Subgroups — C₃×#10596027 #13179308

Order 1728.

1864 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64146	C₂	1	1	yes	maximal, characteristic
3	C₃×#64144	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64138	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3752	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64133	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64105	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64092	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₂²⋊C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#64086	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#64085	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64081	C₂	1	1	yes	maximal, characteristic, complemented
16	#10596027	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₃×#5556	—	3	4	no	maximal
18	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×#638	C₂²	1	1	yes	characteristic
23	C₂×C₃×#638	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
27	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
28	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
32	C₃×#3757	C₂²	1	1	yes	characteristic
33	C₃×#3757	C₂²	1	1	yes	characteristic
34	C₃×#3757	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3757	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3752	C₂²	1	1	yes	characteristic
37	C₃×#3752	C₂²	1	1	yes	characteristic
38	C₃×#3752	C₂²	1	1	yes	characteristic
39	C₃×#3752	C₂²	1	1	yes	characteristic
40	C₃×#3752	C₂²	1	1	yes	characteristic
41	C₃×#3752	C₂²	1	1	yes	characteristic
42	C₃×#3752	C₂²	1	1	yes	characteristic
43	C₃×#3752	C₂²	1	1	yes	characteristic
44	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic, complemented
45	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
46	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
47	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
48	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
49	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
50	C₃×#3750	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃²×C₄×D₄	—	2	4	no	—
54	C₃²×C₄×D₄	D₃	1	4	yes	complemented
55	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
56	#64146	C₂×C₃	1	1	yes	characteristic
57	#64144	C₂×C₃	1	1	yes	characteristic, complemented
58	#64138	C₂×C₃	1	1	yes	characteristic, complemented
59	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#3752	C₂×C₃	1	1	yes	characteristic, complemented
61	#64133	C₂×C₃	1	1	yes	characteristic, complemented
62	#64107	C₂×C₃	1	1	yes	characteristic, complemented
63	#64105	C₂×C₃	1	1	yes	characteristic, complemented
64	#64094	C₂×C₃	1	1	yes	characteristic, complemented
65	#64092	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂²⋊C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
67	#64086	C₂×C₃	1	1	yes	characteristic, complemented
68	#64085	C₂×C₃	1	1	yes	characteristic, complemented
69	#64081	C₂×C₃	1	1	yes	characteristic, complemented
70	C₃×#937	—	3	4	no	—
71	C₃×#935	—	3	4	no	—
72	C₃×#929	—	3	4	no	—
73	C₃×C₄×#67	—	3	4	no	—
74	C₂×C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
75	C₃×#924	—	3	4	no	—
76	C₃×#898	—	3	4	no	—
77	C₃×#896	—	3	4	no	—
78	C₃×#885	—	3	4	no	—
79	C₃×#883	—	3	4	no	—
80	C₃×D₃×C₂²⋊C₄	—	3	4	no	—
81	C₃×#877	—	3	4	no	—
82	C₃×#876	—	3	4	no	—
83	C₃×#872	—	3	4	no	—
84	C₂³×C₃³	C₂³	1	1	yes	characteristic
85	C₂³×C₃³	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
87	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
88	C₂²×C₃×C₃⋊D₃	—	4	1	no	—
89	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
91	C₃³×D₄	—	2	2	no	—
92	C₂×C₃³×C₄	—	4	1	no	—
93	C₂×C₃³×C₄	—	4	1	no	—
94	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
95	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
96	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
97	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
98	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
99	C₃×#638	—	2	2	no	—
100	C₃×#638	—	4	1	no	—
101	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
102	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
108	C₃×C₄×C₃⋊D₃	—	2	2	no	—
109	C₃×C₄×C₃⋊D₃	—	4	1	no	—
110	C₃×#634	—	4	1	no	—
111	C₃×#551	—	9	1	no	—
112	#5556	—	3	4	no	—
113	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
114	C₂³×C₃×D₃	—	3	4	no	—
115	C₂×C₃²×D₄	—	2	4	no	—
116	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
117	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₂²×C₃²×C₄	—	2	4	no	—
119	C₂²×C₃²×C₄	—	2	4	no	—
120	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
121	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	complemented
122	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂×#638	C₂²×C₃	1	1	yes	characteristic
125	C₂×#638	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
129	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₂×C₃×#67	—	3	4	no	—
131	C₂×C₃×#67	—	3	4	no	—
132	C₂²×C₃×Dic₃	—	3	4	no	—
133	C₂×C₃×C₄×D₃	—	3	4	no	—
134	C₂×C₃×C₄×D₃	—	3	4	no	—
135	C₂×C₃×Dic₆	—	3	4	no	—
136	C₃²×C₄⋊C₄	—	2	4	no	—
137	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
138	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₃²×C₂²⋊C₄	—	2	4	no	—
140	C₃²×C₂²⋊C₄	—	2	4	no	—
141	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
142	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
143	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
145	C₃²×C₄²	—	2	4	no	—
146	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
147	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
148	#3757	C₂²×C₃	1	1	yes	characteristic
149	#3757	C₂²×C₃	1	1	yes	characteristic
150	#3757	C₂²×C₃	1	1	yes	characteristic, complemented
151	#3757	C₂²×C₃	1	1	yes	characteristic, complemented
152	#3752	C₂²×C₃	1	1	yes	characteristic
153	#3752	C₂²×C₃	1	1	yes	characteristic
154	#3752	C₂²×C₃	1	1	yes	characteristic
155	#3752	C₂²×C₃	1	1	yes	characteristic
156	#3752	C₂²×C₃	1	1	yes	characteristic
157	#3752	C₂²×C₃	1	1	yes	characteristic
158	#3752	C₂²×C₃	1	1	yes	characteristic
159	#3752	C₂²×C₃	1	1	yes	characteristic
160	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic, complemented
161	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
162	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
163	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
164	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
165	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
166	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₃×#217	—	3	4	no	—
170	C₃×#217	—	3	4	no	—
171	C₃×#217	—	3	4	no	—
172	C₃×#217	—	3	4	no	—
173	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
174	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
175	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
176	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
177	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
178	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
179	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
180	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
181	C₃×C₄⋊Dic₃	—	3	4	no	—
182	C₃×Dic₃⋊C₄	—	3	4	no	—
183	C₃×Dic₃⋊C₄	—	3	4	no	—
184	C₃×Dic₃⋊C₄	—	3	4	no	—
185	C₃×Dic₃⋊C₄	—	3	4	no	—
186	C₃×Dic₃⋊C₄	—	3	4	no	—
187	C₃×Dic₃⋊C₄	—	3	4	no	—
188	C₃×C₄×Dic₃	—	3	4	no	—
189	C₃×C₄×Dic₃	—	3	4	no	—
190	C₂²×C₃³	—	2	1	no	—
191	C₂²×C₃³	—	2	1	no	—
192	C₂²×C₃³	—	2	1	no	—
193	C₂²×C₃³	—	2	1	no	—
194	C₂²×C₃³	—	2	1	no	—
195	C₂²×C₃³	#41	1	2	yes	—
196	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
197	C₂×C₃×C₃⋊D₃	—	2	1	no	—
198	C₂×C₃×C₃⋊D₃	—	2	1	no	—
199	C₂×C₃×C₃⋊D₃	—	2	1	no	—
200	C₂×C₃×C₃⋊D₃	—	2	1	no	—
201	C₂×C₃×C₃⋊D₃	—	2	1	no	—
202	C₂×C₃×C₃⋊D₃	—	4	4	no	—
203	C₂×C₃×C₃⋊D₃	#41	1	2	yes	—
204	C₃³×C₄	—	2	1	no	—
205	C₃³×C₄	—	2	1	no	—
206	C₃³×C₄	—	2	1	no	—
207	C₃³×C₄	—	2	1	no	—
208	C₃³×C₄	—	2	1	no	—
209	C₃×C₃⋊Dic₃	—	2	1	no	—
210	C₃×C₃⋊Dic₃	—	2	1	no	—
211	C₃×C₃⋊Dic₃	—	2	1	no	—
212	C₃×C₃⋊Dic₃	—	2	1	no	—
213	C₃×C₃⋊Dic₃	—	2	1	no	—
214	C₃×C₃⋊Dic₃	—	2	1	no	—
215	C₃×#126	—	9	1	no	—
216	C₃×#126	—	9	1	no	—
217	C₃×#124	—	9	1	no	—
218	C₃×#123	—	9	1	no	—
219	C₃×#123	—	9	1	no	—
220	C₃×#123	—	9	1	no	—
221	C₃×C₂²⋊Q₈	—	9	1	no	—
222	C₃×C₂²⋊Q₈	—	9	1	no	—
223	C₃×#120	—	9	1	no	—
224	C₃×C₄×D₄	—	2	4	no	—
225	C₃×C₄×D₄	—	9	1	no	—
226	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
227	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
228	C₃×#117	—	9	1	no	—
229	C₃×#117	—	9	1	no	—
230	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
231	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
232	#937	—	3	4	no	—
233	#935	—	3	4	no	—
234	#929	—	3	4	no	—
235	C₄×#67	—	3	4	no	—
236	C₂×(C₂×D₃)⋊C₄	—	3	4	no	—
237	#924	—	3	4	no	—
238	#898	—	3	4	no	—
239	#896	—	3	4	no	—
240	#885	—	3	4	no	—
241	#883	—	3	4	no	—
242	D₃×C₂²⋊C₄	—	3	4	no	—
243	#877	—	3	4	no	—
244	#876	—	3	4	no	—
245	#872	—	3	4	no	—
246	C₂³×C₃²	—	2	4	no	—
247	C₂³×C₃²	—	2	4	no	—
248	C₂³×C₃²	C₂²×D₃	1	4	yes	—
249	C₂³×C₃²	C₂²×D₃	1	4	yes	—
250	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
251	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₃⋊D₃	—	2	2	no	—
253	C₂²×C₃⋊D₃	—	2	2	no	—
254	C₂²×C₃⋊D₃	—	4	1	no	—
255	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₃×D₃	—	3	4	no	—
258	C₂²×C₃×D₃	—	3	4	no	—
259	C₂²×C₃×D₃	—	6	8	no	—
260	C₂²×C₃×D₃	—	6	8	no	—
261	C₂²×C₃×D₃	—	12	4	no	—
262	C₃²×D₄	—	2	16	no	—
263	C₃²×D₄	—	2	8	no	—
264	C₃²×D₄	—	2	2	no	—
265	C₂×C₃²×C₄	—	2	4	no	—
266	C₂×C₃²×C₄	—	2	4	no	—
267	C₂×C₃²×C₄	—	2	4	no	—
268	C₂×C₃²×C₄	—	2	4	no	—
269	C₂×C₃²×C₄	—	2	4	no	—
270	C₂×C₃²×C₄	—	4	4	no	—
271	C₂×C₃²×C₄	—	4	4	no	—
272	C₂×C₃²×C₄	—	4	1	no	—
273	C₂×C₃²×C₄	—	4	1	no	—
274	C₂×C₃²×C₄	—	4	8	no	—
275	C₂×C₃²×C₄	—	4	8	no	—
276	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
277	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
278	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
279	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
280	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
281	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
286	#638	—	2	2	no	—
287	#638	—	4	1	no	—
288	C₂×C₃⋊Dic₃	—	2	2	no	—
289	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
295	C₄×C₃⋊D₃	—	2	2	no	—
296	C₄×C₃⋊D₃	—	4	1	no	—
297	#634	—	4	1	no	—
298	C₃×#67	—	6	8	no	—
299	C₃×#67	—	12	4	no	—
300	C₂×C₃×Dic₃	—	3	4	no	—
301	C₂×C₃×Dic₃	—	3	4	no	—
302	C₂×C₃×Dic₃	—	3	4	no	—
303	C₂×C₃×Dic₃	—	3	4	no	—
304	C₂×C₃×Dic₃	—	3	4	no	—
305	C₂×C₃×Dic₃	—	3	4	no	—
306	C₂×C₃×Dic₃	—	6	8	no	—
307	C₃×C₄×D₃	—	6	8	no	—
308	C₃×C₄×D₃	—	12	4	no	—
309	C₃×Dic₆	—	12	4	no	—
310	#551	—	9	1	no	Sylow
311	C₂×C₃³	—	2	2	no	—
312	C₂×C₃³	—	4	1	no	—
313	C₂×C₃³	C₂×#41	1	1	yes	characteristic
314	C₂×C₃³	C₂×#41	1	1	yes	characteristic
315	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
316	C₃×C₃⋊D₃	—	2	2	no	—
317	C₃×C₃⋊D₃	—	4	1	no	—
318	C₂⁴×C₃	—	9	1	no	—
319	C₂³×D₃	—	3	4	no	—
320	C₂×C₃×Q₈	—	9	1	no	—
321	C₂×C₃×D₄	—	2	4	no	—
322	C₂×C₃×D₄	—	9	1	no	—
323	C₂×C₃×D₄	—	9	1	no	—
324	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
325	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
326	C₂²×C₃×C₄	—	2	4	no	—
327	C₂²×C₃×C₄	—	2	4	no	—
328	C₂²×C₃×C₄	—	9	1	no	—
329	C₂²×C₃×C₄	—	9	1	no	—
330	C₂²×C₃×C₄	—	9	1	no	—
331	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
332	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
333	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
335	C₂×#67	—	3	4	no	—
336	C₂×#67	—	3	4	no	—
337	C₂²×Dic₃	—	3	4	no	—
338	C₂×C₄×D₃	—	3	4	no	—
339	C₂×C₄×D₃	—	3	4	no	—
340	C₂×Dic₆	—	3	4	no	—
341	C₃×C₄⋊C₄	—	2	4	no	—
342	C₃×C₄⋊C₄	—	9	1	no	—
343	C₃×C₄⋊C₄	—	9	1	no	—
344	C₃×C₄⋊C₄	—	9	1	no	—
345	C₃×C₄⋊C₄	—	9	1	no	—
346	C₃×C₄⋊C₄	—	9	1	no	—
347	C₃×C₄⋊C₄	—	9	1	no	—
348	C₃×C₄⋊C₄	—	9	1	no	—
349	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
350	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
351	C₃×C₂²⋊C₄	—	2	4	no	—
352	C₃×C₂²⋊C₄	—	2	4	no	—
353	C₃×C₂²⋊C₄	—	9	1	no	—
354	C₃×C₂²⋊C₄	—	9	1	no	—
355	C₃×C₂²⋊C₄	—	9	1	no	—
356	C₃×C₂²⋊C₄	—	9	1	no	—
357	C₃×C₂²⋊C₄	—	9	1	no	—
358	C₃×C₂²⋊C₄	—	9	1	no	—
359	C₃×C₂²⋊C₄	—	9	1	no	—
360	C₃×C₂²⋊C₄	—	9	1	no	—
361	C₃×C₂²⋊C₄	—	9	1	no	—
362	C₃×C₂²⋊C₄	—	9	1	no	—
363	C₃×C₂²⋊C₄	—	9	1	no	—
364	C₃×C₂²⋊C₄	—	9	1	no	—
365	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
366	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
367	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
368	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
369	C₃×C₄²	—	2	4	no	—
370	C₃×C₄²	—	9	1	no	—
371	C₃×C₄²	—	9	1	no	—
372	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
373	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
374	#217	—	3	4	no	—
375	#217	—	3	4	no	—
376	#217	—	3	4	no	—
377	#217	—	3	4	no	—
378	(C₂×D₃)⋊C₄	—	3	4	no	—
379	(C₂×D₃)⋊C₄	—	3	4	no	—
380	(C₂×D₃)⋊C₄	—	3	4	no	—
381	(C₂×D₃)⋊C₄	—	3	4	no	—
382	(C₂×D₃)⋊C₄	—	3	4	no	—
383	(C₂×D₃)⋊C₄	—	3	4	no	—
384	(C₂×D₃)⋊C₄	—	3	4	no	—
385	(C₂×D₃)⋊C₄	—	3	4	no	—
386	C₄⋊Dic₃	—	3	4	no	—
387	Dic₃⋊C₄	—	3	4	no	—
388	Dic₃⋊C₄	—	3	4	no	—
389	Dic₃⋊C₄	—	3	4	no	—
390	Dic₃⋊C₄	—	3	4	no	—
391	Dic₃⋊C₄	—	3	4	no	—
392	Dic₃⋊C₄	—	3	4	no	—
393	C₄×Dic₃	—	3	4	no	—
394	C₄×Dic₃	—	3	4	no	—
395	C₂²×C₃²	—	2	1	no	—
396	C₂²×C₃²	—	2	1	no	—
397	C₂²×C₃²	—	2	8	no	—
398	C₂²×C₃²	—	2	4	no	—
399	C₂²×C₃²	—	2	1	no	—
400	C₂²×C₃²	—	2	1	no	—
401	C₂²×C₃²	—	2	1	no	—
402	C₂²×C₃²	—	2	4	no	—
403	C₂²×C₃²	—	2	8	no	—
404	C₂²×C₃²	—	2	4	no	—
405	C₂²×C₃²	—	2	4	no	—
406	C₂²×C₃²	—	2	4	no	—
407	C₂²×C₃²	—	2	4	no	—
408	C₂²×C₃²	—	4	4	no	—
409	C₂²×C₃²	—	4	4	no	—
410	C₂²×C₃²	—	4	4	no	—
411	C₂²×C₃²	—	4	4	no	—
412	C₂²×C₃²	#235	1	8	yes	—
413	C₂²×C₃²	C₃×#41	1	2	yes	—
414	C₂²×C₃²	C₂³×D₃	1	4	yes	—
415	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
416	C₂×C₃⋊D₃	—	2	1	no	—
417	C₂×C₃⋊D₃	—	2	1	no	—
418	C₂×C₃⋊D₃	—	2	1	no	—
419	C₂×C₃⋊D₃	—	2	1	no	—
420	C₂×C₃⋊D₃	—	2	1	no	—
421	C₂×C₃⋊D₃	—	4	4	no	—
422	C₂×C₃⋊D₃	C₃×#41	1	2	yes	—
423	C₂×C₃×D₃	—	3	8	no	—
424	C₂×C₃×D₃	—	6	4	no	—
425	C₂×C₃×D₃	—	6	4	no	—
426	C₂×C₃×D₃	—	6	4	no	—
427	C₂×C₃×D₃	—	6	4	no	—
428	C₂×C₃×D₃	—	6	4	no	—
429	C₂×C₃×D₃	—	12	16	no	—
430	C₃²×C₄	—	2	8	no	—
431	C₃²×C₄	—	2	8	no	—
432	C₃²×C₄	—	2	4	no	—
433	C₃²×C₄	—	2	4	no	—
434	C₃²×C₄	—	2	1	no	—
435	C₃²×C₄	—	2	1	no	—
436	C₃²×C₄	—	2	1	no	—
437	C₃²×C₄	—	2	1	no	—
438	C₃²×C₄	—	2	1	no	—
439	C₃²×C₄	—	2	4	no	—
440	C₃²×C₄	—	2	4	no	—
441	C₃²×C₄	—	2	4	no	—
442	C₃²×C₄	—	4	4	no	—
443	C₃²×C₄	—	4	4	no	—
444	C₃²×C₄	—	4	4	no	—
445	C₃⋊Dic₃	—	2	1	no	—
446	C₃⋊Dic₃	—	2	1	no	—
447	C₃⋊Dic₃	—	2	1	no	—
448	C₃⋊Dic₃	—	2	1	no	—
449	C₃⋊Dic₃	—	2	1	no	—
450	C₃⋊Dic₃	—	2	1	no	—
451	C₃×Dic₃	—	6	4	no	—
452	C₃×Dic₃	—	6	4	no	—
453	C₃×Dic₃	—	6	4	no	—
454	C₃×Dic₃	—	6	4	no	—
455	C₃×Dic₃	—	6	4	no	—
456	C₃×Dic₃	—	6	4	no	—
457	#126	—	9	1	no	—
458	#126	—	9	1	no	—
459	#124	—	9	1	no	—
460	#123	—	9	1	no	—
461	#123	—	9	1	no	—
462	#123	—	9	1	no	—
463	C₂²⋊Q₈	—	9	1	no	—
464	C₂²⋊Q₈	—	9	1	no	—
465	#120	—	9	1	no	—
466	C₄×D₄	—	9	1	no	—
467	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
468	#117	—	9	1	no	—
469	#117	—	9	1	no	—
470	C₂×C₂²⋊C₄	—	9	1	no	—
471	C₂×C₂²⋊C₄	—	9	1	no	—
472	C₃³	#551	1	1	yes	characteristic, complemented, Sylow
473	C₂³×C₃	—	2	4	no	—
474	C₂³×C₃	—	2	4	no	—
475	C₂³×C₃	—	9	1	no	—
476	C₂³×C₃	—	9	1	no	—
477	C₂³×C₃	—	18	2	no	—
478	C₂³×C₃	—	18	2	no	—
479	C₂³×C₃	—	36	1	no	—
480	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
481	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
482	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
483	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
484	C₂²×D₃	—	3	4	no	—
485	C₂²×D₃	—	3	4	no	—
486	C₂²×D₃	—	6	8	no	—
487	C₂²×D₃	—	6	8	no	—
488	C₂²×D₃	—	12	4	no	—
489	C₃×Q₈	—	36	1	no	—
490	C₃×D₄	—	2	16	no	—
491	C₃×D₄	—	2	8	no	—
492	C₃×D₄	—	2	2	no	—
493	C₃×D₄	—	18	2	no	—
494	C₃×D₄	—	36	1	no	—
495	C₂×C₃×C₄	—	2	4	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	2	4	no	—
498	C₂×C₃×C₄	—	2	4	no	—
499	C₂×C₃×C₄	—	2	4	no	—
500	C₂×C₃×C₄	—	4	4	no	—
501	C₂×C₃×C₄	—	4	4	no	—
502	C₂×C₃×C₄	—	4	1	no	—
503	C₂×C₃×C₄	—	4	1	no	—
504	C₂×C₃×C₄	—	4	8	no	—
505	C₂×C₃×C₄	—	4	8	no	—
506	C₂×C₃×C₄	—	9	1	no	—
507	C₂×C₃×C₄	—	9	1	no	—
508	C₂×C₃×C₄	—	9	1	no	—
509	C₂×C₃×C₄	—	9	1	no	—
510	C₂×C₃×C₄	—	9	1	no	—
511	C₂×C₃×C₄	—	9	1	no	—
512	C₂×C₃×C₄	—	18	2	no	—
513	C₂×C₃×C₄	—	18	2	no	—
514	C₂×C₃×C₄	—	36	1	no	—
515	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
516	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
517	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
518	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
519	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
520	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
522	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
525	#67	—	6	8	no	—
526	#67	—	12	4	no	—
527	C₂×Dic₃	—	3	4	no	—
528	C₂×Dic₃	—	3	4	no	—
529	C₂×Dic₃	—	3	4	no	—
530	C₂×Dic₃	—	3	4	no	—
531	C₂×Dic₃	—	3	4	no	—
532	C₂×Dic₃	—	3	4	no	—
533	C₂×Dic₃	—	6	8	no	—
534	C₄×D₃	—	6	8	no	—
535	C₄×D₃	—	12	4	no	—
536	Dic₆	—	12	4	no	—
537	C₂×C₃²	—	2	2	no	—
538	C₂×C₃²	—	2	4	no	—
539	C₂×C₃²	—	2	4	no	—
540	C₂×C₃²	—	2	4	no	—
541	C₂×C₃²	—	2	8	no	—
542	C₂×C₃²	—	4	8	no	—
543	C₂×C₃²	—	4	8	no	—
544	C₂×C₃²	—	4	4	no	—
545	C₂×C₃²	—	4	1	no	—
546	C₂×C₃²	C₂×#235	1	4	yes	—
547	C₂×C₃²	#1004	1	4	yes	—
548	C₂×C₃²	D₃×#41	1	4	yes	—
549	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
550	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
551	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
552	C₃⋊D₃	—	2	2	no	—
553	C₃⋊D₃	—	4	1	no	—
554	C₃×D₃	—	6	8	no	—
555	C₃×D₃	—	12	4	no	—
556	C₂⁴	—	9	1	no	—
557	C₂×Q₈	—	9	1	no	—
558	C₂×D₄	—	9	1	no	—
559	C₂×D₄	—	9	1	no	—
560	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
561	C₂²×C₄	—	9	1	no	—
562	C₂²×C₄	—	9	1	no	—
563	C₂²×C₄	—	9	1	no	—
564	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
565	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
566	C₄⋊C₄	—	9	1	no	—
567	C₄⋊C₄	—	9	1	no	—
568	C₄⋊C₄	—	9	1	no	—
569	C₄⋊C₄	—	9	1	no	—
570	C₄⋊C₄	—	9	1	no	—
571	C₄⋊C₄	—	9	1	no	—
572	C₄⋊C₄	—	9	1	no	—
573	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
574	C₂²⋊C₄	—	9	1	no	—
575	C₂²⋊C₄	—	9	1	no	—
576	C₂²⋊C₄	—	9	1	no	—
577	C₂²⋊C₄	—	9	1	no	—
578	C₂²⋊C₄	—	9	1	no	—
579	C₂²⋊C₄	—	9	1	no	—
580	C₂²⋊C₄	—	9	1	no	—
581	C₂²⋊C₄	—	9	1	no	—
582	C₂²⋊C₄	—	9	1	no	—
583	C₂²⋊C₄	—	9	1	no	—
584	C₂²⋊C₄	—	9	1	no	—
585	C₂²⋊C₄	—	9	1	no	—
586	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
587	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
588	C₄²	—	9	1	no	—
589	C₄²	—	9	1	no	—
590	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
591	C₂²×C₃	—	2	4	no	—
592	C₂²×C₃	—	2	4	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	2	8	no	—
596	C₂²×C₃	—	2	4	no	—
597	C₂²×C₃	—	2	4	no	—
598	C₂²×C₃	—	2	4	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	2	1	no	—
602	C₂²×C₃	—	2	4	no	—
603	C₂²×C₃	—	2	8	no	—
604	C₂²×C₃	—	4	4	no	—
605	C₂²×C₃	—	4	4	no	—
606	C₂²×C₃	—	4	4	no	—
607	C₂²×C₃	—	4	4	no	—
608	C₂²×C₃	—	9	2	no	—
609	C₂²×C₃	—	18	1	no	—
610	C₂²×C₃	—	18	1	no	—
611	C₂²×C₃	—	18	1	no	—
612	C₂²×C₃	—	18	1	no	—
613	C₂²×C₃	—	18	1	no	—
614	C₂²×C₃	—	36	4	no	—
615	C₂²×C₃	C₃×#235	1	8	yes	—
616	C₂²×C₃	#3828	1	2	yes	—
617	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
618	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
619	C₂×D₃	—	3	8	no	—
620	C₂×D₃	—	6	4	no	—
621	C₂×D₃	—	6	4	no	—
622	C₂×D₃	—	6	4	no	—
623	C₂×D₃	—	6	4	no	—
624	C₂×D₃	—	6	4	no	—
625	C₂×D₃	—	12	16	no	—
626	C₃×C₄	—	2	8	no	—
627	C₃×C₄	—	2	8	no	—
628	C₃×C₄	—	2	4	no	—
629	C₃×C₄	—	2	4	no	—
630	C₃×C₄	—	2	4	no	—
631	C₃×C₄	—	2	4	no	—
632	C₃×C₄	—	2	4	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	2	1	no	—
636	C₃×C₄	—	2	1	no	—
637	C₃×C₄	—	2	1	no	—
638	C₃×C₄	—	4	4	no	—
639	C₃×C₄	—	4	4	no	—
640	C₃×C₄	—	4	4	no	—
641	C₃×C₄	—	18	1	no	—
642	C₃×C₄	—	18	1	no	—
643	C₃×C₄	—	18	1	no	—
644	C₃×C₄	—	18	1	no	—
645	C₃×C₄	—	18	1	no	—
646	C₃×C₄	—	18	1	no	—
647	Dic₃	—	6	4	no	—
648	Dic₃	—	6	4	no	—
649	Dic₃	—	6	4	no	—
650	Dic₃	—	6	4	no	—
651	Dic₃	—	6	4	no	—
652	Dic₃	—	6	4	no	—
653	C₃²	—	2	4	no	—
654	C₃²	#5556	1	4	yes	complemented
655	C₃²	C₃×#551	1	1	yes	characteristic, complemented
656	C₂³	—	9	1	no	—
657	C₂³	—	9	1	no	—
658	C₂³	—	18	2	no	—
659	C₂³	—	18	2	no	—
660	C₂³	—	36	1	no	—
661	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
662	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
663	Q₈	—	36	1	no	—
664	D₄	—	2	2	no	—
665	D₄	—	18	2	no	—
666	D₄	—	36	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	9	1	no	—
670	C₂×C₄	—	9	1	no	—
671	C₂×C₄	—	9	1	no	—
672	C₂×C₄	—	9	1	no	—
673	C₂×C₄	—	9	1	no	—
674	C₂×C₄	—	9	1	no	—
675	C₂×C₄	—	18	2	no	—
676	C₂×C₄	—	18	2	no	—
677	C₂×C₄	—	36	1	no	—
678	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
679	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
680	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
681	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
682	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
683	C₂×C₃	—	2	8	no	—
684	C₂×C₃	—	2	2	no	—
685	C₂×C₃	—	2	4	no	—
686	C₂×C₃	—	2	4	no	—
687	C₂×C₃	—	2	4	no	—
688	C₂×C₃	—	4	8	no	—
689	C₂×C₃	—	4	8	no	—
690	C₂×C₃	—	4	4	no	—
691	C₂×C₃	—	4	1	no	—
692	C₂×C₃	—	18	2	no	—
693	C₂×C₃	—	36	1	no	—
694	C₂×C₃	C₂×C₃×#235	1	4	yes	—
695	C₂×C₃	C₃×#1004	1	4	yes	—
696	C₂×C₃	C₃×D₃×#41	1	4	yes	—
697	C₂×C₃	C₂×#3828	1	1	yes	characteristic
698	C₂×C₃	#64361	1	1	yes	characteristic
699	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
700	D₃	—	6	8	no	—
701	D₃	—	12	4	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	9	2	no	—
708	C₂²	—	18	1	no	—
709	C₂²	—	18	1	no	—
710	C₂²	—	18	1	no	—
711	C₂²	—	18	1	no	—
712	C₂²	—	18	1	no	—
713	C₂²	—	36	4	no	—
714	C₂²	C₃×#3828	1	2	yes	—
715	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	18	1	no	—
722	C₄	—	18	1	no	—
723	C₄	—	18	1	no	—
724	C₄	—	18	1	no	—
725	C₄	—	18	1	no	—
726	C₄	—	18	1	no	—
727	C₃	—	2	4	no	—
728	C₃	C₃×#5556	1	4	yes	complemented
729	C₃	#10596027	1	1	yes	characteristic, direct product factor
730	C₂	—	2	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	18	2	no	—
733	C₂	—	36	1	no	—
734	C₂	C₂×C₃×#3828	1	1	yes	characteristic
735	C₂	C₃×#64361	1	1	yes	characteristic
736	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃×#64146	C₂
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#551
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×D₄	C₂	semidirect
3. C₃×#64144	C₂	semidirect
4. C₃×#64138	C₂	semidirect
5. C₃×C₄×#638	C₂	semidirect
6. C₂×C₃×#3752	C₂	semidirect
7. C₃×#64133	C₂	semidirect
8. C₃×#64107	C₂	semidirect
9. C₃×#64105	C₂	semidirect
10. C₃×#64094	C₂	semidirect
11. C₃×#64092	C₂	semidirect
12. C₃×C₂²⋊C₄×C₃⋊D₃	C₂	semidirect
13. C₃×#64086	C₂	semidirect
14. C₃×#64085	C₂	semidirect
15. C₃×#64081	C₂	semidirect
16. #10596027	C₃	direct (N × H)
21. C₂²×C₃³×C₄	C₂²	semidirect
27. C₂×C₃×#634	C₂²	semidirect
28. C₃³×C₄⋊C₄	C₂²	semidirect
30. C₃³×C₂²⋊C₄	C₂²	semidirect
31. C₃³×C₄²	C₂²	semidirect
34. C₃×#3757	C₂²	semidirect
35. C₃×#3757	C₂²	semidirect
44. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
45. C₃×#3750	C₂²	semidirect
46. C₃×#3750	C₂²	semidirect
47. C₃×#3750	C₂²	semidirect
48. C₃×#3750	C₂²	semidirect
49. C₃×#3750	C₂²	semidirect
50. C₃×#3750	C₂²	semidirect
51. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
52. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
54. C₃²×C₄×D₄	D₃	semidirect
55. C₃²×C₄×D₄	C₂×C₃	semidirect
57. #64144	C₂×C₃	semidirect
58. #64138	C₂×C₃	semidirect
59. C₄×#638	C₂×C₃	semidirect
60. C₂×#3752	C₂×C₃	semidirect
61. #64133	C₂×C₃	semidirect
62. #64107	C₂×C₃	semidirect
63. #64105	C₂×C₃	semidirect
64. #64094	C₂×C₃	semidirect
65. #64092	C₂×C₃	semidirect
66. C₂²⋊C₄×C₃⋊D₃	C₂×C₃	semidirect
67. #64086	C₂×C₃	semidirect
68. #64085	C₂×C₃	semidirect
69. #64081	C₂×C₃	semidirect
121. C₂²×C₃²×C₄	C₂×D₃	semidirect
123. C₂²×C₃²×C₄	C₂²×C₃	semidirect
129. C₂×#634	C₂²×C₃	semidirect
137. C₃²×C₄⋊C₄	C₂×D₃	semidirect
138. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
142. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
144. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
146. C₃²×C₄²	C₂×D₃	semidirect
147. C₃²×C₄²	C₂²×C₃	semidirect
150. #3757	C₂²×C₃	semidirect
151. #3757	C₂²×C₃	semidirect
160. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
161. #3750	C₂²×C₃	semidirect
162. #3750	C₂²×C₃	semidirect
163. #3750	C₂²×C₃	semidirect
164. #3750	C₂²×C₃	semidirect
165. #3750	C₂²×C₃	semidirect
166. #3750	C₂²×C₃	semidirect
167. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
168. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
226. C₃×C₄×D₄	C₃×D₃	semidirect
227. C₃×C₄×D₄	C₃⋊D₃	semidirect
332. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
334. C₂²×C₃×C₄	C₂×C₃⋊D₃	semidirect
349. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
350. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
366. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
368. C₃×C₂²⋊C₄	C₂×C₃⋊D₃	semidirect
372. C₃×C₄²	C₂×C₃×D₃	semidirect
373. C₃×C₄²	C₂×C₃⋊D₃	semidirect
467. C₄×D₄	C₃×C₃⋊D₃	semidirect
472. C₃³	#551	semidirect
565. C₂²×C₄	C₂×C₃×C₃⋊D₃	semidirect
573. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
587. C₂²⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
590. C₄²	C₂×C₃×C₃⋊D₃	semidirect
654. C₃²	#5556	semidirect
655. C₃²	C₃×#551	semidirect
728. C₃	C₃×#5556	semidirect
729. C₃	#10596027	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×D₄	2
C₃×#64146	2
C₃×#64144	2
C₃×#64138	2
C₃×C₄×#638	2
C₂×C₃×#3752	2
C₃×#64133	2
C₃×#64107	2
C₃×#64105	2
C₃×#64094	2
C₃×#64092	2
C₃×C₂²⋊C₄×C₃⋊D₃	2
C₃×#64086	2
C₃×#64085	2
C₃×#64081	2
#10596027	3
C₃×#5556	3

Subgroups — C3×#10596027 #13179308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596027 #13179308