Subgroups — C₃×#10595998 #13179281

Order 1728.

1792 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3752	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64105	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64091	C₂	1	1	yes	maximal, characteristic
9	C₃×#64090	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₂²⋊C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64087	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#64085	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#64084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#64081	C₂	1	1	yes	maximal, characteristic, complemented
16	#10595998	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₃×#5527	—	3	4	no	maximal
18	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×#638	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×C₃⋊D₃	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, complemented
27	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
28	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
33	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3757	C₂²	1	1	yes	characteristic
35	C₃×#3752	C₂²	1	1	yes	characteristic
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, complemented
44	C₃×#3752	C₂²	1	1	yes	characteristic, complemented
45	C₃×#3752	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₄⋊(C₃⋊Dic₃)	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×#3750	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃²×#117	—	2	4	no	—
54	C₃²×#117	D₃	1	4	yes	complemented
55	C₃²×#117	C₂×C₃	1	1	yes	characteristic, complemented
56	#64138	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#3752	C₂×C₃	1	1	yes	characteristic, complemented
58	#64107	C₂×C₃	1	1	yes	characteristic, complemented
59	#64105	C₂×C₃	1	1	yes	characteristic, complemented
60	#64103	C₂×C₃	1	1	yes	characteristic, complemented
61	#64103	C₂×C₃	1	1	yes	characteristic, complemented
62	#64091	C₂×C₃	1	1	yes	characteristic
63	#64090	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂²⋊C₄×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
65	#64087	C₂×C₃	1	1	yes	characteristic, complemented
66	#64085	C₂×C₃	1	1	yes	characteristic, complemented
67	#64084	C₂×C₃	1	1	yes	characteristic, complemented
68	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
69	#64081	C₂×C₃	1	1	yes	characteristic, complemented
70	C₃×#929	—	3	4	no	—
71	C₂×C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
72	C₃×#898	—	3	4	no	—
73	C₃×#896	—	3	4	no	—
74	C₃×#894	—	3	4	no	—
75	C₃×#894	—	3	4	no	—
76	C₃×#882	—	3	4	no	—
77	C₃×#67⋊C₄	—	3	4	no	—
78	C₃×D₃×C₂²⋊C₄	—	3	4	no	—
79	C₃×#878	—	3	4	no	—
80	C₃×#876	—	3	4	no	—
81	C₃×#875	—	3	4	no	—
82	C₃×C₄×D₁₂	—	3	4	no	—
83	C₃×#872	—	3	4	no	—
84	C₂³×C₃³	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
86	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
87	C₂²×C₃×C₃⋊D₃	—	4	1	no	—
88	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
91	C₂×C₃³×C₄	—	2	2	no	—
92	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
93	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
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	C₃×#638	—	2	2	no	—
99	C₂×C₃×C₃⋊Dic₃	—	4	1	no	—
100	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
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	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
106	C₃×C₄⋊(C₃⋊D₃)	—	4	1	no	—
107	C₃×C₄×C₃⋊D₃	—	2	2	no	—
108	C₃×C₄×C₃⋊D₃	—	4	1	no	—
109	C₃×C₄×C₃⋊D₃	—	4	1	no	—
110	C₃×#634	—	4	1	no	—
111	C₃×#551	—	9	1	no	—
112	#5527	—	3	4	no	—
113	C₂³×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
114	C₂³×C₃×D₃	—	3	4	no	—
115	C₂²×C₃²×C₄	—	2	4	no	—
116	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
117	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×#638	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₃×#67	—	3	4	no	—
127	C₂²×C₃×Dic₃	—	3	4	no	—
128	C₂×C₃×D₁₂	—	3	4	no	—
129	C₂×C₃×D₁₂	—	3	4	no	—
130	C₂×C₃×C₄×D₃	—	3	4	no	—
131	C₂×C₃×C₄×D₃	—	3	4	no	—
132	C₂×C₃×C₄×D₃	—	3	4	no	—
133	C₂×C₃×Dic₆	—	3	4	no	—
134	C₃²×C₄⋊C₄	—	2	4	no	—
135	C₃²×C₄⋊C₄	—	2	4	no	—
136	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
137	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	complemented
138	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₃²×C₂²⋊C₄	—	2	4	no	—
141	C₃²×C₂²⋊C₄	—	2	4	no	—
142	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
143	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
144	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₃²×C₄²	—	2	4	no	—
147	C₃²×C₄²	—	2	4	no	—
148	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
149	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
150	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
152	#3757	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	#3752	C₂²×C₃	1	1	yes	characteristic
161	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
162	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
163	#3752	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₄⋊(C₃⋊Dic₃)	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	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
168	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
169	#3750	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₃×#217	—	3	4	no	—
172	C₃×(C₂×D₃)⋊C₄	—	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×(C₂×D₃)⋊C₄	—	3	4	no	—
182	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
183	C₃×C₄⋊Dic₃	—	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×Dic₃⋊C₄	—	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	#41	1	2	yes	—
193	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
194	C₂×C₃×C₃⋊D₃	—	2	1	no	—
195	C₂×C₃×C₃⋊D₃	—	2	1	no	—
196	C₂×C₃×C₃⋊D₃	—	2	1	no	—
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	C₃³×C₄	—	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	—	9	1	no	—
225	C₃×C₄×D₄	—	9	1	no	—
226	C₃×#117	—	2	4	no	—
227	C₃×#117	—	9	1	no	—
228	C₃×#117	C₃×D₃	1	4	yes	complemented
229	C₃×#117	C₃⋊D₃	1	1	yes	characteristic, complemented
230	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
231	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
232	#929	—	3	4	no	—
233	C₂×(C₂×D₃)⋊C₄	—	3	4	no	—
234	#898	—	3	4	no	—
235	#896	—	3	4	no	—
236	#894	—	3	4	no	—
237	#894	—	3	4	no	—
238	#882	—	3	4	no	—
239	#67⋊C₄	—	3	4	no	—
240	D₃×C₂²⋊C₄	—	3	4	no	—
241	#878	—	3	4	no	—
242	#876	—	3	4	no	—
243	#875	—	3	4	no	—
244	C₄×D₁₂	—	3	4	no	—
245	#872	—	3	4	no	—
246	C₂³×C₃²	—	2	4	no	—
247	C₂³×C₃²	C₂²×D₃	1	4	yes	—
248	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
249	C₂²×C₃⋊D₃	—	2	2	no	—
250	C₂²×C₃⋊D₃	—	2	2	no	—
251	C₂²×C₃⋊D₃	—	4	1	no	—
252	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₃×D₃	—	3	4	no	—
256	C₂²×C₃×D₃	—	3	4	no	—
257	C₂²×C₃×D₃	—	3	4	no	—
258	C₂²×C₃×D₃	—	6	8	no	—
259	C₂²×C₃×D₃	—	6	8	no	—
260	C₂²×C₃×D₃	—	12	4	no	—
261	C₂×C₃²×C₄	—	2	16	no	—
262	C₂×C₃²×C₄	—	2	8	no	—
263	C₂×C₃²×C₄	—	2	2	no	—
264	C₂×C₃²×C₄	—	2	4	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	C₂²×D₃	1	4	yes	—
271	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
272	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
273	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
274	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
275	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
276	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
281	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
282	#638	—	2	2	no	—
283	C₂×C₃⋊Dic₃	—	4	1	no	—
284	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
289	C₄⋊(C₃⋊D₃)	—	2	2	no	—
290	C₄⋊(C₃⋊D₃)	—	4	1	no	—
291	C₄×C₃⋊D₃	—	2	2	no	—
292	C₄×C₃⋊D₃	—	4	1	no	—
293	C₄×C₃⋊D₃	—	4	1	no	—
294	#634	—	4	1	no	—
295	C₃×#67	—	6	8	no	—
296	C₂×C₃×Dic₃	—	3	4	no	—
297	C₂×C₃×Dic₃	—	3	4	no	—
298	C₂×C₃×Dic₃	—	3	4	no	—
299	C₂×C₃×Dic₃	—	3	4	no	—
300	C₂×C₃×Dic₃	—	3	4	no	—
301	C₂×C₃×Dic₃	—	12	4	no	—
302	C₃×D₁₂	—	6	8	no	—
303	C₃×D₁₂	—	12	4	no	—
304	C₃×C₄×D₃	—	6	8	no	—
305	C₃×C₄×D₃	—	12	4	no	—
306	C₃×C₄×D₃	—	12	4	no	—
307	C₃×Dic₆	—	12	4	no	—
308	#551	—	9	1	no	Sylow
309	C₂×C₃³	—	2	2	no	—
310	C₂×C₃³	C₂×#41	1	1	yes	characteristic
311	C₂×C₃³	C₂×#41	1	1	yes	characteristic
312	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
313	C₃×C₃⋊D₃	—	2	2	no	—
314	C₃×C₃⋊D₃	—	4	1	no	—
315	C₃×C₃⋊D₃	—	4	1	no	—
316	C₂⁴×C₃	—	9	1	no	—
317	C₂³×D₃	—	3	4	no	—
318	C₂×C₃×Q₈	—	9	1	no	—
319	C₂×C₃×D₄	—	9	1	no	—
320	C₂×C₃×D₄	—	9	1	no	—
321	C₂×C₃×D₄	—	9	1	no	—
322	C₂²×C₃×C₄	—	2	4	no	—
323	C₂²×C₃×C₄	—	9	1	no	—
324	C₂²×C₃×C₄	—	9	1	no	—
325	C₂²×C₃×C₄	—	9	1	no	—
326	C₂²×C₃×C₄	—	9	1	no	—
327	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
328	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
329	C₂×#67	—	3	4	no	—
330	C₂²×Dic₃	—	3	4	no	—
331	C₂×D₁₂	—	3	4	no	—
332	C₂×D₁₂	—	3	4	no	—
333	C₂×C₄×D₃	—	3	4	no	—
334	C₂×C₄×D₃	—	3	4	no	—
335	C₂×C₄×D₃	—	3	4	no	—
336	C₂×Dic₆	—	3	4	no	—
337	C₃×C₄⋊C₄	—	2	4	no	—
338	C₃×C₄⋊C₄	—	2	4	no	—
339	C₃×C₄⋊C₄	—	9	1	no	—
340	C₃×C₄⋊C₄	—	9	1	no	—
341	C₃×C₄⋊C₄	—	9	1	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	C₂×C₃×D₃	1	4	yes	complemented
346	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
347	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
348	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
349	C₃×C₂²⋊C₄	—	2	4	no	—
350	C₃×C₂²⋊C₄	—	2	4	no	—
351	C₃×C₂²⋊C₄	—	9	1	no	—
352	C₃×C₂²⋊C₄	—	9	1	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	C₂×C₃×D₃	1	4	yes	—
364	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
365	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
366	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
367	C₃×C₄²	—	2	4	no	—
368	C₃×C₄²	—	2	4	no	—
369	C₃×C₄²	—	9	1	no	—
370	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
371	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
372	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
373	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
374	#217	—	3	4	no	—
375	(C₂×D₃)⋊C₄	—	3	4	no	—
376	(C₂×D₃)⋊C₄	—	3	4	no	—
377	(C₂×D₃)⋊C₄	—	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	C₄×Dic₃	—	3	4	no	—
393	C₂²×C₃²	—	2	1	no	—
394	C₂²×C₃²	—	2	1	no	—
395	C₂²×C₃²	—	2	4	no	—
396	C₂²×C₃²	—	2	8	no	—
397	C₂²×C₃²	—	2	4	no	—
398	C₂²×C₃²	—	2	4	no	—
399	C₂²×C₃²	—	4	4	no	—
400	C₂²×C₃²	—	4	4	no	—
401	C₂²×C₃²	#235	1	8	yes	—
402	C₂²×C₃²	C₃×#41	1	2	yes	—
403	C₂²×C₃²	C₂³×D₃	1	4	yes	—
404	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
405	C₂×C₃⋊D₃	—	2	1	no	—
406	C₂×C₃⋊D₃	—	2	1	no	—
407	C₂×C₃⋊D₃	—	2	1	no	—
408	C₂×C₃⋊D₃	—	2	1	no	—
409	C₂×C₃⋊D₃	—	2	1	no	—
410	C₂×C₃⋊D₃	—	2	1	no	—
411	C₂×C₃⋊D₃	—	2	1	no	—
412	C₂×C₃⋊D₃	—	2	1	no	—
413	C₂×C₃⋊D₃	—	4	4	no	—
414	C₂×C₃⋊D₃	C₃×#41	1	2	yes	—
415	C₂×C₃×D₃	—	3	8	no	—
416	C₂×C₃×D₃	—	6	4	no	—
417	C₂×C₃×D₃	—	6	4	no	—
418	C₂×C₃×D₃	—	6	4	no	—
419	C₂×C₃×D₃	—	6	4	no	—
420	C₂×C₃×D₃	—	6	4	no	—
421	C₂×C₃×D₃	—	6	4	no	—
422	C₂×C₃×D₃	—	6	4	no	—
423	C₂×C₃×D₃	—	6	4	no	—
424	C₂×C₃×D₃	—	12	16	no	—
425	C₃²×C₄	—	2	8	no	—
426	C₃²×C₄	—	2	8	no	—
427	C₃²×C₄	—	2	4	no	—
428	C₃²×C₄	—	2	4	no	—
429	C₃²×C₄	—	2	1	no	—
430	C₃²×C₄	—	2	1	no	—
431	C₃²×C₄	—	2	1	no	—
432	C₃²×C₄	—	2	1	no	—
433	C₃²×C₄	—	2	1	no	—
434	C₃²×C₄	—	2	1	no	—
435	C₃²×C₄	—	2	4	no	—
436	C₃²×C₄	—	2	4	no	—
437	C₃²×C₄	—	2	4	no	—
438	C₃²×C₄	—	2	4	no	—
439	C₃²×C₄	—	4	4	no	—
440	C₃²×C₄	—	4	4	no	—
441	C₃²×C₄	—	4	4	no	—
442	C₃²×C₄	—	4	4	no	—
443	C₃⋊Dic₃	—	2	1	no	—
444	C₃⋊Dic₃	—	2	1	no	—
445	C₃⋊Dic₃	—	2	1	no	—
446	C₃⋊Dic₃	—	2	1	no	—
447	C₃⋊Dic₃	—	2	1	no	—
448	C₃×Dic₃	—	6	4	no	—
449	C₃×Dic₃	—	6	4	no	—
450	C₃×Dic₃	—	6	4	no	—
451	C₃×Dic₃	—	6	4	no	—
452	C₃×Dic₃	—	6	4	no	—
453	#126	—	9	1	no	—
454	#126	—	9	1	no	—
455	#124	—	9	1	no	—
456	#123	—	9	1	no	—
457	#123	—	9	1	no	—
458	#123	—	9	1	no	—
459	C₂²⋊Q₈	—	9	1	no	—
460	C₂²⋊Q₈	—	9	1	no	—
461	#120	—	9	1	no	—
462	C₄×D₄	—	9	1	no	—
463	C₄×D₄	—	9	1	no	—
464	#117	—	9	1	no	—
465	#117	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
466	C₂×C₂²⋊C₄	—	9	1	no	—
467	C₂×C₂²⋊C₄	—	9	1	no	—
468	C₃³	#551	1	1	yes	characteristic, complemented, Sylow
469	C₂³×C₃	—	2	4	no	—
470	C₂³×C₃	—	9	1	no	—
471	C₂³×C₃	—	9	1	no	—
472	C₂³×C₃	—	9	1	no	—
473	C₂³×C₃	—	18	2	no	—
474	C₂³×C₃	—	18	2	no	—
475	C₂³×C₃	—	36	1	no	—
476	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
477	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
478	C₂²×D₃	—	3	4	no	—
479	C₂²×D₃	—	3	4	no	—
480	C₂²×D₃	—	3	4	no	—
481	C₂²×D₃	—	6	8	no	—
482	C₂²×D₃	—	6	8	no	—
483	C₂²×D₃	—	12	4	no	—
484	C₃×Q₈	—	36	1	no	—
485	C₃×D₄	—	18	2	no	—
486	C₃×D₄	—	18	2	no	—
487	C₃×D₄	—	36	1	no	—
488	C₂×C₃×C₄	—	2	16	no	—
489	C₂×C₃×C₄	—	2	8	no	—
490	C₂×C₃×C₄	—	2	2	no	—
491	C₂×C₃×C₄	—	2	4	no	—
492	C₂×C₃×C₄	—	2	4	no	—
493	C₂×C₃×C₄	—	2	4	no	—
494	C₂×C₃×C₄	—	2	4	no	—
495	C₂×C₃×C₄	—	2	4	no	—
496	C₂×C₃×C₄	—	2	4	no	—
497	C₂×C₃×C₄	—	9	1	no	—
498	C₂×C₃×C₄	—	9	1	no	—
499	C₂×C₃×C₄	—	9	1	no	—
500	C₂×C₃×C₄	—	9	1	no	—
501	C₂×C₃×C₄	—	9	1	no	—
502	C₂×C₃×C₄	—	18	2	no	—
503	C₂×C₃×C₄	—	36	1	no	—
504	C₂×C₃×C₄	—	36	1	no	—
505	C₂×C₃×C₄	—	36	1	no	—
506	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
507	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
508	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
509	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
510	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
511	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
512	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
514	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
515	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
516	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
517	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
518	#67	—	6	8	no	—
519	C₂×Dic₃	—	3	4	no	—
520	C₂×Dic₃	—	3	4	no	—
521	C₂×Dic₃	—	3	4	no	—
522	C₂×Dic₃	—	3	4	no	—
523	C₂×Dic₃	—	3	4	no	—
524	C₂×Dic₃	—	12	4	no	—
525	D₁₂	—	6	8	no	—
526	D₁₂	—	12	4	no	—
527	C₄×D₃	—	6	8	no	—
528	C₄×D₃	—	12	4	no	—
529	C₄×D₃	—	12	4	no	—
530	Dic₆	—	12	4	no	—
531	C₂×C₃²	—	2	2	no	—
532	C₂×C₃²	—	2	4	no	—
533	C₂×C₃²	—	2	4	no	—
534	C₂×C₃²	—	2	4	no	—
535	C₂×C₃²	—	2	8	no	—
536	C₂×C₃²	—	4	8	no	—
537	C₂×C₃²	C₂×#235	1	4	yes	—
538	C₂×C₃²	D₃×#41	1	4	yes	—
539	C₂×C₃²	#1009	1	4	yes	—
540	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
541	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
542	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
543	C₃⋊D₃	—	2	2	no	—
544	C₃⋊D₃	—	4	1	no	—
545	C₃⋊D₃	—	4	1	no	—
546	C₃×D₃	—	6	8	no	—
547	C₃×D₃	—	12	4	no	—
548	C₃×D₃	—	12	4	no	—
549	C₂⁴	—	9	1	no	—
550	C₂×Q₈	—	9	1	no	—
551	C₂×D₄	—	9	1	no	—
552	C₂×D₄	—	9	1	no	—
553	C₂×D₄	—	9	1	no	—
554	C₂²×C₄	—	9	1	no	—
555	C₂²×C₄	—	9	1	no	—
556	C₂²×C₄	—	9	1	no	—
557	C₂²×C₄	—	9	1	no	—
558	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
559	C₄⋊C₄	—	9	1	no	—
560	C₄⋊C₄	—	9	1	no	—
561	C₄⋊C₄	—	9	1	no	—
562	C₄⋊C₄	—	9	1	no	—
563	C₄⋊C₄	—	9	1	no	—
564	C₄⋊C₄	—	9	1	no	—
565	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
566	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
567	C₂²⋊C₄	—	9	1	no	—
568	C₂²⋊C₄	—	9	1	no	—
569	C₂²⋊C₄	—	9	1	no	—
570	C₂²⋊C₄	—	9	1	no	—
571	C₂²⋊C₄	—	9	1	no	—
572	C₂²⋊C₄	—	9	1	no	—
573	C₂²⋊C₄	—	9	1	no	—
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	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
580	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
581	C₄²	—	9	1	no	—
582	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
583	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
584	C₂²×C₃	—	2	4	no	—
585	C₂²×C₃	—	2	4	no	—
586	C₂²×C₃	—	2	1	no	—
587	C₂²×C₃	—	2	1	no	—
588	C₂²×C₃	—	2	4	no	—
589	C₂²×C₃	—	2	8	no	—
590	C₂²×C₃	—	4	4	no	—
591	C₂²×C₃	—	4	4	no	—
592	C₂²×C₃	—	9	2	no	—
593	C₂²×C₃	—	18	1	no	—
594	C₂²×C₃	—	18	1	no	—
595	C₂²×C₃	—	18	1	no	—
596	C₂²×C₃	—	18	1	no	—
597	C₂²×C₃	—	18	1	no	—
598	C₂²×C₃	—	18	1	no	—
599	C₂²×C₃	—	18	1	no	—
600	C₂²×C₃	—	18	1	no	—
601	C₂²×C₃	—	36	4	no	—
602	C₂²×C₃	C₃×#235	1	8	yes	—
603	C₂²×C₃	#3828	1	2	yes	—
604	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
605	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
606	C₂×D₃	—	3	8	no	—
607	C₂×D₃	—	6	4	no	—
608	C₂×D₃	—	6	4	no	—
609	C₂×D₃	—	6	4	no	—
610	C₂×D₃	—	6	4	no	—
611	C₂×D₃	—	6	4	no	—
612	C₂×D₃	—	6	4	no	—
613	C₂×D₃	—	6	4	no	—
614	C₂×D₃	—	6	4	no	—
615	C₂×D₃	—	12	16	no	—
616	C₃×C₄	—	2	8	no	—
617	C₃×C₄	—	2	8	no	—
618	C₃×C₄	—	2	4	no	—
619	C₃×C₄	—	2	4	no	—
620	C₃×C₄	—	2	4	no	—
621	C₃×C₄	—	2	4	no	—
622	C₃×C₄	—	2	4	no	—
623	C₃×C₄	—	2	4	no	—
624	C₃×C₄	—	2	1	no	—
625	C₃×C₄	—	2	1	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	2	1	no	—
630	C₃×C₄	—	4	4	no	—
631	C₃×C₄	—	4	4	no	—
632	C₃×C₄	—	4	4	no	—
633	C₃×C₄	—	4	4	no	—
634	C₃×C₄	—	18	1	no	—
635	C₃×C₄	—	18	1	no	—
636	C₃×C₄	—	18	1	no	—
637	C₃×C₄	—	18	1	no	—
638	C₃×C₄	—	18	1	no	—
639	Dic₃	—	6	4	no	—
640	Dic₃	—	6	4	no	—
641	Dic₃	—	6	4	no	—
642	Dic₃	—	6	4	no	—
643	Dic₃	—	6	4	no	—
644	C₃²	—	2	4	no	—
645	C₃²	#5527	1	4	yes	complemented
646	C₃²	C₃×#551	1	1	yes	characteristic, complemented
647	C₂³	—	9	1	no	—
648	C₂³	—	9	1	no	—
649	C₂³	—	9	1	no	—
650	C₂³	—	18	2	no	—
651	C₂³	—	18	2	no	—
652	C₂³	—	36	1	no	—
653	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
654	Q₈	—	36	1	no	—
655	D₄	—	18	2	no	—
656	D₄	—	18	2	no	—
657	D₄	—	36	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	9	1	no	—
660	C₂×C₄	—	9	1	no	—
661	C₂×C₄	—	9	1	no	—
662	C₂×C₄	—	9	1	no	—
663	C₂×C₄	—	9	1	no	—
664	C₂×C₄	—	18	2	no	—
665	C₂×C₄	—	36	1	no	—
666	C₂×C₄	—	36	1	no	—
667	C₂×C₄	—	36	1	no	—
668	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
669	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
670	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
671	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
672	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
673	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
674	C₂×C₃	—	2	8	no	—
675	C₂×C₃	—	2	2	no	—
676	C₂×C₃	—	2	4	no	—
677	C₂×C₃	—	2	4	no	—
678	C₂×C₃	—	2	4	no	—
679	C₂×C₃	—	4	8	no	—
680	C₂×C₃	—	18	2	no	—
681	C₂×C₃	—	36	1	no	—
682	C₂×C₃	—	36	1	no	—
683	C₂×C₃	C₂×C₃×#235	1	4	yes	—
684	C₂×C₃	C₃×D₃×#41	1	4	yes	—
685	C₂×C₃	C₃×#1009	1	4	yes	—
686	C₂×C₃	C₂×#3828	1	1	yes	characteristic
687	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
688	C₂×C₃	#64366	1	1	yes	characteristic
689	D₃	—	6	8	no	—
690	D₃	—	12	4	no	—
691	D₃	—	12	4	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	9	2	no	—
695	C₂²	—	18	1	no	—
696	C₂²	—	18	1	no	—
697	C₂²	—	18	1	no	—
698	C₂²	—	18	1	no	—
699	C₂²	—	18	1	no	—
700	C₂²	—	18	1	no	—
701	C₂²	—	18	1	no	—
702	C₂²	—	18	1	no	—
703	C₂²	—	36	4	no	—
704	C₂²	C₃×#3828	1	2	yes	—
705	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	18	1	no	—
713	C₄	—	18	1	no	—
714	C₄	—	18	1	no	—
715	C₄	—	18	1	no	—
716	C₄	—	18	1	no	—
717	C₃	—	2	4	no	—
718	C₃	C₃×#5527	1	4	yes	complemented
719	C₃	#10595998	1	1	yes	characteristic, direct product factor
720	C₂	—	2	2	no	—
721	C₂	—	18	2	no	—
722	C₂	—	36	1	no	—
723	C₂	—	36	1	no	—
724	C₂	C₂×C₃×#3828	1	1	yes	characteristic
725	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic
726	C₂	C₃×#64366	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×#117	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃×#64091	C₂
hypercenter	C₃×#117	C₃⋊D₃
hypocenter	C₃²	C₃×#551
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₃³×#117	C₂	semidirect
2. C₃×#64138	C₂	semidirect
3. C₂×C₃×#3752	C₂	semidirect
4. C₃×#64107	C₂	semidirect
5. C₃×#64105	C₂	semidirect
6. C₃×#64103	C₂	semidirect
7. C₃×#64103	C₂	semidirect
9. C₃×#64090	C₂	semidirect
10. C₃×C₂²⋊C₄×C₃⋊D₃	C₂	semidirect
11. C₃×#64087	C₂	semidirect
12. C₃×#64085	C₂	semidirect
13. C₃×#64084	C₂	semidirect
14. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
15. C₃×#64081	C₂	semidirect
16. #10595998	C₃	direct (N × H)
26. C₂×C₃×C₄×C₃⋊D₃	C₂²	semidirect
27. C₂×C₃×#634	C₂²	semidirect
28. C₃³×C₄⋊C₄	C₂²	semidirect
29. C₃³×C₄⋊C₄	C₂²	semidirect
32. C₃³×C₄²	C₂²	semidirect
33. C₃³×C₄²	C₂²	semidirect
43. C₃×#3752	C₂²	semidirect
44. C₃×#3752	C₂²	semidirect
45. C₃×#3752	C₂²	semidirect
46. C₃×C₄⋊(C₃⋊Dic₃)	C₂²	semidirect
47. C₃×#3750	C₂²	semidirect
48. C₃×#3750	C₂²	semidirect
49. C₃×#3750	C₂²	semidirect
50. C₃×#3750	C₂²	semidirect
51. C₃×#3750	C₂²	semidirect
52. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
54. C₃²×#117	D₃	semidirect
55. C₃²×#117	C₂×C₃	semidirect
56. #64138	C₂×C₃	semidirect
57. C₂×#3752	C₂×C₃	semidirect
58. #64107	C₂×C₃	semidirect
59. #64105	C₂×C₃	semidirect
60. #64103	C₂×C₃	semidirect
61. #64103	C₂×C₃	semidirect
63. #64090	C₂×C₃	semidirect
64. C₂²⋊C₄×C₃⋊D₃	C₂×C₃	semidirect
65. #64087	C₂×C₃	semidirect
66. #64085	C₂×C₃	semidirect
67. #64084	C₂×C₃	semidirect
68. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
69. #64081	C₂×C₃	semidirect
124. C₂×C₄×C₃⋊D₃	C₂²×C₃	semidirect
125. C₂×#634	C₂²×C₃	semidirect
136. C₃²×C₄⋊C₄	C₂×D₃	semidirect
137. C₃²×C₄⋊C₄	C₂×D₃	semidirect
138. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
139. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
148. C₃²×C₄²	C₂×D₃	semidirect
149. C₃²×C₄²	C₂×D₃	semidirect
150. C₃²×C₄²	C₂²×C₃	semidirect
151. C₃²×C₄²	C₂²×C₃	semidirect
161. #3752	C₂²×C₃	semidirect
162. #3752	C₂²×C₃	semidirect
163. #3752	C₂²×C₃	semidirect
164. C₄⋊(C₃⋊Dic₃)	C₂²×C₃	semidirect
165. #3750	C₂²×C₃	semidirect
166. #3750	C₂²×C₃	semidirect
167. #3750	C₂²×C₃	semidirect
168. #3750	C₂²×C₃	semidirect
169. #3750	C₂²×C₃	semidirect
170. C₄×C₃⋊Dic₃	C₂²×C₃	semidirect
228. C₃×#117	C₃×D₃	semidirect
229. C₃×#117	C₃⋊D₃	semidirect
345. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
346. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
347. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
348. C₃×C₄⋊C₄	C₂×C₃⋊D₃	semidirect
370. C₃×C₄²	C₂×C₃×D₃	semidirect
371. C₃×C₄²	C₂×C₃×D₃	semidirect
372. C₃×C₄²	C₂×C₃⋊D₃	semidirect
373. C₃×C₄²	C₂×C₃⋊D₃	semidirect
465. #117	C₃×C₃⋊D₃	semidirect
468. C₃³	#551	semidirect
565. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
566. C₄⋊C₄	C₂×C₃×C₃⋊D₃	semidirect
582. C₄²	C₂×C₃×C₃⋊D₃	semidirect
583. C₄²	C₂×C₃×C₃⋊D₃	semidirect
645. C₃²	#5527	semidirect
646. C₃²	C₃×#551	semidirect
718. C₃	C₃×#5527	semidirect
719. C₃	#10595998	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×#117	2
C₃×#64138	2
C₂×C₃×#3752	2
C₃×#64107	2
C₃×#64105	2
C₃×#64103	2
C₃×#64091	2
C₃×#64090	2
C₃×C₂²⋊C₄×C₃⋊D₃	2
C₃×#64087	2
C₃×#64085	2
C₃×#64084	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64081	2
#10595998	3
C₃×#5527	3

Subgroups — C3×#10595998 #13179281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10595998 #13179281