Subgroups — C₂×C₃²×#918 #13179141

Order 1728.

1788 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×C₃²×#239	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃³×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#216	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃²×#215	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#918	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃²×#204	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃²×#137	—	3	1	no	maximal
10	C₂×C₃×#918	C₃	1	4	yes	maximal, direct product factor
11	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
13	C₃²×#239	—	2	2	no	—
14	C₃²×#239	C₂²	1	4	yes	—
15	C₃²×D₃×Q₈	—	2	2	no	—
16	C₃²×D₃×Q₈	C₂²	1	4	yes	complemented
17	C₂×C₃²×D₁₂	—	2	1	no	—
18	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₄×D₃	—	2	1	no	—
20	C₂×C₃²×C₄×D₃	—	2	1	no	—
21	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃²×Dic₆	—	2	1	no	—
23	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
24	C₃³×Q₁₆	C₂²	1	4	yes	complemented
25	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
26	C₃²×#216	C₂²	1	4	yes	complemented
27	C₃²×#215	C₂²	1	4	yes	complemented
28	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₃²×#204	C₂²	1	4	yes	complemented
30	C₃²×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	complemented
31	C₂×C₃²×#41	—	3	1	no	—
32	C₂²×C₃²×Q₈	—	3	1	no	—
33	C₂×C₃×#239	C₂×C₃	1	4	yes	—
34	C₂×C₃×D₃×Q₈	C₂×C₃	1	4	yes	complemented
35	C₃²×#137	—	3	8	no	—
36	C₂×C₃²×Q₁₆	—	2	4	no	—
37	C₂×C₃²×Q₁₆	—	3	1	no	—
38	C₂×C₃²×Q₁₆	D₃	1	1	yes	characteristic, complemented
39	C₂×C₃²×Q₁₆	C₂×C₃	1	4	yes	complemented
40	C₂×C₃²×SD₁₆	—	3	1	no	—
41	C₂×C₃²×SD₁₆	—	3	1	no	—
42	C₂×C₃²×M₁₆	—	3	1	no	—
43	C₂×C₃×#216	C₂×C₃	1	4	yes	complemented
44	C₂×C₃×#215	C₂×C₃	1	4	yes	complemented
45	C₃×#918	C₂×C₃	1	32	yes	direct product factor
46	C₂×C₃×#204	C₂×C₃	1	4	yes	complemented
47	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	4	yes	complemented
48	C₂²×C₃²×D₃	—	2	1	no	—
49	C₂²×C₃²×D₃	D₄	1	1	yes	characteristic
50	C₃³×Q₈	—	2	1	no	—
51	C₃³×Q₈	—	2	1	no	—
52	C₃³×Q₈	C₂³	1	2	yes	—
53	C₃³×Q₈	C₂³	1	2	yes	—
54	C₂×C₃³×C₄	—	2	1	no	—
55	C₂×C₃³×C₄	—	2	1	no	—
56	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
57	C₂×C₃²×Dic₃	—	2	1	no	—
58	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
59	C₃²×D₁₂	—	2	4	no	—
60	C₃²×D₁₂	—	2	1	no	—
61	C₃²×D₁₂	C₂³	1	2	yes	—
62	C₃²×C₄×D₃	—	2	4	no	—
63	C₃²×C₄×D₃	—	2	4	no	—
64	C₃²×C₄×D₃	D₄	1	2	yes	—
65	C₃²×C₄×D₃	C₂³	1	2	yes	—
66	C₃²×Dic₆	—	2	1	no	—
67	C₃²×Dic₆	—	2	4	no	—
68	C₃²×Dic₆	C₂³	1	2	yes	—
69	C₃³×C₈	C₂³	1	2	yes	—
70	C₃²×C₃⋊C₈	C₂³	1	2	yes	—
71	C₂×C₃×#137	—	3	4	no	—
72	C₂×#918	C₃²	1	1	yes	characteristic, direct product factor
73	C₃²×#41	—	3	4	no	—
74	C₃²×#41	—	6	2	no	—
75	C₂×C₃²×Q₈	—	2	4	no	—
76	C₂×C₃²×Q₈	—	2	4	no	—
77	C₂×C₃²×Q₈	—	3	4	no	—
78	C₂×C₃²×Q₈	—	3	1	no	—
79	C₂×C₃²×Q₈	—	6	1	no	—
80	C₂×C₃²×Q₈	—	6	2	no	—
81	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
82	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
84	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
85	C₂×C₃²×D₄	—	3	1	no	—
86	C₂×C₃²×D₄	—	6	1	no	—
87	C₂²×C₃²×C₄	—	3	1	no	—
88	C₂²×C₃²×C₄	—	6	1	no	—
89	C₂²×C₃²×C₄	—	6	1	no	—
90	C₃×#239	—	2	8	no	—
91	C₃×#239	C₂²×C₃	1	16	yes	—
92	C₃×D₃×Q₈	—	2	8	no	—
93	C₃×D₃×Q₈	C₂²×C₃	1	16	yes	complemented
94	C₂×C₃×D₁₂	—	2	4	no	—
95	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
96	C₂×C₃×C₄×D₃	—	2	4	no	—
97	C₂×C₃×C₄×D₃	—	2	4	no	—
98	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
99	C₂×C₃×Dic₆	—	2	4	no	—
100	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
101	C₃²×Q₁₆	—	2	16	no	—
102	C₃²×Q₁₆	—	3	4	no	—
103	C₃²×Q₁₆	C₂×D₃	1	4	yes	complemented
104	C₃²×Q₁₆	C₂²×C₃	1	16	yes	complemented
105	C₃²×SD₁₆	—	3	4	no	—
106	C₃²×SD₁₆	—	3	4	no	—
107	C₃²×M₁₆	—	3	4	no	—
108	C₂×C₃²×C₈	—	2	4	no	—
109	C₂×C₃²×C₈	—	3	1	no	—
110	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
111	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
112	C₃×#216	C₂²×C₃	1	16	yes	complemented
113	C₃×#215	C₂²×C₃	1	16	yes	complemented
114	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
115	C₃×#204	C₂²×C₃	1	16	yes	complemented
116	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	16	yes	complemented
117	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃²×D₃	—	2	2	no	—
119	C₂×C₃²×D₃	—	2	2	no	—
120	C₂×C₃²×D₃	—	4	2	no	—
121	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
122	C₃³×C₄	—	2	2	no	—
123	C₃³×C₄	—	2	2	no	—
124	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
125	C₃³×C₄	C₂⁴	1	1	yes	characteristic
126	C₃²×Dic₃	—	2	2	no	—
127	C₃²×Dic₃	C₂×D₄	1	2	yes	—
128	C₂×C₃×#41	—	3	4	no	—
129	C₂²×C₃×Q₈	—	3	4	no	—
130	C₂×#239	C₂×C₃²	1	1	yes	characteristic
131	C₂×D₃×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
132	C₃×#137	—	3	32	no	—
133	C₂×C₃×Q₁₆	—	2	4	no	—
134	C₂×C₃×Q₁₆	—	3	4	no	—
135	C₂×C₃×Q₁₆	C₃×D₃	1	4	yes	complemented
136	C₂×C₃×Q₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
137	C₂×C₃×SD₁₆	—	3	4	no	—
138	C₂×C₃×SD₁₆	—	3	4	no	—
139	C₂×C₃×M₁₆	—	3	4	no	—
140	C₂×#216	C₂×C₃²	1	1	yes	characteristic, complemented
141	C₂×#215	C₂×C₃²	1	1	yes	characteristic, complemented
142	#918	C₂×C₃²	1	8	yes	direct product factor
143	C₂×#204	C₂×C₃²	1	1	yes	characteristic, complemented
144	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	1	yes	characteristic, complemented
145	C₂³×C₃²	—	3	1	no	—
146	C₂³×C₃²	—	6	1	no	—
147	C₂²×C₃×D₃	—	2	4	no	—
148	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
149	C₃²×Q₈	—	2	1	no	—
150	C₃²×Q₈	—	2	1	no	—
151	C₃²×Q₈	—	2	8	no	—
152	C₃²×Q₈	—	2	8	no	—
153	C₃²×Q₈	—	2	4	no	—
154	C₃²×Q₈	—	2	4	no	—
155	C₃²×Q₈	—	3	2	no	—
156	C₃²×Q₈	—	4	4	no	—
157	C₃²×Q₈	—	4	4	no	—
158	C₃²×Q₈	—	6	4	no	—
159	C₃²×Q₈	—	6	1	no	—
160	C₃²×Q₈	C₂²×D₃	1	2	yes	—
161	C₃²×Q₈	C₂²×D₃	1	2	yes	—
162	C₃²×Q₈	C₂³×C₃	1	8	yes	—
163	C₃²×Q₈	C₂³×C₃	1	8	yes	—
164	C₃²×D₄	—	3	2	no	—
165	C₃²×D₄	—	6	4	no	—
166	C₃²×D₄	—	6	1	no	—
167	C₂×C₃²×C₄	—	2	1	no	—
168	C₂×C₃²×C₄	—	2	1	no	—
169	C₂×C₃²×C₄	—	2	4	no	—
170	C₂×C₃²×C₄	—	2	4	no	—
171	C₂×C₃²×C₄	—	2	4	no	—
172	C₂×C₃²×C₄	—	3	1	no	—
173	C₂×C₃²×C₄	—	3	2	no	—
174	C₂×C₃²×C₄	—	3	2	no	—
175	C₂×C₃²×C₄	—	4	4	no	—
176	C₂×C₃²×C₄	—	4	4	no	—
177	C₂×C₃²×C₄	—	6	4	no	—
178	C₂×C₃²×C₄	—	6	4	no	—
179	C₂×C₃²×C₄	—	6	1	no	—
180	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
182	C₂×C₃×Dic₃	—	2	4	no	—
183	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
184	C₃×D₁₂	—	2	16	no	—
185	C₃×D₁₂	—	2	4	no	—
186	C₃×D₁₂	C₂³×C₃	1	8	yes	—
187	C₃×C₄×D₃	—	2	16	no	—
188	C₃×C₄×D₃	—	2	16	no	—
189	C₃×C₄×D₃	C₃×D₄	1	8	yes	—
190	C₃×C₄×D₃	C₂³×C₃	1	8	yes	—
191	C₃×Dic₆	—	2	4	no	—
192	C₃×Dic₆	—	2	16	no	—
193	C₃×Dic₆	C₂³×C₃	1	8	yes	—
194	C₃²×C₈	—	2	8	no	—
195	C₃²×C₈	—	3	2	no	—
196	C₃²×C₈	C₂²×D₃	1	2	yes	—
197	C₃²×C₈	C₂³×C₃	1	8	yes	—
198	C₃×C₃⋊C₈	C₂³×C₃	1	8	yes	—
199	C₂×#137	—	3	1	no	Sylow
200	C₂×C₃³	#137	1	2	yes	complemented
201	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
202	C₃²×D₃	—	2	2	no	—
203	C₃²×D₃	—	4	2	no	—
204	C₃×#41	—	3	16	no	—
205	C₃×#41	—	6	8	no	—
206	C₂×C₃×Q₈	—	2	4	no	—
207	C₂×C₃×Q₈	—	2	4	no	—
208	C₂×C₃×Q₈	—	3	16	no	—
209	C₂×C₃×Q₈	—	3	4	no	—
210	C₂×C₃×Q₈	—	6	4	no	—
211	C₂×C₃×Q₈	—	6	8	no	—
212	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
213	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
214	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
215	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
216	C₂×C₃×D₄	—	3	4	no	—
217	C₂×C₃×D₄	—	6	4	no	—
218	C₂²×C₃×C₄	—	3	4	no	—
219	C₂²×C₃×C₄	—	6	4	no	—
220	C₂²×C₃×C₄	—	6	4	no	—
221	#239	—	2	2	no	—
222	#239	C₂²×C₃²	1	4	yes	—
223	D₃×Q₈	—	2	2	no	—
224	D₃×Q₈	C₂²×C₃²	1	4	yes	complemented
225	C₂×D₁₂	—	2	1	no	—
226	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
227	C₂×C₄×D₃	—	2	1	no	—
228	C₂×C₄×D₃	—	2	1	no	—
229	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
230	C₂×Dic₆	—	2	1	no	—
231	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
232	C₃×Q₁₆	—	2	16	no	—
233	C₃×Q₁₆	—	3	16	no	—
234	C₃×Q₁₆	C₂×C₃×D₃	1	16	yes	complemented
235	C₃×Q₁₆	C₂²×C₃²	1	4	yes	complemented
236	C₃×SD₁₆	—	3	16	no	—
237	C₃×SD₁₆	—	3	16	no	—
238	C₃×M₁₆	—	3	16	no	—
239	C₂×C₃×C₈	—	2	4	no	—
240	C₂×C₃×C₈	—	3	4	no	—
241	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
242	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
243	#216	C₂²×C₃²	1	4	yes	complemented
244	#215	C₂²×C₃²	1	4	yes	complemented
245	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
246	#204	C₂²×C₃²	1	4	yes	complemented
247	ΓL(1,𝔽₂₅)	C₂²×C₃²	1	4	yes	complemented
248	C₂²×C₃²	—	2	4	no	—
249	C₂²×C₃²	—	3	2	no	—
250	C₂²×C₃²	—	6	2	no	—
251	C₂²×C₃²	—	6	2	no	—
252	C₂²×C₃²	—	12	2	no	—
253	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
254	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
255	C₂×C₃×D₃	—	2	8	no	—
256	C₂×C₃×D₃	—	2	8	no	—
257	C₂×C₃×D₃	—	4	8	no	—
258	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
259	C₃²×C₄	—	2	2	no	—
260	C₃²×C₄	—	2	2	no	—
261	C₃²×C₄	—	2	4	no	—
262	C₃²×C₄	—	2	4	no	—
263	C₃²×C₄	—	2	8	no	—
264	C₃²×C₄	—	2	8	no	—
265	C₃²×C₄	—	3	2	no	—
266	C₃²×C₄	—	4	8	no	—
267	C₃²×C₄	—	4	8	no	—
268	C₃²×C₄	—	6	2	no	—
269	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
270	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
271	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
272	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
273	C₃×Dic₃	—	2	8	no	—
274	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
275	C₂×#41	—	3	1	no	—
276	C₂²×Q₈	—	3	1	no	—
277	#137	—	3	8	no	—
278	C₂×Q₁₆	—	3	1	no	—
279	C₂×Q₁₆	C₃²×D₃	1	1	yes	characteristic, complemented
280	C₂×SD₁₆	—	3	1	no	—
281	C₂×SD₁₆	—	3	1	no	—
282	C₂×M₁₆	—	3	1	no	—
283	C₃³	C₂×#137	1	1	yes	characteristic, complemented, Sylow
284	C₂³×C₃	—	3	4	no	—
285	C₂³×C₃	—	6	4	no	—
286	C₂²×D₃	—	2	1	no	—
287	C₂²×D₃	C₃²×D₄	1	1	yes	characteristic
288	C₃×Q₈	—	2	4	no	—
289	C₃×Q₈	—	2	4	no	—
290	C₃×Q₈	—	2	1	no	—
291	C₃×Q₈	—	2	1	no	—
292	C₃×Q₈	—	2	8	no	—
293	C₃×Q₈	—	2	8	no	—
294	C₃×Q₈	—	3	8	no	—
295	C₃×Q₈	—	4	4	no	—
296	C₃×Q₈	—	4	4	no	—
297	C₃×Q₈	—	6	16	no	—
298	C₃×Q₈	—	6	4	no	—
299	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
300	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
301	C₃×Q₈	C₂³×C₃²	1	2	yes	—
302	C₃×Q₈	C₂³×C₃²	1	2	yes	—
303	C₃×D₄	—	3	8	no	—
304	C₃×D₄	—	6	16	no	—
305	C₃×D₄	—	6	4	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	2	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	2	4	no	—
311	C₂×C₃×C₄	—	3	4	no	—
312	C₂×C₃×C₄	—	3	8	no	—
313	C₂×C₃×C₄	—	3	8	no	—
314	C₂×C₃×C₄	—	4	4	no	—
315	C₂×C₃×C₄	—	4	4	no	—
316	C₂×C₃×C₄	—	6	16	no	—
317	C₂×C₃×C₄	—	6	16	no	—
318	C₂×C₃×C₄	—	6	4	no	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
320	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
321	C₂×Dic₃	—	2	1	no	—
322	C₂×Dic₃	C₃²×D₄	1	1	yes	characteristic
323	D₁₂	—	2	4	no	—
324	D₁₂	—	2	1	no	—
325	D₁₂	C₂³×C₃²	1	2	yes	—
326	C₄×D₃	—	2	4	no	—
327	C₄×D₃	—	2	4	no	—
328	C₄×D₃	C₃²×D₄	1	2	yes	—
329	C₄×D₃	C₂³×C₃²	1	2	yes	—
330	Dic₆	—	2	1	no	—
331	Dic₆	—	2	4	no	—
332	Dic₆	C₂³×C₃²	1	2	yes	—
333	C₃×C₈	—	2	8	no	—
334	C₃×C₈	—	3	8	no	—
335	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
336	C₃×C₈	C₂³×C₃²	1	2	yes	—
337	C₃⋊C₈	C₂³×C₃²	1	2	yes	—
338	C₂×C₃²	—	2	8	no	—
339	C₂×C₃²	—	2	4	no	—
340	C₂×C₃²	—	6	2	no	—
341	C₂×C₃²	—	12	2	no	—
342	C₂×C₃²	#918	1	2	yes	direct product factor
343	C₂×C₃²	C₃×#137	1	8	yes	complemented
344	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
345	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
346	C₃×D₃	—	2	8	no	—
347	C₃×D₃	—	4	8	no	—
348	#41	—	3	4	no	—
349	#41	—	6	2	no	—
350	C₂×Q₈	—	3	4	no	—
351	C₂×Q₈	—	3	1	no	—
352	C₂×Q₈	—	6	1	no	—
353	C₂×Q₈	—	6	2	no	—
354	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
355	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
356	C₂×D₄	—	3	1	no	—
357	C₂×D₄	—	6	1	no	—
358	C₂²×C₄	—	3	1	no	—
359	C₂²×C₄	—	6	1	no	—
360	C₂²×C₄	—	6	1	no	—
361	Q₁₆	—	3	4	no	—
362	Q₁₆	C₂×C₃²×D₃	1	4	yes	complemented
363	SD₁₆	—	3	4	no	—
364	SD₁₆	—	3	4	no	—
365	M₁₆	—	3	4	no	—
366	C₂×C₈	—	3	1	no	—
367	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	3	8	no	—
370	C₂²×C₃	—	6	8	no	—
371	C₂²×C₃	—	6	8	no	—
372	C₂²×C₃	—	12	8	no	—
373	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
374	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
375	C₂×D₃	—	2	2	no	—
376	C₂×D₃	—	2	2	no	—
377	C₂×D₃	—	4	2	no	—
378	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
379	C₃×C₄	—	2	8	no	—
380	C₃×C₄	—	2	8	no	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	4	no	—
384	C₃×C₄	—	2	4	no	—
385	C₃×C₄	—	3	8	no	—
386	C₃×C₄	—	4	8	no	—
387	C₃×C₄	—	4	8	no	—
388	C₃×C₄	—	6	8	no	—
389	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
390	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
391	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
392	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
393	Dic₃	—	2	2	no	—
394	Dic₃	C₂×C₃²×D₄	1	2	yes	—
395	C₃²	—	2	4	no	—
396	C₃²	C₂×#918	1	1	yes	characteristic, direct product factor
397	C₃²	C₂×C₃×#137	1	4	yes	complemented
398	C₂³	—	3	1	no	—
399	C₂³	—	6	1	no	—
400	Q₈	—	2	1	no	—
401	Q₈	—	2	1	no	—
402	Q₈	—	3	2	no	—
403	Q₈	—	6	4	no	—
404	Q₈	—	6	1	no	—
405	Q₈	C₂²×C₃²×D₃	1	2	yes	—
406	Q₈	C₂²×C₃²×D₃	1	2	yes	—
407	D₄	—	3	2	no	—
408	D₄	—	6	4	no	—
409	D₄	—	6	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	3	1	no	—
413	C₂×C₄	—	3	2	no	—
414	C₂×C₄	—	3	2	no	—
415	C₂×C₄	—	6	4	no	—
416	C₂×C₄	—	6	4	no	—
417	C₂×C₄	—	6	1	no	—
418	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
419	C₈	—	3	2	no	—
420	C₈	C₂²×C₃²×D₃	1	2	yes	—
421	C₂×C₃	—	2	8	no	—
422	C₂×C₃	—	2	4	no	—
423	C₂×C₃	—	6	8	no	—
424	C₂×C₃	—	12	8	no	—
425	C₂×C₃	C₃×#918	1	8	yes	direct product factor
426	C₂×C₃	C₃²×#137	1	2	yes	complemented
427	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
428	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
429	D₃	—	2	2	no	—
430	D₃	—	4	2	no	—
431	C₂²	—	3	2	no	—
432	C₂²	—	6	2	no	—
433	C₂²	—	6	2	no	—
434	C₂²	—	12	2	no	—
435	C₂²	C₃²×D₃×D₄	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	3	2	no	—
439	C₄	—	6	2	no	—
440	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
441	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
442	C₃	—	2	4	no	—
443	C₃	C₂×C₃×#918	1	4	yes	direct product factor
444	C₃	C₂×C₃²×#137	1	1	yes	characteristic, complemented
445	C₂	—	6	2	no	—
446	C₂	—	12	2	no	—
447	C₂	C₃²×#918	1	2	yes	direct product factor
448	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×Q₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃²×#239	C₂
hypercenter	C₂×C₃²×Q₁₆	D₃
hypocenter	C₃	C₂×C₃²×#137
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×D₃×Q₈	C₂	semidirect
3. C₂×C₃³×Q₁₆	C₂	semidirect
4. C₂×C₃²×#216	C₂	semidirect
5. C₂×C₃²×#215	C₂	semidirect
6. C₃²×#918	C₂	direct (N × H)
7. C₂×C₃²×#204	C₂	semidirect
8. C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	semidirect
10. C₂×C₃×#918	C₃	direct (N × H)
16. C₃²×D₃×Q₈	C₂²	semidirect
24. C₃³×Q₁₆	C₂²	semidirect
26. C₃²×#216	C₂²	semidirect
27. C₃²×#215	C₂²	semidirect
29. C₃²×#204	C₂²	semidirect
30. C₃²×ΓL(1,𝔽₂₅)	C₂²	semidirect
34. C₂×C₃×D₃×Q₈	C₂×C₃	semidirect
38. C₂×C₃²×Q₁₆	D₃	semidirect
39. C₂×C₃²×Q₁₆	C₂×C₃	semidirect
43. C₂×C₃×#216	C₂×C₃	semidirect
44. C₂×C₃×#215	C₂×C₃	semidirect
45. C₃×#918	C₂×C₃	direct (N × H)
46. C₂×C₃×#204	C₂×C₃	semidirect
47. C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
72. C₂×#918	C₃²	direct (N × H)
93. C₃×D₃×Q₈	C₂²×C₃	semidirect
103. C₃²×Q₁₆	C₂×D₃	semidirect
104. C₃²×Q₁₆	C₂²×C₃	semidirect
112. C₃×#216	C₂²×C₃	semidirect
113. C₃×#215	C₂²×C₃	semidirect
115. C₃×#204	C₂²×C₃	semidirect
116. C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
131. C₂×D₃×Q₈	C₂×C₃²	semidirect
135. C₂×C₃×Q₁₆	C₃×D₃	semidirect
136. C₂×C₃×Q₁₆	C₂×C₃²	semidirect
140. C₂×#216	C₂×C₃²	semidirect
141. C₂×#215	C₂×C₃²	semidirect
142. #918	C₂×C₃²	direct (N × H)
143. C₂×#204	C₂×C₃²	semidirect
144. C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	semidirect
200. C₂×C₃³	#137	semidirect
224. D₃×Q₈	C₂²×C₃²	semidirect
234. C₃×Q₁₆	C₂×C₃×D₃	semidirect
235. C₃×Q₁₆	C₂²×C₃²	semidirect
243. #216	C₂²×C₃²	semidirect
244. #215	C₂²×C₃²	semidirect
246. #204	C₂²×C₃²	semidirect
247. ΓL(1,𝔽₂₅)	C₂²×C₃²	semidirect
279. C₂×Q₁₆	C₃²×D₃	semidirect
283. C₃³	C₂×#137	semidirect
342. C₂×C₃²	#918	direct (N × H)
343. C₂×C₃²	C₃×#137	semidirect
362. Q₁₆	C₂×C₃²×D₃	semidirect
396. C₃²	C₂×#918	direct (N × H)
397. C₃²	C₂×C₃×#137	semidirect
425. C₂×C₃	C₃×#918	direct (N × H)
426. C₂×C₃	C₃²×#137	semidirect
443. C₃	C₂×C₃×#918	direct (N × H)
444. C₃	C₂×C₃²×#137	semidirect
447. C₂	C₃²×#918	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×C₃²×#239	2
C₂×C₃²×D₃×Q₈	2
C₂×C₃³×Q₁₆	2
C₂×C₃²×#216	2
C₂×C₃²×#215	2
C₃²×#918	2
C₂×C₃²×#204	2
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₂×C₃²×#137	3
C₂×C₃×#918	3

Subgroups — C2×C32×#918 #13179141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#918 #13179141