Subgroups — C₃×#10596028 #13179309

Order 1728.

1780 conjugacy classes of subgroups.

The subgroup lattice has 502 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×#64147	C₂	1	1	yes	maximal, characteristic
3	C₃×#64145	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×#638	C₂	1	2	yes	maximal, complemented
5	C₃×#64135	C₂	1	2	yes	maximal, complemented
6	C₃×#64106	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64099	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64092	C₂	1	2	yes	maximal, complemented
9	C₃×#64088	C₂	1	2	yes	maximal, complemented
10	C₃×C₄²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596028	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5557	—	3	4	no	maximal
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	2	yes	—
16	C₂×C₃×#638	C₂²	1	2	yes	—
17	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
20	C₂×C₃×#634	C₂²	1	1	yes	characteristic
21	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₃³×C₄²	C₂²	1	1	yes	characteristic
24	C₃×#3757	C₂²	1	2	yes	—
25	C₃×#3757	C₂²	1	2	yes	—
26	C₃×#3757	C₂²	1	2	yes	—
27	C₃×#3752	C₂²	1	2	yes	—
28	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
29	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
30	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
31	C₃×#3750	C₂²	1	2	yes	—
32	C₃×#3750	C₂²	1	2	yes	—
33	C₃×C₄×C₃⋊Dic₃	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	1	yes	characteristic
37	C₃²×C₄×D₄	—	2	4	no	—
38	C₃²×C₄×D₄	D₃	1	4	yes	complemented
39	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
40	#64147	C₂×C₃	1	1	yes	characteristic
41	#64145	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×#638	C₂×C₃	1	2	yes	complemented
43	#64135	C₂×C₃	1	2	yes	complemented
44	#64106	C₂×C₃	1	1	yes	characteristic, complemented
45	#64099	C₂×C₃	1	1	yes	characteristic, complemented
46	#64092	C₂×C₃	1	2	yes	complemented
47	#64088	C₂×C₃	1	2	yes	complemented
48	C₄²×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×#938	—	3	4	no	—
51	C₃×#936	—	3	4	no	—
52	C₃×C₄×#67	—	3	8	no	—
53	C₃×#926	—	3	8	no	—
54	C₃×#897	—	3	4	no	—
55	C₃×#890	—	3	4	no	—
56	C₃×#883	—	3	8	no	—
57	C₃×#879	—	3	8	no	—
58	C₃×C₄²×D₃	—	3	4	no	—
59	C₃×C₄×Dic₆	—	3	4	no	—
60	C₂³×C₃³	C₂³	1	2	yes	—
61	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
62	C₃³×D₄	—	2	2	no	—
63	C₂×C₃³×C₄	—	2	4	no	—
64	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
65	C₂×C₃³×C₄	C₂³	1	2	yes	—
66	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
68	C₃×#638	—	2	4	no	—
69	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
73	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
74	C₃×C₄×C₃⋊D₃	—	2	2	no	—
75	C₃×C₄×C₃⋊D₃	—	2	2	no	—
76	C₃×C₄×C₃⋊D₃	—	2	2	no	—
77	C₃×#634	—	2	2	no	—
78	C₃×#529	—	9	1	no	—
79	#5557	—	3	4	no	—
80	C₂×C₃²×D₄	—	2	4	no	—
81	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
82	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃²×C₄	—	2	8	no	—
84	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
85	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
86	C₂×#638	C₂²×C₃	1	2	yes	—
87	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
90	C₂×#634	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₃×#67	—	3	8	no	—
92	C₂×C₃×C₄×D₃	—	3	4	no	—
93	C₂×C₃×C₄×D₃	—	3	4	no	—
94	C₂×C₃×C₄×D₃	—	3	4	no	—
95	C₂×C₃×Dic₆	—	3	4	no	—
96	C₃²×C₄⋊C₄	—	2	4	no	—
97	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
98	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₃²×C₂²⋊C₄	—	2	8	no	—
100	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
101	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₃²×C₄²	—	2	4	no	—
103	C₃²×C₄²	C₂×D₃	1	4	yes	—
104	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
105	#3757	C₂²×C₃	1	2	yes	—
106	#3757	C₂²×C₃	1	2	yes	—
107	#3757	C₂²×C₃	1	2	yes	—
108	#3752	C₂²×C₃	1	2	yes	—
109	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
110	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
111	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
112	#3750	C₂²×C₃	1	2	yes	—
113	#3750	C₂²×C₃	1	2	yes	—
114	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
115	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
118	C₃×#217	—	3	8	no	—
119	C₃×#217	—	3	8	no	—
120	C₃×#217	—	3	8	no	—
121	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
122	C₃×C₄⋊Dic₃	—	3	8	no	—
123	C₃×C₄⋊Dic₃	—	3	8	no	—
124	C₃×C₄⋊Dic₃	—	3	4	no	—
125	C₃×Dic₃⋊C₄	—	3	8	no	—
126	C₃×Dic₃⋊C₄	—	3	8	no	—
127	C₃×C₄×Dic₃	—	3	4	no	—
128	C₃×C₄×Dic₃	—	3	4	no	—
129	C₃×C₄×Dic₃	—	3	4	no	—
130	C₃×C₄×Dic₃	—	3	8	no	—
131	C₂²×C₃³	—	2	2	no	—
132	C₂²×C₃³	—	2	2	no	—
133	C₂²×C₃³	—	2	2	no	—
134	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
135	C₂×C₃×C₃⋊D₃	—	2	1	no	—
136	C₂×C₃×C₃⋊D₃	—	2	1	no	—
137	C₂×C₃×C₃⋊D₃	#41	1	2	yes	—
138	C₃³×C₄	—	2	1	no	—
139	C₃³×C₄	—	2	2	no	—
140	C₃³×C₄	#41	1	2	yes	—
141	C₃³×C₄	#41	1	2	yes	—
142	C₃×C₃⋊Dic₃	—	2	2	no	—
143	C₃×C₃⋊Dic₃	—	2	1	no	—
144	C₃×C₃⋊Dic₃	—	2	1	no	—
145	C₃×C₃⋊Dic₃	—	2	1	no	—
146	C₃×C₃⋊Dic₃	—	2	2	no	—
147	C₃×#126	—	9	2	no	—
148	C₃×#125	—	9	1	no	—
149	C₃×#124	—	9	1	no	—
150	C₃×#123	—	9	2	no	—
151	C₃×C₂²⋊Q₈	—	9	1	no	—
152	C₃×#121	—	9	1	no	—
153	C₃×C₄×Q₈	—	9	1	no	—
154	C₃×C₄×D₄	—	2	4	no	—
155	C₃×C₄×D₄	—	9	2	no	—
156	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
157	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic, complemented
158	C₃×#117	—	9	2	no	—
159	C₂×C₃×C₄²	—	9	1	no	—
160	#938	—	3	4	no	—
161	#936	—	3	4	no	—
162	C₄×#67	—	3	8	no	—
163	#926	—	3	8	no	—
164	#897	—	3	4	no	—
165	#890	—	3	4	no	—
166	#883	—	3	8	no	—
167	#879	—	3	8	no	—
168	C₄²×D₃	—	3	4	no	—
169	C₄×Dic₆	—	3	4	no	—
170	C₂³×C₃²	—	2	8	no	—
171	C₂³×C₃²	C₂²×D₃	1	8	yes	—
172	C₂³×C₃²	C₂³×C₃	1	2	yes	—
173	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₃×D₃	—	3	4	no	—
175	C₃²×D₄	—	2	16	no	—
176	C₃²×D₄	—	2	8	no	—
177	C₃²×D₄	—	2	2	no	—
178	C₂×C₃²×C₄	—	2	4	no	—
179	C₂×C₃²×C₄	—	2	4	no	—
180	C₂×C₃²×C₄	—	2	4	no	—
181	C₂×C₃²×C₄	—	2	4	no	—
182	C₂×C₃²×C₄	—	2	8	no	—
183	C₂×C₃²×C₄	—	2	16	no	—
184	C₂×C₃²×C₄	—	4	16	no	—
185	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
186	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
187	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
188	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
189	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
191	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
193	#638	—	2	4	no	—
194	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
198	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
199	C₄×C₃⋊D₃	—	2	2	no	—
200	C₄×C₃⋊D₃	—	2	2	no	—
201	C₄×C₃⋊D₃	—	2	2	no	—
202	#634	—	2	2	no	—
203	C₃×#67	—	6	16	no	—
204	C₂×C₃×Dic₃	—	3	4	no	—
205	C₂×C₃×Dic₃	—	3	4	no	—
206	C₂×C₃×Dic₃	—	3	4	no	—
207	C₂×C₃×Dic₃	—	3	8	no	—
208	C₂×C₃×Dic₃	—	3	8	no	—
209	C₃×C₄×D₃	—	6	8	no	—
210	C₃×C₄×D₃	—	6	8	no	—
211	C₃×C₄×D₃	—	6	8	no	—
212	C₃×Dic₆	—	6	8	no	—
213	#529	—	9	1	no	Sylow
214	C₂×C₃³	—	4	2	no	—
215	C₂×C₃³	C₂×#41	1	1	yes	characteristic
216	C₂×C₃³	C₂×#41	1	1	yes	characteristic
217	C₂×C₃³	C₂×#41	1	1	yes	characteristic
218	C₃×C₃⋊D₃	—	2	2	no	—
219	C₂×C₃×Q₈	—	9	1	no	—
220	C₂×C₃×D₄	—	2	4	no	—
221	C₂×C₃×D₄	—	9	2	no	—
222	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
223	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
224	C₂²×C₃×C₄	—	2	8	no	—
225	C₂²×C₃×C₄	—	9	1	no	—
226	C₂²×C₃×C₄	—	9	1	no	—
227	C₂²×C₃×C₄	—	9	1	no	—
228	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
229	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
230	C₂×#67	—	3	8	no	—
231	C₂×C₄×D₃	—	3	4	no	—
232	C₂×C₄×D₃	—	3	4	no	—
233	C₂×C₄×D₃	—	3	4	no	—
234	C₂×Dic₆	—	3	4	no	—
235	C₃×C₄⋊C₄	—	2	4	no	—
236	C₃×C₄⋊C₄	—	9	2	no	—
237	C₃×C₄⋊C₄	—	9	2	no	—
238	C₃×C₄⋊C₄	—	9	2	no	—
239	C₃×C₄⋊C₄	—	9	2	no	—
240	C₃×C₄⋊C₄	—	9	1	no	—
241	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
242	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
243	C₃×C₂²⋊C₄	—	2	8	no	—
244	C₃×C₂²⋊C₄	—	9	2	no	—
245	C₃×C₂²⋊C₄	—	9	2	no	—
246	C₃×C₂²⋊C₄	—	9	2	no	—
247	C₃×C₂²⋊C₄	—	9	2	no	—
248	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
249	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
250	C₃×C₄²	—	2	4	no	—
251	C₃×C₄²	—	9	1	no	—
252	C₃×C₄²	—	9	1	no	—
253	C₃×C₄²	—	9	1	no	—
254	C₃×C₄²	—	9	2	no	—
255	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
256	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
257	#217	—	3	8	no	—
258	#217	—	3	8	no	—
259	#217	—	3	8	no	—
260	(C₂×D₃)⋊C₄	—	3	8	no	—
261	C₄⋊Dic₃	—	3	4	no	—
262	C₄⋊Dic₃	—	3	8	no	—
263	C₄⋊Dic₃	—	3	8	no	—
264	Dic₃⋊C₄	—	3	8	no	—
265	Dic₃⋊C₄	—	3	8	no	—
266	C₄×Dic₃	—	3	8	no	—
267	C₄×Dic₃	—	3	4	no	—
268	C₄×Dic₃	—	3	4	no	—
269	C₄×Dic₃	—	3	4	no	—
270	C₂²×C₃²	—	2	16	no	—
271	C₂²×C₃²	—	2	8	no	—
272	C₂²×C₃²	—	2	2	no	—
273	C₂²×C₃²	—	2	2	no	—
274	C₂²×C₃²	—	2	2	no	—
275	C₂²×C₃²	—	2	4	no	—
276	C₂²×C₃²	—	2	8	no	—
277	C₂²×C₃²	—	2	8	no	—
278	C₂²×C₃²	—	4	8	no	—
279	C₂²×C₃²	—	4	8	no	—
280	C₂²×C₃²	C₂³×D₃	1	4	yes	—
281	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
282	C₂×C₃⋊D₃	—	2	1	no	—
283	C₂×C₃⋊D₃	—	2	1	no	—
284	C₂×C₃⋊D₃	C₃×#41	1	2	yes	—
285	C₂×C₃×D₃	—	3	8	no	—
286	C₂×C₃×D₃	—	6	4	no	—
287	C₂×C₃×D₃	—	6	4	no	—
288	C₃²×C₄	—	2	1	no	—
289	C₃²×C₄	—	2	2	no	—
290	C₃²×C₄	—	2	8	no	—
291	C₃²×C₄	—	2	8	no	—
292	C₃²×C₄	—	2	8	no	—
293	C₃²×C₄	—	2	4	no	—
294	C₃²×C₄	—	4	4	no	—
295	C₃²×C₄	—	4	8	no	—
296	C₃²×C₄	#235	1	8	yes	—
297	C₃²×C₄	#237	1	8	yes	—
298	C₃²×C₄	C₃×#41	1	2	yes	—
299	C₃²×C₄	C₃×#41	1	2	yes	—
300	C₃⋊Dic₃	—	2	2	no	—
301	C₃⋊Dic₃	—	2	1	no	—
302	C₃⋊Dic₃	—	2	1	no	—
303	C₃⋊Dic₃	—	2	1	no	—
304	C₃⋊Dic₃	—	2	2	no	—
305	C₃×Dic₃	—	6	8	no	—
306	C₃×Dic₃	—	6	4	no	—
307	C₃×Dic₃	—	6	4	no	—
308	C₃×Dic₃	—	6	4	no	—
309	C₃×Dic₃	—	6	8	no	—
310	#126	—	9	2	no	—
311	#125	—	9	1	no	—
312	#124	—	9	1	no	—
313	#123	—	9	2	no	—
314	C₂²⋊Q₈	—	9	1	no	—
315	#121	—	9	1	no	—
316	C₄×Q₈	—	9	1	no	—
317	C₄×D₄	—	9	2	no	—
318	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
319	#117	—	9	2	no	—
320	C₂×C₄²	—	9	1	no	—
321	C₃³	#529	1	1	yes	characteristic, complemented, Sylow
322	C₂³×C₃	—	2	8	no	—
323	C₂³×C₃	—	9	1	no	—
324	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
325	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
326	C₂²×D₃	—	3	4	no	—
327	C₃×Q₈	—	18	2	no	—
328	C₃×D₄	—	2	16	no	—
329	C₃×D₄	—	2	8	no	—
330	C₃×D₄	—	2	2	no	—
331	C₃×D₄	—	18	4	no	—
332	C₂×C₃×C₄	—	2	16	no	—
333	C₂×C₃×C₄	—	2	4	no	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	2	4	no	—
336	C₂×C₃×C₄	—	2	4	no	—
337	C₂×C₃×C₄	—	2	8	no	—
338	C₂×C₃×C₄	—	4	16	no	—
339	C₂×C₃×C₄	—	9	1	no	—
340	C₂×C₃×C₄	—	9	1	no	—
341	C₂×C₃×C₄	—	9	1	no	—
342	C₂×C₃×C₄	—	9	2	no	—
343	C₂×C₃×C₄	—	9	2	no	—
344	C₂×C₃×C₄	—	18	2	no	—
345	C₂×C₃×C₄	—	18	2	no	—
346	C₂×C₃×C₄	—	18	2	no	—
347	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
348	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
351	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
353	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
355	#67	—	6	16	no	—
356	C₂×Dic₃	—	3	4	no	—
357	C₂×Dic₃	—	3	4	no	—
358	C₂×Dic₃	—	3	4	no	—
359	C₂×Dic₃	—	3	8	no	—
360	C₂×Dic₃	—	3	8	no	—
361	C₄×D₃	—	6	8	no	—
362	C₄×D₃	—	6	8	no	—
363	C₄×D₃	—	6	8	no	—
364	Dic₆	—	6	8	no	—
365	C₂×C₃²	—	2	4	no	—
366	C₂×C₃²	—	2	4	no	—
367	C₂×C₃²	—	2	4	no	—
368	C₂×C₃²	—	4	16	no	—
369	C₂×C₃²	—	4	8	no	—
370	C₂×C₃²	—	4	2	no	—
371	C₂×C₃²	C₂×#235	1	4	yes	—
372	C₂×C₃²	C₂×#237	1	4	yes	—
373	C₂×C₃²	D₃×#41	1	4	yes	—
374	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
375	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
376	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
377	C₃⋊D₃	—	2	2	no	—
378	C₃×D₃	—	6	8	no	—
379	C₂×Q₈	—	9	1	no	—
380	C₂×D₄	—	9	2	no	—
381	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
382	C₂²×C₄	—	9	1	no	—
383	C₂²×C₄	—	9	1	no	—
384	C₂²×C₄	—	9	1	no	—
385	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
386	C₄⋊C₄	—	9	2	no	—
387	C₄⋊C₄	—	9	2	no	—
388	C₄⋊C₄	—	9	2	no	—
389	C₄⋊C₄	—	9	1	no	—
390	C₄⋊C₄	—	9	2	no	—
391	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
392	C₂²⋊C₄	—	9	2	no	—
393	C₂²⋊C₄	—	9	2	no	—
394	C₂²⋊C₄	—	9	2	no	—
395	C₂²⋊C₄	—	9	2	no	—
396	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
397	C₄²	—	9	1	no	—
398	C₄²	—	9	1	no	—
399	C₄²	—	9	1	no	—
400	C₄²	—	9	2	no	—
401	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
402	C₂²×C₃	—	2	16	no	—
403	C₂²×C₃	—	2	8	no	—
404	C₂²×C₃	—	2	8	no	—
405	C₂²×C₃	—	2	8	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	4	no	—
410	C₂²×C₃	—	4	8	no	—
411	C₂²×C₃	—	4	8	no	—
412	C₂²×C₃	—	9	2	no	—
413	C₂²×C₃	—	18	1	no	—
414	C₂²×C₃	—	18	1	no	—
415	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
416	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
417	C₂×D₃	—	3	8	no	—
418	C₂×D₃	—	6	4	no	—
419	C₂×D₃	—	6	4	no	—
420	C₃×C₄	—	2	8	no	—
421	C₃×C₄	—	2	4	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	8	no	—
425	C₃×C₄	—	2	8	no	—
426	C₃×C₄	—	4	8	no	—
427	C₃×C₄	—	4	4	no	—
428	C₃×C₄	—	18	1	no	—
429	C₃×C₄	—	18	2	no	—
430	C₃×C₄	—	18	1	no	—
431	C₃×C₄	—	18	1	no	—
432	C₃×C₄	—	18	2	no	—
433	C₃×C₄	C₃×#235	1	8	yes	—
434	C₃×C₄	C₃×#237	1	8	yes	—
435	C₃×C₄	#3828	1	2	yes	—
436	C₃×C₄	#3830	1	2	yes	—
437	Dic₃	—	6	8	no	—
438	Dic₃	—	6	4	no	—
439	Dic₃	—	6	4	no	—
440	Dic₃	—	6	4	no	—
441	Dic₃	—	6	8	no	—
442	C₃²	—	2	4	no	—
443	C₃²	#5557	1	4	yes	complemented
444	C₃²	C₃×#529	1	1	yes	characteristic, complemented
445	C₂³	—	9	1	no	—
446	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
447	Q₈	—	18	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	18	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	9	1	no	—
452	C₂×C₄	—	9	1	no	—
453	C₂×C₄	—	9	1	no	—
454	C₂×C₄	—	9	2	no	—
455	C₂×C₄	—	9	2	no	—
456	C₂×C₄	—	18	2	no	—
457	C₂×C₄	—	18	2	no	—
458	C₂×C₄	—	18	2	no	—
459	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
461	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
463	C₂×C₃	—	2	4	no	—
464	C₂×C₃	—	2	4	no	—
465	C₂×C₃	—	2	4	no	—
466	C₂×C₃	—	4	16	no	—
467	C₂×C₃	—	4	8	no	—
468	C₂×C₃	—	4	2	no	—
469	C₂×C₃	—	18	2	no	—
470	C₂×C₃	C₂×C₃×#235	1	4	yes	—
471	C₂×C₃	C₂×C₃×#237	1	4	yes	—
472	C₂×C₃	C₃×D₃×#41	1	4	yes	—
473	C₂×C₃	C₂×#3828	1	1	yes	characteristic
474	C₂×C₃	C₂×#3830	1	1	yes	characteristic
475	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
476	D₃	—	6	8	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	9	2	no	—
481	C₂²	—	18	1	no	—
482	C₂²	—	18	1	no	—
483	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	1	no	—
486	C₄	—	18	1	no	—
487	C₄	—	18	2	no	—
488	C₄	—	18	1	no	—
489	C₄	—	18	1	no	—
490	C₄	—	18	2	no	—
491	C₄	C₃×#3828	1	2	yes	—
492	C₄	C₃×#3830	1	2	yes	—
493	C₃	—	2	4	no	—
494	C₃	C₃×#5557	1	4	yes	complemented
495	C₃	#10596028	1	1	yes	characteristic, direct product factor
496	C₂	—	4	2	no	—
497	C₂	—	18	2	no	—
498	C₂	C₂×C₃×#3828	1	1	yes	characteristic
499	C₂	C₂×C₃×#3830	1	1	yes	characteristic
500	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×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×#64147	C₂
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#529
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ 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×#64145	C₂	semidirect
4. C₃×C₄×#638	C₂	semidirect
5. C₃×#64135	C₂	semidirect
6. C₃×#64106	C₂	semidirect
7. C₃×#64099	C₂	semidirect
8. C₃×#64092	C₂	semidirect
9. C₃×#64088	C₂	semidirect
10. C₃×C₄²×C₃⋊D₃	C₂	semidirect
11. C₃×C₄×#634	C₂	semidirect
12. #10596028	C₃	direct (N × H)
38. C₃²×C₄×D₄	D₃	semidirect
39. C₃²×C₄×D₄	C₂×C₃	semidirect
41. #64145	C₂×C₃	semidirect
42. C₄×#638	C₂×C₃	semidirect
43. #64135	C₂×C₃	semidirect
44. #64106	C₂×C₃	semidirect
45. #64099	C₂×C₃	semidirect
46. #64092	C₂×C₃	semidirect
47. #64088	C₂×C₃	semidirect
48. C₄²×C₃⋊D₃	C₂×C₃	semidirect
49. C₄×#634	C₂×C₃	semidirect
156. C₃×C₄×D₄	C₃×D₃	semidirect
157. C₃×C₄×D₄	C₃⋊D₃	semidirect
318. C₄×D₄	C₃×C₃⋊D₃	semidirect
321. C₃³	#529	semidirect
443. C₃²	#5557	semidirect
444. C₃²	C₃×#529	semidirect
494. C₃	C₃×#5557	semidirect
495. C₃	#10596028	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×#64147	2
C₃×#64145	2
C₃×C₄×#638	2
C₃×#64135	2
C₃×#64106	2
C₃×#64099	2
C₃×#64092	2
C₃×#64088	2
C₃×C₄²×C₃⋊D₃	2
C₃×C₄×#634	2
#10596028	3
C₃×#5557	3

Subgroups — C3×#10596028 #13179309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596028 #13179309