Subgroups — C₃×#36194 #10654801

Order 768.

1890 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2857	C₂	1	2	yes	maximal, complemented
3	C₃×#2571	C₂	1	2	yes	maximal, complemented
4	C₃×#2563	C₂	1	2	yes	maximal
5	C₃×#2538	C₂	1	2	yes	maximal
6	C₃×#2497	C₂	1	4	yes	maximal, complemented
7	C₃×#2492	C₂	1	4	yes	maximal, complemented
8	C₃×#2439	C₂	1	4	yes	maximal, complemented
9	C₃×#2369	C₂	1	2	yes	maximal, complemented
10	C₃×#2355	C₂	1	2	yes	maximal, complemented
11	C₃×#2354	C₂	1	2	yes	maximal
12	C₃×C₄×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#2285	C₂	1	2	yes	maximal, complemented
14	C₃×C₄²×D₄	C₂	1	1	yes	maximal, characteristic
15	#36194	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
22	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×#117	C₂²	1	4	yes	—
26	C₂²×C₃×C₄²	C₂²	1	2	yes	—
27	C₃×#400	C₂²	1	8	yes	—
28	C₃×#396	C₂²	1	8	yes	—
29	C₃×#393	C₂²	1	8	yes	—
30	C₃×#391	C₂²	1	8	yes	—
31	C₃×#391	C₂²	1	2	yes	—
32	C₃×#391	C₂²	1	4	yes	—
33	C₃×#390	C₂²	1	4	yes	—
34	C₃×#389	C₂²	1	4	yes	—
35	C₃×#389	C₂²	1	4	yes	—
36	C₃×#389	C₂²	1	2	yes	—
37	C₃×#389	C₂²	1	4	yes	—
38	C₃×#389	C₂²	1	2	yes	—
39	C₃×#388	C₂²	1	8	yes	—
40	C₃×#387	C₂²	1	8	yes	—
41	C₃×#384	C₂²	1	2	yes	—
42	C₃×#384	C₂²	1	2	yes	—
43	C₃×#384	C₂²	1	1	yes	characteristic
44	C₃×#384	C₂²	1	2	yes	—
45	C₃×#384	C₂²	1	2	yes	—
46	C₃×#382	C₂²	1	4	yes	—
47	C₃×#382	C₂²	1	4	yes	—
48	C₃×#380	C₂²	1	4	yes	—
49	C₃×#380	C₂²	1	4	yes	—
50	C₃×#380	C₂²	1	4	yes	—
51	C₃×#380	C₂²	1	4	yes	—
52	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₃×C₄×C₄⋊C₄	C₂²	1	4	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	4	yes	—
57	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
58	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	—
60	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
61	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
62	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
63	C₃×C₄³	C₂²	1	1	yes	characteristic
64	#2868	C₂×C₃	1	1	yes	characteristic, complemented
65	#2857	C₂×C₃	1	2	yes	complemented
66	#2571	C₂×C₃	1	2	yes	complemented
67	#2563	C₂×C₃	1	2	yes	—
68	#2538	C₂×C₃	1	2	yes	—
69	#2497	C₂×C₃	1	4	yes	complemented
70	#2492	C₂×C₃	1	4	yes	complemented
71	#2439	C₂×C₃	1	4	yes	complemented
72	#2369	C₂×C₃	1	2	yes	complemented
73	#2355	C₂×C₃	1	2	yes	complemented
74	#2354	C₂×C₃	1	2	yes	—
75	C₄×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
76	#2285	C₂×C₃	1	2	yes	complemented
77	C₄²×D₄	C₂×C₃	1	1	yes	characteristic
78	C₂²×C₃×Q₈	C₂³	1	2	yes	—
79	C₂²×C₃×Q₈	C₂³	1	4	yes	—
80	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
81	C₂³×C₃×C₄	C₂³	1	2	yes	—
82	C₂³×C₃×C₄	C₂³	1	2	yes	—
83	C₂³×C₃×C₄	C₂³	1	2	yes	—
84	C₃×C₄⋊Q₈	—	2	4	no	—
85	C₃×C₄⋊Q₈	—	2	8	no	—
86	C₃×C₄⋊Q₈	—	4	4	no	—
87	C₃×C₄⋊Q₈	—	4	4	no	—
88	C₃×C₂²⋊Q₈	—	4	8	no	—
89	C₃×C₄×Q₈	—	2	8	no	—
90	C₃×C₄×D₄	—	2	4	no	—
91	C₃×C₄×D₄	—	2	4	no	—
92	C₃×C₄×D₄	Q₈	1	8	yes	complemented
93	C₃×#117	—	4	8	no	—
94	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
103	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
108	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	—
109	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
113	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
114	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₃×C₄²	—	2	8	no	—
116	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
117	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂³	1	2	yes	—
120	C₂×C₃×C₄²	C₂³	1	2	yes	—
121	C₂×C₃×C₄²	C₂³	1	2	yes	—
122	C₂×C₃×C₄²	C₂³	1	4	yes	—
123	C₂×C₃×C₄²	C₂³	1	8	yes	—
124	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
128	C₃×#95	C₂³	1	2	yes	—
129	C₃×#95	C₂³	1	2	yes	—
130	C₃×#95	C₂³	1	2	yes	—
131	C₃×#95	C₂³	1	8	yes	—
132	C₃×#95	C₂³	1	8	yes	—
133	C₃×#95	C₂³	1	8	yes	—
134	C₃×#95	C₂³	1	4	yes	—
135	C₃×#95	C₂³	1	4	yes	—
136	C₃×#95	C₂³	1	8	yes	—
137	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
139	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
140	C₂×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
141	C₂×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
142	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
143	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×#117	C₂²×C₃	1	4	yes	—
147	C₂²×C₄²	C₂²×C₃	1	2	yes	—
148	#400	C₂²×C₃	1	8	yes	—
149	#396	C₂²×C₃	1	8	yes	—
150	#393	C₂²×C₃	1	8	yes	—
151	#391	C₂²×C₃	1	2	yes	—
152	#391	C₂²×C₃	1	4	yes	—
153	#391	C₂²×C₃	1	8	yes	—
154	#390	C₂²×C₃	1	4	yes	—
155	#389	C₂²×C₃	1	2	yes	—
156	#389	C₂²×C₃	1	2	yes	—
157	#389	C₂²×C₃	1	4	yes	—
158	#389	C₂²×C₃	1	4	yes	—
159	#389	C₂²×C₃	1	4	yes	—
160	#388	C₂²×C₃	1	8	yes	—
161	#387	C₂²×C₃	1	8	yes	—
162	#384	C₂²×C₃	1	1	yes	characteristic
163	#384	C₂²×C₃	1	2	yes	—
164	#384	C₂²×C₃	1	2	yes	—
165	#384	C₂²×C₃	1	2	yes	—
166	#384	C₂²×C₃	1	2	yes	—
167	#382	C₂²×C₃	1	4	yes	—
168	#382	C₂²×C₃	1	4	yes	—
169	#380	C₂²×C₃	1	4	yes	—
170	#380	C₂²×C₃	1	4	yes	—
171	#380	C₂²×C₃	1	4	yes	—
172	#380	C₂²×C₃	1	4	yes	—
173	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
174	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	—
175	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
177	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
179	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂²×C₃	1	4	yes	—
181	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
182	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
183	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
184	C₄³	C₂²×C₃	1	1	yes	characteristic
185	C₂⁴×C₃	C₂⁴	1	2	yes	—
186	C₂×C₃×Q₈	—	2	4	no	—
187	C₂×C₃×Q₈	—	2	4	no	—
188	C₂×C₃×Q₈	—	2	8	no	—
189	C₂×C₃×Q₈	—	2	4	no	—
190	C₂×C₃×Q₈	—	4	4	no	—
191	C₂×C₃×Q₈	—	4	4	no	—
192	C₂×C₃×D₄	—	2	2	no	—
193	C₂×C₃×D₄	—	2	2	no	—
194	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
195	C₂²×C₃×C₄	—	2	4	no	—
196	C₂²×C₃×C₄	—	2	4	no	—
197	C₂²×C₃×C₄	—	2	4	no	—
198	C₂²×C₃×C₄	—	2	4	no	—
199	C₂²×C₃×C₄	—	2	4	no	—
200	C₂²×C₃×C₄	—	2	4	no	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	—	2	4	no	—
203	C₂²×C₃×C₄	C₂×Q₈	1	8	yes	—
204	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
205	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
206	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
207	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
208	C₂²×C₃×C₄	C₂⁴	1	8	yes	—
209	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
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	1	yes	characteristic
214	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
217	C₃×C₄⋊C₄	—	2	2	no	—
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	—	2	4	no	—
220	C₃×C₄⋊C₄	—	2	8	no	—
221	C₃×C₄⋊C₄	—	2	8	no	—
222	C₃×C₄⋊C₄	—	2	4	no	—
223	C₃×C₄⋊C₄	—	2	4	no	—
224	C₃×C₄⋊C₄	—	2	8	no	—
225	C₃×C₄⋊C₄	—	2	4	no	—
226	C₃×C₄⋊C₄	—	2	8	no	—
227	C₃×C₄⋊C₄	—	2	8	no	—
228	C₃×C₄⋊C₄	—	2	4	no	—
229	C₃×C₄⋊C₄	—	4	8	no	—
230	C₃×C₄⋊C₄	—	4	4	no	—
231	C₃×C₄⋊C₄	—	4	4	no	—
232	C₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
233	C₃×C₂²⋊C₄	—	2	4	no	—
234	C₃×C₂²⋊C₄	—	2	4	no	—
235	C₃×C₂²⋊C₄	—	4	8	no	—
236	C₃×C₂²⋊C₄	—	4	8	no	—
237	C₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
238	C₃×C₄²	—	2	4	no	—
239	C₃×C₄²	—	2	4	no	—
240	C₃×C₄²	—	2	4	no	—
241	C₃×C₄²	—	2	8	no	—
242	C₃×C₄²	—	2	2	no	—
243	C₃×C₄²	—	2	2	no	—
244	C₃×C₄²	—	2	2	no	—
245	C₃×C₄²	—	4	8	no	—
246	C₃×C₄²	C₂×Q₈	1	4	yes	—
247	C₃×C₄²	#41	1	4	yes	—
248	C₃×C₄²	#41	1	4	yes	—
249	C₃×C₄²	#41	1	4	yes	—
250	C₂²×Q₈	C₂³×C₃	1	2	yes	—
251	C₂²×Q₈	C₂³×C₃	1	4	yes	—
252	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
253	C₂³×C₄	C₂³×C₃	1	2	yes	—
254	C₂³×C₄	C₂³×C₃	1	2	yes	—
255	C₂³×C₄	C₂³×C₃	1	2	yes	—
256	C₄⋊Q₈	—	2	4	no	—
257	C₄⋊Q₈	—	2	8	no	—
258	C₄⋊Q₈	—	4	4	no	—
259	C₄⋊Q₈	—	4	4	no	—
260	C₂²⋊Q₈	—	4	8	no	—
261	C₄×Q₈	—	2	8	no	—
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	C₃×Q₈	1	8	yes	complemented
265	#117	—	4	8	no	—
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	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
272	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	—
279	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
287	C₂×C₄²	—	2	8	no	—
288	C₂×C₄²	C₂³×C₃	1	4	yes	—
289	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₃	1	2	yes	—
293	C₂×C₄²	C₂³×C₃	1	2	yes	—
294	C₂×C₄²	C₂³×C₃	1	2	yes	—
295	C₂×C₄²	C₂³×C₃	1	8	yes	—
296	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
300	#95	C₂³×C₃	1	2	yes	—
301	#95	C₂³×C₃	1	2	yes	—
302	#95	C₂³×C₃	1	2	yes	—
303	#95	C₂³×C₃	1	8	yes	—
304	#95	C₂³×C₃	1	8	yes	—
305	#95	C₂³×C₃	1	8	yes	—
306	#95	C₂³×C₃	1	4	yes	—
307	#95	C₂³×C₃	1	4	yes	—
308	#95	C₂³×C₃	1	8	yes	—
309	C₂³×C₃	—	2	2	no	—
310	C₂³×C₃	—	2	2	no	—
311	C₂³×C₃	—	2	2	no	—
312	C₂³×C₃	—	2	2	no	—
313	C₂³×C₃	—	2	2	no	—
314	C₂³×C₃	—	2	2	no	—
315	C₂³×C₃	C₂²×Q₈	1	4	yes	—
316	C₂³×C₃	C₂⁵	1	1	yes	characteristic
317	C₃×Q₈	—	4	8	no	—
318	C₃×Q₈	—	8	8	no	—
319	C₃×D₄	—	2	8	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	16	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	4	no	—
332	C₂×C₃×C₄	—	2	4	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	8	no	—
337	C₂×C₃×C₄	—	2	4	no	—
338	C₂×C₃×C₄	—	2	8	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	2	8	no	—
341	C₂×C₃×C₄	—	2	2	no	—
342	C₂×C₃×C₄	—	2	4	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	4	8	no	—
345	C₂×C₃×C₄	—	4	8	no	—
346	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
347	C₂×C₃×C₄	C₂²×Q₈	1	4	yes	—
348	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
349	C₂×C₃×C₄	C₂²×Q₈	1	2	yes	—
350	C₂×C₃×C₄	C₂×#41	1	2	yes	—
351	C₂×C₃×C₄	C₂×#41	1	2	yes	—
352	C₂×C₃×C₄	C₂×#41	1	2	yes	—
353	C₂×C₃×C₄	C₂×#41	1	2	yes	—
354	C₂×C₃×C₄	C₂×#41	1	2	yes	—
355	C₂×C₃×C₄	C₂×#41	1	2	yes	—
356	C₂×C₃×C₄	C₂×#41	1	2	yes	—
357	C₂×C₃×C₄	C₂×#41	1	2	yes	—
358	C₂×C₃×C₄	C₂×#41	1	2	yes	—
359	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₃×C₄	H(5,𝔽₂)	1	2	yes	—
361	C₂×C₃×C₄	2₋¹⁺⁴	1	2	yes	—
362	C₂⁴	C₂⁴×C₃	1	2	yes	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	2	8	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	4	4	no	—
368	C₂×Q₈	—	4	4	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	C₂×C₃×Q₈	1	8	yes	—
381	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₃	1	8	yes	—
386	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
392	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	4	8	no	—
407	C₄⋊C₄	—	4	4	no	—
408	C₄⋊C₄	—	4	4	no	—
409	C₄⋊C₄	C₂×C₃×Q₈	1	4	yes	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	4	no	—
412	C₂²⋊C₄	—	4	8	no	—
413	C₂²⋊C₄	—	4	8	no	—
414	C₂²⋊C₄	C₂×C₃×Q₈	1	8	yes	—
415	C₄²	—	2	4	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	2	4	no	—
418	C₄²	—	2	8	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	4	8	no	—
423	C₄²	C₂×C₃×Q₈	1	4	yes	—
424	C₄²	C₃×#41	1	4	yes	—
425	C₄²	C₃×#41	1	4	yes	—
426	C₄²	C₃×#41	1	4	yes	—
427	C₂²×C₃	—	2	4	no	—
428	C₂²×C₃	—	2	4	no	—
429	C₂²×C₃	—	2	4	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	4	2	no	—
433	C₂²×C₃	—	4	2	no	—
434	C₂²×C₃	C₂³×Q₈	1	1	yes	characteristic
435	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
436	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
437	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₃×C₄	—	2	4	no	—
442	C₃×C₄	—	2	2	no	—
443	C₃×C₄	—	2	2	no	—
444	C₃×C₄	—	2	2	no	—
445	C₃×C₄	—	4	2	no	—
446	C₃×C₄	—	4	4	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	4	8	no	—
449	C₃×C₄	—	4	4	no	—
450	C₃×C₄	#533	1	4	yes	—
451	C₃×C₄	#554	1	4	yes	—
452	C₃×C₄	#555	1	4	yes	—
453	C₃×C₄	#556	1	4	yes	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	C₂²×C₃×Q₈	1	4	yes	—
461	C₂³	C₂⁵×C₃	1	1	yes	characteristic
462	Q₈	—	4	8	no	—
463	Q₈	—	8	8	no	—
464	D₄	—	2	8	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	16	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
492	C₂×C₄	C₂²×C₃×Q₈	1	4	yes	—
493	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
494	C₂×C₄	C₂²×C₃×Q₈	1	2	yes	—
495	C₂×C₄	C₂×C₃×#41	1	2	yes	—
496	C₂×C₄	C₂×C₃×#41	1	2	yes	—
497	C₂×C₄	C₂×C₃×#41	1	2	yes	—
498	C₂×C₄	C₂×C₃×#41	1	2	yes	—
499	C₂×C₄	C₂×C₃×#41	1	2	yes	—
500	C₂×C₄	C₂×C₃×#41	1	2	yes	—
501	C₂×C₄	C₂×C₃×#41	1	2	yes	—
502	C₂×C₄	C₂×C₃×#41	1	2	yes	—
503	C₂×C₄	C₂×C₃×#41	1	2	yes	—
504	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
505	C₂×C₄	C₃×H(5,𝔽₂)	1	2	yes	—
506	C₂×C₄	C₃×2₋¹⁺⁴	1	2	yes	—
507	C₂×C₃	—	4	4	no	—
508	C₂×C₃	C₂×#533	1	1	yes	characteristic
509	C₂×C₃	C₂×#554	1	1	yes	characteristic
510	C₂×C₃	C₂×#555	1	1	yes	characteristic
511	C₂×C₃	C₂×#556	1	1	yes	characteristic
512	C₂×C₃	#3503	1	1	yes	characteristic
513	C₂×C₃	#3508	1	1	yes	characteristic
514	C₂×C₃	#3511	1	1	yes	characteristic
515	C₂²	—	2	4	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	C₂³×C₃×Q₈	1	1	yes	characteristic
523	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
524	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
525	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
526	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
528	C₂²	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
529	C₄	—	2	4	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	8	no	—
537	C₄	—	4	4	no	—
538	C₄	C₃×#533	1	4	yes	—
539	C₄	C₃×#554	1	4	yes	—
540	C₄	C₃×#555	1	4	yes	—
541	C₄	C₃×#556	1	4	yes	—
542	C₃	#36194	1	1	yes	characteristic, direct product factor, Sylow
543	C₂	—	4	4	no	—
544	C₂	C₂×C₃×#533	1	1	yes	characteristic
545	C₂	C₂×C₃×#554	1	1	yes	characteristic
546	C₂	C₂×C₃×#555	1	1	yes	characteristic
547	C₂	C₂×C₃×#556	1	1	yes	characteristic
548	C₂	C₃×#3503	1	1	yes	characteristic
549	C₂	C₃×#3508	1	1	yes	characteristic
550	C₂	C₃×#3511	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×#2868	C₂	semidirect
2. C₃×#2857	C₂	semidirect
3. C₃×#2571	C₂	semidirect
6. C₃×#2497	C₂	semidirect
7. C₃×#2492	C₂	semidirect
8. C₃×#2439	C₂	semidirect
9. C₃×#2369	C₂	semidirect
10. C₃×#2355	C₂	semidirect
12. C₃×C₄×C₄⋊Q₈	C₂	semidirect
13. C₃×#2285	C₂	semidirect
15. #36194	C₃	direct (N × H)
64. #2868	C₂×C₃	semidirect
65. #2857	C₂×C₃	semidirect
66. #2571	C₂×C₃	semidirect
69. #2497	C₂×C₃	semidirect
70. #2492	C₂×C₃	semidirect
71. #2439	C₂×C₃	semidirect
72. #2369	C₂×C₃	semidirect
73. #2355	C₂×C₃	semidirect
75. C₄×C₄⋊Q₈	C₂×C₃	semidirect
76. #2285	C₂×C₃	semidirect
92. C₃×C₄×D₄	Q₈	semidirect
264. C₄×D₄	C₃×Q₈	semidirect
542. C₃	#36194	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×#2868	2
C₃×#2857	2
C₃×#2571	2
C₃×#2563	2
C₃×#2538	2
C₃×#2497	2
C₃×#2492	2
C₃×#2439	2
C₃×#2369	2
C₃×#2355	2
C₃×#2354	2
C₃×C₄×C₄⋊Q₈	2
C₃×#2285	2
C₃×C₄²×D₄	2
#36194	3

Subgroups — C3×#36194 #10654801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36194 #10654801