Subgroups — C₃×#78549 #11857255

Order 1152.

1209 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#907	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
3	C₃×#5522	C₂	1	1	yes	maximal, characteristic
4	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4708	C₂	1	2	yes	maximal, complemented
9	C₃×#4707	C₂	1	2	yes	maximal, complemented
10	C₃×#4689	C₂	1	2	yes	maximal, complemented
11	C₃×C₄×D₃×C₈	C₂	1	2	yes	maximal, complemented
12	C₃×C₄×#131	—	3	1	no	maximal
13	#78549	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#235	C₂²	1	1	yes	characteristic
15	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃²×#117	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×#208	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×#907	C₄	1	8	yes	complemented
22	C₃×#901	C₄	1	8	yes	complemented
23	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
24	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
25	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
26	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
27	C₃×#893	C₄	1	2	yes	—
28	C₃×#887	C₄	1	2	yes	—
29	C₃×#67⋊C₄	C₄	1	4	yes	—
30	C₃×#872	C₂²	1	2	yes	—
31	C₃×C₄²×D₃	C₂²	1	2	yes	—
32	C₃²×#97	C₂²	1	2	yes	—
33	C₃²×C₄×C₈	C₂²	1	2	yes	—
34	C₃×#815	C₂²	1	2	yes	—
35	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
36	C₃×C₈×Dic₃	C₂²	1	2	yes	—
37	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
40	C₃×#803	C₂²	1	2	yes	—
41	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
42	C₂×C₃×#131	—	3	1	no	—
43	C₂×C₃×#131	—	3	1	no	—
44	C₃×C₄×#41	—	3	1	no	—
45	C₂×#907	C₂×C₃	1	1	yes	characteristic
46	C₂×#901	C₂×C₃	1	1	yes	characteristic
47	#5522	C₂×C₃	1	1	yes	characteristic
48	C₃×#405	—	2	1	no	—
49	C₃×#405	—	3	1	no	—
50	C₃×#405	—	3	2	no	—
51	C₃×#405	—	3	2	no	—
52	C₃×#405	D₃	1	1	yes	characteristic, complemented
53	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×C₄×M₁₆	—	3	1	no	—
55	C₃×C₄×M₁₆	—	3	2	no	—
56	C₂×C₃×C₄×C₈	—	3	1	no	—
57	C₂×C₃×C₄×C₈	—	3	2	no	—
58	Dic₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
60	#4997	C₂×C₃	1	1	yes	characteristic, complemented
61	#4708	C₂×C₃	1	2	yes	complemented
62	#4707	C₂×C₃	1	2	yes	complemented
63	#4689	C₂×C₃	1	2	yes	complemented
64	C₄×D₃×C₈	C₂×C₃	1	2	yes	complemented
65	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
66	C₂×C₃×#67	C₂×C₄	1	2	yes	—
67	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
68	C₃×#235	C₂×C₄	1	4	yes	—
69	C₃×#235	C₂×C₄	1	4	yes	—
70	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
72	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
73	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
74	C₃²×M₁₆	C₂×C₄	1	4	yes	complemented
75	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
76	C₂×C₃²×C₈	C₂³	1	2	yes	—
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
80	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
81	C₃²×C₄²	C₂³	1	2	yes	—
82	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
83	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
84	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
85	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
86	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
87	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
88	C₃×#208	C₂×C₄	1	4	yes	complemented
89	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
90	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
92	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
94	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
95	C₃×D₃×C₈	C₂×C₄	1	8	yes	complemented
96	C₃×D₃×C₈	C₂×C₄	1	8	yes	complemented
97	C₄×#131	—	3	1	no	Sylow
98	C₂×C₃×#41	—	3	1	no	—
99	C₂×#235	C₂²×C₃	1	1	yes	characteristic
100	C₃×#131	—	3	8	no	—
101	C₃×#131	—	3	8	no	—
102	C₂×C₃×M₁₆	—	2	1	no	—
103	C₂×C₃×M₁₆	—	3	1	no	—
104	C₂×C₃×M₁₆	—	3	2	no	—
105	C₂×C₃×M₁₆	—	3	2	no	—
106	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
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	—	3	2	no	—
112	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
113	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
114	C₃×C₄×Q₈	—	3	2	no	—
115	C₃×C₄×D₄	—	3	2	no	—
116	C₃×C₄×D₄	—	3	4	no	—
117	C₃×#117	—	2	1	no	—
118	C₃×#117	—	3	2	no	—
119	C₃×#117	C₂×D₃	1	1	yes	characteristic
120	C₃×#117	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₄²	—	3	1	no	—
122	C₂×C₃×C₄²	—	3	2	no	—
123	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
124	C₂×#208	C₂²×C₃	1	1	yes	characteristic
125	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
126	#907	C₃×C₄	1	8	yes	complemented
127	#901	C₃×C₄	1	8	yes	complemented
128	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
129	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
130	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
131	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
132	#893	C₃×C₄	1	2	yes	—
133	#887	C₃×C₄	1	2	yes	—
134	#67⋊C₄	C₃×C₄	1	4	yes	—
135	#872	C₂²×C₃	1	2	yes	—
136	C₄²×D₃	C₂²×C₃	1	2	yes	—
137	C₃×#97	—	2	2	no	—
138	C₃×#97	—	3	2	no	—
139	C₃×#97	—	3	2	no	—
140	C₃×#97	C₂×D₃	1	2	yes	—
141	C₃×#97	C₂²×C₃	1	2	yes	—
142	C₃×C₄×C₈	—	2	2	no	—
143	C₃×C₄×C₈	—	3	1	no	—
144	C₃×C₄×C₈	—	3	2	no	—
145	C₃×C₄×C₈	—	3	1	no	—
146	C₃×C₄×C₈	—	3	1	no	—
147	C₃×C₄×C₈	—	3	1	no	—
148	C₃×C₄×C₈	—	3	2	no	—
149	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
150	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
151	#815	C₂²×C₃	1	2	yes	—
152	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
153	C₈×Dic₃	C₂²×C₃	1	2	yes	—
154	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
155	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
156	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
157	#803	C₂²×C₃	1	2	yes	—
158	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
159	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
161	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
162	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
164	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
165	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
166	C₃×#67	C₄²	1	8	yes	—
167	C₂×C₃×Dic₃	—	2	4	no	—
168	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
169	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
170	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
171	C₃×D₁₂	C₄²	1	4	yes	—
172	C₃×C₄×D₃	—	2	8	no	—
173	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
174	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
175	C₃×Dic₆	C₄²	1	4	yes	—
176	C₃²×C₈	C₂²×C₄	1	2	yes	—
177	C₃²×C₈	C₂²×C₄	1	4	yes	—
178	C₃²×C₈	C₂²×C₄	1	2	yes	—
179	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
180	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
181	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
182	C₂×#131	—	3	1	no	—
183	C₂×#131	—	3	1	no	—
184	C₄×#41	—	3	1	no	—
185	#405	—	3	1	no	—
186	#405	—	3	2	no	—
187	#405	—	3	2	no	—
188	#405	C₃×D₃	1	1	yes	characteristic, complemented
189	C₄×M₁₆	—	3	1	no	—
190	C₄×M₁₆	—	3	2	no	—
191	C₂×C₄×C₈	—	3	1	no	—
192	C₂×C₄×C₈	—	3	2	no	—
193	C₃×#41	—	3	4	no	—
194	C₃×#41	—	3	4	no	—
195	C₂×C₃×Q₈	—	3	1	no	—
196	C₂×C₃×D₄	—	3	2	no	—
197	C₂×C₃×D₄	—	3	1	no	—
198	C₂²×C₃×C₄	—	2	1	no	—
199	C₂²×C₃×C₄	—	3	2	no	—
200	C₂²×C₃×C₄	—	3	2	no	—
201	C₂²×C₃×C₄	—	3	4	no	—
202	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
204	C₂×#67	C₂×C₃×C₄	1	2	yes	—
205	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
206	#235	C₂×C₃×C₄	1	4	yes	—
207	#235	C₂×C₃×C₄	1	4	yes	—
208	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
210	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
211	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
212	C₃×M₁₆	—	2	4	no	—
213	C₃×M₁₆	—	3	4	no	—
214	C₃×M₁₆	—	3	8	no	—
215	C₃×M₁₆	—	3	8	no	—
216	C₃×M₁₆	C₄×D₃	1	4	yes	complemented
217	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
218	C₂×C₃×C₈	—	2	4	no	—
219	C₂×C₃×C₈	—	2	1	no	—
220	C₂×C₃×C₈	—	2	2	no	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₂×C₃×C₈	—	3	4	no	—
223	C₂×C₃×C₈	—	3	1	no	—
224	C₂×C₃×C₈	—	3	1	no	—
225	C₂×C₃×C₈	—	3	2	no	—
226	C₂×C₃×C₈	—	3	8	no	—
227	C₂×C₃×C₈	—	3	8	no	—
228	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
229	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
230	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
232	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
234	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
235	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	3	4	no	—
238	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
239	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
240	C₃×C₂²⋊C₄	—	2	2	no	—
241	C₃×C₂²⋊C₄	—	3	4	no	—
242	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
243	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
244	C₃×C₄²	—	2	2	no	—
245	C₃×C₄²	—	3	4	no	—
246	C₃×C₄²	—	3	2	no	—
247	C₃×C₄²	—	3	1	no	—
248	C₃×C₄²	—	3	1	no	—
249	C₃×C₄²	C₂²×D₃	1	2	yes	—
250	C₃×C₄²	C₂³×C₃	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
252	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
253	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
254	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
255	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
256	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
257	#208	C₂×C₃×C₄	1	4	yes	complemented
258	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	complemented
259	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
261	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
262	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	8	yes	complemented
263	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	8	yes	complemented
264	D₃×C₈	C₂×C₃×C₄	1	8	yes	complemented
265	D₃×C₈	C₂×C₃×C₄	1	8	yes	complemented
266	C₂²×C₃²	—	2	2	no	—
267	C₂²×C₃²	C₂×C₄²	1	2	yes	—
268	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
269	C₂×C₃×D₃	—	2	4	no	—
270	C₂×C₃×D₃	C₂×C₄²	1	4	yes	—
271	C₃²×C₄	—	2	4	no	—
272	C₃²×C₄	C₂×C₄²	1	2	yes	—
273	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
274	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
275	C₃×Dic₃	—	2	2	no	—
276	C₃×Dic₃	C₂×C₄²	1	4	yes	—
277	C₃×Dic₃	#131	1	4	yes	complemented
278	C₂×#41	—	3	1	no	—
279	#131	—	3	8	no	—
280	#131	—	3	8	no	—
281	C₂×M₁₆	—	3	1	no	—
282	C₂×M₁₆	—	3	2	no	—
283	C₂×M₁₆	—	3	2	no	—
284	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
285	C₂²×C₈	—	3	1	no	—
286	C₂²×C₈	—	3	2	no	—
287	C₂²×C₈	—	3	2	no	—
288	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
289	C₄×Q₈	—	3	2	no	—
290	C₄×D₄	—	3	2	no	—
291	C₄×D₄	—	3	4	no	—
292	#117	—	3	2	no	—
293	#117	C₂×C₃×D₃	1	1	yes	characteristic
294	C₂×C₄²	—	3	1	no	—
295	C₂×C₄²	—	3	2	no	—
296	#97	—	3	2	no	—
297	#97	—	3	2	no	—
298	#97	C₂×C₃×D₃	1	2	yes	—
299	C₄×C₈	—	3	1	no	—
300	C₄×C₈	—	3	1	no	—
301	C₄×C₈	—	3	2	no	—
302	C₄×C₈	—	3	1	no	—
303	C₄×C₈	—	3	1	no	—
304	C₄×C₈	—	3	2	no	—
305	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
306	C₂³×C₃	—	2	1	no	—
307	C₂³×C₃	—	3	2	no	—
308	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
309	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
311	C₃×Q₈	—	3	4	no	—
312	C₃×D₄	—	3	8	no	—
313	C₃×D₄	—	3	4	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	1	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	—	3	2	no	—
320	C₂×C₃×C₄	—	3	2	no	—
321	C₂×C₃×C₄	—	3	4	no	—
322	C₂×C₃×C₄	—	3	4	no	—
323	C₂×C₃×C₄	—	3	2	no	—
324	C₂×C₃×C₄	—	6	8	no	—
325	C₂×C₃×C₄	—	6	4	no	—
326	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
327	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
329	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
330	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
331	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
333	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
334	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
336	#67	C₃×C₄²	1	8	yes	—
337	C₂×Dic₃	—	2	4	no	—
338	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
339	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
340	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
341	D₁₂	C₃×C₄²	1	4	yes	—
342	C₄×D₃	—	2	8	no	—
343	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
344	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
345	Dic₆	C₃×C₄²	1	4	yes	—
346	C₃×C₈	—	2	2	no	—
347	C₃×C₈	—	2	2	no	—
348	C₃×C₈	—	2	4	no	—
349	C₃×C₈	—	3	2	no	—
350	C₃×C₈	—	3	4	no	—
351	C₃×C₈	—	3	2	no	—
352	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
353	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
354	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
355	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
356	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
357	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
358	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
359	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
360	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
361	C₂×C₃²	—	2	2	no	—
362	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
363	C₂×C₃²	C₂×#131	1	2	yes	—
364	C₃×D₃	—	2	4	no	—
365	#41	—	3	4	no	—
366	#41	—	3	4	no	—
367	C₂×Q₈	—	3	1	no	—
368	C₂×D₄	—	3	2	no	—
369	C₂×D₄	—	3	1	no	—
370	C₂²×C₄	—	3	2	no	—
371	C₂²×C₄	—	3	2	no	—
372	C₂²×C₄	—	3	4	no	—
373	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
374	M₁₆	—	3	4	no	—
375	M₁₆	—	3	8	no	—
376	M₁₆	—	3	8	no	—
377	M₁₆	C₃×C₄×D₃	1	4	yes	complemented
378	C₂×C₈	—	3	1	no	—
379	C₂×C₈	—	3	1	no	—
380	C₂×C₈	—	3	2	no	—
381	C₂×C₈	—	3	4	no	—
382	C₂×C₈	—	3	8	no	—
383	C₂×C₈	—	3	8	no	—
384	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
385	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
386	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
387	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
388	C₄⋊C₄	—	3	4	no	—
389	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
390	C₂²⋊C₄	—	3	4	no	—
391	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
392	C₄²	—	3	1	no	—
393	C₄²	—	3	1	no	—
394	C₄²	—	3	4	no	—
395	C₄²	—	3	2	no	—
396	C₄²	C₂²×C₃×D₃	1	2	yes	—
397	C₂²×C₃	—	2	2	no	—
398	C₂²×C₃	—	2	2	no	—
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	3	4	no	—
402	C₂²×C₃	—	4	2	no	—
403	C₂²×C₃	—	6	4	no	—
404	C₂²×C₃	C₄²×D₃	1	2	yes	—
405	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
406	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
407	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
408	C₂×D₃	—	2	4	no	—
409	C₂×D₃	C₂×C₃×C₄²	1	4	yes	—
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	—	3	4	no	—
416	C₃×C₄	—	3	4	no	—
417	C₃×C₄	—	4	4	no	—
418	C₃×C₄	—	6	2	no	—
419	C₃×C₄	C₄²×D₃	1	2	yes	—
420	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
421	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
422	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
423	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
424	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
425	Dic₃	—	2	2	no	—
426	Dic₃	C₂×C₃×C₄²	1	4	yes	—
427	Dic₃	C₃×#131	1	4	yes	complemented
428	C₃²	C₄×#131	1	1	yes	characteristic, complemented, Sylow
429	C₂³	—	3	2	no	—
430	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
431	Q₈	—	3	4	no	—
432	D₄	—	3	8	no	—
433	D₄	—	3	4	no	—
434	C₂×C₄	—	3	2	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	3	4	no	—
437	C₂×C₄	—	3	4	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	6	8	no	—
440	C₂×C₄	—	6	4	no	—
441	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
442	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
443	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
444	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
445	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
446	C₈	—	3	2	no	—
447	C₈	—	3	2	no	—
448	C₈	—	3	4	no	—
449	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
450	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
451	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
452	C₂×C₃	—	2	2	no	—
453	C₂×C₃	—	2	2	no	—
454	C₂×C₃	—	2	2	no	—
455	C₂×C₃	—	2	1	no	—
456	C₂×C₃	—	4	2	no	—
457	C₂×C₃	—	6	4	no	—
458	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
459	C₂×C₃	D₃×#131	1	2	yes	—
460	C₂×C₃	C₂²×C₃×C₄²	1	1	yes	characteristic
461	C₂×C₃	C₂×C₃×#131	1	2	yes	—
462	D₃	—	2	4	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	3	4	no	—
465	C₂²	—	6	4	no	—
466	C₂²	C₃×C₄²×D₃	1	2	yes	—
467	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	3	4	no	—
470	C₄	—	3	4	no	—
471	C₄	—	6	2	no	—
472	C₄	C₃×C₄²×D₃	1	2	yes	—
473	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
474	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
475	C₃	—	2	1	no	—
476	C₃	#78549	1	1	yes	characteristic, direct product factor
477	C₃	C₃×C₄×#131	1	1	yes	characteristic, complemented
478	C₂	—	2	2	no	—
479	C₂	—	6	4	no	—
480	C₂	C₂×C₃×C₄²×D₃	1	1	yes	characteristic
481	C₂	C₃×D₃×#131	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂×C₃	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#405	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₃×C₄×#131
LCS	G ▷ C₂×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
4. C₃²×#405	C₂	semidirect
5. C₃×Dic₃×M₁₆	C₂	semidirect
6. C₂×C₃×C₈×Dic₃	C₂	semidirect
7. C₃×#4997	C₂	semidirect
8. C₃×#4708	C₂	semidirect
9. C₃×#4707	C₂	semidirect
10. C₃×#4689	C₂	semidirect
11. C₃×C₄×D₃×C₈	C₂	semidirect
13. #78549	C₃	direct (N × H)
21. C₃×#907	C₄	semidirect
22. C₃×#901	C₄	semidirect
52. C₃×#405	D₃	semidirect
53. C₃×#405	C₂×C₃	semidirect
58. Dic₃×M₁₆	C₂×C₃	semidirect
59. C₂×C₈×Dic₃	C₂×C₃	semidirect
60. #4997	C₂×C₃	semidirect
61. #4708	C₂×C₃	semidirect
62. #4707	C₂×C₃	semidirect
63. #4689	C₂×C₃	semidirect
64. C₄×D₃×C₈	C₂×C₃	semidirect
74. C₃²×M₁₆	C₂×C₄	semidirect
75. C₂×C₃²×C₈	C₂×C₄	semidirect
88. C₃×#208	C₂×C₄	semidirect
89. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
93. C₃×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
94. C₃×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
95. C₃×D₃×C₈	C₂×C₄	semidirect
96. C₃×D₃×C₈	C₂×C₄	semidirect
126. #907	C₃×C₄	semidirect
127. #901	C₃×C₄	semidirect
188. #405	C₃×D₃	semidirect
216. C₃×M₁₆	C₄×D₃	semidirect
217. C₃×M₁₆	C₂×C₃×C₄	semidirect
228. C₂×C₃×C₈	C₄×D₃	semidirect
229. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
257. #208	C₂×C₃×C₄	semidirect
258. C₂×C₃⋊C₈	C₂×C₃×C₄	semidirect
262. ΓL(1,𝔽₂₅)	C₂×C₃×C₄	semidirect
263. ΓL(1,𝔽₂₅)	C₂×C₃×C₄	semidirect
264. D₃×C₈	C₂×C₃×C₄	semidirect
265. D₃×C₈	C₂×C₃×C₄	semidirect
277. C₃×Dic₃	#131	semidirect
377. M₁₆	C₃×C₄×D₃	semidirect
384. C₂×C₈	C₃×C₄×D₃	semidirect
427. Dic₃	C₃×#131	semidirect
428. C₃²	C₄×#131	semidirect
476. C₃	#78549	direct (N × H)
477. C₃	C₃×C₄×#131	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#907	2
C₂×C₃×#901	2
C₃×#5522	2
C₃²×#405	2
C₃×Dic₃×M₁₆	2
C₂×C₃×C₈×Dic₃	2
C₃×#4997	2
C₃×#4708	2
C₃×#4707	2
C₃×#4689	2
C₃×C₄×D₃×C₈	2
C₃×C₄×#131	3
#78549	3

Subgroups — C3×#78549 #11857255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#78549 #11857255