Subgroups — D₃×#4515 #11796089

Order 1152.

476 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#901	C₂	1	1	yes	maximal, characteristic
2	C₃×D₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#10589381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4515	C₂	1	1	yes	maximal, characteristic, complemented
6	#10589113	C₂	1	1	yes	maximal, characteristic, complemented
7	#10589111	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#4515	—	3	1	no	maximal
9	D₃×#350	—	3	1	no	maximal
10	D₃×#235	C₄	1	1	yes	characteristic
11	#64110	C₂²	1	1	yes	characteristic
12	C₃×#901	C₂²	1	1	yes	characteristic
13	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
14	#63817	C₄	1	1	yes	characteristic
15	#63814	C₄	1	1	yes	characteristic
16	D₃×#208	C₄	1	1	yes	characteristic
17	#63804	—	2	1	no	—
18	#63803	—	2	1	no	—
19	D₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
20	D₃²×C₈	—	2	1	no	—
21	C₃²×M₃₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃⋊(C₃⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
23	C₃×#812	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃×#798	—	2	1	no	—
26	C₃×D₃×C₁₆	—	2	1	no	—
27	D₃×C₃⋊C₁₆	—	2	1	no	—
28	D₃×C₃⋊C₁₆	—	2	1	no	—
29	D₃×#131	—	3	1	no	—
30	C₂×#901	—	3	1	no	—
31	C₂×C₃×M₃₂	—	3	1	no	—
32	C₂²×C₃⋊C₁₆	—	3	1	no	—
33	D₃×M₃₂	D₃	1	1	yes	characteristic, complemented
34	C₂×D₃×C₁₆	—	3	1	no	—
35	C₃×#350	—	3	1	no	—
36	#4561	—	3	1	no	—
37	#4515	—	3	1	no	—
38	#4515	—	3	1	no	—
39	#4515	—	3	1	no	—
40	#4515	—	3	1	no	—
41	#4515	—	6	1	no	—
42	#4515	D₃	1	1	yes	characteristic, direct product factor
43	#4508	—	3	1	no	—
44	#3828	C₂×C₄	1	1	yes	characteristic
45	C₃×#235	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
47	D₃×#67	—	2	1	no	—
48	#3804	—	2	1	no	—
49	D₃×D₁₂	C₈	1	1	yes	characteristic
50	C₄×D₃²	—	2	1	no	—
51	#3799	C₈	1	1	yes	characteristic
52	#3798	—	2	1	no	—
53	#3795	C₈	1	1	yes	characteristic
54	D₃×Dic₆	C₈	1	1	yes	characteristic
55	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
56	#3748	C₂×C₄	1	1	yes	characteristic
57	#3743	—	2	1	no	—
58	C₈×C₃⋊D₃	—	2	1	no	—
59	C₃×#208	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
62	C₃×D₃×C₈	—	2	1	no	—
63	C₃×D₃×C₈	D₄	1	1	yes	characteristic
64	C₃×D₃×C₈	D₄	1	1	yes	characteristic
65	C₃×D₃×C₈	D₄	1	1	yes	characteristic
66	C₃×D₃×C₈	D₄	1	1	yes	characteristic
67	#3712	—	2	1	no	—
68	#3711	—	2	1	no	—
69	#3711	—	2	1	no	—
70	#3710	—	2	1	no	—
71	D₃×C₃⋊C₈	—	2	1	no	—
72	D₃×C₃⋊C₈	—	2	1	no	—
73	C₃²×C₁₆	—	2	1	no	—
74	C₃⋊(C₃⋊C₁₆)	—	2	1	no	—
75	C₃×C₃⋊C₁₆	—	2	1	no	—
76	C₃×C₃⋊C₁₆	—	2	1	no	—
77	C₂×#350	—	9	1	no	Sylow
78	D₃×#41	—	3	1	no	—
79	C₂×#235	—	3	1	no	—
80	C₃×#131	—	3	1	no	—
81	C₂²×C₃×C₈	—	3	1	no	—
82	#948	—	3	1	no	—
83	C₂×#208	—	3	1	no	—
84	#907	—	3	1	no	—
85	#907	—	6	1	no	—
86	D₃×M₁₆	—	3	1	no	—
87	D₃×M₁₆	—	6	1	no	—
88	#901	—	3	1	no	—
89	#901	—	3	1	no	—
90	#901	—	3	1	no	—
91	#901	—	3	1	no	—
92	#901	—	6	1	no	—
93	#901	—	6	1	no	—
94	#901	—	6	1	no	—
95	#901	—	6	1	no	—
96	#901	C₂×D₃	1	1	yes	characteristic
97	C₂×ΓL(1,𝔽₂₅)	—	6	1	no	—
98	C₂×D₃×C₈	—	6	1	no	—
99	C₂×D₃×C₈	—	6	1	no	—
100	C₂×D₃×C₈	C₂×D₃	1	1	yes	characteristic
101	C₃×M₃₂	—	2	1	no	—
102	C₃×M₃₂	—	3	1	no	—
103	C₃×M₃₂	—	6	1	no	—
104	C₃×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
105	C₃×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
106	C₂×C₃×C₁₆	—	3	1	no	—
107	C₂×C₃×C₁₆	—	6	1	no	—
108	#812	C₂×D₃	1	1	yes	characteristic, complemented
109	C₂×C₃⋊C₁₆	—	3	1	no	—
110	C₂×C₃⋊C₁₆	—	3	1	no	—
111	C₂×C₃⋊C₁₆	—	6	1	no	—
112	C₂×C₃⋊C₁₆	—	6	1	no	—
113	C₂×C₃⋊C₁₆	—	6	1	no	—
114	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic, complemented
115	#798	—	2	1	no	—
116	D₃×C₁₆	—	2	1	no	—
117	D₃×C₁₆	—	6	1	no	—
118	D₃×C₁₆	—	6	1	no	—
119	C₂²×C₃×D₃	M₁₆	1	1	yes	characteristic
120	C₂×D₃²	—	2	1	no	—
121	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
122	#638	—	2	1	no	—
123	C₄⋊(C₃⋊D₃)	C₂×C₈	1	1	yes	characteristic
124	C₄×C₃⋊D₃	—	2	1	no	—
125	#634	C₂×C₈	1	1	yes	characteristic
126	C₃×#67	—	2	1	no	—
127	C₂×C₃×Dic₃	M₁₆	1	1	yes	characteristic
128	C₃×D₁₂	C₂×C₈	1	1	yes	characteristic
129	C₃×C₄×D₃	—	2	1	no	—
130	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₃×C₄×D₃	C₂×C₈	1	1	yes	characteristic
133	C₃×C₄×D₃	C₂×C₈	1	1	yes	characteristic
134	C₃×Dic₆	C₂×C₈	1	1	yes	characteristic
135	#627	—	2	1	no	—
136	#626	—	2	1	no	—
137	#626	—	2	1	no	—
138	#625	—	2	1	no	—
139	#624	—	2	1	no	—
140	D₃×Dic₃	—	2	1	no	—
141	D₃×Dic₃	—	2	1	no	—
142	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
143	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
144	C₃⋊(C₃⋊C₈)	—	2	1	no	—
145	C₃×C₃⋊C₈	—	2	1	no	—
146	C₃×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
147	C₃×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×#131	—	9	1	no	—
149	C₂×M₃₂	—	3	1	no	—
150	C₂²×C₁₆	—	9	1	no	—
151	#350	—	3	1	no	—
152	#350	—	9	1	no	—
153	#350	—	9	1	no	—
154	#350	—	9	1	no	—
155	C₃×#41	—	3	1	no	—
156	C₂²×C₃×C₄	—	3	1	no	—
157	C₂×#67	—	6	1	no	—
158	#239	—	3	1	no	—
159	D₃×Q₈	—	3	1	no	—
160	#237	—	3	1	no	—
161	#237	—	6	1	no	—
162	D₃×D₄	—	3	1	no	—
163	D₃×D₄	—	6	1	no	—
164	#235	—	3	1	no	—
165	#235	—	3	1	no	—
166	#235	—	3	1	no	—
167	#235	—	3	1	no	—
168	#235	—	6	1	no	—
169	#235	—	6	1	no	—
170	#235	—	6	1	no	—
171	#235	—	6	1	no	—
172	#235	C₄×D₃	1	1	yes	characteristic
173	C₂×D₁₂	—	3	1	no	—
174	C₂×C₄×D₃	—	6	1	no	—
175	C₂×C₄×D₃	—	6	1	no	—
176	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
177	C₂×Dic₆	—	3	1	no	—
178	C₃×M₁₆	—	3	1	no	—
179	C₃×M₁₆	—	6	1	no	—
180	C₂×C₃×C₈	—	2	1	no	—
181	C₂×C₃×C₈	—	3	1	no	—
182	C₂×C₃×C₈	—	3	1	no	—
183	C₂×C₃×C₈	—	3	1	no	—
184	C₂×C₃×C₈	—	3	1	no	—
185	C₂×C₃×C₈	—	3	1	no	—
186	C₂×C₃×C₈	—	6	1	no	—
187	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
188	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
189	#208	—	3	1	no	—
190	#208	—	3	1	no	—
191	#208	—	6	1	no	—
192	#208	—	6	1	no	—
193	#208	—	6	1	no	—
194	#208	C₄×D₃	1	1	yes	characteristic
195	C₂×C₃⋊C₈	—	6	1	no	—
196	C₂×C₃⋊C₈	—	6	1	no	—
197	C₂×C₃⋊C₈	C₄×D₃	1	1	yes	characteristic
198	ΓL(1,𝔽₂₅)	—	2	1	no	—
199	ΓL(1,𝔽₂₅)	—	6	1	no	—
200	ΓL(1,𝔽₂₅)	—	6	1	no	—
201	ΓL(1,𝔽₂₅)	—	6	1	no	—
202	ΓL(1,𝔽₂₅)	—	6	1	no	—
203	ΓL(1,𝔽₂₅)	—	6	1	no	—
204	ΓL(1,𝔽₂₅)	—	6	1	no	—
205	ΓL(1,𝔽₂₅)	—	12	1	no	—
206	D₃×C₈	—	2	1	no	—
207	D₃×C₈	—	6	1	no	—
208	D₃×C₈	—	6	1	no	—
209	D₃×C₈	—	6	1	no	—
210	D₃×C₈	—	6	1	no	—
211	D₃×C₈	—	6	1	no	—
212	D₃×C₈	—	6	1	no	—
213	D₃×C₈	—	12	1	no	—
214	D₃×C₈	D₁₂	1	1	yes	characteristic
215	D₃×C₈	D₁₂	1	1	yes	characteristic
216	D₃×C₈	#67	1	1	yes	characteristic
217	D₃×C₈	#67	1	1	yes	characteristic
218	C₃×C₁₆	—	2	1	no	—
219	C₃×C₁₆	—	2	1	no	—
220	C₃×C₁₆	—	4	1	no	—
221	C₃×C₁₆	—	6	1	no	—
222	C₃×C₁₆	—	6	1	no	—
223	C₃⋊C₁₆	—	2	1	no	—
224	C₃⋊C₁₆	—	2	1	no	—
225	C₃⋊C₁₆	—	6	1	no	—
226	C₃⋊C₁₆	—	6	1	no	—
227	C₃⋊C₁₆	—	12	1	no	—
228	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
229	C₂×C₃⋊D₃	—	2	1	no	—
230	C₂×C₃×D₃	—	2	2	no	—
231	C₂×C₃×D₃	—	2	1	no	—
232	C₂×C₃×D₃	C₂²⋊C₈	1	1	yes	characteristic
233	C₂×C₃×D₃	C₂²⋊C₈	1	1	yes	characteristic
234	D₃²	—	4	2	no	—
235	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
237	C₃⋊Dic₃	—	2	1	no	—
238	C₃×Dic₃	—	2	1	no	—
239	C₃×Dic₃	C₂²⋊C₈	1	1	yes	characteristic
240	C₃×Dic₃	C₂²⋊C₈	1	1	yes	characteristic
241	C₂×#41	—	9	1	no	—
242	#131	—	3	1	no	—
243	#131	—	9	1	no	—
244	#131	—	9	1	no	—
245	#131	—	9	1	no	—
246	#131	—	18	1	no	—
247	#131	—	18	1	no	—
248	C₂×M₁₆	—	9	1	no	—
249	C₂×M₁₆	—	18	1	no	—
250	C₂²×C₈	—	3	1	no	—
251	C₂²×C₈	—	18	1	no	—
252	M₃₂	—	3	1	no	—
253	M₃₂	—	6	1	no	—
254	M₃₂	D₃²	1	1	yes	characteristic, complemented
255	C₂×C₁₆	—	3	1	no	—
256	C₂×C₁₆	—	6	1	no	—
257	C₂×C₁₆	—	9	1	no	—
258	C₂×C₁₆	—	18	1	no	—
259	C₂×C₁₆	—	18	1	no	—
260	C₂³×C₃	—	3	1	no	—
261	C₂²×D₃	—	6	1	no	—
262	C₂²×D₃	—	6	1	no	—
263	C₂²×D₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
264	C₃×Q₈	—	3	1	no	—
265	C₃×D₄	—	3	1	no	—
266	C₃×D₄	—	6	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	3	1	no	—
269	C₂×C₃×C₄	—	3	1	no	—
270	C₂×C₃×C₄	—	3	1	no	—
271	C₂×C₃×C₄	—	3	1	no	—
272	C₂×C₃×C₄	—	3	1	no	—
273	C₂×C₃×C₄	—	6	1	no	—
274	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
276	#67	—	2	1	no	—
277	#67	—	6	1	no	—
278	#67	—	6	1	no	—
279	#67	—	6	1	no	—
280	#67	—	6	1	no	—
281	#67	—	6	1	no	—
282	#67	—	6	1	no	—
283	#67	—	12	1	no	—
284	C₂×Dic₃	—	6	1	no	—
285	C₂×Dic₃	—	6	1	no	—
286	C₂×Dic₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
287	D₁₂	—	3	1	no	—
288	D₁₂	—	3	1	no	—
289	D₁₂	—	6	1	no	—
290	D₁₂	—	6	1	no	—
291	D₁₂	—	6	1	no	—
292	D₁₂	D₃×C₈	1	1	yes	characteristic
293	C₄×D₃	—	2	1	no	—
294	C₄×D₃	—	6	1	no	—
295	C₄×D₃	—	6	1	no	—
296	C₄×D₃	—	6	1	no	—
297	C₄×D₃	—	6	1	no	—
298	C₄×D₃	—	6	1	no	—
299	C₄×D₃	—	6	1	no	—
300	C₄×D₃	—	12	1	no	—
301	C₄×D₃	D₃×C₈	1	1	yes	characteristic
302	C₄×D₃	D₃×C₈	1	1	yes	characteristic
303	C₄×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
304	C₄×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
305	Dic₆	—	3	1	no	—
306	Dic₆	—	3	1	no	—
307	Dic₆	—	6	1	no	—
308	Dic₆	—	6	1	no	—
309	Dic₆	—	6	1	no	—
310	Dic₆	D₃×C₈	1	1	yes	characteristic
311	C₃×C₈	—	2	1	no	—
312	C₃×C₈	—	2	1	no	—
313	C₃×C₈	—	3	1	no	—
314	C₃×C₈	—	3	1	no	—
315	C₃×C₈	—	6	1	no	—
316	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
317	C₃×C₈	D₃×D₄	1	1	yes	characteristic
318	C₃×C₈	D₃×D₄	1	1	yes	characteristic
319	C₃×C₈	C₂×#67	1	1	yes	characteristic
320	C₃⋊C₈	—	2	1	no	—
321	C₃⋊C₈	—	6	1	no	—
322	C₃⋊C₈	—	6	1	no	—
323	C₃⋊C₈	—	12	1	no	—
324	C₃⋊C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
325	C₃⋊C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
326	C₂×C₃²	—	2	1	no	—
327	C₂×C₃²	C₂×C₂²⋊C₈	1	1	yes	characteristic
328	C₃⋊D₃	—	4	1	no	—
329	C₃×D₃	—	2	1	no	—
330	C₃×D₃	—	4	1	no	—
331	C₃×D₃	#350	1	2	yes	complemented
332	#41	—	3	1	no	—
333	#41	—	9	1	no	—
334	#41	—	9	1	no	—
335	#41	—	9	1	no	—
336	#41	—	18	1	no	—
337	#41	—	18	1	no	—
338	C₂×Q₈	—	9	1	no	—
339	C₂×D₄	—	9	1	no	—
340	C₂×D₄	—	18	1	no	—
341	C₂²×C₄	—	3	1	no	—
342	C₂²×C₄	—	18	1	no	—
343	M₁₆	—	3	1	no	—
344	M₁₆	—	6	1	no	—
345	M₁₆	—	9	1	no	—
346	M₁₆	—	18	1	no	—
347	M₁₆	—	18	1	no	—
348	M₁₆	—	18	1	no	—
349	M₁₆	—	18	1	no	—
350	C₂×C₈	—	3	1	no	—
351	C₂×C₈	—	3	1	no	—
352	C₂×C₈	—	3	1	no	—
353	C₂×C₈	—	3	1	no	—
354	C₂×C₈	—	3	1	no	—
355	C₂×C₈	—	6	1	no	—
356	C₂×C₈	—	18	1	no	—
357	C₂×C₈	—	18	1	no	—
358	C₂×C₈	—	18	1	no	—
359	C₂×C₈	—	18	1	no	—
360	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
361	C₁₆	—	2	1	no	—
362	C₁₆	—	6	1	no	—
363	C₁₆	—	6	1	no	—
364	C₁₆	—	18	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	3	1	no	—
367	C₂²×C₃	—	3	1	no	—
368	C₂²×C₃	—	6	2	no	—
369	C₂²×C₃	—	6	1	no	—
370	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
371	C₂²×C₃	D₃×M₁₆	1	1	yes	characteristic
372	C₂×D₃	—	2	2	no	—
373	C₂×D₃	—	2	1	no	—
374	C₂×D₃	—	6	1	no	—
375	C₂×D₃	—	6	1	no	—
376	C₂×D₃	—	12	1	no	—
377	C₂×D₃	—	12	2	no	—
378	C₂×D₃	—	12	2	no	—
379	C₂×D₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
380	C₂×D₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	3	1	no	—
384	C₃×C₄	—	3	1	no	—
385	C₃×C₄	—	6	1	no	—
386	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
387	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
388	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
389	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
390	Dic₃	—	2	1	no	—
391	Dic₃	—	6	1	no	—
392	Dic₃	—	6	1	no	—
393	Dic₃	—	12	1	no	—
394	Dic₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
395	Dic₃	(C₂×D₃)⋊C₈	1	1	yes	characteristic
396	C₃²	C₂×#350	1	1	yes	characteristic, complemented, Sylow
397	C₂³	—	3	1	no	—
398	C₂³	—	18	1	no	—
399	Q₈	—	3	1	no	—
400	Q₈	—	9	1	no	—
401	Q₈	—	18	1	no	—
402	D₄	—	3	1	no	—
403	D₄	—	6	1	no	—
404	D₄	—	9	1	no	—
405	D₄	—	18	1	no	—
406	D₄	—	18	1	no	—
407	D₄	—	18	1	no	—
408	D₄	—	18	1	no	—
409	C₂×C₄	—	3	1	no	—
410	C₂×C₄	—	3	1	no	—
411	C₂×C₄	—	3	1	no	—
412	C₂×C₄	—	3	1	no	—
413	C₂×C₄	—	3	1	no	—
414	C₂×C₄	—	6	1	no	—
415	C₂×C₄	—	18	1	no	—
416	C₂×C₄	—	18	1	no	—
417	C₂×C₄	—	18	1	no	—
418	C₂×C₄	—	18	1	no	—
419	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
420	C₈	—	3	1	no	—
421	C₈	—	3	1	no	—
422	C₈	—	6	1	no	—
423	C₈	—	18	1	no	—
424	C₈	D₃×D₁₂	1	1	yes	characteristic
425	C₈	D₃×#67	1	1	yes	characteristic
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	3	2	no	—
430	C₂×C₃	—	4	1	no	—
431	C₂×C₃	—	6	1	no	—
432	C₂×C₃	—	12	1	no	—
433	C₂×C₃	D₃×C₂²⋊C₈	1	1	yes	characteristic
434	C₂×C₃	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
435	D₃	—	2	1	no	—
436	D₃	—	4	1	no	—
437	D₃	—	12	1	no	—
438	D₃	—	12	1	no	—
439	D₃	—	24	1	no	—
440	D₃	#4515	1	2	yes	direct product factor
441	C₂²	—	3	1	no	—
442	C₂²	—	3	1	no	—
443	C₂²	—	6	2	no	—
444	C₂²	—	6	1	no	—
445	C₂²	—	18	1	no	—
446	C₂²	—	36	2	no	—
447	C₂²	D₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
448	C₄	—	3	1	no	—
449	C₄	—	3	1	no	—
450	C₄	—	6	1	no	—
451	C₄	—	18	1	no	—
452	C₄	D₃²×C₈	1	1	yes	characteristic
453	C₄	D₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
454	C₃	—	2	1	no	—
455	C₃	D₃×#350	1	1	yes	characteristic, complemented
456	C₃	C₂×#4515	1	1	yes	characteristic, complemented
457	C₂	—	2	1	no	—
458	C₂	—	3	2	no	—
459	C₂	—	6	1	no	—
460	C₂	—	12	1	no	—
461	C₂	—	36	1	no	—
462	C₂	D₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₃×#67
commutator	C₃²×C₄	C₂²×C₈
Frattini	C₂×C₈	C₂×D₃²
Fitting	C₃²×M₃₂	C₂²
socle	C₂×C₃²	C₂×C₂²⋊C₈
prime radical	D₃×#235	C₄
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	M₃₂	D₃²
hypocenter	C₃²	C₂×#350
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₃×D₃×M₃₂	C₂	semidirect
3. C₂×D₃×C₃⋊C₁₆	C₂	semidirect
4. #10589381	C₂	semidirect
5. C₃×#4515	C₂	semidirect
6. #10589113	C₂	semidirect
7. #10589111	C₂	semidirect
21. C₃²×M₃₂	C₂²	semidirect
22. C₂×C₃⋊(C₃⋊C₁₆)	C₂²	semidirect
23. C₃×#812	C₂²	semidirect
24. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
33. D₃×M₃₂	D₃	semidirect
42. #4515	D₃	direct (N × H)
104. C₃×M₃₂	C₂×D₃	semidirect
105. C₃×M₃₂	C₂×D₃	semidirect
108. #812	C₂×D₃	semidirect
114. C₂×C₃⋊C₁₆	C₂×D₃	semidirect
254. M₃₂	D₃²	semidirect
331. C₃×D₃	#350	semidirect
396. C₃²	C₂×#350	semidirect
440. D₃	#4515	direct (N × H)
455. C₃	D₃×#350	semidirect
456. C₃	C₂×#4515	semidirect

Maximal subgroups

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

subgroup	index
D₃×#901	2
C₃×D₃×M₃₂	2
C₂×D₃×C₃⋊C₁₆	2
#10589381	2
C₃×#4515	2
#10589113	2
#10589111	2
C₂×#4515	3
D₃×#350	3

Subgroups — D3×#4515 #11796089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#4515 #11796089