Subgroups — C₃×#10596039 #13179319

Order 1728.

1552 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64156	C₂	1	1	yes	maximal, characteristic
3	C₃×#64153	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64107	C₂	1	2	yes	maximal, complemented
5	C₃×#64105	C₂	1	2	yes	maximal, complemented
6	C₃×#64102	C₂	1	1	yes	maximal, characteristic
7	C₃×#64096	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64085	C₂	1	2	yes	maximal, complemented
9	C₃×#64084	C₂	1	1	yes	maximal, characteristic
10	C₃×#64081	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596039	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5568	—	3	4	no	maximal
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
17	C₂×C₃×#634	C₂²	1	1	yes	characteristic
18	C₂×C₃×#634	C₂²	1	1	yes	characteristic
19	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃³×C₄²	C₂²	1	1	yes	characteristic
22	C₃³×C₄²	C₂²	1	2	yes	—
23	C₃×#3752	C₂²	1	2	yes	—
24	C₃×#3752	C₂²	1	2	yes	—
25	C₃×#3752	C₂²	1	2	yes	—
26	C₃×#3752	C₂²	1	2	yes	—
27	C₃×#3752	C₂²	1	2	yes	—
28	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
29	C₃×#3750	C₂²	1	1	yes	characteristic
30	C₃×#3750	C₂²	1	1	yes	characteristic
31	C₃×#3750	C₂²	1	2	yes	—
32	C₃×#3750	C₂²	1	2	yes	—
33	C₃×#3750	C₂²	1	2	yes	—
34	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
37	C₃²×C₄×Q₈	—	2	4	no	—
38	C₃²×C₄×Q₈	D₃	1	4	yes	complemented
39	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
40	#64156	C₂×C₃	1	1	yes	characteristic
41	#64153	C₂×C₃	1	1	yes	characteristic, complemented
42	#64107	C₂×C₃	1	2	yes	complemented
43	#64105	C₂×C₃	1	2	yes	complemented
44	#64102	C₂×C₃	1	1	yes	characteristic
45	#64096	C₂×C₃	1	1	yes	characteristic, complemented
46	#64085	C₂×C₃	1	2	yes	complemented
47	#64084	C₂×C₃	1	1	yes	characteristic
48	#64081	C₂×C₃	1	2	yes	complemented
49	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×#947	—	3	4	no	—
51	C₃×#944	—	3	4	no	—
52	C₃×#898	—	3	8	no	—
53	C₃×#896	—	3	8	no	—
54	C₃×#893	—	3	4	no	—
55	C₃×#887	—	3	4	no	—
56	C₃×#876	—	3	8	no	—
57	C₃×#875	—	3	4	no	—
58	C₃×#872	—	3	8	no	—
59	C₃×C₄×Dic₆	—	3	4	no	—
60	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
61	C₃³×Q₈	—	2	2	no	—
62	C₂×C₃³×C₄	C₂³	1	2	yes	—
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
64	C₂×C₃³×C₄	C₂³	1	2	yes	—
65	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
66	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
71	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
72	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
73	C₃×C₄×C₃⋊D₃	—	2	4	no	—
74	C₃×#634	—	2	2	no	—
75	C₃×#634	—	2	2	no	—
76	C₃×#556	—	9	1	no	—
77	#5568	—	3	4	no	—
78	C₂×C₃²×Q₈	—	2	4	no	—
79	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
80	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
83	C₂×#634	C₂²×C₃	1	1	yes	characteristic
84	C₂×#634	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₃×D₁₂	—	3	4	no	—
86	C₂×C₃×C₄×D₃	—	3	8	no	—
87	C₂×C₃×Dic₆	—	3	4	no	—
88	C₂×C₃×Dic₆	—	3	4	no	—
89	C₃²×C₄⋊C₄	—	2	4	no	—
90	C₃²×C₄⋊C₄	—	2	8	no	—
91	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
92	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
93	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₃²×C₄²	—	2	4	no	—
96	C₃²×C₄²	—	2	8	no	—
97	C₃²×C₄²	C₂×D₃	1	4	yes	—
98	C₃²×C₄²	C₂×D₃	1	8	yes	—
99	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
100	C₃²×C₄²	C₂²×C₃	1	2	yes	—
101	#3752	C₂²×C₃	1	2	yes	—
102	#3752	C₂²×C₃	1	2	yes	—
103	#3752	C₂²×C₃	1	2	yes	—
104	#3752	C₂²×C₃	1	2	yes	—
105	#3752	C₂²×C₃	1	2	yes	—
106	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
107	#3750	C₂²×C₃	1	1	yes	characteristic
108	#3750	C₂²×C₃	1	1	yes	characteristic
109	#3750	C₂²×C₃	1	2	yes	—
110	#3750	C₂²×C₃	1	2	yes	—
111	#3750	C₂²×C₃	1	2	yes	—
112	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
115	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
116	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
117	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
118	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
119	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
120	C₃×C₄⋊Dic₃	—	3	4	no	—
121	C₃×Dic₃⋊C₄	—	3	8	no	—
122	C₃×Dic₃⋊C₄	—	3	8	no	—
123	C₃×Dic₃⋊C₄	—	3	8	no	—
124	C₃×Dic₃⋊C₄	—	3	4	no	—
125	C₃×Dic₃⋊C₄	—	3	4	no	—
126	C₃×C₄×Dic₃	—	3	8	no	—
127	C₃×C₄×Dic₃	—	3	4	no	—
128	C₃×C₄×Dic₃	—	3	4	no	—
129	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
130	C₂×C₃×C₃⋊D₃	—	2	2	no	—
131	C₂×C₃×C₃⋊D₃	—	2	2	no	—
132	C₂×C₃×C₃⋊D₃	—	2	2	no	—
133	C₃³×C₄	—	2	2	no	—
134	C₃³×C₄	—	2	1	no	—
135	C₃³×C₄	—	2	2	no	—
136	C₃³×C₄	—	2	1	no	—
137	C₃³×C₄	#41	1	2	yes	—
138	C₃×C₃⋊Dic₃	—	2	2	no	—
139	C₃×C₃⋊Dic₃	—	2	1	no	—
140	C₃×C₃⋊Dic₃	—	2	1	no	—
141	C₃×C₃⋊Dic₃	—	2	1	no	—
142	C₃×C₃⋊Dic₃	#41	1	2	yes	—
143	C₃×C₄⋊Q₈	—	9	1	no	—
144	C₃×#126	—	9	2	no	—
145	C₃×#126	—	9	2	no	—
146	C₃×#124	—	9	1	no	—
147	C₃×#124	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	2	no	—
149	C₃×C₄×Q₈	—	2	4	no	—
150	C₃×C₄×Q₈	—	9	1	no	—
151	C₃×C₄×Q₈	—	9	1	no	—
152	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
153	C₃×C₄×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
154	C₃×C₄×D₄	—	9	1	no	—
155	C₃×#117	—	9	2	no	—
156	#947	—	3	4	no	—
157	#944	—	3	4	no	—
158	#898	—	3	8	no	—
159	#896	—	3	8	no	—
160	#893	—	3	4	no	—
161	#887	—	3	4	no	—
162	#876	—	3	8	no	—
163	#875	—	3	4	no	—
164	#872	—	3	8	no	—
165	C₄×Dic₆	—	3	4	no	—
166	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
167	C₂²×C₃×D₃	—	3	8	no	—
168	C₃²×Q₈	—	2	16	no	—
169	C₃²×Q₈	—	2	8	no	—
170	C₃²×Q₈	—	2	2	no	—
171	C₂×C₃²×C₄	—	2	4	no	—
172	C₂×C₃²×C₄	—	2	8	no	—
173	C₂×C₃²×C₄	—	2	4	no	—
174	C₂×C₃²×C₄	—	2	8	no	—
175	C₂×C₃²×C₄	—	2	4	no	—
176	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
177	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
178	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
179	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
180	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
181	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
182	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
183	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
184	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
190	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
191	C₄⋊(C₃⋊D₃)	—	2	2	no	—
192	C₄×C₃⋊D₃	—	2	4	no	—
193	#634	—	2	2	no	—
194	#634	—	2	2	no	—
195	C₂×C₃×Dic₃	—	3	4	no	—
196	C₂×C₃×Dic₃	—	3	4	no	—
197	C₂×C₃×Dic₃	—	3	4	no	—
198	C₂×C₃×Dic₃	—	3	8	no	—
199	C₂×C₃×Dic₃	—	3	4	no	—
200	C₃×D₁₂	—	6	8	no	—
201	C₃×C₄×D₃	—	6	16	no	—
202	C₃×Dic₆	—	6	8	no	—
203	C₃×Dic₆	—	6	8	no	—
204	#556	—	9	1	no	Sylow
205	C₂×C₃³	C₂×#41	1	1	yes	characteristic
206	C₂×C₃³	C₂×#41	1	1	yes	characteristic
207	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
208	C₃×C₃⋊D₃	—	4	2	no	—
209	C₂×C₃×Q₈	—	2	4	no	—
210	C₂×C₃×Q₈	—	9	1	no	—
211	C₂×C₃×Q₈	—	9	1	no	—
212	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
213	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
214	C₂×C₃×D₄	—	9	1	no	—
215	C₂²×C₃×C₄	—	9	2	no	—
216	C₂×D₁₂	—	3	4	no	—
217	C₂×C₄×D₃	—	3	8	no	—
218	C₂×Dic₆	—	3	4	no	—
219	C₂×Dic₆	—	3	4	no	—
220	C₃×C₄⋊C₄	—	2	4	no	—
221	C₃×C₄⋊C₄	—	2	8	no	—
222	C₃×C₄⋊C₄	—	9	1	no	—
223	C₃×C₄⋊C₄	—	9	2	no	—
224	C₃×C₄⋊C₄	—	9	2	no	—
225	C₃×C₄⋊C₄	—	9	1	no	—
226	C₃×C₄⋊C₄	—	9	2	no	—
227	C₃×C₄⋊C₄	—	9	1	no	—
228	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
229	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
230	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
231	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
232	C₃×C₂²⋊C₄	—	9	2	no	—
233	C₃×C₂²⋊C₄	—	9	2	no	—
234	C₃×C₂²⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	—	9	2	no	—
236	C₃×C₂²⋊C₄	—	9	2	no	—
237	C₃×C₄²	—	2	8	no	—
238	C₃×C₄²	—	2	4	no	—
239	C₃×C₄²	—	9	2	no	—
240	C₃×C₄²	—	9	1	no	—
241	C₃×C₄²	—	9	1	no	—
242	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
243	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
244	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	—
245	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
246	(C₂×D₃)⋊C₄	—	3	8	no	—
247	(C₂×D₃)⋊C₄	—	3	8	no	—
248	(C₂×D₃)⋊C₄	—	3	8	no	—
249	(C₂×D₃)⋊C₄	—	3	8	no	—
250	(C₂×D₃)⋊C₄	—	3	8	no	—
251	C₄⋊Dic₃	—	3	4	no	—
252	Dic₃⋊C₄	—	3	4	no	—
253	Dic₃⋊C₄	—	3	4	no	—
254	Dic₃⋊C₄	—	3	8	no	—
255	Dic₃⋊C₄	—	3	8	no	—
256	Dic₃⋊C₄	—	3	8	no	—
257	C₄×Dic₃	—	3	4	no	—
258	C₄×Dic₃	—	3	4	no	—
259	C₄×Dic₃	—	3	8	no	—
260	C₂²×C₃²	—	2	4	no	—
261	C₂²×C₃²	C₂³×D₃	1	4	yes	—
262	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
263	C₂×C₃⋊D₃	—	2	2	no	—
264	C₂×C₃⋊D₃	—	2	2	no	—
265	C₂×C₃⋊D₃	—	2	2	no	—
266	C₂×C₃×D₃	—	6	8	no	—
267	C₂×C₃×D₃	—	6	8	no	—
268	C₂×C₃×D₃	—	6	8	no	—
269	C₃²×C₄	—	2	8	no	—
270	C₃²×C₄	—	2	16	no	—
271	C₃²×C₄	—	2	8	no	—
272	C₃²×C₄	—	2	4	no	—
273	C₃²×C₄	—	2	1	no	—
274	C₃²×C₄	—	2	2	no	—
275	C₃²×C₄	—	2	2	no	—
276	C₃²×C₄	—	2	1	no	—
277	C₃²×C₄	—	2	8	no	—
278	C₃²×C₄	—	2	4	no	—
279	C₃²×C₄	—	2	8	no	—
280	C₃²×C₄	—	4	4	no	—
281	C₃²×C₄	—	4	8	no	—
282	C₃²×C₄	#235	1	8	yes	—
283	C₃²×C₄	C₃×#41	1	2	yes	—
284	C₃⋊Dic₃	—	2	2	no	—
285	C₃⋊Dic₃	—	2	1	no	—
286	C₃⋊Dic₃	—	2	1	no	—
287	C₃⋊Dic₃	—	2	1	no	—
288	C₃⋊Dic₃	C₃×#41	1	2	yes	—
289	C₃×Dic₃	—	3	8	no	—
290	C₃×Dic₃	—	6	8	no	—
291	C₃×Dic₃	—	6	4	no	—
292	C₃×Dic₃	—	6	4	no	—
293	C₃×Dic₃	—	6	4	no	—
294	C₄⋊Q₈	—	9	1	no	—
295	#126	—	9	2	no	—
296	#126	—	9	2	no	—
297	#124	—	9	1	no	—
298	#124	—	9	1	no	—
299	C₂²⋊Q₈	—	9	2	no	—
300	C₄×Q₈	—	9	1	no	—
301	C₄×Q₈	—	9	1	no	—
302	C₄×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
303	C₄×D₄	—	9	1	no	—
304	#117	—	9	2	no	—
305	C₃³	#556	1	1	yes	characteristic, complemented, Sylow
306	C₂³×C₃	—	9	2	no	—
307	C₂²×D₃	—	3	8	no	—
308	C₃×Q₈	—	2	16	no	—
309	C₃×Q₈	—	2	8	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	18	2	no	—
312	C₃×Q₈	—	18	2	no	—
313	C₃×D₄	—	18	2	no	—
314	C₂×C₃×C₄	—	2	4	no	—
315	C₂×C₃×C₄	—	2	8	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	8	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	9	1	no	—
320	C₂×C₃×C₄	—	9	1	no	—
321	C₂×C₃×C₄	—	9	1	no	—
322	C₂×C₃×C₄	—	9	2	no	—
323	C₂×C₃×C₄	—	9	1	no	—
324	C₂×C₃×C₄	—	18	4	no	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
328	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
330	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
333	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
335	C₂×Dic₃	—	3	4	no	—
336	C₂×Dic₃	—	3	4	no	—
337	C₂×Dic₃	—	3	4	no	—
338	C₂×Dic₃	—	3	8	no	—
339	C₂×Dic₃	—	3	4	no	—
340	D₁₂	—	6	8	no	—
341	C₄×D₃	—	6	16	no	—
342	Dic₆	—	6	8	no	—
343	Dic₆	—	6	8	no	—
344	C₂×C₃²	—	2	4	no	—
345	C₂×C₃²	—	2	4	no	—
346	C₂×C₃²	—	2	4	no	—
347	C₂×C₃²	C₂×#235	1	4	yes	—
348	C₂×C₃²	#1007	1	4	yes	—
349	C₂×C₃²	D₃×#41	1	4	yes	—
350	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
351	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
352	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
353	C₃⋊D₃	—	4	2	no	—
354	C₃×D₃	—	12	8	no	—
355	C₂×Q₈	—	9	1	no	—
356	C₂×Q₈	—	9	1	no	—
357	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
358	C₂×D₄	—	9	1	no	—
359	C₂²×C₄	—	9	2	no	—
360	C₄⋊C₄	—	9	1	no	—
361	C₄⋊C₄	—	9	2	no	—
362	C₄⋊C₄	—	9	2	no	—
363	C₄⋊C₄	—	9	1	no	—
364	C₄⋊C₄	—	9	1	no	—
365	C₄⋊C₄	—	9	2	no	—
366	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
368	C₂²⋊C₄	—	9	2	no	—
369	C₂²⋊C₄	—	9	2	no	—
370	C₂²⋊C₄	—	9	2	no	—
371	C₂²⋊C₄	—	9	2	no	—
372	C₂²⋊C₄	—	9	2	no	—
373	C₄²	—	9	2	no	—
374	C₄²	—	9	1	no	—
375	C₄²	—	9	1	no	—
376	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	—
377	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	18	2	no	—
380	C₂²×C₃	—	18	2	no	—
381	C₂²×C₃	—	18	2	no	—
382	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
383	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
384	C₂×D₃	—	6	8	no	—
385	C₂×D₃	—	6	8	no	—
386	C₂×D₃	—	6	8	no	—
387	C₃×C₄	—	2	16	no	—
388	C₃×C₄	—	2	8	no	—
389	C₃×C₄	—	2	8	no	—
390	C₃×C₄	—	2	4	no	—
391	C₃×C₄	—	2	4	no	—
392	C₃×C₄	—	2	8	no	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	8	no	—
398	C₃×C₄	—	4	8	no	—
399	C₃×C₄	—	4	4	no	—
400	C₃×C₄	—	9	2	no	—
401	C₃×C₄	—	18	2	no	—
402	C₃×C₄	—	18	1	no	—
403	C₃×C₄	—	18	1	no	—
404	C₃×C₄	—	18	1	no	—
405	C₃×C₄	C₃×#235	1	8	yes	—
406	C₃×C₄	#3828	1	2	yes	—
407	Dic₃	—	3	8	no	—
408	Dic₃	—	6	8	no	—
409	Dic₃	—	6	4	no	—
410	Dic₃	—	6	4	no	—
411	Dic₃	—	6	4	no	—
412	C₃²	—	2	4	no	—
413	C₃²	#5568	1	4	yes	complemented
414	C₃²	C₃×#556	1	1	yes	characteristic, complemented
415	C₂³	—	9	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	18	2	no	—
418	Q₈	—	18	2	no	—
419	D₄	—	18	2	no	—
420	C₂×C₄	—	9	1	no	—
421	C₂×C₄	—	9	1	no	—
422	C₂×C₄	—	9	1	no	—
423	C₂×C₄	—	9	2	no	—
424	C₂×C₄	—	9	1	no	—
425	C₂×C₄	—	18	4	no	—
426	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
427	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
429	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
431	C₂×C₃	—	2	4	no	—
432	C₂×C₃	—	2	4	no	—
433	C₂×C₃	—	2	4	no	—
434	C₂×C₃	—	36	2	no	—
435	C₂×C₃	C₂×C₃×#235	1	4	yes	—
436	C₂×C₃	C₃×#1007	1	4	yes	—
437	C₂×C₃	C₃×D₃×#41	1	4	yes	—
438	C₂×C₃	C₂×#3828	1	1	yes	characteristic
439	C₂×C₃	#64364	1	1	yes	characteristic
440	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
441	D₃	—	12	8	no	—
442	C₂²	—	18	2	no	—
443	C₂²	—	18	2	no	—
444	C₂²	—	18	2	no	—
445	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	9	2	no	—
451	C₄	—	18	2	no	—
452	C₄	—	18	1	no	—
453	C₄	—	18	1	no	—
454	C₄	—	18	1	no	—
455	C₄	C₃×#3828	1	2	yes	—
456	C₃	—	2	4	no	—
457	C₃	C₃×#5568	1	4	yes	complemented
458	C₃	#10596039	1	1	yes	characteristic, direct product factor
459	C₂	—	36	2	no	—
460	C₂	C₂×C₃×#3828	1	1	yes	characteristic
461	C₂	C₃×#64364	1	1	yes	characteristic
462	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×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²
hypercenter	C₃×C₄×Q₈	C₃⋊D₃
hypocenter	C₃²	C₃×#556
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×Q₈	C₂	semidirect
3. C₃×#64153	C₂	semidirect
4. C₃×#64107	C₂	semidirect
5. C₃×#64105	C₂	semidirect
7. C₃×#64096	C₂	semidirect
8. C₃×#64085	C₂	semidirect
10. C₃×#64081	C₂	semidirect
11. C₃×C₄×#634	C₂	semidirect
12. #10596039	C₃	direct (N × H)
38. C₃²×C₄×Q₈	D₃	semidirect
39. C₃²×C₄×Q₈	C₂×C₃	semidirect
41. #64153	C₂×C₃	semidirect
42. #64107	C₂×C₃	semidirect
43. #64105	C₂×C₃	semidirect
45. #64096	C₂×C₃	semidirect
46. #64085	C₂×C₃	semidirect
48. #64081	C₂×C₃	semidirect
49. C₄×#634	C₂×C₃	semidirect
152. C₃×C₄×Q₈	C₃×D₃	semidirect
153. C₃×C₄×Q₈	C₃⋊D₃	semidirect
302. C₄×Q₈	C₃×C₃⋊D₃	semidirect
305. C₃³	#556	semidirect
413. C₃²	#5568	semidirect
414. C₃²	C₃×#556	semidirect
457. C₃	C₃×#5568	semidirect
458. C₃	#10596039	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×Q₈	2
C₃×#64156	2
C₃×#64153	2
C₃×#64107	2
C₃×#64105	2
C₃×#64102	2
C₃×#64096	2
C₃×#64085	2
C₃×#64084	2
C₃×#64081	2
C₃×C₄×#634	2
#10596039	3
C₃×#5568	3

Subgroups — C3×#10596039 #13179319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596039 #13179319