Subgroups — C₂×C₃²×#950 #13179201

Order 1728.

2252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#950	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃²×#216	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃²×#215	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃²×#214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃²×#213	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₃²×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃²×#135	—	3	1	no	maximal
10	C₂×C₃×#950	C₃	1	4	yes	maximal, direct product factor
11	C₃³×#41	—	2	2	no	—
12	C₃³×#41	C₂²	1	4	yes	complemented
13	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃³×D₄	—	2	1	no	—
15	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃³×C₄	—	2	1	no	—
17	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃²×#67	—	2	1	no	—
19	C₃²×#235	—	2	2	no	—
20	C₃²×#235	C₂²	1	4	yes	complemented
21	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₃²×C₄×D₃	—	2	1	no	—
23	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic
24	C₃²×#216	C₂²	1	4	yes	complemented
25	C₃²×#215	C₂²	1	4	yes	complemented
26	C₃²×#214	C₂²	1	4	yes	complemented
27	C₃²×#213	C₂²	1	4	yes	complemented
28	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₃²×C₃⋊C₈	C₂²	1	4	yes	complemented
31	C₂×C₃²×#41	—	2	4	no	—
32	C₂×C₃²×#41	—	3	1	no	—
33	C₂×C₃²×#41	D₃	1	1	yes	characteristic, complemented
34	C₂×C₃²×#41	C₂×C₃	1	4	yes	complemented
35	C₂×C₃×#235	C₂×C₃	1	4	yes	complemented
36	C₃²×#135	—	3	8	no	—
37	C₂×C₃²×Q₁₆	—	3	1	no	—
38	C₂×C₃²×SD₁₆	—	3	1	no	—
39	C₂×C₃²×SD₁₆	—	3	1	no	—
40	C₂×C₃²×D₈	—	3	1	no	—
41	C₂²×C₃²×C₈	—	3	1	no	—
42	C₃×#950	C₂×C₃	1	32	yes	direct product factor
43	C₂×C₃×#216	C₂×C₃	1	4	yes	complemented
44	C₂×C₃×#215	C₂×C₃	1	4	yes	complemented
45	C₂×C₃×#214	C₂×C₃	1	4	yes	complemented
46	C₂×C₃×#213	C₂×C₃	1	4	yes	complemented
47	C₂²×C₃×C₃⋊C₈	C₂×C₃	1	4	yes	complemented
48	C₂³×C₃³	—	2	1	no	—
49	C₂³×C₃³	D₄	1	1	yes	characteristic
50	C₂²×C₃²×D₃	—	2	1	no	—
51	C₃³×Q₈	—	2	1	no	—
52	C₃³×Q₈	C₂³	1	2	yes	—
53	C₃³×D₄	—	2	4	no	—
54	C₃³×D₄	—	2	1	no	—
55	C₃³×D₄	C₂³	1	2	yes	—
56	C₂×C₃³×C₄	—	2	1	no	—
57	C₂×C₃³×C₄	—	2	4	no	—
58	C₂×C₃³×C₄	D₄	1	2	yes	—
59	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
60	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
61	C₂×C₃³×C₄	C₂³	1	2	yes	—
62	C₃²×#67	—	2	4	no	—
63	C₂×C₃²×Dic₃	—	2	1	no	—
64	C₃²×D₁₂	—	2	1	no	—
65	C₃²×D₁₂	C₂³	1	2	yes	—
66	C₃²×C₄×D₃	—	2	4	no	—
67	C₃²×Dic₆	—	2	1	no	—
68	C₃²×Dic₆	C₂³	1	2	yes	—
69	C₃²×C₃⋊C₈	C₂³	1	2	yes	—
70	C₃²×C₃⋊C₈	C₂³	1	2	yes	—
71	C₂×C₃×#135	—	3	4	no	—
72	C₂×#950	C₃²	1	1	yes	characteristic, direct product factor
73	C₃²×#41	—	2	16	no	—
74	C₃²×#41	—	2	16	no	—
75	C₃²×#41	—	2	2	no	—
76	C₃²×#41	—	2	8	no	—
77	C₃²×#41	—	3	4	no	—
78	C₃²×#41	—	6	2	no	—
79	C₃²×#41	C₂×D₃	1	4	yes	complemented
80	C₃²×#41	C₂²×C₃	1	16	yes	complemented
81	C₂×C₃²×Q₈	—	2	4	no	—
82	C₂×C₃²×Q₈	—	3	1	no	—
83	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
84	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	—
85	C₂×C₃²×D₄	—	2	8	no	—
86	C₂×C₃²×D₄	—	2	4	no	—
87	C₂×C₃²×D₄	—	2	1	no	—
88	C₂×C₃²×D₄	—	2	4	no	—
89	C₂×C₃²×D₄	—	3	1	no	—
90	C₂×C₃²×D₄	—	6	1	no	—
91	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
92	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
93	C₂²×C₃²×C₄	—	2	8	no	—
94	C₂²×C₃²×C₄	—	2	4	no	—
95	C₂²×C₃²×C₄	—	2	1	no	—
96	C₂²×C₃²×C₄	—	2	4	no	—
97	C₂²×C₃²×C₄	—	6	1	no	—
98	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
100	C₂×C₃×#67	—	2	4	no	—
101	C₃×#235	—	2	8	no	—
102	C₃×#235	C₂²×C₃	1	16	yes	complemented
103	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
104	C₂×C₃×C₄×D₃	—	2	4	no	—
105	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	—
106	C₃²×Q₁₆	—	3	4	no	—
107	C₃²×SD₁₆	—	3	4	no	—
108	C₃²×SD₁₆	—	3	4	no	—
109	C₃²×D₈	—	3	4	no	—
110	C₂×C₃²×C₈	—	3	1	no	—
111	C₂×C₃²×C₈	—	3	1	no	—
112	C₂×C₃²×C₈	—	3	4	no	—
113	C₃×#216	C₂²×C₃	1	16	yes	complemented
114	C₃×#215	C₂²×C₃	1	16	yes	complemented
115	C₃×#214	C₂²×C₃	1	16	yes	complemented
116	C₃×#213	C₂²×C₃	1	16	yes	complemented
117	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
118	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
119	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	16	yes	complemented
120	C₂²×C₃³	—	2	2	no	—
121	C₂²×C₃³	—	2	2	no	—
122	C₂²×C₃³	—	4	2	no	—
123	C₂²×C₃³	C₂×D₄	1	2	yes	—
124	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃²×D₃	—	2	2	no	—
126	C₂×C₃²×D₃	—	4	2	no	—
127	C₃³×C₄	—	2	2	no	—
128	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
129	C₃³×C₄	C₂×D₄	1	2	yes	—
130	C₃³×C₄	C₂⁴	1	1	yes	characteristic
131	C₃²×Dic₃	—	2	2	no	—
132	C₂×C₃×#41	—	2	4	no	—
133	C₂×C₃×#41	—	3	4	no	—
134	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
135	C₂×C₃×#41	C₂×C₃²	1	1	yes	characteristic, complemented
136	C₂×#235	C₂×C₃²	1	1	yes	characteristic, complemented
137	C₃×#135	—	3	32	no	—
138	C₂×C₃×Q₁₆	—	3	4	no	—
139	C₂×C₃×SD₁₆	—	3	4	no	—
140	C₂×C₃×SD₁₆	—	3	4	no	—
141	C₂×C₃×D₈	—	3	4	no	—
142	C₂²×C₃×C₈	—	3	4	no	—
143	#950	C₂×C₃²	1	8	yes	direct product factor
144	C₂×#216	C₂×C₃²	1	1	yes	characteristic, complemented
145	C₂×#215	C₂×C₃²	1	1	yes	characteristic, complemented
146	C₂×#214	C₂×C₃²	1	1	yes	characteristic, complemented
147	C₂×#213	C₂×C₃²	1	1	yes	characteristic, complemented
148	C₂²×C₃⋊C₈	C₂×C₃²	1	1	yes	characteristic, complemented
149	C₂³×C₃²	—	2	8	no	—
150	C₂³×C₃²	—	2	1	no	—
151	C₂³×C₃²	—	2	4	no	—
152	C₂³×C₃²	—	2	4	no	—
153	C₂³×C₃²	—	6	1	no	—
154	C₂³×C₃²	#67	1	1	yes	characteristic
155	C₂³×C₃²	C₃×D₄	1	4	yes	—
156	C₂²×C₃×D₃	—	2	4	no	—
157	C₃²×Q₈	—	2	8	no	—
158	C₃²×Q₈	—	2	1	no	—
159	C₃²×Q₈	—	2	4	no	—
160	C₃²×Q₈	—	2	8	no	—
161	C₃²×Q₈	—	3	2	no	—
162	C₃²×Q₈	—	6	1	no	—
163	C₃²×Q₈	C₂²×D₃	1	2	yes	—
164	C₃²×Q₈	C₂³×C₃	1	8	yes	—
165	C₃²×D₄	—	2	32	no	—
166	C₃²×D₄	—	2	8	no	—
167	C₃²×D₄	—	2	4	no	—
168	C₃²×D₄	—	2	16	no	—
169	C₃²×D₄	—	2	1	no	—
170	C₃²×D₄	—	2	4	no	—
171	C₃²×D₄	—	2	8	no	—
172	C₃²×D₄	—	3	2	no	—
173	C₃²×D₄	—	6	4	no	—
174	C₃²×D₄	—	6	1	no	—
175	C₃²×D₄	C₂²×D₃	1	2	yes	—
176	C₃²×D₄	C₂³×C₃	1	8	yes	—
177	C₂×C₃²×C₄	—	2	8	no	—
178	C₂×C₃²×C₄	—	2	32	no	—
179	C₂×C₃²×C₄	—	2	1	no	—
180	C₂×C₃²×C₄	—	2	4	no	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	16	no	—
183	C₂×C₃²×C₄	—	2	4	no	—
184	C₂×C₃²×C₄	—	2	8	no	—
185	C₂×C₃²×C₄	—	2	4	no	—
186	C₂×C₃²×C₄	—	2	8	no	—
187	C₂×C₃²×C₄	—	6	1	no	—
188	C₂×C₃²×C₄	—	6	4	no	—
189	C₂×C₃²×C₄	#67	1	2	yes	—
190	C₂×C₃²×C₄	#67	1	1	yes	characteristic
191	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
192	C₂×C₃²×C₄	C₃×D₄	1	8	yes	—
193	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
195	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
196	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
197	C₃×#67	—	2	16	no	—
198	C₂×C₃×Dic₃	—	2	4	no	—
199	C₃×D₁₂	—	2	4	no	—
200	C₃×D₁₂	C₂³×C₃	1	8	yes	—
201	C₃×C₄×D₃	—	2	16	no	—
202	C₃×Dic₆	—	2	4	no	—
203	C₃×Dic₆	C₂³×C₃	1	8	yes	—
204	C₃²×C₈	—	3	2	no	—
205	C₃²×C₈	—	3	2	no	—
206	C₃×C₃⋊C₈	C₂³×C₃	1	8	yes	—
207	C₃×C₃⋊C₈	C₂³×C₃	1	8	yes	—
208	C₂×#135	—	3	1	no	Sylow
209	C₂×C₃³	—	2	2	no	—
210	C₂×C₃³	—	4	2	no	—
211	C₂×C₃³	#135	1	2	yes	complemented
212	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
213	C₃²×D₃	—	4	2	no	—
214	C₃×#41	—	2	16	no	—
215	C₃×#41	—	2	8	no	—
216	C₃×#41	—	2	2	no	—
217	C₃×#41	—	2	16	no	—
218	C₃×#41	—	3	16	no	—
219	C₃×#41	—	6	8	no	—
220	C₃×#41	C₂×C₃×D₃	1	16	yes	complemented
221	C₃×#41	C₂²×C₃²	1	4	yes	complemented
222	C₂×C₃×Q₈	—	2	4	no	—
223	C₂×C₃×Q₈	—	3	4	no	—
224	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
225	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
226	C₂×C₃×D₄	—	2	8	no	—
227	C₂×C₃×D₄	—	2	4	no	—
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	—	2	4	no	—
230	C₂×C₃×D₄	—	3	4	no	—
231	C₂×C₃×D₄	—	6	4	no	—
232	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
233	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
234	C₂²×C₃×C₄	—	2	8	no	—
235	C₂²×C₃×C₄	—	2	4	no	—
236	C₂²×C₃×C₄	—	2	1	no	—
237	C₂²×C₃×C₄	—	2	4	no	—
238	C₂²×C₃×C₄	—	6	4	no	—
239	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
240	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
241	C₂×#67	—	2	1	no	—
242	#235	—	2	2	no	—
243	#235	C₂²×C₃²	1	4	yes	complemented
244	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
245	C₂×C₄×D₃	—	2	1	no	—
246	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic
247	C₃×Q₁₆	—	3	16	no	—
248	C₃×SD₁₆	—	3	16	no	—
249	C₃×SD₁₆	—	3	16	no	—
250	C₃×D₈	—	3	16	no	—
251	C₂×C₃×C₈	—	3	4	no	—
252	C₂×C₃×C₈	—	3	4	no	—
253	C₂×C₃×C₈	—	3	16	no	—
254	#216	C₂²×C₃²	1	4	yes	complemented
255	#215	C₂²×C₃²	1	4	yes	complemented
256	#214	C₂²×C₃²	1	4	yes	complemented
257	#213	C₂²×C₃²	1	4	yes	complemented
258	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
259	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
260	C₂×C₃⋊C₈	C₂²×C₃²	1	4	yes	complemented
261	C₂²×C₃²	—	2	2	no	—
262	C₂²×C₃²	—	2	16	no	—
263	C₂²×C₃²	—	2	2	no	—
264	C₂²×C₃²	—	2	8	no	—
265	C₂²×C₃²	—	2	4	no	—
266	C₂²×C₃²	—	2	8	no	—
267	C₂²×C₃²	—	2	8	no	—
268	C₂²×C₃²	—	4	8	no	—
269	C₂²×C₃²	—	4	16	no	—
270	C₂²×C₃²	—	4	2	no	—
271	C₂²×C₃²	—	4	8	no	—
272	C₂²×C₃²	—	6	2	no	—
273	C₂²×C₃²	—	12	2	no	—
274	C₂²×C₃²	C₂×#67	1	2	yes	—
275	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
276	C₂²×C₃²	C₂×C₃×D₄	1	8	yes	—
277	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
278	C₂×C₃×D₃	—	2	8	no	—
279	C₂×C₃×D₃	—	4	8	no	—
280	C₃²×C₄	—	2	16	no	—
281	C₃²×C₄	—	2	2	no	—
282	C₃²×C₄	—	2	8	no	—
283	C₃²×C₄	—	2	4	no	—
284	C₃²×C₄	—	2	8	no	—
285	C₃²×C₄	—	2	4	no	—
286	C₃²×C₄	—	6	2	no	—
287	C₃²×C₄	C₂×#67	1	2	yes	—
288	C₃²×C₄	C₂×#67	1	1	yes	characteristic
289	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
290	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
291	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
292	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
293	C₃×Dic₃	—	2	8	no	—
294	C₂×#41	—	3	1	no	—
295	C₂×#41	C₃²×D₃	1	1	yes	characteristic, complemented
296	#135	—	3	8	no	—
297	C₂×Q₁₆	—	3	1	no	—
298	C₂×SD₁₆	—	3	1	no	—
299	C₂×SD₁₆	—	3	1	no	—
300	C₂×D₈	—	3	1	no	—
301	C₂²×C₈	—	3	1	no	—
302	C₃³	C₂×#135	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₃	—	2	8	no	—
304	C₂³×C₃	—	2	4	no	—
305	C₂³×C₃	—	2	1	no	—
306	C₂³×C₃	—	2	4	no	—
307	C₂³×C₃	—	6	4	no	—
308	C₂³×C₃	C₃×#67	1	4	yes	—
309	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
310	C₂²×D₃	—	2	1	no	—
311	C₃×Q₈	—	2	8	no	—
312	C₃×Q₈	—	2	4	no	—
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	—	2	8	no	—
315	C₃×Q₈	—	3	8	no	—
316	C₃×Q₈	—	6	4	no	—
317	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
318	C₃×Q₈	C₂³×C₃²	1	2	yes	—
319	C₃×D₄	—	2	32	no	—
320	C₃×D₄	—	2	8	no	—
321	C₃×D₄	—	2	16	no	—
322	C₃×D₄	—	2	4	no	—
323	C₃×D₄	—	2	4	no	—
324	C₃×D₄	—	2	1	no	—
325	C₃×D₄	—	2	8	no	—
326	C₃×D₄	—	3	8	no	—
327	C₃×D₄	—	6	16	no	—
328	C₃×D₄	—	6	4	no	—
329	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
330	C₃×D₄	C₂³×C₃²	1	2	yes	—
331	C₂×C₃×C₄	—	2	8	no	—
332	C₂×C₃×C₄	—	2	32	no	—
333	C₂×C₃×C₄	—	2	4	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	16	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	4	no	—
338	C₂×C₃×C₄	—	2	8	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	2	8	no	—
341	C₂×C₃×C₄	—	6	4	no	—
342	C₂×C₃×C₄	—	6	16	no	—
343	C₂×C₃×C₄	C₃×#67	1	8	yes	—
344	C₂×C₃×C₄	C₃×#67	1	4	yes	—
345	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
346	C₂×C₃×C₄	C₃²×D₄	1	2	yes	—
347	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
348	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
349	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
351	#67	—	2	4	no	—
352	C₂×Dic₃	—	2	1	no	—
353	D₁₂	—	2	1	no	—
354	D₁₂	C₂³×C₃²	1	2	yes	—
355	C₄×D₃	—	2	4	no	—
356	Dic₆	—	2	1	no	—
357	Dic₆	C₂³×C₃²	1	2	yes	—
358	C₃×C₈	—	3	8	no	—
359	C₃×C₈	—	3	8	no	—
360	C₃⋊C₈	C₂³×C₃²	1	2	yes	—
361	C₃⋊C₈	C₂³×C₃²	1	2	yes	—
362	C₂×C₃²	—	2	2	no	—
363	C₂×C₃²	—	2	8	no	—
364	C₂×C₃²	—	2	4	no	—
365	C₂×C₃²	—	2	8	no	—
366	C₂×C₃²	—	4	8	no	—
367	C₂×C₃²	—	4	16	no	—
368	C₂×C₃²	—	4	8	no	—
369	C₂×C₃²	—	4	2	no	—
370	C₂×C₃²	—	12	2	no	—
371	C₂×C₃²	#950	1	2	yes	direct product factor
372	C₂×C₃²	C₃×#135	1	8	yes	complemented
373	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
374	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
375	C₃×D₃	—	4	8	no	—
376	#41	—	2	2	no	—
377	#41	—	3	4	no	—
378	#41	—	6	2	no	—
379	#41	C₂×C₃²×D₃	1	4	yes	complemented
380	C₂×Q₈	—	3	1	no	—
381	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	3	1	no	—
384	C₂×D₄	—	6	1	no	—
385	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	6	1	no	—
388	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
389	Q₁₆	—	3	4	no	—
390	SD₁₆	—	3	4	no	—
391	SD₁₆	—	3	4	no	—
392	D₈	—	3	4	no	—
393	C₂×C₈	—	3	1	no	—
394	C₂×C₈	—	3	1	no	—
395	C₂×C₈	—	3	4	no	—
396	C₂²×C₃	—	2	8	no	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	16	no	—
399	C₂²×C₃	—	2	8	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	2	4	no	—
402	C₂²×C₃	—	2	8	no	—
403	C₂²×C₃	—	4	8	no	—
404	C₂²×C₃	—	4	16	no	—
405	C₂²×C₃	—	4	8	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	6	8	no	—
408	C₂²×C₃	—	12	8	no	—
409	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
410	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
411	C₂²×C₃	C₂×C₃²×D₄	1	2	yes	—
412	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
413	C₂×D₃	—	2	2	no	—
414	C₂×D₃	—	4	2	no	—
415	C₃×C₄	—	2	16	no	—
416	C₃×C₄	—	2	8	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	4	no	—
419	C₃×C₄	—	2	8	no	—
420	C₃×C₄	—	2	4	no	—
421	C₃×C₄	—	6	8	no	—
422	C₃×C₄	C₂×C₃×#67	1	8	yes	—
423	C₃×C₄	C₂×C₃×#67	1	4	yes	—
424	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
425	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
426	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
427	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
428	Dic₃	—	2	2	no	—
429	C₃²	—	2	4	no	—
430	C₃²	C₂×#950	1	1	yes	characteristic, direct product factor
431	C₃²	C₂×C₃×#135	1	4	yes	complemented
432	C₂³	—	2	1	no	—
433	C₂³	—	6	1	no	—
434	C₂³	C₃²×#67	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	3	2	no	—
437	Q₈	—	6	1	no	—
438	Q₈	C₂²×C₃²×D₃	1	2	yes	—
439	D₄	—	2	4	no	—
440	D₄	—	2	1	no	—
441	D₄	—	3	2	no	—
442	D₄	—	6	4	no	—
443	D₄	—	6	1	no	—
444	D₄	C₂²×C₃²×D₃	1	2	yes	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	6	1	no	—
448	C₂×C₄	—	6	4	no	—
449	C₂×C₄	C₃²×#67	1	1	yes	characteristic
450	C₂×C₄	C₃²×#67	1	2	yes	—
451	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
452	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
453	C₈	—	3	2	no	—
454	C₈	—	3	2	no	—
455	C₂×C₃	—	2	2	no	—
456	C₂×C₃	—	2	8	no	—
457	C₂×C₃	—	2	8	no	—
458	C₂×C₃	—	2	4	no	—
459	C₂×C₃	—	4	8	no	—
460	C₂×C₃	—	4	16	no	—
461	C₂×C₃	—	4	2	no	—
462	C₂×C₃	—	4	8	no	—
463	C₂×C₃	—	12	8	no	—
464	C₂×C₃	C₃×#950	1	8	yes	direct product factor
465	C₂×C₃	C₃²×#135	1	2	yes	complemented
466	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
467	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
468	D₃	—	4	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	6	2	no	—
473	C₂²	—	12	2	no	—
474	C₂²	C₂×C₃²×#67	1	2	yes	—
475	C₂²	C₂×C₃²×#67	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	6	2	no	—
478	C₄	C₂×C₃²×#67	1	2	yes	—
479	C₄	C₂×C₃²×#67	1	1	yes	characteristic
480	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
481	C₃	—	2	4	no	—
482	C₃	C₂×C₃×#950	1	4	yes	direct product factor
483	C₃	C₂×C₃²×#135	1	1	yes	characteristic, complemented
484	C₂	—	2	2	no	—
485	C₂	—	4	2	no	—
486	C₂	—	12	2	no	—
487	C₂	C₃²×#950	1	2	yes	direct product factor
488	C₂	C₂²×C₃²×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	#67
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂×C₃²×#41	D₃
hypocenter	C₃	C₂×C₃²×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ C₂×C₃²×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×#41	C₂	semidirect
2. C₂×C₃²×#235	C₂	semidirect
3. C₃²×#950	C₂	direct (N × H)
4. C₂×C₃²×#216	C₂	semidirect
5. C₂×C₃²×#215	C₂	semidirect
6. C₂×C₃²×#214	C₂	semidirect
7. C₂×C₃²×#213	C₂	semidirect
8. C₂²×C₃²×C₃⋊C₈	C₂	semidirect
10. C₂×C₃×#950	C₃	direct (N × H)
12. C₃³×#41	C₂²	semidirect
20. C₃²×#235	C₂²	semidirect
24. C₃²×#216	C₂²	semidirect
25. C₃²×#215	C₂²	semidirect
26. C₃²×#214	C₂²	semidirect
27. C₃²×#213	C₂²	semidirect
30. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
33. C₂×C₃²×#41	D₃	semidirect
34. C₂×C₃²×#41	C₂×C₃	semidirect
35. C₂×C₃×#235	C₂×C₃	semidirect
42. C₃×#950	C₂×C₃	direct (N × H)
43. C₂×C₃×#216	C₂×C₃	semidirect
44. C₂×C₃×#215	C₂×C₃	semidirect
45. C₂×C₃×#214	C₂×C₃	semidirect
46. C₂×C₃×#213	C₂×C₃	semidirect
47. C₂²×C₃×C₃⋊C₈	C₂×C₃	semidirect
72. C₂×#950	C₃²	direct (N × H)
79. C₃²×#41	C₂×D₃	semidirect
80. C₃²×#41	C₂²×C₃	semidirect
102. C₃×#235	C₂²×C₃	semidirect
113. C₃×#216	C₂²×C₃	semidirect
114. C₃×#215	C₂²×C₃	semidirect
115. C₃×#214	C₂²×C₃	semidirect
116. C₃×#213	C₂²×C₃	semidirect
119. C₂×C₃×C₃⋊C₈	C₂²×C₃	semidirect
134. C₂×C₃×#41	C₃×D₃	semidirect
135. C₂×C₃×#41	C₂×C₃²	semidirect
136. C₂×#235	C₂×C₃²	semidirect
143. #950	C₂×C₃²	direct (N × H)
144. C₂×#216	C₂×C₃²	semidirect
145. C₂×#215	C₂×C₃²	semidirect
146. C₂×#214	C₂×C₃²	semidirect
147. C₂×#213	C₂×C₃²	semidirect
148. C₂²×C₃⋊C₈	C₂×C₃²	semidirect
211. C₂×C₃³	#135	semidirect
220. C₃×#41	C₂×C₃×D₃	semidirect
221. C₃×#41	C₂²×C₃²	semidirect
243. #235	C₂²×C₃²	semidirect
254. #216	C₂²×C₃²	semidirect
255. #215	C₂²×C₃²	semidirect
256. #214	C₂²×C₃²	semidirect
257. #213	C₂²×C₃²	semidirect
260. C₂×C₃⋊C₈	C₂²×C₃²	semidirect
295. C₂×#41	C₃²×D₃	semidirect
302. C₃³	C₂×#135	semidirect
371. C₂×C₃²	#950	direct (N × H)
372. C₂×C₃²	C₃×#135	semidirect
379. #41	C₂×C₃²×D₃	semidirect
430. C₃²	C₂×#950	direct (N × H)
431. C₃²	C₂×C₃×#135	semidirect
464. C₂×C₃	C₃×#950	direct (N × H)
465. C₂×C₃	C₃²×#135	semidirect
482. C₃	C₂×C₃×#950	direct (N × H)
483. C₃	C₂×C₃²×#135	semidirect
487. C₂	C₃²×#950	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×C₃³×#41	2
C₂×C₃²×#235	2
C₃²×#950	2
C₂×C₃²×#216	2
C₂×C₃²×#215	2
C₂×C₃²×#214	2
C₂×C₃²×#213	2
C₂²×C₃²×C₃⋊C₈	2
C₂×C₃²×#135	3
C₂×C₃×#950	3

Subgroups — C2×C32×#950 #13179201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×#950 #13179201