Subgroups — C₃×#79276 #11861537

Order 1152.

971 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
2	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4834	C₂	1	2	yes	maximal, complemented
5	C₃×#4830	C₂	1	2	yes	maximal, complemented
6	C₃×#67⋊C₈	C₂	1	4	yes	maximal, complemented
7	C₃×#4685	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₃×C₈	C₂	1	2	yes	maximal, complemented
9	C₃×C₈×#41	—	3	1	no	maximal
10	#79276	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₄	1	1	yes	characteristic
12	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
13	C₃×C₄×#67	C₄	1	2	yes	—
14	C₃×C₄×#67	C₂²	1	2	yes	—
15	C₃×#926	C₄	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
17	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
18	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
19	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
20	C₃×#872	C₄	1	2	yes	—
21	C₃×C₄²×D₃	C₂²	1	2	yes	—
22	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
23	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
24	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
25	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₃²×C₄×C₈	C₂²	1	2	yes	—
27	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
28	C₃×Dic₃⋊C₈	C₂²	1	4	yes	—
29	C₃×C₈×Dic₃	C₂²	1	4	yes	—
30	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
33	C₃×C₄×#41	—	3	1	no	—
34	C₄×#235	C₂×C₃	1	1	yes	characteristic
35	C₃×C₈×Q₈	—	3	2	no	—
36	C₃×C₈×D₄	—	3	2	no	—
37	C₃×C₈×D₄	—	3	4	no	—
38	C₃×#431	—	2	1	no	—
39	C₃×#431	—	3	2	no	—
40	C₃×#431	D₃	1	1	yes	characteristic, complemented
41	C₃×#431	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₃×C₄×C₈	—	3	1	no	—
43	C₂×C₃×C₄×C₈	—	3	2	no	—
44	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
45	#4834	C₂×C₃	1	2	yes	complemented
46	#4830	C₂×C₃	1	2	yes	complemented
47	#67⋊C₈	C₂×C₃	1	4	yes	complemented
48	#4685	C₂×C₃	1	2	yes	complemented
49	C₄×D₃×C₈	C₂×C₃	1	2	yes	complemented
50	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
53	C₂×C₃×#67	C₂×C₄	1	2	yes	—
54	C₃×#235	C₈	1	8	yes	complemented
55	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
57	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
59	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃²×C₈	C₂³	1	4	yes	—
61	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
62	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
63	C₃²×C₄²	C₂³	1	1	yes	characteristic
64	C₃²×C₄²	C₂³	1	1	yes	characteristic
65	C₃×#217	C₂×C₄	1	2	yes	—
66	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
67	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
68	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
71	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
72	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
73	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
74	C₃×C₄×Dic₃	C₂³	1	2	yes	—
75	C₂×C₃×C₃⋊C₈	—	2	4	no	—
76	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
77	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
78	C₃×D₃×C₈	—	2	8	no	—
79	C₈×#41	—	3	1	no	Sylow
80	C₂×C₃×#41	—	3	1	no	—
81	C₂×#235	C₃×C₄	1	1	yes	characteristic
82	C₂²×C₃×C₈	—	3	2	no	—
83	C₂²×C₃×C₈	—	3	4	no	—
84	C₃×C₄×Q₈	—	3	1	no	—
85	C₃×C₄×Q₈	—	3	1	no	—
86	C₃×C₄×D₄	—	3	2	no	—
87	C₃×C₄×D₄	—	3	2	no	—
88	C₃×C₄×D₄	—	3	1	no	—
89	C₃×C₄×D₄	—	3	1	no	—
90	C₃×#117	—	3	1	no	—
91	C₃×#117	—	3	2	no	—
92	C₂×C₃×C₄²	—	2	1	no	—
93	C₂×C₃×C₄²	—	3	2	no	—
94	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
95	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
96	C₄×#67	C₃×C₄	1	2	yes	—
97	C₄×#67	C₂²×C₃	1	2	yes	—
98	#926	C₃×C₄	1	1	yes	characteristic
99	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
100	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
101	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
102	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
103	#872	C₃×C₄	1	2	yes	—
104	C₄²×D₃	C₂²×C₃	1	2	yes	—
105	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
106	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
107	C₃×C₄⋊C₈	—	2	2	no	—
108	C₃×C₄⋊C₈	—	3	4	no	—
109	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
110	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
111	C₃×C₂²⋊C₈	—	2	2	no	—
112	C₃×C₂²⋊C₈	—	3	4	no	—
113	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
114	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
115	C₃×C₄×C₈	—	2	2	no	—
116	C₃×C₄×C₈	—	3	4	no	—
117	C₃×C₄×C₈	—	3	2	no	—
118	C₃×C₄×C₈	—	3	1	no	—
119	C₃×C₄×C₈	—	3	1	no	—
120	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
121	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
122	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
123	Dic₃⋊C₈	C₂²×C₃	1	4	yes	—
124	C₈×Dic₃	C₂²×C₃	1	4	yes	—
125	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
126	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
128	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
130	C₂×C₃²×C₄	—	2	2	no	—
131	C₂×C₃²×C₄	—	2	2	no	—
132	C₂×C₃²×C₄	C₂×C₈	1	4	yes	complemented
133	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
139	C₃×#67	C₂×C₈	1	8	yes	complemented
140	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
141	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
143	C₃×D₁₂	C₂×C₈	1	4	yes	complemented
144	C₃×C₄×D₃	—	2	4	no	—
145	C₃×C₄×D₃	—	2	4	no	—
146	C₃×C₄×D₃	C₂×C₈	1	8	yes	complemented
147	C₃×Dic₆	C₂×C₈	1	4	yes	complemented
148	C₃²×C₈	—	2	4	no	—
149	C₃×C₃⋊C₈	—	2	2	no	—
150	C₃×C₃⋊C₈	#41	1	4	yes	complemented
151	C₄×#41	—	3	1	no	—
152	C₈×Q₈	—	3	2	no	—
153	C₈×D₄	—	3	2	no	—
154	C₈×D₄	—	3	4	no	—
155	#431	—	3	2	no	—
156	#431	C₃×D₃	1	1	yes	characteristic, complemented
157	C₂×C₄×C₈	—	3	1	no	—
158	C₂×C₄×C₈	—	3	2	no	—
159	C₃×#41	—	3	8	no	—
160	C₂×C₃×Q₈	—	3	1	no	—
161	C₂×C₃×D₄	—	3	2	no	—
162	C₂×C₃×D₄	—	3	1	no	—
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	—	3	2	no	—
167	C₂²×C₃×C₄	—	3	2	no	—
168	C₂²×C₃×C₄	—	3	2	no	—
169	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
175	C₂×#67	C₂×C₃×C₄	1	2	yes	—
176	#235	C₃×C₈	1	8	yes	complemented
177	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
179	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
180	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
181	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂×C₃×C₈	—	2	4	no	—
183	C₂×C₃×C₈	—	3	2	no	—
184	C₂×C₃×C₈	—	3	2	no	—
185	C₂×C₃×C₈	—	6	8	no	—
186	C₂×C₃×C₈	—	6	4	no	—
187	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
188	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
189	C₃×C₄⋊C₄	—	3	2	no	—
190	C₃×C₄⋊C₄	—	3	2	no	—
191	C₃×C₄⋊C₄	—	3	1	no	—
192	C₃×C₄⋊C₄	—	3	1	no	—
193	C₃×C₂²⋊C₄	—	3	2	no	—
194	C₃×C₂²⋊C₄	—	3	2	no	—
195	C₃×C₂²⋊C₄	—	3	2	no	—
196	C₃×C₄²	—	2	1	no	—
197	C₃×C₄²	—	2	1	no	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	—	3	2	no	—
201	C₃×C₄²	—	3	2	no	—
202	C₃×C₄²	—	3	2	no	—
203	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
204	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
205	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
206	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
207	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
208	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
209	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
210	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
211	#217	C₂×C₃×C₄	1	2	yes	—
212	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
213	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
214	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
215	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
216	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
217	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
218	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
219	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
220	C₄×Dic₃	C₂³×C₃	1	2	yes	—
221	C₂×C₃⋊C₈	—	2	4	no	—
222	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
223	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
224	D₃×C₈	—	2	8	no	—
225	C₂²×C₃²	—	2	1	no	—
226	C₂²×C₃²	—	2	1	no	—
227	C₂²×C₃²	C₂²×C₈	1	2	yes	—
228	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₃×D₃	—	2	2	no	—
230	C₂×C₃×D₃	—	2	2	no	—
231	C₂×C₃×D₃	C₂²×C₈	1	4	yes	—
232	C₃²×C₄	—	2	1	no	—
233	C₃²×C₄	—	2	1	no	—
234	C₃²×C₄	C₂²×C₈	1	2	yes	—
235	C₃²×C₄	C₂²×C₈	1	2	yes	—
236	C₃²×C₄	#131	1	2	yes	—
237	C₃²×C₄	C₂×#41	1	2	yes	—
238	C₃×Dic₃	—	2	2	no	—
239	C₃×Dic₃	—	2	2	no	—
240	C₃×Dic₃	C₂²×C₈	1	4	yes	—
241	C₂×#41	—	3	1	no	—
242	C₂²×C₈	—	3	2	no	—
243	C₂²×C₈	—	3	4	no	—
244	C₄×Q₈	—	3	1	no	—
245	C₄×Q₈	—	3	1	no	—
246	C₄×D₄	—	3	2	no	—
247	C₄×D₄	—	3	2	no	—
248	C₄×D₄	—	3	1	no	—
249	C₄×D₄	—	3	1	no	—
250	#117	—	3	1	no	—
251	#117	—	3	2	no	—
252	C₂×C₄²	—	3	2	no	—
253	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
254	C₄⋊C₈	—	3	4	no	—
255	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
256	C₂²⋊C₈	—	3	4	no	—
257	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
258	C₄×C₈	—	3	4	no	—
259	C₄×C₈	—	3	1	no	—
260	C₄×C₈	—	3	1	no	—
261	C₄×C₈	—	3	2	no	—
262	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
263	C₂³×C₃	—	2	1	no	—
264	C₂³×C₃	—	3	2	no	—
265	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
266	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
268	C₃×Q₈	—	3	4	no	—
269	C₃×D₄	—	3	8	no	—
270	C₃×D₄	—	3	4	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	3	2	no	—
283	C₂×C₃×C₄	—	3	8	no	—
284	C₂×C₃×C₄	—	3	2	no	—
285	C₂×C₃×C₄	—	3	2	no	—
286	C₂×C₃×C₄	—	4	2	no	—
287	C₂×C₃×C₄	—	4	2	no	—
288	C₂×C₃×C₄	—	6	4	no	—
289	C₂×C₃×C₄	—	6	4	no	—
290	C₂×C₃×C₄	D₃×C₈	1	4	yes	complemented
291	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	complemented
292	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₄×D₃	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	C₂²×C₃×C₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
304	#67	C₂×C₃×C₈	1	8	yes	complemented
305	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
306	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
307	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
308	D₁₂	C₂×C₃×C₈	1	4	yes	complemented
309	C₄×D₃	—	2	4	no	—
310	C₄×D₃	—	2	4	no	—
311	C₄×D₃	C₂×C₃×C₈	1	8	yes	complemented
312	Dic₆	C₂×C₃×C₈	1	4	yes	complemented
313	C₃×C₈	—	2	4	no	—
314	C₃×C₈	—	2	4	no	—
315	C₃×C₈	—	3	4	no	—
316	C₃×C₈	—	4	4	no	—
317	C₃×C₈	—	6	2	no	—
318	C₃⋊C₈	—	2	2	no	—
319	C₃⋊C₈	C₃×#41	1	4	yes	complemented
320	C₂×C₃²	—	2	2	no	—
321	C₂×C₃²	C₄×#41	1	1	yes	characteristic
322	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
323	C₂×C₃²	C₂×#131	1	1	yes	characteristic
324	C₃×D₃	—	2	4	no	—
325	#41	—	3	8	no	—
326	C₂×Q₈	—	3	1	no	—
327	C₂×D₄	—	3	2	no	—
328	C₂×D₄	—	3	1	no	—
329	C₂²×C₄	—	3	2	no	—
330	C₂²×C₄	—	3	2	no	—
331	C₂²×C₄	—	3	2	no	—
332	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
333	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
334	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×C₈	—	3	2	no	—
336	C₂×C₈	—	3	2	no	—
337	C₂×C₈	—	6	8	no	—
338	C₂×C₈	—	6	4	no	—
339	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
340	C₄⋊C₄	—	3	2	no	—
341	C₄⋊C₄	—	3	2	no	—
342	C₄⋊C₄	—	3	1	no	—
343	C₄⋊C₄	—	3	1	no	—
344	C₂²⋊C₄	—	3	2	no	—
345	C₂²⋊C₄	—	3	2	no	—
346	C₂²⋊C₄	—	3	2	no	—
347	C₄²	—	3	2	no	—
348	C₄²	—	3	2	no	—
349	C₄²	—	3	2	no	—
350	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
351	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
352	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
353	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
354	C₂²×C₃	—	2	1	no	—
355	C₂²×C₃	—	2	1	no	—
356	C₂²×C₃	—	2	1	no	—
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	2	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	3	4	no	—
361	C₂²×C₃	—	4	1	no	—
362	C₂²×C₃	—	4	1	no	—
363	C₂²×C₃	—	6	2	no	—
364	C₂²×C₃	—	6	2	no	—
365	C₂²×C₃	C₂×D₃×C₈	1	2	yes	—
366	C₂²×C₃	C₂²×C₃×C₈	1	2	yes	—
367	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
368	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
369	C₂×D₃	—	2	2	no	—
370	C₂×D₃	—	2	2	no	—
371	C₂×D₃	C₂²×C₃×C₈	1	4	yes	—
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	2	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	3	4	no	—
381	C₃×C₄	—	4	1	no	—
382	C₃×C₄	—	4	1	no	—
383	C₃×C₄	—	6	2	no	—
384	C₃×C₄	—	6	2	no	—
385	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
386	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
387	C₃×C₄	#907	1	2	yes	—
388	C₃×C₄	C₂²×C₃×C₈	1	2	yes	—
389	C₃×C₄	C₂²×C₃×C₈	1	2	yes	—
390	C₃×C₄	C₃×#131	1	2	yes	—
391	C₃×C₄	D₃×#41	1	2	yes	—
392	C₃×C₄	C₂×C₃×#41	1	2	yes	—
393	Dic₃	—	2	2	no	—
394	Dic₃	—	2	2	no	—
395	Dic₃	C₂²×C₃×C₈	1	4	yes	—
396	C₃²	C₈×#41	1	1	yes	characteristic, complemented, Sylow
397	C₂³	—	3	2	no	—
398	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
399	Q₈	—	3	4	no	—
400	D₄	—	3	8	no	—
401	D₄	—	3	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	3	2	no	—
405	C₂×C₄	—	3	8	no	—
406	C₂×C₄	—	3	2	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	6	4	no	—
409	C₂×C₄	—	6	4	no	—
410	C₂×C₄	C₃×D₃×C₈	1	4	yes	complemented
411	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
413	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
414	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
415	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
416	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	3	4	no	—
419	C₈	—	6	2	no	—
420	C₂×C₃	—	2	2	no	—
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	2	1	no	—
425	C₂×C₃	—	4	2	no	—
426	C₂×C₃	—	6	4	no	—
427	C₂×C₃	#5522	1	1	yes	characteristic
428	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
429	C₂×C₃	C₂×#907	1	1	yes	characteristic
430	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
431	C₂×C₃	C₂³×C₃×C₈	1	1	yes	characteristic
432	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
433	D₃	—	2	4	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	3	4	no	—
437	C₂²	—	6	2	no	—
438	C₂²	—	6	2	no	—
439	C₂²	C₂×C₃×D₃×C₈	1	2	yes	—
440	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	3	4	no	—
444	C₄	—	6	2	no	—
445	C₄	—	6	2	no	—
446	C₄	C₂×C₃×D₃×C₈	1	2	yes	—
447	C₄	C₂×C₃×D₃×C₈	1	2	yes	—
448	C₄	C₃×#907	1	2	yes	—
449	C₄	C₃×D₃×#41	1	2	yes	—
450	C₃	—	2	1	no	—
451	C₃	#79276	1	1	yes	characteristic, direct product factor
452	C₃	C₃×C₈×#41	1	1	yes	characteristic, complemented
453	C₂	—	2	2	no	—
454	C₂	—	6	4	no	—
455	C₂	C₃×#5522	1	1	yes	characteristic
456	C₂	C₂²×C₃×D₃×C₈	1	1	yes	characteristic
457	C₂	C₂×C₃×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂²×D₃
commutator	C₂×C₃	C₂³×C₃×C₈
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#431	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#431	D₃
hypocenter	C₃	C₃×C₈×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃²×#431	C₂	semidirect
3. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
4. C₃×#4834	C₂	semidirect
5. C₃×#4830	C₂	semidirect
6. C₃×#67⋊C₈	C₂	semidirect
7. C₃×#4685	C₂	semidirect
8. C₃×C₄×D₃×C₈	C₂	semidirect
10. #79276	C₃	direct (N × H)
40. C₃×#431	D₃	semidirect
41. C₃×#431	C₂×C₃	semidirect
44. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
45. #4834	C₂×C₃	semidirect
46. #4830	C₂×C₃	semidirect
47. #67⋊C₈	C₂×C₃	semidirect
48. #4685	C₂×C₃	semidirect
49. C₄×D₃×C₈	C₂×C₃	semidirect
54. C₃×#235	C₈	semidirect
132. C₂×C₃²×C₄	C₂×C₈	semidirect
139. C₃×#67	C₂×C₈	semidirect
143. C₃×D₁₂	C₂×C₈	semidirect
146. C₃×C₄×D₃	C₂×C₈	semidirect
147. C₃×Dic₆	C₂×C₈	semidirect
150. C₃×C₃⋊C₈	#41	semidirect
156. #431	C₃×D₃	semidirect
176. #235	C₃×C₈	semidirect
290. C₂×C₃×C₄	D₃×C₈	semidirect
291. C₂×C₃×C₄	C₂×C₃×C₈	semidirect
304. #67	C₂×C₃×C₈	semidirect
308. D₁₂	C₂×C₃×C₈	semidirect
311. C₄×D₃	C₂×C₃×C₈	semidirect
312. Dic₆	C₂×C₃×C₈	semidirect
319. C₃⋊C₈	C₃×#41	semidirect
396. C₃²	C₈×#41	semidirect
410. C₂×C₄	C₃×D₃×C₈	semidirect
451. C₃	#79276	direct (N × H)
452. C₃	C₃×C₈×#41	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#235	2
C₃²×#431	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×#4834	2
C₃×#4830	2
C₃×#67⋊C₈	2
C₃×#4685	2
C₃×C₄×D₃×C₈	2
C₃×C₈×#41	3
#79276	3

Subgroups — C3×#79276 #11861537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79276 #11861537