Subgroups — C₃×#36163 #10654770

Order 768.

2808 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2849	C₂	1	2	yes	maximal
4	C₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#2484	C₂	1	2	yes	maximal, complemented
8	C₃×#2481	C₂	1	4	yes	maximal, complemented
9	C₃×#2473	C₂	1	4	yes	maximal, complemented
10	C₃×#2442	C₂	1	2	yes	maximal, complemented
11	C₃×#2417	C₂	1	2	yes	maximal, complemented
12	C₃×#2413	C₂	1	2	yes	maximal, complemented
13	C₃×#2360	C₂	1	2	yes	maximal, complemented
14	C₃×#2352	C₂	1	2	yes	maximal, complemented
15	C₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₄×#120	C₂	1	1	yes	maximal, characteristic
17	C₃×#2280	C₂	1	2	yes	maximal, complemented
18	#36163	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂⁴×C₃×C₄	C₂²	1	1	yes	characteristic
20	C₂⁴×C₃×C₄	C₂²	1	2	yes	—
21	C₃×#552	—	2	8	no	—
22	C₂×C₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₃×#125	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×#125	C₂²	1	2	yes	complemented
25	C₂×C₃×#123	C₂²	1	2	yes	—
26	C₂×C₃×#123	C₂²	1	2	yes	—
27	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#120	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
33	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×#117	C₂²	1	2	yes	—
35	C₂×C₃×#117	C₂²	1	2	yes	—
36	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₃×C₄⋊C₄	—	2	8	no	—
38	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
39	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₃×C₄⋊C₄	C₂²	1	4	yes	—
42	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₃×#400	C₂²	1	4	yes	complemented
45	C₃×#400	C₂²	1	4	yes	complemented
46	C₃×#398	C₂²	1	4	yes	complemented
47	C₃×#398	C₂²	1	4	yes	complemented
48	C₃×#398	C₂²	1	2	yes	complemented
49	C₃×#397	C₂²	1	2	yes	complemented
50	C₃×#396	C₂²	1	4	yes	complemented
51	C₃×#391	C₂²	1	2	yes	complemented
52	C₃×#389	C₂²	1	4	yes	complemented
53	C₃×#389	C₂²	1	2	yes	complemented
54	C₃×#389	C₂²	1	2	yes	complemented
55	C₃×#388	C₂²	1	4	yes	complemented
56	C₃×#387	C₂²	1	4	yes	complemented
57	C₃×#387	C₂²	1	4	yes	complemented
58	C₃×#387	C₂²	1	4	yes	complemented
59	C₃×#386	C₂²	1	1	yes	characteristic
60	C₃×#386	C₂²	1	4	yes	—
61	C₃×#386	C₂²	1	2	yes	—
62	C₃×#386	C₂²	1	4	yes	—
63	C₃×#385	C₂²	1	4	yes	—
64	C₃×#385	C₂²	1	2	yes	—
65	C₃×#385	C₂²	1	4	yes	—
66	C₃×#385	C₂²	1	2	yes	—
67	C₃×#385	C₂²	1	4	yes	—
68	C₃×#385	C₂²	1	1	yes	characteristic
69	C₃×#382	C₂²	1	2	yes	complemented
70	C₃×#381	C₂²	1	2	yes	—
71	C₃×#381	C₂²	1	2	yes	—
72	C₃×#381	C₂²	1	2	yes	—
73	C₃×#381	C₂²	1	2	yes	—
74	C₃×#380	C₂²	1	4	yes	—
75	C₃×#380	C₂²	1	4	yes	—
76	C₃×#380	C₂²	1	2	yes	—
77	C₃×#380	C₂²	1	1	yes	characteristic
78	C₃×#380	C₂²	1	2	yes	complemented
79	C₃×#379	C₂²	1	1	yes	characteristic
80	C₃×#379	C₂²	1	2	yes	—
81	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	—
83	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
84	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	—
85	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
86	C₂×#552	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂³×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
88	#2849	C₂×C₃	1	2	yes	—
89	#2848	C₂×C₃	1	1	yes	characteristic, complemented
90	#2503	C₂×C₃	1	1	yes	characteristic, complemented
91	#2486	C₂×C₃	1	1	yes	characteristic, complemented
92	#2484	C₂×C₃	1	2	yes	complemented
93	#2481	C₂×C₃	1	4	yes	complemented
94	#2473	C₂×C₃	1	4	yes	complemented
95	#2442	C₂×C₃	1	2	yes	complemented
96	#2417	C₂×C₃	1	2	yes	complemented
97	#2413	C₂×C₃	1	2	yes	complemented
98	#2360	C₂×C₃	1	2	yes	complemented
99	#2352	C₂×C₃	1	2	yes	complemented
100	#2344	C₂×C₃	1	1	yes	characteristic, complemented
101	C₄×#120	C₂×C₃	1	1	yes	characteristic
102	#2280	C₂×C₃	1	2	yes	complemented
103	C₂⁵×C₃	C₂³	1	1	yes	characteristic
104	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₃×D₄	C₂³	1	2	yes	—
106	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
107	C₂³×C₃×C₄	—	2	4	no	—
108	C₂³×C₃×C₄	—	2	8	no	—
109	C₂³×C₃×C₄	—	2	8	no	—
110	C₂³×C₃×C₄	—	2	8	no	—
111	C₂³×C₃×C₄	—	4	4	no	—
112	C₂³×C₃×C₄	C₂³	1	2	yes	—
113	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
114	C₂³×C₃×C₄	C₂³	1	2	yes	—
115	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
116	C₂³×C₃×C₄	C₂³	1	4	yes	—
117	C₂³×C₃×C₄	C₂³	1	4	yes	—
118	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂³	1	2	yes	—
120	C₂³×C₃×C₄	C₂³	1	2	yes	—
121	C₃×#126	—	2	8	no	—
122	C₃×#125	—	2	8	no	—
123	C₃×#125	—	2	4	no	—
124	C₃×#123	—	2	8	no	—
125	C₃×#123	—	4	4	no	—
126	C₃×C₂²⋊Q₈	—	2	4	no	—
127	C₃×C₂²⋊Q₈	—	2	8	no	—
128	C₃×C₂²⋊Q₈	—	2	4	no	—
129	C₃×#120	—	2	4	no	—
130	C₃×C₄×Q₈	—	2	4	no	—
131	C₃×C₄×D₄	—	2	4	no	—
132	C₃×C₄×D₄	—	2	8	no	—
133	C₃×#117	—	2	8	no	—
134	C₃×#117	—	2	4	no	—
135	C₃×#117	—	4	4	no	—
136	C₂×C₃×C₄⋊C₄	—	2	8	no	—
137	C₂×C₃×C₄⋊C₄	—	2	4	no	—
138	C₂×C₃×C₄⋊C₄	—	2	8	no	—
139	C₂×C₃×C₄⋊C₄	—	2	8	no	—
140	C₂×C₃×C₄⋊C₄	—	2	16	no	—
141	C₂×C₃×C₄⋊C₄	D₄	1	8	yes	complemented
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
155	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
157	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
158	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
176	C₂×C₃×C₄²	C₂³	1	2	yes	—
177	C₂×C₃×C₄²	C₂³	1	2	yes	—
178	C₂×C₃×C₄²	C₂³	1	2	yes	—
179	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂³	1	4	yes	—
181	C₃×#95	C₂³	1	4	yes	—
182	C₃×#95	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	4	yes	—
184	C₃×#95	C₂³	1	4	yes	—
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	2	yes	—
187	C₃×#95	C₂³	1	2	yes	—
188	C₃×#95	C₂³	1	4	yes	—
189	C₃×#95	C₂³	1	2	yes	—
190	C₃×#95	C₂³	1	4	yes	—
191	C₃×#95	C₂³	1	4	yes	—
192	C₃×#95	C₂³	1	4	yes	—
193	C₃×#95	C₂³	1	4	yes	—
194	C₂⁴×C₄	C₂²×C₃	1	1	yes	characteristic
195	C₂⁴×C₄	C₂²×C₃	1	2	yes	—
196	#552	—	2	8	no	—
197	C₂×#126	C₂²×C₃	1	2	yes	complemented
198	C₂×#125	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₂×#125	C₂²×C₃	1	2	yes	complemented
200	C₂×#123	C₂²×C₃	1	2	yes	—
201	C₂×#123	C₂²×C₃	1	2	yes	—
202	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
203	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
204	C₂×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
205	C₂×#120	C₂²×C₃	1	1	yes	characteristic
206	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
207	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
208	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
209	C₂×#117	C₂²×C₃	1	2	yes	—
210	C₂×#117	C₂²×C₃	1	2	yes	—
211	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
212	C₂²×C₄⋊C₄	—	2	8	no	—
213	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₃	1	4	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
218	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
219	#400	C₂²×C₃	1	4	yes	complemented
220	#400	C₂²×C₃	1	4	yes	complemented
221	#398	C₂²×C₃	1	4	yes	complemented
222	#398	C₂²×C₃	1	4	yes	complemented
223	#398	C₂²×C₃	1	2	yes	complemented
224	#397	C₂²×C₃	1	2	yes	complemented
225	#396	C₂²×C₃	1	4	yes	complemented
226	#391	C₂²×C₃	1	2	yes	complemented
227	#389	C₂²×C₃	1	2	yes	complemented
228	#389	C₂²×C₃	1	4	yes	complemented
229	#389	C₂²×C₃	1	2	yes	complemented
230	#388	C₂²×C₃	1	4	yes	complemented
231	#387	C₂²×C₃	1	4	yes	complemented
232	#387	C₂²×C₃	1	4	yes	complemented
233	#387	C₂²×C₃	1	4	yes	complemented
234	#386	C₂²×C₃	1	4	yes	—
235	#386	C₂²×C₃	1	4	yes	—
236	#386	C₂²×C₃	1	1	yes	characteristic
237	#386	C₂²×C₃	1	2	yes	—
238	#385	C₂²×C₃	1	2	yes	—
239	#385	C₂²×C₃	1	4	yes	—
240	#385	C₂²×C₃	1	4	yes	—
241	#385	C₂²×C₃	1	4	yes	—
242	#385	C₂²×C₃	1	2	yes	—
243	#385	C₂²×C₃	1	1	yes	characteristic
244	#382	C₂²×C₃	1	2	yes	complemented
245	#381	C₂²×C₃	1	2	yes	—
246	#381	C₂²×C₃	1	2	yes	—
247	#381	C₂²×C₃	1	2	yes	—
248	#381	C₂²×C₃	1	2	yes	—
249	#380	C₂²×C₃	1	1	yes	characteristic
250	#380	C₂²×C₃	1	2	yes	—
251	#380	C₂²×C₃	1	4	yes	—
252	#380	C₂²×C₃	1	4	yes	—
253	#380	C₂²×C₃	1	2	yes	complemented
254	#379	C₂²×C₃	1	2	yes	—
255	#379	C₂²×C₃	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
257	C₄×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
258	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
259	C₄×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
260	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
261	C₂⁴×C₃	—	2	2	no	—
262	C₂⁴×C₃	—	2	4	no	—
263	C₂⁴×C₃	—	2	2	no	—
264	C₂⁴×C₃	—	2	4	no	—
265	C₂⁴×C₃	#41	1	4	yes	—
266	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₃	C₂⁴	1	2	yes	—
269	C₂×C₃×Q₈	—	2	2	no	—
270	C₂×C₃×Q₈	—	2	4	no	—
271	C₂×C₃×D₄	—	2	2	no	—
272	C₂×C₃×D₄	—	2	4	no	—
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	—	2	4	no	—
275	C₂×C₃×D₄	—	2	2	no	—
276	C₂×C₃×D₄	—	2	4	no	—
277	C₂²×C₃×C₄	—	2	32	no	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	—	2	4	no	—
280	C₂²×C₃×C₄	—	2	4	no	—
281	C₂²×C₃×C₄	—	2	4	no	—
282	C₂²×C₃×C₄	—	2	4	no	—
283	C₂²×C₃×C₄	—	2	4	no	—
284	C₂²×C₃×C₄	—	2	4	no	—
285	C₂²×C₃×C₄	—	2	4	no	—
286	C₂²×C₃×C₄	—	2	4	no	—
287	C₂²×C₃×C₄	—	2	4	no	—
288	C₂²×C₃×C₄	—	2	4	no	—
289	C₂²×C₃×C₄	—	2	8	no	—
290	C₂²×C₃×C₄	—	2	8	no	—
291	C₂²×C₃×C₄	—	2	4	no	—
292	C₂²×C₃×C₄	—	2	4	no	—
293	C₂²×C₃×C₄	—	2	8	no	—
294	C₂²×C₃×C₄	—	2	8	no	—
295	C₂²×C₃×C₄	—	2	2	no	—
296	C₂²×C₃×C₄	—	2	4	no	—
297	C₂²×C₃×C₄	—	4	4	no	—
298	C₂²×C₃×C₄	—	4	4	no	—
299	C₂²×C₃×C₄	—	4	32	no	—
300	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
301	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
302	C₂²×C₃×C₄	#41	1	8	yes	—
303	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
304	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
306	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
307	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
308	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
309	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
310	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
311	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
314	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
315	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
316	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
317	C₃×C₄⋊C₄	—	2	8	no	—
318	C₃×C₄⋊C₄	—	2	8	no	—
319	C₃×C₄⋊C₄	—	2	4	no	—
320	C₃×C₄⋊C₄	—	2	4	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	2	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	2	no	—
325	C₃×C₄⋊C₄	—	2	4	no	—
326	C₃×C₄⋊C₄	—	2	4	no	—
327	C₃×C₄⋊C₄	—	2	4	no	—
328	C₃×C₄⋊C₄	—	2	4	no	—
329	C₃×C₄⋊C₄	—	2	4	no	—
330	C₃×C₄⋊C₄	—	2	8	no	—
331	C₃×C₄⋊C₄	—	4	4	no	—
332	C₃×C₄⋊C₄	—	4	4	no	—
333	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
334	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
335	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
336	C₃×C₂²⋊C₄	—	2	2	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	2	no	—
340	C₃×C₂²⋊C₄	—	2	4	no	—
341	C₃×C₂²⋊C₄	—	2	8	no	—
342	C₃×C₂²⋊C₄	—	2	2	no	—
343	C₃×C₂²⋊C₄	—	2	4	no	—
344	C₃×C₂²⋊C₄	—	2	4	no	—
345	C₃×C₂²⋊C₄	—	2	8	no	—
346	C₃×C₂²⋊C₄	—	2	4	no	—
347	C₃×C₂²⋊C₄	—	2	2	no	—
348	C₃×C₂²⋊C₄	—	2	4	no	—
349	C₃×C₂²⋊C₄	—	2	4	no	—
350	C₃×C₂²⋊C₄	—	4	4	no	—
351	C₃×C₄²	—	2	4	no	—
352	C₃×C₄²	—	2	4	no	—
353	C₃×C₄²	—	2	2	no	—
354	C₃×C₄²	—	2	4	no	—
355	C₃×C₄²	—	4	4	no	—
356	C₂⁵	C₂³×C₃	1	1	yes	characteristic
357	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₃	1	2	yes	—
360	C₂³×C₄	—	2	4	no	—
361	C₂³×C₄	—	2	8	no	—
362	C₂³×C₄	—	2	8	no	—
363	C₂³×C₄	—	2	8	no	—
364	C₂³×C₄	—	4	4	no	—
365	C₂³×C₄	C₂³×C₃	1	2	yes	—
366	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₃	1	2	yes	—
368	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₃	1	4	yes	—
370	C₂³×C₄	C₂³×C₃	1	4	yes	—
371	C₂³×C₄	C₂³×C₃	1	2	yes	—
372	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₃	1	2	yes	—
374	#126	—	2	8	no	—
375	#125	—	2	8	no	—
376	#125	—	2	4	no	—
377	#123	—	2	8	no	—
378	#123	—	4	4	no	—
379	C₂²⋊Q₈	—	2	4	no	—
380	C₂²⋊Q₈	—	2	8	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	#120	—	2	4	no	—
383	C₄×Q₈	—	2	4	no	—
384	C₄×D₄	—	2	4	no	—
385	C₄×D₄	—	2	8	no	—
386	#117	—	2	8	no	—
387	#117	—	2	4	no	—
388	#117	—	4	4	no	—
389	C₂×C₄⋊C₄	—	2	8	no	—
390	C₂×C₄⋊C₄	—	2	4	no	—
391	C₂×C₄⋊C₄	—	2	8	no	—
392	C₂×C₄⋊C₄	—	2	8	no	—
393	C₂×C₄⋊C₄	—	2	16	no	—
394	C₂×C₄⋊C₄	C₃×D₄	1	8	yes	complemented
395	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
429	C₂×C₄²	C₂³×C₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₃	1	4	yes	—
434	#95	C₂³×C₃	1	4	yes	—
435	#95	C₂³×C₃	1	4	yes	—
436	#95	C₂³×C₃	1	4	yes	—
437	#95	C₂³×C₃	1	4	yes	—
438	#95	C₂³×C₃	1	2	yes	—
439	#95	C₂³×C₃	1	2	yes	—
440	#95	C₂³×C₃	1	2	yes	—
441	#95	C₂³×C₃	1	4	yes	—
442	#95	C₂³×C₃	1	2	yes	—
443	#95	C₂³×C₃	1	4	yes	—
444	#95	C₂³×C₃	1	4	yes	—
445	#95	C₂³×C₃	1	4	yes	—
446	#95	C₂³×C₃	1	4	yes	—
447	C₂³×C₃	—	2	8	no	—
448	C₂³×C₃	—	2	8	no	—
449	C₂³×C₃	—	2	16	no	—
450	C₂³×C₃	—	2	8	no	—
451	C₂³×C₃	—	2	16	no	—
452	C₂³×C₃	—	2	2	no	—
453	C₂³×C₃	—	2	2	no	—
454	C₂³×C₃	—	2	2	no	—
455	C₂³×C₃	—	2	2	no	—
456	C₂³×C₃	—	2	2	no	—
457	C₂³×C₃	—	2	2	no	—
458	C₂³×C₃	—	2	1	no	—
459	C₂³×C₃	—	2	2	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	1	no	—
462	C₂³×C₃	—	2	2	no	—
463	C₂³×C₃	C₂²×D₄	1	2	yes	—
464	C₂³×C₃	C₂×#41	1	2	yes	—
465	C₂³×C₃	C₂×#41	1	4	yes	—
466	C₂³×C₃	C₂×#41	1	4	yes	—
467	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
468	C₂³×C₃	2₋¹⁺⁴	1	4	yes	—
469	C₂³×C₃	C₂⁵	1	1	yes	characteristic
470	C₃×Q₈	—	4	4	no	—
471	C₃×D₄	—	4	4	no	—
472	C₃×D₄	—	4	8	no	—
473	C₂×C₃×C₄	—	2	16	no	—
474	C₂×C₃×C₄	—	2	8	no	—
475	C₂×C₃×C₄	—	2	16	no	—
476	C₂×C₃×C₄	—	2	2	no	—
477	C₂×C₃×C₄	—	2	2	no	—
478	C₂×C₃×C₄	—	2	2	no	—
479	C₂×C₃×C₄	—	2	2	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	2	2	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	8	no	—
484	C₂×C₃×C₄	—	2	16	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	2	no	—
488	C₂×C₃×C₄	—	2	2	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	4	no	—
491	C₂×C₃×C₄	—	2	2	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	2	no	—
495	C₂×C₃×C₄	—	2	4	no	—
496	C₂×C₃×C₄	—	2	2	no	—
497	C₂×C₃×C₄	—	2	4	no	—
498	C₂×C₃×C₄	—	2	4	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	4	no	—
501	C₂×C₃×C₄	—	2	4	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	4	no	—
505	C₂×C₃×C₄	—	2	2	no	—
506	C₂×C₃×C₄	—	2	4	no	—
507	C₂×C₃×C₄	—	2	2	no	—
508	C₂×C₃×C₄	—	4	16	no	—
509	C₂×C₃×C₄	—	4	16	no	—
510	C₂×C₃×C₄	—	4	8	no	—
511	C₂×C₃×C₄	—	4	4	no	—
512	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
513	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
514	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
515	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
516	C₂×C₃×C₄	C₂×#41	1	4	yes	—
517	C₂×C₃×C₄	C₂×#41	1	4	yes	—
518	C₂⁴	—	2	2	no	—
519	C₂⁴	—	2	4	no	—
520	C₂⁴	—	2	2	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	C₃×#41	1	4	yes	—
523	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
524	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
525	C₂⁴	C₂⁴×C₃	1	2	yes	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	4	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂²×C₄	—	2	32	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	2	4	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	8	no	—
547	C₂²×C₄	—	2	8	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	8	no	—
551	C₂²×C₄	—	2	8	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	4	4	no	—
555	C₂²×C₄	—	4	4	no	—
556	C₂²×C₄	—	4	32	no	—
557	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
558	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
559	C₂²×C₄	C₃×#41	1	8	yes	—
560	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
562	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
565	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
569	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
570	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
574	C₄⋊C₄	—	2	8	no	—
575	C₄⋊C₄	—	2	8	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	2	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	4	no	—
587	C₄⋊C₄	—	2	8	no	—
588	C₄⋊C₄	—	4	4	no	—
589	C₄⋊C₄	—	4	4	no	—
590	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
591	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
592	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	4	no	—
612	C₄²	—	4	4	no	—
613	C₂²×C₃	—	2	32	no	—
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	2	4	no	—
616	C₂²×C₃	—	2	4	no	—
617	C₂²×C₃	—	2	4	no	—
618	C₂²×C₃	—	2	4	no	—
619	C₂²×C₃	—	2	2	no	—
620	C₂²×C₃	—	2	4	no	—
621	C₂²×C₃	—	2	4	no	—
622	C₂²×C₃	—	2	4	no	—
623	C₂²×C₃	—	2	4	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	—	4	1	no	—
626	C₂²×C₃	—	4	2	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	4	2	no	—
629	C₂²×C₃	#546	1	4	yes	—
630	C₂²×C₃	#552	1	8	yes	complemented
631	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
632	C₂²×C₃	C₂²×#41	1	2	yes	—
633	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
634	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂²×C₃	C₂×2₋¹⁺⁴	1	2	yes	—
636	C₃×C₄	—	2	2	no	—
637	C₃×C₄	—	2	4	no	—
638	C₃×C₄	—	2	4	no	—
639	C₃×C₄	—	2	4	no	—
640	C₃×C₄	—	4	1	no	—
641	C₃×C₄	—	4	2	no	—
642	C₃×C₄	—	4	4	no	—
643	C₃×C₄	—	4	1	no	—
644	C₃×C₄	—	4	2	no	—
645	C₃×C₄	—	4	1	no	—
646	C₃×C₄	—	4	2	no	—
647	C₃×C₄	—	4	2	no	—
648	C₃×C₄	—	4	4	no	—
649	C₃×C₄	#525	1	4	yes	—
650	C₂³	—	2	8	no	—
651	C₂³	—	2	8	no	—
652	C₂³	—	2	16	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	8	no	—
660	C₂³	—	2	16	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	2	no	—
666	C₂³	C₂²×C₃×D₄	1	2	yes	—
667	C₂³	C₂×C₃×#41	1	2	yes	—
668	C₂³	C₂×C₃×#41	1	4	yes	—
669	C₂³	C₂×C₃×#41	1	4	yes	—
670	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
671	C₂³	C₃×2₋¹⁺⁴	1	4	yes	—
672	C₂³	C₂⁵×C₃	1	1	yes	characteristic
673	Q₈	—	4	4	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	8	no	—
676	C₂×C₄	—	2	16	no	—
677	C₂×C₄	—	2	8	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	—	2	2	no	—
685	C₂×C₄	—	2	16	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	16	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	4	16	no	—
712	C₂×C₄	—	4	16	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
716	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
717	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
718	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
719	C₂×C₄	C₂×C₃×#41	1	4	yes	—
720	C₂×C₄	C₂×C₃×#41	1	4	yes	—
721	C₂×C₃	—	2	4	no	—
722	C₂×C₃	—	2	8	no	—
723	C₂×C₃	—	8	1	no	—
724	C₂×C₃	C₂×#525	1	1	yes	characteristic
725	C₂×C₃	C₂×#546	1	1	yes	characteristic
726	C₂×C₃	C₂×#552	1	2	yes	—
727	C₂×C₃	#3486	1	1	yes	characteristic
728	C₂×C₃	#3492	1	2	yes	—
729	C₂²	—	2	32	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	2	no	—
745	C₂²	C₃×#546	1	4	yes	—
746	C₂²	C₃×#552	1	8	yes	complemented
747	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
748	C₂²	C₂²×C₃×#41	1	2	yes	—
749	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
750	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂²	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
752	C₄	—	2	2	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	2	4	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	4	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	4	no	—
765	C₄	C₃×#525	1	4	yes	—
766	C₃	#36163	1	1	yes	characteristic, direct product factor, Sylow
767	C₂	—	2	4	no	—
768	C₂	—	2	8	no	—
769	C₂	—	8	1	no	—
770	C₂	C₂×C₃×#525	1	1	yes	characteristic
771	C₂	C₂×C₃×#546	1	1	yes	characteristic
772	C₂	C₂×C₃×#552	1	2	yes	—
773	C₂	C₃×#3486	1	1	yes	characteristic
774	C₂	C₃×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂×C₃×#120	C₂²
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. C₂×C₃×#552	C₂	semidirect
2. C₂³×C₃×C₄⋊C₄	C₂	semidirect
4. C₃×#2848	C₂	semidirect
5. C₃×#2503	C₂	semidirect
6. C₃×#2486	C₂	semidirect
7. C₃×#2484	C₂	semidirect
8. C₃×#2481	C₂	semidirect
9. C₃×#2473	C₂	semidirect
10. C₃×#2442	C₂	semidirect
11. C₃×#2417	C₂	semidirect
12. C₃×#2413	C₂	semidirect
13. C₃×#2360	C₂	semidirect
14. C₃×#2352	C₂	semidirect
15. C₃×#2344	C₂	semidirect
17. C₃×#2280	C₂	semidirect
18. #36163	C₃	direct (N × H)
22. C₂×C₃×#126	C₂²	semidirect
23. C₂×C₃×#125	C₂²	semidirect
24. C₂×C₃×#125	C₂²	semidirect
29. C₂×C₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₃×C₄×Q₈	C₂²	semidirect
36. C₂×C₃×#117	C₂²	semidirect
44. C₃×#400	C₂²	semidirect
45. C₃×#400	C₂²	semidirect
46. C₃×#398	C₂²	semidirect
47. C₃×#398	C₂²	semidirect
48. C₃×#398	C₂²	semidirect
49. C₃×#397	C₂²	semidirect
50. C₃×#396	C₂²	semidirect
51. C₃×#391	C₂²	semidirect
52. C₃×#389	C₂²	semidirect
53. C₃×#389	C₂²	semidirect
54. C₃×#389	C₂²	semidirect
55. C₃×#388	C₂²	semidirect
56. C₃×#387	C₂²	semidirect
57. C₃×#387	C₂²	semidirect
58. C₃×#387	C₂²	semidirect
69. C₃×#382	C₂²	semidirect
78. C₃×#380	C₂²	semidirect
81. C₃×C₄×C₄⋊C₄	C₂²	semidirect
86. C₂×#552	C₂×C₃	semidirect
87. C₂³×C₄⋊C₄	C₂×C₃	semidirect
89. #2848	C₂×C₃	semidirect
90. #2503	C₂×C₃	semidirect
91. #2486	C₂×C₃	semidirect
92. #2484	C₂×C₃	semidirect
93. #2481	C₂×C₃	semidirect
94. #2473	C₂×C₃	semidirect
95. #2442	C₂×C₃	semidirect
96. #2417	C₂×C₃	semidirect
97. #2413	C₂×C₃	semidirect
98. #2360	C₂×C₃	semidirect
99. #2352	C₂×C₃	semidirect
100. #2344	C₂×C₃	semidirect
102. #2280	C₂×C₃	semidirect
141. C₂×C₃×C₄⋊C₄	D₄	semidirect
197. C₂×#126	C₂²×C₃	semidirect
198. C₂×#125	C₂²×C₃	semidirect
199. C₂×#125	C₂²×C₃	semidirect
204. C₂×C₂²⋊Q₈	C₂²×C₃	semidirect
206. C₂×C₄×Q₈	C₂²×C₃	semidirect
211. C₂×#117	C₂²×C₃	semidirect
219. #400	C₂²×C₃	semidirect
220. #400	C₂²×C₃	semidirect
221. #398	C₂²×C₃	semidirect
222. #398	C₂²×C₃	semidirect
223. #398	C₂²×C₃	semidirect
224. #397	C₂²×C₃	semidirect
225. #396	C₂²×C₃	semidirect
226. #391	C₂²×C₃	semidirect
227. #389	C₂²×C₃	semidirect
228. #389	C₂²×C₃	semidirect
229. #389	C₂²×C₃	semidirect
230. #388	C₂²×C₃	semidirect
231. #387	C₂²×C₃	semidirect
232. #387	C₂²×C₃	semidirect
233. #387	C₂²×C₃	semidirect
244. #382	C₂²×C₃	semidirect
253. #380	C₂²×C₃	semidirect
256. C₄×C₄⋊C₄	C₂²×C₃	semidirect
394. C₂×C₄⋊C₄	C₃×D₄	semidirect
630. C₂²×C₃	#552	semidirect
746. C₂²	C₃×#552	semidirect
766. C₃	#36163	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×#552	2
C₂³×C₃×C₄⋊C₄	2
C₃×#2849	2
C₃×#2848	2
C₃×#2503	2
C₃×#2486	2
C₃×#2484	2
C₃×#2481	2
C₃×#2473	2
C₃×#2442	2
C₃×#2417	2
C₃×#2413	2
C₃×#2360	2
C₃×#2352	2
C₃×#2344	2
C₃×C₄×#120	2
C₃×#2280	2
#36163	3

Subgroups — C3×#36163 #10654770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36163 #10654770