Subgroups — C₃×#10596010 #13179291

Order 1728.

1744 conjugacy classes of subgroups.

The subgroup lattice has 478 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
2	C₃×D₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₃×D₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₃×#64133	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#3750	C₂	1	2	yes	maximal, complemented
6	C₃×#64099	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64087	C₂	1	2	yes	maximal, complemented
9	C₃×#64087	C₂	1	2	yes	maximal, complemented
10	C₃×#64079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596010	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5539	—	3	4	no	maximal
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃³×C₄	C₂²	1	2	yes	—
16	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
17	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×#634	C₂²	1	1	yes	characteristic
19	C₂×C₃×#634	C₂²	1	2	yes	—
20	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₃³×C₄²	C₂²	1	1	yes	characteristic
23	C₃×#3757	C₂²	1	2	yes	—
24	C₃×#3757	C₂²	1	2	yes	—
25	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
26	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
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×#3750	C₂²	1	2	yes	—
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	—
39	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
40	D₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic
41	D₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic
42	#64133	C₂×C₃	1	2	yes	complemented
43	C₂×#3750	C₂×C₃	1	2	yes	complemented
44	#64099	C₂×C₃	1	1	yes	characteristic, complemented
45	#64097	C₂×C₃	1	1	yes	characteristic, complemented
46	#64087	C₂×C₃	1	2	yes	complemented
47	#64087	C₂×C₃	1	2	yes	complemented
48	#64079	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×D₄×Dic₃	—	3	4	no	—
51	C₃×D₄×Dic₃	—	3	4	no	—
52	C₃×#924	—	3	8	no	—
53	C₂×C₃×Dic₃⋊C₄	—	3	8	no	—
54	C₃×#890	—	3	4	no	—
55	C₃×#888	—	3	4	no	—
56	C₃×#878	—	3	8	no	—
57	C₃×#878	—	3	8	no	—
58	C₃×#870	—	3	4	no	—
59	C₃×C₄×Dic₆	—	3	4	no	—
60	C₂³×C₃³	C₂³	1	2	yes	—
61	C₃³×D₄	Q₈	1	4	yes	complemented
62	C₂×C₃³×C₄	—	4	2	no	—
63	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
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×C₃×C₃⋊Dic₃	—	2	4	no	—
68	C₂×C₃×C₃⋊Dic₃	—	4	2	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	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
75	C₃×#634	—	2	2	no	—
76	C₃×#634	—	4	2	no	—
77	C₃×#554	—	9	1	no	—
78	#5539	—	3	4	no	—
79	C₂×C₃²×D₄	—	2	4	no	—
80	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
81	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃²×C₄	—	2	8	no	—
83	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
84	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
85	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
86	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
87	C₂×#634	C₂²×C₃	1	1	yes	characteristic
88	C₂×#634	C₂²×C₃	1	2	yes	—
89	C₂²×C₃×Dic₃	—	3	8	no	—
90	C₂²×C₃×Dic₃	—	3	8	no	—
91	C₂×C₃×Dic₆	—	3	4	no	—
92	C₂×C₃×Dic₆	—	3	8	no	—
93	C₃²×C₄⋊C₄	—	2	4	no	—
94	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
95	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₃²×C₂²⋊C₄	—	2	8	no	—
97	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
98	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃²×C₄²	—	2	4	no	—
100	C₃²×C₄²	C₂×D₃	1	4	yes	—
101	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
102	#3757	C₂²×C₃	1	2	yes	—
103	#3757	C₂²×C₃	1	2	yes	—
104	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
105	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
106	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
107	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
108	#3750	C₂²×C₃	1	1	yes	characteristic
109	#3750	C₂²×C₃	1	1	yes	characteristic
110	#3750	C₂²×C₃	1	2	yes	—
111	#3750	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	1	yes	characteristic
115	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
116	C₃×#217	—	3	8	no	—
117	C₃×#217	—	3	8	no	—
118	C₃×C₄⋊Dic₃	—	3	4	no	—
119	C₃×C₄⋊Dic₃	—	3	8	no	—
120	C₃×C₄⋊Dic₃	—	3	4	no	—
121	C₃×C₄⋊Dic₃	—	3	4	no	—
122	C₃×Dic₃⋊C₄	—	3	8	no	—
123	C₃×Dic₃⋊C₄	—	3	8	no	—
124	C₃×Dic₃⋊C₄	—	3	8	no	—
125	C₃×Dic₃⋊C₄	—	3	4	no	—
126	C₃×Dic₃⋊C₄	—	3	8	no	—
127	C₃×Dic₃⋊C₄	—	3	4	no	—
128	C₃×C₄×Dic₃	—	3	4	no	—
129	C₃×C₄×Dic₃	—	3	4	no	—
130	C₂²×C₃³	—	2	2	no	—
131	C₂²×C₃³	—	2	2	no	—
132	C₂²×C₃³	C₂×Q₈	1	4	yes	—
133	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
134	C₃³×C₄	—	2	1	no	—
135	C₃³×C₄	—	2	1	no	—
136	C₃³×C₄	—	2	2	no	—
137	C₃³×C₄	C₂×Q₈	1	2	yes	—
138	C₃×C₃⋊Dic₃	—	2	1	no	—
139	C₃×C₃⋊Dic₃	—	2	2	no	—
140	C₃×C₃⋊Dic₃	—	2	1	no	—
141	C₃×C₃⋊Dic₃	—	2	2	no	—
142	C₃×C₃⋊Dic₃	—	2	1	no	—
143	C₃×C₃⋊Dic₃	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	9	1	no	—
145	C₃×#125	—	9	1	no	—
146	C₃×#125	—	9	1	no	—
147	C₃×C₂²⋊Q₈	—	9	2	no	—
148	C₃×C₂²⋊Q₈	—	9	2	no	—
149	C₃×C₂²⋊Q₈	—	9	2	no	—
150	C₃×C₄×Q₈	—	9	1	no	—
151	C₃×C₄×D₄	—	2	4	no	—
152	C₃×C₄×D₄	—	9	1	no	—
153	C₃×C₄×D₄	—	9	1	no	—
154	C₃×C₄×D₄	C₃×D₃	1	4	yes	—
155	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	—	9	2	no	—
157	D₄×Dic₃	—	3	4	no	—
158	D₄×Dic₃	—	3	4	no	—
159	#924	—	3	8	no	—
160	C₂×Dic₃⋊C₄	—	3	8	no	—
161	#890	—	3	4	no	—
162	#888	—	3	4	no	—
163	#878	—	3	8	no	—
164	#878	—	3	8	no	—
165	#870	—	3	4	no	—
166	C₄×Dic₆	—	3	4	no	—
167	C₂³×C₃²	—	2	8	no	—
168	C₂³×C₃²	C₂²×D₃	1	8	yes	—
169	C₂³×C₃²	C₂³×C₃	1	2	yes	—
170	C₃²×D₄	—	2	16	no	—
171	C₃²×D₄	Dic₆	1	16	yes	complemented
172	C₃²×D₄	C₃×Q₈	1	4	yes	complemented
173	C₂×C₃²×C₄	—	2	4	no	—
174	C₂×C₃²×C₄	—	2	4	no	—
175	C₂×C₃²×C₄	—	2	4	no	—
176	C₂×C₃²×C₄	—	2	8	no	—
177	C₂×C₃²×C₄	—	4	8	no	—
178	C₂×C₃²×C₄	—	4	2	no	—
179	C₂×C₃²×C₄	—	4	16	no	—
180	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
181	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
182	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
183	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
184	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
187	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₃⋊Dic₃	—	2	4	no	—
189	C₂×C₃⋊Dic₃	—	4	2	no	—
190	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
194	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
195	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
196	#634	—	2	2	no	—
197	#634	—	4	2	no	—
198	C₂×C₃×Dic₃	—	3	4	no	—
199	C₂×C₃×Dic₃	—	3	4	no	—
200	C₂×C₃×Dic₃	—	3	4	no	—
201	C₂×C₃×Dic₃	—	3	4	no	—
202	C₂×C₃×Dic₃	—	3	8	no	—
203	C₂×C₃×Dic₃	—	3	8	no	—
204	C₂×C₃×Dic₃	—	6	16	no	—
205	C₂×C₃×Dic₃	—	12	8	no	—
206	C₃×Dic₆	—	6	8	no	—
207	C₃×Dic₆	—	12	8	no	—
208	#554	—	9	1	no	Sylow
209	C₂×C₃³	—	2	4	no	—
210	C₂×C₃³	C₂²×Q₈	1	1	yes	characteristic
211	C₂×C₃³	C₂×#41	1	1	yes	characteristic
212	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₃×Q₈	—	9	1	no	—
214	C₂×C₃×Q₈	—	9	2	no	—
215	C₂×C₃×D₄	—	2	4	no	—
216	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
217	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	—	2	8	no	—
219	C₂²×C₃×C₄	—	9	2	no	—
220	C₂²×C₃×C₄	—	9	2	no	—
221	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
222	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
223	C₂²×Dic₃	—	3	8	no	—
224	C₂²×Dic₃	—	3	8	no	—
225	C₂×Dic₆	—	3	4	no	—
226	C₂×Dic₆	—	3	8	no	—
227	C₃×C₄⋊C₄	—	2	4	no	—
228	C₃×C₄⋊C₄	—	9	1	no	—
229	C₃×C₄⋊C₄	—	9	2	no	—
230	C₃×C₄⋊C₄	—	9	2	no	—
231	C₃×C₄⋊C₄	—	9	2	no	—
232	C₃×C₄⋊C₄	—	9	1	no	—
233	C₃×C₄⋊C₄	—	9	2	no	—
234	C₃×C₄⋊C₄	—	9	1	no	—
235	C₃×C₄⋊C₄	—	9	1	no	—
236	C₃×C₄⋊C₄	—	9	1	no	—
237	C₃×C₄⋊C₄	—	9	2	no	—
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
239	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
240	C₃×C₂²⋊C₄	—	2	8	no	—
241	C₃×C₂²⋊C₄	—	9	2	no	—
242	C₃×C₂²⋊C₄	—	9	2	no	—
243	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
244	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
245	C₃×C₄²	—	2	4	no	—
246	C₃×C₄²	—	9	1	no	—
247	C₃×C₄²	—	9	1	no	—
248	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
249	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
250	#217	—	3	8	no	—
251	#217	—	3	8	no	—
252	C₄⋊Dic₃	—	3	4	no	—
253	C₄⋊Dic₃	—	3	4	no	—
254	C₄⋊Dic₃	—	3	4	no	—
255	C₄⋊Dic₃	—	3	8	no	—
256	Dic₃⋊C₄	—	3	4	no	—
257	Dic₃⋊C₄	—	3	4	no	—
258	Dic₃⋊C₄	—	3	8	no	—
259	Dic₃⋊C₄	—	3	8	no	—
260	Dic₃⋊C₄	—	3	8	no	—
261	Dic₃⋊C₄	—	3	8	no	—
262	C₄×Dic₃	—	3	4	no	—
263	C₄×Dic₃	—	3	4	no	—
264	C₂²×C₃²	—	2	2	no	—
265	C₂²×C₃²	—	2	2	no	—
266	C₂²×C₃²	—	2	4	no	—
267	C₂²×C₃²	—	2	16	no	—
268	C₂²×C₃²	—	2	8	no	—
269	C₂²×C₃²	—	2	8	no	—
270	C₂²×C₃²	—	4	8	no	—
271	C₂²×C₃²	—	4	8	no	—
272	C₂²×C₃²	C₂×Dic₆	1	16	yes	—
273	C₂²×C₃²	C₂×C₃×Q₈	1	4	yes	—
274	C₂²×C₃²	C₂³×D₃	1	4	yes	—
275	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
276	C₃²×C₄	—	2	8	no	—
277	C₃²×C₄	—	2	4	no	—
278	C₃²×C₄	—	2	1	no	—
279	C₃²×C₄	—	2	2	no	—
280	C₃²×C₄	—	2	1	no	—
281	C₃²×C₄	—	2	8	no	—
282	C₃²×C₄	—	2	8	no	—
283	C₃²×C₄	—	2	4	no	—
284	C₃²×C₄	—	4	4	no	—
285	C₃²×C₄	—	4	8	no	—
286	C₃²×C₄	C₂×Dic₆	1	8	yes	—
287	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
288	C₃⋊Dic₃	—	2	1	no	—
289	C₃⋊Dic₃	—	2	2	no	—
290	C₃⋊Dic₃	—	2	1	no	—
291	C₃⋊Dic₃	—	2	2	no	—
292	C₃⋊Dic₃	—	2	1	no	—
293	C₃⋊Dic₃	C₃×#41	1	2	yes	—
294	C₃×Dic₃	—	3	8	no	—
295	C₃×Dic₃	—	6	4	no	—
296	C₃×Dic₃	—	6	8	no	—
297	C₃×Dic₃	—	6	4	no	—
298	C₃×Dic₃	—	6	4	no	—
299	C₃×Dic₃	—	6	8	no	—
300	C₄⋊Q₈	—	9	1	no	—
301	#125	—	9	1	no	—
302	#125	—	9	1	no	—
303	C₂²⋊Q₈	—	9	2	no	—
304	C₂²⋊Q₈	—	9	2	no	—
305	C₂²⋊Q₈	—	9	2	no	—
306	C₄×Q₈	—	9	1	no	—
307	C₄×D₄	—	9	1	no	—
308	C₄×D₄	—	9	1	no	—
309	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	9	2	no	—
311	C₃³	#554	1	1	yes	characteristic, complemented, Sylow
312	C₂³×C₃	—	2	8	no	—
313	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
314	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
315	C₃×Q₈	—	18	2	no	—
316	C₃×Q₈	—	36	2	no	—
317	C₃×D₄	—	2	16	no	—
318	C₃×D₄	C₃×Dic₆	1	16	yes	complemented
319	C₃×D₄	#634	1	4	yes	complemented
320	C₂×C₃×C₄	—	2	4	no	—
321	C₂×C₃×C₄	—	2	4	no	—
322	C₂×C₃×C₄	—	2	4	no	—
323	C₂×C₃×C₄	—	2	8	no	—
324	C₂×C₃×C₄	—	4	8	no	—
325	C₂×C₃×C₄	—	4	2	no	—
326	C₂×C₃×C₄	—	4	16	no	—
327	C₂×C₃×C₄	—	9	1	no	—
328	C₂×C₃×C₄	—	9	1	no	—
329	C₂×C₃×C₄	—	9	1	no	—
330	C₂×C₃×C₄	—	9	1	no	—
331	C₂×C₃×C₄	—	9	2	no	—
332	C₂×C₃×C₄	—	9	2	no	—
333	C₂×C₃×C₄	—	18	4	no	—
334	C₂×C₃×C₄	—	36	2	no	—
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
336	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
337	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
339	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
342	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
343	C₂×Dic₃	—	3	4	no	—
344	C₂×Dic₃	—	3	4	no	—
345	C₂×Dic₃	—	3	4	no	—
346	C₂×Dic₃	—	3	4	no	—
347	C₂×Dic₃	—	3	8	no	—
348	C₂×Dic₃	—	3	8	no	—
349	C₂×Dic₃	—	6	16	no	—
350	C₂×Dic₃	—	12	8	no	—
351	Dic₆	—	6	8	no	—
352	Dic₆	—	12	8	no	—
353	C₂×C₃²	—	2	4	no	—
354	C₂×C₃²	—	2	4	no	—
355	C₂×C₃²	—	2	4	no	—
356	C₂×C₃²	—	2	4	no	—
357	C₂×C₃²	—	2	16	no	—
358	C₂×C₃²	—	4	16	no	—
359	C₂×C₃²	C₂²×Dic₆	1	4	yes	—
360	C₂×C₃²	#1004	1	4	yes	—
361	C₂×C₃²	D₃×#41	1	4	yes	—
362	C₂×C₃²	C₂²×C₃×Q₈	1	1	yes	characteristic
363	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
364	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂×Q₈	—	9	1	no	—
366	C₂×Q₈	—	9	2	no	—
367	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
368	C₂²×C₄	—	9	2	no	—
369	C₂²×C₄	—	9	2	no	—
370	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
371	C₄⋊C₄	—	9	1	no	—
372	C₄⋊C₄	—	9	2	no	—
373	C₄⋊C₄	—	9	2	no	—
374	C₄⋊C₄	—	9	2	no	—
375	C₄⋊C₄	—	9	1	no	—
376	C₄⋊C₄	—	9	1	no	—
377	C₄⋊C₄	—	9	1	no	—
378	C₄⋊C₄	—	9	1	no	—
379	C₄⋊C₄	—	9	2	no	—
380	C₄⋊C₄	—	9	2	no	—
381	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
382	C₂²⋊C₄	—	9	2	no	—
383	C₂²⋊C₄	—	9	2	no	—
384	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
385	C₄²	—	9	1	no	—
386	C₄²	—	9	1	no	—
387	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
388	C₂²×C₃	—	2	8	no	—
389	C₂²×C₃	—	2	8	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	—	2	4	no	—
393	C₂²×C₃	—	2	16	no	—
394	C₂²×C₃	—	4	8	no	—
395	C₂²×C₃	—	4	8	no	—
396	C₂²×C₃	C₂×C₃×Dic₆	1	16	yes	—
397	C₂²×C₃	C₂×#634	1	4	yes	—
398	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
399	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
400	C₃×C₄	—	2	8	no	—
401	C₃×C₄	—	2	8	no	—
402	C₃×C₄	—	2	4	no	—
403	C₃×C₄	—	2	4	no	—
404	C₃×C₄	—	2	1	no	—
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	8	no	—
408	C₃×C₄	—	4	8	no	—
409	C₃×C₄	—	4	4	no	—
410	C₃×C₄	—	9	2	no	—
411	C₃×C₄	—	18	1	no	—
412	C₃×C₄	—	18	2	no	—
413	C₃×C₄	—	18	1	no	—
414	C₃×C₄	—	18	2	no	—
415	C₃×C₄	—	18	1	no	—
416	C₃×C₄	C₂×C₃×Dic₆	1	8	yes	—
417	C₃×C₄	C₂×#634	1	2	yes	—
418	Dic₃	—	3	8	no	—
419	Dic₃	—	6	4	no	—
420	Dic₃	—	6	8	no	—
421	Dic₃	—	6	4	no	—
422	Dic₃	—	6	4	no	—
423	Dic₃	—	6	8	no	—
424	C₃²	—	2	4	no	—
425	C₃²	#5539	1	4	yes	complemented
426	C₃²	C₃×#554	1	1	yes	characteristic, complemented
427	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
428	Q₈	—	18	2	no	—
429	Q₈	—	36	2	no	—
430	D₄	C₃×#634	1	4	yes	complemented
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	9	1	no	—
433	C₂×C₄	—	9	1	no	—
434	C₂×C₄	—	9	1	no	—
435	C₂×C₄	—	9	1	no	—
436	C₂×C₄	—	9	2	no	—
437	C₂×C₄	—	9	2	no	—
438	C₂×C₄	—	18	4	no	—
439	C₂×C₄	—	36	2	no	—
440	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
441	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
443	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
444	C₂×C₃	—	2	16	no	—
445	C₂×C₃	—	2	4	no	—
446	C₂×C₃	—	2	4	no	—
447	C₂×C₃	—	2	4	no	—
448	C₂×C₃	—	2	4	no	—
449	C₂×C₃	—	4	16	no	—
450	C₂×C₃	C₂²×C₃×Dic₆	1	4	yes	—
451	C₂×C₃	C₃×#1004	1	4	yes	—
452	C₂×C₃	C₃×D₃×#41	1	4	yes	—
453	C₂×C₃	C₂²×#634	1	1	yes	characteristic
454	C₂×C₃	#64361	1	1	yes	characteristic
455	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	C₂×C₃×#634	1	4	yes	—
459	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	1	no	—
463	C₄	—	9	2	no	—
464	C₄	—	18	1	no	—
465	C₄	—	18	2	no	—
466	C₄	—	18	1	no	—
467	C₄	—	18	2	no	—
468	C₄	—	18	1	no	—
469	C₄	C₂×C₃×#634	1	2	yes	—
470	C₃	—	2	4	no	—
471	C₃	C₃×#5539	1	4	yes	complemented
472	C₃	#10596010	1	1	yes	characteristic, direct product factor
473	C₂	—	2	4	no	—
474	C₂	C₂²×C₃×#634	1	1	yes	characteristic
475	C₂	C₃×#64361	1	1	yes	characteristic
476	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	C₂×C₃³×D₄	C₂²
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#554
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
4. C₃×#64133	C₂	semidirect
5. C₂×C₃×#3750	C₂	semidirect
6. C₃×#64099	C₂	semidirect
7. C₃×#64097	C₂	semidirect
8. C₃×#64087	C₂	semidirect
9. C₃×#64087	C₂	semidirect
10. C₃×#64079	C₂	semidirect
11. C₃×C₄×#634	C₂	semidirect
12. #10596010	C₃	direct (N × H)
42. #64133	C₂×C₃	semidirect
43. C₂×#3750	C₂×C₃	semidirect
44. #64099	C₂×C₃	semidirect
45. #64097	C₂×C₃	semidirect
46. #64087	C₂×C₃	semidirect
47. #64087	C₂×C₃	semidirect
48. #64079	C₂×C₃	semidirect
49. C₄×#634	C₂×C₃	semidirect
61. C₃³×D₄	Q₈	semidirect
171. C₃²×D₄	Dic₆	semidirect
172. C₃²×D₄	C₃×Q₈	semidirect
311. C₃³	#554	semidirect
318. C₃×D₄	C₃×Dic₆	semidirect
319. C₃×D₄	#634	semidirect
425. C₃²	#5539	semidirect
426. C₃²	C₃×#554	semidirect
430. D₄	C₃×#634	semidirect
471. C₃	C₃×#5539	semidirect
472. C₃	#10596010	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×D₄×C₃⋊Dic₃	2
C₃×#64133	2
C₂×C₃×#3750	2
C₃×#64099	2
C₃×#64097	2
C₃×#64087	2
C₃×#64079	2
C₃×C₄×#634	2
#10596010	3
C₃×#5539	3

Subgroups — C3×#10596010 #13179291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596010 #13179291