Subgroups — C₃×D₃×#423 #11858233

Order 1152.

1215 conjugacy classes of subgroups.

The subgroup lattice has 480 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	2	yes	maximal
2	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
3	C₃²×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5118	C₂	1	2	yes	maximal, complemented
5	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4837	C₂	1	4	yes	maximal, complemented
7	C₃×D₃×C₄⋊C₈	C₂	1	4	yes	maximal, complemented
8	C₂×C₃×#423	—	3	1	no	maximal
9	D₃×#423	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×C₄×D₃	C₄	1	2	yes	—
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₃	C₄	1	2	yes	—
15	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₃×#208	C₂²	1	2	yes	—
17	C₃×D₃×M₁₆	—	2	8	no	—
18	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
19	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
20	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
21	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
22	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
23	C₃×C₄²×D₃	C₄	1	1	yes	characteristic
24	C₃×C₄²×D₃	C₂²	1	2	yes	—
25	C₃×C₄²×D₃	C₂²	1	2	yes	—
26	C₃²×C₄⋊C₈	C₂²	1	4	yes	complemented
27	C₃×Dic₃⋊C₈	C₂²	1	8	yes	complemented
28	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
29	C₂²×C₃×M₁₆	—	3	2	no	—
30	C₂²×C₃×C₄²	—	3	1	no	—
31	C₂×D₃×M₁₆	C₂×C₃	1	2	yes	—
32	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
33	C₃×#423	—	2	1	no	—
34	C₃×#423	—	3	2	no	—
35	C₃×#423	—	3	1	no	—
36	C₃×#423	—	3	4	no	—
37	C₃×#423	D₃	1	1	yes	characteristic, direct product factor
38	C₃×#423	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄⋊C₈	—	3	4	no	—
40	#5118	C₂×C₃	1	2	yes	complemented
41	#4924	C₂×C₃	1	1	yes	characteristic, complemented
42	#4837	C₂×C₃	1	4	yes	complemented
43	D₃×C₄⋊C₈	C₂×C₃	1	4	yes	complemented
44	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
46	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
48	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₄×D₃	—	2	8	no	—
50	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
51	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
52	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
53	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₄×D₃	D₄	1	4	yes	—
57	C₂×C₃×C₄×D₃	Q₈	1	4	yes	—
58	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
60	C₃²×M₁₆	—	2	4	no	—
61	C₂×C₃²×C₈	C₂³	1	4	yes	—
62	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
63	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
64	C₃²×C₄²	C₂³	1	2	yes	—
65	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
66	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
68	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
69	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
70	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄×Dic₃	C₂³	1	2	yes	—
72	C₃×#208	—	2	4	no	—
73	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
74	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
75	C₃×D₃×C₈	—	2	8	no	—
76	C₂×#423	—	3	1	no	Sylow
77	C₂³×C₃×C₄	—	3	1	no	—
78	C₂³×C₃×C₄	—	3	2	no	—
79	C₂²×C₄×D₃	C₃×C₄	1	2	yes	—
80	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×M₁₆	—	2	2	no	—
82	C₂×C₃×M₁₆	—	3	2	no	—
83	C₂×C₃×M₁₆	—	3	4	no	—
84	C₂×C₃×M₁₆	—	6	8	no	—
85	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
86	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
87	C₂²×C₃×C₈	—	3	4	no	—
88	C₂×C₃×C₄²	—	2	1	no	—
89	C₂×C₃×C₄²	—	3	2	no	—
90	C₂×C₃×C₄²	—	3	1	no	—
91	C₂×C₃×C₄²	—	3	1	no	—
92	C₂×C₃×C₄²	—	3	1	no	—
93	C₂×C₃×C₄²	—	3	1	no	—
94	C₂×C₃×C₄²	—	3	1	no	—
95	C₂×C₃×C₄²	—	3	2	no	—
96	C₂×C₃×C₄²	—	3	2	no	—
97	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
98	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄×Dic₃	C₃×C₄	1	2	yes	—
100	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
101	C₂×#208	C₂²×C₃	1	2	yes	—
102	D₃×M₁₆	—	2	8	no	—
103	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
104	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
105	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
106	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
107	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
108	C₄²×D₃	C₃×C₄	1	1	yes	characteristic
109	C₄²×D₃	C₂²×C₃	1	2	yes	—
110	C₄²×D₃	C₂²×C₃	1	2	yes	—
111	C₃×C₄⋊C₈	—	2	4	no	—
112	C₃×C₄⋊C₈	—	3	8	no	—
113	C₃×C₄⋊C₈	—	3	4	no	—
114	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
115	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
116	Dic₃⋊C₈	C₂²×C₃	1	8	yes	complemented
117	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
118	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₃×D₃	—	2	4	no	—
120	C₂²×C₃×D₃	C₄⋊C₄	1	4	yes	—
121	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	—	2	4	no	—
124	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
125	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
127	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
128	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
129	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
130	C₂×C₃×Dic₃	—	2	4	no	—
131	C₂×C₃×Dic₃	C₄⋊C₄	1	4	yes	—
132	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
133	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
136	C₃×C₄×D₃	—	2	4	no	—
137	C₃×C₄×D₃	—	2	4	no	—
138	C₃×C₄×D₃	—	2	4	no	—
139	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
140	C₃×C₄×D₃	C₄⋊C₄	1	4	yes	—
141	C₃×C₄×D₃	M₁₆	1	8	yes	complemented
142	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
143	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
144	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
145	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
146	C₃²×C₈	—	2	4	no	—
147	C₃×C₃⋊C₈	—	2	4	no	—
148	C₂²×M₁₆	—	3	2	no	—
149	C₂²×C₄²	—	3	1	no	—
150	#423	—	3	2	no	—
151	#423	—	3	1	no	—
152	#423	—	3	4	no	—
153	#423	C₃×D₃	1	1	yes	characteristic, direct product factor
154	C₂×C₄⋊C₈	—	3	4	no	—
155	C₂⁴×C₃	—	3	1	no	—
156	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	—	2	2	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	3	1	no	—
160	C₂²×C₃×C₄	—	3	1	no	—
161	C₂²×C₃×C₄	—	3	1	no	—
162	C₂²×C₃×C₄	—	3	2	no	—
163	C₂²×C₃×C₄	—	3	4	no	—
164	C₂²×C₃×C₄	—	3	4	no	—
165	C₂²×C₃×C₄	—	3	1	no	—
166	C₂²×C₃×C₄	—	3	1	no	—
167	C₂²×C₃×C₄	—	3	2	no	—
168	C₂²×C₃×C₄	—	3	2	no	—
169	C₂²×C₃×C₄	—	3	2	no	—
170	C₂²×C₃×C₄	—	3	2	no	—
171	C₂²×C₃×C₄	—	6	8	no	—
172	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
173	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
174	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
177	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
178	C₂×C₄×D₃	—	2	8	no	—
179	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
180	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
181	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
182	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
184	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
185	C₂×C₄×D₃	C₃×D₄	1	4	yes	—
186	C₂×C₄×D₃	C₃×Q₈	1	4	yes	—
187	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
189	C₃×M₁₆	—	2	4	no	—
190	C₃×M₁₆	—	2	4	no	—
191	C₃×M₁₆	—	4	4	no	—
192	C₃×M₁₆	—	6	8	no	—
193	C₃×M₁₆	—	6	4	no	—
194	C₂×C₃×C₈	—	2	4	no	—
195	C₂×C₃×C₈	—	3	4	no	—
196	C₂×C₃×C₈	—	6	8	no	—
197	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
198	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₃×C₄²	—	2	2	no	—
202	C₃×C₄²	—	3	2	no	—
203	C₃×C₄²	—	3	1	no	—
204	C₃×C₄²	—	3	2	no	—
205	C₃×C₄²	—	3	2	no	—
206	C₃×C₄²	—	3	2	no	—
207	C₃×C₄²	—	3	1	no	—
208	C₃×C₄²	—	3	2	no	—
209	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
210	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
211	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
212	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
213	C₃×C₄²	C₂²×D₃	1	2	yes	—
214	C₃×C₄²	C₂³×C₃	1	2	yes	—
215	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
216	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
217	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
218	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
219	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
220	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
221	C₄×Dic₃	C₂³×C₃	1	2	yes	—
222	#208	—	2	4	no	—
223	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
224	ΓL(1,𝔽₂₅)	—	2	8	no	—
225	D₃×C₈	—	2	8	no	—
226	C₂²×C₃²	—	2	2	no	—
227	C₂²×C₃²	C₂×C₄⋊C₄	1	2	yes	—
228	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₃×D₃	—	2	2	no	—
230	C₂×C₃×D₃	—	2	8	no	—
231	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
232	C₂×C₃×D₃	C₂×C₄⋊C₄	1	2	yes	—
233	C₂×C₃×D₃	C₂×M₁₆	1	4	yes	—
234	C₃²×C₄	—	2	2	no	—
235	C₃²×C₄	C₂×C₄⋊C₄	1	2	yes	—
236	C₃²×C₄	C₂×M₁₆	1	4	yes	complemented
237	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
238	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
239	C₃×Dic₃	—	2	2	no	—
240	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
241	C₃×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
242	C₃×Dic₃	C₂×M₁₆	1	4	yes	complemented
243	C₂³×C₄	—	3	1	no	—
244	C₂³×C₄	—	3	2	no	—
245	C₂×M₁₆	—	3	2	no	—
246	C₂×M₁₆	—	3	4	no	—
247	C₂×M₁₆	—	6	8	no	—
248	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
249	C₂²×C₈	—	3	4	no	—
250	C₂×C₄²	—	3	2	no	—
251	C₂×C₄²	—	3	1	no	—
252	C₂×C₄²	—	3	1	no	—
253	C₂×C₄²	—	3	1	no	—
254	C₂×C₄²	—	3	1	no	—
255	C₂×C₄²	—	3	1	no	—
256	C₂×C₄²	—	3	2	no	—
257	C₂×C₄²	—	3	2	no	—
258	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
259	C₄⋊C₈	—	3	8	no	—
260	C₄⋊C₈	—	3	4	no	—
261	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
262	C₂³×C₃	—	2	1	no	—
263	C₂³×C₃	—	3	1	no	—
264	C₂³×C₃	—	3	4	no	—
265	C₂³×C₃	—	3	1	no	—
266	C₂³×C₃	—	6	4	no	—
267	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
268	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
269	C₂²×D₃	—	2	4	no	—
270	C₂²×D₃	C₃×C₄⋊C₄	1	4	yes	—
271	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
272	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
273	C₂×C₃×C₄	—	2	4	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	3	4	no	—
282	C₂×C₃×C₄	—	3	2	no	—
283	C₂×C₃×C₄	—	3	1	no	—
284	C₂×C₃×C₄	—	3	1	no	—
285	C₂×C₃×C₄	—	3	4	no	—
286	C₂×C₃×C₄	—	3	4	no	—
287	C₂×C₃×C₄	—	3	8	no	—
288	C₂×C₃×C₄	—	3	2	no	—
289	C₂×C₃×C₄	—	3	2	no	—
290	C₂×C₃×C₄	—	3	2	no	—
291	C₂×C₃×C₄	—	3	2	no	—
292	C₂×C₃×C₄	—	3	2	no	—
293	C₂×C₃×C₄	—	4	4	no	—
294	C₂×C₃×C₄	—	6	4	no	—
295	C₂×C₃×C₄	—	6	4	no	—
296	C₂×C₃×C₄	—	6	4	no	—
297	C₂×C₃×C₄	—	6	4	no	—
298	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
299	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
301	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
302	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
303	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
304	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
308	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
310	C₂×Dic₃	—	2	4	no	—
311	C₂×Dic₃	C₃×C₄⋊C₄	1	4	yes	—
312	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
313	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
314	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
316	C₄×D₃	—	2	4	no	—
317	C₄×D₃	—	2	4	no	—
318	C₄×D₃	—	2	4	no	—
319	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
320	C₄×D₃	C₃×C₄⋊C₄	1	4	yes	—
321	C₄×D₃	C₃×M₁₆	1	8	yes	complemented
322	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
323	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
324	C₄×D₃	C₂×C₃×Q₈	1	2	yes	—
325	C₄×D₃	C₂×C₃×Q₈	1	2	yes	—
326	C₃×C₈	—	2	4	no	—
327	C₃×C₈	—	2	4	no	—
328	C₃×C₈	—	4	4	no	—
329	C₃×C₈	—	6	4	no	—
330	C₃⋊C₈	—	2	4	no	—
331	C₂×C₃²	—	2	2	no	—
332	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₃²	C₂²×M₁₆	1	2	yes	—
334	C₃×D₃	—	2	2	no	—
335	C₃×D₃	#423	1	4	yes	direct product factor
336	C₂⁴	—	3	1	no	—
337	C₂²×C₄	—	3	1	no	—
338	C₂²×C₄	—	3	1	no	—
339	C₂²×C₄	—	3	1	no	—
340	C₂²×C₄	—	3	1	no	—
341	C₂²×C₄	—	3	1	no	—
342	C₂²×C₄	—	3	2	no	—
343	C₂²×C₄	—	3	4	no	—
344	C₂²×C₄	—	3	4	no	—
345	C₂²×C₄	—	3	2	no	—
346	C₂²×C₄	—	3	2	no	—
347	C₂²×C₄	—	3	2	no	—
348	C₂²×C₄	—	3	2	no	—
349	C₂²×C₄	—	6	8	no	—
350	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
351	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
352	M₁₆	—	2	4	no	—
353	M₁₆	—	6	8	no	—
354	M₁₆	—	6	4	no	—
355	C₂×C₈	—	3	4	no	—
356	C₂×C₈	—	6	8	no	—
357	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
358	C₄²	—	3	2	no	—
359	C₄²	—	3	2	no	—
360	C₄²	—	3	1	no	—
361	C₄²	—	3	2	no	—
362	C₄²	—	3	2	no	—
363	C₄²	—	3	2	no	—
364	C₄²	—	3	1	no	—
365	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
366	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
367	C₄²	C₂²×C₃×D₃	1	2	yes	—
368	C₂²×C₃	—	2	2	no	—
369	C₂²×C₃	—	2	2	no	—
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	—	3	4	no	—
373	C₂²×C₃	—	3	2	no	—
374	C₂²×C₃	—	3	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	—	6	8	no	—
377	C₂²×C₃	—	6	2	no	—
378	C₂²×C₃	D₃×C₄⋊C₄	1	2	yes	—
379	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
380	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
381	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
382	C₂×D₃	—	2	2	no	—
383	C₂×D₃	—	2	8	no	—
384	C₂×D₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
385	C₂×D₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
386	C₂×D₃	C₂×C₃×M₁₆	1	4	yes	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	4	no	—
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	3	4	no	—
394	C₃×C₄	—	3	2	no	—
395	C₃×C₄	—	3	2	no	—
396	C₃×C₄	—	4	2	no	—
397	C₃×C₄	—	6	2	no	—
398	C₃×C₄	D₃×C₄⋊C₄	1	2	yes	—
399	C₃×C₄	D₃×M₁₆	1	4	yes	complemented
400	C₃×C₄	C₂×C₃×C₄⋊C₄	1	2	yes	—
401	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	complemented
402	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
403	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
404	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
405	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
406	Dic₃	—	2	2	no	—
407	Dic₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
408	Dic₃	C₂×C₃×C₄⋊C₄	1	2	yes	—
409	Dic₃	C₂×C₃×M₁₆	1	4	yes	complemented
410	C₃²	C₂×#423	1	1	yes	characteristic, complemented, Sylow
411	C₂³	—	3	1	no	—
412	C₂³	—	3	4	no	—
413	C₂³	—	3	1	no	—
414	C₂³	—	6	4	no	—
415	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	3	4	no	—
418	C₂×C₄	—	3	2	no	—
419	C₂×C₄	—	3	1	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	4	no	—
422	C₂×C₄	—	3	4	no	—
423	C₂×C₄	—	3	8	no	—
424	C₂×C₄	—	3	2	no	—
425	C₂×C₄	—	3	2	no	—
426	C₂×C₄	—	3	2	no	—
427	C₂×C₄	—	3	2	no	—
428	C₂×C₄	—	3	2	no	—
429	C₂×C₄	—	6	4	no	—
430	C₂×C₄	—	6	4	no	—
431	C₂×C₄	—	6	4	no	—
432	C₂×C₄	—	6	4	no	—
433	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
434	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
435	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
436	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
437	C₂×C₄	C₃×D₃×Q₈	1	2	yes	—
438	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
439	C₈	—	2	4	no	—
440	C₈	—	6	4	no	—
441	C₂×C₃	—	2	2	no	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	—	2	2	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	3	4	no	—
446	C₂×C₃	—	4	2	no	—
447	C₂×C₃	—	6	2	no	—
448	C₂×C₃	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
449	C₂×C₃	C₂×D₃×M₁₆	1	2	yes	—
450	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
451	C₂×C₃	C₂²×C₃×M₁₆	1	2	yes	—
452	D₃	—	2	2	no	—
453	D₃	C₃×#423	1	4	yes	direct product factor
454	C₂²	—	2	2	no	—
455	C₂²	—	3	4	no	—
456	C₂²	—	3	2	no	—
457	C₂²	—	3	2	no	—
458	C₂²	—	6	8	no	—
459	C₂²	—	6	2	no	—
460	C₂²	C₃×D₃×C₄⋊C₄	1	2	yes	—
461	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	3	4	no	—
464	C₄	—	3	2	no	—
465	C₄	—	3	2	no	—
466	C₄	—	6	2	no	—
467	C₄	C₃×D₃×C₄⋊C₄	1	2	yes	—
468	C₄	C₃×D₃×M₁₆	1	4	yes	complemented
469	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
470	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
471	C₃	—	2	1	no	—
472	C₃	D₃×#423	1	1	yes	characteristic, direct product factor
473	C₃	C₂×C₃×#423	1	1	yes	characteristic, complemented
474	C₂	—	2	2	no	—
475	C₂	—	3	4	no	—
476	C₂	—	6	2	no	—
477	C₂	C₂×C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
478	C₂	C₂×C₃×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#423	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#423	D₃
hypocenter	C₃	C₂×C₃×#423
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#423

Complements

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

N	H ≅ G/N	type
3. C₃²×#423	C₂	semidirect
4. C₃×#5118	C₂	semidirect
5. C₃×#4924	C₂	semidirect
6. C₃×#4837	C₂	semidirect
7. C₃×D₃×C₄⋊C₈	C₂	semidirect
9. D₃×#423	C₃	direct (N × H)
26. C₃²×C₄⋊C₈	C₂²	semidirect
27. C₃×Dic₃⋊C₈	C₂²	semidirect
28. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
37. C₃×#423	D₃	direct (N × H)
38. C₃×#423	C₂×C₃	semidirect
40. #5118	C₂×C₃	semidirect
41. #4924	C₂×C₃	semidirect
42. #4837	C₂×C₃	semidirect
43. D₃×C₄⋊C₈	C₂×C₃	semidirect
114. C₃×C₄⋊C₈	C₂×D₃	semidirect
115. C₃×C₄⋊C₈	C₂²×C₃	semidirect
116. Dic₃⋊C₈	C₂²×C₃	semidirect
117. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
141. C₃×C₄×D₃	M₁₆	semidirect
153. #423	C₃×D₃	direct (N × H)
236. C₃²×C₄	C₂×M₁₆	semidirect
242. C₃×Dic₃	C₂×M₁₆	semidirect
261. C₄⋊C₈	C₂×C₃×D₃	semidirect
321. C₄×D₃	C₃×M₁₆	semidirect
335. C₃×D₃	#423	direct (N × H)
399. C₃×C₄	D₃×M₁₆	semidirect
401. C₃×C₄	C₂×C₃×M₁₆	semidirect
409. Dic₃	C₂×C₃×M₁₆	semidirect
410. C₃²	C₂×#423	semidirect
453. D₃	C₃×#423	direct (N × H)
468. C₄	C₃×D₃×M₁₆	semidirect
472. C₃	D₃×#423	direct (N × H)
473. C₃	C₂×C₃×#423	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
C₂×C₃×C₄²×D₃	2
C₃²×#423	2
C₃×#5118	2
C₃×#4924	2
C₃×#4837	2
C₃×D₃×C₄⋊C₈	2
C₂×C₃×#423	3
D₃×#423	3

Subgroups — C3×D3×#423 #11858233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#423 #11858233