Subgroups — C₃×#18673 #10637280

Order 768.

872 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3518	C₂	1	1	yes	maximal, characteristic
2	C₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1650	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1645	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1637	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1634	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1633	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1554	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	#18673	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×Q₈²	C₂²	1	1	yes	characteristic
18	C₃×#556	—	2	1	no	—
19	C₃×#556	—	2	2	no	—
20	C₃×#556	—	2	1	no	—
21	C₃×#556	C₂²	1	1	yes	characteristic
22	C₃×#555	—	2	1	no	—
23	C₃×#555	C₂²	1	1	yes	characteristic
24	C₃×D₄×Q₈	C₂²	1	1	yes	characteristic
25	C₃×#548	—	2	1	no	—
26	C₃×#542	—	2	2	no	—
27	C₃×#542	—	2	1	no	—
28	C₃×#533	—	2	1	no	—
29	C₃×#533	C₂²	1	1	yes	characteristic
30	C₃×#533	C₂²	1	1	yes	characteristic
31	C₃×#529	—	2	1	no	—
32	C₃×#529	C₂²	1	1	yes	characteristic
33	C₃×#519	—	2	1	no	—
34	C₃×C₄×#41	C₂²	1	1	yes	characteristic
35	C₃×#500	C₂²	1	1	yes	characteristic
36	C₃×#499	—	2	1	no	—
37	C₃×#494	C₂²	1	1	yes	characteristic
38	C₃×#488	—	2	1	no	—
39	C₃×#487	C₂²	1	1	yes	characteristic
40	C₃×#487	C₂²	1	1	yes	characteristic
41	C₃×#485	—	2	1	no	—
42	C₃×#485	—	2	1	no	—
43	C₃×#482	—	2	1	no	—
44	C₃×#477	C₂²	1	1	yes	characteristic
45	C₃×#477	C₂²	1	1	yes	characteristic
46	C₃×#476	C₂²	1	1	yes	characteristic
47	C₃×#476	C₂²	1	1	yes	characteristic
48	C₃×#475	C₂²	1	1	yes	characteristic
49	C₃×#474	C₂²	1	1	yes	characteristic
50	C₃×#467	—	2	2	no	—
51	C₃×#462	C₂²	1	1	yes	characteristic
52	C₃×#461	C₂²	1	1	yes	characteristic
53	C₃×#452	—	2	1	no	—
54	C₃×#441	—	2	1	no	—
55	C₃×#440	—	2	1	no	—
56	C₃×C₄×Q₁₆	—	2	2	no	—
57	C₃×#432	C₂²	1	1	yes	characteristic
58	C₃×#431	C₂²	1	1	yes	characteristic
59	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
60	C₃×#333	C₂²	1	1	yes	characteristic
61	C₃×#333	C₂²	1	1	yes	characteristic
62	C₃×#332	C₂²	1	1	yes	characteristic
63	C₃×#332	C₂²	1	1	yes	characteristic
64	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
72	#3518	C₂×C₃	1	1	yes	characteristic
73	#3233	C₂×C₃	1	1	yes	characteristic, complemented
74	#3170	C₂×C₃	1	1	yes	characteristic, complemented
75	#3116	C₂×C₃	1	1	yes	characteristic, complemented
76	#1650	C₂×C₃	1	1	yes	characteristic, complemented
77	#1649	C₂×C₃	1	1	yes	characteristic, complemented
78	#1646	C₂×C₃	1	1	yes	characteristic, complemented
79	#1645	C₂×C₃	1	1	yes	characteristic, complemented
80	#1638	C₂×C₃	1	1	yes	characteristic, complemented
81	#1637	C₂×C₃	1	1	yes	characteristic, complemented
82	#1634	C₂×C₃	1	1	yes	characteristic, complemented
83	#1633	C₂×C₃	1	1	yes	characteristic, complemented
84	#1554	C₂×C₃	1	1	yes	characteristic, complemented
85	#1494	C₂×C₃	1	1	yes	characteristic, complemented
86	#1476	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂×C₃×#41	D₄	1	1	yes	characteristic
88	C₂²×C₃×Q₈	—	2	1	no	—
89	C₂×C₃×Q₁₆	—	2	2	no	—
90	C₂×C₃×Q₁₆	—	2	1	no	—
91	C₂×C₃×SD₁₆	—	2	1	no	—
92	C₂²×C₃×C₈	—	2	1	no	—
93	C₃×C₄⋊Q₈	—	2	2	no	—
94	C₃×C₄⋊Q₈	—	2	1	no	—
95	C₃×C₄⋊Q₈	—	2	1	no	—
96	C₃×C₄⋊Q₈	—	2	1	no	—
97	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
99	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
100	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₃×#126	—	2	2	no	—
102	C₃×#126	—	2	2	no	—
103	C₃×#126	—	2	2	no	—
104	C₃×#126	—	2	2	no	—
105	C₃×#126	—	2	1	no	—
106	C₃×#125	—	2	1	no	—
107	C₃×#125	—	2	1	no	—
108	C₃×#125	D₄	1	1	yes	characteristic
109	C₃×#124	—	2	2	no	—
110	C₃×#124	—	2	2	no	—
111	C₃×#124	—	2	2	no	—
112	C₃×#124	—	2	2	no	—
113	C₃×#124	—	2	1	no	—
114	C₃×#124	D₄	1	1	yes	characteristic
115	C₃×#123	—	2	2	no	—
116	C₃×#123	—	2	1	no	—
117	C₃×C₂²⋊Q₈	—	2	2	no	—
118	C₃×C₂²⋊Q₈	—	2	2	no	—
119	C₃×C₂²⋊Q₈	—	2	1	no	—
120	C₃×C₂²⋊Q₈	—	2	1	no	—
121	C₃×C₂²⋊Q₈	—	2	1	no	—
122	C₃×C₂²⋊Q₈	—	2	2	no	—
123	C₃×C₂²⋊Q₈	—	2	1	no	—
124	C₃×C₂²⋊Q₈	—	2	1	no	—
125	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
126	C₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₃×#121	—	2	2	no	—
128	C₃×#121	—	2	1	no	—
129	C₃×#121	—	2	1	no	—
130	C₃×#121	D₄	1	1	yes	characteristic
131	C₃×C₄×Q₈	—	2	2	no	—
132	C₃×C₄×Q₈	—	2	2	no	—
133	C₃×C₄×Q₈	—	2	2	no	—
134	C₃×C₄×Q₈	—	2	1	no	—
135	C₃×C₄×Q₈	—	2	1	no	—
136	C₃×C₄×Q₈	—	2	1	no	—
137	C₃×C₄×Q₈	—	2	1	no	—
138	C₃×C₄×Q₈	—	2	1	no	—
139	C₃×C₄×Q₈	—	2	1	no	—
140	C₃×C₄×Q₈	D₄	1	2	yes	—
141	C₃×C₄×Q₈	D₄	1	1	yes	characteristic
142	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
143	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
144	C₃×C₄×D₄	—	2	2	no	—
145	C₃×C₄×D₄	—	2	1	no	—
146	C₃×C₄×D₄	—	2	1	no	—
147	C₃×C₄×D₄	—	2	1	no	—
148	C₃×C₄×D₄	—	2	1	no	—
149	C₃×C₄×D₄	D₄	1	1	yes	characteristic
150	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
151	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
152	C₃×#117	—	2	2	no	—
153	C₃×#117	—	2	2	no	—
154	C₃×#117	—	2	1	no	—
155	C₃×#117	—	2	1	no	—
156	C₃×#117	—	2	1	no	—
157	C₃×#117	—	2	1	no	—
158	C₃×#117	—	2	1	no	—
159	C₃×#117	—	2	1	no	—
160	C₃×#117	—	2	1	no	—
161	C₃×#117	D₄	1	1	yes	characteristic
162	C₂×C₃×C₄²	—	2	1	no	—
163	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
164	C₃×#107	—	2	2	no	—
165	C₃×#107	—	2	1	no	—
166	C₃×#107	—	2	1	no	—
167	C₃×#107	—	2	1	no	—
168	C₃×#106	—	2	1	no	—
169	C₃×#106	—	2	1	no	—
170	C₃×#106	—	2	1	no	—
171	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
172	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
173	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
174	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₃×#103	—	2	2	no	—
176	C₃×#103	—	2	1	no	—
177	C₃×#103	—	2	1	no	—
178	C₃×#103	—	2	1	no	—
179	C₃×#103	—	2	2	no	—
180	C₃×#103	—	2	1	no	—
181	C₃×#103	—	2	1	no	—
182	C₃×#102	—	2	1	no	—
183	C₃×#102	—	2	1	no	—
184	C₃×#102	—	2	1	no	—
185	C₃×C₂²⋊C₈	—	2	1	no	—
186	C₃×C₂²⋊C₈	—	2	1	no	—
187	C₃×#97	—	2	1	no	—
188	C₃×C₄×C₈	—	2	1	no	—
189	C₃×C₄×C₈	—	2	1	no	—
190	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
191	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
192	Q₈²	C₂²×C₃	1	1	yes	characteristic
193	#556	—	2	1	no	—
194	#556	—	2	2	no	—
195	#556	—	2	1	no	—
196	#556	C₂²×C₃	1	1	yes	characteristic
197	#555	—	2	1	no	—
198	#555	C₂²×C₃	1	1	yes	characteristic
199	D₄×Q₈	C₂²×C₃	1	1	yes	characteristic
200	#548	—	2	1	no	—
201	#542	—	2	2	no	—
202	#542	—	2	1	no	—
203	#533	—	2	1	no	—
204	#533	C₂²×C₃	1	1	yes	characteristic
205	#533	C₂²×C₃	1	1	yes	characteristic
206	#529	—	2	1	no	—
207	#529	C₂²×C₃	1	1	yes	characteristic
208	#519	—	2	1	no	—
209	C₄×#41	C₂²×C₃	1	1	yes	characteristic
210	#500	C₂²×C₃	1	1	yes	characteristic
211	#499	—	2	1	no	—
212	#494	C₂²×C₃	1	1	yes	characteristic
213	#488	—	2	1	no	—
214	#487	C₂²×C₃	1	1	yes	characteristic
215	#487	C₂²×C₃	1	1	yes	characteristic
216	#485	—	2	1	no	—
217	#485	—	2	1	no	—
218	#482	—	2	1	no	—
219	#477	C₂²×C₃	1	1	yes	characteristic
220	#477	C₂²×C₃	1	1	yes	characteristic
221	#476	C₂²×C₃	1	1	yes	characteristic
222	#476	C₂²×C₃	1	1	yes	characteristic
223	#475	C₂²×C₃	1	1	yes	characteristic
224	#474	C₂²×C₃	1	1	yes	characteristic
225	#467	—	2	2	no	—
226	#462	C₂²×C₃	1	1	yes	characteristic
227	#461	C₂²×C₃	1	1	yes	characteristic
228	#452	—	2	1	no	—
229	#441	—	2	1	no	—
230	#440	—	2	1	no	—
231	C₄×Q₁₆	—	2	2	no	—
232	#432	C₂²×C₃	1	1	yes	characteristic
233	#431	C₂²×C₃	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
235	#333	C₂²×C₃	1	1	yes	characteristic
236	#333	C₂²×C₃	1	1	yes	characteristic
237	#332	C₂²×C₃	1	1	yes	characteristic
238	#332	C₂²×C₃	1	1	yes	characteristic
239	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
240	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
241	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
242	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
243	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
244	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
245	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
246	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
247	C₃×#41	—	2	2	no	—
248	C₃×#41	—	4	1	no	—
249	C₂×C₃×Q₈	—	2	2	no	—
250	C₂×C₃×Q₈	—	2	2	no	—
251	C₂×C₃×Q₈	—	2	1	no	—
252	C₂×C₃×Q₈	—	2	1	no	—
253	C₂×C₃×Q₈	—	2	1	no	—
254	C₂×C₃×Q₈	—	4	2	no	—
255	C₂×C₃×Q₈	—	4	2	no	—
256	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
257	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
258	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
259	C₂×C₃×D₄	—	2	1	no	—
260	C₂×C₃×D₄	—	2	2	no	—
261	C₂×C₃×D₄	—	2	1	no	—
262	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
263	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₃×C₄	—	2	2	no	—
265	C₂²×C₃×C₄	—	2	1	no	—
266	C₂²×C₃×C₄	—	2	1	no	—
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	—	2	1	no	—
269	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
272	C₃×Q₁₆	—	4	4	no	—
273	C₃×Q₁₆	—	4	2	no	—
274	C₃×SD₁₆	—	4	2	no	—
275	C₂×C₃×C₈	—	2	1	no	—
276	C₂×C₃×C₈	—	2	1	no	—
277	C₂×C₃×C₈	—	2	1	no	—
278	C₂×C₃×C₈	—	2	1	no	—
279	C₂×C₃×C₈	—	2	1	no	—
280	C₂×C₃×C₈	—	2	1	no	—
281	C₂×C₃×C₈	—	4	2	no	—
282	C₃×C₄⋊C₄	—	2	2	no	—
283	C₃×C₄⋊C₄	—	2	2	no	—
284	C₃×C₄⋊C₄	—	2	2	no	—
285	C₃×C₄⋊C₄	—	2	2	no	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	—	2	1	no	—
288	C₃×C₄⋊C₄	—	2	2	no	—
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	—	2	1	no	—
291	C₃×C₄⋊C₄	—	2	2	no	—
292	C₃×C₄⋊C₄	—	2	1	no	—
293	C₃×C₄⋊C₄	—	2	1	no	—
294	C₃×C₄⋊C₄	—	2	1	no	—
295	C₃×C₄⋊C₄	—	2	1	no	—
296	C₃×C₄⋊C₄	—	2	1	no	—
297	C₃×C₄⋊C₄	—	2	1	no	—
298	C₃×C₄⋊C₄	—	2	1	no	—
299	C₃×C₄⋊C₄	—	2	1	no	—
300	C₃×C₄⋊C₄	—	2	1	no	—
301	C₃×C₄⋊C₄	—	4	1	no	—
302	C₃×C₄⋊C₄	—	4	1	no	—
303	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
307	C₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₃×C₂²⋊C₄	—	2	2	no	—
309	C₃×C₂²⋊C₄	—	2	2	no	—
310	C₃×C₂²⋊C₄	—	2	2	no	—
311	C₃×C₂²⋊C₄	—	2	2	no	—
312	C₃×C₂²⋊C₄	—	2	2	no	—
313	C₃×C₂²⋊C₄	—	2	2	no	—
314	C₃×C₂²⋊C₄	—	2	1	no	—
315	C₃×C₂²⋊C₄	—	2	1	no	—
316	C₃×C₂²⋊C₄	—	2	1	no	—
317	C₃×C₂²⋊C₄	—	2	1	no	—
318	C₃×C₂²⋊C₄	—	2	1	no	—
319	C₃×C₂²⋊C₄	—	2	1	no	—
320	C₃×C₂²⋊C₄	—	2	1	no	—
321	C₃×C₂²⋊C₄	—	2	1	no	—
322	C₃×C₂²⋊C₄	—	4	1	no	—
323	C₃×C₄²	—	2	2	no	—
324	C₃×C₄²	—	2	2	no	—
325	C₃×C₄²	—	2	2	no	—
326	C₃×C₄²	—	2	1	no	—
327	C₃×C₄²	—	2	1	no	—
328	C₃×C₄²	—	2	2	no	—
329	C₃×C₄²	—	2	1	no	—
330	C₃×C₄²	—	2	1	no	—
331	C₃×C₄²	—	4	1	no	—
332	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
333	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
334	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
335	C₃×C₄²	C₂⁴	1	1	yes	characteristic
336	C₂×#41	C₃×D₄	1	1	yes	characteristic
337	C₂²×Q₈	—	2	1	no	—
338	C₂×Q₁₆	—	2	2	no	—
339	C₂×Q₁₆	—	2	1	no	—
340	C₂×SD₁₆	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
349	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
350	#126	—	2	2	no	—
351	#126	—	2	2	no	—
352	#126	—	2	2	no	—
353	#126	—	2	2	no	—
354	#126	—	2	1	no	—
355	#125	—	2	1	no	—
356	#125	—	2	1	no	—
357	#125	C₃×D₄	1	1	yes	characteristic
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#124	—	2	2	no	—
361	#124	—	2	2	no	—
362	#124	—	2	1	no	—
363	#124	C₃×D₄	1	1	yes	characteristic
364	#123	—	2	2	no	—
365	#123	—	2	1	no	—
366	C₂²⋊Q₈	—	2	2	no	—
367	C₂²⋊Q₈	—	2	2	no	—
368	C₂²⋊Q₈	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	C₃×D₄	1	1	yes	characteristic
375	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
376	#121	—	2	2	no	—
377	#121	—	2	1	no	—
378	#121	—	2	1	no	—
379	#121	C₃×D₄	1	1	yes	characteristic
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	2	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	C₃×D₄	1	1	yes	characteristic
390	C₄×Q₈	C₃×D₄	1	2	yes	—
391	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
392	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
393	C₄×D₄	—	2	2	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	C₃×D₄	1	1	yes	characteristic
399	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
400	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
401	#117	—	2	2	no	—
402	#117	—	2	2	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	C₃×D₄	1	1	yes	characteristic
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
413	#107	—	2	2	no	—
414	#107	—	2	1	no	—
415	#107	—	2	1	no	—
416	#107	—	2	1	no	—
417	#106	—	2	1	no	—
418	#106	—	2	1	no	—
419	#106	—	2	1	no	—
420	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
424	#103	—	2	2	no	—
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	2	no	—
429	#103	—	2	1	no	—
430	#103	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	#97	—	2	1	no	—
437	C₄×C₈	—	2	1	no	—
438	C₄×C₈	—	2	1	no	—
439	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
440	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
441	C₂³×C₃	—	2	1	no	—
442	C₂³×C₃	—	2	1	no	—
443	C₂³×C₃	#120	1	1	yes	characteristic
444	C₃×Q₈	—	2	1	no	—
445	C₃×Q₈	—	2	1	no	—
446	C₃×Q₈	—	2	1	no	—
447	C₃×Q₈	—	4	2	no	—
448	C₃×Q₈	—	4	4	no	—
449	C₃×Q₈	—	4	2	no	—
450	C₃×Q₈	—	4	1	no	—
451	C₃×Q₈	—	4	1	no	—
452	C₃×Q₈	—	4	1	no	—
453	C₃×Q₈	—	4	1	no	—
454	C₃×Q₈	—	8	2	no	—
455	C₃×Q₈	#135	1	2	yes	—
456	C₃×D₄	—	2	1	no	—
457	C₃×D₄	—	2	1	no	—
458	C₃×D₄	—	2	1	no	—
459	C₃×D₄	—	2	1	no	—
460	C₃×D₄	—	4	2	no	—
461	C₃×D₄	—	8	1	no	—
462	C₃×D₄	—	8	2	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	—	2	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	2	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	2	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	4	1	no	—
476	C₂×C₃×C₄	—	4	2	no	—
477	C₂×C₃×C₄	—	4	4	no	—
478	C₂×C₃×C₄	—	4	1	no	—
479	C₂×C₃×C₄	—	4	1	no	—
480	C₂×C₃×C₄	—	4	1	no	—
481	C₂×C₃×C₄	—	4	1	no	—
482	C₂×C₃×C₄	—	4	1	no	—
483	C₂×C₃×C₄	—	4	1	no	—
484	C₂×C₃×C₄	—	8	1	no	—
485	C₂×C₃×C₄	#120	1	1	yes	characteristic
486	C₂×C₃×C₄	#120	1	1	yes	characteristic
487	C₂×C₃×C₄	#120	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
491	C₃×C₈	—	2	2	no	—
492	C₃×C₈	—	4	1	no	—
493	C₃×C₈	—	4	1	no	—
494	C₃×C₈	—	4	1	no	—
495	C₃×C₈	—	4	1	no	—
496	C₃×C₈	—	4	1	no	—
497	#41	—	2	2	no	—
498	#41	—	4	1	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	2	no	—
506	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
507	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
508	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
513	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
522	Q₁₆	—	4	4	no	—
523	Q₁₆	—	4	2	no	—
524	SD₁₆	—	4	2	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	4	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	—	4	1	no	—
553	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
554	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
555	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
556	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
557	C₄⋊C₄	C₂×C₃×D₄	1	1	yes	characteristic
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	4	1	no	—
582	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
583	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
584	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
585	C₄²	C₂⁴×C₃	1	1	yes	characteristic
586	C₂²×C₃	—	2	1	no	—
587	C₂²×C₃	—	2	1	no	—
588	C₂²×C₃	—	2	1	no	—
589	C₂²×C₃	—	4	1	no	—
590	C₂²×C₃	—	4	1	no	—
591	C₂²×C₃	—	4	1	no	—
592	C₂²×C₃	—	4	1	no	—
593	C₂²×C₃	—	4	1	no	—
594	C₂²×C₃	—	4	1	no	—
595	C₂²×C₃	C₂×#120	1	1	yes	characteristic
596	C₃×C₄	—	2	1	no	—
597	C₃×C₄	—	2	2	no	—
598	C₃×C₄	—	2	1	no	—
599	C₃×C₄	—	2	1	no	—
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	4	2	no	—
602	C₃×C₄	—	4	1	no	—
603	C₃×C₄	—	4	1	no	—
604	C₃×C₄	—	4	1	no	—
605	C₃×C₄	—	4	1	no	—
606	C₃×C₄	—	4	2	no	—
607	C₃×C₄	—	4	1	no	—
608	C₃×C₄	—	8	1	no	—
609	C₃×C₄	—	8	1	no	—
610	C₃×C₄	C₂×#135	1	1	yes	characteristic
611	C₃×C₄	#575	1	1	yes	characteristic
612	C₃×C₄	#578	1	1	yes	characteristic
613	C₃×C₄	#578	1	1	yes	characteristic
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	C₃×#120	1	1	yes	characteristic
617	Q₈	—	2	1	no	—
618	Q₈	—	2	1	no	—
619	Q₈	—	2	1	no	—
620	Q₈	—	4	2	no	—
621	Q₈	—	4	4	no	—
622	Q₈	—	4	2	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	Q₈	—	4	1	no	—
627	Q₈	—	8	2	no	—
628	Q₈	C₃×#135	1	2	yes	—
629	D₄	—	2	1	no	—
630	D₄	—	2	1	no	—
631	D₄	—	2	1	no	—
632	D₄	—	2	1	no	—
633	D₄	—	4	2	no	—
634	D₄	—	8	1	no	—
635	D₄	—	8	2	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	2	no	—
650	C₂×C₄	—	4	4	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	8	1	no	—
658	C₂×C₄	C₃×#120	1	1	yes	characteristic
659	C₂×C₄	C₃×#120	1	1	yes	characteristic
660	C₂×C₄	C₃×#120	1	1	yes	characteristic
661	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
662	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
663	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
664	C₈	—	2	2	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	1	no	—
667	C₈	—	4	1	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₂×C₃	—	4	1	no	—
671	C₂×C₃	—	8	1	no	—
672	C₂×C₃	—	8	1	no	—
673	C₂×C₃	#3002	1	1	yes	characteristic
674	C₂×C₃	#3011	1	1	yes	characteristic
675	C₂×C₃	#3018	1	1	yes	characteristic
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	C₂×C₃×#120	1	1	yes	characteristic
686	C₄	—	2	1	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	1	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	1	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	C₂×C₃×#135	1	1	yes	characteristic
701	C₄	C₃×#575	1	1	yes	characteristic
702	C₄	C₃×#578	1	1	yes	characteristic
703	C₄	C₃×#578	1	1	yes	characteristic
704	C₃	#18673	1	1	yes	characteristic, direct product factor, Sylow
705	C₂	—	4	1	no	—
706	C₂	—	8	1	no	—
707	C₂	—	8	1	no	—
708	C₂	C₃×#3002	1	1	yes	characteristic
709	C₂	C₃×#3011	1	1	yes	characteristic
710	C₂	C₃×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃
prime radical	C₃×#3518	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#3233	C₂	semidirect
3. C₃×#3170	C₂	semidirect
4. C₃×#3116	C₂	semidirect
5. C₃×#1650	C₂	semidirect
6. C₃×#1649	C₂	semidirect
7. C₃×#1646	C₂	semidirect
8. C₃×#1645	C₂	semidirect
9. C₃×#1638	C₂	semidirect
10. C₃×#1637	C₂	semidirect
11. C₃×#1634	C₂	semidirect
12. C₃×#1633	C₂	semidirect
13. C₃×#1554	C₂	semidirect
14. C₃×#1494	C₂	semidirect
15. C₃×#1476	C₂	semidirect
16. #18673	C₃	direct (N × H)
73. #3233	C₂×C₃	semidirect
74. #3170	C₂×C₃	semidirect
75. #3116	C₂×C₃	semidirect
76. #1650	C₂×C₃	semidirect
77. #1649	C₂×C₃	semidirect
78. #1646	C₂×C₃	semidirect
79. #1645	C₂×C₃	semidirect
80. #1638	C₂×C₃	semidirect
81. #1637	C₂×C₃	semidirect
82. #1634	C₂×C₃	semidirect
83. #1633	C₂×C₃	semidirect
84. #1554	C₂×C₃	semidirect
85. #1494	C₂×C₃	semidirect
86. #1476	C₂×C₃	semidirect
704. C₃	#18673	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×#3518	2
C₃×#3233	2
C₃×#3170	2
C₃×#3116	2
C₃×#1650	2
C₃×#1649	2
C₃×#1646	2
C₃×#1645	2
C₃×#1638	2
C₃×#1637	2
C₃×#1634	2
C₃×#1633	2
C₃×#1554	2
C₃×#1494	2
C₃×#1476	2
#18673	3

Subgroups — C3×#18673 #10637280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#18673 #10637280