Subgroups — C₃×D₃×#405 #11857171

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×D₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×D₃×#117	C₂	1	1	yes	maximal, characteristic
4	C₃²×#405	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5122	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5101	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×D₃×#97	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	C₂×C₃×#405	—	3	1	no	maximal
13	D₃×#405	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂²×C₃×C₄×D₃	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	C₃×#926	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×D₃×M₁₆	C₄	1	8	yes	complemented
22	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	C₂×C₃×D₃×C₈	C₄	1	8	yes	complemented
24	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
25	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
29	C₃×#892	C₄	1	2	yes	—
30	C₃×D₃×C₄⋊C₄	C₄	1	2	yes	—
31	C₃×D₃×C₂²⋊C₄	C₄	1	2	yes	—
32	C₃×#877	C₄	1	2	yes	—
33	C₃×#872	C₂²	1	2	yes	—
34	C₃×C₄²×D₃	C₂²	1	2	yes	—
35	C₃²×#97	C₂²	1	2	yes	complemented
36	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
37	C₃×#815	C₂²	1	2	yes	complemented
38	C₃×#815	C₂²	1	2	yes	complemented
39	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
40	C₃×C₈×Dic₃	C₂²	1	2	yes	complemented
41	C₃×#803	C₂²	1	2	yes	complemented
42	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
43	C₂²×C₃×M₁₆	—	3	1	no	—
44	C₂³×C₃×C₈	—	3	1	no	—
45	C₂×C₃×#117	—	3	1	no	—
46	C₂×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic
47	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
48	D₃×#117	C₂×C₃	1	1	yes	characteristic
49	C₃×#405	—	2	1	no	—
50	C₃×#405	—	3	1	no	—
51	C₃×#405	—	3	1	no	—
52	C₃×#405	—	3	1	no	—
53	C₃×#405	—	3	2	no	—
54	C₃×#405	—	3	2	no	—
55	C₃×#405	D₃	1	1	yes	characteristic, direct product factor
56	C₃×#405	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×C₃×#97	—	3	2	no	—
58	C₂×C₃×C₄×C₈	—	3	2	no	—
59	#5122	C₂×C₃	1	1	yes	characteristic, complemented
60	#5101	C₂×C₃	1	1	yes	characteristic, complemented
61	#4997	C₂×C₃	1	1	yes	characteristic, complemented
62	#4708	C₂×C₃	1	2	yes	complemented
63	D₃×#97	C₂×C₃	1	2	yes	complemented
64	#4689	C₂×C₃	1	2	yes	complemented
65	C₄×D₃×C₈	C₂×C₃	1	2	yes	complemented
66	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
68	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
70	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
73	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
74	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
76	C₃²×M₁₆	C₂×C₄	1	4	yes	complemented
77	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃²×C₈	C₂³	1	2	yes	—
80	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
81	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
82	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
83	C₃²×C₄²	C₂³	1	2	yes	—
84	C₃×#217	C₂×C₄	1	2	yes	—
85	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
86	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
87	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
88	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
89	C₃×C₄×Dic₃	C₂³	1	2	yes	—
90	C₃×#208	C₂×C₄	1	4	yes	complemented
91	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
92	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
95	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	8	yes	complemented
96	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
97	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
98	C₃×D₃×C₈	C₂×C₄	1	8	yes	—
99	C₃×D₃×C₈	C₂×C₄	1	4	yes	complemented
100	C₃×D₃×C₈	C₂×C₄	1	4	yes	complemented
101	C₂×#405	—	3	1	no	Sylow
102	C₂³×C₃×C₄	—	3	1	no	—
103	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₃×M₁₆	—	2	1	no	—
105	C₂×C₃×M₁₆	—	3	1	no	—
106	C₂×C₃×M₁₆	—	3	8	no	—
107	C₂×C₃×M₁₆	—	3	2	no	—
108	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
109	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₃×C₈	—	2	1	no	—
111	C₂²×C₃×C₈	—	3	1	no	—
112	C₂²×C₃×C₈	—	3	8	no	—
113	C₂²×C₃×C₈	—	3	1	no	—
114	C₂²×C₃×C₈	—	3	1	no	—
115	C₂²×C₃×C₈	—	3	2	no	—
116	C₂²×C₃×C₈	—	3	1	no	—
117	C₂²×C₃×C₈	—	3	1	no	—
118	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
119	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
120	C₃×#117	—	2	1	no	—
121	C₃×#117	—	3	1	no	—
122	C₃×#117	—	3	2	no	—
123	C₃×#117	—	3	2	no	—
124	C₃×#117	—	3	2	no	—
125	C₃×#117	C₂×D₃	1	1	yes	characteristic
126	C₃×#117	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	—	3	2	no	—
128	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
129	C₂×C₃×C₄²	—	3	2	no	—
130	#926	C₂²×C₃	1	1	yes	characteristic
131	C₂×#208	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
133	D₃×M₁₆	C₃×C₄	1	8	yes	complemented
134	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
135	C₂×D₃×C₈	C₃×C₄	1	8	yes	complemented
136	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
137	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
138	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
139	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
140	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
141	#892	C₃×C₄	1	2	yes	—
142	D₃×C₄⋊C₄	C₃×C₄	1	2	yes	—
143	D₃×C₂²⋊C₄	C₃×C₄	1	2	yes	—
144	#877	C₃×C₄	1	2	yes	—
145	#872	C₂²×C₃	1	2	yes	—
146	C₄²×D₃	C₂²×C₃	1	2	yes	—
147	C₃×#97	—	2	2	no	—
148	C₃×#97	—	3	2	no	—
149	C₃×#97	—	3	2	no	—
150	C₃×#97	—	3	2	no	—
151	C₃×#97	C₂×D₃	1	2	yes	complemented
152	C₃×#97	C₂²×C₃	1	2	yes	complemented
153	C₃×C₄×C₈	—	2	2	no	—
154	C₃×C₄×C₈	—	3	2	no	—
155	C₃×C₄×C₈	—	3	2	no	—
156	C₃×C₄×C₈	—	3	2	no	—
157	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
158	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
159	#815	C₂²×C₃	1	2	yes	complemented
160	#815	C₂²×C₃	1	2	yes	complemented
161	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
162	C₈×Dic₃	C₂²×C₃	1	2	yes	complemented
163	#803	C₂²×C₃	1	2	yes	complemented
164	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
165	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₃×D₃	—	2	4	no	—
167	C₂²×C₃×D₃	C₄²	1	4	yes	—
168	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
171	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
173	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
174	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
175	C₂×C₃×Dic₃	C₄²	1	4	yes	—
176	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
177	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
179	C₃×C₄×D₃	—	2	8	no	—
180	C₃×C₄×D₃	C₄²	1	4	yes	—
181	C₃×C₄×D₃	C₄²	1	4	yes	—
182	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
183	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
184	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
185	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
186	C₃²×C₈	C₂²×C₄	1	2	yes	—
187	C₃²×C₈	C₂²×C₄	1	2	yes	—
188	C₃²×C₈	C₂²×C₄	1	4	yes	—
189	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
190	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
191	C₃×C₃⋊C₈	C₂²×C₄	1	4	yes	—
192	C₂²×M₁₆	—	3	1	no	—
193	C₂³×C₈	—	3	1	no	—
194	C₂×#117	—	3	1	no	—
195	#405	—	3	1	no	—
196	#405	—	3	1	no	—
197	#405	—	3	1	no	—
198	#405	—	3	2	no	—
199	#405	—	3	2	no	—
200	#405	C₃×D₃	1	1	yes	characteristic, direct product factor
201	C₂×#97	—	3	2	no	—
202	C₂×C₄×C₈	—	3	2	no	—
203	C₂⁴×C₃	—	3	1	no	—
204	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	3	1	no	—
207	C₂²×C₃×C₄	—	3	1	no	—
208	C₂²×C₃×C₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	3	4	no	—
210	C₂²×C₃×C₄	—	3	4	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	—	3	1	no	—
213	C₂²×C₃×C₄	—	3	4	no	—
214	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
217	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
218	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
219	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
220	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
221	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
222	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
224	C₃×M₁₆	—	2	4	no	—
225	C₃×M₁₆	—	3	4	no	—
226	C₃×M₁₆	—	3	8	no	—
227	C₃×M₁₆	C₄×D₃	1	4	yes	complemented
228	C₃×M₁₆	C₂×C₃×C₄	1	4	yes	complemented
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	4	no	—
234	C₂×C₃×C₈	—	3	1	no	—
235	C₂×C₃×C₈	—	3	2	no	—
236	C₂×C₃×C₈	—	3	1	no	—
237	C₂×C₃×C₈	—	3	4	no	—
238	C₂×C₃×C₈	—	3	4	no	—
239	C₂×C₃×C₈	—	3	8	no	—
240	C₂×C₃×C₈	—	3	4	no	—
241	C₂×C₃×C₈	—	3	4	no	—
242	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
243	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
244	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
245	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
248	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
249	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
250	C₃×C₄⋊C₄	—	2	2	no	—
251	C₃×C₄⋊C₄	—	3	4	no	—
252	C₃×C₄⋊C₄	—	3	2	no	—
253	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
254	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₂²⋊C₄	—	3	2	no	—
257	C₃×C₂²⋊C₄	—	3	4	no	—
258	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
259	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
260	C₃×C₄²	—	2	2	no	—
261	C₃×C₄²	—	3	4	no	—
262	C₃×C₄²	—	3	2	no	—
263	C₃×C₄²	C₂²×D₃	1	2	yes	—
264	C₃×C₄²	C₂³×C₃	1	2	yes	—
265	#217	C₂×C₃×C₄	1	2	yes	—
266	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
267	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
268	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
269	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
270	C₄×Dic₃	C₂³×C₃	1	2	yes	—
271	#208	C₂×C₃×C₄	1	4	yes	complemented
272	C₂×C₃⋊C₈	C₂×C₃×C₄	1	4	yes	complemented
273	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
275	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
276	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	8	yes	complemented
277	D₃×C₈	C₂×C₃×C₄	1	4	yes	—
278	D₃×C₈	C₂×C₃×C₄	1	4	yes	—
279	D₃×C₈	C₂×C₃×C₄	1	8	yes	—
280	D₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
281	D₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
282	C₂²×C₃²	—	2	2	no	—
283	C₂²×C₃²	C₂×C₄²	1	2	yes	—
284	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₃×D₃	—	2	2	no	—
286	C₂×C₃×D₃	—	2	8	no	—
287	C₂×C₃×D₃	C₂×C₄²	1	2	yes	—
288	C₂×C₃×D₃	C₂×C₄²	1	2	yes	—
289	C₂×C₃×D₃	#131	1	4	yes	—
290	C₃²×C₄	—	2	4	no	—
291	C₃²×C₄	C₂×C₄²	1	2	yes	—
292	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
293	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
294	C₃×Dic₃	—	2	4	no	—
295	C₃×Dic₃	C₂×C₄²	1	2	yes	—
296	C₃×Dic₃	C₂×C₄²	1	2	yes	—
297	C₂³×C₄	—	3	1	no	—
298	C₂×M₁₆	—	3	1	no	—
299	C₂×M₁₆	—	3	8	no	—
300	C₂×M₁₆	—	3	2	no	—
301	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
302	C₂²×C₈	—	3	1	no	—
303	C₂²×C₈	—	3	8	no	—
304	C₂²×C₈	—	3	1	no	—
305	C₂²×C₈	—	3	1	no	—
306	C₂²×C₈	—	3	1	no	—
307	C₂²×C₈	—	3	1	no	—
308	C₂²×C₈	—	3	2	no	—
309	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
310	#117	—	3	1	no	—
311	#117	—	3	2	no	—
312	#117	—	3	2	no	—
313	#117	—	3	2	no	—
314	#117	C₂×C₃×D₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	3	2	no	—
316	C₂×C₂²⋊C₄	—	3	2	no	—
317	C₂×C₄²	—	3	2	no	—
318	#97	—	3	2	no	—
319	#97	—	3	2	no	—
320	#97	—	3	2	no	—
321	#97	C₂×C₃×D₃	1	2	yes	complemented
322	C₄×C₈	—	3	2	no	—
323	C₄×C₈	—	3	2	no	—
324	C₄×C₈	—	3	2	no	—
325	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
326	C₂³×C₃	—	2	1	no	—
327	C₂³×C₃	—	3	1	no	—
328	C₂³×C₃	—	3	4	no	—
329	C₂³×C₃	—	3	1	no	—
330	C₂³×C₃	—	6	4	no	—
331	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
332	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
333	C₂²×D₃	—	2	4	no	—
334	C₂²×D₃	C₃×C₄²	1	4	yes	—
335	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
336	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	4	no	—
342	C₂×C₃×C₄	—	3	4	no	—
343	C₂×C₃×C₄	—	3	1	no	—
344	C₂×C₃×C₄	—	3	1	no	—
345	C₂×C₃×C₄	—	3	4	no	—
346	C₂×C₃×C₄	—	3	4	no	—
347	C₂×C₃×C₄	—	3	2	no	—
348	C₂×C₃×C₄	—	3	2	no	—
349	C₂×C₃×C₄	—	3	2	no	—
350	C₂×C₃×C₄	—	3	2	no	—
351	C₂×C₃×C₄	—	3	4	no	—
352	C₂×C₃×C₄	—	6	8	no	—
353	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
354	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
356	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
357	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
358	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
360	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
361	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
363	C₂×Dic₃	C₃×C₄²	1	4	yes	—
364	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
365	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
366	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
367	C₄×D₃	—	2	8	no	—
368	C₄×D₃	C₃×C₄²	1	4	yes	—
369	C₄×D₃	C₃×C₄²	1	4	yes	—
370	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
371	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
372	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
373	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
374	C₃×C₈	—	2	2	no	—
375	C₃×C₈	—	2	2	no	—
376	C₃×C₈	—	2	4	no	—
377	C₃×C₈	—	3	2	no	—
378	C₃×C₈	—	3	2	no	—
379	C₃×C₈	—	3	4	no	—
380	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
381	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
382	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
383	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
384	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
385	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
386	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
387	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
388	C₃⋊C₈	C₂²×C₃×C₄	1	4	yes	—
389	C₂×C₃²	—	2	2	no	—
390	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
391	C₂×C₃²	C₂×#131	1	2	yes	—
392	C₃×D₃	—	2	2	no	—
393	C₃×D₃	#405	1	4	yes	direct product factor
394	C₂⁴	—	3	1	no	—
395	C₂²×C₄	—	3	1	no	—
396	C₂²×C₄	—	3	1	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	—	3	1	no	—
399	C₂²×C₄	—	3	1	no	—
400	C₂²×C₄	—	3	4	no	—
401	C₂²×C₄	—	3	4	no	—
402	C₂²×C₄	—	3	4	no	—
403	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
404	M₁₆	—	3	4	no	—
405	M₁₆	—	3	8	no	—
406	M₁₆	C₃×C₄×D₃	1	4	yes	complemented
407	C₂×C₈	—	3	1	no	—
408	C₂×C₈	—	3	2	no	—
409	C₂×C₈	—	3	1	no	—
410	C₂×C₈	—	3	4	no	—
411	C₂×C₈	—	3	4	no	—
412	C₂×C₈	—	3	4	no	—
413	C₂×C₈	—	3	4	no	—
414	C₂×C₈	—	3	4	no	—
415	C₂×C₈	—	3	8	no	—
416	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
417	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
418	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
419	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
420	C₄⋊C₄	—	3	4	no	—
421	C₄⋊C₄	—	3	2	no	—
422	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
423	C₂²⋊C₄	—	3	2	no	—
424	C₂²⋊C₄	—	3	4	no	—
425	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
426	C₄²	—	3	2	no	—
427	C₄²	—	3	4	no	—
428	C₄²	C₂²×C₃×D₃	1	2	yes	—
429	C₂²×C₃	—	2	2	no	—
430	C₂²×C₃	—	2	2	no	—
431	C₂²×C₃	—	2	1	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	3	2	no	—
434	C₂²×C₃	—	3	4	no	—
435	C₂²×C₃	—	3	2	no	—
436	C₂²×C₃	—	4	2	no	—
437	C₂²×C₃	—	6	8	no	—
438	C₂²×C₃	—	6	2	no	—
439	C₂²×C₃	C₄²×D₃	1	2	yes	—
440	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
441	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
442	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
443	C₂×D₃	—	2	2	no	—
444	C₂×D₃	—	2	8	no	—
445	C₂×D₃	C₂×C₃×C₄²	1	2	yes	—
446	C₂×D₃	C₂×C₃×C₄²	1	2	yes	—
447	C₂×D₃	C₃×#131	1	4	yes	—
448	C₃×C₄	—	2	4	no	—
449	C₃×C₄	—	2	4	no	—
450	C₃×C₄	—	2	1	no	—
451	C₃×C₄	—	2	1	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	3	2	no	—
454	C₃×C₄	—	3	2	no	—
455	C₃×C₄	—	4	4	no	—
456	C₃×C₄	—	6	4	no	—
457	C₃×C₄	C₄²×D₃	1	2	yes	—
458	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
459	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
460	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
461	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
462	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
463	Dic₃	—	2	4	no	—
464	Dic₃	C₂×C₃×C₄²	1	2	yes	—
465	Dic₃	C₂×C₃×C₄²	1	2	yes	—
466	C₃²	C₂×#405	1	1	yes	characteristic, complemented, Sylow
467	C₂³	—	3	1	no	—
468	C₂³	—	3	1	no	—
469	C₂³	—	3	4	no	—
470	C₂³	—	6	4	no	—
471	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
472	C₂×C₄	—	3	1	no	—
473	C₂×C₄	—	3	1	no	—
474	C₂×C₄	—	3	4	no	—
475	C₂×C₄	—	3	2	no	—
476	C₂×C₄	—	3	2	no	—
477	C₂×C₄	—	3	2	no	—
478	C₂×C₄	—	3	2	no	—
479	C₂×C₄	—	3	4	no	—
480	C₂×C₄	—	3	4	no	—
481	C₂×C₄	—	3	4	no	—
482	C₂×C₄	—	6	8	no	—
483	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
484	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
485	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
486	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
487	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
488	C₈	—	3	2	no	—
489	C₈	—	3	2	no	—
490	C₈	—	3	4	no	—
491	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
492	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
493	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
494	C₂×C₃	—	2	2	no	—
495	C₂×C₃	—	2	2	no	—
496	C₂×C₃	—	2	2	no	—
497	C₂×C₃	—	2	1	no	—
498	C₂×C₃	—	3	4	no	—
499	C₂×C₃	—	4	2	no	—
500	C₂×C₃	—	6	2	no	—
501	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
502	C₂×C₃	D₃×#131	1	2	yes	—
503	C₂×C₃	C₂²×C₃×C₄²	1	1	yes	characteristic
504	C₂×C₃	C₂×C₃×#131	1	2	yes	—
505	D₃	—	2	2	no	—
506	D₃	C₃×#405	1	4	yes	direct product factor
507	C₂²	—	2	2	no	—
508	C₂²	—	3	4	no	—
509	C₂²	—	3	2	no	—
510	C₂²	—	3	2	no	—
511	C₂²	—	6	8	no	—
512	C₂²	—	6	2	no	—
513	C₂²	C₃×C₄²×D₃	1	2	yes	—
514	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
515	C₄	—	2	4	no	—
516	C₄	—	3	2	no	—
517	C₄	—	3	2	no	—
518	C₄	—	6	4	no	—
519	C₄	C₃×C₄²×D₃	1	2	yes	—
520	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
521	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
522	C₃	—	2	1	no	—
523	C₃	D₃×#405	1	1	yes	characteristic, direct product factor
524	C₃	C₂×C₃×#405	1	1	yes	characteristic, complemented
525	C₂	—	2	2	no	—
526	C₂	—	3	4	no	—
527	C₂	—	6	2	no	—
528	C₂	C₂×C₃×C₄²×D₃	1	1	yes	characteristic
529	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	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#405	D₃
hypocenter	C₃	C₂×C₃×#405
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×#5122	C₂	semidirect
6. C₃×#5101	C₂	semidirect
7. C₃×#4997	C₂	semidirect
8. C₃×#4708	C₂	semidirect
9. C₃×D₃×#97	C₂	semidirect
10. C₃×#4689	C₂	semidirect
11. C₃×C₄×D₃×C₈	C₂	semidirect
13. D₃×#405	C₃	direct (N × H)
21. C₃×D₃×M₁₆	C₄	semidirect
23. C₂×C₃×D₃×C₈	C₄	semidirect
35. C₃²×#97	C₂²	semidirect
36. C₃²×C₄×C₈	C₂²	semidirect
37. C₃×#815	C₂²	semidirect
38. C₃×#815	C₂²	semidirect
39. C₃×C₈×Dic₃	C₂²	semidirect
40. C₃×C₈×Dic₃	C₂²	semidirect
41. C₃×#803	C₂²	semidirect
42. C₃×C₄×C₃⋊C₈	C₂²	semidirect
55. C₃×#405	D₃	direct (N × H)
56. C₃×#405	C₂×C₃	semidirect
59. #5122	C₂×C₃	semidirect
60. #5101	C₂×C₃	semidirect
61. #4997	C₂×C₃	semidirect
62. #4708	C₂×C₃	semidirect
63. D₃×#97	C₂×C₃	semidirect
64. #4689	C₂×C₃	semidirect
65. C₄×D₃×C₈	C₂×C₃	semidirect
76. C₃²×M₁₆	C₂×C₄	semidirect
77. C₂×C₃²×C₈	C₂×C₄	semidirect
90. C₃×#208	C₂×C₄	semidirect
91. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
95. C₃×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
99. C₃×D₃×C₈	C₂×C₄	semidirect
100. C₃×D₃×C₈	C₂×C₄	semidirect
133. D₃×M₁₆	C₃×C₄	semidirect
135. C₂×D₃×C₈	C₃×C₄	semidirect
151. C₃×#97	C₂×D₃	semidirect
152. C₃×#97	C₂²×C₃	semidirect
157. C₃×C₄×C₈	C₂×D₃	semidirect
158. C₃×C₄×C₈	C₂²×C₃	semidirect
159. #815	C₂²×C₃	semidirect
160. #815	C₂²×C₃	semidirect
161. C₈×Dic₃	C₂²×C₃	semidirect
162. C₈×Dic₃	C₂²×C₃	semidirect
163. #803	C₂²×C₃	semidirect
164. C₄×C₃⋊C₈	C₂²×C₃	semidirect
200. #405	C₃×D₃	direct (N × H)
227. C₃×M₁₆	C₄×D₃	semidirect
228. C₃×M₁₆	C₂×C₃×C₄	semidirect
242. C₂×C₃×C₈	C₄×D₃	semidirect
243. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
271. #208	C₂×C₃×C₄	semidirect
272. C₂×C₃⋊C₈	C₂×C₃×C₄	semidirect
276. ΓL(1,𝔽₂₅)	C₂×C₃×C₄	semidirect
280. D₃×C₈	C₂×C₃×C₄	semidirect
281. D₃×C₈	C₂×C₃×C₄	semidirect
321. #97	C₂×C₃×D₃	semidirect
325. C₄×C₈	C₂×C₃×D₃	semidirect
393. C₃×D₃	#405	direct (N × H)
406. M₁₆	C₃×C₄×D₃	semidirect
416. C₂×C₈	C₃×C₄×D₃	semidirect
466. C₃²	C₂×#405	semidirect
506. D₃	C₃×#405	direct (N × H)
523. C₃	D₃×#405	direct (N × H)
524. C₃	C₂×C₃×#405	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×M₁₆	2
C₂²×C₃×D₃×C₈	2
C₃×D₃×#117	2
C₃²×#405	2
C₃×#5122	2
C₃×#5101	2
C₃×#4997	2
C₃×#4708	2
C₃×D₃×#97	2
C₃×#4689	2
C₃×C₄×D₃×C₈	2
C₂×C₃×#405	3
D₃×#405	3

Subgroups — C3×D3×#405 #11857171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#405 #11857171