Subgroups — C₃×#61803 #10680410

Order 768.

1732 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3506	C₂	1	1	yes	maximal, characteristic
3	C₃×#3353	C₂	1	2	yes	maximal, complemented
4	C₃×#3350	C₂	1	4	yes	maximal, complemented
5	C₃×#3340	C₂	1	2	yes	maximal, complemented
6	C₃×#3329	C₂	1	2	yes	maximal, complemented
7	C₃×#3320	C₂	1	4	yes	maximal, complemented
8	C₃×#3298	C₂	1	2	yes	maximal, complemented
9	C₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3200	C₂	1	4	yes	maximal, complemented
12	C₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3097	C₂	1	4	yes	maximal, complemented
15	C₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	#61803	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#563	—	2	2	no	—
18	C₃×#559	—	2	1	no	—
19	C₃×#559	—	2	2	no	—
20	C₃×Q₈²	—	2	1	no	—
21	C₃×#556	—	2	1	no	—
22	C₃×#556	C₂²	1	2	yes	complemented
23	C₃×#556	C₂²	1	2	yes	complemented
24	C₃×#555	C₂²	1	2	yes	—
25	C₃×#553	C₂²	1	4	yes	—
26	C₃×#550	—	2	1	no	—
27	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
28	C₃×D₄×Q₈	C₂²	1	2	yes	complemented
29	C₃×#547	C₂²	1	2	yes	—
30	C₃×#542	—	2	2	no	—
31	C₃×#542	—	2	2	no	—
32	C₃×#538	—	2	2	no	—
33	C₃×#536	C₂²	1	4	yes	—
34	C₃×#535	C₂²	1	2	yes	—
35	C₃×#533	C₂²	1	1	yes	characteristic
36	C₃×#533	C₂²	1	1	yes	characteristic
37	C₃×#533	C₂²	1	1	yes	characteristic
38	C₃×#532	C₂²	1	1	yes	characteristic
39	C₃×#525	—	2	2	no	—
40	C₃×#520	C₂²	1	2	yes	—
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₃×#501	C₂²	1	2	yes	complemented
43	C₃×#500	C₂²	1	1	yes	characteristic, complemented
44	C₃×#498	C₂²	1	1	yes	characteristic, complemented
45	C₃×#491	C₂²	1	2	yes	complemented
46	C₃×#487	C₂²	1	1	yes	characteristic, complemented
47	C₃×#487	C₂²	1	1	yes	characteristic, complemented
48	C₃×#485	C₂²	1	4	yes	—
49	C₃×#485	C₂²	1	4	yes	—
50	C₃×#485	C₂²	1	4	yes	complemented
51	C₃×#485	C₂²	1	4	yes	complemented
52	C₃×#484	C₂²	1	2	yes	—
53	C₃×#484	C₂²	1	4	yes	complemented
54	C₃×#483	C₂²	1	2	yes	—
55	C₃×#483	C₂²	1	4	yes	complemented
56	C₃×#482	C₂²	1	4	yes	—
57	C₃×#482	C₂²	1	4	yes	—
58	C₃×#479	C₂²	1	4	yes	complemented
59	C₃×#477	C₂²	1	2	yes	complemented
60	C₃×#476	C₂²	1	2	yes	—
61	C₃×#475	C₂²	1	2	yes	complemented
62	C₃×#474	C₂²	1	2	yes	—
63	C₃×#468	C₂²	1	4	yes	—
64	C₃×#468	C₂²	1	4	yes	—
65	C₃×#465	C₂²	1	4	yes	—
66	C₃×#465	C₂²	1	4	yes	—
67	C₃×#461	C₂²	1	2	yes	—
68	C₃×#461	C₂²	1	2	yes	—
69	C₃×#450	C₂²	1	2	yes	—
70	C₃×#450	C₂²	1	2	yes	—
71	C₃×#448	C₂²	1	4	yes	—
72	C₃×#448	C₂²	1	4	yes	—
73	C₃×#440	C₂²	1	4	yes	—
74	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
75	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
76	C₃×#436	C₂²	1	2	yes	complemented
77	C₃×#435	C₂²	1	4	yes	complemented
78	C₃×C₈×D₄	C₂²	1	2	yes	complemented
79	C₃×#432	C₂²	1	1	yes	characteristic
80	C₃×#431	C₂²	1	1	yes	characteristic
81	C₃×#428	C₂²	1	4	yes	complemented
82	C₃×#427	C₂²	1	4	yes	complemented
83	C₃×#419	C₂²	1	4	yes	complemented
84	C₂×C₃×#103	C₂²	1	4	yes	complemented
85	C₃×#408	C₂²	1	4	yes	—
86	#3550	C₂×C₃	1	1	yes	characteristic, complemented
87	#3506	C₂×C₃	1	1	yes	characteristic
88	#3353	C₂×C₃	1	2	yes	complemented
89	#3350	C₂×C₃	1	4	yes	complemented
90	#3340	C₂×C₃	1	2	yes	complemented
91	#3329	C₂×C₃	1	2	yes	complemented
92	#3320	C₂×C₃	1	4	yes	complemented
93	#3298	C₂×C₃	1	2	yes	complemented
94	#3237	C₂×C₃	1	1	yes	characteristic, complemented
95	#3231	C₂×C₃	1	1	yes	characteristic, complemented
96	#3200	C₂×C₃	1	4	yes	complemented
97	#3110	C₂×C₃	1	1	yes	characteristic, complemented
98	#3101	C₂×C₃	1	1	yes	characteristic, complemented
99	#3097	C₂×C₃	1	4	yes	complemented
100	#2981	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₃×#41	—	2	2	no	—
102	C₂×C₃×#41	C₂³	1	2	yes	—
103	C₂²×C₃×Q₈	C₂³	1	4	yes	—
104	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
108	C₂×C₃×SD₁₆	C₂³	1	4	yes	—
109	C₂×C₃×M₁₆	C₂³	1	4	yes	—
110	C₂²×C₃×C₈	C₂³	1	4	yes	—
111	C₃×C₄⋊Q₈	—	2	4	no	—
112	C₃×C₄⋊Q₈	—	2	2	no	—
113	C₃×C₄⋊Q₈	—	2	2	no	—
114	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
115	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₃×#127	—	2	2	no	—
122	C₃×#127	D₄	1	1	yes	characteristic
123	C₃×#126	—	2	4	no	—
124	C₃×#126	—	2	4	no	—
125	C₃×#126	—	2	4	no	—
126	C₃×#125	—	2	1	no	—
127	C₃×#125	—	2	1	no	—
128	C₃×#125	C₂³	1	2	yes	—
129	C₃×#124	—	2	2	no	—
130	C₃×#124	—	2	2	no	—
131	C₃×#124	—	2	2	no	—
132	C₃×#124	—	2	4	no	—
133	C₃×#124	—	2	4	no	—
134	C₃×#124	D₄	1	2	yes	—
135	C₃×#123	—	2	4	no	—
136	C₃×#123	—	2	4	no	—
137	C₃×#123	—	2	4	no	—
138	C₃×#123	—	2	4	no	—
139	C₃×C₂²⋊Q₈	—	2	1	no	—
140	C₃×C₂²⋊Q₈	—	2	1	no	—
141	C₃×C₂²⋊Q₈	—	2	1	no	—
142	C₃×C₂²⋊Q₈	—	2	1	no	—
143	C₃×C₂²⋊Q₈	—	2	2	no	—
144	C₃×C₂²⋊Q₈	—	2	4	no	—
145	C₃×C₂²⋊Q₈	—	2	4	no	—
146	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₃×#121	—	2	2	no	—
151	C₃×#121	—	2	4	no	—
152	C₃×#121	D₄	1	2	yes	—
153	C₃×#121	D₄	1	2	yes	—
154	C₃×#121	C₂³	1	4	yes	—
155	C₃×#121	C₂³	1	4	yes	—
156	C₃×#120	—	2	4	no	—
157	C₃×C₄×Q₈	—	2	2	no	—
158	C₃×C₄×Q₈	—	2	2	no	—
159	C₃×C₄×Q₈	—	2	2	no	—
160	C₃×C₄×Q₈	—	2	1	no	—
161	C₃×C₄×Q₈	—	2	1	no	—
162	C₃×C₄×Q₈	—	2	1	no	—
163	C₃×C₄×Q₈	—	2	1	no	—
164	C₃×C₄×Q₈	C₂³	1	2	yes	—
165	C₃×C₄×Q₈	C₂³	1	2	yes	—
166	C₃×C₄×D₄	—	2	2	no	—
167	C₃×C₄×D₄	—	2	2	no	—
168	C₃×C₄×D₄	—	2	2	no	—
169	C₃×C₄×D₄	—	2	4	no	—
170	C₃×C₄×D₄	—	2	4	no	—
171	C₃×C₄×D₄	—	2	1	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	C₂³	1	2	yes	—
174	C₃×C₄×D₄	C₂³	1	2	yes	—
175	C₃×C₄×D₄	C₂³	1	2	yes	—
176	C₃×C₄×D₄	C₂³	1	2	yes	—
177	C₃×#117	—	2	1	no	—
178	C₃×#117	—	2	1	no	—
179	C₃×#117	—	2	2	no	—
180	C₃×#117	C₂³	1	4	yes	—
181	C₃×#117	C₂³	1	4	yes	—
182	C₃×#117	C₂³	1	2	yes	—
183	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
187	C₃×#107	C₂³	1	4	yes	—
188	C₃×#107	C₂³	1	4	yes	—
189	C₃×#107	C₂³	1	4	yes	—
190	C₃×#106	C₂³	1	2	yes	—
191	C₃×#106	C₂³	1	4	yes	—
192	C₃×#106	C₂³	1	2	yes	—
193	C₃×#106	C₂³	1	4	yes	—
194	C₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₃×C₄⋊C₈	C₂³	1	2	yes	—
196	C₃×#103	C₂³	1	2	yes	—
197	C₃×#103	C₂³	1	4	yes	—
198	C₃×#103	C₂³	1	4	yes	—
199	C₃×#103	C₂³	1	4	yes	—
200	C₃×#103	C₂³	1	2	yes	—
201	C₃×#103	C₂³	1	4	yes	—
202	C₃×#103	C₂³	1	4	yes	—
203	C₃×#102	C₂³	1	2	yes	—
204	C₃×#102	C₂³	1	2	yes	—
205	C₃×#102	C₂³	1	4	yes	—
206	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
207	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
208	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
210	C₃×#97	C₂³	1	2	yes	—
211	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
212	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
213	#563	—	2	2	no	—
214	#559	—	2	1	no	—
215	#559	—	2	2	no	—
216	Q₈²	—	2	1	no	—
217	#556	—	2	1	no	—
218	#556	C₂²×C₃	1	2	yes	complemented
219	#556	C₂²×C₃	1	2	yes	complemented
220	#555	C₂²×C₃	1	2	yes	—
221	#553	C₂²×C₃	1	4	yes	—
222	#550	—	2	1	no	—
223	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
224	D₄×Q₈	C₂²×C₃	1	2	yes	complemented
225	#547	C₂²×C₃	1	2	yes	—
226	#542	—	2	2	no	—
227	#542	—	2	2	no	—
228	#538	—	2	2	no	—
229	#536	C₂²×C₃	1	4	yes	—
230	#535	C₂²×C₃	1	2	yes	—
231	#533	C₂²×C₃	1	1	yes	characteristic
232	#533	C₂²×C₃	1	1	yes	characteristic
233	#533	C₂²×C₃	1	1	yes	characteristic
234	#532	C₂²×C₃	1	1	yes	characteristic
235	#525	—	2	2	no	—
236	#520	C₂²×C₃	1	2	yes	—
237	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
238	#501	C₂²×C₃	1	2	yes	complemented
239	#500	C₂²×C₃	1	1	yes	characteristic, complemented
240	#498	C₂²×C₃	1	1	yes	characteristic, complemented
241	#491	C₂²×C₃	1	2	yes	complemented
242	#487	C₂²×C₃	1	1	yes	characteristic, complemented
243	#487	C₂²×C₃	1	1	yes	characteristic, complemented
244	#485	C₂²×C₃	1	4	yes	—
245	#485	C₂²×C₃	1	4	yes	—
246	#485	C₂²×C₃	1	4	yes	complemented
247	#485	C₂²×C₃	1	4	yes	complemented
248	#484	C₂²×C₃	1	2	yes	—
249	#484	C₂²×C₃	1	4	yes	complemented
250	#483	C₂²×C₃	1	2	yes	—
251	#483	C₂²×C₃	1	4	yes	complemented
252	#482	C₂²×C₃	1	4	yes	—
253	#482	C₂²×C₃	1	4	yes	—
254	#479	C₂²×C₃	1	4	yes	complemented
255	#477	C₂²×C₃	1	2	yes	complemented
256	#476	C₂²×C₃	1	2	yes	—
257	#475	C₂²×C₃	1	2	yes	complemented
258	#474	C₂²×C₃	1	2	yes	—
259	#468	C₂²×C₃	1	4	yes	—
260	#468	C₂²×C₃	1	4	yes	—
261	#465	C₂²×C₃	1	4	yes	—
262	#465	C₂²×C₃	1	4	yes	—
263	#461	C₂²×C₃	1	2	yes	—
264	#461	C₂²×C₃	1	2	yes	—
265	#450	C₂²×C₃	1	2	yes	—
266	#450	C₂²×C₃	1	2	yes	—
267	#448	C₂²×C₃	1	4	yes	—
268	#448	C₂²×C₃	1	4	yes	—
269	#440	C₂²×C₃	1	4	yes	—
270	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
271	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
272	#436	C₂²×C₃	1	2	yes	complemented
273	#435	C₂²×C₃	1	4	yes	complemented
274	C₈×D₄	C₂²×C₃	1	2	yes	complemented
275	#432	C₂²×C₃	1	1	yes	characteristic
276	#431	C₂²×C₃	1	1	yes	characteristic
277	#428	C₂²×C₃	1	4	yes	complemented
278	#427	C₂²×C₃	1	4	yes	complemented
279	#419	C₂²×C₃	1	4	yes	complemented
280	C₂×#103	C₂²×C₃	1	4	yes	complemented
281	#408	C₂²×C₃	1	4	yes	—
282	C₂⁴×C₃	—	2	1	no	—
283	C₃×#41	—	4	4	no	—
284	C₃×#41	—	8	4	no	—
285	C₂×C₃×Q₈	—	2	1	no	—
286	C₂×C₃×Q₈	—	2	1	no	—
287	C₂×C₃×Q₈	—	2	1	no	—
288	C₂×C₃×Q₈	—	2	1	no	—
289	C₂×C₃×Q₈	—	2	4	no	—
290	C₂×C₃×Q₈	—	4	4	no	—
291	C₂×C₃×Q₈	—	4	4	no	—
292	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
293	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
294	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	4	no	—
297	C₂×C₃×D₄	—	2	1	no	—
298	C₂×C₃×D₄	—	4	2	no	—
299	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
300	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
301	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
302	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
303	C₂×C₃×D₄	C₂⁴	1	2	yes	—
304	C₂²×C₃×C₄	—	2	1	no	—
305	C₂²×C₃×C₄	—	2	4	no	—
306	C₂²×C₃×C₄	—	2	4	no	—
307	C₂²×C₃×C₄	—	2	2	no	—
308	C₂²×C₃×C₄	—	2	2	no	—
309	C₂²×C₃×C₄	—	8	2	no	—
310	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
314	C₃×SD₁₆	—	4	2	no	—
315	C₃×SD₁₆	—	4	4	no	—
316	C₃×SD₁₆	—	4	2	no	—
317	C₃×M₁₆	—	4	4	no	—
318	C₂×C₃×C₈	—	4	4	no	—
319	C₂×C₃×C₈	C₂⁴	1	2	yes	—
320	C₂×C₃×C₈	C₂⁴	1	2	yes	—
321	C₂×C₃×C₈	C₂⁴	1	4	yes	—
322	C₃×C₄⋊C₄	—	2	1	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	1	no	—
325	C₃×C₄⋊C₄	—	2	1	no	—
326	C₃×C₄⋊C₄	—	2	1	no	—
327	C₃×C₄⋊C₄	—	2	1	no	—
328	C₃×C₄⋊C₄	—	2	1	no	—
329	C₃×C₄⋊C₄	—	2	2	no	—
330	C₃×C₄⋊C₄	—	2	1	no	—
331	C₃×C₄⋊C₄	—	2	1	no	—
332	C₃×C₄⋊C₄	—	2	2	no	—
333	C₃×C₄⋊C₄	—	2	4	no	—
334	C₃×C₄⋊C₄	—	2	4	no	—
335	C₃×C₄⋊C₄	—	2	1	no	—
336	C₃×C₄⋊C₄	—	2	2	no	—
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	2	no	—
339	C₃×C₄⋊C₄	—	2	2	no	—
340	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
341	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
342	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
343	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
344	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
345	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₃×C₂²⋊C₄	—	2	2	no	—
348	C₃×C₂²⋊C₄	—	2	2	no	—
349	C₃×C₂²⋊C₄	—	2	2	no	—
350	C₃×C₂²⋊C₄	—	2	4	no	—
351	C₃×C₂²⋊C₄	—	2	4	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	4	no	—
354	C₃×C₂²⋊C₄	—	2	2	no	—
355	C₃×C₂²⋊C₄	—	2	2	no	—
356	C₃×C₂²⋊C₄	—	2	4	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
359	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
360	C₃×C₄²	—	2	4	no	—
361	C₃×C₄²	—	2	2	no	—
362	C₃×C₄²	—	2	2	no	—
363	C₃×C₄²	—	2	2	no	—
364	C₃×C₄²	—	2	4	no	—
365	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
366	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
367	C₃×C₄²	C₂⁴	1	1	yes	characteristic
368	C₃×C₄²	C₂⁴	1	1	yes	characteristic
369	C₂×#41	—	2	2	no	—
370	C₂×#41	C₂³×C₃	1	2	yes	—
371	C₂²×Q₈	C₂³×C₃	1	4	yes	—
372	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
373	C₂³×C₄	—	2	1	no	—
374	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
375	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
376	C₂×SD₁₆	C₂³×C₃	1	4	yes	—
377	C₂×M₁₆	C₂³×C₃	1	4	yes	—
378	C₂²×C₈	C₂³×C₃	1	4	yes	—
379	C₄⋊Q₈	—	2	4	no	—
380	C₄⋊Q₈	—	2	2	no	—
381	C₄⋊Q₈	—	2	2	no	—
382	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
383	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
384	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
385	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
386	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
387	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
388	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
389	#127	—	2	2	no	—
390	#127	C₃×D₄	1	1	yes	characteristic
391	#126	—	2	4	no	—
392	#126	—	2	4	no	—
393	#126	—	2	4	no	—
394	#125	—	2	1	no	—
395	#125	—	2	1	no	—
396	#125	C₂³×C₃	1	2	yes	—
397	#124	—	2	2	no	—
398	#124	—	2	4	no	—
399	#124	—	2	2	no	—
400	#124	—	2	2	no	—
401	#124	—	2	4	no	—
402	#124	C₃×D₄	1	2	yes	—
403	#123	—	2	4	no	—
404	#123	—	2	4	no	—
405	#123	—	2	4	no	—
406	#123	—	2	4	no	—
407	C₂²⋊Q₈	—	2	1	no	—
408	C₂²⋊Q₈	—	2	1	no	—
409	C₂²⋊Q₈	—	2	1	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	C₂²⋊Q₈	—	2	2	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	—	2	4	no	—
414	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
415	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
416	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
417	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
418	#121	—	2	2	no	—
419	#121	—	2	4	no	—
420	#121	C₃×D₄	1	2	yes	—
421	#121	C₃×D₄	1	2	yes	—
422	#121	C₂³×C₃	1	4	yes	—
423	#121	C₂³×C₃	1	4	yes	—
424	#120	—	2	4	no	—
425	C₄×Q₈	—	2	2	no	—
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	—	2	2	no	—
428	C₄×Q₈	—	2	1	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	C₂³×C₃	1	2	yes	—
433	C₄×Q₈	C₂³×C₃	1	2	yes	—
434	C₄×D₄	—	2	4	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	4	no	—
439	C₄×D₄	—	2	1	no	—
440	C₄×D₄	—	2	1	no	—
441	C₄×D₄	C₂³×C₃	1	2	yes	—
442	C₄×D₄	C₂³×C₃	1	2	yes	—
443	C₄×D₄	C₂³×C₃	1	2	yes	—
444	C₄×D₄	C₂³×C₃	1	2	yes	—
445	#117	—	2	1	no	—
446	#117	—	2	1	no	—
447	#117	—	2	2	no	—
448	#117	C₂³×C₃	1	2	yes	—
449	#117	C₂³×C₃	1	4	yes	—
450	#117	C₂³×C₃	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
455	#107	C₂³×C₃	1	4	yes	—
456	#107	C₂³×C₃	1	4	yes	—
457	#107	C₂³×C₃	1	4	yes	—
458	#106	C₂³×C₃	1	2	yes	—
459	#106	C₂³×C₃	1	4	yes	—
460	#106	C₂³×C₃	1	2	yes	—
461	#106	C₂³×C₃	1	4	yes	—
462	C₄⋊C₈	C₂³×C₃	1	2	yes	—
463	C₄⋊C₈	C₂³×C₃	1	2	yes	—
464	#103	C₂³×C₃	1	2	yes	—
465	#103	C₂³×C₃	1	4	yes	—
466	#103	C₂³×C₃	1	4	yes	—
467	#103	C₂³×C₃	1	4	yes	—
468	#103	C₂³×C₃	1	2	yes	—
469	#103	C₂³×C₃	1	4	yes	—
470	#103	C₂³×C₃	1	4	yes	—
471	#102	C₂³×C₃	1	2	yes	—
472	#102	C₂³×C₃	1	2	yes	—
473	#102	C₂³×C₃	1	4	yes	—
474	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
475	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
476	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
477	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
478	#97	C₂³×C₃	1	2	yes	—
479	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
480	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
481	C₂³×C₃	—	2	2	no	—
482	C₂³×C₃	—	4	2	no	—
483	C₂³×C₃	—	8	1	no	—
484	C₂³×C₃	—	8	1	no	—
485	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
486	C₂³×C₃	C₂²×D₄	1	4	yes	—
487	C₃×Q₈	—	2	2	no	—
488	C₃×Q₈	—	2	4	no	—
489	C₃×Q₈	—	2	2	no	—
490	C₃×Q₈	—	4	2	no	—
491	C₃×Q₈	—	4	2	no	—
492	C₃×Q₈	—	4	2	no	—
493	C₃×Q₈	—	4	2	no	—
494	C₃×Q₈	—	8	1	no	—
495	C₃×Q₈	—	8	4	no	—
496	C₃×D₄	—	2	4	no	—
497	C₃×D₄	—	2	2	no	—
498	C₃×D₄	—	2	2	no	—
499	C₃×D₄	—	4	2	no	—
500	C₃×D₄	—	4	2	no	—
501	C₃×D₄	—	4	4	no	—
502	C₃×D₄	—	4	2	no	—
503	C₃×D₄	—	8	4	no	—
504	C₃×D₄	—	8	4	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	4	no	—
507	C₂×C₃×C₄	—	2	4	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	2	2	no	—
510	C₂×C₃×C₄	—	2	2	no	—
511	C₂×C₃×C₄	—	2	2	no	—
512	C₂×C₃×C₄	—	2	2	no	—
513	C₂×C₃×C₄	—	2	2	no	—
514	C₂×C₃×C₄	—	2	2	no	—
515	C₂×C₃×C₄	—	2	2	no	—
516	C₂×C₃×C₄	—	4	1	no	—
517	C₂×C₃×C₄	—	4	4	no	—
518	C₂×C₃×C₄	—	8	2	no	—
519	C₂×C₃×C₄	—	8	1	no	—
520	C₂×C₃×C₄	—	8	4	no	—
521	C₂×C₃×C₄	—	8	4	no	—
522	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
525	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
529	C₃×C₈	—	2	2	no	—
530	C₃×C₈	—	2	4	no	—
531	C₃×C₈	—	2	2	no	—
532	C₂⁴	—	2	1	no	—
533	#41	—	4	4	no	—
534	#41	—	8	4	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	4	4	no	—
541	C₂×Q₈	—	4	4	no	—
542	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
543	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
544	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
550	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
551	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
552	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
553	C₂×D₄	C₂⁴×C₃	1	2	yes	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	8	2	no	—
560	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
561	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
563	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
564	SD₁₆	—	4	2	no	—
565	SD₁₆	—	4	4	no	—
566	SD₁₆	—	4	2	no	—
567	M₁₆	—	4	4	no	—
568	C₂×C₈	—	4	4	no	—
569	C₂×C₈	C₂⁴×C₃	1	2	yes	—
570	C₂×C₈	C₂⁴×C₃	1	2	yes	—
571	C₂×C₈	C₂⁴×C₃	1	4	yes	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	2	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
591	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
592	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
593	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
594	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
595	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
596	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
609	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	2	no	—
614	C₄²	—	2	4	no	—
615	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
616	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
617	C₄²	C₂⁴×C₃	1	1	yes	characteristic
618	C₄²	C₂⁴×C₃	1	1	yes	characteristic
619	C₂²×C₃	—	2	1	no	—
620	C₂²×C₃	—	2	4	no	—
621	C₂²×C₃	—	2	4	no	—
622	C₂²×C₃	—	2	1	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	2	4	no	—
625	C₂²×C₃	—	4	2	no	—
626	C₂²×C₃	—	4	2	no	—
627	C₂²×C₃	—	4	2	no	—
628	C₂²×C₃	—	8	4	no	—
629	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
630	C₃×C₄	—	2	1	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	2	1	no	—
633	C₃×C₄	—	2	4	no	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	4	2	no	—
636	C₃×C₄	—	4	2	no	—
637	C₃×C₄	—	4	2	no	—
638	C₃×C₄	—	4	2	no	—
639	C₃×C₄	—	4	2	no	—
640	C₃×C₄	—	4	2	no	—
641	C₃×C₄	—	4	2	no	—
642	C₃×C₄	#577	1	2	yes	—
643	C₃×C₄	#585	1	2	yes	—
644	C₂³	—	2	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	8	1	no	—
647	C₂³	—	8	1	no	—
648	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
649	C₂³	C₂²×C₃×D₄	1	4	yes	—
650	Q₈	—	2	2	no	—
651	Q₈	—	2	4	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	4	2	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	4	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	8	4	no	—
658	Q₈	—	8	1	no	—
659	D₄	—	2	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	2	no	—
665	D₄	—	4	2	no	—
666	D₄	—	8	4	no	—
667	D₄	—	8	4	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	4	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	8	2	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	8	4	no	—
684	C₂×C₄	—	8	4	no	—
685	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
686	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
687	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
688	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
689	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
690	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
691	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
692	C₈	—	2	2	no	—
693	C₈	—	2	4	no	—
694	C₈	—	2	2	no	—
695	C₂×C₃	—	4	4	no	—
696	C₂×C₃	—	4	1	no	—
697	C₂×C₃	—	8	2	no	—
698	C₂×C₃	#3485	1	1	yes	characteristic
699	C₂×C₃	C₂×#577	1	1	yes	characteristic
700	C₂×C₃	#3586	1	1	yes	characteristic
701	C₂²	—	2	4	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	8	4	no	—
711	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
712	C₄	—	2	1	no	—
713	C₄	—	2	4	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	C₃×#577	1	2	yes	—
725	C₄	C₃×#585	1	2	yes	—
726	C₃	#61803	1	1	yes	characteristic, direct product factor, Sylow
727	C₂	—	4	1	no	—
728	C₂	—	4	4	no	—
729	C₂	—	8	2	no	—
730	C₂	C₃×#3485	1	1	yes	characteristic
731	C₂	C₂×C₃×#577	1	1	yes	characteristic
732	C₂	C₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3550	C₂	semidirect
3. C₃×#3353	C₂	semidirect
4. C₃×#3350	C₂	semidirect
5. C₃×#3340	C₂	semidirect
6. C₃×#3329	C₂	semidirect
7. C₃×#3320	C₂	semidirect
8. C₃×#3298	C₂	semidirect
9. C₃×#3237	C₂	semidirect
10. C₃×#3231	C₂	semidirect
11. C₃×#3200	C₂	semidirect
12. C₃×#3110	C₂	semidirect
13. C₃×#3101	C₂	semidirect
14. C₃×#3097	C₂	semidirect
15. C₃×#2981	C₂	semidirect
16. #61803	C₃	direct (N × H)
22. C₃×#556	C₂²	semidirect
23. C₃×#556	C₂²	semidirect
27. C₃×D₄×Q₈	C₂²	semidirect
28. C₃×D₄×Q₈	C₂²	semidirect
42. C₃×#501	C₂²	semidirect
43. C₃×#500	C₂²	semidirect
44. C₃×#498	C₂²	semidirect
45. C₃×#491	C₂²	semidirect
46. C₃×#487	C₂²	semidirect
47. C₃×#487	C₂²	semidirect
50. C₃×#485	C₂²	semidirect
51. C₃×#485	C₂²	semidirect
53. C₃×#484	C₂²	semidirect
55. C₃×#483	C₂²	semidirect
58. C₃×#479	C₂²	semidirect
59. C₃×#477	C₂²	semidirect
61. C₃×#475	C₂²	semidirect
76. C₃×#436	C₂²	semidirect
77. C₃×#435	C₂²	semidirect
78. C₃×C₈×D₄	C₂²	semidirect
81. C₃×#428	C₂²	semidirect
82. C₃×#427	C₂²	semidirect
83. C₃×#419	C₂²	semidirect
84. C₂×C₃×#103	C₂²	semidirect
86. #3550	C₂×C₃	semidirect
88. #3353	C₂×C₃	semidirect
89. #3350	C₂×C₃	semidirect
90. #3340	C₂×C₃	semidirect
91. #3329	C₂×C₃	semidirect
92. #3320	C₂×C₃	semidirect
93. #3298	C₂×C₃	semidirect
94. #3237	C₂×C₃	semidirect
95. #3231	C₂×C₃	semidirect
96. #3200	C₂×C₃	semidirect
97. #3110	C₂×C₃	semidirect
98. #3101	C₂×C₃	semidirect
99. #3097	C₂×C₃	semidirect
100. #2981	C₂×C₃	semidirect
218. #556	C₂²×C₃	semidirect
219. #556	C₂²×C₃	semidirect
223. D₄×Q₈	C₂²×C₃	semidirect
224. D₄×Q₈	C₂²×C₃	semidirect
238. #501	C₂²×C₃	semidirect
239. #500	C₂²×C₃	semidirect
240. #498	C₂²×C₃	semidirect
241. #491	C₂²×C₃	semidirect
242. #487	C₂²×C₃	semidirect
243. #487	C₂²×C₃	semidirect
246. #485	C₂²×C₃	semidirect
247. #485	C₂²×C₃	semidirect
249. #484	C₂²×C₃	semidirect
251. #483	C₂²×C₃	semidirect
254. #479	C₂²×C₃	semidirect
255. #477	C₂²×C₃	semidirect
257. #475	C₂²×C₃	semidirect
272. #436	C₂²×C₃	semidirect
273. #435	C₂²×C₃	semidirect
274. C₈×D₄	C₂²×C₃	semidirect
277. #428	C₂²×C₃	semidirect
278. #427	C₂²×C₃	semidirect
279. #419	C₂²×C₃	semidirect
280. C₂×#103	C₂²×C₃	semidirect
726. C₃	#61803	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×#3550	2
C₃×#3506	2
C₃×#3353	2
C₃×#3350	2
C₃×#3340	2
C₃×#3329	2
C₃×#3320	2
C₃×#3298	2
C₃×#3237	2
C₃×#3231	2
C₃×#3200	2
C₃×#3110	2
C₃×#3101	2
C₃×#3097	2
C₃×#2981	2
#61803	3

Subgroups — C3×#61803 #10680410

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61803 #10680410