Subgroups — C₃×#17994 #10636601

Order 768.

748 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	C₃×#3100	C₂	1	1	yes	maximal, characteristic
2	C₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1589	C₂	1	2	yes	maximal, complemented
5	C₃×#1581	C₂	1	2	yes	maximal, complemented
6	C₃×#1581	C₂	1	2	yes	maximal, complemented
7	C₃×C₈×D₈	C₂	1	2	yes	maximal, complemented
8	C₃×#1571	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#17994	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#131	—	2	1	no	—
14	C₂²×C₃×M₁₆	—	2	1	no	—
15	C₃×#532	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
17	C₃×#480	C₄	1	2	yes	—
18	C₃×#474	C₄	1	1	yes	characteristic
19	C₃×#474	C₄	1	1	yes	characteristic
20	C₃×#459	C₄	1	1	yes	characteristic
21	C₃×#459	C₄	1	1	yes	characteristic
22	C₃×#447	C₄	1	2	yes	—
23	C₃×C₄×D₈	C₂²	1	2	yes	—
24	C₃×C₄×D₈	C₂²	1	2	yes	—
25	C₃×#436	C₂²	1	2	yes	—
26	C₃×#436	C₂²	1	2	yes	complemented
27	C₃×#435	—	2	2	no	—
28	C₃×#435	—	2	2	no	—
29	C₃×C₈×D₄	C₂²	1	2	yes	—
30	C₃×C₈×D₄	C₂²	1	2	yes	complemented
31	C₃×#431	C₂²	1	1	yes	characteristic
32	C₃×#423	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×#408	—	2	1	no	—
35	C₃×#407	—	2	1	no	—
36	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
38	C₃×#335	C₂²	1	2	yes	complemented
39	C₃×#335	C₂²	1	2	yes	complemented
40	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₃×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₃×D₄⋊C₈	C₂²	1	2	yes	complemented
46	C₃×#322	C₂²	1	2	yes	complemented
47	C₃×C₈²	C₂²	1	2	yes	complemented
48	#3100	C₂×C₃	1	1	yes	characteristic
49	#2935	C₂×C₃	1	1	yes	characteristic, complemented
50	D₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
51	#1589	C₂×C₃	1	2	yes	complemented
52	#1581	C₂×C₃	1	2	yes	complemented
53	#1581	C₂×C₃	1	2	yes	complemented
54	C₈×D₈	C₂×C₃	1	2	yes	complemented
55	#1571	C₂×C₃	1	1	yes	characteristic, complemented
56	#1492	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
58	C₈×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×#41	—	2	1	no	—
60	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₃×C₄	—	2	1	no	—
62	C₂×C₃×D₈	C₂×C₄	1	2	yes	—
63	C₂×C₃×D₈	C₂×C₄	1	2	yes	—
64	C₃×#131	—	4	4	no	—
65	C₂×C₃×M₁₆	—	2	1	no	—
66	C₂×C₃×M₁₆	—	2	2	no	—
67	C₂×C₃×M₁₆	—	2	2	no	—
68	C₂×C₃×M₁₆	—	4	4	no	—
69	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
70	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
71	C₂²×C₃×C₈	—	2	1	no	—
72	C₂²×C₃×C₈	—	2	1	no	—
73	C₂²×C₃×C₈	—	2	2	no	—
74	C₂²×C₃×C₈	—	2	2	no	—
75	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
76	C₃×#127	C₂×C₄	1	1	yes	characteristic
77	C₃×#124	—	2	1	no	—
78	C₃×#121	—	2	1	no	—
79	C₃×#121	C₂×C₄	1	2	yes	—
80	C₃×C₄×D₄	—	2	1	no	—
81	C₃×C₄×D₄	—	2	1	no	—
82	C₃×C₄×D₄	—	2	1	no	—
83	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
85	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
86	C₃×C₄×D₄	C₂³	1	2	yes	—
87	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
91	C₃×#107	C₂×C₄	1	2	yes	—
92	C₃×#107	C₂×C₄	1	2	yes	—
93	C₃×C₄⋊C₈	—	2	1	no	—
94	C₃×C₄⋊C₈	—	2	1	no	—
95	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₃×C₄⋊C₈	C₂³	1	2	yes	—
100	C₃×#102	C₂×C₄	1	2	yes	—
101	C₃×#102	C₂×C₄	1	2	yes	—
102	C₃×#102	C₂×C₄	1	2	yes	—
103	C₃×#102	C₂×C₄	1	2	yes	—
104	C₃×C₂²⋊C₈	—	2	2	no	—
105	C₃×C₂²⋊C₈	—	2	2	no	—
106	C₃×C₂²⋊C₈	—	2	2	no	—
107	C₃×C₂²⋊C₈	—	2	2	no	—
108	C₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
109	C₃×#97	D₄	1	2	yes	—
110	C₃×C₄×C₈	—	2	1	no	—
111	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
112	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
113	C₃×C₄×C₈	C₂³	1	2	yes	—
114	C₃×C₄×C₈	C₂³	1	2	yes	—
115	C₂×#131	—	2	1	no	—
116	C₂²×M₁₆	—	2	1	no	—
117	#532	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
119	#480	C₃×C₄	1	2	yes	—
120	#474	C₃×C₄	1	1	yes	characteristic
121	#474	C₃×C₄	1	1	yes	characteristic
122	#459	C₃×C₄	1	1	yes	characteristic
123	#459	C₃×C₄	1	1	yes	characteristic
124	#447	C₃×C₄	1	2	yes	—
125	C₄×D₈	C₂²×C₃	1	2	yes	—
126	C₄×D₈	C₂²×C₃	1	2	yes	—
127	#436	C₂²×C₃	1	2	yes	—
128	#436	C₂²×C₃	1	2	yes	complemented
129	#435	—	2	2	no	—
130	#435	—	2	2	no	—
131	C₈×D₄	C₂²×C₃	1	2	yes	—
132	C₈×D₄	C₂²×C₃	1	2	yes	complemented
133	#431	C₂²×C₃	1	1	yes	characteristic
134	#423	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
136	#408	—	2	1	no	—
137	#407	—	2	1	no	—
138	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
140	#335	C₂²×C₃	1	2	yes	complemented
141	#335	C₂²×C₃	1	2	yes	complemented
142	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
143	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
144	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
145	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
146	D₄⋊C₈	C₂²×C₃	1	2	yes	complemented
147	D₄⋊C₈	C₂²×C₃	1	2	yes	complemented
148	#322	C₂²×C₃	1	2	yes	complemented
149	C₈²	C₂²×C₃	1	2	yes	complemented
150	C₂⁴×C₃	—	2	1	no	—
151	C₃×#41	—	4	2	no	—
152	C₃×#41	—	4	2	no	—
153	C₂×C₃×Q₈	—	2	1	no	—
154	C₂×C₃×D₄	—	2	2	no	—
155	C₂×C₃×D₄	—	2	2	no	—
156	C₂×C₃×D₄	—	2	1	no	—
157	C₂×C₃×D₄	—	2	1	no	—
158	C₂×C₃×D₄	—	2	1	no	—
159	C₂×C₃×D₄	—	4	1	no	—
160	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
162	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	—	2	1	no	—
167	C₂²×C₃×C₄	—	2	2	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	4	2	no	—
170	C₂²×C₃×C₄	—	4	2	no	—
171	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	#41	1	1	yes	characteristic
174	C₃×D₈	—	2	4	no	—
175	C₃×D₈	—	4	2	no	—
176	C₃×M₁₆	—	2	2	no	—
177	C₃×M₁₆	—	4	2	no	—
178	C₃×M₁₆	—	4	4	no	—
179	C₃×M₁₆	—	4	4	no	—
180	C₃×M₁₆	D₈	1	4	yes	complemented
181	C₂×C₃×C₈	—	2	1	no	—
182	C₂×C₃×C₈	—	2	1	no	—
183	C₂×C₃×C₈	—	2	2	no	—
184	C₂×C₃×C₈	—	2	1	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	4	2	no	—
187	C₂×C₃×C₈	—	4	2	no	—
188	C₂×C₃×C₈	—	4	4	no	—
189	C₂×C₃×C₈	—	4	4	no	—
190	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
191	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
193	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
194	C₃×C₄⋊C₄	—	2	1	no	—
195	C₃×C₄⋊C₄	—	2	1	no	—
196	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
199	C₃×C₂²⋊C₄	—	2	1	no	—
200	C₃×C₂²⋊C₄	—	2	1	no	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	—	2	1	no	—
203	C₃×C₂²⋊C₄	—	2	1	no	—
204	C₃×C₂²⋊C₄	—	2	2	no	—
205	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
206	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
207	C₃×C₄²	#41	1	1	yes	characteristic
208	C₃×C₄²	C₂⁴	1	1	yes	characteristic
209	C₂×#41	—	2	1	no	—
210	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
211	C₂³×C₄	—	2	1	no	—
212	C₂×D₈	C₂×C₃×C₄	1	2	yes	—
213	C₂×D₈	C₂×C₃×C₄	1	2	yes	—
214	#131	—	4	4	no	—
215	C₂×M₁₆	—	2	1	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	4	4	no	—
219	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
220	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
221	C₂²×C₈	—	2	1	no	—
222	C₂²×C₈	—	2	1	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₄⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
226	#127	C₂×C₃×C₄	1	1	yes	characteristic
227	#124	—	2	1	no	—
228	#121	—	2	1	no	—
229	#121	C₂×C₃×C₄	1	2	yes	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	2	1	no	—
233	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
234	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
235	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
236	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
237	C₄×D₄	C₂³×C₃	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
241	#107	C₂×C₃×C₄	1	2	yes	—
242	#107	C₂×C₃×C₄	1	2	yes	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
246	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
247	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
248	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
249	C₄⋊C₈	C₂³×C₃	1	2	yes	—
250	#102	C₂×C₃×C₄	1	2	yes	—
251	#102	C₂×C₃×C₄	1	2	yes	—
252	#102	C₂×C₃×C₄	1	2	yes	—
253	#102	C₂×C₃×C₄	1	2	yes	—
254	C₂²⋊C₈	—	2	2	no	—
255	C₂²⋊C₈	—	2	2	no	—
256	C₂²⋊C₈	—	2	2	no	—
257	C₂²⋊C₈	—	2	2	no	—
258	C₂²⋊C₈	C₂×C₃×C₄	1	2	yes	—
259	#97	C₃×D₄	1	2	yes	—
260	C₄×C₈	—	2	1	no	—
261	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₃	1	2	yes	—
264	C₄×C₈	C₂³×C₃	1	2	yes	—
265	C₂³×C₃	—	2	1	no	—
266	C₂³×C₃	—	2	1	no	—
267	C₂³×C₃	—	2	2	no	—
268	C₂³×C₃	—	4	2	no	—
269	C₂³×C₃	—	4	2	no	—
270	C₂³×C₃	—	8	1	no	—
271	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
272	C₃×Q₈	—	4	2	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	2	1	no	—
275	C₃×D₄	—	2	1	no	—
276	C₃×D₄	—	2	1	no	—
277	C₃×D₄	—	2	2	no	—
278	C₃×D₄	—	4	2	no	—
279	C₃×D₄	—	4	4	no	—
280	C₃×D₄	—	4	2	no	—
281	C₃×D₄	—	8	1	no	—
282	C₃×D₄	#131	1	2	yes	complemented
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	4	1	no	—
289	C₂×C₃×C₄	—	4	2	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	4	2	no	—
292	C₂×C₃×C₄	—	4	1	no	—
293	C₂×C₃×C₄	—	4	1	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	—	4	2	no	—
296	C₂×C₃×C₄	—	4	2	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×D₈	1	2	yes	—
302	C₂×C₃×C₄	#135	1	2	yes	—
303	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
306	C₃×C₈	—	2	2	no	—
307	C₃×C₈	—	2	2	no	—
308	C₃×C₈	—	2	2	no	—
309	C₃×C₈	—	2	2	no	—
310	C₃×C₈	—	4	1	no	—
311	C₃×C₈	—	4	1	no	—
312	C₃×C₈	—	4	1	no	—
313	C₃×C₈	—	4	2	no	—
314	C₃×C₈	C₂×D₈	1	4	yes	—
315	C₂⁴	—	2	1	no	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
326	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
327	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₃×#41	1	1	yes	characteristic
339	D₈	—	2	4	no	—
340	D₈	—	4	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	4	4	no	—
344	M₁₆	—	4	4	no	—
345	M₁₆	C₃×D₈	1	4	yes	complemented
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	4	4	no	—
354	C₂×C₈	—	4	4	no	—
355	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
356	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
357	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
358	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
371	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
372	C₄²	C₃×#41	1	1	yes	characteristic
373	C₄²	C₂⁴×C₃	1	1	yes	characteristic
374	C₂²×C₃	—	2	1	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	4	1	no	—
378	C₂²×C₃	—	4	1	no	—
379	C₂²×C₃	—	4	1	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	4	1	no	—
382	C₂²×C₃	—	4	2	no	—
383	C₂²×C₃	—	4	2	no	—
384	C₂²×C₃	—	4	1	no	—
385	C₂²×C₃	—	8	4	no	—
386	C₂²×C₃	C₄×D₈	1	2	yes	—
387	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	4	1	no	—
392	C₃×C₄	—	4	1	no	—
393	C₃×C₄	—	4	2	no	—
394	C₃×C₄	C₄×D₈	1	2	yes	—
395	C₃×C₄	C₂×#131	1	1	yes	characteristic
396	C₃×C₄	#568	1	1	yes	characteristic
397	C₃×C₄	C₂²×D₈	1	1	yes	characteristic
398	C₃×C₄	C₂×#135	1	1	yes	characteristic
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	1	no	—
405	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
406	Q₈	—	4	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	1	no	—
409	D₄	—	2	1	no	—
410	D₄	—	2	1	no	—
411	D₄	—	2	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	8	1	no	—
416	D₄	C₃×#131	1	2	yes	complemented
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
433	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
434	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
435	C₂×C₄	C₂×C₃×D₈	1	2	yes	—
436	C₂×C₄	C₃×#135	1	2	yes	—
437	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	2	no	—
448	C₈	C₂×C₃×D₈	1	4	yes	—
449	C₂×C₃	—	2	2	no	—
450	C₂×C₃	—	4	2	no	—
451	C₂×C₃	—	8	2	no	—
452	C₂×C₃	—	8	1	no	—
453	C₂×C₃	#2933	1	1	yes	characteristic
454	C₂×C₃	C₂×C₄×D₈	1	1	yes	characteristic
455	C₂×C₃	#2956	1	1	yes	characteristic
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	8	4	no	—
468	C₂²	C₃×C₄×D₈	1	2	yes	—
469	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	C₃×C₄×D₈	1	2	yes	—
477	C₄	C₂×C₃×#131	1	1	yes	characteristic
478	C₄	C₃×#568	1	1	yes	characteristic
479	C₄	C₂²×C₃×D₈	1	1	yes	characteristic
480	C₄	C₂×C₃×#135	1	1	yes	characteristic
481	C₃	#17994	1	1	yes	characteristic, direct product factor, Sylow
482	C₂	—	2	2	no	—
483	C₂	—	4	2	no	—
484	C₂	—	8	1	no	—
485	C₂	—	8	2	no	—
486	C₂	C₃×#2933	1	1	yes	characteristic
487	C₂	C₂×C₃×C₄×D₈	1	1	yes	characteristic
488	C₂	C₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₄²	C₂⁴×C₃
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₃×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2935	C₂	semidirect
3. C₃×D₄×M₁₆	C₂	semidirect
4. C₃×#1589	C₂	semidirect
5. C₃×#1581	C₂	semidirect
6. C₃×#1581	C₂	semidirect
7. C₃×C₈×D₈	C₂	semidirect
8. C₃×#1571	C₂	semidirect
9. C₃×#1492	C₂	semidirect
10. C₂×C₃×D₄⋊C₈	C₂	semidirect
11. C₃×C₈×M₁₆	C₂	semidirect
12. #17994	C₃	direct (N × H)
26. C₃×#436	C₂²	semidirect
30. C₃×C₈×D₄	C₂²	semidirect
38. C₃×#335	C₂²	semidirect
39. C₃×#335	C₂²	semidirect
44. C₃×D₄⋊C₈	C₂²	semidirect
45. C₃×D₄⋊C₈	C₂²	semidirect
46. C₃×#322	C₂²	semidirect
47. C₃×C₈²	C₂²	semidirect
49. #2935	C₂×C₃	semidirect
50. D₄×M₁₆	C₂×C₃	semidirect
51. #1589	C₂×C₃	semidirect
52. #1581	C₂×C₃	semidirect
53. #1581	C₂×C₃	semidirect
54. C₈×D₈	C₂×C₃	semidirect
55. #1571	C₂×C₃	semidirect
56. #1492	C₂×C₃	semidirect
57. C₂×D₄⋊C₈	C₂×C₃	semidirect
58. C₈×M₁₆	C₂×C₃	semidirect
128. #436	C₂²×C₃	semidirect
132. C₈×D₄	C₂²×C₃	semidirect
140. #335	C₂²×C₃	semidirect
141. #335	C₂²×C₃	semidirect
146. D₄⋊C₈	C₂²×C₃	semidirect
147. D₄⋊C₈	C₂²×C₃	semidirect
148. #322	C₂²×C₃	semidirect
149. C₈²	C₂²×C₃	semidirect
180. C₃×M₁₆	D₈	semidirect
282. C₃×D₄	#131	semidirect
345. M₁₆	C₃×D₈	semidirect
416. D₄	C₃×#131	semidirect
481. C₃	#17994	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3100	2
C₃×#2935	2
C₃×D₄×M₁₆	2
C₃×#1589	2
C₃×#1581	2
C₃×C₈×D₈	2
C₃×#1571	2
C₃×#1492	2
C₂×C₃×D₄⋊C₈	2
C₃×C₈×M₁₆	2
#17994	3

Subgroups — C3×#17994 #10636601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17994 #10636601