Subgroups — C₃×#34393 #10653000

Order 768.

2510 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₃×#2377	C₂	1	4	yes	maximal, complemented
3	C₃×#2366	C₂	1	2	yes	maximal, complemented
4	C₃×#2365	C₂	1	2	yes	maximal, complemented
5	C₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₃×#2349	C₂	1	2	yes	maximal, complemented
7	C₃×#2341	C₂	1	2	yes	maximal, complemented
8	C₃×#2339	C₂	1	2	yes	maximal, complemented
9	C₃×#2326	C₂	1	4	yes	maximal, complemented
10	C₃×#2324	C₂	1	4	yes	maximal, complemented
11	C₃×#2318	C₂	1	4	yes	maximal, complemented
12	C₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
14	#34393	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂²×C₃×#41	C₂²	1	2	yes	—
16	C₃×#532	C₄	1	16	yes	complemented
17	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₃×#124	C₂²	1	2	yes	—
20	C₂×C₃×#121	C₂²	1	2	yes	—
21	C₂×C₃×#121	C₂²	1	2	yes	—
22	C₂×C₃×C₄×Q₈	C₂²	1	4	yes	—
23	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
24	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
25	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
26	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
27	C₂×C₃×#117	C₂²	1	2	yes	—
28	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
29	C₃×#391	C₂²	1	4	yes	—
30	C₃×#390	C₂²	1	4	yes	—
31	C₃×#390	C₂²	1	4	yes	—
32	C₃×#390	C₂²	1	8	yes	—
33	C₃×#389	C₂²	1	4	yes	—
34	C₃×#388	C₂²	1	8	yes	—
35	C₃×#388	C₂²	1	8	yes	—
36	C₃×#387	C₂²	1	8	yes	—
37	C₃×#386	C₂²	1	8	yes	—
38	C₃×#386	C₂²	1	8	yes	—
39	C₃×#385	C₂²	1	8	yes	—
40	C₃×#385	C₂²	1	8	yes	—
41	C₃×#384	C₂²	1	2	yes	—
42	C₃×#383	C₂²	1	2	yes	—
43	C₃×#382	C₂²	1	1	yes	characteristic
44	C₃×#382	C₂²	1	1	yes	characteristic
45	C₃×#382	C₂²	1	2	yes	—
46	C₃×#381	C₂²	1	2	yes	—
47	C₃×#381	C₂²	1	4	yes	—
48	C₃×#380	C₂²	1	2	yes	—
49	C₃×#380	C₂²	1	2	yes	—
50	C₃×#380	C₂²	1	1	yes	characteristic
51	C₃×#380	C₂²	1	1	yes	characteristic
52	C₃×#380	C₂²	1	4	yes	—
53	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
54	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
55	C₃×C₄×C₄⋊C₄	C₂²	1	4	yes	—
56	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
57	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
58	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
59	C₃×#376	C₂²	1	2	yes	—
60	C₂×C₃×#95	C₂²	1	4	yes	—
61	C₂×#532	C₂×C₃	1	1	yes	characteristic
62	#2377	C₂×C₃	1	4	yes	complemented
63	#2366	C₂×C₃	1	2	yes	complemented
64	#2365	C₂×C₃	1	2	yes	complemented
65	#2357	C₂×C₃	1	2	yes	complemented
66	#2349	C₂×C₃	1	2	yes	complemented
67	#2341	C₂×C₃	1	2	yes	complemented
68	#2339	C₂×C₃	1	2	yes	complemented
69	#2326	C₂×C₃	1	4	yes	complemented
70	#2324	C₂×C₃	1	4	yes	complemented
71	#2318	C₂×C₃	1	4	yes	complemented
72	#2285	C₂×C₃	1	1	yes	characteristic, complemented
73	#2283	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×C₃×#41	—	4	8	no	—
75	C₂×C₃×#41	C₂×C₄	1	16	yes	complemented
76	C₂²×C₃×Q₈	C₂³	1	2	yes	—
77	C₂²×C₃×D₄	C₂³	1	2	yes	—
78	C₂²×C₃×D₄	C₂³	1	2	yes	—
79	C₂²×C₃×D₄	C₂³	1	4	yes	—
80	C₂²×C₃×D₄	C₂³	1	2	yes	—
81	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
82	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
83	C₂³×C₃×C₄	C₂³	1	8	yes	—
84	C₂³×C₃×C₄	C₂³	1	4	yes	—
85	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
86	C₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
87	C₃×#127	C₂×C₄	1	8	yes	—
88	C₃×#124	C₂×C₄	1	16	yes	complemented
89	C₃×#121	C₂×C₄	1	16	yes	complemented
90	C₃×#121	C₂×C₄	1	16	yes	complemented
91	C₃×C₄×Q₈	—	4	8	no	—
92	C₃×C₄×D₄	—	4	8	no	—
93	C₃×C₄×D₄	—	4	8	no	—
94	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
95	C₃×C₄×D₄	C₂×C₄	1	16	yes	complemented
96	C₃×#117	—	4	4	no	—
97	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
103	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
114	C₂×C₃×C₄²	C₂×C₄	1	8	yes	complemented
115	C₂×C₃×C₄²	C₂³	1	4	yes	—
116	C₂×C₃×C₄²	C₂³	1	4	yes	—
117	C₂×C₃×C₄²	C₂³	1	8	yes	—
118	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
120	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
122	C₃×#95	C₂³	1	2	yes	—
123	C₃×#95	C₂³	1	2	yes	—
124	C₃×#95	C₂³	1	8	yes	—
125	C₃×#95	C₂³	1	4	yes	—
126	C₃×#95	C₂³	1	2	yes	—
127	C₃×#95	C₂³	1	2	yes	—
128	C₃×#95	C₂³	1	2	yes	—
129	C₃×#95	C₂³	1	2	yes	—
130	C₃×#95	C₂³	1	4	yes	—
131	C₃×#95	C₂³	1	4	yes	—
132	C₃×#95	C₂³	1	8	yes	—
133	C₂²×#41	C₂²×C₃	1	2	yes	—
134	#532	C₃×C₄	1	16	yes	complemented
135	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
136	C₂×#127	C₂²×C₃	1	1	yes	characteristic
137	C₂×#124	C₂²×C₃	1	2	yes	—
138	C₂×#121	C₂²×C₃	1	2	yes	—
139	C₂×#121	C₂²×C₃	1	2	yes	—
140	C₂×C₄×Q₈	C₂²×C₃	1	4	yes	—
141	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
142	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
143	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
144	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
145	C₂×#117	C₂²×C₃	1	2	yes	—
146	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
147	#391	C₂²×C₃	1	4	yes	—
148	#390	C₂²×C₃	1	8	yes	—
149	#390	C₂²×C₃	1	4	yes	—
150	#390	C₂²×C₃	1	4	yes	—
151	#389	C₂²×C₃	1	4	yes	—
152	#388	C₂²×C₃	1	8	yes	—
153	#388	C₂²×C₃	1	8	yes	—
154	#387	C₂²×C₃	1	8	yes	—
155	#386	C₂²×C₃	1	8	yes	—
156	#386	C₂²×C₃	1	8	yes	—
157	#385	C₂²×C₃	1	8	yes	—
158	#385	C₂²×C₃	1	8	yes	—
159	#384	C₂²×C₃	1	2	yes	—
160	#383	C₂²×C₃	1	2	yes	—
161	#382	C₂²×C₃	1	2	yes	—
162	#382	C₂²×C₃	1	1	yes	characteristic
163	#382	C₂²×C₃	1	1	yes	characteristic
164	#381	C₂²×C₃	1	4	yes	—
165	#381	C₂²×C₃	1	2	yes	—
166	#380	C₂²×C₃	1	4	yes	—
167	#380	C₂²×C₃	1	2	yes	—
168	#380	C₂²×C₃	1	1	yes	characteristic
169	#380	C₂²×C₃	1	1	yes	characteristic
170	#380	C₂²×C₃	1	2	yes	—
171	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
172	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
173	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
174	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
175	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
176	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
177	#376	C₂²×C₃	1	2	yes	—
178	C₂×#95	C₂²×C₃	1	4	yes	—
179	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
180	C₂⁴×C₃	C₂⁴	1	4	yes	—
181	C₃×#41	—	4	32	no	—
182	C₂×C₃×Q₈	—	2	8	no	—
183	C₂×C₃×Q₈	C₂²×C₄	1	8	yes	—
184	C₂×C₃×D₄	—	2	4	no	—
185	C₂×C₃×D₄	—	2	8	no	—
186	C₂×C₃×D₄	—	2	4	no	—
187	C₂×C₃×D₄	—	4	4	no	—
188	C₂×C₃×D₄	—	4	8	no	—
189	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
190	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
191	C₂×C₃×D₄	C₂²×C₄	1	8	yes	—
192	C₂×C₃×D₄	C₂²×C₄	1	16	yes	—
193	C₂²×C₃×C₄	—	2	2	no	—
194	C₂²×C₃×C₄	—	2	4	no	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	—	4	2	no	—
197	C₂²×C₃×C₄	—	4	8	no	—
198	C₂²×C₃×C₄	—	4	8	no	—
199	C₂²×C₃×C₄	—	4	8	no	—
200	C₂²×C₃×C₄	—	4	8	no	—
201	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
202	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
203	C₂²×C₃×C₄	C₂²×C₄	1	4	yes	—
204	C₂²×C₃×C₄	C₂²×C₄	1	16	yes	—
205	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
206	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
207	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
208	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
209	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
210	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
211	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
214	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
216	C₃×C₄⋊C₄	—	2	4	no	—
217	C₃×C₄⋊C₄	—	2	4	no	—
218	C₃×C₄⋊C₄	—	2	4	no	—
219	C₃×C₄⋊C₄	—	2	4	no	—
220	C₃×C₄⋊C₄	—	4	4	no	—
221	C₃×C₄⋊C₄	—	4	4	no	—
222	C₃×C₄⋊C₄	—	4	8	no	—
223	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
224	C₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
225	C₃×C₂²⋊C₄	—	4	8	no	—
226	C₃×C₂²⋊C₄	—	4	4	no	—
227	C₃×C₂²⋊C₄	—	4	2	no	—
228	C₃×C₂²⋊C₄	—	4	2	no	—
229	C₃×C₂²⋊C₄	—	4	8	no	—
230	C₃×C₂²⋊C₄	—	4	8	no	—
231	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
232	C₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
233	C₃×C₄²	—	2	8	no	—
234	C₃×C₄²	—	2	8	no	—
235	C₃×C₄²	—	4	8	no	—
236	C₃×C₄²	C₂²×C₄	1	4	yes	—
237	C₃×C₄²	C₂²×C₄	1	4	yes	—
238	C₃×C₄²	C₂²×C₄	1	4	yes	—
239	C₃×C₄²	C₂²×C₄	1	4	yes	—
240	C₂×#41	—	4	8	no	—
241	C₂×#41	C₂×C₃×C₄	1	16	yes	complemented
242	C₂²×Q₈	C₂³×C₃	1	2	yes	—
243	C₂²×D₄	C₂³×C₃	1	2	yes	—
244	C₂²×D₄	C₂³×C₃	1	2	yes	—
245	C₂²×D₄	C₂³×C₃	1	2	yes	—
246	C₂²×D₄	C₂³×C₃	1	4	yes	—
247	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₃	1	8	yes	—
250	C₂³×C₄	C₂³×C₃	1	4	yes	—
251	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
252	C₄⋊Q₈	C₂×C₃×C₄	1	8	yes	complemented
253	#127	C₂×C₃×C₄	1	8	yes	—
254	#124	C₂×C₃×C₄	1	16	yes	complemented
255	#121	C₂×C₃×C₄	1	16	yes	complemented
256	#121	C₂×C₃×C₄	1	16	yes	complemented
257	C₄×Q₈	—	4	8	no	—
258	C₄×D₄	—	4	8	no	—
259	C₄×D₄	—	4	8	no	—
260	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
261	C₄×D₄	C₂×C₃×C₄	1	16	yes	complemented
262	#117	—	4	4	no	—
263	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
269	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
280	C₂×C₄²	C₂×C₃×C₄	1	8	yes	complemented
281	C₂×C₄²	C₂³×C₃	1	4	yes	—
282	C₂×C₄²	C₂³×C₃	1	4	yes	—
283	C₂×C₄²	C₂³×C₃	1	8	yes	—
284	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
288	#95	C₂³×C₃	1	2	yes	—
289	#95	C₂³×C₃	1	2	yes	—
290	#95	C₂³×C₃	1	8	yes	—
291	#95	C₂³×C₃	1	4	yes	—
292	#95	C₂³×C₃	1	2	yes	—
293	#95	C₂³×C₃	1	2	yes	—
294	#95	C₂³×C₃	1	2	yes	—
295	#95	C₂³×C₃	1	2	yes	—
296	#95	C₂³×C₃	1	4	yes	—
297	#95	C₂³×C₃	1	4	yes	—
298	#95	C₂³×C₃	1	8	yes	—
299	C₂³×C₃	—	2	1	no	—
300	C₂³×C₃	—	2	4	no	—
301	C₂³×C₃	—	2	8	no	—
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	2	1	no	—
304	C₂³×C₃	—	2	4	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	8	no	—
307	C₂³×C₃	C₂³×C₄	1	8	yes	—
308	C₂³×C₃	C₂³×C₄	1	2	yes	—
309	C₂³×C₃	C₂⁵	1	1	yes	characteristic
310	C₃×Q₈	—	2	16	no	—
311	C₃×D₄	—	2	16	no	—
312	C₃×D₄	—	2	16	no	—
313	C₃×D₄	—	4	8	no	—
314	C₃×D₄	—	4	16	no	—
315	C₂×C₃×C₄	—	2	8	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	8	no	—
322	C₂×C₃×C₄	—	2	8	no	—
323	C₂×C₃×C₄	—	2	4	no	—
324	C₂×C₃×C₄	—	2	4	no	—
325	C₂×C₃×C₄	—	2	4	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	2	4	no	—
328	C₂×C₃×C₄	—	2	4	no	—
329	C₂×C₃×C₄	—	2	4	no	—
330	C₂×C₃×C₄	—	2	4	no	—
331	C₂×C₃×C₄	—	2	4	no	—
332	C₂×C₃×C₄	—	2	4	no	—
333	C₂×C₃×C₄	—	2	4	no	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	4	4	no	—
336	C₂×C₃×C₄	—	4	16	no	—
337	C₂×C₃×C₄	—	8	16	no	—
338	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
339	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
340	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
341	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
342	C₂×C₃×C₄	C₂³×C₄	1	8	yes	—
343	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
344	C₂×C₃×C₄	C₂³×C₄	1	2	yes	—
345	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
346	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
347	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
348	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
349	C₂⁴	C₂⁴×C₃	1	4	yes	—
350	#41	—	4	32	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂×Q₈	C₂²×C₃×C₄	1	8	yes	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	4	8	no	—
357	C₂×D₄	—	4	4	no	—
358	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
359	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
360	C₂×D₄	C₂²×C₃×C₄	1	8	yes	—
361	C₂×D₄	C₂²×C₃×C₄	1	16	yes	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	8	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	8	no	—
368	C₂²×C₄	—	4	8	no	—
369	C₂²×C₄	—	4	8	no	—
370	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
371	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
372	C₂²×C₄	C₂²×C₃×C₄	1	4	yes	—
373	C₂²×C₄	C₂²×C₃×C₄	1	16	yes	—
374	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	8	no	—
391	C₄⋊C₄	—	4	4	no	—
392	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
393	C₄⋊C₄	C₂²×C₃×C₄	1	8	yes	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	8	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₂²⋊C₄	—	4	8	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
401	C₂²⋊C₄	C₂²×C₃×C₄	1	16	yes	—
402	C₄²	—	2	8	no	—
403	C₄²	—	2	8	no	—
404	C₄²	—	4	8	no	—
405	C₄²	C₂²×C₃×C₄	1	4	yes	—
406	C₄²	C₂²×C₃×C₄	1	4	yes	—
407	C₄²	C₂²×C₃×C₄	1	4	yes	—
408	C₄²	C₂²×C₃×C₄	1	4	yes	—
409	C₂²×C₃	—	2	2	no	—
410	C₂²×C₃	—	2	8	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	8	no	—
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	8	no	—
415	C₂²×C₃	—	4	8	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	—	4	8	no	—
418	C₂²×C₃	—	4	2	no	—
419	C₂²×C₃	C₂⁴×C₄	1	1	yes	characteristic
420	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
421	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂²×C₃	#585	1	2	yes	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	8	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	4	4	no	—
430	C₃×C₄	—	4	4	no	—
431	C₃×C₄	—	4	4	no	—
432	C₃×C₄	—	4	4	no	—
433	C₃×C₄	#518	1	4	yes	—
434	C₃×C₄	#520	1	4	yes	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	8	no	—
443	C₂³	C₂³×C₃×C₄	1	8	yes	—
444	C₂³	C₂³×C₃×C₄	1	2	yes	—
445	C₂³	C₂⁵×C₃	1	1	yes	characteristic
446	Q₈	—	2	16	no	—
447	D₄	—	2	16	no	—
448	D₄	—	2	16	no	—
449	D₄	—	4	16	no	—
450	D₄	—	4	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	4	16	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	8	16	no	—
474	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
475	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
476	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
477	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
478	C₂×C₄	C₂³×C₃×C₄	1	8	yes	—
479	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
480	C₂×C₄	C₂³×C₃×C₄	1	2	yes	—
481	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
482	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
483	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
484	C₂×C₃	—	4	2	no	—
485	C₂×C₃	—	4	8	no	—
486	C₂×C₃	C₂×#518	1	1	yes	characteristic
487	C₂×C₃	C₂×#520	1	1	yes	characteristic
488	C₂×C₃	#3428	1	1	yes	characteristic
489	C₂×C₃	#3546	1	2	yes	—
490	C₂×C₃	#3554	1	2	yes	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	4	8	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	8	no	—
500	C₂²	—	4	2	no	—
501	C₂²	C₂⁴×C₃×C₄	1	1	yes	characteristic
502	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
503	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
505	C₂²	C₃×#585	1	2	yes	—
506	C₄	—	2	2	no	—
507	C₄	—	2	8	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	4	no	—
515	C₄	C₃×#518	1	4	yes	—
516	C₄	C₃×#520	1	4	yes	—
517	C₃	#34393	1	1	yes	characteristic, direct product factor, Sylow
518	C₂	—	4	2	no	—
519	C₂	—	4	8	no	—
520	C₂	C₂×C₃×#518	1	1	yes	characteristic
521	C₂	C₂×C₃×#520	1	1	yes	characteristic
522	C₂	C₃×#3428	1	1	yes	characteristic
523	C₂	C₃×#3546	1	2	yes	—
524	C₂	C₃×#3554	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator	C₂²	C₂⁴×C₃×C₄
Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2377	C₂	semidirect
3. C₃×#2366	C₂	semidirect
4. C₃×#2365	C₂	semidirect
5. C₃×#2357	C₂	semidirect
6. C₃×#2349	C₂	semidirect
7. C₃×#2341	C₂	semidirect
8. C₃×#2339	C₂	semidirect
9. C₃×#2326	C₂	semidirect
10. C₃×#2324	C₂	semidirect
11. C₃×#2318	C₂	semidirect
12. C₃×#2285	C₂	semidirect
13. C₃×#2283	C₂	semidirect
14. #34393	C₃	direct (N × H)
16. C₃×#532	C₄	semidirect
62. #2377	C₂×C₃	semidirect
63. #2366	C₂×C₃	semidirect
64. #2365	C₂×C₃	semidirect
65. #2357	C₂×C₃	semidirect
66. #2349	C₂×C₃	semidirect
67. #2341	C₂×C₃	semidirect
68. #2339	C₂×C₃	semidirect
69. #2326	C₂×C₃	semidirect
70. #2324	C₂×C₃	semidirect
71. #2318	C₂×C₃	semidirect
72. #2285	C₂×C₃	semidirect
73. #2283	C₂×C₃	semidirect
75. C₂×C₃×#41	C₂×C₄	semidirect
86. C₃×C₄⋊Q₈	C₂×C₄	semidirect
88. C₃×#124	C₂×C₄	semidirect
89. C₃×#121	C₂×C₄	semidirect
90. C₃×#121	C₂×C₄	semidirect
94. C₃×C₄×D₄	C₂×C₄	semidirect
95. C₃×C₄×D₄	C₂×C₄	semidirect
114. C₂×C₃×C₄²	C₂×C₄	semidirect
134. #532	C₃×C₄	semidirect
241. C₂×#41	C₂×C₃×C₄	semidirect
252. C₄⋊Q₈	C₂×C₃×C₄	semidirect
254. #124	C₂×C₃×C₄	semidirect
255. #121	C₂×C₃×C₄	semidirect
256. #121	C₂×C₃×C₄	semidirect
260. C₄×D₄	C₂×C₃×C₄	semidirect
261. C₄×D₄	C₂×C₃×C₄	semidirect
280. C₂×C₄²	C₂×C₃×C₄	semidirect
517. C₃	#34393	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#532	2
C₃×#2377	2
C₃×#2366	2
C₃×#2365	2
C₃×#2357	2
C₃×#2349	2
C₃×#2341	2
C₃×#2339	2
C₃×#2326	2
C₃×#2324	2
C₃×#2318	2
C₃×#2285	2
C₃×#2283	2
#34393	3

Subgroups — C3×#34393 #10653000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#34393 #10653000