Subgroups — C₃×#68661 #11783097

Order 1152.

891 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	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#872	C₂	1	1	yes	maximal, characteristic
4	C₃²×#336	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4524	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1729	—	3	1	no	maximal
9	#68661	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
15	C₂×C₃×Dic₃⋊C₄	C₄	1	2	yes	—
16	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
20	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
21	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	4	yes	complemented
22	C₂×C₃×D₃×C₈	—	2	2	no	—
23	C₂×C₃×D₃×C₈	—	2	2	no	—
24	C₂×C₃×D₃×C₈	C₄	1	4	yes	complemented
25	C₃×#872	—	2	2	no	—
26	C₃×#872	—	2	2	no	—
27	C₂²×C₃×M₁₆	—	3	1	no	—
28	C₂³×C₃×C₈	—	3	1	no	—
29	C₂×C₃×#117	—	3	1	no	—
30	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
31	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
32	C₂×#872	C₂×C₃	1	1	yes	characteristic
33	C₃×#336	—	2	1	no	—
34	C₃×#336	—	3	1	no	—
35	C₃×#336	—	3	1	no	—
36	C₃×#336	—	3	1	no	—
37	C₃×#336	D₃	1	1	yes	characteristic, complemented
38	C₃×#336	C₂×C₃	1	1	yes	characteristic, complemented
39	#4550	C₂×C₃	1	1	yes	characteristic, complemented
40	#4550	C₂×C₃	1	1	yes	characteristic, complemented
41	#4524	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
44	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
46	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
50	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
51	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
52	C₂×C₃×C₄×D₃	Q₈	1	2	yes	—
53	C₂×C₃²×C₈	—	2	1	no	—
54	C₂×C₃²×C₈	—	2	1	no	—
55	C₂×C₃²×C₈	—	2	1	no	—
56	C₂×C₃²×C₈	—	2	1	no	—
57	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
58	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
59	C₃²×C₄²	—	2	1	no	—
60	C₃²×C₄²	—	2	1	no	—
61	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
62	C₃×Dic₃⋊C₄	—	2	4	no	—
63	C₃×C₄×Dic₃	—	2	1	no	—
64	C₃×C₄×Dic₃	—	2	1	no	—
65	C₂×C₃×C₃⋊C₈	—	2	1	no	—
66	C₂×C₃×C₃⋊C₈	—	2	1	no	—
67	C₂×C₃×C₃⋊C₈	—	2	1	no	—
68	C₂×C₃×C₃⋊C₈	—	2	1	no	—
69	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
70	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
71	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
72	C₃×D₃×C₈	—	2	8	no	—
73	#1729	—	3	1	no	Sylow
74	C₂³×C₃×C₄	—	3	1	no	—
75	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃×M₁₆	—	3	4	no	—
77	C₂×C₃×M₁₆	—	6	2	no	—
78	C₂×C₃×M₁₆	—	6	2	no	—
79	C₂²×C₃×C₈	—	2	1	no	—
80	C₂²×C₃×C₈	—	2	1	no	—
81	C₂²×C₃×C₈	—	3	1	no	—
82	C₂²×C₃×C₈	—	3	1	no	—
83	C₂²×C₃×C₈	—	3	4	no	—
84	C₂²×C₃×C₈	—	6	2	no	—
85	C₂²×C₃×C₈	—	6	2	no	—
86	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
87	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
88	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
90	C₃×#117	—	6	2	no	—
91	C₃×#117	—	6	2	no	—
92	C₂×C₃×C₄⋊C₄	—	3	2	no	—
93	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
94	C₂×C₃×C₄²	—	2	1	no	—
95	C₂×C₃×C₄²	—	3	1	no	—
96	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
97	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
98	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
99	C₂×Dic₃⋊C₄	C₃×C₄	1	2	yes	—
100	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
103	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
104	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
105	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	4	yes	complemented
106	C₂×D₃×C₈	—	2	2	no	—
107	C₂×D₃×C₈	—	2	2	no	—
108	C₂×D₃×C₈	C₃×C₄	1	4	yes	complemented
109	#872	—	2	2	no	—
110	#872	—	2	2	no	—
111	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₃×D₃	—	2	2	no	—
113	C₂²×C₃×D₃	—	2	2	no	—
114	C₂²×C₃×D₃	C₄²	1	2	yes	—
115	C₂²×C₃×D₃	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
117	C₂×C₃²×C₄	—	2	2	no	—
118	C₂×C₃²×C₄	—	2	2	no	—
119	C₂×C₃²×C₄	—	2	2	no	—
120	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
126	C₂×C₃×Dic₃	—	2	2	no	—
127	C₂×C₃×Dic₃	—	2	2	no	—
128	C₂×C₃×Dic₃	—	2	2	no	—
129	C₂×C₃×Dic₃	C₄²	1	2	yes	—
130	C₂×C₃×Dic₃	C₂²⋊C₄	1	2	yes	—
131	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
132	C₃×C₄×D₃	C₂²⋊C₄	1	4	yes	—
133	C₃×C₄×D₃	C₂²⋊C₄	1	4	yes	—
134	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
135	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
136	C₃²×C₈	—	2	2	no	—
137	C₃²×C₈	—	2	2	no	—
138	C₃×C₃⋊C₈	—	2	2	no	—
139	C₃×C₃⋊C₈	—	2	2	no	—
140	C₂²×M₁₆	—	3	1	no	—
141	C₂³×C₈	—	3	1	no	—
142	C₂×#117	—	3	1	no	—
143	#336	—	3	1	no	—
144	#336	—	3	1	no	—
145	#336	—	3	1	no	—
146	#336	C₃×D₃	1	1	yes	characteristic, complemented
147	C₂⁴×C₃	—	3	1	no	—
148	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂²×C₃×C₄	—	2	2	no	—
150	C₂²×C₃×C₄	—	2	1	no	—
151	C₂²×C₃×C₄	—	3	1	no	—
152	C₂²×C₃×C₄	—	3	2	no	—
153	C₂²×C₃×C₄	—	3	2	no	—
154	C₂²×C₃×C₄	—	3	2	no	—
155	C₂²×C₃×C₄	—	3	2	no	—
156	C₂²×C₃×C₄	—	3	2	no	—
157	C₂²×C₃×C₄	—	3	2	no	—
158	C₂²×C₃×C₄	—	3	2	no	—
159	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
160	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
161	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
163	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
164	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
166	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
167	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
168	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
169	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
170	C₂×C₄×D₃	C₃×Q₈	1	2	yes	—
171	C₃×M₁₆	—	6	8	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	2	1	no	—
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	—	2	1	no	—
176	C₂×C₃×C₈	—	2	1	no	—
177	C₂×C₃×C₈	—	2	1	no	—
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₂×C₃×C₈	—	2	2	no	—
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	3	2	no	—
183	C₂×C₃×C₈	—	3	2	no	—
184	C₂×C₃×C₈	—	4	1	no	—
185	C₂×C₃×C₈	—	4	1	no	—
186	C₂×C₃×C₈	—	4	1	no	—
187	C₂×C₃×C₈	—	4	1	no	—
188	C₂×C₃×C₈	—	6	8	no	—
189	C₂×C₃×C₈	—	6	1	no	—
190	C₂×C₃×C₈	—	6	1	no	—
191	C₂×C₃×C₈	—	6	1	no	—
192	C₂×C₃×C₈	—	6	1	no	—
193	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
194	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
195	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
196	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
197	C₃×C₄⋊C₄	—	6	4	no	—
198	C₃×C₂²⋊C₄	—	6	4	no	—
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₃×C₄²	—	2	1	no	—
202	C₃×C₄²	—	2	1	no	—
203	C₃×C₄²	—	4	1	no	—
204	C₃×C₄²	—	4	1	no	—
205	C₃×C₄²	—	6	1	no	—
206	C₃×C₄²	—	6	1	no	—
207	(C₂×D₃)⋊C₄	—	2	4	no	—
208	Dic₃⋊C₄	—	2	4	no	—
209	C₄×Dic₃	—	2	1	no	—
210	C₄×Dic₃	—	2	1	no	—
211	C₂×C₃⋊C₈	—	2	1	no	—
212	C₂×C₃⋊C₈	—	2	1	no	—
213	C₂×C₃⋊C₈	—	2	1	no	—
214	C₂×C₃⋊C₈	—	2	1	no	—
215	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
216	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
217	ΓL(1,𝔽₂₅)	—	2	8	no	—
218	D₃×C₈	—	2	8	no	—
219	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
220	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₂²×C₃²	#131	1	2	yes	—
223	C₂²×C₃²	#131	1	2	yes	—
224	C₂×C₃×D₃	—	2	2	no	—
225	C₂×C₃×D₃	—	2	2	no	—
226	C₂×C₃×D₃	—	2	4	no	—
227	C₂×C₃×D₃	—	2	4	no	—
228	C₂×C₃×D₃	#95	1	4	yes	—
229	C₃²×C₄	—	4	2	no	—
230	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₃×Dic₃	—	4	2	no	—
235	C₃×Dic₃	#95	1	4	yes	—
236	C₂³×C₄	—	3	1	no	—
237	C₂×M₁₆	—	3	4	no	—
238	C₂×M₁₆	—	6	2	no	—
239	C₂×M₁₆	—	6	2	no	—
240	C₂²×C₈	—	3	1	no	—
241	C₂²×C₈	—	3	1	no	—
242	C₂²×C₈	—	3	4	no	—
243	C₂²×C₈	—	6	2	no	—
244	C₂²×C₈	—	6	2	no	—
245	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
246	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
247	#117	—	6	2	no	—
248	#117	—	6	2	no	—
249	C₂×C₄⋊C₄	—	3	2	no	—
250	C₂×C₂²⋊C₄	—	3	2	no	—
251	C₂×C₄²	—	3	1	no	—
252	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	3	2	no	—
255	C₂³×C₃	—	3	2	no	—
256	C₂³×C₃	—	3	2	no	—
257	C₂³×C₃	—	6	2	no	—
258	C₂³×C₃	—	6	2	no	—
259	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
260	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂²×D₃	—	2	2	no	—
262	C₂²×D₃	—	2	2	no	—
263	C₂²×D₃	C₃×C₄²	1	2	yes	—
264	C₂²×D₃	C₃×C₂²⋊C₄	1	2	yes	—
265	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	3	2	no	—
280	C₂×C₃×C₄	—	3	2	no	—
281	C₂×C₃×C₄	—	3	2	no	—
282	C₂×C₃×C₄	—	3	4	no	—
283	C₂×C₃×C₄	—	3	4	no	—
284	C₂×C₃×C₄	—	3	4	no	—
285	C₂×C₃×C₄	—	3	4	no	—
286	C₂×C₃×C₄	—	4	2	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	—	6	2	no	—
289	C₂×C₃×C₄	—	6	2	no	—
290	C₂×C₃×C₄	—	6	2	no	—
291	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
303	C₂×Dic₃	—	2	2	no	—
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	—	2	2	no	—
306	C₂×Dic₃	C₃×C₄²	1	2	yes	—
307	C₂×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
308	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
309	C₄×D₃	C₃×C₂²⋊C₄	1	4	yes	—
310	C₄×D₃	C₃×C₂²⋊C₄	1	4	yes	—
311	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
312	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
313	C₃×C₈	—	2	2	no	—
314	C₃×C₈	—	2	2	no	—
315	C₃×C₈	—	2	2	no	—
316	C₃×C₈	—	2	2	no	—
317	C₃×C₈	—	4	2	no	—
318	C₃×C₈	—	4	2	no	—
319	C₃×C₈	—	6	2	no	—
320	C₃×C₈	—	6	2	no	—
321	C₃⋊C₈	—	2	2	no	—
322	C₃⋊C₈	—	2	2	no	—
323	C₂×C₃²	C₂×#95	1	1	yes	characteristic
324	C₂×C₃²	#405	1	1	yes	characteristic
325	C₂×C₃²	#405	1	1	yes	characteristic
326	C₂×C₃²	#408	1	2	yes	—
327	C₂×C₃²	#424	1	2	yes	—
328	C₃×D₃	—	2	4	no	—
329	C₂⁴	—	3	1	no	—
330	C₂²×C₄	—	3	1	no	—
331	C₂²×C₄	—	3	2	no	—
332	C₂²×C₄	—	3	2	no	—
333	C₂²×C₄	—	3	2	no	—
334	C₂²×C₄	—	3	2	no	—
335	C₂²×C₄	—	3	2	no	—
336	C₂²×C₄	—	3	2	no	—
337	C₂²×C₄	—	3	2	no	—
338	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
339	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	M₁₆	—	6	8	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	3	2	no	—
346	C₂×C₈	—	3	2	no	—
347	C₂×C₈	—	6	8	no	—
348	C₂×C₈	—	6	1	no	—
349	C₂×C₈	—	6	1	no	—
350	C₂×C₈	—	6	1	no	—
351	C₂×C₈	—	6	1	no	—
352	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
353	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
354	C₄⋊C₄	—	6	4	no	—
355	C₂²⋊C₄	—	6	4	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	6	1	no	—
359	C₄²	—	6	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	3	4	no	—
366	C₂²×C₃	—	6	2	no	—
367	C₂²×C₃	—	6	2	no	—
368	C₂²×C₃	—	6	4	no	—
369	C₂²×C₃	—	6	4	no	—
370	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
371	C₂²×C₃	D₃×C₂²⋊C₄	1	1	yes	characteristic
372	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
373	C₂²×C₃	#901	1	2	yes	—
374	C₂²×C₃	#907	1	2	yes	—
375	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
376	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
377	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
378	C₂²×C₃	C₃×#131	1	2	yes	—
379	C₂²×C₃	C₃×#131	1	2	yes	—
380	C₂×D₃	—	2	2	no	—
381	C₂×D₃	—	2	2	no	—
382	C₂×D₃	—	2	4	no	—
383	C₂×D₃	—	2	4	no	—
384	C₂×D₃	C₃×#95	1	4	yes	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	3	4	no	—
390	C₃×C₄	—	4	4	no	—
391	C₃×C₄	—	4	2	no	—
392	C₃×C₄	—	4	2	no	—
393	C₃×C₄	—	12	2	no	—
394	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
395	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
396	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
397	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
398	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
399	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
400	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
401	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
402	Dic₃	—	4	2	no	—
403	Dic₃	C₃×#95	1	4	yes	—
404	C₃²	#1729	1	1	yes	characteristic, complemented, Sylow
405	C₂³	—	3	2	no	—
406	C₂³	—	3	2	no	—
407	C₂³	—	3	2	no	—
408	C₂³	—	6	2	no	—
409	C₂³	—	6	2	no	—
410	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	3	2	no	—
415	C₂×C₄	—	3	2	no	—
416	C₂×C₄	—	3	2	no	—
417	C₂×C₄	—	3	4	no	—
418	C₂×C₄	—	3	4	no	—
419	C₂×C₄	—	3	4	no	—
420	C₂×C₄	—	3	4	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	—	6	2	no	—
423	C₂×C₄	—	6	2	no	—
424	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
425	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
426	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
427	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
428	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
429	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	2	2	no	—
432	C₈	—	6	2	no	—
433	C₈	—	6	2	no	—
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	2	no	—
438	C₂×C₃	—	2	2	no	—
439	C₂×C₃	—	6	4	no	—
440	C₂×C₃	D₃×#95	1	1	yes	characteristic
441	C₂×C₃	#4689	1	1	yes	characteristic
442	C₂×C₃	#4708	1	1	yes	characteristic
443	C₂×C₃	#4727	1	2	yes	—
444	C₂×C₃	#4839	1	2	yes	—
445	C₂×C₃	C₂×C₃×#95	1	1	yes	characteristic
446	C₂×C₃	C₃×#405	1	1	yes	characteristic
447	C₂×C₃	C₃×#405	1	1	yes	characteristic
448	C₂×C₃	C₃×#408	1	2	yes	—
449	C₂×C₃	C₃×#424	1	2	yes	—
450	D₃	—	2	4	no	—
451	C₂²	—	3	4	no	—
452	C₂²	—	6	2	no	—
453	C₂²	—	6	2	no	—
454	C₂²	—	6	4	no	—
455	C₂²	—	6	4	no	—
456	C₂²	C₃×C₄²×D₃	1	1	yes	characteristic
457	C₂²	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
458	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
459	C₂²	C₃×#901	1	2	yes	—
460	C₂²	C₃×#907	1	2	yes	—
461	C₄	—	3	4	no	—
462	C₄	—	4	2	no	—
463	C₄	—	12	2	no	—
464	C₄	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
465	C₄	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
466	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
467	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
468	C₃	—	2	1	no	—
469	C₃	#68661	1	1	yes	characteristic, direct product factor
470	C₃	C₃×#1729	1	1	yes	characteristic, complemented
471	C₂	—	6	4	no	—
472	C₂	C₃×D₃×#95	1	1	yes	characteristic
473	C₂	C₃×#4689	1	1	yes	characteristic
474	C₂	C₃×#4708	1	1	yes	characteristic
475	C₂	C₃×#4727	1	2	yes	—
476	C₂	C₃×#4839	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂²×C₃	C₂×C₃×C₄²
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#336	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×#336	D₃
hypocenter	C₃	C₃×#1729
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₃×#336

Complements

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

N	H ≅ G/N	type
4. C₃²×#336	C₂	semidirect
5. C₃×#4550	C₂	semidirect
6. C₃×#4550	C₂	semidirect
7. C₃×#4524	C₂	semidirect
9. #68661	C₃	direct (N × H)
21. C₂×C₃×ΓL(1,𝔽₂₅)	C₄	semidirect
24. C₂×C₃×D₃×C₈	C₄	semidirect
37. C₃×#336	D₃	semidirect
38. C₃×#336	C₂×C₃	semidirect
39. #4550	C₂×C₃	semidirect
40. #4550	C₂×C₃	semidirect
41. #4524	C₂×C₃	semidirect
105. C₂×ΓL(1,𝔽₂₅)	C₃×C₄	semidirect
108. C₂×D₃×C₈	C₃×C₄	semidirect
146. #336	C₃×D₃	semidirect
404. C₃²	#1729	semidirect
469. C₃	#68661	direct (N × H)
470. C₃	C₃×#1729	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂²×C₃×D₃×C₈	2
C₂×C₃×#872	2
C₃²×#336	2
C₃×#4550	2
C₃×#4524	2
C₃×#1729	3
#68661	3

Subgroups — C3×#68661 #11783097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68661 #11783097