Subgroups — C₃×#83786 #11859464

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5832	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5234	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5129	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5128	C₂	1	4	yes	maximal, complemented
7	C₃×#5118	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₈×#67	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2931	—	3	1	no	maximal
11	#83786	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
13	C₂×C₃×#235	C₂²	1	1	yes	characteristic
14	C₃²×#131	—	2	4	no	—
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
17	C₂²×C₃²×C₈	C₂²	1	2	yes	—
18	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
19	C₃×#947	C₄	1	1	yes	characteristic
20	C₃×#944	C₄	1	1	yes	characteristic
21	C₃×#940	C₄	1	1	yes	characteristic
22	C₃×#939	C₄	1	4	yes	—
23	C₃×#936	C₄	1	1	yes	characteristic
24	C₃×C₄×#67	C₂²	1	4	yes	—
25	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₃×#208	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×#901	—	2	4	no	—
29	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
30	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
31	C₃×#830	C₂²	1	4	yes	—
32	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
33	C₃×Dic₃⋊C₈	C₂²	1	4	yes	—
34	C₃×C₈×Dic₃	C₂²	1	2	yes	—
35	C₃×C₈×Dic₃	C₂²	1	2	yes	—
36	C₂×C₃×#131	—	2	1	no	—
37	C₂×C₃×#131	—	3	1	no	—
38	C₂×C₃×#131	D₃	1	1	yes	characteristic, complemented
39	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic, complemented
40	C₃×#532	—	3	1	no	—
41	#5832	C₂×C₃	1	1	yes	characteristic
42	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×#436	—	3	4	no	—
44	C₃×C₈×D₄	—	3	4	no	—
45	C₃×#423	—	3	1	no	—
46	C₃×#408	—	3	1	no	—
47	C₃×#408	—	3	1	no	—
48	C₂×C₃×C₄×C₈	—	3	1	no	—
49	#5234	C₂×C₃	1	1	yes	characteristic, complemented
50	#5129	C₂×C₃	1	1	yes	characteristic, complemented
51	#5128	C₂×C₃	1	4	yes	complemented
52	#5118	C₂×C₃	1	1	yes	characteristic, complemented
53	C₈×#67	C₂×C₃	1	4	yes	complemented
54	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃²×#41	—	2	2	no	—
56	C₃²×#41	—	2	2	no	—
57	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
60	C₂²×C₃²×C₄	C₂³	1	2	yes	—
61	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×#67	C₂×C₄	1	4	yes	—
63	C₂×C₃×#67	C₂×C₄	1	2	yes	—
64	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
65	C₃×#235	—	2	2	no	—
66	C₃×#235	—	2	2	no	—
67	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
69	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
70	C₃²×M₁₆	—	2	2	no	—
71	C₃²×M₁₆	—	2	4	no	—
72	C₂×C₃²×C₈	—	2	4	no	—
73	C₂×C₃²×C₈	D₄	1	4	yes	complemented
74	C₂×C₃²×C₈	C₂³	1	2	yes	—
75	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
76	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
77	C₃×#217	C₂×C₄	1	4	yes	—
78	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
79	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
80	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₃	C₂³	1	2	yes	—
83	C₃×#208	—	2	2	no	—
84	C₂×C₃×C₃⋊C₈	—	2	2	no	—
85	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
86	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
87	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
88	C₃×D₃×C₈	—	2	4	no	—
89	#2931	—	3	1	no	Sylow
90	C₂×C₃×#41	—	2	1	no	—
91	C₂×C₃×#41	—	3	1	no	—
92	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
93	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
94	C₂×#235	C₂²×C₃	1	1	yes	characteristic
95	C₃×#131	—	2	8	no	—
96	C₃×#131	—	2	4	no	—
97	C₃×#131	—	2	4	no	—
98	C₃×#131	—	6	4	no	—
99	C₂×C₃×M₁₆	—	2	1	no	—
100	C₂×C₃×M₁₆	—	2	2	no	—
101	C₂×C₃×M₁₆	—	3	1	no	—
102	C₂×C₃×M₁₆	—	3	2	no	—
103	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
104	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
105	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
106	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₃×C₈	—	2	2	no	—
108	C₂²×C₃×C₈	—	2	1	no	—
109	C₂²×C₃×C₈	—	3	1	no	—
110	C₂²×C₃×C₈	—	3	2	no	—
111	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
112	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
113	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
114	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
115	C₃×C₄⋊Q₈	—	3	1	no	—
116	C₃×#127	—	3	1	no	—
117	C₃×#124	—	3	1	no	—
118	C₃×#124	—	3	1	no	—
119	C₃×#121	—	3	4	no	—
120	C₃×C₄×D₄	—	3	4	no	—
121	C₂×C₃×C₄²	—	3	1	no	—
122	#947	C₃×C₄	1	1	yes	characteristic
123	#944	C₃×C₄	1	1	yes	characteristic
124	#940	C₃×C₄	1	1	yes	characteristic
125	#939	C₃×C₄	1	4	yes	—
126	#936	C₃×C₄	1	1	yes	characteristic
127	C₄×#67	C₂²×C₃	1	4	yes	—
128	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
129	C₂×#208	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
131	#901	—	2	4	no	—
132	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
133	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
134	C₃×C₄⋊C₈	—	3	4	no	—
135	C₃×C₂²⋊C₈	—	3	4	no	—
136	C₃×C₂²⋊C₈	—	3	4	no	—
137	C₃×C₄×C₈	—	3	2	no	—
138	C₃×C₄×C₈	—	3	2	no	—
139	#830	C₂²×C₃	1	4	yes	—
140	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
141	Dic₃⋊C₈	C₂²×C₃	1	4	yes	—
142	C₈×Dic₃	C₂²×C₃	1	2	yes	—
143	C₈×Dic₃	C₂²×C₃	1	2	yes	—
144	C₂³×C₃²	C₂²×C₄	1	2	yes	—
145	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
147	C₃²×Q₈	—	2	2	no	—
148	C₃²×D₄	—	2	4	no	—
149	C₃²×D₄	—	2	2	no	—
150	C₂×C₃²×C₄	—	2	2	no	—
151	C₂×C₃²×C₄	—	2	2	no	—
152	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
153	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
155	C₂×C₃²×C₄	#41	1	2	yes	—
156	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
157	C₃×#67	—	2	4	no	—
158	C₃×#67	—	2	8	no	—
159	C₂×C₃×Dic₃	—	2	4	no	—
160	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
161	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
162	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
163	C₃×D₁₂	—	2	2	no	—
164	C₃×C₄×D₃	—	2	2	no	—
165	C₃×C₄×D₃	—	2	2	no	—
166	C₃×Dic₆	—	2	2	no	—
167	C₃²×C₈	—	2	2	no	—
168	C₃²×C₈	C₂×D₄	1	2	yes	—
169	C₃²×C₈	C₂×D₄	1	2	yes	—
170	C₃×C₃⋊C₈	—	2	2	no	—
171	C₃×C₃⋊C₈	—	2	2	no	—
172	C₂×#131	—	3	1	no	—
173	C₂×#131	C₃×D₃	1	1	yes	characteristic, complemented
174	#532	—	3	1	no	—
175	#436	—	3	4	no	—
176	C₈×D₄	—	3	4	no	—
177	#423	—	3	1	no	—
178	#408	—	3	1	no	—
179	#408	—	3	1	no	—
180	C₂×C₄×C₈	—	3	1	no	—
181	C₃×#41	—	2	4	no	—
182	C₃×#41	—	2	4	no	—
183	C₃×#41	—	2	2	no	—
184	C₃×#41	—	2	2	no	—
185	C₃×#41	—	2	2	no	—
186	C₃×#41	—	2	2	no	—
187	C₃×#41	—	6	2	no	—
188	C₃×#41	—	6	2	no	—
189	C₂×C₃×Q₈	—	2	1	no	—
190	C₂×C₃×Q₈	—	3	1	no	—
191	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
192	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
193	C₂×C₃×D₄	—	2	2	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×C₃×D₄	—	3	4	no	—
196	C₂×C₃×D₄	—	3	2	no	—
197	C₂×C₃×D₄	—	3	1	no	—
198	C₂×C₃×D₄	C₄×D₃	1	2	yes	—
199	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
200	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
201	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	1	no	—
204	C₂²×C₃×C₄	—	3	2	no	—
205	C₂²×C₃×C₄	—	3	2	no	—
206	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
207	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
210	C₂×#67	C₂×C₃×C₄	1	4	yes	—
211	C₂×#67	C₂×C₃×C₄	1	2	yes	—
212	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
213	#235	—	2	2	no	—
214	#235	—	2	2	no	—
215	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
216	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
217	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
218	C₃×M₁₆	—	2	4	no	—
219	C₃×M₁₆	—	2	8	no	—
220	C₃×M₁₆	—	2	2	no	—
221	C₃×M₁₆	—	2	2	no	—
222	C₃×M₁₆	—	2	4	no	—
223	C₃×M₁₆	—	2	4	no	—
224	C₃×M₁₆	—	6	2	no	—
225	C₃×M₁₆	—	6	4	no	—
226	C₂×C₃×C₈	—	2	8	no	—
227	C₂×C₃×C₈	—	2	4	no	—
228	C₂×C₃×C₈	—	2	4	no	—
229	C₂×C₃×C₈	—	2	4	no	—
230	C₂×C₃×C₈	—	2	1	no	—
231	C₂×C₃×C₈	—	2	2	no	—
232	C₂×C₃×C₈	—	2	1	no	—
233	C₂×C₃×C₈	—	3	2	no	—
234	C₂×C₃×C₈	—	3	2	no	—
235	C₂×C₃×C₈	—	6	2	no	—
236	C₂×C₃×C₈	—	6	4	no	—
237	C₂×C₃×C₈	#67	1	4	yes	complemented
238	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
239	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
240	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
241	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
242	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
243	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
245	C₃×C₄⋊C₄	—	3	4	no	—
246	C₃×C₂²⋊C₄	—	3	4	no	—
247	C₃×C₂²⋊C₄	—	3	4	no	—
248	C₃×C₄²	—	3	1	no	—
249	C₃×C₄²	—	3	1	no	—
250	C₃×C₄²	—	3	2	no	—
251	#217	C₂×C₃×C₄	1	4	yes	—
252	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
253	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
254	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
255	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
256	C₄×Dic₃	C₂³×C₃	1	2	yes	—
257	#208	—	2	2	no	—
258	C₂×C₃⋊C₈	—	2	2	no	—
259	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
260	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
261	ΓL(1,𝔽₂₅)	—	2	4	no	—
262	D₃×C₈	—	2	4	no	—
263	C₂²×C₃²	—	2	2	no	—
264	C₂²×C₃²	—	2	2	no	—
265	C₂²×C₃²	—	2	4	no	—
266	C₂²×C₃²	C₄×D₄	1	2	yes	—
267	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₃×D₃	—	2	2	no	—
269	C₂×C₃×D₃	—	2	4	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	C₄×D₄	1	2	yes	—
272	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
273	C₃²×C₄	C₂×#41	1	1	yes	characteristic
274	C₃×Dic₃	—	2	2	no	—
275	C₃×Dic₃	—	2	2	no	—
276	C₃×Dic₃	#131	1	4	yes	complemented
277	C₂×#41	—	3	1	no	—
278	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
279	#131	—	2	4	no	—
280	#131	—	6	4	no	—
281	C₂×M₁₆	—	3	1	no	—
282	C₂×M₁₆	—	3	2	no	—
283	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
284	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
285	C₂²×C₈	—	3	1	no	—
286	C₂²×C₈	—	3	2	no	—
287	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
288	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
289	C₄⋊Q₈	—	3	1	no	—
290	#127	—	3	1	no	—
291	#124	—	3	1	no	—
292	#124	—	3	1	no	—
293	#121	—	3	4	no	—
294	C₄×D₄	—	3	4	no	—
295	C₂×C₄²	—	3	1	no	—
296	C₄⋊C₈	—	3	4	no	—
297	C₂²⋊C₈	—	3	4	no	—
298	C₂²⋊C₈	—	3	4	no	—
299	C₄×C₈	—	3	2	no	—
300	C₄×C₈	—	3	2	no	—
301	C₂³×C₃	—	2	2	no	—
302	C₂³×C₃	—	2	1	no	—
303	C₂³×C₃	—	3	2	no	—
304	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
305	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
306	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
307	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
308	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
309	C₃×Q₈	—	2	4	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	6	2	no	—
313	C₃×D₄	—	2	8	no	—
314	C₃×D₄	—	2	4	no	—
315	C₃×D₄	—	2	4	no	—
316	C₃×D₄	—	2	4	no	—
317	C₃×D₄	—	2	2	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	—	6	8	no	—
320	C₃×D₄	—	6	4	no	—
321	C₃×D₄	—	6	2	no	—
322	C₂×C₃×C₄	—	2	4	no	—
323	C₂×C₃×C₄	—	2	4	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	3	2	no	—
334	C₂×C₃×C₄	—	3	2	no	—
335	C₂×C₃×C₄	—	3	2	no	—
336	C₂×C₃×C₄	—	6	4	no	—
337	C₂×C₃×C₄	—	6	2	no	—
338	C₂×C₃×C₄	—	6	2	no	—
339	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
340	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
341	C₂×C₃×C₄	#235	1	2	yes	—
342	C₂×C₃×C₄	C₂×#67	1	2	yes	—
343	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
344	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
346	C₂×C₃×C₄	C₃×#41	1	2	yes	—
347	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
349	#67	—	2	4	no	—
350	#67	—	2	8	no	—
351	C₂×Dic₃	—	2	4	no	—
352	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
353	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
354	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
355	D₁₂	—	2	2	no	—
356	C₄×D₃	—	2	2	no	—
357	C₄×D₃	—	2	2	no	—
358	Dic₆	—	2	2	no	—
359	C₃×C₈	—	2	4	no	—
360	C₃×C₈	—	2	2	no	—
361	C₃×C₈	—	2	2	no	—
362	C₃×C₈	—	2	2	no	—
363	C₃×C₈	—	2	2	no	—
364	C₃×C₈	—	6	2	no	—
365	C₃×C₈	—	6	2	no	—
366	C₃×C₈	C₂×#67	1	2	yes	—
367	C₃×C₈	C₂×#67	1	2	yes	—
368	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
369	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
370	C₃⋊C₈	—	2	2	no	—
371	C₃⋊C₈	—	2	2	no	—
372	C₂×C₃²	—	2	2	no	—
373	C₂×C₃²	—	4	2	no	—
374	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
375	C₂×C₃²	C₂×#131	1	2	yes	—
376	C₃×D₃	—	4	2	no	—
377	#41	—	2	2	no	—
378	#41	—	2	2	no	—
379	#41	—	6	2	no	—
380	#41	—	6	2	no	—
381	C₂×Q₈	—	3	1	no	—
382	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
383	C₂×D₄	—	3	4	no	—
384	C₂×D₄	—	3	2	no	—
385	C₂×D₄	—	3	1	no	—
386	C₂×D₄	C₃×C₄×D₃	1	2	yes	—
387	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
388	C₂²×C₄	—	3	2	no	—
389	C₂²×C₄	—	3	2	no	—
390	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
391	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	4	no	—
394	M₁₆	—	6	2	no	—
395	M₁₆	—	6	4	no	—
396	C₂×C₈	—	2	4	no	—
397	C₂×C₈	—	3	2	no	—
398	C₂×C₈	—	3	2	no	—
399	C₂×C₈	—	6	2	no	—
400	C₂×C₈	—	6	4	no	—
401	C₂×C₈	C₃×#67	1	4	yes	complemented
402	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
403	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
404	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
405	C₄⋊C₄	—	3	4	no	—
406	C₂²⋊C₄	—	3	4	no	—
407	C₂²⋊C₄	—	3	4	no	—
408	C₄²	—	3	2	no	—
409	C₄²	—	3	1	no	—
410	C₄²	—	3	1	no	—
411	C₂²×C₃	—	2	2	no	—
412	C₂²×C₃	—	2	2	no	—
413	C₂²×C₃	—	2	4	no	—
414	C₂²×C₃	—	2	4	no	—
415	C₂²×C₃	—	2	4	no	—
416	C₂²×C₃	—	2	2	no	—
417	C₂²×C₃	—	2	2	no	—
418	C₂²×C₃	—	2	2	no	—
419	C₂²×C₃	—	2	1	no	—
420	C₂²×C₃	—	4	2	no	—
421	C₂²×C₃	—	4	4	no	—
422	C₂²×C₃	—	6	4	no	—
423	C₂²×C₃	—	6	2	no	—
424	C₂²×C₃	C₄×#67	1	2	yes	—
425	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
426	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
427	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
428	C₂×D₃	—	2	4	no	—
429	C₂×D₃	—	2	2	no	—
430	C₃×C₄	—	2	4	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	2	no	—
434	C₃×C₄	—	2	1	no	—
435	C₃×C₄	—	2	1	no	—
436	C₃×C₄	—	3	4	no	—
437	C₃×C₄	—	6	2	no	—
438	C₃×C₄	—	6	2	no	—
439	C₃×C₄	C₄×#67	1	2	yes	—
440	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
441	C₃×C₄	C₂×#235	1	1	yes	characteristic
442	C₃×C₄	C₂²×#67	1	1	yes	characteristic
443	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
444	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
445	Dic₃	—	2	2	no	—
446	Dic₃	—	2	2	no	—
447	Dic₃	C₃×#131	1	4	yes	complemented
448	C₃²	#2931	1	1	yes	characteristic, complemented, Sylow
449	C₂³	—	3	2	no	—
450	C₂³	C₂×C₃×C₄×D₃	1	2	yes	—
451	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	6	2	no	—
454	D₄	—	2	4	no	—
455	D₄	—	2	2	no	—
456	D₄	—	6	8	no	—
457	D₄	—	6	4	no	—
458	D₄	—	6	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	3	2	no	—
462	C₂×C₄	—	3	2	no	—
463	C₂×C₄	—	3	2	no	—
464	C₂×C₄	—	6	4	no	—
465	C₂×C₄	—	6	2	no	—
466	C₂×C₄	—	6	2	no	—
467	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
468	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
469	C₂×C₄	C₃×#235	1	2	yes	—
470	C₂×C₄	C₂×C₃×#67	1	2	yes	—
471	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
472	C₈	—	2	2	no	—
473	C₈	—	6	2	no	—
474	C₈	—	6	2	no	—
475	C₈	C₂×C₃×#67	1	2	yes	—
476	C₈	C₂×C₃×#67	1	2	yes	—
477	C₂×C₃	—	2	2	no	—
478	C₂×C₃	—	2	2	no	—
479	C₂×C₃	—	2	2	no	—
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	4	2	no	—
482	C₂×C₃	—	4	4	no	—
483	C₂×C₃	—	4	2	no	—
484	C₂×C₃	—	4	2	no	—
485	C₂×C₃	—	12	2	no	—
486	C₂×C₃	D₃×#131	1	2	yes	—
487	C₂×C₃	C₂×C₄×#67	1	1	yes	characteristic
488	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
489	C₂×C₃	C₂×C₃×#131	1	2	yes	—
490	D₃	—	4	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	6	4	no	—
495	C₂²	—	6	2	no	—
496	C₂²	C₃×C₄×#67	1	2	yes	—
497	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	3	4	no	—
500	C₄	—	6	2	no	—
501	C₄	—	6	2	no	—
502	C₄	C₃×C₄×#67	1	2	yes	—
503	C₄	C₂×C₃×#235	1	1	yes	characteristic
504	C₄	C₂²×C₃×#67	1	1	yes	characteristic
505	C₃	—	2	1	no	—
506	C₃	#83786	1	1	yes	characteristic, direct product factor
507	C₃	C₃×#2931	1	1	yes	characteristic, complemented
508	C₂	—	2	2	no	—
509	C₂	—	4	2	no	—
510	C₂	—	12	2	no	—
511	C₂	C₃×D₃×#131	1	2	yes	—
512	C₂	C₂×C₃×C₄×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#131	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5832	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₃
hypocenter	C₃	C₃×#2931
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#131	C₂	semidirect
3. C₂×C₃×#901	C₂	semidirect
4. C₃×#5234	C₂	semidirect
5. C₃×#5129	C₂	semidirect
6. C₃×#5128	C₂	semidirect
7. C₃×#5118	C₂	semidirect
8. C₃×C₈×#67	C₂	semidirect
9. C₂×C₃×C₈×Dic₃	C₂	semidirect
11. #83786	C₃	direct (N × H)
38. C₂×C₃×#131	D₃	semidirect
39. C₂×C₃×#131	C₂×C₃	semidirect
42. C₂×#901	C₂×C₃	semidirect
49. #5234	C₂×C₃	semidirect
50. #5129	C₂×C₃	semidirect
51. #5128	C₂×C₃	semidirect
52. #5118	C₂×C₃	semidirect
53. C₈×#67	C₂×C₃	semidirect
54. C₂×C₈×Dic₃	C₂×C₃	semidirect
73. C₂×C₃²×C₈	D₄	semidirect
173. C₂×#131	C₃×D₃	semidirect
237. C₂×C₃×C₈	#67	semidirect
238. C₂×C₃×C₈	C₃×D₄	semidirect
276. C₃×Dic₃	#131	semidirect
401. C₂×C₈	C₃×#67	semidirect
447. Dic₃	C₃×#131	semidirect
448. C₃²	#2931	semidirect
506. C₃	#83786	direct (N × H)
507. C₃	C₃×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#131	2
C₃×#5832	2
C₂×C₃×#901	2
C₃×#5234	2
C₃×#5129	2
C₃×#5128	2
C₃×#5118	2
C₃×C₈×#67	2
C₂×C₃×C₈×Dic₃	2
C₃×#2931	3
#83786	3

Subgroups — C3×#83786 #11859464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83786 #11859464