Subgroups — C₃×#61789 #10680396

Order 768.

1718 conjugacy classes of subgroups.

The subgroup lattice has 788 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×#3511	C₂	1	1	yes	maximal, characteristic
3	C₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₃×#3353	C₂	1	2	yes	maximal, complemented
5	C₃×#3342	C₂	1	2	yes	maximal, complemented
6	C₃×#3340	C₂	1	2	yes	maximal, complemented
7	C₃×#3329	C₂	1	2	yes	maximal, complemented
8	C₃×#3328	C₂	1	2	yes	maximal, complemented
9	C₃×#3299	C₂	1	2	yes	maximal, complemented
10	C₃×#3298	C₂	1	2	yes	maximal, complemented
11	C₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#3201	C₂	1	4	yes	maximal, complemented
14	C₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3097	C₂	1	4	yes	maximal, complemented
17	C₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
18	#61789	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃×#563	—	2	2	no	—
20	C₃×#559	—	2	1	no	—
21	C₃×Q₈²	—	2	1	no	—
22	C₃×#556	C₂²	1	2	yes	—
23	C₃×#556	C₂²	1	2	yes	—
24	C₃×#556	C₂²	1	2	yes	—
25	C₃×#555	C₂²	1	2	yes	—
26	C₃×#554	C₂²	1	2	yes	—
27	C₃×#553	—	2	2	no	—
28	C₃×D₄×Q₈	C₂²	1	2	yes	—
29	C₃×D₄×Q₈	C₂²	1	2	yes	—
30	C₃×#548	—	2	2	no	—
31	C₃×#547	C₂²	1	2	yes	—
32	C₃×#542	—	2	2	no	—
33	C₃×#542	—	2	2	no	—
34	C₃×#542	—	2	2	no	—
35	C₃×#537	C₂²	1	2	yes	—
36	C₃×#536	C₂²	1	4	yes	—
37	C₃×#533	—	2	1	no	—
38	C₃×#533	C₂²	1	1	yes	characteristic
39	C₃×#533	C₂²	1	1	yes	characteristic
40	C₃×#532	—	2	1	no	—
41	C₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃×#520	C₂²	1	2	yes	—
44	C₃×C₄×#41	C₂²	1	1	yes	characteristic
45	C₃×#500	C₂²	1	2	yes	—
46	C₃×#498	C₂²	1	2	yes	—
47	C₃×#487	C₂²	1	2	yes	—
48	C₃×#487	C₂²	1	2	yes	—
49	C₃×#485	C₂²	1	4	yes	—
50	C₃×#485	C₂²	1	4	yes	—
51	C₃×#485	C₂²	1	4	yes	—
52	C₃×#485	C₂²	1	2	yes	—
53	C₃×#485	C₂²	1	2	yes	—
54	C₃×#484	C₂²	1	4	yes	—
55	C₃×#484	C₂²	1	4	yes	—
56	C₃×#483	C₂²	1	4	yes	—
57	C₃×#483	C₂²	1	4	yes	—
58	C₃×#482	C₂²	1	4	yes	—
59	C₃×#477	C₂²	1	2	yes	—
60	C₃×#477	C₂²	1	2	yes	—
61	C₃×#475	C₂²	1	2	yes	—
62	C₃×#475	C₂²	1	2	yes	—
63	C₃×#475	C₂²	1	1	yes	characteristic
64	C₃×#475	C₂²	1	1	yes	characteristic
65	C₃×#474	C₂²	1	1	yes	characteristic
66	C₃×#474	C₂²	1	1	yes	characteristic
67	C₃×#470	C₂²	1	4	yes	—
68	C₃×#468	C₂²	1	4	yes	—
69	C₃×#467	C₂²	1	4	yes	—
70	C₃×#465	C₂²	1	4	yes	—
71	C₃×#462	C₂²	1	1	yes	characteristic
72	C₃×#462	C₂²	1	1	yes	characteristic
73	C₃×#461	C₂²	1	1	yes	characteristic
74	C₃×#461	C₂²	1	1	yes	characteristic
75	C₃×#452	C₂²	1	2	yes	—
76	C₃×#452	C₂²	1	2	yes	—
77	C₃×#451	C₂²	1	4	yes	—
78	C₃×#448	C₂²	1	4	yes	—
79	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
80	C₃×C₄×Q₁₆	C₂²	1	2	yes	—
81	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
82	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
83	C₃×#436	C₂²	1	2	yes	—
84	C₃×#436	C₂²	1	2	yes	—
85	C₃×C₈×D₄	C₂²	1	2	yes	—
86	C₃×C₈×D₄	C₂²	1	2	yes	—
87	C₃×#431	C₂²	1	1	yes	characteristic
88	C₃×#431	C₂²	1	1	yes	characteristic
89	C₃×#428	C₂²	1	4	yes	—
90	C₃×#427	C₂²	1	4	yes	—
91	C₃×#419	C₂²	1	4	yes	—
92	C₂×C₃×#103	C₂²	1	4	yes	—
93	C₃×#408	C₂²	1	4	yes	—
94	#3550	C₂×C₃	1	1	yes	characteristic, complemented
95	#3511	C₂×C₃	1	1	yes	characteristic
96	#3356	C₂×C₃	1	2	yes	complemented
97	#3353	C₂×C₃	1	2	yes	complemented
98	#3342	C₂×C₃	1	2	yes	complemented
99	#3340	C₂×C₃	1	2	yes	complemented
100	#3329	C₂×C₃	1	2	yes	complemented
101	#3328	C₂×C₃	1	2	yes	complemented
102	#3299	C₂×C₃	1	2	yes	complemented
103	#3298	C₂×C₃	1	2	yes	complemented
104	#3230	C₂×C₃	1	1	yes	characteristic, complemented
105	#3229	C₂×C₃	1	1	yes	characteristic, complemented
106	#3201	C₂×C₃	1	4	yes	complemented
107	#3107	C₂×C₃	1	1	yes	characteristic, complemented
108	#3107	C₂×C₃	1	1	yes	characteristic, complemented
109	#3097	C₂×C₃	1	4	yes	complemented
110	#2979	C₂×C₃	1	1	yes	characteristic, complemented
111	C₂×C₃×#41	—	2	2	no	—
112	C₂×C₃×#41	C₂³	1	1	yes	characteristic
113	C₂×C₃×#41	C₂³	1	2	yes	—
114	C₂²×C₃×Q₈	—	2	1	no	—
115	C₂²×C₃×Q₈	C₂³	1	4	yes	—
116	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
117	C₂×C₃×Q₁₆	C₂³	1	2	yes	—
118	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₃×SD₁₆	C₂³	1	2	yes	—
120	C₂×C₃×M₁₆	C₂³	1	4	yes	—
121	C₂²×C₃×C₈	C₂³	1	4	yes	—
122	C₃×C₄⋊Q₈	—	2	4	no	—
123	C₃×C₄⋊Q₈	—	2	2	no	—
124	C₃×C₄⋊Q₈	—	2	2	no	—
125	C₃×C₄⋊Q₈	—	2	1	no	—
126	C₃×C₄⋊Q₈	—	2	1	no	—
127	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
128	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
129	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₃×C₄⋊Q₈	C₂³	1	2	yes	—
134	C₃×#127	D₄	1	1	yes	characteristic
135	C₃×#126	—	2	4	no	—
136	C₃×#126	—	2	4	no	—
137	C₃×#126	—	2	4	no	—
138	C₃×#125	—	2	2	no	—
139	C₃×#125	—	2	1	no	—
140	C₃×#125	—	2	1	no	—
141	C₃×#124	—	2	2	no	—
142	C₃×#124	—	2	2	no	—
143	C₃×#124	—	2	2	no	—
144	C₃×#124	—	2	4	no	—
145	C₃×#124	—	2	4	no	—
146	C₃×#124	D₄	1	2	yes	—
147	C₃×#123	—	2	4	no	—
148	C₃×#123	—	2	4	no	—
149	C₃×#123	—	2	4	no	—
150	C₃×C₂²⋊Q₈	—	2	2	no	—
151	C₃×C₂²⋊Q₈	—	2	1	no	—
152	C₃×C₂²⋊Q₈	—	2	1	no	—
153	C₃×C₂²⋊Q₈	—	2	2	no	—
154	C₃×C₂²⋊Q₈	—	2	4	no	—
155	C₃×C₂²⋊Q₈	—	2	4	no	—
156	C₃×C₂²⋊Q₈	—	2	4	no	—
157	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
158	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
159	C₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
161	C₃×C₂²⋊Q₈	C₂³	1	4	yes	—
162	C₃×#121	—	2	2	no	—
163	C₃×#121	—	2	2	no	—
164	C₃×#121	—	2	4	no	—
165	C₃×#121	D₄	1	2	yes	—
166	C₃×#121	D₄	1	2	yes	—
167	C₃×#121	C₂³	1	4	yes	—
168	C₃×C₄×Q₈	—	2	2	no	—
169	C₃×C₄×Q₈	—	2	2	no	—
170	C₃×C₄×Q₈	—	2	2	no	—
171	C₃×C₄×Q₈	—	2	2	no	—
172	C₃×C₄×Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	—	2	1	no	—
174	C₃×C₄×Q₈	C₂³	1	2	yes	—
175	C₃×C₄×Q₈	C₂³	1	2	yes	—
176	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
177	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
178	C₃×C₄×D₄	—	2	2	no	—
179	C₃×C₄×D₄	—	2	2	no	—
180	C₃×C₄×D₄	—	2	2	no	—
181	C₃×C₄×D₄	—	2	4	no	—
182	C₃×C₄×D₄	—	2	2	no	—
183	C₃×C₄×D₄	—	2	1	no	—
184	C₃×C₄×D₄	—	2	1	no	—
185	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
186	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
187	C₃×C₄×D₄	C₂³	1	2	yes	—
188	C₃×C₄×D₄	C₂³	1	2	yes	—
189	C₃×#117	—	2	1	no	—
190	C₃×#117	—	2	1	no	—
191	C₃×#117	—	2	2	no	—
192	C₃×#117	—	2	1	no	—
193	C₃×#117	C₂³	1	4	yes	—
194	C₃×#117	C₂³	1	4	yes	—
195	C₃×#117	C₂³	1	1	yes	characteristic
196	C₂×C₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
198	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
199	C₂×C₃×C₄²	—	2	1	no	—
200	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
201	C₃×#107	C₂³	1	2	yes	—
202	C₃×#107	C₂³	1	4	yes	—
203	C₃×#107	C₂³	1	2	yes	—
204	C₃×#107	C₂³	1	4	yes	—
205	C₃×#106	C₂³	1	2	yes	—
206	C₃×#106	C₂³	1	4	yes	—
207	C₃×#106	C₂³	1	2	yes	—
208	C₃×#106	C₂³	1	4	yes	—
209	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
210	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
211	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₃×#103	C₂³	1	2	yes	—
214	C₃×#103	C₂³	1	2	yes	—
215	C₃×#103	C₂³	1	4	yes	—
216	C₃×#103	C₂³	1	4	yes	—
217	C₃×#103	C₂³	1	2	yes	—
218	C₃×#103	C₂³	1	2	yes	—
219	C₃×#103	C₂³	1	4	yes	—
220	C₃×#103	C₂³	1	4	yes	—
221	C₃×#103	C₂³	1	2	yes	—
222	C₃×#103	C₂³	1	2	yes	—
223	C₃×#102	C₂³	1	2	yes	—
224	C₃×#102	C₂³	1	2	yes	—
225	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₃×C₄×C₈	C₂³	1	2	yes	—
230	C₃×C₄×C₈	C₂³	1	2	yes	—
231	#563	—	2	2	no	—
232	#559	—	2	1	no	—
233	Q₈²	—	2	1	no	—
234	#556	C₂²×C₃	1	2	yes	—
235	#556	C₂²×C₃	1	2	yes	—
236	#556	C₂²×C₃	1	2	yes	—
237	#555	C₂²×C₃	1	2	yes	—
238	#554	C₂²×C₃	1	2	yes	—
239	#553	—	2	2	no	—
240	D₄×Q₈	C₂²×C₃	1	2	yes	—
241	D₄×Q₈	C₂²×C₃	1	2	yes	—
242	#548	—	2	2	no	—
243	#547	C₂²×C₃	1	2	yes	—
244	#542	—	2	2	no	—
245	#542	—	2	2	no	—
246	#542	—	2	2	no	—
247	#537	C₂²×C₃	1	2	yes	—
248	#536	C₂²×C₃	1	4	yes	—
249	#533	—	2	1	no	—
250	#533	C₂²×C₃	1	1	yes	characteristic
251	#533	C₂²×C₃	1	1	yes	characteristic
252	#532	—	2	1	no	—
253	#532	C₂²×C₃	1	1	yes	characteristic
254	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
255	#520	C₂²×C₃	1	2	yes	—
256	C₄×#41	C₂²×C₃	1	1	yes	characteristic
257	#500	C₂²×C₃	1	2	yes	—
258	#498	C₂²×C₃	1	2	yes	—
259	#487	C₂²×C₃	1	2	yes	—
260	#487	C₂²×C₃	1	2	yes	—
261	#485	C₂²×C₃	1	4	yes	—
262	#485	C₂²×C₃	1	4	yes	—
263	#485	C₂²×C₃	1	4	yes	—
264	#485	C₂²×C₃	1	2	yes	—
265	#485	C₂²×C₃	1	2	yes	—
266	#484	C₂²×C₃	1	4	yes	—
267	#484	C₂²×C₃	1	4	yes	—
268	#483	C₂²×C₃	1	4	yes	—
269	#483	C₂²×C₃	1	4	yes	—
270	#482	C₂²×C₃	1	4	yes	—
271	#477	C₂²×C₃	1	2	yes	—
272	#477	C₂²×C₃	1	2	yes	—
273	#475	C₂²×C₃	1	2	yes	—
274	#475	C₂²×C₃	1	1	yes	characteristic
275	#475	C₂²×C₃	1	2	yes	—
276	#475	C₂²×C₃	1	1	yes	characteristic
277	#474	C₂²×C₃	1	1	yes	characteristic
278	#474	C₂²×C₃	1	1	yes	characteristic
279	#470	C₂²×C₃	1	4	yes	—
280	#468	C₂²×C₃	1	4	yes	—
281	#467	C₂²×C₃	1	4	yes	—
282	#465	C₂²×C₃	1	4	yes	—
283	#462	C₂²×C₃	1	1	yes	characteristic
284	#462	C₂²×C₃	1	1	yes	characteristic
285	#461	C₂²×C₃	1	1	yes	characteristic
286	#461	C₂²×C₃	1	1	yes	characteristic
287	#452	C₂²×C₃	1	2	yes	—
288	#452	C₂²×C₃	1	2	yes	—
289	#451	C₂²×C₃	1	4	yes	—
290	#448	C₂²×C₃	1	4	yes	—
291	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
292	C₄×Q₁₆	C₂²×C₃	1	2	yes	—
293	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
294	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
295	#436	C₂²×C₃	1	2	yes	—
296	#436	C₂²×C₃	1	2	yes	—
297	C₈×D₄	C₂²×C₃	1	2	yes	—
298	C₈×D₄	C₂²×C₃	1	2	yes	—
299	#431	C₂²×C₃	1	1	yes	characteristic
300	#431	C₂²×C₃	1	1	yes	characteristic
301	#428	C₂²×C₃	1	4	yes	—
302	#427	C₂²×C₃	1	4	yes	—
303	#419	C₂²×C₃	1	4	yes	—
304	C₂×#103	C₂²×C₃	1	4	yes	—
305	#408	C₂²×C₃	1	4	yes	—
306	C₃×#41	—	4	2	no	—
307	C₃×#41	—	4	2	no	—
308	C₃×#41	—	4	1	no	—
309	C₃×#41	—	4	1	no	—
310	C₃×#41	—	8	4	no	—
311	C₂×C₃×Q₈	—	2	1	no	—
312	C₂×C₃×Q₈	—	2	1	no	—
313	C₂×C₃×Q₈	—	2	2	no	—
314	C₂×C₃×Q₈	—	2	2	no	—
315	C₂×C₃×Q₈	—	2	4	no	—
316	C₂×C₃×Q₈	—	4	4	no	—
317	C₂×C₃×Q₈	—	4	4	no	—
318	C₂×C₃×Q₈	—	8	2	no	—
319	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
320	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
321	C₂×C₃×Q₈	C₂⁴	1	2	yes	—
322	C₂×C₃×Q₈	C₂⁴	1	1	yes	characteristic
323	C₂×C₃×D₄	—	2	1	no	—
324	C₂×C₃×D₄	—	2	4	no	—
325	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
326	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
327	C₂×C₃×D₄	C₂×D₄	1	4	yes	—
328	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
329	C₂×C₃×D₄	C₂⁴	1	1	yes	characteristic
330	C₂²×C₃×C₄	—	2	2	no	—
331	C₂²×C₃×C₄	—	2	4	no	—
332	C₂²×C₃×C₄	—	2	4	no	—
333	C₂²×C₃×C₄	—	2	1	no	—
334	C₂²×C₃×C₄	—	2	1	no	—
335	C₂²×C₃×C₄	—	2	1	no	—
336	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
340	C₃×Q₁₆	—	4	2	no	—
341	C₃×Q₁₆	—	4	2	no	—
342	C₃×SD₁₆	—	4	2	no	—
343	C₃×SD₁₆	—	4	2	no	—
344	C₃×M₁₆	—	4	4	no	—
345	C₂×C₃×C₈	—	4	4	no	—
346	C₂×C₃×C₈	C₂⁴	1	2	yes	—
347	C₂×C₃×C₈	C₂⁴	1	2	yes	—
348	C₂×C₃×C₈	C₂⁴	1	2	yes	—
349	C₂×C₃×C₈	C₂⁴	1	2	yes	—
350	C₃×C₄⋊C₄	—	2	2	no	—
351	C₃×C₄⋊C₄	—	2	2	no	—
352	C₃×C₄⋊C₄	—	2	2	no	—
353	C₃×C₄⋊C₄	—	2	4	no	—
354	C₃×C₄⋊C₄	—	2	1	no	—
355	C₃×C₄⋊C₄	—	2	1	no	—
356	C₃×C₄⋊C₄	—	2	1	no	—
357	C₃×C₄⋊C₄	—	2	1	no	—
358	C₃×C₄⋊C₄	—	2	1	no	—
359	C₃×C₄⋊C₄	—	2	1	no	—
360	C₃×C₄⋊C₄	—	2	1	no	—
361	C₃×C₄⋊C₄	—	2	1	no	—
362	C₃×C₄⋊C₄	—	2	4	no	—
363	C₃×C₄⋊C₄	—	2	4	no	—
364	C₃×C₄⋊C₄	—	2	4	no	—
365	C₃×C₄⋊C₄	—	2	2	no	—
366	C₃×C₄⋊C₄	—	2	2	no	—
367	C₃×C₄⋊C₄	—	2	2	no	—
368	C₃×C₄⋊C₄	—	2	2	no	—
369	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
370	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
371	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
372	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
373	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
374	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
375	C₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
376	C₃×C₂²⋊C₄	—	2	2	no	—
377	C₃×C₂²⋊C₄	—	2	2	no	—
378	C₃×C₂²⋊C₄	—	2	1	no	—
379	C₃×C₂²⋊C₄	—	2	4	no	—
380	C₃×C₂²⋊C₄	—	2	4	no	—
381	C₃×C₂²⋊C₄	—	2	4	no	—
382	C₃×C₂²⋊C₄	—	2	4	no	—
383	C₃×C₂²⋊C₄	—	2	4	no	—
384	C₃×C₂²⋊C₄	—	2	1	no	—
385	C₃×C₂²⋊C₄	—	2	1	no	—
386	C₃×C₂²⋊C₄	—	2	4	no	—
387	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
388	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
389	C₃×C₄²	—	2	1	no	—
390	C₃×C₄²	—	2	1	no	—
391	C₃×C₄²	—	2	1	no	—
392	C₃×C₄²	—	2	4	no	—
393	C₃×C₄²	—	2	2	no	—
394	C₃×C₄²	—	2	2	no	—
395	C₃×C₄²	—	2	4	no	—
396	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
397	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
398	C₃×C₄²	C₂⁴	1	1	yes	characteristic
399	C₃×C₄²	C₂⁴	1	1	yes	characteristic
400	C₂×#41	—	2	2	no	—
401	C₂×#41	C₂³×C₃	1	1	yes	characteristic
402	C₂×#41	C₂³×C₃	1	2	yes	—
403	C₂²×Q₈	—	2	1	no	—
404	C₂²×Q₈	C₂³×C₃	1	4	yes	—
405	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
406	C₂×Q₁₆	C₂³×C₃	1	2	yes	—
407	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
408	C₂×SD₁₆	C₂³×C₃	1	2	yes	—
409	C₂×M₁₆	C₂³×C₃	1	4	yes	—
410	C₂²×C₈	C₂³×C₃	1	4	yes	—
411	C₄⋊Q₈	—	2	4	no	—
412	C₄⋊Q₈	—	2	2	no	—
413	C₄⋊Q₈	—	2	2	no	—
414	C₄⋊Q₈	—	2	1	no	—
415	C₄⋊Q₈	—	2	1	no	—
416	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
417	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
418	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
419	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
420	C₄⋊Q₈	C₂³×C₃	1	2	yes	—
421	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
422	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
423	#127	C₃×D₄	1	1	yes	characteristic
424	#126	—	2	4	no	—
425	#126	—	2	4	no	—
426	#126	—	2	4	no	—
427	#125	—	2	2	no	—
428	#125	—	2	1	no	—
429	#125	—	2	1	no	—
430	#124	—	2	2	no	—
431	#124	—	2	4	no	—
432	#124	—	2	2	no	—
433	#124	—	2	2	no	—
434	#124	—	2	4	no	—
435	#124	C₃×D₄	1	2	yes	—
436	#123	—	2	4	no	—
437	#123	—	2	4	no	—
438	#123	—	2	4	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	—	2	1	no	—
441	C₂²⋊Q₈	—	2	1	no	—
442	C₂²⋊Q₈	—	2	2	no	—
443	C₂²⋊Q₈	—	2	4	no	—
444	C₂²⋊Q₈	—	2	4	no	—
445	C₂²⋊Q₈	—	2	4	no	—
446	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
447	C₂²⋊Q₈	C₂³×C₃	1	2	yes	—
448	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
449	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
450	C₂²⋊Q₈	C₂³×C₃	1	4	yes	—
451	#121	—	2	2	no	—
452	#121	—	2	2	no	—
453	#121	—	2	4	no	—
454	#121	C₃×D₄	1	2	yes	—
455	#121	C₃×D₄	1	2	yes	—
456	#121	C₂³×C₃	1	4	yes	—
457	C₄×Q₈	—	2	2	no	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	1	no	—
462	C₄×Q₈	—	2	1	no	—
463	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
464	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
465	C₄×Q₈	C₂³×C₃	1	2	yes	—
466	C₄×Q₈	C₂³×C₃	1	2	yes	—
467	C₄×D₄	—	2	2	no	—
468	C₄×D₄	—	2	4	no	—
469	C₄×D₄	—	2	2	no	—
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	2	2	no	—
472	C₄×D₄	—	2	1	no	—
473	C₄×D₄	—	2	1	no	—
474	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
475	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
476	C₄×D₄	C₂³×C₃	1	2	yes	—
477	C₄×D₄	C₂³×C₃	1	2	yes	—
478	#117	—	2	1	no	—
479	#117	—	2	1	no	—
480	#117	—	2	2	no	—
481	#117	—	2	1	no	—
482	#117	C₂³×C₃	1	1	yes	characteristic
483	#117	C₂³×C₃	1	4	yes	—
484	#117	C₂³×C₃	1	4	yes	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
490	#107	C₂³×C₃	1	2	yes	—
491	#107	C₂³×C₃	1	4	yes	—
492	#107	C₂³×C₃	1	2	yes	—
493	#107	C₂³×C₃	1	4	yes	—
494	#106	C₂³×C₃	1	2	yes	—
495	#106	C₂³×C₃	1	4	yes	—
496	#106	C₂³×C₃	1	2	yes	—
497	#106	C₂³×C₃	1	4	yes	—
498	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
499	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
500	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
501	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
502	#103	C₂³×C₃	1	2	yes	—
503	#103	C₂³×C₃	1	2	yes	—
504	#103	C₂³×C₃	1	4	yes	—
505	#103	C₂³×C₃	1	4	yes	—
506	#103	C₂³×C₃	1	2	yes	—
507	#103	C₂³×C₃	1	2	yes	—
508	#103	C₂³×C₃	1	4	yes	—
509	#103	C₂³×C₃	1	4	yes	—
510	#103	C₂³×C₃	1	2	yes	—
511	#103	C₂³×C₃	1	2	yes	—
512	#102	C₂³×C₃	1	2	yes	—
513	#102	C₂³×C₃	1	2	yes	—
514	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
515	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
516	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
517	C₂²⋊C₈	C₂³×C₃	1	4	yes	—
518	C₄×C₈	C₂³×C₃	1	2	yes	—
519	C₄×C₈	C₂³×C₃	1	2	yes	—
520	C₂³×C₃	—	2	1	no	—
521	C₂³×C₃	C₂²×D₄	1	4	yes	—
522	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
523	C₃×Q₈	—	2	2	no	—
524	C₃×Q₈	—	2	2	no	—
525	C₃×Q₈	—	2	1	no	—
526	C₃×Q₈	—	2	1	no	—
527	C₃×Q₈	—	2	2	no	—
528	C₃×Q₈	—	2	2	no	—
529	C₃×Q₈	—	4	2	no	—
530	C₃×Q₈	—	4	2	no	—
531	C₃×Q₈	—	4	4	no	—
532	C₃×Q₈	—	4	2	no	—
533	C₃×Q₈	—	8	4	no	—
534	C₃×Q₈	—	8	2	no	—
535	C₃×D₄	—	2	4	no	—
536	C₃×D₄	—	2	4	no	—
537	C₃×D₄	—	2	1	no	—
538	C₃×D₄	—	2	1	no	—
539	C₃×D₄	—	4	2	no	—
540	C₃×D₄	—	4	4	no	—
541	C₃×D₄	—	4	2	no	—
542	C₃×D₄	—	8	4	no	—
543	C₂×C₃×C₄	—	2	2	no	—
544	C₂×C₃×C₄	—	2	2	no	—
545	C₂×C₃×C₄	—	2	4	no	—
546	C₂×C₃×C₄	—	2	4	no	—
547	C₂×C₃×C₄	—	2	1	no	—
548	C₂×C₃×C₄	—	2	1	no	—
549	C₂×C₃×C₄	—	2	1	no	—
550	C₂×C₃×C₄	—	2	2	no	—
551	C₂×C₃×C₄	—	2	2	no	—
552	C₂×C₃×C₄	—	2	1	no	—
553	C₂×C₃×C₄	—	2	1	no	—
554	C₂×C₃×C₄	—	2	2	no	—
555	C₂×C₃×C₄	—	2	2	no	—
556	C₂×C₃×C₄	—	2	4	no	—
557	C₂×C₃×C₄	—	4	2	no	—
558	C₂×C₃×C₄	—	4	2	no	—
559	C₂×C₃×C₄	—	4	2	no	—
560	C₂×C₃×C₄	—	8	4	no	—
561	C₂×C₃×C₄	—	8	2	no	—
562	C₂×C₃×C₄	—	8	4	no	—
563	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
564	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
565	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
570	C₃×C₈	—	2	2	no	—
571	C₃×C₈	—	2	2	no	—
572	C₃×C₈	—	2	2	no	—
573	C₃×C₈	—	2	2	no	—
574	#41	—	4	2	no	—
575	#41	—	4	2	no	—
576	#41	—	4	1	no	—
577	#41	—	4	1	no	—
578	#41	—	8	4	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	4	no	—
584	C₂×Q₈	—	4	4	no	—
585	C₂×Q₈	—	4	4	no	—
586	C₂×Q₈	—	8	2	no	—
587	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
588	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
589	C₂×Q₈	C₂⁴×C₃	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₃	1	1	yes	characteristic
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
594	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
595	C₂×D₄	C₂×C₃×D₄	1	4	yes	—
596	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
597	C₂×D₄	C₂⁴×C₃	1	1	yes	characteristic
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
605	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
606	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
608	Q₁₆	—	4	2	no	—
609	Q₁₆	—	4	2	no	—
610	SD₁₆	—	4	2	no	—
611	SD₁₆	—	4	2	no	—
612	M₁₆	—	4	4	no	—
613	C₂×C₈	—	4	4	no	—
614	C₂×C₈	C₂⁴×C₃	1	2	yes	—
615	C₂×C₈	C₂⁴×C₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₃	1	2	yes	—
617	C₂×C₈	C₂⁴×C₃	1	2	yes	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
638	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
642	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
643	C₄⋊C₄	C₂⁴×C₃	1	1	yes	characteristic
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
656	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	4	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	2	no	—
663	C₄²	—	2	4	no	—
664	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
665	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
666	C₄²	C₂⁴×C₃	1	1	yes	characteristic
667	C₄²	C₂⁴×C₃	1	1	yes	characteristic
668	C₂²×C₃	—	2	4	no	—
669	C₂²×C₃	—	2	1	no	—
670	C₂²×C₃	—	2	1	no	—
671	C₂²×C₃	—	2	4	no	—
672	C₂²×C₃	—	2	1	no	—
673	C₂²×C₃	—	2	4	no	—
674	C₂²×C₃	—	4	1	no	—
675	C₂²×C₃	—	4	1	no	—
676	C₂²×C₃	—	4	1	no	—
677	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
678	C₃×C₄	—	2	1	no	—
679	C₃×C₄	—	2	4	no	—
680	C₃×C₄	—	2	1	no	—
681	C₃×C₄	—	2	1	no	—
682	C₃×C₄	—	4	1	no	—
683	C₃×C₄	—	4	2	no	—
684	C₃×C₄	—	4	2	no	—
685	C₃×C₄	—	4	1	no	—
686	C₃×C₄	—	4	4	no	—
687	C₃×C₄	—	4	2	no	—
688	C₃×C₄	—	4	1	no	—
689	C₃×C₄	—	4	2	no	—
690	C₃×C₄	#577	1	2	yes	—
691	C₃×C₄	#578	1	2	yes	—
692	C₃×C₄	#585	1	1	yes	characteristic
693	C₃×C₄	#585	1	1	yes	characteristic
694	C₂³	—	2	1	no	—
695	C₂³	C₂²×C₃×D₄	1	4	yes	—
696	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	1	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	2	no	—
702	Q₈	—	2	2	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	4	4	no	—
705	Q₈	—	4	2	no	—
706	Q₈	—	4	2	no	—
707	Q₈	—	8	4	no	—
708	Q₈	—	8	2	no	—
709	D₄	—	2	4	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	1	no	—
712	D₄	—	2	1	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	4	no	—
715	D₄	—	4	2	no	—
716	D₄	—	8	4	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	4	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	4	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	8	4	no	—
735	C₂×C₄	—	8	2	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
738	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
739	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
740	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
741	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
742	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
743	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
744	C₈	—	2	2	no	—
745	C₈	—	2	2	no	—
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₂×C₃	—	4	4	no	—
749	C₂×C₃	—	4	1	no	—
750	C₂×C₃	—	8	1	no	—
751	C₂×C₃	#3485	1	1	yes	characteristic
752	C₂×C₃	C₂×#577	1	1	yes	characteristic
753	C₂×C₃	C₂×#578	1	1	yes	characteristic
754	C₂²	—	2	4	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	4	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
764	C₄	—	2	1	no	—
765	C₄	—	2	4	no	—
766	C₄	—	2	1	no	—
767	C₄	—	2	1	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	4	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	2	no	—
776	C₄	C₃×#577	1	2	yes	—
777	C₄	C₃×#578	1	2	yes	—
778	C₄	C₃×#585	1	1	yes	characteristic
779	C₄	C₃×#585	1	1	yes	characteristic
780	C₃	#61789	1	1	yes	characteristic, direct product factor, Sylow
781	C₂	—	4	4	no	—
782	C₂	—	4	1	no	—
783	C₂	—	8	1	no	—
784	C₂	C₃×#3485	1	1	yes	characteristic
785	C₂	C₂×C₃×#577	1	1	yes	characteristic
786	C₂	C₂×C₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₃×#3511	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×#3356	C₂	semidirect
4. C₃×#3353	C₂	semidirect
5. C₃×#3342	C₂	semidirect
6. C₃×#3340	C₂	semidirect
7. C₃×#3329	C₂	semidirect
8. C₃×#3328	C₂	semidirect
9. C₃×#3299	C₂	semidirect
10. C₃×#3298	C₂	semidirect
11. C₃×#3230	C₂	semidirect
12. C₃×#3229	C₂	semidirect
13. C₃×#3201	C₂	semidirect
14. C₃×#3107	C₂	semidirect
15. C₃×#3107	C₂	semidirect
16. C₃×#3097	C₂	semidirect
17. C₃×#2979	C₂	semidirect
18. #61789	C₃	direct (N × H)
94. #3550	C₂×C₃	semidirect
96. #3356	C₂×C₃	semidirect
97. #3353	C₂×C₃	semidirect
98. #3342	C₂×C₃	semidirect
99. #3340	C₂×C₃	semidirect
100. #3329	C₂×C₃	semidirect
101. #3328	C₂×C₃	semidirect
102. #3299	C₂×C₃	semidirect
103. #3298	C₂×C₃	semidirect
104. #3230	C₂×C₃	semidirect
105. #3229	C₂×C₃	semidirect
106. #3201	C₂×C₃	semidirect
107. #3107	C₂×C₃	semidirect
108. #3107	C₂×C₃	semidirect
109. #3097	C₂×C₃	semidirect
110. #2979	C₂×C₃	semidirect
780. C₃	#61789	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×#3511	2
C₃×#3356	2
C₃×#3353	2
C₃×#3342	2
C₃×#3340	2
C₃×#3329	2
C₃×#3328	2
C₃×#3299	2
C₃×#3298	2
C₃×#3230	2
C₃×#3229	2
C₃×#3201	2
C₃×#3107	2
C₃×#3097	2
C₃×#2979	2
#61789	3

Subgroups — C3×#61789 #10680396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61789 #10680396