃²×Q₁₆	D₃	1	1	yes	characteristic
34	C₂×C₃×#216	—	3	1	no	—
35	C₂×C₃×#215	—	3	1	no	—
36	C₃×#918	—	3	8	no	—
37	C₂×C₃×#204	—	3	1	no	—
38	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	1	no	—
39	C₂×#3701	C₂×C₃	1	1	yes	characteristic
40	C₂×Q₈×D₉	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₉×Q₁₆	—	2	1	no	—
42	C₂×C₉×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#3675	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#3674	C₂×C₃	1	1	yes	characteristic, complemented
45	#63480	C₂×C₃	1	8	yes	direct product factor
46	C₂×#3664	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#3663	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×C₃×D₉	—	2	1	no	—
49	C₂²×C₃×D₉	D₄	1	1	yes	characteristic
50	C₃×Q₈×C₉	—	2	1	no	—
51	C₃×Q₈×C₉	—	2	1	no	—
52	C₃×Q₈×C₉	C₂³	1	2	yes	—
53	C₃×Q₈×C₉	C₂³	1	2	yes	—
54	C₂×C₃×C₄×C₉	—	2	1	no	—
55	C₂×C₃×C₄×C₉	—	2	1	no	—
56	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
57	C₂×C₃×Dic₉	—	2	1	no	—
58	C₂×C₃×Dic₉	D₄	1	1	yes	characteristic
59	C₃×D₃₆	—	2	4	no	—
60	C₃×D₃₆	—	2	1	no	—
61	C₃×D₃₆	C₂³	1	2	yes	—
62	C₃×C₄×D₉	—	2	4	no	—
63	C₃×C₄×D₉	—	2	4	no	—
64	C₃×C₄×D₉	D₄	1	2	yes	—
65	C₃×C₄×D₉	C₂³	1	2	yes	—
66	C₃×Dic₁₈	—	2	1	no	—
67	C₃×Dic₁₈	—	2	4	no	—
68	C₃×Dic₁₈	C₂³	1	2	yes	—
69	C₃×C₈×C₉	C₂³	1	2	yes	—
70	C₃×C₉⋊C₈	C₂³	1	2	yes	—
71	C₂×C₃×#137	—	9	1	no	—
72	C₂×#918	—	3	1	no	—
73	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
75	C₃×#239	—	3	4	no	—
76	C₃×#239	—	6	2	no	—
77	C₃×D₃×Q₈	—	3	4	no	—
78	C₃×D₃×Q₈	—	6	2	no	—
79	C₂×C₃×D₁₂	—	3	1	no	—
80	C₂×C₃×D₁₂	—	6	1	no	—
81	C₂×C₃×C₄×D₃	—	3	1	no	—
82	C₂×C₃×C₄×D₃	—	6	1	no	—
83	C₂×C₃×C₄×D₃	—	6	1	no	—
84	C₂×C₃×Dic₆	—	3	1	no	—
85	C₂×C₃×Dic₆	—	6	1	no	—
86	C₃²×Q₁₆	C₂×D₃	1	4	yes	—
87	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
88	C₃×#216	—	3	4	no	—
89	C₃×#215	—	3	4	no	—
90	C₂×C₃×C₃⋊C₈	—	3	1	no	—
91	C₃×#204	—	3	4	no	—
92	C₃×ΓL(1,𝔽₂₅)	—	3	4	no	—
93	C₂×Q₈×C₉	—	2	1	no	—
94	C₂×Q₈×C₉	—	2	1	no	—
95	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
96	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
97	#3701	—	2	2	no	—
98	#3701	C₂²×C₃	1	4	yes	—
99	Q₈×D₉	—	2	2	no	—
100	Q₈×D₉	C₂²×C₃	1	4	yes	complemented
101	C₂×D₃₆	—	2	1	no	—
102	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₄×D₉	—	2	1	no	—
104	C₂×C₄×D₉	—	2	1	no	—
105	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
106	C₂×Dic₁₈	—	2	1	no	—
107	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
108	C₉×Q₁₆	—	2	4	no	—
109	C₉×Q₁₆	C₂²×C₃	1	4	yes	complemented
110	C₂×C₈×C₉	—	2	1	no	—
111	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
112	#3675	C₂²×C₃	1	4	yes	complemented
113	#3674	C₂²×C₃	1	4	yes	complemented
114	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
115	#3664	C₂²×C₃	1	4	yes	complemented
116	#3663	C₂²×C₃	1	4	yes	complemented
117	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×D₉	—	2	2	no	—
119	C₂×C₃×D₉	—	2	2	no	—
120	C₂×C₃×D₉	—	4	2	no	—
121	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
122	C₃×C₄×C₉	—	2	2	no	—
123	C₃×C₄×C₉	—	2	2	no	—
124	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
125	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
126	C₃×Dic₉	—	2	2	no	—
127	C₃×Dic₉	C₂×D₄	1	2	yes	—
128	C₂×C₃×#41	—	9	1	no	—
129	C₂²×C₃×Q₈	—	9	1	no	—
130	C₂×#239	—	3	1	no	—
131	C₂×D₃×Q₈	—	3	1	no	—
132	C₃×#137	—	9	8	no	—
133	C₂×C₃×Q₁₆	—	2	1	no	—
134	C₂×C₃×Q₁₆	—	9	1	no	—
135	C₂×C₃×Q₁₆	D₉	1	1	yes	characteristic, complemented
136	C₂×C₃×Q₁₆	C₃×D₃	1	1	yes	characteristic
137	C₂×C₃×SD₁₆	—	9	1	no	—
138	C₂×C₃×SD₁₆	—	9	1	no	—
139	C₂×C₃×M₁₆	—	9	1	no	—
140	C₂×#216	—	3	1	no	—
141	C₂×#215	—	3	1	no	—
142	#918	—	3	8	no	—
143	C₂×#204	—	3	1	no	—
144	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
145	C₂²×C₃×D₃	—	3	1	no	—
146	C₂²×C₃×D₃	—	6	1	no	—
147	C₃²×Q₈	—	2	1	no	—
148	C₃²×Q₈	—	2	1	no	—
149	C₃²×Q₈	C₂²×D₃	1	2	yes	—
150	C₃²×Q₈	C₂²×D₃	1	2	yes	—
151	C₂×C₃²×C₄	—	2	1	no	—
152	C₂×C₃²×C₄	—	2	1	no	—
153	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
154	C₂×C₃×Dic₃	—	3	1	no	—
155	C₂×C₃×Dic₃	—	6	1	no	—
156	C₃×D₁₂	—	3	2	no	—
157	C₃×D₁₂	—	6	4	no	—
158	C₃×D₁₂	—	6	1	no	—
159	C₃×C₄×D₃	—	3	2	no	—
160	C₃×C₄×D₃	—	3	2	no	—
161	C₃×C₄×D₃	—	6	4	no	—
162	C₃×C₄×D₃	—	6	4	no	—
163	C₃×Dic₆	—	3	2	no	—
164	C₃×Dic₆	—	6	4	no	—
165	C₃×Dic₆	—	6	1	no	—
166	C₂²×D₉	—	2	1	no	—
167	C₂²×D₉	C₃×D₄	1	1	yes	characteristic
168	C₃²×C₈	C₂²×D₃	1	2	yes	—
169	C₃×C₃⋊C₈	—	3	2	no	—
170	Q₈×C₉	—	2	1	no	—
171	Q₈×C₉	—	2	1	no	—
172	Q₈×C₉	—	2	2	no	—
173	Q₈×C₉	—	2	2	no	—
174	Q₈×C₉	—	4	1	no	—
175	Q₈×C₉	—	4	1	no	—
176	Q₈×C₉	C₂³×C₃	1	2	yes	—
177	Q₈×C₉	C₂³×C₃	1	2	yes	—
178	C₂×C₄×C₉	—	2	1	no	—
179	C₂×C₄×C₉	—	2	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	4	1	no	—
182	C₂×C₄×C₉	—	4	1	no	—
183	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
184	C₂×Dic₉	—	2	1	no	—
185	C₂×Dic₉	C₃×D₄	1	1	yes	characteristic
186	D₃₆	—	2	4	no	—
187	D₃₆	—	2	1	no	—
188	D₃₆	C₂³×C₃	1	2	yes	—
189	C₄×D₉	—	2	4	no	—
190	C₄×D₉	—	2	4	no	—
191	C₄×D₉	C₃×D₄	1	2	yes	—
192	C₄×D₉	C₂³×C₃	1	2	yes	—
193	Dic₁₈	—	2	1	no	—
194	Dic₁₈	—	2	4	no	—
195	Dic₁₈	C₂³×C₃	1	2	yes	—
196	C₈×C₉	—	2	2	no	—
197	C₈×C₉	C₂³×C₃	1	2	yes	—
198	C₉⋊C₈	C₂³×C₃	1	2	yes	—
199	C₂×#137	—	9	1	no	Sylow
200	C₂×C₃×C₉	#137	1	2	yes	complemented
201	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
202	C₃×D₉	—	2	2	no	—
203	C₃×D₉	—	4	2	no	—
204	C₃×#41	—	9	4	no	—
205	C₃×#41	—	18	2	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	—	2	1	no	—
208	C₂×C₃×Q₈	—	9	4	no	—
209	C₂×C₃×Q₈	—	9	1	no	—
210	C₂×C₃×Q₈	—	18	1	no	—
211	C₂×C₃×Q₈	—	18	2	no	—
212	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
213	C₂×C₃×Q₈	C₂×D₉	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
215	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
216	C₂×C₃×D₄	—	9	1	no	—
217	C₂×C₃×D₄	—	18	1	no	—
218	C₂²×C₃×C₄	—	9	1	no	—
219	C₂²×C₃×C₄	—	18	1	no	—
220	C₂²×C₃×C₄	—	18	1	no	—
221	#239	—	3	4	no	—
222	#239	—	6	2	no	—
223	D₃×Q₈	—	3	4	no	—
224	D₃×Q₈	—	6	2	no	—
225	C₂×D₁₂	—	3	1	no	—
226	C₂×D₁₂	—	6	1	no	—
227	C₂×C₄×D₃	—	3	1	no	—
228	C₂×C₄×D₃	—	6	1	no	—
229	C₂×C₄×D₃	—	6	1	no	—
230	C₂×Dic₆	—	3	1	no	—
231	C₂×Dic₆	—	6	1	no	—
232	C₃×Q₁₆	—	2	4	no	—
233	C₃×Q₁₆	—	9	4	no	—
234	C₃×Q₁₆	C₂×D₉	1	4	yes	complemented
235	C₃×Q₁₆	C₂×C₃×D₃	1	4	yes	—
236	C₃×SD₁₆	—	9	4	no	—
237	C₃×SD₁₆	—	9	4	no	—
238	C₃×M₁₆	—	9	4	no	—
239	C₂×C₃×C₈	—	2	1	no	—
240	C₂×C₃×C₈	—	9	1	no	—
241	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic
242	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
243	#216	—	3	4	no	—
244	#215	—	3	4	no	—
245	C₂×C₃⋊C₈	—	3	1	no	—
246	#204	—	3	4	no	—
247	ΓL(1,𝔽₂₅)	—	3	4	no	—
248	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
249	C₂×C₃×D₃	—	3	2	no	—
250	C₂×C₃×D₃	—	6	2	no	—
251	C₂×C₃×D₃	—	6	2	no	—
252	C₂×C₃×D₃	—	12	2	no	—
253	C₃²×C₄	—	2	2	no	—
254	C₃²×C₄	—	2	2	no	—
255	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
256	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
257	C₃×Dic₃	—	3	2	no	—
258	C₃×Dic₃	—	6	2	no	—
259	C₂²×C₉	—	2	1	no	—
260	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
261	C₂×D₉	—	2	2	no	—
262	C₂×D₉	—	2	2	no	—
263	C₂×D₉	—	4	2	no	—
264	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
265	C₄×C₉	—	2	2	no	—
266	C₄×C₉	—	2	2	no	—
267	C₄×C₉	—	2	1	no	—
268	C₄×C₉	—	2	1	no	—
269	C₄×C₉	—	4	2	no	—
270	C₄×C₉	—	4	2	no	—
271	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
272	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
273	Dic₉	—	2	2	no	—
274	Dic₉	C₂×C₃×D₄	1	2	yes	—
275	C₂×#41	—	9	1	no	—
276	C₂²×Q₈	—	9	1	no	—
277	#137	—	9	8	no	—
278	C₂×Q₁₆	—	9	1	no	—
279	C₂×Q₁₆	C₃×D₉	1	1	yes	characteristic, complemented
280	C₂×SD₁₆	—	9	1	no	—
281	C₂×SD₁₆	—	9	1	no	—
282	C₂×M₁₆	—	9	1	no	—
283	C₃×C₉	C₂×#137	1	1	yes	characteristic, complemented, Sylow
284	C₂³×C₃	—	9	1	no	—
285	C₂³×C₃	—	18	1	no	—
286	C₂²×D₃	—	3	1	no	—
287	C₂²×D₃	—	6	1	no	—
288	C₃×Q₈	—	2	1	no	—
289	C₃×Q₈	—	2	1	no	—
290	C₃×Q₈	—	2	1	no	—
291	C₃×Q₈	—	2	1	no	—
292	C₃×Q₈	—	2	2	no	—
293	C₃×Q₈	—	2	2	no	—
294	C₃×Q₈	—	4	1	no	—
295	C₃×Q₈	—	4	1	no	—
296	C₃×Q₈	—	9	2	no	—
297	C₃×Q₈	—	18	4	no	—
298	C₃×Q₈	—	18	1	no	—
299	C₃×Q₈	C₂²×D₉	1	2	yes	—
300	C₃×Q₈	C₂²×D₉	1	2	yes	—
301	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
302	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
303	C₃×D₄	—	9	2	no	—
304	C₃×D₄	—	18	4	no	—
305	C₃×D₄	—	18	1	no	—
306	C₂×C₃×C₄	—	2	1	no	—
307	C₂×C₃×C₄	—	2	1	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	1	no	—
311	C₂×C₃×C₄	—	4	1	no	—
312	C₂×C₃×C₄	—	4	1	no	—
313	C₂×C₃×C₄	—	9	1	no	—
314	C₂×C₃×C₄	—	9	2	no	—
315	C₂×C₃×C₄	—	9	2	no	—
316	C₂×C₃×C₄	—	18	4	no	—
317	C₂×C₃×C₄	—	18	4	no	—
318	C₂×C₃×C₄	—	18	1	no	—
319	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
321	C₂×Dic₃	—	3	1	no	—
322	C₂×Dic₃	—	6	1	no	—
323	D₁₂	—	3	2	no	—
324	D₁₂	—	6	4	no	—
325	D₁₂	—	6	1	no	—
326	C₄×D₃	—	3	2	no	—
327	C₄×D₃	—	3	2	no	—
328	C₄×D₃	—	6	4	no	—
329	C₄×D₃	—	6	4	no	—
330	Dic₆	—	3	2	no	—
331	Dic₆	—	6	4	no	—
332	Dic₆	—	6	1	no	—
333	C₃×C₈	—	2	2	no	—
334	C₃×C₈	—	9	2	no	—
335	C₃×C₈	C₂²×D₉	1	2	yes	—
336	C₃×C₈	C₂²×C₃×D₃	1	2	yes	—
337	C₃⋊C₈	—	3	2	no	—
338	C₂×C₃²	#918	1	2	yes	—
339	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
340	C₃×D₃	—	6	2	no	—
341	C₃×D₃	—	12	2	no	—
342	C₂×C₉	—	2	2	no	—
343	C₂×C₉	—	2	1	no	—
344	C₂×C₉	C₃×#137	1	2	yes	complemented
345	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
346	D₉	—	2	2	no	—
347	D₉	—	4	2	no	—
348	#41	—	9	4	no	—
349	#41	—	18	2	no	—
350	C₂×Q₈	—	9	4	no	—
351	C₂×Q₈	—	9	1	no	—
352	C₂×Q₈	—	18	1	no	—
353	C₂×Q₈	—	18	2	no	—
354	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
355	C₂×Q₈	C₂×C₃×D₉	1	1	yes	characteristic
356	C₂×D₄	—	9	1	no	—
357	C₂×D₄	—	18	1	no	—
358	C₂²×C₄	—	9	1	no	—
359	C₂²×C₄	—	18	1	no	—
360	C₂²×C₄	—	18	1	no	—
361	Q₁₆	—	9	4	no	—
362	Q₁₆	C₂×C₃×D₉	1	4	yes	complemented
363	SD₁₆	—	9	4	no	—
364	SD₁₆	—	9	4	no	—
365	M₁₆	—	9	4	no	—
366	C₂×C₈	—	9	1	no	—
367	C₂×C₈	C₂×C₃×D₉	1	1	yes	characteristic
368	C₂²×C₃	—	2	1	no	—
369	C₂²×C₃	—	9	2	no	—
370	C₂²×C₃	—	18	2	no	—
371	C₂²×C₃	—	18	2	no	—
372	C₂²×C₃	—	36	2	no	—
373	C₂²×C₃	D₄×D₉	1	1	yes	characteristic
374	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
375	C₂×D₃	—	3	2	no	—
376	C₂×D₃	—	6	2	no	—
377	C₂×D₃	—	6	2	no	—
378	C₂×D₃	—	12	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	4	2	no	—
386	C₃×C₄	—	4	2	no	—
387	C₃×C₄	—	9	2	no	—
388	C₃×C₄	—	18	2	no	—
389	C₃×C₄	D₄×D₉	1	1	yes	characteristic
390	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
391	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
392	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
393	Dic₃	—	3	2	no	—
394	Dic₃	—	6	2	no	—
395	C₃²	C₂×#918	1	1	yes	characteristic
396	C₉	—	2	1	no	—
397	C₉	C₂×C₃×#137	1	1	yes	characteristic, complemented
398	C₂³	—	9	1	no	—
399	C₂³	—	18	1	no	—
400	Q₈	—	2	1	no	—
401	Q₈	—	2	1	no	—
402	Q₈	—	9	2	no	—
403	Q₈	—	18	4	no	—
404	Q₈	—	18	1	no	—
405	Q₈	C₂²×C₃×D₉	1	2	yes	—
406	Q₈	C₂²×C₃×D₉	1	2	yes	—
407	D₄	—	9	2	no	—
408	D₄	—	18	4	no	—
409	D₄	—	18	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	9	1	no	—
413	C₂×C₄	—	9	2	no	—
414	C₂×C₄	—	9	2	no	—
415	C₂×C₄	—	18	4	no	—
416	C₂×C₄	—	18	4	no	—
417	C₂×C₄	—	18	1	no	—
418	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
419	C₈	—	9	2	no	—
420	C₈	C₂²×C₃×D₉	1	2	yes	—
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	18	2	no	—
424	C₂×C₃	—	36	2	no	—
425	C₂×C₃	#63480	1	2	yes	direct product factor
426	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
427	C₂×C₃	C₃×#918	1	2	yes	—
428	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
429	D₃	—	6	2	no	—
430	D₃	—	12	2	no	—
431	C₂²	—	9	2	no	—
432	C₂²	—	18	2	no	—
433	C₂²	—	18	2	no	—
434	C₂²	—	36	2	no	—
435	C₂²	C₃×D₄×D₉	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	9	2	no	—
439	C₄	—	18	2	no	—
440	C₄	C₃×D₄×D₉	1	1	yes	characteristic
441	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
442	C₃	—	2	1	no	—
443	C₃	C₂×#63480	1	1	yes	characteristic, direct product factor
444	C₃	C₂×C₃×#918	1	1	yes	characteristic
445	C₂	—	18	2	no	—
446	C₂	—	36	2	no	—
447	C₂	C₃×#63480	1	2	yes	direct product factor
448	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×D₉
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×Q₁₆	C₂
socle	C₂²×C₃²	D₃×D₄
prime radical	C₂×C₃×#3701	C₂
hypercenter	C₂×C₃×Q₁₆	D₉
hypocenter	C₉	C₂×C₃×#137
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Q₈×D₉	C₂	semidirect
3. C₂×C₃×C₉×Q₁₆	C₂	semidirect
4. C₂×C₃×#3675	C₂	semidirect
5. C₂×C₃×#3674	C₂	semidirect
6. C₃×#63480	C₂	direct (N × H)
7. C₂×C₃×#3664	C₂	semidirect
8. C₂×C₃×#3663	C₂	semidirect
10. C₂×#63480	C₃	direct (N × H)
16. C₃×Q₈×D₉	C₂²	semidirect
24. C₃×C₉×Q₁₆	C₂²	semidirect
26. C₃×#3675	C₂²	semidirect
27. C₃×#3674	C₂²	semidirect
29. C₃×#3664	C₂²	semidirect
30. C₃×#3663	C₂²	semidirect
40. C₂×Q₈×D₉	C₂×C₃	semidirect
42. C₂×C₉×Q₁₆	C₂×C₃	semidirect
43. C₂×#3675	C₂×C₃	semidirect
44. C₂×#3674	C₂×C₃	semidirect
45. #63480	C₂×C₃	direct (N × H)
46. C₂×#3664	C₂×C₃	semidirect
47. C₂×#3663	C₂×C₃	semidirect
100. Q₈×D₉	C₂²×C₃	semidirect
109. C₉×Q₁₆	C₂²×C₃	semidirect
112. #3675	C₂²×C₃	semidirect
113. #3674	C₂²×C₃	semidirect
115. #3664	C₂²×C₃	semidirect
116. #3663	C₂²×C₃	semidirect
135. C₂×C₃×Q₁₆	D₉	semidirect
200. C₂×C₃×C₉	#137	semidirect
234. C₃×Q₁₆	C₂×D₉	semidirect
279. C₂×Q₁₆	C₃×D₉	semidirect
283. C₃×C₉	C₂×#137	semidirect
344. C₂×C₉	C₃×#137	semidirect
362. Q₁₆	C₂×C₃×D₉	semidirect
397. C₉	C₂×C₃×#137	semidirect
425. C₂×C₃	#63480	direct (N × H)
443. C₃	C₂×#63480	direct (N × H)
447. C₂	C₃×#63480	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3701	2
C₂×C₃×Q₈×D₉	2
C₂×C₃×C₉×Q₁₆	2
C₂×C₃×#3675	2
C₂×C₃×#3674	2
C₃×#63480	2
C₂×C₃×#3664	2
C₂×C₃×#3663	2
C₂×C₃×#918	3
C₂×#63480	3

Subgroups — C2×C3×#63480 #13153456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63480 #13153456