Subgroups — C₃×#61847 #10680454

Order 768.

1772 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#3389	C₂	1	4	yes	maximal, complemented
4	C₃×#3384	C₂	1	2	yes	maximal, complemented
5	C₃×#3380	C₂	1	2	yes	maximal, complemented
6	C₃×#3366	C₂	1	2	yes	maximal, complemented
7	C₃×#3366	C₂	1	4	yes	maximal, complemented
8	C₃×#3358	C₂	1	2	yes	maximal, complemented
9	C₃×#3241	C₂	1	4	yes	maximal, complemented
10	C₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3122	C₂	1	4	yes	maximal, complemented
13	C₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	#61847	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#562	—	2	2	no	—
18	C₃×#554	—	2	1	no	—
19	C₃×#554	—	2	2	no	—
20	C₃×#554	C₂²	1	4	yes	—
21	C₃×#554	C₂²	1	2	yes	—
22	C₃×#554	C₂²	1	2	yes	complemented
23	C₃×#554	C₂²	1	2	yes	complemented
24	C₃×#550	C₂²	1	2	yes	complemented
25	C₃×#550	C₂²	1	2	yes	complemented
26	C₃×D₄×Q₈	—	2	1	no	—
27	C₃×D₄×Q₈	C₂²	1	2	yes	—
28	C₃×#547	—	2	1	no	—
29	C₃×#547	—	2	1	no	—
30	C₃×#544	C₂²	1	2	yes	—
31	C₃×#543	—	2	2	no	—
32	C₃×#540	C₂²	1	4	yes	—
33	C₃×#537	—	2	2	no	—
34	C₃×#537	—	2	2	no	—
35	C₃×#533	C₂²	1	1	yes	characteristic
36	C₃×#533	C₂²	1	1	yes	characteristic
37	C₃×#532	C₂²	1	1	yes	characteristic
38	C₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₂²⋊Q₈	—	2	2	no	—
40	C₃×#518	C₂²	1	2	yes	—
41	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
42	C₃×#501	C₂²	1	4	yes	complemented
43	C₃×#501	C₂²	1	2	yes	complemented
44	C₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₃×#499	C₂²	1	4	yes	complemented
46	C₃×#498	C₂²	1	1	yes	characteristic, complemented
47	C₃×#490	C₂²	1	2	yes	complemented
48	C₃×#490	C₂²	1	4	yes	complemented
49	C₃×#486	C₂²	1	1	yes	characteristic, complemented
50	C₃×#486	C₂²	1	1	yes	characteristic, complemented
51	C₃×#486	C₂²	1	4	yes	complemented
52	C₃×#482	C₂²	1	4	yes	—
53	C₃×#482	C₂²	1	4	yes	—
54	C₃×#481	C₂²	1	2	yes	—
55	C₃×#480	C₂²	1	2	yes	—
56	C₃×#478	C₂²	1	4	yes	—
57	C₃×#478	C₂²	1	4	yes	—
58	C₃×#478	C₂²	1	4	yes	complemented
59	C₃×#478	C₂²	1	4	yes	complemented
60	C₃×#478	C₂²	1	4	yes	complemented
61	C₃×#476	C₂²	1	2	yes	—
62	C₃×#476	C₂²	1	4	yes	complemented
63	C₃×#476	C₂²	1	2	yes	complemented
64	C₃×#474	C₂²	1	2	yes	—
65	C₃×#474	C₂²	1	2	yes	complemented
66	C₃×#474	C₂²	1	4	yes	complemented
67	C₃×#459	C₂²	1	2	yes	—
68	C₃×#459	C₂²	1	2	yes	—
69	C₃×#459	C₂²	1	4	yes	—
70	C₃×#459	C₂²	1	4	yes	—
71	C₃×#447	C₂²	1	2	yes	—
72	C₃×#447	C₂²	1	2	yes	—
73	C₃×#446	C₂²	1	2	yes	complemented
74	C₃×#446	C₂²	1	4	yes	complemented
75	C₃×C₈×Q₈	C₂²	1	2	yes	complemented
76	C₃×#442	C₂²	1	4	yes	—
77	C₃×#442	C₂²	1	4	yes	—
78	C₃×#442	C₂²	1	4	yes	—
79	C₃×C₄×D₈	C₂²	1	2	yes	—
80	C₃×C₄×D₈	C₂²	1	4	yes	—
81	C₃×C₄×D₈	C₂²	1	2	yes	—
82	C₃×C₄×D₈	C₂²	1	4	yes	—
83	C₃×#433	C₂²	1	4	yes	—
84	C₃×#432	C₂²	1	1	yes	characteristic
85	C₃×#431	C₂²	1	1	yes	characteristic
86	#3548	C₂×C₃	1	1	yes	characteristic, complemented
87	#3501	C₂×C₃	1	1	yes	characteristic, complemented
88	#3389	C₂×C₃	1	4	yes	complemented
89	#3384	C₂×C₃	1	2	yes	complemented
90	#3380	C₂×C₃	1	2	yes	complemented
91	#3366	C₂×C₃	1	2	yes	complemented
92	#3366	C₂×C₃	1	4	yes	complemented
93	#3358	C₂×C₃	1	2	yes	complemented
94	#3241	C₂×C₃	1	4	yes	complemented
95	#3235	C₂×C₃	1	1	yes	characteristic, complemented
96	#3228	C₂×C₃	1	1	yes	characteristic, complemented
97	#3122	C₂×C₃	1	4	yes	complemented
98	#3109	C₂×C₃	1	1	yes	characteristic, complemented
99	#3100	C₂×C₃	1	1	yes	characteristic, complemented
100	#2985	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂×C₃×#41	—	2	2	no	—
102	C₂×C₃×#41	—	2	2	no	—
103	C₂×C₃×#41	—	2	1	no	—
104	C₂×C₃×#41	—	2	1	no	—
105	C₂²×C₃×Q₈	—	2	2	no	—
106	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
107	C₂³×C₃×C₄	—	2	1	no	—
108	C₂×C₃×D₈	C₂³	1	2	yes	—
109	C₂×C₃×D₈	C₂³	1	2	yes	—
110	C₂×C₃×D₈	C₂³	1	4	yes	—
111	C₃×C₄⋊Q₈	—	2	2	no	—
112	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₃×#127	C₂³	1	1	yes	characteristic
120	C₃×#127	C₂³	1	1	yes	characteristic
121	C₃×#127	C₂³	1	4	yes	—
122	C₃×#125	—	2	2	no	—
123	C₃×#125	D₄	1	2	yes	—
124	C₃×#125	C₂³	1	2	yes	—
125	C₃×#125	C₂³	1	4	yes	—
126	C₃×#125	C₂³	1	4	yes	—
127	C₃×#124	—	2	1	no	—
128	C₃×#124	—	2	1	no	—
129	C₃×#123	—	2	4	no	—
130	C₃×#123	—	2	4	no	—
131	C₃×C₂²⋊Q₈	—	2	2	no	—
132	C₃×C₂²⋊Q₈	—	2	2	no	—
133	C₃×C₂²⋊Q₈	—	2	2	no	—
134	C₃×C₂²⋊Q₈	—	2	4	no	—
135	C₃×C₂²⋊Q₈	—	2	1	no	—
136	C₃×C₂²⋊Q₈	—	2	1	no	—
137	C₃×C₂²⋊Q₈	—	2	4	no	—
138	C₃×C₂²⋊Q₈	—	2	4	no	—
139	C₃×C₂²⋊Q₈	—	2	2	no	—
140	C₃×C₂²⋊Q₈	—	2	4	no	—
141	C₃×C₂²⋊Q₈	—	2	4	no	—
142	C₃×C₂²⋊Q₈	—	2	4	no	—
143	C₃×C₂²⋊Q₈	—	2	4	no	—
144	C₃×C₂²⋊Q₈	—	2	4	no	—
145	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
146	C₃×C₂²⋊Q₈	D₄	1	2	yes	—
147	C₃×#121	—	2	1	no	—
148	C₃×#121	—	2	1	no	—
149	C₃×#121	—	2	4	no	—
150	C₃×#121	—	2	4	no	—
151	C₃×#121	—	2	2	no	—
152	C₃×#121	—	2	2	no	—
153	C₃×#121	—	2	4	no	—
154	C₃×#121	—	2	4	no	—
155	C₃×#121	C₂³	1	2	yes	—
156	C₃×#121	C₂³	1	2	yes	—
157	C₃×C₄×Q₈	—	2	1	no	—
158	C₃×C₄×Q₈	—	2	1	no	—
159	C₃×C₄×Q₈	C₂³	1	2	yes	—
160	C₃×C₄×Q₈	C₂³	1	2	yes	—
161	C₃×C₄×D₄	—	2	2	no	—
162	C₃×C₄×D₄	—	2	2	no	—
163	C₃×C₄×D₄	—	2	1	no	—
164	C₃×C₄×D₄	—	2	1	no	—
165	C₃×C₄×D₄	—	2	1	no	—
166	C₃×C₄×D₄	—	2	1	no	—
167	C₃×C₄×D₄	C₂³	1	2	yes	—
168	C₃×C₄×D₄	C₂³	1	2	yes	—
169	C₃×C₄×D₄	C₂³	1	4	yes	—
170	C₃×C₄×D₄	C₂³	1	4	yes	—
171	C₃×C₄×D₄	C₂³	1	4	yes	—
172	C₃×C₄×D₄	C₂³	1	4	yes	—
173	C₃×C₄×D₄	C₂³	1	2	yes	—
174	C₃×C₄×D₄	C₂³	1	2	yes	—
175	C₃×#117	C₂³	1	2	yes	—
176	C₃×#117	C₂³	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	—	2	4	no	—
178	C₂×C₃×C₄⋊C₄	—	2	2	no	—
179	C₂×C₃×C₄⋊C₄	—	2	2	no	—
180	C₂×C₃×C₄⋊C₄	—	2	2	no	—
181	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
184	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
185	C₃×#107	C₂³	1	2	yes	—
186	C₃×#107	C₂³	1	2	yes	—
187	C₃×#107	C₂³	1	4	yes	—
188	C₃×#107	C₂³	1	4	yes	—
189	C₃×#106	C₂³	1	4	yes	—
190	C₃×#106	C₂³	1	4	yes	—
191	C₃×#106	C₂³	1	4	yes	—
192	C₃×C₄⋊C₈	C₂³	1	2	yes	—
193	C₃×C₄⋊C₈	C₂³	1	2	yes	—
194	C₃×C₄⋊C₈	C₂³	1	4	yes	—
195	C₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₃×#102	C₂³	1	2	yes	—
197	C₃×#102	C₂³	1	2	yes	—
198	C₃×#102	C₂³	1	4	yes	—
199	C₃×#102	C₂³	1	4	yes	—
200	C₃×#102	C₂³	1	2	yes	—
201	C₃×#102	C₂³	1	4	yes	—
202	C₃×#102	C₂³	1	2	yes	—
203	C₃×#102	C₂³	1	4	yes	—
204	C₃×#102	C₂³	1	4	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×#97	C₂³	1	2	yes	—
209	C₃×#97	C₂³	1	4	yes	—
210	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
211	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
212	C₃×C₄×C₈	C₂³	1	4	yes	—
213	#562	—	2	2	no	—
214	#554	—	2	1	no	—
215	#554	—	2	2	no	—
216	#554	C₂²×C₃	1	2	yes	—
217	#554	C₂²×C₃	1	4	yes	—
218	#554	C₂²×C₃	1	2	yes	complemented
219	#554	C₂²×C₃	1	2	yes	complemented
220	#550	C₂²×C₃	1	2	yes	complemented
221	#550	C₂²×C₃	1	2	yes	complemented
222	D₄×Q₈	—	2	1	no	—
223	D₄×Q₈	C₂²×C₃	1	2	yes	—
224	#547	—	2	1	no	—
225	#547	—	2	1	no	—
226	#544	C₂²×C₃	1	2	yes	—
227	#543	—	2	2	no	—
228	#540	C₂²×C₃	1	4	yes	—
229	#537	—	2	2	no	—
230	#537	—	2	2	no	—
231	#533	C₂²×C₃	1	1	yes	characteristic
232	#533	C₂²×C₃	1	1	yes	characteristic
233	#532	C₂²×C₃	1	1	yes	characteristic
234	#532	C₂²×C₃	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	—	2	2	no	—
236	#518	C₂²×C₃	1	2	yes	—
237	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
238	#501	C₂²×C₃	1	4	yes	complemented
239	#501	C₂²×C₃	1	2	yes	complemented
240	#500	C₂²×C₃	1	1	yes	characteristic, complemented
241	#499	C₂²×C₃	1	4	yes	complemented
242	#498	C₂²×C₃	1	1	yes	characteristic, complemented
243	#490	C₂²×C₃	1	2	yes	complemented
244	#490	C₂²×C₃	1	4	yes	complemented
245	#486	C₂²×C₃	1	1	yes	characteristic, complemented
246	#486	C₂²×C₃	1	4	yes	complemented
247	#486	C₂²×C₃	1	1	yes	characteristic, complemented
248	#482	C₂²×C₃	1	4	yes	—
249	#482	C₂²×C₃	1	4	yes	—
250	#481	C₂²×C₃	1	2	yes	—
251	#480	C₂²×C₃	1	2	yes	—
252	#478	C₂²×C₃	1	4	yes	—
253	#478	C₂²×C₃	1	4	yes	—
254	#478	C₂²×C₃	1	4	yes	complemented
255	#478	C₂²×C₃	1	4	yes	complemented
256	#478	C₂²×C₃	1	4	yes	complemented
257	#476	C₂²×C₃	1	2	yes	—
258	#476	C₂²×C₃	1	2	yes	complemented
259	#476	C₂²×C₃	1	4	yes	complemented
260	#474	C₂²×C₃	1	2	yes	—
261	#474	C₂²×C₃	1	2	yes	complemented
262	#474	C₂²×C₃	1	4	yes	complemented
263	#459	C₂²×C₃	1	2	yes	—
264	#459	C₂²×C₃	1	2	yes	—
265	#459	C₂²×C₃	1	4	yes	—
266	#459	C₂²×C₃	1	4	yes	—
267	#447	C₂²×C₃	1	2	yes	—
268	#447	C₂²×C₃	1	2	yes	—
269	#446	C₂²×C₃	1	2	yes	complemented
270	#446	C₂²×C₃	1	4	yes	complemented
271	C₈×Q₈	C₂²×C₃	1	2	yes	complemented
272	#442	C₂²×C₃	1	4	yes	—
273	#442	C₂²×C₃	1	4	yes	—
274	#442	C₂²×C₃	1	4	yes	—
275	C₄×D₈	C₂²×C₃	1	2	yes	—
276	C₄×D₈	C₂²×C₃	1	2	yes	—
277	C₄×D₈	C₂²×C₃	1	4	yes	—
278	C₄×D₈	C₂²×C₃	1	4	yes	—
279	#433	C₂²×C₃	1	4	yes	—
280	#432	C₂²×C₃	1	1	yes	characteristic
281	#431	C₂²×C₃	1	1	yes	characteristic
282	C₂⁴×C₃	—	2	1	no	—
283	C₃×#41	—	8	2	no	—
284	C₃×#41	—	8	2	no	—
285	C₃×#41	—	8	4	no	—
286	C₃×#41	—	8	4	no	—
287	C₂×C₃×Q₈	—	2	1	no	—
288	C₂×C₃×Q₈	—	2	1	no	—
289	C₂×C₃×Q₈	—	2	1	no	—
290	C₂×C₃×Q₈	—	2	1	no	—
291	C₂×C₃×Q₈	—	2	4	no	—
292	C₂×C₃×Q₈	—	8	4	no	—
293	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
294	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
295	C₂×C₃×D₄	—	2	4	no	—
296	C₂×C₃×D₄	—	2	2	no	—
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	—	2	1	no	—
299	C₂×C₃×D₄	—	2	1	no	—
300	C₂×C₃×D₄	—	2	1	no	—
301	C₂×C₃×D₄	—	2	4	no	—
302	C₂×C₃×D₄	—	2	4	no	—
303	C₂×C₃×D₄	—	2	1	no	—
304	C₂×C₃×D₄	—	2	1	no	—
305	C₂×C₃×D₄	C₂⁴	1	2	yes	—
306	C₂×C₃×D₄	C₂⁴	1	2	yes	—
307	C₂×C₃×D₄	C₂⁴	1	2	yes	—
308	C₂²×C₃×C₄	—	2	1	no	—
309	C₂²×C₃×C₄	—	2	2	no	—
310	C₂²×C₃×C₄	—	2	2	no	—
311	C₂²×C₃×C₄	—	2	2	no	—
312	C₂²×C₃×C₄	—	2	4	no	—
313	C₂²×C₃×C₄	—	2	4	no	—
314	C₂²×C₃×C₄	—	2	2	no	—
315	C₂²×C₃×C₄	—	2	4	no	—
316	C₂²×C₃×C₄	—	2	4	no	—
317	C₂²×C₃×C₄	—	8	2	no	—
318	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
321	C₃×D₈	—	2	4	no	—
322	C₃×D₈	—	2	4	no	—
323	C₃×D₈	—	2	8	no	—
324	C₂×C₃×C₈	C₂⁴	1	2	yes	—
325	C₂×C₃×C₈	C₂⁴	1	2	yes	—
326	C₂×C₃×C₈	C₂⁴	1	4	yes	—
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	4	no	—
332	C₃×C₄⋊C₄	—	2	4	no	—
333	C₃×C₄⋊C₄	—	2	4	no	—
334	C₃×C₄⋊C₄	—	2	4	no	—
335	C₃×C₄⋊C₄	—	2	4	no	—
336	C₃×C₄⋊C₄	—	2	1	no	—
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	1	no	—
339	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
340	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
341	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
342	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
343	C₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
344	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
345	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
346	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
347	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
349	C₃×C₄⋊C₄	C₂⁴	1	2	yes	—
350	C₃×C₂²⋊C₄	—	2	2	no	—
351	C₃×C₂²⋊C₄	—	2	4	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	2	2	no	—
354	C₃×C₂²⋊C₄	—	2	2	no	—
355	C₃×C₂²⋊C₄	—	2	2	no	—
356	C₃×C₂²⋊C₄	—	2	2	no	—
357	C₃×C₂²⋊C₄	—	2	4	no	—
358	C₃×C₂²⋊C₄	—	2	4	no	—
359	C₃×C₂²⋊C₄	—	2	2	no	—
360	C₃×C₂²⋊C₄	—	2	2	no	—
361	C₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
362	C₃×C₄²	—	2	2	no	—
363	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
364	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
365	C₃×C₄²	C₂⁴	1	1	yes	characteristic
366	C₃×C₄²	C₂⁴	1	4	yes	—
367	C₃×C₄²	C₂⁴	1	1	yes	characteristic
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂²×Q₈	—	2	2	no	—
373	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
374	C₂³×C₄	—	2	1	no	—
375	C₂×D₈	C₂³×C₃	1	2	yes	—
376	C₂×D₈	C₂³×C₃	1	2	yes	—
377	C₂×D₈	C₂³×C₃	1	4	yes	—
378	C₄⋊Q₈	—	2	2	no	—
379	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
380	C₄⋊Q₈	C₃×D₄	1	1	yes	characteristic
381	C₄⋊Q₈	C₂³×C₃	1	1	yes	characteristic
382	C₄⋊Q₈	C₂³×C₃	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	4	yes	—
386	#127	C₂³×C₃	1	1	yes	characteristic
387	#127	C₂³×C₃	1	1	yes	characteristic
388	#127	C₂³×C₃	1	4	yes	—
389	#125	—	2	2	no	—
390	#125	C₃×D₄	1	2	yes	—
391	#125	C₂³×C₃	1	2	yes	—
392	#125	C₂³×C₃	1	4	yes	—
393	#125	C₂³×C₃	1	4	yes	—
394	#124	—	2	1	no	—
395	#124	—	2	1	no	—
396	#123	—	2	4	no	—
397	#123	—	2	4	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	4	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	—	2	4	no	—
406	C₂²⋊Q₈	—	2	4	no	—
407	C₂²⋊Q₈	—	2	4	no	—
408	C₂²⋊Q₈	—	2	4	no	—
409	C₂²⋊Q₈	—	2	4	no	—
410	C₂²⋊Q₈	—	2	4	no	—
411	C₂²⋊Q₈	—	2	4	no	—
412	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
413	C₂²⋊Q₈	C₃×D₄	1	2	yes	—
414	#121	—	2	1	no	—
415	#121	—	2	1	no	—
416	#121	—	2	2	no	—
417	#121	—	2	2	no	—
418	#121	—	2	4	no	—
419	#121	—	2	4	no	—
420	#121	—	2	4	no	—
421	#121	—	2	4	no	—
422	#121	C₂³×C₃	1	2	yes	—
423	#121	C₂³×C₃	1	2	yes	—
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×Q₈	C₂³×C₃	1	2	yes	—
427	C₄×Q₈	C₂³×C₃	1	2	yes	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	2	1	no	—
434	C₄×D₄	C₂³×C₃	1	2	yes	—
435	C₄×D₄	C₂³×C₃	1	2	yes	—
436	C₄×D₄	C₂³×C₃	1	4	yes	—
437	C₄×D₄	C₂³×C₃	1	4	yes	—
438	C₄×D₄	C₂³×C₃	1	2	yes	—
439	C₄×D₄	C₂³×C₃	1	2	yes	—
440	C₄×D₄	C₂³×C₃	1	4	yes	—
441	C₄×D₄	C₂³×C₃	1	4	yes	—
442	#117	C₂³×C₃	1	2	yes	—
443	#117	C₂³×C₃	1	2	yes	—
444	C₂×C₄⋊C₄	—	2	4	no	—
445	C₂×C₄⋊C₄	—	2	2	no	—
446	C₂×C₄⋊C₄	—	2	2	no	—
447	C₂×C₄⋊C₄	—	2	2	no	—
448	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	—	2	4	no	—
451	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
452	#107	C₂³×C₃	1	2	yes	—
453	#107	C₂³×C₃	1	2	yes	—
454	#107	C₂³×C₃	1	4	yes	—
455	#107	C₂³×C₃	1	4	yes	—
456	#106	C₂³×C₃	1	4	yes	—
457	#106	C₂³×C₃	1	4	yes	—
458	#106	C₂³×C₃	1	4	yes	—
459	C₄⋊C₈	C₂³×C₃	1	2	yes	—
460	C₄⋊C₈	C₂³×C₃	1	2	yes	—
461	C₄⋊C₈	C₂³×C₃	1	4	yes	—
462	C₄⋊C₈	C₂³×C₃	1	4	yes	—
463	#102	C₂³×C₃	1	2	yes	—
464	#102	C₂³×C₃	1	2	yes	—
465	#102	C₂³×C₃	1	4	yes	—
466	#102	C₂³×C₃	1	4	yes	—
467	#102	C₂³×C₃	1	2	yes	—
468	#102	C₂³×C₃	1	4	yes	—
469	#102	C₂³×C₃	1	2	yes	—
470	#102	C₂³×C₃	1	4	yes	—
471	#102	C₂³×C₃	1	4	yes	—
472	#102	C₂³×C₃	1	4	yes	—
473	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
474	C₂²⋊C₈	C₂³×C₃	1	2	yes	—
475	#97	C₂³×C₃	1	2	yes	—
476	#97	C₂³×C₃	1	4	yes	—
477	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
478	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
479	C₄×C₈	C₂³×C₃	1	4	yes	—
480	C₂³×C₃	—	2	4	no	—
481	C₂³×C₃	—	2	2	no	—
482	C₂³×C₃	—	2	2	no	—
483	C₂³×C₃	—	2	2	no	—
484	C₂³×C₃	—	8	1	no	—
485	C₂³×C₃	—	8	1	no	—
486	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
487	C₃×Q₈	—	2	4	no	—
488	C₃×Q₈	—	4	2	no	—
489	C₃×Q₈	—	4	2	no	—
490	C₃×Q₈	—	8	1	no	—
491	C₃×Q₈	—	8	4	no	—
492	C₃×Q₈	—	8	1	no	—
493	C₃×Q₈	—	8	1	no	—
494	C₃×D₄	—	2	4	no	—
495	C₃×D₄	—	2	2	no	—
496	C₃×D₄	—	2	2	no	—
497	C₃×D₄	—	2	4	no	—
498	C₃×D₄	—	2	2	no	—
499	C₃×D₄	—	4	2	no	—
500	C₃×D₄	—	4	2	no	—
501	C₃×D₄	—	8	1	no	—
502	C₃×D₄	—	8	4	no	—
503	C₃×D₄	—	8	1	no	—
504	C₃×D₄	—	8	4	no	—
505	C₃×D₄	—	8	2	no	—
506	C₃×D₄	—	8	2	no	—
507	C₃×D₄	2₋¹⁺⁴	1	4	yes	—
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	—	4	1	no	—
516	C₂×C₃×C₄	—	4	4	no	—
517	C₂×C₃×C₄	—	4	4	no	—
518	C₂×C₃×C₄	—	4	4	no	—
519	C₂×C₃×C₄	—	8	4	no	—
520	C₂×C₃×C₄	—	8	2	no	—
521	C₂×C₃×C₄	—	8	4	no	—
522	C₂×C₃×C₄	—	8	4	no	—
523	C₂×C₃×C₄	—	8	4	no	—
524	C₂×C₃×C₄	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
530	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
531	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
533	C₃×C₈	—	2	2	no	—
534	C₃×C₈	—	2	2	no	—
535	C₃×C₈	—	2	4	no	—
536	C₂⁴	—	2	1	no	—
537	#41	—	8	2	no	—
538	#41	—	8	2	no	—
539	#41	—	8	4	no	—
540	#41	—	8	4	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	8	4	no	—
547	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
548	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	C₂⁴×C₃	1	2	yes	—
560	C₂×D₄	C₂⁴×C₃	1	2	yes	—
561	C₂×D₄	C₂⁴×C₃	1	2	yes	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	8	2	no	—
572	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
573	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
575	D₈	—	2	4	no	—
576	D₈	—	2	4	no	—
577	D₈	—	2	8	no	—
578	C₂×C₈	C₂⁴×C₃	1	2	yes	—
579	C₂×C₈	C₂⁴×C₃	1	2	yes	—
580	C₂×C₈	C₂⁴×C₃	1	4	yes	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
594	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
595	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
596	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
597	C₄⋊C₄	C₂×C₃×D₄	1	2	yes	—
598	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
599	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
601	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
602	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
603	C₄⋊C₄	C₂⁴×C₃	1	2	yes	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	C₂×C₃×D₄	1	4	yes	—
616	C₄²	—	2	2	no	—
617	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
618	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
619	C₄²	C₂⁴×C₃	1	1	yes	characteristic
620	C₄²	C₂⁴×C₃	1	4	yes	—
621	C₄²	C₂⁴×C₃	1	1	yes	characteristic
622	C₂²×C₃	—	2	1	no	—
623	C₂²×C₃	—	2	1	no	—
624	C₂²×C₃	—	2	4	no	—
625	C₂²×C₃	—	2	1	no	—
626	C₂²×C₃	—	4	2	no	—
627	C₂²×C₃	—	4	2	no	—
628	C₂²×C₃	—	4	2	no	—
629	C₂²×C₃	—	4	2	no	—
630	C₂²×C₃	—	4	2	no	—
631	C₂²×C₃	—	4	2	no	—
632	C₂²×C₃	—	4	2	no	—
633	C₂²×C₃	—	4	2	no	—
634	C₂²×C₃	—	8	4	no	—
635	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
636	C₃×C₄	—	2	1	no	—
637	C₃×C₄	—	2	1	no	—
638	C₃×C₄	—	2	4	no	—
639	C₃×C₄	—	2	1	no	—
640	C₃×C₄	—	2	1	no	—
641	C₃×C₄	—	2	4	no	—
642	C₃×C₄	—	4	2	no	—
643	C₃×C₄	—	4	2	no	—
644	C₃×C₄	—	4	2	no	—
645	C₃×C₄	—	4	2	no	—
646	C₃×C₄	—	4	2	no	—
647	C₃×C₄	#576	1	2	yes	—
648	C₃×C₄	C₂×2₋¹⁺⁴	1	2	yes	—
649	C₂³	—	2	4	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	8	1	no	—
654	C₂³	—	8	1	no	—
655	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
656	Q₈	—	2	4	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	8	4	no	—
660	Q₈	—	8	1	no	—
661	Q₈	—	8	1	no	—
662	Q₈	—	8	1	no	—
663	D₄	—	2	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	4	2	no	—
669	D₄	—	4	2	no	—
670	D₄	—	8	1	no	—
671	D₄	—	8	4	no	—
672	D₄	—	8	1	no	—
673	D₄	—	8	4	no	—
674	D₄	—	8	2	no	—
675	D₄	—	8	2	no	—
676	D₄	C₃×2₋¹⁺⁴	1	4	yes	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	8	2	no	—
689	C₂×C₄	—	8	4	no	—
690	C₂×C₄	—	8	4	no	—
691	C₂×C₄	—	8	4	no	—
692	C₂×C₄	—	8	4	no	—
693	C₂×C₄	—	8	1	no	—
694	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
695	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
696	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
697	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
698	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
699	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
700	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
701	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
702	C₈	—	2	2	no	—
703	C₈	—	2	2	no	—
704	C₈	—	2	4	no	—
705	C₂×C₃	—	4	1	no	—
706	C₂×C₃	—	4	4	no	—
707	C₂×C₃	—	8	2	no	—
708	C₂×C₃	—	8	2	no	—
709	C₂×C₃	#3486	1	1	yes	characteristic
710	C₂×C₃	C₂×#576	1	1	yes	characteristic
711	C₂×C₃	#3585	1	1	yes	characteristic
712	C₂²	—	2	1	no	—
713	C₂²	—	2	4	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	8	4	no	—
725	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	4	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	4	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	C₃×#576	1	2	yes	—
738	C₄	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
739	C₃	#61847	1	1	yes	characteristic, direct product factor, Sylow
740	C₂	—	4	1	no	—
741	C₂	—	4	4	no	—
742	C₂	—	8	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₃×#3486	1	1	yes	characteristic
745	C₂	C₂×C₃×#576	1	1	yes	characteristic
746	C₂	C₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3548	C₂	semidirect
2. C₃×#3501	C₂	semidirect
3. C₃×#3389	C₂	semidirect
4. C₃×#3384	C₂	semidirect
5. C₃×#3380	C₂	semidirect
6. C₃×#3366	C₂	semidirect
7. C₃×#3366	C₂	semidirect
8. C₃×#3358	C₂	semidirect
9. C₃×#3241	C₂	semidirect
10. C₃×#3235	C₂	semidirect
11. C₃×#3228	C₂	semidirect
12. C₃×#3122	C₂	semidirect
13. C₃×#3109	C₂	semidirect
14. C₃×#3100	C₂	semidirect
15. C₃×#2985	C₂	semidirect
16. #61847	C₃	direct (N × H)
22. C₃×#554	C₂²	semidirect
23. C₃×#554	C₂²	semidirect
24. C₃×#550	C₂²	semidirect
25. C₃×#550	C₂²	semidirect
42. C₃×#501	C₂²	semidirect
43. C₃×#501	C₂²	semidirect
44. C₃×#500	C₂²	semidirect
45. C₃×#499	C₂²	semidirect
46. C₃×#498	C₂²	semidirect
47. C₃×#490	C₂²	semidirect
48. C₃×#490	C₂²	semidirect
49. C₃×#486	C₂²	semidirect
50. C₃×#486	C₂²	semidirect
51. C₃×#486	C₂²	semidirect
58. C₃×#478	C₂²	semidirect
59. C₃×#478	C₂²	semidirect
60. C₃×#478	C₂²	semidirect
62. C₃×#476	C₂²	semidirect
63. C₃×#476	C₂²	semidirect
65. C₃×#474	C₂²	semidirect
66. C₃×#474	C₂²	semidirect
73. C₃×#446	C₂²	semidirect
74. C₃×#446	C₂²	semidirect
75. C₃×C₈×Q₈	C₂²	semidirect
86. #3548	C₂×C₃	semidirect
87. #3501	C₂×C₃	semidirect
88. #3389	C₂×C₃	semidirect
89. #3384	C₂×C₃	semidirect
90. #3380	C₂×C₃	semidirect
91. #3366	C₂×C₃	semidirect
92. #3366	C₂×C₃	semidirect
93. #3358	C₂×C₃	semidirect
94. #3241	C₂×C₃	semidirect
95. #3235	C₂×C₃	semidirect
96. #3228	C₂×C₃	semidirect
97. #3122	C₂×C₃	semidirect
98. #3109	C₂×C₃	semidirect
99. #3100	C₂×C₃	semidirect
100. #2985	C₂×C₃	semidirect
218. #554	C₂²×C₃	semidirect
219. #554	C₂²×C₃	semidirect
220. #550	C₂²×C₃	semidirect
221. #550	C₂²×C₃	semidirect
238. #501	C₂²×C₃	semidirect
239. #501	C₂²×C₃	semidirect
240. #500	C₂²×C₃	semidirect
241. #499	C₂²×C₃	semidirect
242. #498	C₂²×C₃	semidirect
243. #490	C₂²×C₃	semidirect
244. #490	C₂²×C₃	semidirect
245. #486	C₂²×C₃	semidirect
246. #486	C₂²×C₃	semidirect
247. #486	C₂²×C₃	semidirect
254. #478	C₂²×C₃	semidirect
255. #478	C₂²×C₃	semidirect
256. #478	C₂²×C₃	semidirect
258. #476	C₂²×C₃	semidirect
259. #476	C₂²×C₃	semidirect
261. #474	C₂²×C₃	semidirect
262. #474	C₂²×C₃	semidirect
269. #446	C₂²×C₃	semidirect
270. #446	C₂²×C₃	semidirect
271. C₈×Q₈	C₂²×C₃	semidirect
739. C₃	#61847	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×#3548	2
C₃×#3501	2
C₃×#3389	2
C₃×#3384	2
C₃×#3380	2
C₃×#3366	2
C₃×#3358	2
C₃×#3241	2
C₃×#3235	2
C₃×#3228	2
C₃×#3122	2
C₃×#3109	2
C₃×#3100	2
C₃×#2985	2
#61847	3

Subgroups — C3×#61847 #10680454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#61847 #10680454