Subgroups — C₃×#10948645 #72222778

Order 2304.

1368 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#82009	C₂	1	1	yes	maximal, characteristic
2	C₃×#79249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#79106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#69310	C₂	1	4	yes	maximal, complemented
5	C₃×#69309	C₂	1	4	yes	maximal, complemented
6	C₃×#70687	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#4488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#71425	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃²×#365	C₂	1	1	yes	maximal, characteristic, complemented
10	#10948645	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#33469	—	3	1	no	maximal
12	C₃×#5745	—	2	1	no	—
13	C₂×C₃×#904	C₂²	1	1	yes	characteristic
14	C₂×C₃×#904	C₂²	1	1	yes	characteristic
15	C₃×#5504	—	2	1	no	—
16	C₂×C₃²×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₃²×#108	C₂²	1	1	yes	characteristic
18	C₂×C₃²×#106	C₂²	1	1	yes	characteristic
19	C₃×#5139	—	2	1	no	—
20	C₃×#5101	C₂²	1	1	yes	characteristic
21	C₂×C₃×#812	C₂²	1	1	yes	characteristic
22	C₃×#4966	—	2	1	no	—
23	C₃×#4909	C₄	1	2	yes	complemented
24	C₃×#4909	C₂²	1	2	yes	—
25	C₃×#4908	C₄	1	2	yes	complemented
26	C₃×#4908	C₂²	1	2	yes	—
27	C₃×#4904	C₄	1	4	yes	complemented
28	C₃×#4895	—	2	2	no	—
29	C₃×#4894	C₂²	1	4	yes	—
30	C₃×#4869	C₂²	1	2	yes	complemented
31	C₃×#4853	C₂²	1	2	yes	complemented
32	C₃×#4852	—	2	2	no	—
33	C₃²×#365	C₂²	1	4	yes	complemented
34	C₃×#4512	C₂²	1	4	yes	complemented
35	C₃×#4496	C₂²	1	2	yes	complemented
36	C₃×#4495	C₂²	1	2	yes	complemented
37	C₃×#4488	C₂²	1	4	yes	—
38	C₃×#3414	—	3	1	no	—
39	C₃×#2957	—	3	1	no	—
40	C₃×#2952	—	3	1	no	—
41	#82009	C₂×C₃	1	1	yes	characteristic
42	#79249	C₂×C₃	1	1	yes	characteristic, complemented
43	#79106	C₂×C₃	1	1	yes	characteristic, complemented
44	C₃×AGL(1,ℤ/16)	—	3	4	no	—
45	C₃×#2180	—	3	4	no	—
46	C₂×C₃×#365	—	2	1	no	—
47	C₂×C₃×#365	D₃	1	1	yes	characteristic, complemented
48	C₂×C₃×#365	C₂×C₃	1	1	yes	characteristic, complemented
49	C₃×#2148	—	3	1	no	—
50	C₂×C₃×#360	—	3	1	no	—
51	C₃×#2110	—	3	1	no	—
52	#71425	C₂×C₃	1	1	yes	characteristic, complemented
53	#70687	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#4488	C₂×C₃	1	1	yes	characteristic, complemented
55	#69310	C₂×C₃	1	4	yes	complemented
56	#69309	C₂×C₃	1	4	yes	complemented
57	C₂×C₃×#235	—	2	1	no	—
58	C₂×C₃×#235	—	2	1	no	—
59	C₂×C₃²×M₁₆	—	2	1	no	—
60	C₂²×C₃²×C₈	C₂³	1	1	yes	characteristic
61	C₂×C₃²×C₄⋊C₄	—	2	1	no	—
62	C₃×C₄×#67	—	4	2	no	—
63	C₃×#926	D₄	1	1	yes	characteristic
64	C₂×C₃×#208	D₄	1	1	yes	characteristic
65	C₃×#907	—	2	4	no	—
66	C₃×D₃×M₁₆	—	4	2	no	—
67	C₂×C₃×Dic₁₂	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂×C₃×Dic₁₂	C₂³	1	1	yes	characteristic
69	C₃×#904	—	2	1	no	—
70	C₃×#904	—	2	1	no	—
71	C₃×#904	—	2	1	no	—
72	C₃×#904	—	2	1	no	—
73	C₃×#904	C₂×C₄	1	2	yes	—
74	C₃×#904	C₂×C₄	1	2	yes	—
75	C₃×#904	C₂×C₄	1	2	yes	complemented
76	C₃×#904	C₂³	1	2	yes	—
77	C₂×C₃×D₂₄	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×C₃×D₂₄	C₂³	1	1	yes	characteristic
79	C₂×C₃×#204	—	2	1	no	—
80	C₂×C₃×#204	—	2	1	no	—
81	C₃×#901	—	4	2	no	—
82	C₃×#893	—	2	2	no	—
83	C₃×#892	—	4	1	no	—
84	C₃×D₃×C₄⋊C₄	—	4	1	no	—
85	C₃×#887	—	2	2	no	—
86	C₃²×M₃₂	C₂×C₄	1	2	yes	complemented
87	C₃²×M₃₂	C₂³	1	2	yes	—
88	C₂×C₃²×C₁₆	C₂×C₄	1	2	yes	complemented
89	C₃²×#108	—	2	1	no	—
90	C₃²×#108	C₂³	1	2	yes	—
91	C₃²×#106	—	2	1	no	—
92	C₃²×#106	C₂³	1	2	yes	—
93	C₃×#825	—	2	4	no	—
94	C₃×#815	C₂³	1	2	yes	—
95	C₃×C₈×Dic₃	D₄	1	2	yes	—
96	C₃×#812	—	2	1	no	—
97	C₃×#812	C₂³	1	2	yes	—
98	C₂×C₃×C₃⋊C₁₆	—	2	1	no	—
99	C₃×#810	—	2	2	no	—
100	C₃×#809	—	2	2	no	—
101	C₃×Dic₂₄	C₂×C₄	1	4	yes	complemented
102	C₃×#800	C₂×C₄	1	4	yes	complemented
103	C₃×#800	C₂×C₄	1	4	yes	complemented
104	C₃×D₄₈	C₂×C₄	1	4	yes	complemented
105	#33469	—	3	1	no	Sylow
106	C₂×C₃×#135	—	3	1	no	—
107	C₂×C₃×#135	—	3	1	no	—
108	C₃×#568	—	6	1	no	—
109	C₃×#520	—	6	1	no	—
110	#5745	—	2	1	no	—
111	C₂×#904	C₂²×C₃	1	1	yes	characteristic
112	C₂×#904	C₂²×C₃	1	1	yes	characteristic
113	#5504	—	2	1	no	—
114	C₃×#510	—	3	2	no	—
115	C₃×#510	—	3	2	no	—
116	C₃×#509	—	3	2	no	—
117	C₃×#509	—	3	2	no	—
118	C₃×#508	—	3	4	no	—
119	C₂×C₃×M₃₂	—	2	1	no	—
120	C₂×C₃×M₃₂	—	3	1	no	—
121	C₂×C₃×M₃₂	C₂×D₃	1	1	yes	characteristic
122	C₂×C₃×M₃₂	C₂²×C₃	1	1	yes	characteristic
123	C₃×#444	—	3	4	no	—
124	C₃×#443	—	6	2	no	—
125	C₃×#442	—	3	2	no	—
126	C₃×#441	—	3	2	no	—
127	C₃×C₄×SD₁₆	—	6	2	no	—
128	C₂×C₃×#108	—	2	1	no	—
129	C₂×C₃×#108	C₂×D₃	1	1	yes	characteristic
130	C₂×C₃×#108	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×#106	—	2	1	no	—
132	C₂×C₃×#106	C₂×D₃	1	1	yes	characteristic
133	C₂×C₃×#106	C₂²×C₃	1	1	yes	characteristic
134	C₃×#421	—	6	1	no	—
135	C₃×#417	—	6	1	no	—
136	C₃×#405	—	3	1	no	—
137	#5139	—	2	1	no	—
138	#5101	C₂²×C₃	1	1	yes	characteristic
139	C₂×#812	C₂²×C₃	1	1	yes	characteristic
140	#4966	—	2	1	no	—
141	#4909	C₃×C₄	1	2	yes	complemented
142	#4909	C₂²×C₃	1	2	yes	—
143	#4908	C₃×C₄	1	2	yes	complemented
144	#4908	C₂²×C₃	1	2	yes	—
145	#4904	C₃×C₄	1	4	yes	complemented
146	#4895	—	2	2	no	—
147	#4894	C₂²×C₃	1	4	yes	—
148	#4869	C₂²×C₃	1	2	yes	complemented
149	#4853	C₂²×C₃	1	2	yes	complemented
150	#4852	—	2	2	no	—
151	C₃×#365	—	2	4	no	—
152	C₃×#365	C₂×D₃	1	4	yes	complemented
153	C₃×#365	C₂²×C₃	1	4	yes	complemented
154	C₃×#362	—	3	2	no	—
155	C₃×#361	—	3	2	no	—
156	C₃×#360	—	3	4	no	—
157	C₃×#347	—	3	4	no	—
158	#4512	C₂²×C₃	1	4	yes	complemented
159	#4496	C₂²×C₃	1	2	yes	complemented
160	#4495	C₂²×C₃	1	2	yes	complemented
161	#4488	C₂²×C₃	1	4	yes	—
162	C₂²×C₃²×C₄	—	4	1	no	—
163	C₂²×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃×#67	—	4	1	no	—
165	C₂×C₃×#67	—	4	1	no	—
166	C₃×#235	—	2	2	no	—
167	C₃×#235	—	2	2	no	—
168	C₃×#235	—	2	2	no	—
169	C₃×#235	—	2	2	no	—
170	C₃×#235	—	4	1	no	—
171	C₃×#235	—	4	1	no	—
172	C₃×#235	—	4	1	no	—
173	C₃×#235	—	4	1	no	—
174	C₂×C₃×D₁₂	—	2	1	no	—
175	C₂×C₃×D₁₂	—	2	1	no	—
176	C₂×C₃×C₄×D₃	—	4	1	no	—
177	C₂×C₃×C₄×D₃	—	4	1	no	—
178	C₂×C₃×C₄×D₃	—	4	2	no	—
179	C₂×C₃×Dic₆	—	2	1	no	—
180	C₂×C₃×Dic₆	—	2	1	no	—
181	C₃²×M₁₆	—	2	2	no	—
182	C₃²×M₁₆	—	4	1	no	—
183	C₂×C₃²×C₈	—	4	1	no	—
184	C₂×C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₃²×C₈	C₂×D₄	1	1	yes	characteristic
187	C₂×C₃²×C₈	#41	1	1	yes	characteristic
188	C₂×C₃²×C₈	#41	1	1	yes	characteristic
189	C₂×C₃²×C₈	C₂⁴	1	1	yes	characteristic
190	C₃²×C₄⋊C₄	—	2	2	no	—
191	C₃²×C₄⋊C₄	—	4	1	no	—
192	C₃×#217	—	2	1	no	—
193	C₃×(C₂×D₃)⋊C₄	—	4	2	no	—
194	C₃×C₄⋊Dic₃	—	2	1	no	—
195	C₃×Dic₃⋊C₄	—	4	2	no	—
196	C₃×C₄×Dic₃	—	4	2	no	—
197	C₃×C₄×Dic₃	C₂×D₄	1	2	yes	—
198	C₃×#208	—	2	1	no	—
199	C₃×#208	—	2	1	no	—
200	C₂×C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
201	C₃×Dic₁₂	—	2	1	no	—
202	C₃×Dic₁₂	—	2	1	no	—
203	C₃×Dic₁₂	C₂²×C₄	1	2	yes	—
204	C₃×Dic₁₂	C₂²×C₄	1	2	yes	—
205	C₃×D₂₄	—	2	1	no	—
206	C₃×D₂₄	—	2	1	no	—
207	C₃×D₂₄	C₂²×C₄	1	2	yes	—
208	C₃×D₂₄	C₂²×C₄	1	2	yes	—
209	C₃×#204	—	2	2	no	—
210	C₃×#204	—	2	2	no	—
211	C₃×#204	—	2	2	no	—
212	C₃×#204	—	2	2	no	—
213	C₃×ΓL(1,𝔽₂₅)	—	4	4	no	—
214	C₃×D₃×C₈	—	4	4	no	—
215	C₃²×C₁₆	C₂²×C₄	1	4	yes	—
216	C₃×C₃⋊C₁₆	—	2	2	no	—
217	#3414	—	3	1	no	—
218	#2957	—	3	1	no	—
219	#2952	—	3	1	no	—
220	AGL(1,ℤ/16)	—	3	4	no	—
221	#2180	—	3	4	no	—
222	C₂×#365	C₃×D₃	1	1	yes	characteristic, complemented
223	#2148	—	3	1	no	—
224	C₂×#360	—	3	1	no	—
225	#2110	—	3	1	no	—
226	C₂×C₃×#41	—	6	1	no	—
227	C₂×C₃×#41	—	6	1	no	—
228	C₂×#235	—	2	1	no	—
229	C₂×#235	—	2	1	no	—
230	C₃×#135	—	3	2	no	—
231	C₃×#135	—	3	2	no	—
232	C₃×#135	—	3	2	no	—
233	C₃×#135	—	3	2	no	—
234	C₃×#135	—	6	1	no	—
235	C₃×#135	—	6	1	no	—
236	C₃×#135	—	6	1	no	—
237	C₃×#135	—	6	1	no	—
238	C₂×C₃×Q₁₆	—	3	1	no	—
239	C₂×C₃×Q₁₆	—	3	1	no	—
240	C₂×C₃×SD₁₆	—	6	1	no	—
241	C₂×C₃×SD₁₆	—	6	1	no	—
242	C₂×C₃×D₈	—	3	1	no	—
243	C₂×C₃×D₈	—	3	1	no	—
244	C₃×#131	—	6	4	no	—
245	C₃×#131	—	12	2	no	—
246	C₂×C₃×M₁₆	—	2	1	no	—
247	C₂×C₃×M₁₆	—	2	1	no	—
248	C₂×C₃×M₁₆	—	3	1	no	—
249	C₂×C₃×M₁₆	—	4	1	no	—
250	C₂×C₃×M₁₆	—	12	2	no	—
251	C₂²×C₃×C₈	—	2	1	no	—
252	C₂²×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
253	C₂²×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
254	C₃×C₄×Q₈	—	6	2	no	—
255	C₃×C₄×D₄	—	6	2	no	—
256	C₃×C₄×D₄	—	12	2	no	—
257	C₃×#117	—	3	1	no	—
258	C₃×#117	—	12	1	no	—
259	C₂×C₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₃×C₄⋊C₄	—	2	1	no	—
261	C₂×C₃×C₄⋊C₄	—	4	1	no	—
262	C₂×C₃×C₄⋊C₄	—	12	1	no	—
263	C₄×#67	—	4	2	no	—
264	#926	C₃×D₄	1	1	yes	characteristic
265	C₂×#208	C₃×D₄	1	1	yes	characteristic
266	#907	—	2	4	no	—
267	D₃×M₁₆	—	4	2	no	—
268	C₂×Dic₁₂	C₂×C₃×C₄	1	1	yes	characteristic, complemented
269	C₂×Dic₁₂	C₂³×C₃	1	1	yes	characteristic
270	#904	—	2	1	no	—
271	#904	—	2	1	no	—
272	#904	—	2	1	no	—
273	#904	—	2	1	no	—
274	#904	C₂×C₃×C₄	1	2	yes	—
275	#904	C₂×C₃×C₄	1	2	yes	—
276	#904	C₂×C₃×C₄	1	2	yes	complemented
277	#904	C₂³×C₃	1	2	yes	—
278	C₂×D₂₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
279	C₂×D₂₄	C₂³×C₃	1	1	yes	characteristic
280	C₂×#204	—	2	1	no	—
281	C₂×#204	—	2	1	no	—
282	#901	—	4	2	no	—
283	#893	—	2	2	no	—
284	#892	—	4	1	no	—
285	D₃×C₄⋊C₄	—	4	1	no	—
286	#887	—	2	2	no	—
287	C₃×Q₃₂	—	3	4	no	—
288	C₃×SD₃₂	—	3	4	no	—
289	C₃×SD₃₂	—	3	4	no	—
290	C₃×D₁₆	—	3	4	no	—
291	C₃×M₃₂	—	2	2	no	—
292	C₃×M₃₂	—	2	2	no	—
293	C₃×M₃₂	—	3	2	no	—
294	C₃×M₃₂	—	6	1	no	—
295	C₃×M₃₂	C₄×D₃	1	2	yes	complemented
296	C₃×M₃₂	C₂×C₃×C₄	1	2	yes	complemented
297	C₃×M₃₂	C₂²×D₃	1	2	yes	—
298	C₃×M₃₂	C₂³×C₃	1	2	yes	—
299	C₂×C₃×C₁₆	—	2	2	no	—
300	C₂×C₃×C₁₆	—	6	1	no	—
301	C₂×C₃×C₁₆	C₄×D₃	1	2	yes	complemented
302	C₂×C₃×C₁₆	C₂×C₃×C₄	1	2	yes	complemented
303	C₃×#108	—	2	1	no	—
304	C₃×#108	—	2	1	no	—
305	C₃×#108	—	2	2	no	—
306	C₃×#108	—	4	1	no	—
307	C₃×#108	C₂²×D₃	1	2	yes	—
308	C₃×#108	C₂³×C₃	1	2	yes	—
309	C₃×#106	—	2	1	no	—
310	C₃×#106	—	2	1	no	—
311	C₃×#106	—	2	2	no	—
312	C₃×#106	—	4	1	no	—
313	C₃×#106	C₂²×D₃	1	2	yes	—
314	C₃×#106	C₂³×C₃	1	2	yes	—
315	C₃×#104	—	6	4	no	—
316	C₃×#103	—	6	2	no	—
317	C₃×#102	—	6	2	no	—
318	C₃×#97	—	3	2	no	—
319	C₃×C₄×C₈	—	3	2	no	—
320	#825	—	2	4	no	—
321	#815	C₂³×C₃	1	2	yes	—
322	C₈×Dic₃	C₃×D₄	1	2	yes	—
323	#812	—	2	1	no	—
324	#812	C₂³×C₃	1	2	yes	—
325	C₂×C₃⋊C₁₆	—	2	1	no	—
326	#810	—	2	2	no	—
327	#809	—	2	2	no	—
328	Dic₂₄	C₂×C₃×C₄	1	4	yes	complemented
329	#800	C₂×C₃×C₄	1	4	yes	complemented
330	#800	C₂×C₃×C₄	1	4	yes	complemented
331	D₄₈	C₂×C₃×C₄	1	4	yes	complemented
332	C₂³×C₃²	AGL(1,ℤ/8)	1	1	yes	characteristic
333	C₂²×C₃×D₃	—	4	1	no	—
334	C₂²×C₃×D₃	—	4	1	no	—
335	C₂×C₃²×C₄	—	4	2	no	—
336	C₂×C₃²×C₄	—	16	1	no	—
337	C₂×C₃²×C₄	C₄×D₄	1	1	yes	characteristic
338	C₂×C₃²×C₄	C₄×D₄	1	1	yes	characteristic
339	C₂×C₃²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂×C₃²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₂×C₃²×C₄	AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
343	C₃×#67	—	4	2	no	—
344	C₃×#67	—	4	2	no	—
345	C₃×#67	—	4	2	no	—
346	C₃×#67	—	4	2	no	—
347	C₂×C₃×Dic₃	—	2	2	no	—
348	C₂×C₃×Dic₃	—	4	1	no	—
349	C₂×C₃×Dic₃	—	4	1	no	—
350	C₃×D₁₂	—	2	2	no	—
351	C₃×D₁₂	—	2	2	no	—
352	C₃×D₁₂	—	4	1	no	—
353	C₃×D₁₂	—	4	1	no	—
354	C₃×C₄×D₃	—	4	2	no	—
355	C₃×C₄×D₃	—	4	2	no	—
356	C₃×C₄×D₃	—	4	2	no	—
357	C₃×C₄×D₃	—	4	2	no	—
358	C₃×C₄×D₃	—	16	2	no	—
359	C₃×Dic₆	—	2	2	no	—
360	C₃×Dic₆	—	2	2	no	—
361	C₃×Dic₆	—	4	1	no	—
362	C₃×Dic₆	—	4	1	no	—
363	C₃²×C₈	—	4	2	no	—
364	C₃²×C₈	C₄×D₄	1	1	yes	characteristic
365	C₃²×C₈	C₄×D₄	1	1	yes	characteristic
366	C₃²×C₈	C₂³×C₄	1	1	yes	characteristic
367	C₃²×C₈	C₂×#41	1	1	yes	characteristic
368	C₃×C₃⋊C₈	—	2	2	no	—
369	C₂×#135	—	3	1	no	—
370	C₂×#135	—	3	1	no	—
371	#568	—	6	1	no	—
372	#520	—	6	1	no	—
373	#510	—	3	2	no	—
374	#510	—	3	2	no	—
375	#509	—	3	2	no	—
376	#509	—	3	2	no	—
377	#508	—	3	4	no	—
378	C₂×M₃₂	—	3	1	no	—
379	C₂×M₃₂	C₂×C₃×D₃	1	1	yes	characteristic
380	#444	—	3	4	no	—
381	#443	—	6	2	no	—
382	#442	—	3	2	no	—
383	#441	—	3	2	no	—
384	C₄×SD₁₆	—	6	2	no	—
385	C₂×#108	C₂×C₃×D₃	1	1	yes	characteristic
386	C₂×#106	C₂×C₃×D₃	1	1	yes	characteristic
387	#421	—	6	1	no	—
388	#417	—	6	1	no	—
389	#405	—	3	1	no	—
390	#365	C₂×C₃×D₃	1	4	yes	complemented
391	#362	—	3	2	no	—
392	#361	—	3	2	no	—
393	#360	—	3	4	no	—
394	#347	—	3	4	no	—
395	C₃×#41	—	6	2	no	—
396	C₃×#41	—	6	2	no	—
397	C₃×#41	—	6	2	no	—
398	C₃×#41	—	6	2	no	—
399	C₃×#41	—	12	1	no	—
400	C₃×#41	—	12	1	no	—
401	C₃×#41	—	12	1	no	—
402	C₃×#41	—	12	1	no	—
403	C₂×C₃×Q₈	—	6	1	no	—
404	C₂×C₃×Q₈	—	6	1	no	—
405	C₂×C₃×D₄	—	6	1	no	—
406	C₂×C₃×D₄	—	6	1	no	—
407	C₂×C₃×D₄	—	12	1	no	—
408	C₂×C₃×D₄	—	12	1	no	—
409	C₂²×C₃×C₄	—	2	1	no	—
410	C₂²×C₃×C₄	—	4	1	no	—
411	C₂²×C₃×C₄	—	4	1	no	—
412	C₂²×C₃×C₄	—	8	1	no	—
413	C₂²×C₃×C₄	—	12	2	no	—
414	C₂²×C₃×C₄	—	12	1	no	—
415	C₂²×C₃×C₄	—	12	1	no	—
416	C₂²×C₃×C₄	D₃×D₄	1	1	yes	characteristic
417	C₂²×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
418	C₂×#67	—	4	1	no	—
419	C₂×#67	—	4	1	no	—
420	#235	—	2	2	no	—
421	#235	—	2	2	no	—
422	#235	—	2	2	no	—
423	#235	—	2	2	no	—
424	#235	—	4	1	no	—
425	#235	—	4	1	no	—
426	#235	—	4	1	no	—
427	#235	—	4	1	no	—
428	C₂×D₁₂	—	2	1	no	—
429	C₂×D₁₂	—	2	1	no	—
430	C₂×C₄×D₃	—	4	1	no	—
431	C₂×C₄×D₃	—	4	1	no	—
432	C₂×C₄×D₃	—	4	2	no	—
433	C₂×Dic₆	—	2	1	no	—
434	C₂×Dic₆	—	2	1	no	—
435	C₃×Q₁₆	—	3	2	no	—
436	C₃×Q₁₆	—	3	2	no	—
437	C₃×Q₁₆	—	6	1	no	—
438	C₃×Q₁₆	—	6	1	no	—
439	C₃×SD₁₆	—	6	2	no	—
440	C₃×SD₁₆	—	6	2	no	—
441	C₃×SD₁₆	—	6	2	no	—
442	C₃×SD₁₆	—	6	2	no	—
443	C₃×D₈	—	3	2	no	—
444	C₃×D₈	—	3	2	no	—
445	C₃×D₈	—	6	1	no	—
446	C₃×D₈	—	6	1	no	—
447	C₃×M₁₆	—	2	2	no	—
448	C₃×M₁₆	—	2	2	no	—
449	C₃×M₁₆	—	4	2	no	—
450	C₃×M₁₆	—	4	1	no	—
451	C₃×M₁₆	—	4	1	no	—
452	C₃×M₁₆	—	6	1	no	—
453	C₃×M₁₆	—	6	1	no	—
454	C₃×M₁₆	—	8	1	no	—
455	C₃×M₁₆	—	12	4	no	—
456	C₂×C₃×C₈	—	2	1	no	—
457	C₂×C₃×C₈	—	2	1	no	—
458	C₂×C₃×C₈	—	2	1	no	—
459	C₂×C₃×C₈	—	2	1	no	—
460	C₂×C₃×C₈	—	2	1	no	—
461	C₂×C₃×C₈	—	2	1	no	—
462	C₂×C₃×C₈	—	3	2	no	—
463	C₂×C₃×C₈	—	4	1	no	—
464	C₂×C₃×C₈	—	4	1	no	—
465	C₂×C₃×C₈	—	8	1	no	—
466	C₂×C₃×C₈	—	12	4	no	—
467	C₂×C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
468	C₂×C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
469	C₂×C₃×C₈	D₃×D₄	1	1	yes	characteristic
470	C₂×C₃×C₈	#239	1	1	yes	characteristic
471	C₂×C₃×C₈	#239	1	1	yes	characteristic
472	C₂×C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
473	C₂×C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
474	C₂×C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
475	C₂×C₃×C₈	C₃×#41	1	1	yes	characteristic
476	C₂×C₃×C₈	C₃×#41	1	1	yes	characteristic
477	C₂×C₃×C₈	C₂³×D₃	1	1	yes	characteristic
478	C₂×C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
479	C₃×C₄⋊C₄	—	2	2	no	—
480	C₃×C₄⋊C₄	—	2	2	no	—
481	C₃×C₄⋊C₄	—	4	2	no	—
482	C₃×C₄⋊C₄	—	4	1	no	—
483	C₃×C₄⋊C₄	—	4	1	no	—
484	C₃×C₄⋊C₄	—	6	1	no	—
485	C₃×C₄⋊C₄	—	8	1	no	—
486	C₃×C₄⋊C₄	—	12	2	no	—
487	C₃×C₂²⋊C₄	—	6	1	no	—
488	C₃×C₂²⋊C₄	—	12	2	no	—
489	C₃×C₄²	—	3	2	no	—
490	C₃×C₄²	—	12	2	no	—
491	#217	—	2	1	no	—
492	(C₂×D₃)⋊C₄	—	4	2	no	—
493	C₄⋊Dic₃	—	2	1	no	—
494	Dic₃⋊C₄	—	4	2	no	—
495	C₄×Dic₃	—	4	2	no	—
496	C₄×Dic₃	C₂×C₃×D₄	1	2	yes	—
497	#208	—	2	1	no	—
498	#208	—	2	1	no	—
499	C₂×C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
500	Dic₁₂	—	2	1	no	—
501	Dic₁₂	—	2	1	no	—
502	Dic₁₂	C₂²×C₃×C₄	1	2	yes	—
503	Dic₁₂	C₂²×C₃×C₄	1	2	yes	—
504	D₂₄	—	2	1	no	—
505	D₂₄	—	2	1	no	—
506	D₂₄	C₂²×C₃×C₄	1	2	yes	—
507	D₂₄	C₂²×C₃×C₄	1	2	yes	—
508	#204	—	2	2	no	—
509	#204	—	2	2	no	—
510	#204	—	2	2	no	—
511	#204	—	2	2	no	—
512	ΓL(1,𝔽₂₅)	—	4	4	no	—
513	D₃×C₈	—	4	4	no	—
514	C₃×C₁₆	—	2	4	no	—
515	C₃×C₁₆	—	6	2	no	—
516	C₃×C₁₆	C₂×C₄×D₃	1	4	yes	—
517	C₃×C₁₆	C₂²×C₃×C₄	1	4	yes	—
518	C₃⋊C₁₆	—	2	2	no	—
519	C₂²×C₃²	—	4	1	no	—
520	C₂²×C₃²	#442	1	1	yes	characteristic
521	C₂²×C₃²	#442	1	1	yes	characteristic
522	C₂²×C₃²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
523	C₂×C₃×D₃	—	4	2	no	—
524	C₂×C₃×D₃	—	4	2	no	—
525	C₂×C₃×D₃	—	8	1	no	—
526	C₂×C₃×D₃	—	8	1	no	—
527	C₂×C₃×D₃	—	16	1	no	—
528	C₃²×C₄	—	8	2	no	—
529	C₃²×C₄	#442	1	1	yes	characteristic
530	C₃²×C₄	#442	1	1	yes	characteristic
531	C₃²×C₄	C₂×C₄×D₄	1	1	yes	characteristic
532	C₃²×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
533	C₃×Dic₃	—	4	2	no	—
534	C₃×Dic₃	—	4	2	no	—
535	C₃×Dic₃	—	4	2	no	—
536	C₂×#41	—	6	1	no	—
537	C₂×#41	—	6	1	no	—
538	#135	—	3	2	no	—
539	#135	—	3	2	no	—
540	#135	—	3	2	no	—
541	#135	—	3	2	no	—
542	#135	—	6	1	no	—
543	#135	—	6	1	no	—
544	#135	—	6	1	no	—
545	#135	—	6	1	no	—
546	C₂×Q₁₆	—	3	1	no	—
547	C₂×Q₁₆	—	3	1	no	—
548	C₂×SD₁₆	—	6	1	no	—
549	C₂×SD₁₆	—	6	1	no	—
550	C₂×D₈	—	3	1	no	—
551	C₂×D₈	—	3	1	no	—
552	#131	—	6	4	no	—
553	#131	—	12	2	no	—
554	C₂×M₁₆	—	2	1	no	—
555	C₂×M₁₆	—	3	1	no	—
556	C₂×M₁₆	—	12	2	no	—
557	C₂²×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
558	C₄×Q₈	—	6	2	no	—
559	C₄×D₄	—	6	2	no	—
560	C₄×D₄	—	12	2	no	—
561	#117	—	3	1	no	—
562	#117	—	12	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	12	1	no	—
565	Q₃₂	—	3	4	no	—
566	SD₃₂	—	3	4	no	—
567	SD₃₂	—	3	4	no	—
568	D₁₆	—	3	4	no	—
569	M₃₂	—	3	2	no	—
570	M₃₂	—	6	1	no	—
571	M₃₂	C₃×C₄×D₃	1	2	yes	complemented
572	M₃₂	C₂²×C₃×D₃	1	2	yes	—
573	C₂×C₁₆	—	6	1	no	—
574	C₂×C₁₆	C₃×C₄×D₃	1	2	yes	complemented
575	#108	—	2	1	no	—
576	#108	C₂²×C₃×D₃	1	2	yes	—
577	#106	—	2	1	no	—
578	#106	C₂²×C₃×D₃	1	2	yes	—
579	#104	—	6	4	no	—
580	#103	—	6	2	no	—
581	#102	—	6	2	no	—
582	#97	—	3	2	no	—
583	C₄×C₈	—	3	2	no	—
584	C₂³×C₃	—	2	1	no	—
585	C₂³×C₃	—	12	1	no	—
586	C₂³×C₃	—	12	1	no	—
587	C₂³×C₃	#914	1	1	yes	characteristic
588	C₂³×C₃	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
589	C₂²×D₃	—	4	1	no	—
590	C₂²×D₃	—	4	1	no	—
591	C₃×Q₈	—	6	2	no	—
592	C₃×Q₈	—	6	2	no	—
593	C₃×Q₈	—	12	1	no	—
594	C₃×Q₈	—	12	1	no	—
595	C₃×D₄	—	6	2	no	—
596	C₃×D₄	—	6	2	no	—
597	C₃×D₄	—	12	2	no	—
598	C₃×D₄	—	12	2	no	—
599	C₃×D₄	—	12	2	no	—
600	C₃×D₄	—	12	2	no	—
601	C₃×D₄	—	12	1	no	—
602	C₃×D₄	—	12	1	no	—
603	C₂×C₃×C₄	—	2	1	no	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	4	2	no	—
610	C₂×C₃×C₄	—	4	2	no	—
611	C₂×C₃×C₄	—	6	2	no	—
612	C₂×C₃×C₄	—	8	2	no	—
613	C₂×C₃×C₄	—	12	1	no	—
614	C₂×C₃×C₄	—	12	1	no	—
615	C₂×C₃×C₄	—	12	2	no	—
616	C₂×C₃×C₄	—	12	2	no	—
617	C₂×C₃×C₄	—	12	2	no	—
618	C₂×C₃×C₄	—	12	2	no	—
619	C₂×C₃×C₄	—	16	1	no	—
620	C₂×C₃×C₄	—	16	1	no	—
621	C₂×C₃×C₄	—	16	2	no	—
622	C₂×C₃×C₄	—	48	2	no	—
623	C₂×C₃×C₄	#893	1	1	yes	characteristic
624	C₂×C₃×C₄	#893	1	1	yes	characteristic
625	C₂×C₃×C₄	#914	1	1	yes	characteristic
626	C₂×C₃×C₄	#914	1	1	yes	characteristic
627	C₂×C₃×C₄	#914	1	1	yes	characteristic
628	C₂×C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
629	C₂×C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
630	C₂×C₃×C₄	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
631	C₂×C₃×C₄	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
632	C₂×C₃×C₄	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
633	C₂×C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
634	C₂×C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
635	#67	—	4	2	no	—
636	#67	—	4	2	no	—
637	#67	—	4	2	no	—
638	#67	—	4	2	no	—
639	C₂×Dic₃	—	2	2	no	—
640	C₂×Dic₃	—	4	1	no	—
641	C₂×Dic₃	—	4	1	no	—
642	D₁₂	—	2	2	no	—
643	D₁₂	—	2	2	no	—
644	D₁₂	—	4	1	no	—
645	D₁₂	—	4	1	no	—
646	C₄×D₃	—	4	2	no	—
647	C₄×D₃	—	4	2	no	—
648	C₄×D₃	—	4	2	no	—
649	C₄×D₃	—	4	2	no	—
650	C₄×D₃	—	16	2	no	—
651	Dic₆	—	2	2	no	—
652	Dic₆	—	2	2	no	—
653	Dic₆	—	4	1	no	—
654	Dic₆	—	4	1	no	—
655	C₃×C₈	—	2	1	no	—
656	C₃×C₈	—	2	1	no	—
657	C₃×C₈	—	2	1	no	—
658	C₃×C₈	—	2	1	no	—
659	C₃×C₈	—	4	2	no	—
660	C₃×C₈	—	4	2	no	—
661	C₃×C₈	—	6	2	no	—
662	C₃×C₈	—	8	2	no	—
663	C₃×C₈	#893	1	1	yes	characteristic
664	C₃×C₈	#893	1	1	yes	characteristic
665	C₃×C₈	C₃×C₄×D₄	1	1	yes	characteristic
666	C₃×C₈	C₃×C₄×D₄	1	1	yes	characteristic
667	C₃×C₈	C₂²×C₄×D₃	1	1	yes	characteristic
668	C₃×C₈	C₂×#239	1	1	yes	characteristic
669	C₃×C₈	C₂³×C₃×C₄	1	1	yes	characteristic
670	C₃×C₈	C₂×C₃×#41	1	1	yes	characteristic
671	C₃⋊C₈	—	2	2	no	—
672	C₂×C₃²	—	2	1	no	—
673	C₂×C₃²	—	2	1	no	—
674	C₂×C₃²	—	2	1	no	—
675	C₂×C₃²	C₂×#442	1	1	yes	characteristic
676	C₃×D₃	—	8	2	no	—
677	C₃×D₃	—	8	2	no	—
678	#41	—	6	2	no	—
679	#41	—	6	2	no	—
680	#41	—	6	2	no	—
681	#41	—	6	2	no	—
682	#41	—	12	1	no	—
683	#41	—	12	1	no	—
684	#41	—	12	1	no	—
685	#41	—	12	1	no	—
686	C₂×Q₈	—	6	1	no	—
687	C₂×Q₈	—	6	1	no	—
688	C₂×D₄	—	6	1	no	—
689	C₂×D₄	—	6	1	no	—
690	C₂×D₄	—	12	1	no	—
691	C₂×D₄	—	12	1	no	—
692	C₂²×C₄	—	4	1	no	—
693	C₂²×C₄	—	12	2	no	—
694	C₂²×C₄	—	12	1	no	—
695	C₂²×C₄	—	12	1	no	—
696	C₂²×C₄	C₃×D₃×D₄	1	1	yes	characteristic
697	Q₁₆	—	3	2	no	—
698	Q₁₆	—	3	2	no	—
699	Q₁₆	—	6	1	no	—
700	Q₁₆	—	6	1	no	—
701	SD₁₆	—	6	2	no	—
702	SD₁₆	—	6	2	no	—
703	SD₁₆	—	6	2	no	—
704	SD₁₆	—	6	2	no	—
705	D₈	—	3	2	no	—
706	D₈	—	3	2	no	—
707	D₈	—	6	1	no	—
708	D₈	—	6	1	no	—
709	M₁₆	—	2	2	no	—
710	M₁₆	—	4	1	no	—
711	M₁₆	—	6	1	no	—
712	M₁₆	—	6	1	no	—
713	M₁₆	—	12	4	no	—
714	C₂×C₈	—	3	2	no	—
715	C₂×C₈	—	4	1	no	—
716	C₂×C₈	—	12	4	no	—
717	C₂×C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
718	C₂×C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
719	C₂×C₈	C₃×D₃×D₄	1	1	yes	characteristic
720	C₂×C₈	C₃×#239	1	1	yes	characteristic
721	C₂×C₈	C₃×#239	1	1	yes	characteristic
722	C₂×C₈	C₂³×C₃×D₃	1	1	yes	characteristic
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	4	1	no	—
725	C₄⋊C₄	—	6	1	no	—
726	C₄⋊C₄	—	12	2	no	—
727	C₂²⋊C₄	—	6	1	no	—
728	C₂²⋊C₄	—	12	2	no	—
729	C₄²	—	3	2	no	—
730	C₄²	—	12	2	no	—
731	C₁₆	—	6	2	no	—
732	C₁₆	C₂×C₃×C₄×D₃	1	4	yes	—
733	C₂²×C₃	—	2	1	no	—
734	C₂²×C₃	—	2	1	no	—
735	C₂²×C₃	—	2	1	no	—
736	C₂²×C₃	—	4	1	no	—
737	C₂²×C₃	—	4	1	no	—
738	C₂²×C₃	—	4	2	no	—
739	C₂²×C₃	—	12	2	no	—
740	C₂²×C₃	—	12	2	no	—
741	C₂²×C₃	—	24	1	no	—
742	C₂²×C₃	—	24	1	no	—
743	C₂²×C₃	—	48	1	no	—
744	C₂²×C₃	#4869	1	1	yes	characteristic
745	C₂²×C₃	#4869	1	1	yes	characteristic
746	C₂²×C₃	C₃×#442	1	1	yes	characteristic
747	C₂²×C₃	C₃×#442	1	1	yes	characteristic
748	C₂²×C₃	C₂×#914	1	1	yes	characteristic
749	C₂²×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
750	C₂×D₃	—	4	2	no	—
751	C₂×D₃	—	4	2	no	—
752	C₂×D₃	—	8	1	no	—
753	C₂×D₃	—	8	1	no	—
754	C₂×D₃	—	16	1	no	—
755	C₃×C₄	—	2	1	no	—
756	C₃×C₄	—	2	1	no	—
757	C₃×C₄	—	2	1	no	—
758	C₃×C₄	—	2	1	no	—
759	C₃×C₄	—	8	2	no	—
760	C₃×C₄	—	8	2	no	—
761	C₃×C₄	—	12	2	no	—
762	C₃×C₄	—	12	2	no	—
763	C₃×C₄	—	12	2	no	—
764	C₃×C₄	—	16	2	no	—
765	C₃×C₄	#4869	1	1	yes	characteristic
766	C₃×C₄	#4869	1	1	yes	characteristic
767	C₃×C₄	C₃×#442	1	1	yes	characteristic
768	C₃×C₄	C₃×#442	1	1	yes	characteristic
769	C₃×C₄	C₂×#893	1	1	yes	characteristic
770	C₃×C₄	C₂×#914	1	1	yes	characteristic
771	C₃×C₄	C₂×C₃×C₄×D₄	1	1	yes	characteristic
772	C₃×C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
773	Dic₃	—	4	2	no	—
774	Dic₃	—	4	2	no	—
775	Dic₃	—	4	2	no	—
776	C₃²	#33469	1	1	yes	characteristic, complemented, Sylow
777	C₂³	—	12	1	no	—
778	C₂³	—	12	1	no	—
779	C₂³	C₃×#914	1	1	yes	characteristic
780	Q₈	—	6	2	no	—
781	Q₈	—	6	2	no	—
782	Q₈	—	12	1	no	—
783	Q₈	—	12	1	no	—
784	D₄	—	6	2	no	—
785	D₄	—	6	2	no	—
786	D₄	—	12	2	no	—
787	D₄	—	12	2	no	—
788	D₄	—	12	2	no	—
789	D₄	—	12	2	no	—
790	D₄	—	12	1	no	—
791	D₄	—	12	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	6	2	no	—
794	C₂×C₄	—	12	1	no	—
795	C₂×C₄	—	12	1	no	—
796	C₂×C₄	—	12	2	no	—
797	C₂×C₄	—	12	2	no	—
798	C₂×C₄	—	12	2	no	—
799	C₂×C₄	—	12	2	no	—
800	C₂×C₄	—	16	1	no	—
801	C₂×C₄	—	48	2	no	—
802	C₂×C₄	C₃×#893	1	1	yes	characteristic
803	C₂×C₄	C₃×#893	1	1	yes	characteristic
804	C₂×C₄	C₃×#914	1	1	yes	characteristic
805	C₂×C₄	C₃×#914	1	1	yes	characteristic
806	C₂×C₄	C₃×#914	1	1	yes	characteristic
807	C₂×C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
808	C₈	—	4	2	no	—
809	C₈	—	6	2	no	—
810	C₈	C₃×#893	1	1	yes	characteristic
811	C₈	C₃×#893	1	1	yes	characteristic
812	C₈	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
813	C₈	C₂×C₃×#239	1	1	yes	characteristic
814	C₂×C₃	—	2	2	no	—
815	C₂×C₃	—	2	1	no	—
816	C₂×C₃	—	2	1	no	—
817	C₂×C₃	—	2	1	no	—
818	C₂×C₃	—	2	1	no	—
819	C₂×C₃	—	2	1	no	—
820	C₂×C₃	—	2	1	no	—
821	C₂×C₃	—	2	1	no	—
822	C₂×C₃	—	4	1	no	—
823	C₂×C₃	—	4	1	no	—
824	C₂×C₃	—	24	2	no	—
825	C₂×C₃	—	24	2	no	—
826	C₂×C₃	C₂×#4869	1	1	yes	characteristic
827	C₂×C₃	C₂×C₃×#442	1	1	yes	characteristic
828	D₃	—	8	2	no	—
829	D₃	—	8	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	12	2	no	—
832	C₂²	—	12	2	no	—
833	C₂²	—	24	1	no	—
834	C₂²	—	24	1	no	—
835	C₂²	—	48	1	no	—
836	C₂²	C₃×#4869	1	1	yes	characteristic
837	C₂²	C₃×#4869	1	1	yes	characteristic
838	C₂²	C₂×C₃×#914	1	1	yes	characteristic
839	C₄	—	8	2	no	—
840	C₄	—	12	2	no	—
841	C₄	—	12	2	no	—
842	C₄	—	12	2	no	—
843	C₄	C₃×#4869	1	1	yes	characteristic
844	C₄	C₃×#4869	1	1	yes	characteristic
845	C₄	C₂×C₃×#893	1	1	yes	characteristic
846	C₄	C₂×C₃×#914	1	1	yes	characteristic
847	C₃	—	2	1	no	—
848	C₃	C₃×#33469	1	1	yes	characteristic, complemented
849	C₃	#10948645	1	1	yes	characteristic, direct product factor
850	C₂	—	2	1	no	—
851	C₂	—	2	1	no	—
852	C₂	—	2	1	no	—
853	C₂	—	24	2	no	—
854	C₂	—	24	2	no	—
855	C₂	C₂×C₃×#4869	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×#4869
commutator	C₃×C₈	C₂³×C₃×C₄
Frattini	C₂×C₈	C₂³×C₃×D₃
Fitting	C₂×C₃²×#365	C₂
socle	C₂×C₃²	C₂×#442
prime radical	C₃×#82009	C₂
cosocle	C₂×C₃×C₈	C₂⁴×C₃
hypercenter	C₂×C₃×#365	D₃
hypocenter	C₃	C₃×#33469
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×#365

Complements

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

N	H ≅ G/N	type
2. C₃×#79249	C₂	semidirect
3. C₃×#79106	C₂	semidirect
4. C₃×#69310	C₂	semidirect
5. C₃×#69309	C₂	semidirect
6. C₃×#70687	C₂	semidirect
7. C₂×C₃×#4488	C₂	semidirect
8. C₃×#71425	C₂	semidirect
9. C₂×C₃²×#365	C₂	semidirect
10. #10948645	C₃	direct (N × H)
23. C₃×#4909	C₄	semidirect
25. C₃×#4908	C₄	semidirect
27. C₃×#4904	C₄	semidirect
30. C₃×#4869	C₂²	semidirect
31. C₃×#4853	C₂²	semidirect
33. C₃²×#365	C₂²	semidirect
34. C₃×#4512	C₂²	semidirect
35. C₃×#4496	C₂²	semidirect
36. C₃×#4495	C₂²	semidirect
42. #79249	C₂×C₃	semidirect
43. #79106	C₂×C₃	semidirect
47. C₂×C₃×#365	D₃	semidirect
48. C₂×C₃×#365	C₂×C₃	semidirect
52. #71425	C₂×C₃	semidirect
53. #70687	C₂×C₃	semidirect
54. C₂×#4488	C₂×C₃	semidirect
55. #69310	C₂×C₃	semidirect
56. #69309	C₂×C₃	semidirect
67. C₂×C₃×Dic₁₂	C₂×C₄	semidirect
75. C₃×#904	C₂×C₄	semidirect
77. C₂×C₃×D₂₄	C₂×C₄	semidirect
86. C₃²×M₃₂	C₂×C₄	semidirect
88. C₂×C₃²×C₁₆	C₂×C₄	semidirect
101. C₃×Dic₂₄	C₂×C₄	semidirect
102. C₃×#800	C₂×C₄	semidirect
103. C₃×#800	C₂×C₄	semidirect
104. C₃×D₄₈	C₂×C₄	semidirect
141. #4909	C₃×C₄	semidirect
143. #4908	C₃×C₄	semidirect
145. #4904	C₃×C₄	semidirect
148. #4869	C₂²×C₃	semidirect
149. #4853	C₂²×C₃	semidirect
152. C₃×#365	C₂×D₃	semidirect
153. C₃×#365	C₂²×C₃	semidirect
158. #4512	C₂²×C₃	semidirect
159. #4496	C₂²×C₃	semidirect
160. #4495	C₂²×C₃	semidirect
222. C₂×#365	C₃×D₃	semidirect
268. C₂×Dic₁₂	C₂×C₃×C₄	semidirect
276. #904	C₂×C₃×C₄	semidirect
278. C₂×D₂₄	C₂×C₃×C₄	semidirect
295. C₃×M₃₂	C₄×D₃	semidirect
296. C₃×M₃₂	C₂×C₃×C₄	semidirect
301. C₂×C₃×C₁₆	C₄×D₃	semidirect
302. C₂×C₃×C₁₆	C₂×C₃×C₄	semidirect
328. Dic₂₄	C₂×C₃×C₄	semidirect
329. #800	C₂×C₃×C₄	semidirect
330. #800	C₂×C₃×C₄	semidirect
331. D₄₈	C₂×C₃×C₄	semidirect
390. #365	C₂×C₃×D₃	semidirect
571. M₃₂	C₃×C₄×D₃	semidirect
574. C₂×C₁₆	C₃×C₄×D₃	semidirect
776. C₃²	#33469	semidirect
848. C₃	C₃×#33469	semidirect
849. C₃	#10948645	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×#82009	2
C₃×#79249	2
C₃×#79106	2
C₃×#69310	2
C₃×#69309	2
C₃×#70687	2
C₂×C₃×#4488	2
C₃×#71425	2
C₂×C₃²×#365	2
#10948645	3
C₃×#33469	3

Subgroups — C3×#10948645 #72222778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10948645 #72222778