Subgroups — C₃×#78553 #11859322

Order 1152.

1105 conjugacy classes of subgroups.

The subgroup lattice has 491 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5524	C₂	1	1	yes	maximal, characteristic
4	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5129	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5126	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4999	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4706	C₂	1	4	yes	maximal, complemented
9	C₃×C₈×D₁₂	C₂	1	4	yes	maximal, complemented
10	C₃×#2929	—	3	1	no	maximal
11	#78553	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₃×#235	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₃²×#117	C₂²	1	1	yes	characteristic
17	C₂×C₃×#208	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₃×#901	—	2	4	no	—
20	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
21	C₂×C₃×D₃×C₈	—	2	4	no	—
22	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
23	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
24	C₂×C₃×D₃×C₈	C₂²	1	2	yes	complemented
25	C₃×#897	C₄	1	2	yes	—
26	C₃×#895	C₄	1	2	yes	—
27	C₃×#886	C₄	1	2	yes	—
28	C₃×#882	C₄	1	2	yes	—
29	C₃×C₄×D₁₂	C₂²	1	4	yes	—
30	C₃²×#97	C₂²	1	2	yes	complemented
31	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
32	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
33	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	complemented
34	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
35	C₂×C₃×#131	—	3	1	no	—
36	C₂³×C₃×C₈	—	3	1	no	—
37	C₃×#525	—	3	1	no	—
38	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
40	#5524	C₂×C₃	1	1	yes	characteristic
41	C₃×#435	—	3	4	no	—
42	C₃×C₈×D₄	—	3	4	no	—
43	C₃×#424	—	3	1	no	—
44	C₃×#408	—	3	1	no	—
45	C₃×#407	—	3	1	no	—
46	C₃×#405	—	2	1	no	—
47	C₃×#405	D₃	1	1	yes	characteristic, complemented
48	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
49	#5129	C₂×C₃	1	1	yes	characteristic, complemented
50	#5126	C₂×C₃	1	1	yes	characteristic, complemented
51	#4999	C₂×C₃	1	1	yes	characteristic, complemented
52	#4706	C₂×C₃	1	4	yes	complemented
53	C₈×D₁₂	C₂×C₃	1	4	yes	complemented
54	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×#67	C₂×C₄	1	2	yes	—
57	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
58	C₃×#235	—	2	2	no	—
59	C₃×#235	—	2	2	no	—
60	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
61	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₃	—	2	2	no	—
63	C₂×C₃×C₄×D₃	—	2	2	no	—
64	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
65	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
66	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
67	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
68	C₃²×M₁₆	—	2	2	no	—
69	C₂×C₃²×C₈	D₄	1	4	yes	complemented
70	C₂×C₃²×C₈	C₂³	1	2	yes	—
71	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
73	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
74	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₃²×C₄²	C₂³	1	2	yes	—
76	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
77	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
78	C₃×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
79	C₃×#208	—	2	2	no	—
80	C₂×C₃×C₃⋊C₈	—	2	2	no	—
81	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
82	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
83	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
84	C₃×D₃×C₈	—	2	4	no	—
85	C₃×D₃×C₈	—	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	—	3	1	no	—
90	C₂×#235	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
92	C₃×#131	—	6	4	no	—
93	C₂×C₃×M₁₆	—	2	1	no	—
94	C₂×C₃×M₁₆	—	3	1	no	—
95	C₂×C₃×M₁₆	—	3	2	no	—
96	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
97	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₃×C₈	—	2	1	no	—
99	C₂²×C₃×C₈	—	3	1	no	—
100	C₂²×C₃×C₈	—	3	2	no	—
101	C₂²×C₃×C₈	—	3	2	no	—
102	C₂²×C₃×C₈	—	3	2	no	—
103	C₂²×C₃×C₈	—	6	4	no	—
104	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
105	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
106	C₃×#123	—	3	2	no	—
107	C₃×C₂²⋊Q₈	—	3	2	no	—
108	C₃×#121	—	3	2	no	—
109	C₃×#120	—	3	2	no	—
110	C₃×C₄×D₄	—	3	4	no	—
111	C₃×#117	—	2	1	no	—
112	C₃×#117	C₂×D₃	1	1	yes	characteristic
113	C₃×#117	C₂²×C₃	1	1	yes	characteristic
114	C₂×#208	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	#901	—	2	4	no	—
117	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	complemented
118	C₂×D₃×C₈	—	2	4	no	—
119	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
120	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
121	C₂×D₃×C₈	C₂²×C₃	1	2	yes	complemented
122	#897	C₃×C₄	1	2	yes	—
123	#895	C₃×C₄	1	2	yes	—
124	#886	C₃×C₄	1	2	yes	—
125	#882	C₃×C₄	1	2	yes	—
126	C₄×D₁₂	C₂²×C₃	1	4	yes	—
127	C₃×C₄⋊C₈	—	3	4	no	—
128	C₃×C₂²⋊C₈	—	3	4	no	—
129	C₃×C₂²⋊C₈	—	3	4	no	—
130	C₃×#97	—	2	2	no	—
131	C₃×#97	C₂×D₃	1	2	yes	complemented
132	C₃×#97	C₂²×C₃	1	2	yes	complemented
133	C₃×C₄×C₈	—	2	2	no	—
134	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
135	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
136	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
137	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	complemented
138	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
139	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₃×D₃	—	2	2	no	—
141	C₂²×C₃×D₃	—	2	4	no	—
142	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
143	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
144	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
145	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
147	C₂×C₃²×C₄	#41	1	2	yes	—
148	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
149	C₃×#67	—	2	4	no	—
150	C₂×C₃×Dic₃	—	2	2	no	—
151	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
152	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
153	C₃×D₁₂	—	2	8	no	—
154	C₃×D₁₂	—	2	2	no	—
155	C₃×C₄×D₃	—	2	4	no	—
156	C₃×C₄×D₃	—	2	2	no	—
157	C₃×C₄×D₃	—	2	2	no	—
158	C₃×C₄×D₃	—	2	2	no	—
159	C₃×C₄×D₃	—	2	2	no	—
160	C₃×Dic₆	—	2	2	no	—
161	C₃²×C₈	—	2	2	no	—
162	C₃²×C₈	C₂×D₄	1	2	yes	—
163	C₃²×C₈	C₂×D₄	1	2	yes	—
164	C₃×C₃⋊C₈	—	2	2	no	—
165	C₃×C₃⋊C₈	—	2	2	no	—
166	C₂×#131	—	3	1	no	—
167	C₂³×C₈	—	3	1	no	—
168	#525	—	3	1	no	—
169	#435	—	3	4	no	—
170	C₈×D₄	—	3	4	no	—
171	#424	—	3	1	no	—
172	#408	—	3	1	no	—
173	#407	—	3	1	no	—
174	#405	C₃×D₃	1	1	yes	characteristic, complemented
175	C₂⁴×C₃	—	3	1	no	—
176	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
177	C₃×#41	—	6	2	no	—
178	C₃×#41	—	6	2	no	—
179	C₂×C₃×Q₈	—	3	1	no	—
180	C₂×C₃×D₄	—	3	2	no	—
181	C₂×C₃×D₄	—	3	4	no	—
182	C₂×C₃×D₄	—	3	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	3	1	no	—
185	C₂²×C₃×C₄	—	3	2	no	—
186	C₂²×C₃×C₄	—	3	2	no	—
187	C₂²×C₃×C₄	—	3	2	no	—
188	C₂²×C₃×C₄	—	6	2	no	—
189	C₂²×C₃×C₄	—	6	2	no	—
190	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
191	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
192	C₂×#67	C₂×C₃×C₄	1	2	yes	—
193	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
194	#235	—	2	2	no	—
195	#235	—	2	2	no	—
196	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
197	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
198	C₂×C₄×D₃	—	2	2	no	—
199	C₂×C₄×D₃	—	2	2	no	—
200	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
201	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
202	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
203	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
204	C₃×M₁₆	—	2	4	no	—
205	C₃×M₁₆	—	2	2	no	—
206	C₃×M₁₆	—	2	2	no	—
207	C₃×M₁₆	—	6	2	no	—
208	C₃×M₁₆	—	6	4	no	—
209	C₂×C₃×C₈	—	2	4	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	2	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	3	2	no	—
214	C₂×C₃×C₈	—	3	2	no	—
215	C₂×C₃×C₈	—	6	2	no	—
216	C₂×C₃×C₈	—	6	4	no	—
217	C₂×C₃×C₈	—	6	4	no	—
218	C₂×C₃×C₈	—	6	4	no	—
219	C₂×C₃×C₈	D₁₂	1	4	yes	complemented
220	C₂×C₃×C₈	C₃×D₄	1	4	yes	complemented
221	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
222	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
223	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
224	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
225	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
226	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	3	4	no	—
229	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
230	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₂²⋊C₄	—	3	4	no	—
233	C₃×C₂²⋊C₄	—	3	4	no	—
234	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
235	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
236	C₃×C₄²	—	2	2	no	—
237	C₃×C₄²	C₂²×D₃	1	2	yes	—
238	C₃×C₄²	C₂³×C₃	1	2	yes	—
239	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
240	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
241	C₄⋊Dic₃	C₂×C₃×C₄	1	4	yes	—
242	#208	—	2	2	no	—
243	C₂×C₃⋊C₈	—	2	2	no	—
244	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
245	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
246	ΓL(1,𝔽₂₅)	—	2	4	no	—
247	D₃×C₈	—	2	4	no	—
248	D₃×C₈	—	2	4	no	—
249	D₃×C₈	—	2	4	no	—
250	C₂²×C₃²	—	2	2	no	—
251	C₂²×C₃²	C₄×D₄	1	2	yes	—
252	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
253	C₂×C₃×D₃	—	2	8	no	—
254	C₂×C₃×D₃	—	2	2	no	—
255	C₂×C₃×D₃	—	2	2	no	—
256	C₂×C₃×D₃	—	2	2	no	—
257	C₂×C₃×D₃	—	2	4	no	—
258	C₂×C₃×D₃	#131	1	4	yes	complemented
259	C₃²×C₄	—	2	4	no	—
260	C₃²×C₄	C₄×D₄	1	2	yes	—
261	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
262	C₃²×C₄	C₂×#41	1	1	yes	characteristic
263	C₃×Dic₃	—	2	2	no	—
264	C₃×Dic₃	—	2	2	no	—
265	C₂×#41	—	3	1	no	—
266	C₂³×C₄	—	3	1	no	—
267	#131	—	6	4	no	—
268	C₂×M₁₆	—	3	1	no	—
269	C₂×M₁₆	—	3	2	no	—
270	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
271	C₂²×C₈	—	3	1	no	—
272	C₂²×C₈	—	3	2	no	—
273	C₂²×C₈	—	3	2	no	—
274	C₂²×C₈	—	3	2	no	—
275	C₂²×C₈	—	6	4	no	—
276	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
277	#123	—	3	2	no	—
278	C₂²⋊Q₈	—	3	2	no	—
279	#121	—	3	2	no	—
280	#120	—	3	2	no	—
281	C₄×D₄	—	3	4	no	—
282	#117	C₂×C₃×D₃	1	1	yes	characteristic
283	C₄⋊C₈	—	3	4	no	—
284	C₂²⋊C₈	—	3	4	no	—
285	C₂²⋊C₈	—	3	4	no	—
286	#97	C₂×C₃×D₃	1	2	yes	complemented
287	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
288	C₂³×C₃	—	2	1	no	—
289	C₂³×C₃	—	3	2	no	—
290	C₂³×C₃	—	3	2	no	—
291	C₂³×C₃	—	6	4	no	—
292	C₂³×C₃	—	6	2	no	—
293	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
294	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
295	C₂²×D₃	—	2	2	no	—
296	C₂²×D₃	—	2	4	no	—
297	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
298	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
299	C₃×Q₈	—	6	2	no	—
300	C₃×D₄	—	6	8	no	—
301	C₃×D₄	—	6	4	no	—
302	C₃×D₄	—	6	2	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	4	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	3	2	no	—
309	C₂×C₃×C₄	—	3	2	no	—
310	C₂×C₃×C₄	—	6	2	no	—
311	C₂×C₃×C₄	—	6	4	no	—
312	C₂×C₃×C₄	—	6	2	no	—
313	C₂×C₃×C₄	—	6	2	no	—
314	C₂×C₃×C₄	—	6	2	no	—
315	C₂×C₃×C₄	—	6	2	no	—
316	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
317	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
319	C₂×C₃×C₄	#235	1	2	yes	—
320	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
321	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
323	C₂×C₃×C₄	C₃×#41	1	2	yes	—
324	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
326	#67	—	2	4	no	—
327	C₂×Dic₃	—	2	2	no	—
328	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
329	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
330	D₁₂	—	2	8	no	—
331	D₁₂	—	2	2	no	—
332	C₄×D₃	—	2	4	no	—
333	C₄×D₃	—	2	2	no	—
334	C₄×D₃	—	2	2	no	—
335	C₄×D₃	—	2	2	no	—
336	C₄×D₃	—	2	2	no	—
337	Dic₆	—	2	2	no	—
338	C₃×C₈	—	2	4	no	—
339	C₃×C₈	—	2	2	no	—
340	C₃×C₈	—	2	2	no	—
341	C₃×C₈	—	2	2	no	—
342	C₃×C₈	—	2	2	no	—
343	C₃×C₈	—	6	2	no	—
344	C₃×C₈	—	6	2	no	—
345	C₃×C₈	C₂×D₁₂	1	2	yes	—
346	C₃×C₈	C₂×D₁₂	1	2	yes	—
347	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
348	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
349	C₃⋊C₈	—	2	2	no	—
350	C₃⋊C₈	—	2	2	no	—
351	C₂×C₃²	—	2	2	no	—
352	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂×C₃²	C₂×#131	1	2	yes	—
354	C₃×D₃	—	2	4	no	—
355	C₃×D₃	—	4	2	no	—
356	C₂⁴	—	3	1	no	—
357	#41	—	6	2	no	—
358	#41	—	6	2	no	—
359	C₂×Q₈	—	3	1	no	—
360	C₂×D₄	—	3	2	no	—
361	C₂×D₄	—	3	4	no	—
362	C₂×D₄	—	3	1	no	—
363	C₂²×C₄	—	3	1	no	—
364	C₂²×C₄	—	3	2	no	—
365	C₂²×C₄	—	3	2	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	6	2	no	—
368	C₂²×C₄	—	6	2	no	—
369	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
370	M₁₆	—	2	2	no	—
371	M₁₆	—	6	2	no	—
372	M₁₆	—	6	4	no	—
373	C₂×C₈	—	3	2	no	—
374	C₂×C₈	—	3	2	no	—
375	C₂×C₈	—	6	2	no	—
376	C₂×C₈	—	6	4	no	—
377	C₂×C₈	—	6	4	no	—
378	C₂×C₈	—	6	4	no	—
379	C₂×C₈	C₃×D₁₂	1	4	yes	complemented
380	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
381	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
382	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
383	C₄⋊C₄	—	3	4	no	—
384	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
385	C₂²⋊C₄	—	3	4	no	—
386	C₂²⋊C₄	—	3	4	no	—
387	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
388	C₄²	C₂²×C₃×D₃	1	2	yes	—
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	1	no	—
392	C₂²×C₃	—	2	2	no	—
393	C₂²×C₃	—	3	4	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	6	8	no	—
396	C₂²×C₃	—	6	2	no	—
397	C₂²×C₃	—	6	2	no	—
398	C₂²×C₃	—	6	2	no	—
399	C₂²×C₃	—	6	4	no	—
400	C₂²×C₃	C₄×D₁₂	1	2	yes	—
401	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
402	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
403	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
404	C₂×D₃	—	2	8	no	—
405	C₂×D₃	—	2	2	no	—
406	C₂×D₃	—	2	2	no	—
407	C₂×D₃	—	2	4	no	—
408	C₂×D₃	—	2	2	no	—
409	C₂×D₃	C₃×#131	1	4	yes	complemented
410	C₃×C₄	—	2	4	no	—
411	C₃×C₄	—	2	4	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	4	4	no	—
416	C₃×C₄	—	6	2	no	—
417	C₃×C₄	—	6	2	no	—
418	C₃×C₄	C₄×D₁₂	1	2	yes	—
419	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
420	C₃×C₄	C₂²×D₁₂	1	1	yes	characteristic
421	C₃×C₄	C₂×#235	1	1	yes	characteristic
422	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
423	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
424	Dic₃	—	2	2	no	—
425	Dic₃	—	2	2	no	—
426	C₃²	#2929	1	1	yes	characteristic, complemented, Sylow
427	C₂³	—	3	2	no	—
428	C₂³	—	3	2	no	—
429	C₂³	—	6	4	no	—
430	C₂³	—	6	2	no	—
431	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
432	Q₈	—	6	2	no	—
433	D₄	—	6	8	no	—
434	D₄	—	6	4	no	—
435	D₄	—	6	2	no	—
436	C₂×C₄	—	3	2	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	6	2	no	—
439	C₂×C₄	—	6	2	no	—
440	C₂×C₄	—	6	2	no	—
441	C₂×C₄	—	6	2	no	—
442	C₂×C₄	—	6	2	no	—
443	C₂×C₄	—	6	4	no	—
444	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
445	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
446	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
447	C₂×C₄	C₃×#235	1	2	yes	—
448	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	6	2	no	—
451	C₈	—	6	2	no	—
452	C₈	C₂×C₃×D₁₂	1	2	yes	—
453	C₈	C₂×C₃×D₁₂	1	2	yes	—
454	C₂×C₃	—	2	2	no	—
455	C₂×C₃	—	2	2	no	—
456	C₂×C₃	—	2	2	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	4	2	no	—
459	C₂×C₃	—	6	4	no	—
460	C₂×C₃	—	12	2	no	—
461	C₂×C₃	C₂×C₄×D₁₂	1	1	yes	characteristic
462	C₂×C₃	D₃×#131	1	2	yes	—
463	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
464	C₂×C₃	C₂×C₃×#131	1	2	yes	—
465	D₃	—	2	4	no	—
466	D₃	—	4	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	3	4	no	—
469	C₂²	—	6	8	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	6	4	no	—
473	C₂²	—	6	2	no	—
474	C₂²	C₃×C₄×D₁₂	1	2	yes	—
475	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
476	C₄	—	2	4	no	—
477	C₄	—	6	2	no	—
478	C₄	—	6	2	no	—
479	C₄	C₃×C₄×D₁₂	1	2	yes	—
480	C₄	C₂²×C₃×D₁₂	1	1	yes	characteristic
481	C₄	C₂×C₃×#235	1	1	yes	characteristic
482	C₃	—	2	1	no	—
483	C₃	#78553	1	1	yes	characteristic, direct product factor
484	C₃	C₃×#2929	1	1	yes	characteristic, complemented
485	C₂	—	2	2	no	—
486	C₂	—	6	4	no	—
487	C₂	—	12	2	no	—
488	C₂	C₂×C₃×C₄×D₁₂	1	1	yes	characteristic
489	C₂	C₃×D₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5524	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×#2929
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×#405

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#901	C₂	semidirect
2. C₂²×C₃×D₃×C₈	C₂	semidirect
4. C₃²×#405	C₂	semidirect
5. C₃×#5129	C₂	semidirect
6. C₃×#5126	C₂	semidirect
7. C₃×#4999	C₂	semidirect
8. C₃×#4706	C₂	semidirect
9. C₃×C₈×D₁₂	C₂	semidirect
11. #78553	C₃	direct (N × H)
20. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
24. C₂×C₃×D₃×C₈	C₂²	semidirect
30. C₃²×#97	C₂²	semidirect
31. C₃²×C₄×C₈	C₂²	semidirect
33. C₃×(C₂×D₃)⋊C₈	C₂²	semidirect
34. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
38. C₂×#901	C₂×C₃	semidirect
39. C₂²×D₃×C₈	C₂×C₃	semidirect
47. C₃×#405	D₃	semidirect
48. C₃×#405	C₂×C₃	semidirect
49. #5129	C₂×C₃	semidirect
50. #5126	C₂×C₃	semidirect
51. #4999	C₂×C₃	semidirect
52. #4706	C₂×C₃	semidirect
53. C₈×D₁₂	C₂×C₃	semidirect
69. C₂×C₃²×C₈	D₄	semidirect
117. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
121. C₂×D₃×C₈	C₂²×C₃	semidirect
131. C₃×#97	C₂×D₃	semidirect
132. C₃×#97	C₂²×C₃	semidirect
134. C₃×C₄×C₈	C₂×D₃	semidirect
135. C₃×C₄×C₈	C₂²×C₃	semidirect
137. (C₂×D₃)⋊C₈	C₂²×C₃	semidirect
138. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
174. #405	C₃×D₃	semidirect
219. C₂×C₃×C₈	D₁₂	semidirect
220. C₂×C₃×C₈	C₃×D₄	semidirect
258. C₂×C₃×D₃	#131	semidirect
286. #97	C₂×C₃×D₃	semidirect
287. C₄×C₈	C₂×C₃×D₃	semidirect
379. C₂×C₈	C₃×D₁₂	semidirect
409. C₂×D₃	C₃×#131	semidirect
426. C₃²	#2929	semidirect
483. C₃	#78553	direct (N × H)
484. 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
C₂×C₃×#901	2
C₂²×C₃×D₃×C₈	2
C₃×#5524	2
C₃²×#405	2
C₃×#5129	2
C₃×#5126	2
C₃×#4999	2
C₃×#4706	2
C₃×C₈×D₁₂	2
C₃×#2929	3
#78553	3

Subgroups — C3×#78553 #11859322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78553 #11859322