Subgroups — C₃×#83734 #11859316

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5791	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5111	C₂	1	4	yes	maximal, complemented
6	C₃×#5110	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₈×#67	C₂	1	4	yes	maximal, complemented
8	C₃×#5102	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5101	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#2929	—	3	1	no	maximal
11	#83734	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×#235	C₂²	1	1	yes	characteristic
14	C₂²×C₃²×C₈	—	2	4	no	—
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	2	yes	—
17	C₂²×C₃²×C₈	C₂²	1	2	yes	—
18	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
19	C₃×#953	C₄	1	2	yes	—
20	C₃×#930	C₄	1	2	yes	—
21	C₃×#929	C₄	1	2	yes	—
22	C₃×C₄×#67	C₂²	1	4	yes	—
23	C₃×#926	C₂²	1	1	yes	characteristic
24	C₃×#924	C₄	1	2	yes	—
25	C₂×C₃×#208	C₂²	1	1	yes	characteristic
26	C₂×C₃×#208	C₂²	1	1	yes	characteristic
27	C₃×#901	—	2	4	no	—
28	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
29	C₂×C₃×D₃×C₈	C₂²	1	2	yes	complemented
30	C₃×#830	C₂²	1	4	yes	—
31	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
32	C₃×#815	C₂²	1	2	yes	complemented
33	C₃×Dic₃⋊C₈	C₂²	1	4	yes	complemented
34	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
35	C₂×C₃×#131	—	3	1	no	—
36	C₂³×C₃×C₈	—	2	1	no	—
37	C₂³×C₃×C₈	D₃	1	1	yes	characteristic, complemented
38	C₂³×C₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×#525	—	3	1	no	—
40	#5791	C₂×C₃	1	1	yes	characteristic
41	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
42	C₃×#435	—	3	4	no	—
43	C₃×C₈×D₄	—	3	4	no	—
44	C₃×#424	—	3	1	no	—
45	C₃×#408	—	3	1	no	—
46	C₃×#407	—	3	1	no	—
47	C₃×#405	—	3	1	no	—
48	#5207	C₂×C₃	1	1	yes	characteristic, complemented
49	#5111	C₂×C₃	1	4	yes	complemented
50	#5110	C₂×C₃	1	1	yes	characteristic, complemented
51	C₈×#67	C₂×C₃	1	4	yes	complemented
52	#5102	C₂×C₃	1	1	yes	characteristic, complemented
53	#5101	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃²×C₄	—	2	2	no	—
56	C₂²×C₃²×C₄	—	2	2	no	—
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	C₂×C₃×#67	C₂×C₄	1	4	yes	—
62	C₂×C₃×#67	C₂×C₄	1	2	yes	—
63	C₃×#235	—	2	2	no	—
64	C₃×#235	—	2	2	no	—
65	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
67	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃²×C₈	—	2	2	no	—
69	C₂×C₃²×C₈	—	2	4	no	—
70	C₂×C₃²×C₈	—	2	4	no	—
71	C₂×C₃²×C₈	D₄	1	4	yes	complemented
72	C₂×C₃²×C₈	C₂³	1	2	yes	—
73	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
75	C₃×#217	C₂×C₄	1	4	yes	—
76	C₃×#217	C₂×C₄	1	2	yes	—
77	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
78	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
79	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
80	C₃×C₄×Dic₃	C₂³	1	2	yes	—
81	C₃×#208	—	2	2	no	—
82	C₃×#208	—	2	2	no	—
83	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
84	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
85	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
86	C₃×D₃×C₈	—	2	4	no	—
87	#2929	—	3	1	no	Sylow
88	C₂×C₃×#41	—	3	1	no	—
89	C₂³×C₃×C₄	—	2	1	no	—
90	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
91	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×#235	C₂²×C₃	1	1	yes	characteristic
93	C₃×#131	—	6	4	no	—
94	C₂×C₃×M₁₆	—	3	1	no	—
95	C₂×C₃×M₁₆	—	3	1	no	—
96	C₂×C₃×M₁₆	—	3	2	no	—
97	C₂²×C₃×C₈	—	2	8	no	—
98	C₂²×C₃×C₈	—	2	4	no	—
99	C₂²×C₃×C₈	—	2	4	no	—
100	C₂²×C₃×C₈	—	2	1	no	—
101	C₂²×C₃×C₈	—	2	2	no	—
102	C₂²×C₃×C₈	—	2	2	no	—
103	C₂²×C₃×C₈	—	2	1	no	—
104	C₂²×C₃×C₈	—	3	2	no	—
105	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
106	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
107	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
108	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
109	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
111	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
112	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×#123	—	3	2	no	—
114	C₃×C₂²⋊Q₈	—	3	2	no	—
115	C₃×#121	—	3	2	no	—
116	C₃×#120	—	3	2	no	—
117	C₃×C₄×D₄	—	3	4	no	—
118	C₃×#117	—	3	1	no	—
119	#953	C₃×C₄	1	2	yes	—
120	#930	C₃×C₄	1	2	yes	—
121	#929	C₃×C₄	1	2	yes	—
122	C₄×#67	C₂²×C₃	1	4	yes	—
123	#926	C₂²×C₃	1	1	yes	characteristic
124	#924	C₃×C₄	1	2	yes	—
125	C₂×#208	C₂²×C₃	1	1	yes	characteristic
126	C₂×#208	C₂²×C₃	1	1	yes	characteristic
127	#901	—	2	4	no	—
128	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	complemented
129	C₂×D₃×C₈	C₂²×C₃	1	2	yes	complemented
130	C₃×C₄⋊C₈	—	3	4	no	—
131	C₃×C₂²⋊C₈	—	3	4	no	—
132	C₃×C₂²⋊C₈	—	3	4	no	—
133	C₃×#97	—	3	2	no	—
134	C₃×C₄×C₈	—	3	2	no	—
135	#830	C₂²×C₃	1	4	yes	—
136	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	complemented
137	#815	C₂²×C₃	1	2	yes	complemented
138	Dic₃⋊C₈	C₂²×C₃	1	4	yes	complemented
139	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
140	C₂³×C₃²	—	2	2	no	—
141	C₂³×C₃²	—	2	4	no	—
142	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
143	C₂³×C₃²	C₂²×C₄	1	2	yes	—
144	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
145	C₂×C₃²×C₄	—	2	2	no	—
146	C₂×C₃²×C₄	—	2	4	no	—
147	C₂×C₃²×C₄	—	2	2	no	—
148	C₂×C₃²×C₄	—	2	2	no	—
149	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
150	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
152	C₂×C₃²×C₄	#41	1	2	yes	—
153	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
154	C₃×#67	—	2	4	no	—
155	C₃×#67	—	2	8	no	—
156	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
157	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
158	C₃×D₁₂	—	2	2	no	—
159	C₃×C₄×D₃	—	2	2	no	—
160	C₃×C₄×D₃	—	2	2	no	—
161	C₃×Dic₆	—	2	2	no	—
162	C₃²×C₈	—	2	2	no	—
163	C₃²×C₈	C₂×D₄	1	2	yes	—
164	C₃²×C₈	C₂×D₄	1	2	yes	—
165	C₃×C₃⋊C₈	—	2	2	no	—
166	C₃×C₃⋊C₈	—	2	2	no	—
167	C₂×#131	—	3	1	no	—
168	C₂³×C₈	C₃×D₃	1	1	yes	characteristic, complemented
169	#525	—	3	1	no	—
170	#435	—	3	4	no	—
171	C₈×D₄	—	3	4	no	—
172	#424	—	3	1	no	—
173	#408	—	3	1	no	—
174	#407	—	3	1	no	—
175	#405	—	3	1	no	—
176	C₂⁴×C₃	—	2	1	no	—
177	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
178	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
179	C₃×#41	—	6	2	no	—
180	C₃×#41	—	6	2	no	—
181	C₂×C₃×Q₈	—	3	1	no	—
182	C₂×C₃×D₄	—	3	4	no	—
183	C₂×C₃×D₄	—	3	2	no	—
184	C₂×C₃×D₄	—	3	1	no	—
185	C₂²×C₃×C₄	—	2	4	no	—
186	C₂²×C₃×C₄	—	2	4	no	—
187	C₂²×C₃×C₄	—	2	2	no	—
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	2	2	no	—
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	—	2	1	no	—
193	C₂²×C₃×C₄	—	2	2	no	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	3	2	no	—
196	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
197	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
199	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
201	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
203	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
204	C₂×#67	C₂×C₃×C₄	1	4	yes	—
205	C₂×#67	C₂×C₃×C₄	1	2	yes	—
206	#235	—	2	2	no	—
207	#235	—	2	2	no	—
208	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
210	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
211	C₃×M₁₆	—	6	2	no	—
212	C₃×M₁₆	—	6	2	no	—
213	C₃×M₁₆	—	6	4	no	—
214	C₂×C₃×C₈	—	2	4	no	—
215	C₂×C₃×C₈	—	2	8	no	—
216	C₂×C₃×C₈	—	2	8	no	—
217	C₂×C₃×C₈	—	2	2	no	—
218	C₂×C₃×C₈	—	2	2	no	—
219	C₂×C₃×C₈	—	2	4	no	—
220	C₂×C₃×C₈	—	2	4	no	—
221	C₂×C₃×C₈	—	2	4	no	—
222	C₂×C₃×C₈	—	2	4	no	—
223	C₂×C₃×C₈	—	2	4	no	—
224	C₂×C₃×C₈	—	2	2	no	—
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	—	2	1	no	—
227	C₂×C₃×C₈	—	3	2	no	—
228	C₂×C₃×C₈	—	3	2	no	—
229	C₂×C₃×C₈	—	6	4	no	—
230	C₂×C₃×C₈	#67	1	4	yes	complemented
231	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
232	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
233	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
235	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
236	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
238	C₃×C₄⋊C₄	—	3	4	no	—
239	C₃×C₄⋊C₄	—	3	2	no	—
240	C₃×C₂²⋊C₄	—	3	2	no	—
241	C₃×C₂²⋊C₄	—	3	4	no	—
242	C₃×C₂²⋊C₄	—	3	4	no	—
243	C₃×C₄²	—	3	2	no	—
244	#217	C₂×C₃×C₄	1	4	yes	—
245	#217	C₂×C₃×C₄	1	2	yes	—
246	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
247	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
248	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
249	C₄×Dic₃	C₂³×C₃	1	2	yes	—
250	#208	—	2	2	no	—
251	#208	—	2	2	no	—
252	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
253	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
254	ΓL(1,𝔽₂₅)	—	2	4	no	—
255	D₃×C₈	—	2	4	no	—
256	C₂²×C₃²	—	2	8	no	—
257	C₂²×C₃²	—	2	2	no	—
258	C₂²×C₃²	—	2	2	no	—
259	C₂²×C₃²	—	2	2	no	—
260	C₂²×C₃²	C₄×D₄	1	2	yes	—
261	C₂²×C₃²	#131	1	4	yes	complemented
262	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₃×D₃	—	2	2	no	—
264	C₂×C₃×D₃	—	2	4	no	—
265	C₃²×C₄	—	2	2	no	—
266	C₃²×C₄	C₄×D₄	1	2	yes	—
267	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
268	C₃²×C₄	C₂×#41	1	1	yes	characteristic
269	C₃×Dic₃	—	2	2	no	—
270	C₃×Dic₃	—	2	4	no	—
271	C₂×#41	—	3	1	no	—
272	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
273	#131	—	6	4	no	—
274	C₂×M₁₆	—	3	1	no	—
275	C₂×M₁₆	—	3	1	no	—
276	C₂×M₁₆	—	3	2	no	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	—	3	2	no	—
279	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
280	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
281	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
282	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
283	#123	—	3	2	no	—
284	C₂²⋊Q₈	—	3	2	no	—
285	#121	—	3	2	no	—
286	#120	—	3	2	no	—
287	C₄×D₄	—	3	4	no	—
288	#117	—	3	1	no	—
289	C₄⋊C₈	—	3	4	no	—
290	C₂²⋊C₈	—	3	4	no	—
291	C₂²⋊C₈	—	3	4	no	—
292	#97	—	3	2	no	—
293	C₄×C₈	—	3	2	no	—
294	C₂³×C₃	—	2	4	no	—
295	C₂³×C₃	—	2	8	no	—
296	C₂³×C₃	—	2	4	no	—
297	C₂³×C₃	—	2	2	no	—
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	—	2	4	no	—
300	C₂³×C₃	—	2	2	no	—
301	C₂³×C₃	—	2	1	no	—
302	C₂³×C₃	—	3	2	no	—
303	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
304	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
305	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
306	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
307	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
308	C₃×Q₈	—	6	2	no	—
309	C₃×D₄	—	6	8	no	—
310	C₃×D₄	—	6	4	no	—
311	C₃×D₄	—	6	2	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	4	no	—
314	C₂×C₃×C₄	—	2	8	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	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	2	no	—
329	C₂×C₃×C₄	—	3	4	no	—
330	C₂×C₃×C₄	—	3	2	no	—
331	C₂×C₃×C₄	—	6	2	no	—
332	C₂×C₃×C₄	—	6	2	no	—
333	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
334	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	#235	1	2	yes	—
336	C₂×C₃×C₄	C₂×#67	1	2	yes	—
337	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
338	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
340	C₂×C₃×C₄	C₃×#41	1	2	yes	—
341	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
343	#67	—	2	4	no	—
344	#67	—	2	8	no	—
345	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
346	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
347	D₁₂	—	2	2	no	—
348	C₄×D₃	—	2	2	no	—
349	C₄×D₃	—	2	2	no	—
350	Dic₆	—	2	2	no	—
351	C₃×C₈	—	2	4	no	—
352	C₃×C₈	—	2	2	no	—
353	C₃×C₈	—	2	2	no	—
354	C₃×C₈	—	2	2	no	—
355	C₃×C₈	—	2	2	no	—
356	C₃×C₈	—	6	2	no	—
357	C₃×C₈	—	6	2	no	—
358	C₃×C₈	C₂×#67	1	2	yes	—
359	C₃×C₈	C₂×#67	1	2	yes	—
360	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
361	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
362	C₃⋊C₈	—	2	2	no	—
363	C₃⋊C₈	—	2	2	no	—
364	C₂×C₃²	—	2	2	no	—
365	C₂×C₃²	—	2	4	no	—
366	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
367	C₂×C₃²	C₂×#131	1	2	yes	—
368	C₃×D₃	—	4	2	no	—
369	C₂⁴	C₃×C₄×D₃	1	1	yes	characteristic
370	#41	—	6	2	no	—
371	#41	—	6	2	no	—
372	C₂×Q₈	—	3	1	no	—
373	C₂×D₄	—	3	4	no	—
374	C₂×D₄	—	3	2	no	—
375	C₂×D₄	—	3	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	3	2	no	—
379	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
380	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
382	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
383	M₁₆	—	6	2	no	—
384	M₁₆	—	6	2	no	—
385	M₁₆	—	6	4	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	3	2	no	—
390	C₂×C₈	—	3	2	no	—
391	C₂×C₈	—	6	4	no	—
392	C₂×C₈	C₃×#67	1	4	yes	complemented
393	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
394	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
395	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
396	C₄⋊C₄	—	3	2	no	—
397	C₄⋊C₄	—	3	4	no	—
398	C₂²⋊C₄	—	3	2	no	—
399	C₂²⋊C₄	—	3	4	no	—
400	C₂²⋊C₄	—	3	4	no	—
401	C₄²	—	3	2	no	—
402	C₂²×C₃	—	2	4	no	—
403	C₂²×C₃	—	2	16	no	—
404	C₂²×C₃	—	2	8	no	—
405	C₂²×C₃	—	2	8	no	—
406	C₂²×C₃	—	2	4	no	—
407	C₂²×C₃	—	2	4	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	2	no	—
413	C₂²×C₃	—	2	2	no	—
414	C₂²×C₃	—	2	4	no	—
415	C₂²×C₃	—	2	2	no	—
416	C₂²×C₃	—	2	1	no	—
417	C₂²×C₃	—	6	4	no	—
418	C₂²×C₃	—	6	2	no	—
419	C₂²×C₃	#901	1	4	yes	complemented
420	C₂²×C₃	C₄×#67	1	2	yes	—
421	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
422	C₂²×C₃	C₃×#131	1	4	yes	complemented
423	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
424	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
425	C₂×D₃	—	2	4	no	—
426	C₂×D₃	—	2	2	no	—
427	C₃×C₄	—	2	4	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	6	4	no	—
434	C₃×C₄	—	6	2	no	—
435	C₃×C₄	C₄×#67	1	2	yes	—
436	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
437	C₃×C₄	C₂×#235	1	1	yes	characteristic
438	C₃×C₄	C₂²×#67	1	1	yes	characteristic
439	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
440	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
441	Dic₃	—	2	4	no	—
442	Dic₃	—	2	2	no	—
443	C₃²	#2929	1	1	yes	characteristic, complemented, Sylow
444	C₂³	—	2	4	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	3	2	no	—
447	C₂³	C₂×C₃×C₄×D₃	1	2	yes	—
448	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
449	Q₈	—	6	2	no	—
450	D₄	—	6	8	no	—
451	D₄	—	6	4	no	—
452	D₄	—	6	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	3	4	no	—
458	C₂×C₄	—	3	2	no	—
459	C₂×C₄	—	6	2	no	—
460	C₂×C₄	—	6	2	no	—
461	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
462	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
463	C₂×C₄	C₃×#235	1	2	yes	—
464	C₂×C₄	C₂×C₃×#67	1	2	yes	—
465	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
466	C₈	—	2	2	no	—
467	C₈	—	6	2	no	—
468	C₈	—	6	2	no	—
469	C₈	C₂×C₃×#67	1	2	yes	—
470	C₈	C₂×C₃×#67	1	2	yes	—
471	C₂×C₃	—	2	8	no	—
472	C₂×C₃	—	2	4	no	—
473	C₂×C₃	—	2	4	no	—
474	C₂×C₃	—	2	2	no	—
475	C₂×C₃	—	2	2	no	—
476	C₂×C₃	—	2	4	no	—
477	C₂×C₃	—	2	1	no	—
478	C₂×C₃	—	2	2	no	—
479	C₂×C₃	—	12	2	no	—
480	C₂×C₃	C₂×#901	1	2	yes	—
481	C₂×C₃	C₂×C₄×#67	1	1	yes	characteristic
482	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
483	C₂×C₃	C₂×C₃×#131	1	2	yes	—
484	D₃	—	4	2	no	—
485	C₂²	—	2	8	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	6	2	no	—
490	C₂²	—	6	4	no	—
491	C₂²	C₃×#901	1	4	yes	complemented
492	C₂²	C₃×C₄×#67	1	2	yes	—
493	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	6	2	no	—
496	C₄	—	6	4	no	—
497	C₄	C₃×C₄×#67	1	2	yes	—
498	C₄	C₂×C₃×#235	1	1	yes	characteristic
499	C₄	C₂²×C₃×#67	1	1	yes	characteristic
500	C₃	—	2	1	no	—
501	C₃	#83734	1	1	yes	characteristic, direct product factor
502	C₃	C₃×#2929	1	1	yes	characteristic, complemented
503	C₂	—	2	4	no	—
504	C₂	—	2	2	no	—
505	C₂	—	12	2	no	—
506	C₂	C₂×C₃×#901	1	2	yes	—
507	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	C₂³×C₃²×C₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5791	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂³×C₃×C₈	D₃
hypocenter	C₃	C₃×#2929
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂³×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃²×C₈	C₂	semidirect
3. C₂×C₃×#901	C₂	semidirect
4. C₃×#5207	C₂	semidirect
5. C₃×#5111	C₂	semidirect
6. C₃×#5110	C₂	semidirect
7. C₃×C₈×#67	C₂	semidirect
8. C₃×#5102	C₂	semidirect
9. C₃×#5101	C₂	semidirect
11. #83734	C₃	direct (N × H)
28. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
29. C₂×C₃×D₃×C₈	C₂²	semidirect
31. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
32. C₃×#815	C₂²	semidirect
33. C₃×Dic₃⋊C₈	C₂²	semidirect
34. C₃×C₈×Dic₃	C₂²	semidirect
37. C₂³×C₃×C₈	D₃	semidirect
38. C₂³×C₃×C₈	C₂×C₃	semidirect
41. C₂×#901	C₂×C₃	semidirect
48. #5207	C₂×C₃	semidirect
49. #5111	C₂×C₃	semidirect
50. #5110	C₂×C₃	semidirect
51. C₈×#67	C₂×C₃	semidirect
52. #5102	C₂×C₃	semidirect
53. #5101	C₂×C₃	semidirect
71. C₂×C₃²×C₈	D₄	semidirect
128. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
129. C₂×D₃×C₈	C₂²×C₃	semidirect
136. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
137. #815	C₂²×C₃	semidirect
138. Dic₃⋊C₈	C₂²×C₃	semidirect
139. C₈×Dic₃	C₂²×C₃	semidirect
168. C₂³×C₈	C₃×D₃	semidirect
230. C₂×C₃×C₈	#67	semidirect
231. C₂×C₃×C₈	C₃×D₄	semidirect
261. C₂²×C₃²	#131	semidirect
392. C₂×C₈	C₃×#67	semidirect
419. C₂²×C₃	#901	semidirect
422. C₂²×C₃	C₃×#131	semidirect
443. C₃²	#2929	semidirect
491. C₂²	C₃×#901	semidirect
501. C₃	#83734	direct (N × H)
502. C₃	C₃×#2929	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃²×C₈	2
C₃×#5791	2
C₂×C₃×#901	2
C₃×#5207	2
C₃×#5111	2
C₃×#5110	2
C₃×C₈×#67	2
C₃×#5102	2
C₃×#5101	2
C₃×#2929	3
#83734	3

Subgroups — C3×#83734 #11859316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83734 #11859316