Subgroups — C₃×#36162 #10654769

Order 768.

2860 conjugacy classes of subgroups.

The subgroup lattice has 778 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	C₂²×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#2849	C₂	1	2	yes	maximal, complemented
5	C₃×#2482	C₂	1	2	yes	maximal, complemented
6	C₃×#2467	C₂	1	4	yes	maximal, complemented
7	C₃×#2460	C₂	1	4	yes	maximal, complemented
8	C₃×#2454	C₂	1	2	yes	maximal, complemented
9	C₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2427	C₂	1	2	yes	maximal, complemented
11	C₃×#2411	C₂	1	2	yes	maximal, complemented
12	C₃×#2408	C₂	1	1	yes	maximal, characteristic
13	C₃×#2367	C₂	1	2	yes	maximal, complemented
14	C₃×#2363	C₂	1	2	yes	maximal, complemented
15	C₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×C₄×#123	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#2280	C₂	1	2	yes	maximal, complemented
18	#36162	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₃×D₄	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×#124	C₂²	1	2	yes	—
26	C₂×C₃×#123	C₂²	1	2	yes	—
27	C₂×C₃×#123	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×#121	C₂²	1	2	yes	—
31	C₂×C₃×#120	C₂²	1	2	yes	—
32	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₄×D₄	—	2	8	no	—
34	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
35	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
36	C₂×C₃×C₄×D₄	C₂²	1	4	yes	—
37	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×#117	C₂²	1	2	yes	—
39	C₂×C₃×#117	C₂²	1	2	yes	—
40	C₂×C₃×#117	C₂²	1	1	yes	characteristic, complemented
41	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
43	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
44	C₃×#399	C₂²	1	4	yes	complemented
45	C₃×#397	C₂²	1	4	yes	complemented
46	C₃×#396	C₂²	1	4	yes	complemented
47	C₃×#394	C₂²	1	2	yes	—
48	C₃×#394	C₂²	1	4	yes	—
49	C₃×#394	C₂²	1	4	yes	complemented
50	C₃×#392	C₂²	1	2	yes	—
51	C₃×#391	C₂²	1	2	yes	complemented
52	C₃×#390	C₂²	1	2	yes	—
53	C₃×#390	C₂²	1	2	yes	—
54	C₃×#390	C₂²	1	4	yes	complemented
55	C₃×#389	C₂²	1	2	yes	complemented
56	C₃×#389	C₂²	1	2	yes	complemented
57	C₃×#388	C₂²	1	4	yes	complemented
58	C₃×#388	C₂²	1	4	yes	complemented
59	C₃×#388	C₂²	1	4	yes	complemented
60	C₃×#388	C₂²	1	2	yes	complemented
61	C₃×#387	C₂²	1	2	yes	complemented
62	C₃×#387	C₂²	1	4	yes	complemented
63	C₃×#387	C₂²	1	4	yes	complemented
64	C₃×#386	C₂²	1	1	yes	characteristic
65	C₃×#386	C₂²	1	4	yes	complemented
66	C₃×#386	C₂²	1	4	yes	complemented
67	C₃×#385	C₂²	1	2	yes	—
68	C₃×#385	C₂²	1	1	yes	characteristic
69	C₃×#385	C₂²	1	4	yes	complemented
70	C₃×#385	C₂²	1	4	yes	complemented
71	C₃×#381	C₂²	1	2	yes	—
72	C₃×#381	C₂²	1	1	yes	characteristic
73	C₃×#381	C₂²	1	2	yes	—
74	C₃×#380	C₂²	1	1	yes	characteristic
75	C₃×#380	C₂²	1	4	yes	complemented
76	C₃×#380	C₂²	1	4	yes	complemented
77	C₃×#379	C₂²	1	2	yes	—
78	C₃×#379	C₂²	1	2	yes	—
79	C₃×#379	C₂²	1	2	yes	—
80	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₃×C₄×C₄⋊C₄	C₂²	1	2	yes	complemented
82	C₃×C₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
83	C₃×C₄×C₂²⋊C₄	C₂²	1	2	yes	complemented
84	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
85	C₃×C₄×C₂²⋊C₄	C₂²	1	4	yes	complemented
86	C₂×#552	C₂×C₃	1	1	yes	characteristic, complemented
87	C₂²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
88	#2855	C₂×C₃	1	1	yes	characteristic, complemented
89	#2849	C₂×C₃	1	2	yes	complemented
90	#2482	C₂×C₃	1	2	yes	complemented
91	#2467	C₂×C₃	1	4	yes	complemented
92	#2460	C₂×C₃	1	4	yes	complemented
93	#2454	C₂×C₃	1	2	yes	complemented
94	#2435	C₂×C₃	1	1	yes	characteristic, complemented
95	#2427	C₂×C₃	1	2	yes	complemented
96	#2411	C₂×C₃	1	2	yes	complemented
97	#2408	C₂×C₃	1	1	yes	characteristic
98	#2367	C₂×C₃	1	2	yes	complemented
99	#2363	C₂×C₃	1	2	yes	complemented
100	#2344	C₂×C₃	1	1	yes	characteristic, complemented
101	C₄×#123	C₂×C₃	1	1	yes	characteristic, complemented
102	#2280	C₂×C₃	1	2	yes	complemented
103	C₂⁵×C₃	C₂³	1	2	yes	—
104	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
105	C₂²×C₃×D₄	—	2	8	no	—
106	C₂²×C₃×D₄	—	2	4	no	—
107	C₂²×C₃×D₄	C₂³	1	2	yes	—
108	C₂²×C₃×D₄	C₂³	1	1	yes	characteristic
109	C₂²×C₃×D₄	C₂³	1	2	yes	—
110	C₂²×C₃×D₄	C₂³	1	4	yes	—
111	C₂³×C₃×C₄	—	2	8	no	—
112	C₂³×C₃×C₄	—	2	8	no	—
113	C₂³×C₃×C₄	—	4	4	no	—
114	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂³	1	4	yes	—
116	C₂³×C₃×C₄	C₂³	1	4	yes	—
117	C₂³×C₃×C₄	C₂³	1	2	yes	—
118	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
119	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
120	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
121	C₃×#126	—	2	8	no	—
122	C₃×#125	—	2	8	no	—
123	C₃×#125	—	2	4	no	—
124	C₃×#124	—	2	8	no	—
125	C₃×#123	—	2	8	no	—
126	C₃×#123	—	2	4	no	—
127	C₃×C₂²⋊Q₈	—	2	4	no	—
128	C₃×C₂²⋊Q₈	—	2	4	no	—
129	C₃×#121	—	2	8	no	—
130	C₃×#120	—	4	4	no	—
131	C₃×C₄×Q₈	—	2	4	no	—
132	C₃×C₄×D₄	—	2	4	no	—
133	C₃×C₄×D₄	—	2	8	no	—
134	C₃×C₄×D₄	—	2	8	no	—
135	C₃×C₄×D₄	—	2	16	no	—
136	C₃×#117	—	2	8	no	—
137	C₃×#117	—	2	4	no	—
138	C₃×#117	—	4	4	no	—
139	C₂×C₃×C₄⋊C₄	D₄	1	8	yes	complemented
140	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
151	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	—
152	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
156	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
172	C₂×C₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
174	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
175	C₂×C₃×C₄²	—	2	4	no	—
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	2	yes	—
180	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂³	1	2	yes	—
182	C₂×C₃×C₄²	C₂³	1	4	yes	—
183	C₃×#95	C₂³	1	2	yes	—
184	C₃×#95	C₂³	1	2	yes	—
185	C₃×#95	C₂³	1	2	yes	—
186	C₃×#95	C₂³	1	4	yes	—
187	C₃×#95	C₂³	1	4	yes	—
188	C₃×#95	C₂³	1	2	yes	—
189	C₃×#95	C₂³	1	4	yes	—
190	C₃×#95	C₂³	1	2	yes	—
191	C₃×#95	C₂³	1	2	yes	—
192	C₃×#95	C₂³	1	4	yes	—
193	C₃×#95	C₂³	1	4	yes	—
194	C₂³×D₄	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×#124	C₂²×C₃	1	2	yes	—
201	C₂×#123	C₂²×C₃	1	1	yes	characteristic
202	C₂×#123	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×#121	C₂²×C₃	1	2	yes	—
206	C₂×#120	C₂²×C₃	1	2	yes	—
207	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
208	C₂×C₄×D₄	—	2	8	no	—
209	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
211	C₂×C₄×D₄	C₂²×C₃	1	4	yes	—
212	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
213	C₂×#117	C₂²×C₃	1	2	yes	—
214	C₂×#117	C₂²×C₃	1	2	yes	—
215	C₂×#117	C₂²×C₃	1	1	yes	characteristic, complemented
216	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
218	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
219	#399	C₂²×C₃	1	4	yes	complemented
220	#397	C₂²×C₃	1	4	yes	complemented
221	#396	C₂²×C₃	1	4	yes	complemented
222	#394	C₂²×C₃	1	2	yes	—
223	#394	C₂²×C₃	1	4	yes	—
224	#394	C₂²×C₃	1	4	yes	complemented
225	#392	C₂²×C₃	1	2	yes	—
226	#391	C₂²×C₃	1	2	yes	complemented
227	#390	C₂²×C₃	1	2	yes	—
228	#390	C₂²×C₃	1	2	yes	—
229	#390	C₂²×C₃	1	4	yes	complemented
230	#389	C₂²×C₃	1	2	yes	complemented
231	#389	C₂²×C₃	1	2	yes	complemented
232	#388	C₂²×C₃	1	4	yes	complemented
233	#388	C₂²×C₃	1	4	yes	complemented
234	#388	C₂²×C₃	1	4	yes	complemented
235	#388	C₂²×C₃	1	2	yes	complemented
236	#387	C₂²×C₃	1	4	yes	complemented
237	#387	C₂²×C₃	1	4	yes	complemented
238	#387	C₂²×C₃	1	2	yes	complemented
239	#386	C₂²×C₃	1	1	yes	characteristic
240	#386	C₂²×C₃	1	4	yes	complemented
241	#386	C₂²×C₃	1	4	yes	complemented
242	#385	C₂²×C₃	1	2	yes	—
243	#385	C₂²×C₃	1	1	yes	characteristic
244	#385	C₂²×C₃	1	4	yes	complemented
245	#385	C₂²×C₃	1	4	yes	complemented
246	#381	C₂²×C₃	1	2	yes	—
247	#381	C₂²×C₃	1	2	yes	—
248	#381	C₂²×C₃	1	1	yes	characteristic
249	#380	C₂²×C₃	1	1	yes	characteristic
250	#380	C₂²×C₃	1	4	yes	complemented
251	#380	C₂²×C₃	1	4	yes	complemented
252	#379	C₂²×C₃	1	2	yes	—
253	#379	C₂²×C₃	1	2	yes	—
254	#379	C₂²×C₃	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
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	2	yes	complemented
259	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
260	C₄×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
261	C₂⁴×C₃	—	2	4	no	—
262	C₂⁴×C₃	—	2	8	no	—
263	C₂⁴×C₃	—	2	4	no	—
264	C₂⁴×C₃	—	2	4	no	—
265	C₂⁴×C₃	—	4	4	no	—
266	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₃	C₂⁴	1	4	yes	—
268	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×Q₈	—	2	2	no	—
270	C₂×C₃×Q₈	—	2	4	no	—
271	C₂×C₃×D₄	—	2	32	no	—
272	C₂×C₃×D₄	—	2	8	no	—
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	—	2	2	no	—
275	C₂×C₃×D₄	—	2	2	no	—
276	C₂×C₃×D₄	—	2	8	no	—
277	C₂×C₃×D₄	—	2	4	no	—
278	C₂×C₃×D₄	—	2	4	no	—
279	C₂×C₃×D₄	—	2	4	no	—
280	C₂×C₃×D₄	—	4	4	no	—
281	C₂×C₃×D₄	—	4	4	no	—
282	C₂×C₃×D₄	#41	1	8	yes	—
283	C₂²×C₃×C₄	—	2	2	no	—
284	C₂²×C₃×C₄	—	2	4	no	—
285	C₂²×C₃×C₄	—	2	4	no	—
286	C₂²×C₃×C₄	—	2	2	no	—
287	C₂²×C₃×C₄	—	2	4	no	—
288	C₂²×C₃×C₄	—	2	2	no	—
289	C₂²×C₃×C₄	—	2	2	no	—
290	C₂²×C₃×C₄	—	2	8	no	—
291	C₂²×C₃×C₄	—	2	8	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	—	4	4	no	—
296	C₂²×C₃×C₄	—	4	4	no	—
297	C₂²×C₃×C₄	—	4	2	no	—
298	C₂²×C₃×C₄	—	4	32	no	—
299	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
300	C₂²×C₃×C₄	C₂×D₄	1	8	yes	—
301	C₂²×C₃×C₄	#41	1	4	yes	—
302	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
303	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
304	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
305	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
306	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
307	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
308	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
309	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
310	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
311	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
313	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
314	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
315	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
316	C₃×C₄⋊C₄	—	2	4	no	—
317	C₃×C₄⋊C₄	—	2	2	no	—
318	C₃×C₄⋊C₄	—	2	4	no	—
319	C₃×C₄⋊C₄	—	2	2	no	—
320	C₃×C₄⋊C₄	—	2	4	no	—
321	C₃×C₄⋊C₄	—	2	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	2	4	no	—
325	C₃×C₄⋊C₄	—	4	2	no	—
326	C₃×C₄⋊C₄	—	4	4	no	—
327	C₃×C₄⋊C₄	—	4	4	no	—
328	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
329	C₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
330	C₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
331	C₃×C₂²⋊C₄	—	2	2	no	—
332	C₃×C₂²⋊C₄	—	2	4	no	—
333	C₃×C₂²⋊C₄	—	2	8	no	—
334	C₃×C₂²⋊C₄	—	2	2	no	—
335	C₃×C₂²⋊C₄	—	2	8	no	—
336	C₃×C₂²⋊C₄	—	2	8	no	—
337	C₃×C₂²⋊C₄	—	2	2	no	—
338	C₃×C₂²⋊C₄	—	2	4	no	—
339	C₃×C₂²⋊C₄	—	2	8	no	—
340	C₃×C₂²⋊C₄	—	2	8	no	—
341	C₃×C₂²⋊C₄	—	2	4	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	—	4	4	no	—
346	C₃×C₂²⋊C₄	—	4	2	no	—
347	C₃×C₂²⋊C₄	—	4	4	no	—
348	C₃×C₂²⋊C₄	—	4	4	no	—
349	C₃×C₂²⋊C₄	—	4	4	no	—
350	C₃×C₄²	—	2	4	no	—
351	C₃×C₄²	—	2	4	no	—
352	C₃×C₄²	—	2	4	no	—
353	C₃×C₄²	—	2	4	no	—
354	C₃×C₄²	—	2	2	no	—
355	C₃×C₄²	—	2	4	no	—
356	C₃×C₄²	—	4	4	no	—
357	C₂⁵	C₂³×C₃	1	2	yes	—
358	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
359	C₂²×D₄	—	2	8	no	—
360	C₂²×D₄	—	2	4	no	—
361	C₂²×D₄	C₂³×C₃	1	2	yes	—
362	C₂²×D₄	C₂³×C₃	1	1	yes	characteristic
363	C₂²×D₄	C₂³×C₃	1	2	yes	—
364	C₂²×D₄	C₂³×C₃	1	4	yes	—
365	C₂³×C₄	—	2	8	no	—
366	C₂³×C₄	—	2	8	no	—
367	C₂³×C₄	—	4	4	no	—
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	1	yes	characteristic
374	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
375	#126	—	2	8	no	—
376	#125	—	2	8	no	—
377	#125	—	2	4	no	—
378	#124	—	2	8	no	—
379	#123	—	2	8	no	—
380	#123	—	2	4	no	—
381	C₂²⋊Q₈	—	2	4	no	—
382	C₂²⋊Q₈	—	2	4	no	—
383	#121	—	2	8	no	—
384	#120	—	4	4	no	—
385	C₄×Q₈	—	2	4	no	—
386	C₄×D₄	—	2	4	no	—
387	C₄×D₄	—	2	8	no	—
388	C₄×D₄	—	2	8	no	—
389	C₄×D₄	—	2	16	no	—
390	#117	—	2	8	no	—
391	#117	—	2	4	no	—
392	#117	—	4	4	no	—
393	C₂×C₄⋊C₄	C₃×D₄	1	8	yes	complemented
394	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	2	yes	—
402	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
409	C₂×C₂²⋊C₄	—	2	8	no	—
410	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
429	C₂×C₄²	—	2	4	no	—
430	C₂×C₄²	C₂³×C₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₃	1	2	yes	—
432	C₂×C₄²	C₂³×C₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₃	1	2	yes	—
436	C₂×C₄²	C₂³×C₃	1	4	yes	—
437	#95	C₂³×C₃	1	2	yes	—
438	#95	C₂³×C₃	1	2	yes	—
439	#95	C₂³×C₃	1	2	yes	—
440	#95	C₂³×C₃	1	4	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	2	yes	—
445	#95	C₂³×C₃	1	2	yes	—
446	#95	C₂³×C₃	1	4	yes	—
447	#95	C₂³×C₃	1	4	yes	—
448	C₂³×C₃	—	2	2	no	—
449	C₂³×C₃	—	2	2	no	—
450	C₂³×C₃	—	2	16	no	—
451	C₂³×C₃	—	2	4	no	—
452	C₂³×C₃	—	2	4	no	—
453	C₂³×C₃	—	2	4	no	—
454	C₂³×C₃	—	2	4	no	—
455	C₂³×C₃	—	2	4	no	—
456	C₂³×C₃	—	2	4	no	—
457	C₂³×C₃	—	2	1	no	—
458	C₂³×C₃	—	2	1	no	—
459	C₂³×C₃	—	2	2	no	—
460	C₂³×C₃	—	2	1	no	—
461	C₂³×C₃	—	2	2	no	—
462	C₂³×C₃	—	4	16	no	—
463	C₂³×C₃	—	4	16	no	—
464	C₂³×C₃	—	4	8	no	—
465	C₂³×C₃	—	4	8	no	—
466	C₂³×C₃	C₂²×D₄	1	2	yes	—
467	C₂³×C₃	C₂×#41	1	8	yes	—
468	C₂³×C₃	C₂×#41	1	2	yes	—
469	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
470	C₂³×C₃	C₂⁵	1	1	yes	characteristic
471	C₃×Q₈	—	4	4	no	—
472	C₃×D₄	—	2	16	no	—
473	C₃×D₄	—	2	16	no	—
474	C₃×D₄	—	4	4	no	—
475	C₃×D₄	—	8	8	no	—
476	C₂×C₃×C₄	—	2	8	no	—
477	C₂×C₃×C₄	—	2	16	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	2	no	—
484	C₂×C₃×C₄	—	2	2	no	—
485	C₂×C₃×C₄	—	2	8	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	2	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	2	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	2	no	—
493	C₂×C₃×C₄	—	2	2	no	—
494	C₂×C₃×C₄	—	2	2	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	2	4	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	4	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	4	no	—
506	C₂×C₃×C₄	—	2	2	no	—
507	C₂×C₃×C₄	—	2	4	no	—
508	C₂×C₃×C₄	—	2	2	no	—
509	C₂×C₃×C₄	—	4	16	no	—
510	C₂×C₃×C₄	—	4	16	no	—
511	C₂×C₃×C₄	—	4	4	no	—
512	C₂×C₃×C₄	—	4	4	no	—
513	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
514	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
515	C₂×C₃×C₄	C₂²×D₄	1	4	yes	—
516	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
517	C₂×C₃×C₄	C₂×#41	1	4	yes	—
518	C₂×C₃×C₄	C₂×#41	1	4	yes	—
519	C₂⁴	—	2	4	no	—
520	C₂⁴	—	2	8	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	4	no	—
523	C₂⁴	—	4	4	no	—
524	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
525	C₂⁴	C₂⁴×C₃	1	4	yes	—
526	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	4	no	—
529	C₂×D₄	—	2	32	no	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	8	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	C₃×#41	1	8	yes	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	8	no	—
549	C₂²×C₄	—	2	8	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	8	no	—
552	C₂²×C₄	—	2	8	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	—	4	4	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	32	no	—
557	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
558	C₂²×C₄	C₂×C₃×D₄	1	8	yes	—
559	C₂²×C₄	C₃×#41	1	4	yes	—
560	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
561	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
562	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
564	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₃	1	2	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	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	4	4	no	—
584	C₄⋊C₄	—	4	2	no	—
585	C₄⋊C₄	—	4	4	no	—
586	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
587	C₄⋊C₄	C₂×C₃×D₄	1	4	yes	—
588	C₄⋊C₄	C₂×C₃×D₄	1	8	yes	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	8	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	8	no	—
594	C₂²⋊C₄	—	2	8	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	4	4	no	—
604	C₂²⋊C₄	—	4	4	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	4	4	no	—
607	C₂²⋊C₄	—	4	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	4	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	4	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	4	no	—
614	C₄²	—	4	4	no	—
615	C₂²×C₃	—	2	2	no	—
616	C₂²×C₃	—	2	4	no	—
617	C₂²×C₃	—	2	2	no	—
618	C₂²×C₃	—	2	4	no	—
619	C₂²×C₃	—	2	8	no	—
620	C₂²×C₃	—	2	8	no	—
621	C₂²×C₃	—	2	8	no	—
622	C₂²×C₃	—	4	32	no	—
623	C₂²×C₃	—	4	4	no	—
624	C₂²×C₃	—	4	4	no	—
625	C₂²×C₃	—	4	4	no	—
626	C₂²×C₃	—	4	4	no	—
627	C₂²×C₃	—	4	1	no	—
628	C₂²×C₃	—	4	1	no	—
629	C₂²×C₃	—	4	2	no	—
630	C₂²×C₃	—	4	1	no	—
631	C₂²×C₃	—	4	2	no	—
632	C₂²×C₃	#546	1	4	yes	—
633	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
634	C₂²×C₃	C₂²×#41	1	2	yes	—
635	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
636	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
637	C₂²×C₃	#585	1	2	yes	—
638	C₃×C₄	—	2	2	no	—
639	C₃×C₄	—	2	4	no	—
640	C₃×C₄	—	2	4	no	—
641	C₃×C₄	—	2	4	no	—
642	C₃×C₄	—	4	1	no	—
643	C₃×C₄	—	4	2	no	—
644	C₃×C₄	—	4	1	no	—
645	C₃×C₄	—	4	2	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	2	no	—
648	C₃×C₄	—	4	2	no	—
649	C₃×C₄	—	4	2	no	—
650	C₃×C₄	—	4	4	no	—
651	C₃×C₄	#525	1	4	yes	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	16	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	2	4	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	16	no	—
667	C₂³	—	4	16	no	—
668	C₂³	—	4	8	no	—
669	C₂³	—	4	8	no	—
670	C₂³	C₂²×C₃×D₄	1	2	yes	—
671	C₂³	C₂×C₃×#41	1	8	yes	—
672	C₂³	C₂×C₃×#41	1	2	yes	—
673	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
674	C₂³	C₂⁵×C₃	1	1	yes	characteristic
675	Q₈	—	4	4	no	—
676	D₄	—	2	16	no	—
677	D₄	—	2	16	no	—
678	D₄	—	4	4	no	—
679	D₄	—	8	8	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	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	4	16	no	—
714	C₂×C₄	—	4	16	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
718	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
719	C₂×C₄	C₂²×C₃×D₄	1	4	yes	—
720	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
721	C₂×C₄	C₂×C₃×#41	1	4	yes	—
722	C₂×C₄	C₂×C₃×#41	1	4	yes	—
723	C₂×C₃	—	2	4	no	—
724	C₂×C₃	—	4	8	no	—
725	C₂×C₃	—	8	1	no	—
726	C₂×C₃	C₂×#525	1	1	yes	characteristic
727	C₂×C₃	C₂×#546	1	1	yes	characteristic
728	C₂×C₃	#3475	1	2	yes	—
729	C₂×C₃	#3487	1	1	yes	characteristic
730	C₂×C₃	#3513	1	2	yes	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	8	no	—
736	C₂²	—	2	8	no	—
737	C₂²	—	2	8	no	—
738	C₂²	—	4	32	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	C₃×#546	1	4	yes	—
749	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
750	C₂²	C₂²×C₃×#41	1	2	yes	—
751	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
752	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂²	C₃×#585	1	2	yes	—
754	C₄	—	2	2	no	—
755	C₄	—	2	4	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	4	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	4	no	—
766	C₄	—	4	2	no	—
767	C₄	C₃×#525	1	4	yes	—
768	C₃	#36162	1	1	yes	characteristic, direct product factor, Sylow
769	C₂	—	2	4	no	—
770	C₂	—	4	8	no	—
771	C₂	—	8	1	no	—
772	C₂	C₂×C₃×#525	1	1	yes	characteristic
773	C₂	C₂×C₃×#546	1	1	yes	characteristic
774	C₂	C₃×#3475	1	2	yes	—
775	C₂	C₃×#3487	1	1	yes	characteristic
776	C₂	C₃×#3513	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₃×#2408	C₂
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. C₂²×C₃×C₄×D₄	C₂	semidirect
3. C₃×#2855	C₂	semidirect
4. C₃×#2849	C₂	semidirect
5. C₃×#2482	C₂	semidirect
6. C₃×#2467	C₂	semidirect
7. C₃×#2460	C₂	semidirect
8. C₃×#2454	C₂	semidirect
9. C₃×#2435	C₂	semidirect
10. C₃×#2427	C₂	semidirect
11. C₃×#2411	C₂	semidirect
13. C₃×#2367	C₂	semidirect
14. C₃×#2363	C₂	semidirect
15. C₃×#2344	C₂	semidirect
16. C₃×C₄×#123	C₂	semidirect
17. C₃×#2280	C₂	semidirect
18. #36162	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
32. C₂×C₃×C₄×Q₈	C₂²	semidirect
40. C₂×C₃×#117	C₂²	semidirect
44. C₃×#399	C₂²	semidirect
45. C₃×#397	C₂²	semidirect
46. C₃×#396	C₂²	semidirect
49. C₃×#394	C₂²	semidirect
51. C₃×#391	C₂²	semidirect
54. C₃×#390	C₂²	semidirect
55. C₃×#389	C₂²	semidirect
56. C₃×#389	C₂²	semidirect
57. C₃×#388	C₂²	semidirect
58. C₃×#388	C₂²	semidirect
59. C₃×#388	C₂²	semidirect
60. C₃×#388	C₂²	semidirect
61. C₃×#387	C₂²	semidirect
62. C₃×#387	C₂²	semidirect
63. C₃×#387	C₂²	semidirect
65. C₃×#386	C₂²	semidirect
66. C₃×#386	C₂²	semidirect
69. C₃×#385	C₂²	semidirect
70. C₃×#385	C₂²	semidirect
75. C₃×#380	C₂²	semidirect
76. C₃×#380	C₂²	semidirect
80. C₃×C₄×C₄⋊C₄	C₂²	semidirect
81. C₃×C₄×C₄⋊C₄	C₂²	semidirect
83. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
84. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
85. C₃×C₄×C₂²⋊C₄	C₂²	semidirect
86. C₂×#552	C₂×C₃	semidirect
87. C₂²×C₄×D₄	C₂×C₃	semidirect
88. #2855	C₂×C₃	semidirect
89. #2849	C₂×C₃	semidirect
90. #2482	C₂×C₃	semidirect
91. #2467	C₂×C₃	semidirect
92. #2460	C₂×C₃	semidirect
93. #2454	C₂×C₃	semidirect
94. #2435	C₂×C₃	semidirect
95. #2427	C₂×C₃	semidirect
96. #2411	C₂×C₃	semidirect
98. #2367	C₂×C₃	semidirect
99. #2363	C₂×C₃	semidirect
100. #2344	C₂×C₃	semidirect
101. C₄×#123	C₂×C₃	semidirect
102. #2280	C₂×C₃	semidirect
139. 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
207. C₂×C₄×Q₈	C₂²×C₃	semidirect
215. C₂×#117	C₂²×C₃	semidirect
219. #399	C₂²×C₃	semidirect
220. #397	C₂²×C₃	semidirect
221. #396	C₂²×C₃	semidirect
224. #394	C₂²×C₃	semidirect
226. #391	C₂²×C₃	semidirect
229. #390	C₂²×C₃	semidirect
230. #389	C₂²×C₃	semidirect
231. #389	C₂²×C₃	semidirect
232. #388	C₂²×C₃	semidirect
233. #388	C₂²×C₃	semidirect
234. #388	C₂²×C₃	semidirect
235. #388	C₂²×C₃	semidirect
236. #387	C₂²×C₃	semidirect
237. #387	C₂²×C₃	semidirect
238. #387	C₂²×C₃	semidirect
240. #386	C₂²×C₃	semidirect
241. #386	C₂²×C₃	semidirect
244. #385	C₂²×C₃	semidirect
245. #385	C₂²×C₃	semidirect
250. #380	C₂²×C₃	semidirect
251. #380	C₂²×C₃	semidirect
255. C₄×C₄⋊C₄	C₂²×C₃	semidirect
256. C₄×C₄⋊C₄	C₂²×C₃	semidirect
258. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
259. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
260. C₄×C₂²⋊C₄	C₂²×C₃	semidirect
393. C₂×C₄⋊C₄	C₃×D₄	semidirect
768. C₃	#36162	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
C₂²×C₃×C₄×D₄	2
C₃×#2855	2
C₃×#2849	2
C₃×#2482	2
C₃×#2467	2
C₃×#2460	2
C₃×#2454	2
C₃×#2435	2
C₃×#2427	2
C₃×#2411	2
C₃×#2408	2
C₃×#2367	2
C₃×#2363	2
C₃×#2344	2
C₃×C₄×#123	2
C₃×#2280	2
#36162	3

Subgroups — C3×#36162 #10654769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#36162 #10654769