Subgroups — C₃×#82515 #11859087

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#5234	C₂	1	2	yes	maximal
3	C₃×#5000	C₂	1	4	yes	maximal, complemented
4	C₃×#4997	C₂	1	2	yes	maximal, complemented
5	C₃×#4926	C₂	1	2	yes	maximal, complemented
6	C₃×#4925	C₂	1	2	yes	maximal, complemented
7	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#2925	—	3	1	no	maximal
10	#82515	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
12	C₃²×C₄×Q₈	C₄	1	1	yes	characteristic
13	C₃²×C₄×Q₈	C₄	1	1	yes	characteristic
14	C₃²×C₄×D₄	C₄	1	2	yes	—
15	C₃²×C₄×D₄	C₄	1	1	yes	characteristic
16	C₃²×C₄×D₄	C₄	1	2	yes	—
17	C₃²×C₄×D₄	C₄	1	1	yes	characteristic
18	C₃²×#117	C₂²	1	1	yes	characteristic
19	C₃²×#117	C₂²	1	2	yes	—
20	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
21	C₂×C₃²×C₄²	C₂²	1	2	yes	—
22	C₂×C₃×#208	C₂²	1	2	yes	—
23	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
24	C₃×#830	C₂²	1	4	yes	—
25	C₃×#830	C₂²	1	4	yes	—
26	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
29	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
30	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
31	C₃×#803	C₂²	1	4	yes	—
32	C₃×C₄×C₃⋊C₈	C₂²	1	4	yes	—
33	C₃×C₄×#41	—	2	1	no	—
34	C₃×C₄×#41	D₃	1	1	yes	characteristic
35	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
36	C₃×#433	—	3	4	no	—
37	C₃×#432	—	3	2	no	—
38	C₃×#431	—	3	2	no	—
39	C₃×#423	—	3	1	no	—
40	C₂×C₃×C₄⋊C₈	—	3	1	no	—
41	C₃×#408	—	3	2	no	—
42	C₃×#405	—	3	2	no	—
43	#5234	C₂×C₃	1	2	yes	—
44	#5000	C₂×C₃	1	4	yes	complemented
45	#4997	C₂×C₃	1	2	yes	complemented
46	#4926	C₂×C₃	1	2	yes	complemented
47	#4925	C₂×C₃	1	2	yes	complemented
48	#4924	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃²×#41	—	2	2	no	—
51	C₃²×#41	—	2	2	no	—
52	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
54	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
56	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
58	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₃²×C₄	C₂³	1	2	yes	—
60	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
61	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
67	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
68	C₃²×C₄²	C₂×C₄	1	2	yes	—
69	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
70	C₃²×C₄²	C₂×C₄	1	2	yes	—
71	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
72	C₃²×C₄²	C₂³	1	2	yes	—
73	C₃²×C₄²	C₂³	1	1	yes	characteristic
74	C₃²×C₄²	C₂³	1	1	yes	characteristic
75	C₃×#208	—	2	4	no	—
76	C₂×C₃×C₃⋊C₈	—	2	4	no	—
77	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
78	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
79	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
80	#2925	—	3	1	no	Sylow
81	C₂×C₃×#41	—	2	1	no	—
82	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₃×M₁₆	—	3	2	no	—
85	C₂²×C₃×C₈	—	3	2	no	—
86	C₃×C₄×Q₈	—	2	1	no	—
87	C₃×C₄×Q₈	—	2	1	no	—
88	C₃×C₄×Q₈	Dic₃	1	1	yes	characteristic
89	C₃×C₄×Q₈	Dic₃	1	1	yes	characteristic
90	C₃×C₄×Q₈	C₃×C₄	1	1	yes	characteristic
91	C₃×C₄×Q₈	C₃×C₄	1	1	yes	characteristic
92	C₃×C₄×D₄	—	2	2	no	—
93	C₃×C₄×D₄	—	2	1	no	—
94	C₃×C₄×D₄	—	2	2	no	—
95	C₃×C₄×D₄	—	2	1	no	—
96	C₃×C₄×D₄	Dic₃	1	2	yes	—
97	C₃×C₄×D₄	Dic₃	1	1	yes	characteristic
98	C₃×C₄×D₄	Dic₃	1	2	yes	—
99	C₃×C₄×D₄	Dic₃	1	1	yes	characteristic
100	C₃×C₄×D₄	C₃×C₄	1	2	yes	—
101	C₃×C₄×D₄	C₃×C₄	1	1	yes	characteristic
102	C₃×C₄×D₄	C₃×C₄	1	2	yes	—
103	C₃×C₄×D₄	C₃×C₄	1	1	yes	characteristic
104	C₃×#117	—	2	1	no	—
105	C₃×#117	—	2	2	no	—
106	C₃×#117	C₂×D₃	1	1	yes	characteristic
107	C₃×#117	C₂×D₃	1	2	yes	—
108	C₃×#117	C₂²×C₃	1	1	yes	characteristic
109	C₃×#117	C₂²×C₃	1	2	yes	—
110	C₂×C₃×C₄²	—	2	1	no	—
111	C₂×C₃×C₄²	—	2	2	no	—
112	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
113	C₂×C₃×C₄²	C₂×D₃	1	2	yes	—
114	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₄²	C₂²×C₃	1	2	yes	—
116	C₂×#208	C₂²×C₃	1	2	yes	—
117	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
118	C₃×C₄⋊C₈	—	3	1	no	—
119	C₃×C₄⋊C₈	—	3	1	no	—
120	C₃×C₄⋊C₈	—	3	2	no	—
121	C₃×C₄⋊C₈	—	3	2	no	—
122	C₃×C₄⋊C₈	—	3	2	no	—
123	C₃×C₂²⋊C₈	—	3	4	no	—
124	C₃×C₂²⋊C₈	—	3	4	no	—
125	C₃×#97	—	3	4	no	—
126	C₃×C₄×C₈	—	3	4	no	—
127	#830	C₂²×C₃	1	4	yes	—
128	#830	C₂²×C₃	1	4	yes	—
129	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
130	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
131	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
132	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
133	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
134	#803	C₂²×C₃	1	4	yes	—
135	C₄×C₃⋊C₈	C₂²×C₃	1	4	yes	—
136	C₂³×C₃²	C₂²×C₄	1	2	yes	—
137	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
138	C₃²×Q₈	—	2	2	no	—
139	C₃²×D₄	—	2	4	no	—
140	C₃²×D₄	—	2	2	no	—
141	C₂×C₃²×C₄	—	2	2	no	—
142	C₂×C₃²×C₄	—	2	2	no	—
143	C₂×C₃²×C₄	—	2	2	no	—
144	C₂×C₃²×C₄	—	2	4	no	—
145	C₂×C₃²×C₄	—	4	1	no	—
146	C₂×C₃²×C₄	—	4	2	no	—
147	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
149	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
150	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
152	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₃²×C₄	#41	1	2	yes	—
156	C₂×C₃²×C₄	#41	1	2	yes	—
157	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
158	C₃×C₃⋊C₈	—	2	2	no	—
159	C₃×C₃⋊C₈	—	2	2	no	—
160	C₃×C₃⋊C₈	—	2	4	no	—
161	C₄×#41	C₃×D₃	1	1	yes	characteristic
162	#433	—	3	4	no	—
163	#432	—	3	2	no	—
164	#431	—	3	2	no	—
165	#423	—	3	1	no	—
166	C₂×C₄⋊C₈	—	3	1	no	—
167	#408	—	3	2	no	—
168	#405	—	3	2	no	—
169	C₃×#41	—	2	4	no	—
170	C₃×#41	—	2	4	no	—
171	C₃×#41	—	2	2	no	—
172	C₃×#41	—	2	2	no	—
173	C₃×#41	—	2	2	no	—
174	C₃×#41	—	2	2	no	—
175	C₂×C₃×Q₈	—	2	1	no	—
176	C₂×C₃×Q₈	C₂×Dic₃	1	1	yes	characteristic
177	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂×C₃×D₄	—	2	2	no	—
179	C₂×C₃×D₄	—	2	1	no	—
180	C₂×C₃×D₄	C₂×Dic₃	1	2	yes	—
181	C₂×C₃×D₄	C₂×Dic₃	1	1	yes	characteristic
182	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
183	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	2	2	no	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
191	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
193	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
195	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
197	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
199	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
201	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
202	C₃×M₁₆	—	6	4	no	—
203	C₂×C₃×C₈	—	3	2	no	—
204	C₂×C₃×C₈	—	3	4	no	—
205	C₂×C₃×C₈	—	3	2	no	—
206	C₂×C₃×C₈	—	6	4	no	—
207	C₃×C₄⋊C₄	—	2	2	no	—
208	C₃×C₄⋊C₄	—	2	2	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	—	2	1	no	—
211	C₃×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
212	C₃×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
213	C₃×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
214	C₃×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
215	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
216	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
217	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
218	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
219	C₃×C₂²⋊C₄	—	2	2	no	—
220	C₃×C₂²⋊C₄	—	2	2	no	—
221	C₃×C₂²⋊C₄	—	2	2	no	—
222	C₃×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
223	C₃×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
224	C₃×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
225	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
226	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
227	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
228	C₃×C₄²	—	2	2	no	—
229	C₃×C₄²	—	2	1	no	—
230	C₃×C₄²	—	2	2	no	—
231	C₃×C₄²	—	2	1	no	—
232	C₃×C₄²	—	2	1	no	—
233	C₃×C₄²	—	2	2	no	—
234	C₃×C₄²	—	2	1	no	—
235	C₃×C₄²	C₂×Dic₃	1	2	yes	—
236	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
237	C₃×C₄²	C₂×Dic₃	1	2	yes	—
238	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
239	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
240	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
241	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
242	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
243	C₃×C₄²	C₂²×D₃	1	2	yes	—
244	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
245	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
246	C₃×C₄²	C₂³×C₃	1	2	yes	—
247	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
248	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
249	#208	—	2	4	no	—
250	C₂×C₃⋊C₈	—	2	4	no	—
251	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
252	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
253	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
254	C₂²×C₃²	—	2	2	no	—
255	C₂²×C₃²	—	2	1	no	—
256	C₂²×C₃²	—	2	1	no	—
257	C₂²×C₃²	—	2	2	no	—
258	C₂²×C₃²	—	2	2	no	—
259	C₂²×C₃²	#117	1	2	yes	—
260	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	—	2	1	no	—
263	C₃²×C₄	—	2	1	no	—
264	C₃²×C₄	—	2	2	no	—
265	C₃²×C₄	—	2	1	no	—
266	C₃²×C₄	—	2	2	no	—
267	C₃²×C₄	#117	1	2	yes	—
268	C₃²×C₄	#131	1	2	yes	—
269	C₃²×C₄	C₂×#41	1	1	yes	characteristic
270	C₃²×C₄	C₂×#41	1	1	yes	characteristic
271	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
272	C₂×M₁₆	—	3	2	no	—
273	C₂²×C₈	—	3	2	no	—
274	C₄×Q₈	C₃×Dic₃	1	1	yes	characteristic
275	C₄×Q₈	C₃×Dic₃	1	1	yes	characteristic
276	C₄×D₄	C₃×Dic₃	1	2	yes	—
277	C₄×D₄	C₃×Dic₃	1	1	yes	characteristic
278	C₄×D₄	C₃×Dic₃	1	2	yes	—
279	C₄×D₄	C₃×Dic₃	1	1	yes	characteristic
280	#117	C₂×C₃×D₃	1	1	yes	characteristic
281	#117	C₂×C₃×D₃	1	2	yes	—
282	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
283	C₂×C₄²	C₂×C₃×D₃	1	2	yes	—
284	C₄⋊C₈	—	3	1	no	—
285	C₄⋊C₈	—	3	1	no	—
286	C₄⋊C₈	—	3	2	no	—
287	C₄⋊C₈	—	3	2	no	—
288	C₄⋊C₈	—	3	2	no	—
289	C₂²⋊C₈	—	3	4	no	—
290	C₂²⋊C₈	—	3	4	no	—
291	#97	—	3	4	no	—
292	C₄×C₈	—	3	4	no	—
293	C₂³×C₃	—	2	2	no	—
294	C₂³×C₃	—	2	1	no	—
295	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
296	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
297	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
298	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
299	C₃×Q₈	—	2	4	no	—
300	C₃×Q₈	—	2	2	no	—
301	C₃×Q₈	—	2	2	no	—
302	C₃×D₄	—	2	8	no	—
303	C₃×D₄	—	2	4	no	—
304	C₃×D₄	—	2	4	no	—
305	C₃×D₄	—	2	4	no	—
306	C₃×D₄	—	2	2	no	—
307	C₃×D₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	4	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	4	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	4	2	no	—
330	C₂×C₃×C₄	—	4	4	no	—
331	C₂×C₃×C₄	—	4	1	no	—
332	C₂×C₃×C₄	—	4	2	no	—
333	C₂×C₃×C₄	—	4	1	no	—
334	C₂×C₃×C₄	—	4	2	no	—
335	C₂×C₃×C₄	—	4	2	no	—
336	C₂×C₃×C₄	—	4	4	no	—
337	C₂×C₃×C₄	#235	1	2	yes	—
338	C₂×C₃×C₄	#235	1	2	yes	—
339	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
341	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
342	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
344	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
349	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
350	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
352	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
355	C₂×C₃×C₄	C₃×#41	1	2	yes	—
356	C₂×C₃×C₄	C₃×#41	1	2	yes	—
357	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
358	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
359	C₃×C₈	—	6	2	no	—
360	C₃×C₈	—	6	2	no	—
361	C₃×C₈	—	6	4	no	—
362	C₃⋊C₈	—	2	2	no	—
363	C₃⋊C₈	—	2	2	no	—
364	C₃⋊C₈	—	2	4	no	—
365	C₂×C₃²	—	2	2	no	—
366	C₂×C₃²	—	4	2	no	—
367	C₂×C₃²	C₂×#117	1	1	yes	characteristic
368	C₂×C₃²	C₂×#131	1	1	yes	characteristic
369	C₂×C₃²	#568	1	1	yes	characteristic
370	#41	—	2	2	no	—
371	#41	—	2	2	no	—
372	C₂×Q₈	C₂×C₃×Dic₃	1	1	yes	characteristic
373	C₂×D₄	C₂×C₃×Dic₃	1	2	yes	—
374	C₂×D₄	C₂×C₃×Dic₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
376	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
378	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
379	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
380	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
381	M₁₆	—	6	4	no	—
382	C₂×C₈	—	3	2	no	—
383	C₂×C₈	—	3	4	no	—
384	C₂×C₈	—	3	2	no	—
385	C₂×C₈	—	6	4	no	—
386	C₄⋊C₄	C₂×C₃×Dic₃	1	2	yes	—
387	C₄⋊C₄	C₂×C₃×Dic₃	1	2	yes	—
388	C₄⋊C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
389	C₄⋊C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
390	C₂²⋊C₄	C₂×C₃×Dic₃	1	2	yes	—
391	C₂²⋊C₄	C₂×C₃×Dic₃	1	2	yes	—
392	C₂²⋊C₄	C₂×C₃×Dic₃	1	2	yes	—
393	C₄²	C₂×C₃×Dic₃	1	2	yes	—
394	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
395	C₄²	C₂×C₃×Dic₃	1	2	yes	—
396	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
397	C₄²	C₂²×C₃×D₃	1	2	yes	—
398	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
399	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
400	C₂²×C₃	—	2	1	no	—
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	4	no	—
405	C₂²×C₃	—	2	2	no	—
406	C₂²×C₃	—	2	2	no	—
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	2	2	no	—
410	C₂²×C₃	—	2	2	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	1	no	—
413	C₂²×C₃	—	4	1	no	—
414	C₂²×C₃	—	4	1	no	—
415	C₂²×C₃	—	4	2	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	#926	1	2	yes	—
418	C₂²×C₃	C₃×#117	1	2	yes	—
419	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
420	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
421	C₃×C₄	—	2	4	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	1	no	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	2	2	no	—
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	2	2	no	—
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	2	1	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	2	no	—
443	C₃×C₄	#926	1	2	yes	—
444	C₃×C₄	#948	1	2	yes	—
445	C₃×C₄	C₃×#117	1	2	yes	—
446	C₃×C₄	C₃×#131	1	2	yes	—
447	C₃×C₄	C₂×#235	1	1	yes	characteristic
448	C₃×C₄	C₂×#235	1	1	yes	characteristic
449	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
450	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
451	C₃²	#2925	1	1	yes	characteristic, complemented, Sylow
452	C₂³	C₂²×C₃×Dic₃	1	2	yes	—
453	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	D₄	—	2	4	no	—
456	D₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	C₃×#235	1	2	yes	—
464	C₂×C₄	C₃×#235	1	2	yes	—
465	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
467	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
468	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
470	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
473	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
474	C₈	—	6	2	no	—
475	C₈	—	6	2	no	—
476	C₈	—	6	4	no	—
477	C₂×C₃	—	2	2	no	—
478	C₂×C₃	—	2	2	no	—
479	C₂×C₃	—	2	1	no	—
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	2	1	no	—
482	C₂×C₃	—	4	2	no	—
483	C₂×C₃	—	4	4	no	—
484	C₂×C₃	—	4	2	no	—
485	C₂×C₃	—	4	2	no	—
486	C₂×C₃	C₂×#926	1	1	yes	characteristic
487	C₂×C₃	C₂×#948	1	1	yes	characteristic
488	C₂×C₃	#5819	1	1	yes	characteristic
489	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
490	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
491	C₂×C₃	C₃×#568	1	1	yes	characteristic
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	C₃×#926	1	2	yes	—
498	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	2	1	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	2	no	—
505	C₄	C₃×#926	1	2	yes	—
506	C₄	C₃×#948	1	2	yes	—
507	C₄	C₂×C₃×#235	1	1	yes	characteristic
508	C₄	C₂×C₃×#235	1	1	yes	characteristic
509	C₃	—	2	1	no	—
510	C₃	#82515	1	1	yes	characteristic, direct product factor
511	C₃	C₃×#2925	1	1	yes	characteristic, complemented
512	C₂	—	2	2	no	—
513	C₂	—	4	2	no	—
514	C₂	C₂×C₃×#926	1	1	yes	characteristic
515	C₂	C₂×C₃×#948	1	1	yes	characteristic
516	C₂	C₃×#5819	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×#41	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃²×#41	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×#41	D₃
hypocenter	C₃	C₃×#2925
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
3. C₃×#5000	C₂	semidirect
4. C₃×#4997	C₂	semidirect
5. C₃×#4926	C₂	semidirect
6. C₃×#4925	C₂	semidirect
7. C₃×#4924	C₂	semidirect
8. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
10. #82515	C₃	direct (N × H)
44. #5000	C₂×C₃	semidirect
45. #4997	C₂×C₃	semidirect
46. #4926	C₂×C₃	semidirect
47. #4925	C₂×C₃	semidirect
48. #4924	C₂×C₃	semidirect
49. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
451. C₃²	#2925	semidirect
510. C₃	#82515	direct (N × H)
511. C₃	C₃×#2925	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄×#41	2
C₃×#5234	2
C₃×#5000	2
C₃×#4997	2
C₃×#4926	2
C₃×#4925	2
C₃×#4924	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₃×#2925	3
#82515	3

Subgroups — C3×#82515 #11859087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#82515 #11859087