Subgroups — C₃×#82036 #11899672

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 557 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5769	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#5757	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5194	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#826	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4916	C₂	1	2	yes	maximal, complemented
7	C₃×#4914	C₂	1	2	yes	maximal, complemented
8	C₃×#4911	C₂	1	2	yes	maximal, complemented
9	C₃×D₃×D₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×#4908	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3415	—	3	1	no	maximal
13	#82036	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×#1009	—	2	1	no	—
15	C₃×#1004	—	2	1	no	—
16	C₃²×#135	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×#949	—	2	1	no	—
19	C₃×#932	—	2	1	no	—
20	C₃×#919	C₂²	1	2	yes	complemented
21	C₃×#914	—	2	2	no	—
22	C₃×#912	C₂²	1	2	yes	complemented
23	C₃×#911	—	2	2	no	—
24	C₃×D₃×D₈	C₂²	1	2	yes	complemented
25	C₃×D₃×D₈	C₂²	1	2	yes	complemented
26	C₃×#904	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×#901	C₂²	1	1	yes	characteristic
29	C₃²×SD₃₂	C₂²	1	2	yes	complemented
30	C₃²×D₁₆	C₂²	1	2	yes	complemented
31	C₃²×M₃₂	C₂²	1	1	yes	characteristic, complemented
32	C₃×#829	C₂²	1	1	yes	characteristic, complemented
33	C₃×#828	C₂²	1	1	yes	characteristic, complemented
34	C₃×#827	C₂²	1	1	yes	characteristic, complemented
35	C₃×#826	C₂²	1	1	yes	characteristic, complemented
36	C₃×#826	C₂²	1	2	yes	complemented
37	C₃×#826	C₂²	1	2	yes	complemented
38	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₃×#800	C₂²	1	2	yes	complemented
40	C₃×D₄₈	C₂²	1	2	yes	complemented
41	C₃×#798	C₂²	1	2	yes	complemented
42	C₃×D₃×C₁₆	C₂²	1	2	yes	complemented
43	C₃×#576	—	3	1	no	—
44	C₃×#576	—	3	1	no	—
45	#5769	C₂×C₃	1	1	yes	characteristic, complemented
46	#5757	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#509	—	2	1	no	—
48	C₃×#509	—	3	2	no	—
49	C₃×#509	—	3	2	no	—
50	C₃×#509	—	3	1	no	—
51	C₃×#509	D₃	1	1	yes	characteristic, complemented
52	C₃×#509	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×#508	—	3	1	no	—
54	C₃×#508	—	3	2	no	—
55	C₂×C₃×D₁₆	—	3	1	no	—
56	C₂×C₃×D₁₆	—	3	2	no	—
57	C₃×#504	—	3	1	no	—
58	#5194	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#826	C₂×C₃	1	1	yes	characteristic, complemented
60	#4916	C₂×C₃	1	2	yes	complemented
61	#4914	C₂×C₃	1	2	yes	complemented
62	#4911	C₂×C₃	1	2	yes	complemented
63	D₃×D₁₆	C₂×C₃	1	2	yes	complemented
64	#4908	C₂×C₃	1	1	yes	characteristic, complemented
65	#4907	C₂×C₃	1	1	yes	characteristic, complemented
66	C₃²×#41	—	2	1	no	—
67	C₂×C₃²×D₄	—	2	1	no	—
68	C₂×C₃×#67	—	4	2	no	—
69	C₃×#239	—	2	2	no	—
70	C₃×#237	—	2	2	no	—
71	C₃×#237	—	4	1	no	—
72	C₃×D₃×D₄	—	2	2	no	—
73	C₃×D₃×D₄	—	2	2	no	—
74	C₃×D₃×D₄	—	4	2	no	—
75	C₃×D₃×D₄	—	4	1	no	—
76	C₃×#235	—	2	1	no	—
77	C₃×#235	—	4	1	no	—
78	C₃×#235	D₄	1	1	yes	characteristic
79	C₂×C₃×D₁₂	—	2	1	no	—
80	C₂×C₃×D₁₂	—	4	1	no	—
81	C₃²×Q₁₆	C₂³	1	1	yes	characteristic
82	C₃²×SD₁₆	—	2	1	no	—
83	C₃²×D₈	—	2	1	no	—
84	C₃²×D₈	C₂³	1	1	yes	characteristic
85	C₃²×D₈	C₂³	1	2	yes	—
86	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
87	C₃×#215	—	2	2	no	—
88	C₃×#214	—	2	2	no	—
89	C₃×#213	—	2	2	no	—
90	C₃×#213	—	2	2	no	—
91	C₃×#208	D₄	1	1	yes	characteristic
92	C₃×Dic₁₂	C₂³	1	1	yes	characteristic
93	C₃×D₂₄	—	2	1	no	—
94	C₃×D₂₄	C₂³	1	2	yes	—
95	C₃×D₂₄	C₂³	1	1	yes	characteristic
96	C₃×#204	—	2	1	no	—
97	C₃×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
98	C₃×D₃×C₈	C₂³	1	2	yes	—
99	C₃²×C₁₆	C₂³	1	2	yes	—
100	C₃×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
101	C₃×C₃⋊C₁₆	C₂³	1	1	yes	characteristic
102	#3415	—	3	1	no	Sylow
103	C₃×H(5,𝔽₂)	—	6	1	no	—
104	C₃×H(5,𝔽₂)	—	6	1	no	—
105	#1009	—	2	1	no	—
106	#1004	—	2	1	no	—
107	C₃×AGL(1,ℤ/8)	—	6	2	no	—
108	C₃×AGL(1,ℤ/8)	—	6	2	no	—
109	C₃×AGL(1,ℤ/8)	—	6	1	no	—
110	C₃×AGL(1,ℤ/8)	—	6	1	no	—
111	C₃×#135	—	2	1	no	—
112	C₃×#135	—	3	2	no	—
113	C₃×#135	—	3	2	no	—
114	C₃×#135	—	3	1	no	—
115	C₃×#135	C₂×D₃	1	1	yes	characteristic, complemented
116	C₃×#135	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×C₃×D₈	—	2	1	no	—
118	C₂×C₃×D₈	—	3	2	no	—
119	C₂×C₃×D₈	—	3	2	no	—
120	C₂×C₃×D₈	—	3	1	no	—
121	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic, complemented
122	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₃×#131	—	3	1	no	—
124	#949	—	2	1	no	—
125	#932	—	2	1	no	—
126	#919	C₂²×C₃	1	2	yes	complemented
127	#914	—	2	2	no	—
128	#912	C₂²×C₃	1	2	yes	complemented
129	#911	—	2	2	no	—
130	D₃×D₈	C₂²×C₃	1	2	yes	complemented
131	D₃×D₈	C₂²×C₃	1	2	yes	complemented
132	#904	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic, complemented
134	#901	C₂²×C₃	1	1	yes	characteristic
135	C₃×Q₃₂	—	3	1	no	—
136	C₃×SD₃₂	—	2	2	no	—
137	C₃×SD₃₂	—	3	1	no	—
138	C₃×SD₃₂	—	3	1	no	—
139	C₃×SD₃₂	—	3	2	no	—
140	C₃×SD₃₂	C₂×D₃	1	2	yes	complemented
141	C₃×SD₃₂	C₂²×C₃	1	2	yes	complemented
142	C₃×D₁₆	—	2	2	no	—
143	C₃×D₁₆	—	3	2	no	—
144	C₃×D₁₆	—	3	1	no	—
145	C₃×D₁₆	—	3	2	no	—
146	C₃×D₁₆	—	3	2	no	—
147	C₃×D₁₆	C₂×D₃	1	2	yes	complemented
148	C₃×D₁₆	C₂²×C₃	1	2	yes	complemented
149	C₃×M₃₂	—	2	1	no	—
150	C₃×M₃₂	—	3	2	no	—
151	C₃×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
152	C₃×M₃₂	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₂×C₃×C₁₆	—	3	1	no	—
154	C₂×C₃×C₁₆	—	3	2	no	—
155	#829	C₂²×C₃	1	1	yes	characteristic, complemented
156	#828	C₂²×C₃	1	1	yes	characteristic, complemented
157	#827	C₂²×C₃	1	1	yes	characteristic, complemented
158	#826	C₂²×C₃	1	2	yes	complemented
159	#826	C₂²×C₃	1	2	yes	complemented
160	#826	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×C₃⋊C₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
162	#800	C₂²×C₃	1	2	yes	complemented
163	D₄₈	C₂²×C₃	1	2	yes	complemented
164	#798	C₂²×C₃	1	2	yes	complemented
165	D₃×C₁₆	C₂²×C₃	1	2	yes	complemented
166	C₂³×C₃²	—	4	1	no	—
167	C₂²×C₃×D₃	—	4	1	no	—
168	C₂²×C₃×D₃	—	4	2	no	—
169	C₂²×C₃×D₃	—	4	2	no	—
170	C₃²×Q₈	—	2	1	no	—
171	C₃²×D₄	—	2	1	no	—
172	C₃²×D₄	—	2	2	no	—
173	C₃²×D₄	—	4	1	no	—
174	C₃²×D₄	—	4	1	no	—
175	C₂×C₃²×C₄	—	4	1	no	—
176	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
177	C₃×#67	—	4	1	no	—
178	C₃×#67	—	4	2	no	—
179	C₃×#67	—	4	2	no	—
180	C₃×#67	—	4	2	no	—
181	C₃×#67	D₈	1	2	yes	—
182	C₂×C₃×Dic₃	—	4	2	no	—
183	C₃×D₁₂	—	2	1	no	—
184	C₃×D₁₂	—	2	2	no	—
185	C₃×D₁₂	—	4	2	no	—
186	C₃×D₁₂	—	4	1	no	—
187	C₃×D₁₂	D₈	1	1	yes	characteristic
188	C₃×C₄×D₃	—	4	1	no	—
189	C₃×C₄×D₃	—	4	2	no	—
190	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
191	C₃×Dic₆	—	2	1	no	—
192	C₃×Dic₆	D₈	1	1	yes	characteristic
193	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
194	C₃²×C₈	C₂⁴	1	1	yes	characteristic
195	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
196	#576	—	3	1	no	—
197	#576	—	3	1	no	—
198	#509	—	3	2	no	—
199	#509	—	3	2	no	—
200	#509	—	3	1	no	—
201	#509	C₃×D₃	1	1	yes	characteristic, complemented
202	#508	—	3	1	no	—
203	#508	—	3	2	no	—
204	C₂×D₁₆	—	3	1	no	—
205	C₂×D₁₆	—	3	2	no	—
206	#504	—	3	1	no	—
207	C₃×#41	—	2	1	no	—
208	C₃×#41	—	2	1	no	—
209	C₃×#41	—	3	1	no	—
210	C₃×#41	—	4	1	no	—
211	C₃×#41	—	6	2	no	—
212	C₃×#41	—	6	2	no	—
213	C₃×#41	—	6	1	no	—
214	C₃×#41	—	12	1	no	—
215	C₃×#41	—	12	1	no	—
216	C₂×C₃×D₄	—	2	1	no	—
217	C₂×C₃×D₄	—	2	1	no	—
218	C₂×C₃×D₄	—	4	1	no	—
219	C₂×C₃×D₄	—	6	2	no	—
220	C₂×C₃×D₄	—	6	2	no	—
221	C₂×C₃×D₄	—	6	1	no	—
222	C₂×C₃×D₄	—	12	1	no	—
223	C₂×C₃×D₄	—	12	2	no	—
224	C₂×C₃×D₄	—	12	1	no	—
225	C₂×C₃×D₄	—	12	2	no	—
226	C₂×#67	—	4	2	no	—
227	#239	—	2	2	no	—
228	#237	—	2	2	no	—
229	#237	—	4	1	no	—
230	D₃×D₄	—	2	2	no	—
231	D₃×D₄	—	2	2	no	—
232	D₃×D₄	—	4	2	no	—
233	D₃×D₄	—	4	1	no	—
234	#235	—	2	1	no	—
235	#235	—	4	1	no	—
236	#235	C₃×D₄	1	1	yes	characteristic
237	C₂×D₁₂	—	2	1	no	—
238	C₂×D₁₂	—	4	1	no	—
239	C₃×Q₁₆	—	2	1	no	—
240	C₃×Q₁₆	—	3	1	no	—
241	C₃×Q₁₆	C₂²×D₃	1	1	yes	characteristic
242	C₃×Q₁₆	C₂³×C₃	1	1	yes	characteristic
243	C₃×SD₁₆	—	2	1	no	—
244	C₃×SD₁₆	—	2	1	no	—
245	C₃×SD₁₆	—	4	1	no	—
246	C₃×SD₁₆	—	6	2	no	—
247	C₃×SD₁₆	—	6	2	no	—
248	C₃×SD₁₆	—	6	1	no	—
249	C₃×D₈	—	2	1	no	—
250	C₃×D₈	—	2	1	no	—
251	C₃×D₈	—	2	1	no	—
252	C₃×D₈	—	2	2	no	—
253	C₃×D₈	—	3	2	no	—
254	C₃×D₈	—	3	1	no	—
255	C₃×D₈	—	4	1	no	—
256	C₃×D₈	—	6	2	no	—
257	C₃×D₈	—	6	2	no	—
258	C₃×D₈	—	6	1	no	—
259	C₃×D₈	C₂²×D₃	1	2	yes	—
260	C₃×D₈	C₂²×D₃	1	1	yes	characteristic
261	C₃×D₈	C₂³×C₃	1	2	yes	—
262	C₃×D₈	C₂³×C₃	1	1	yes	characteristic
263	C₃×M₁₆	—	3	1	no	—
264	C₃×M₁₆	—	3	2	no	—
265	C₂×C₃×C₈	—	2	1	no	—
266	C₂×C₃×C₈	—	3	2	no	—
267	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
269	#215	—	2	2	no	—
270	#214	—	2	2	no	—
271	#213	—	2	2	no	—
272	#213	—	2	2	no	—
273	#208	C₃×D₄	1	1	yes	characteristic
274	Dic₁₂	C₂³×C₃	1	1	yes	characteristic
275	D₂₄	—	2	1	no	—
276	D₂₄	C₂³×C₃	1	1	yes	characteristic
277	D₂₄	C₂³×C₃	1	2	yes	—
278	#204	—	2	1	no	—
279	ΓL(1,𝔽₂₅)	C₃×D₄	1	2	yes	—
280	D₃×C₈	C₂³×C₃	1	2	yes	—
281	C₃×C₁₆	—	2	2	no	—
282	C₃×C₁₆	—	3	1	no	—
283	C₃×C₁₆	—	3	1	no	—
284	C₃×C₁₆	C₂²×D₃	1	2	yes	—
285	C₃×C₁₆	C₂³×C₃	1	2	yes	—
286	C₃⋊C₁₆	C₂³×C₃	1	1	yes	characteristic
287	C₃⋊C₁₆	C₂³×C₃	1	1	yes	characteristic
288	C₂²×C₃²	—	4	2	no	—
289	C₂²×C₃²	—	4	1	no	—
290	C₂²×C₃²	—	16	1	no	—
291	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
292	C₂×C₃×D₃	—	4	2	no	—
293	C₂×C₃×D₃	—	4	1	no	—
294	C₂×C₃×D₃	—	16	2	no	—
295	C₂×C₃×D₃	—	16	2	no	—
296	C₂×C₃×D₃	—	16	1	no	—
297	C₂×C₃×D₃	C₂×D₈	1	2	yes	—
298	C₃²×C₄	—	4	1	no	—
299	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
300	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
301	C₃×Dic₃	—	4	1	no	—
302	C₃×Dic₃	C₂×D₈	1	2	yes	—
303	H(5,𝔽₂)	—	6	1	no	—
304	H(5,𝔽₂)	—	6	1	no	—
305	AGL(1,ℤ/8)	—	6	2	no	—
306	AGL(1,ℤ/8)	—	6	2	no	—
307	AGL(1,ℤ/8)	—	6	1	no	—
308	AGL(1,ℤ/8)	—	6	1	no	—
309	#135	—	3	2	no	—
310	#135	—	3	2	no	—
311	#135	—	3	1	no	—
312	#135	C₂×C₃×D₃	1	1	yes	characteristic, complemented
313	C₂×D₈	—	3	2	no	—
314	C₂×D₈	—	3	2	no	—
315	C₂×D₈	—	3	1	no	—
316	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
317	#131	—	3	1	no	—
318	Q₃₂	—	3	1	no	—
319	SD₃₂	—	3	1	no	—
320	SD₃₂	—	3	1	no	—
321	SD₃₂	—	3	2	no	—
322	SD₃₂	C₂×C₃×D₃	1	2	yes	complemented
323	D₁₆	—	3	2	no	—
324	D₁₆	—	3	1	no	—
325	D₁₆	—	3	2	no	—
326	D₁₆	—	3	2	no	—
327	D₁₆	C₂×C₃×D₃	1	2	yes	complemented
328	M₃₂	—	3	2	no	—
329	M₃₂	C₂×C₃×D₃	1	1	yes	characteristic, complemented
330	C₂×C₁₆	—	3	1	no	—
331	C₂×C₁₆	—	3	2	no	—
332	C₂³×C₃	—	4	1	no	—
333	C₂³×C₃	—	4	1	no	—
334	C₂³×C₃	—	8	1	no	—
335	C₂³×C₃	—	12	2	no	—
336	C₂³×C₃	—	12	2	no	—
337	C₂³×C₃	—	12	1	no	—
338	C₂²×D₃	—	4	1	no	—
339	C₂²×D₃	—	4	2	no	—
340	C₂²×D₃	—	4	2	no	—
341	C₃×Q₈	—	2	1	no	—
342	C₃×Q₈	—	2	1	no	—
343	C₃×Q₈	—	3	1	no	—
344	C₃×Q₈	—	4	1	no	—
345	C₃×Q₈	—	6	1	no	—
346	C₃×D₄	—	2	2	no	—
347	C₃×D₄	—	2	1	no	—
348	C₃×D₄	—	2	1	no	—
349	C₃×D₄	—	2	2	no	—
350	C₃×D₄	—	3	2	no	—
351	C₃×D₄	—	3	1	no	—
352	C₃×D₄	—	4	2	no	—
353	C₃×D₄	—	4	1	no	—
354	C₃×D₄	—	4	1	no	—
355	C₃×D₄	—	4	1	no	—
356	C₃×D₄	—	4	1	no	—
357	C₃×D₄	—	4	1	no	—
358	C₃×D₄	—	6	1	no	—
359	C₃×D₄	—	6	2	no	—
360	C₃×D₄	—	8	1	no	—
361	C₃×D₄	—	8	1	no	—
362	C₃×D₄	—	12	2	no	—
363	C₃×D₄	—	12	2	no	—
364	C₃×D₄	—	12	2	no	—
365	C₃×D₄	—	12	2	no	—
366	C₃×D₄	—	12	1	no	—
367	C₃×D₄	—	12	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	3	2	no	—
370	C₂×C₃×C₄	—	4	1	no	—
371	C₂×C₃×C₄	—	4	1	no	—
372	C₂×C₃×C₄	—	8	1	no	—
373	C₂×C₃×C₄	—	12	2	no	—
374	C₂×C₃×C₄	—	12	2	no	—
375	C₂×C₃×C₄	—	12	1	no	—
376	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
378	#67	—	4	1	no	—
379	#67	—	4	2	no	—
380	#67	—	4	2	no	—
381	#67	—	4	2	no	—
382	#67	C₃×D₈	1	2	yes	—
383	C₂×Dic₃	—	4	2	no	—
384	D₁₂	—	2	1	no	—
385	D₁₂	—	2	2	no	—
386	D₁₂	—	4	2	no	—
387	D₁₂	—	4	1	no	—
388	D₁₂	C₃×D₈	1	1	yes	characteristic
389	C₄×D₃	—	4	1	no	—
390	C₄×D₃	—	4	2	no	—
391	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
392	Dic₆	—	2	1	no	—
393	Dic₆	C₃×D₈	1	1	yes	characteristic
394	C₃×C₈	—	2	1	no	—
395	C₃×C₈	—	2	1	no	—
396	C₃×C₈	—	3	2	no	—
397	C₃×C₈	D₃×D₄	1	1	yes	characteristic
398	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
399	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
400	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
401	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
402	C₂×C₃²	—	2	1	no	—
403	C₂×C₃²	—	8	1	no	—
404	C₂×C₃²	—	8	2	no	—
405	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
406	C₃×D₃	—	2	2	no	—
407	C₃×D₃	—	8	2	no	—
408	C₃×D₃	—	8	1	no	—
409	#41	—	2	1	no	—
410	#41	—	3	1	no	—
411	#41	—	6	2	no	—
412	#41	—	6	2	no	—
413	#41	—	6	1	no	—
414	#41	—	12	1	no	—
415	#41	—	12	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	6	2	no	—
418	C₂×D₄	—	6	2	no	—
419	C₂×D₄	—	6	1	no	—
420	C₂×D₄	—	12	1	no	—
421	C₂×D₄	—	12	2	no	—
422	C₂×D₄	—	12	1	no	—
423	C₂×D₄	—	12	2	no	—
424	Q₁₆	—	3	1	no	—
425	Q₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
426	SD₁₆	—	2	1	no	—
427	SD₁₆	—	6	2	no	—
428	SD₁₆	—	6	2	no	—
429	SD₁₆	—	6	1	no	—
430	D₈	—	2	1	no	—
431	D₈	—	3	2	no	—
432	D₈	—	3	1	no	—
433	D₈	—	6	2	no	—
434	D₈	—	6	2	no	—
435	D₈	—	6	1	no	—
436	D₈	C₂²×C₃×D₃	1	2	yes	—
437	D₈	C₂²×C₃×D₃	1	1	yes	characteristic
438	M₁₆	—	3	1	no	—
439	M₁₆	—	3	2	no	—
440	C₂×C₈	—	3	2	no	—
441	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
442	C₁₆	—	3	1	no	—
443	C₁₆	—	3	1	no	—
444	C₁₆	C₂²×C₃×D₃	1	2	yes	—
445	C₂²×C₃	—	2	1	no	—
446	C₂²×C₃	—	3	2	no	—
447	C₂²×C₃	—	4	2	no	—
448	C₂²×C₃	—	4	1	no	—
449	C₂²×C₃	—	4	1	no	—
450	C₂²×C₃	—	4	2	no	—
451	C₂²×C₃	—	8	1	no	—
452	C₂²×C₃	—	8	2	no	—
453	C₂²×C₃	—	12	2	no	—
454	C₂²×C₃	—	12	1	no	—
455	C₂²×C₃	—	16	1	no	—
456	C₂²×C₃	—	16	1	no	—
457	C₂²×C₃	—	16	2	no	—
458	C₂²×C₃	—	48	1	no	—
459	C₂²×C₃	—	48	2	no	—
460	C₂²×C₃	—	48	2	no	—
461	C₂²×C₃	D₃×D₈	1	1	yes	characteristic
462	C₂²×C₃	C₂×C₃×D₈	1	1	yes	characteristic
463	C₂×D₃	—	4	2	no	—
464	C₂×D₃	—	4	1	no	—
465	C₂×D₃	—	16	2	no	—
466	C₂×D₃	—	16	2	no	—
467	C₂×D₃	—	16	1	no	—
468	C₂×D₃	C₂×C₃×D₈	1	2	yes	—
469	C₃×C₄	—	2	1	no	—
470	C₃×C₄	—	2	1	no	—
471	C₃×C₄	—	3	2	no	—
472	C₃×C₄	—	4	1	no	—
473	C₃×C₄	—	4	1	no	—
474	C₃×C₄	—	8	1	no	—
475	C₃×C₄	—	12	1	no	—
476	C₃×C₄	D₃×D₈	1	1	yes	characteristic
477	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
478	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
479	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
480	Dic₃	—	4	1	no	—
481	Dic₃	C₂×C₃×D₈	1	2	yes	—
482	C₃²	#3415	1	1	yes	characteristic, complemented, Sylow
483	C₂³	—	4	1	no	—
484	C₂³	—	12	2	no	—
485	C₂³	—	12	2	no	—
486	C₂³	—	12	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	3	1	no	—
489	Q₈	—	6	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	1	no	—
492	D₄	—	3	2	no	—
493	D₄	—	3	1	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	6	1	no	—
497	D₄	—	6	2	no	—
498	D₄	—	12	2	no	—
499	D₄	—	12	2	no	—
500	D₄	—	12	2	no	—
501	D₄	—	12	2	no	—
502	D₄	—	12	1	no	—
503	D₄	—	12	1	no	—
504	C₂×C₄	—	3	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	12	2	no	—
507	C₂×C₄	—	12	2	no	—
508	C₂×C₄	—	12	1	no	—
509	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
510	C₈	—	3	2	no	—
511	C₈	C₃×D₃×D₄	1	1	yes	characteristic
512	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
513	C₂×C₃	—	2	1	no	—
514	C₂×C₃	—	2	1	no	—
515	C₂×C₃	—	2	1	no	—
516	C₂×C₃	—	4	1	no	—
517	C₂×C₃	—	6	2	no	—
518	C₂×C₃	—	8	1	no	—
519	C₂×C₃	—	8	2	no	—
520	C₂×C₃	—	8	2	no	—
521	C₂×C₃	—	8	1	no	—
522	C₂×C₃	—	16	2	no	—
523	C₂×C₃	—	16	1	no	—
524	C₂×C₃	—	24	2	no	—
525	C₂×C₃	—	24	1	no	—
526	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
527	C₂×C₃	C₂²×C₃×D₈	1	1	yes	characteristic
528	D₃	—	2	2	no	—
529	D₃	—	8	2	no	—
530	D₃	—	8	1	no	—
531	C₂²	—	3	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	12	2	no	—
535	C₂²	—	12	1	no	—
536	C₂²	—	16	1	no	—
537	C₂²	—	48	1	no	—
538	C₂²	—	48	2	no	—
539	C₂²	—	48	2	no	—
540	C₂²	C₃×D₃×D₈	1	1	yes	characteristic
541	C₄	—	3	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	12	1	no	—
544	C₄	C₃×D₃×D₈	1	1	yes	characteristic
545	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
546	C₃	—	2	1	no	—
547	C₃	#82036	1	1	yes	characteristic, direct product factor
548	C₃	C₃×#3415	1	1	yes	characteristic, complemented
549	C₂	—	2	1	no	—
550	C₂	—	6	2	no	—
551	C₂	—	8	2	no	—
552	C₂	—	8	1	no	—
553	C₂	—	24	2	no	—
554	C₂	—	24	1	no	—
555	C₂	C₂×C₃×D₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₃×D₈
commutator, cosocle	C₃×C₈	C₂⁴×C₃
Frattini	C₈	C₂³×C₃×D₃
Fitting	C₃²×#509	C₂
socle	C₂×C₃²	C₂²×D₈
hypercenter	C₃×#509	D₃
hypocenter	C₃	C₃×#3415
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#509

Complements

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

N	H ≅ G/N	type
1. C₃×#5769	C₂	semidirect
2. C₃×#5757	C₂	semidirect
3. C₃²×#509	C₂	semidirect
4. C₃×#5194	C₂	semidirect
5. C₂×C₃×#826	C₂	semidirect
6. C₃×#4916	C₂	semidirect
7. C₃×#4914	C₂	semidirect
8. C₃×#4911	C₂	semidirect
9. C₃×D₃×D₁₆	C₂	semidirect
10. C₃×#4908	C₂	semidirect
11. C₃×#4907	C₂	semidirect
13. #82036	C₃	direct (N × H)
16. C₃²×#135	C₂²	semidirect
17. C₂×C₃²×D₈	C₂²	semidirect
20. C₃×#919	C₂²	semidirect
22. C₃×#912	C₂²	semidirect
24. C₃×D₃×D₈	C₂²	semidirect
25. C₃×D₃×D₈	C₂²	semidirect
26. C₃×#904	C₂²	semidirect
27. C₂×C₃×D₂₄	C₂²	semidirect
29. C₃²×SD₃₂	C₂²	semidirect
30. C₃²×D₁₆	C₂²	semidirect
31. C₃²×M₃₂	C₂²	semidirect
32. C₃×#829	C₂²	semidirect
33. C₃×#828	C₂²	semidirect
34. C₃×#827	C₂²	semidirect
35. C₃×#826	C₂²	semidirect
36. C₃×#826	C₂²	semidirect
37. C₃×#826	C₂²	semidirect
38. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
39. C₃×#800	C₂²	semidirect
40. C₃×D₄₈	C₂²	semidirect
41. C₃×#798	C₂²	semidirect
42. C₃×D₃×C₁₆	C₂²	semidirect
45. #5769	C₂×C₃	semidirect
46. #5757	C₂×C₃	semidirect
51. C₃×#509	D₃	semidirect
52. C₃×#509	C₂×C₃	semidirect
58. #5194	C₂×C₃	semidirect
59. C₂×#826	C₂×C₃	semidirect
60. #4916	C₂×C₃	semidirect
61. #4914	C₂×C₃	semidirect
62. #4911	C₂×C₃	semidirect
63. D₃×D₁₆	C₂×C₃	semidirect
64. #4908	C₂×C₃	semidirect
65. #4907	C₂×C₃	semidirect
115. C₃×#135	C₂×D₃	semidirect
116. C₃×#135	C₂²×C₃	semidirect
121. C₂×C₃×D₈	C₂×D₃	semidirect
122. C₂×C₃×D₈	C₂²×C₃	semidirect
126. #919	C₂²×C₃	semidirect
128. #912	C₂²×C₃	semidirect
130. D₃×D₈	C₂²×C₃	semidirect
131. D₃×D₈	C₂²×C₃	semidirect
132. #904	C₂²×C₃	semidirect
133. C₂×D₂₄	C₂²×C₃	semidirect
140. C₃×SD₃₂	C₂×D₃	semidirect
141. C₃×SD₃₂	C₂²×C₃	semidirect
147. C₃×D₁₆	C₂×D₃	semidirect
148. C₃×D₁₆	C₂²×C₃	semidirect
151. C₃×M₃₂	C₂×D₃	semidirect
152. C₃×M₃₂	C₂²×C₃	semidirect
155. #829	C₂²×C₃	semidirect
156. #828	C₂²×C₃	semidirect
157. #827	C₂²×C₃	semidirect
158. #826	C₂²×C₃	semidirect
159. #826	C₂²×C₃	semidirect
160. #826	C₂²×C₃	semidirect
161. C₂×C₃⋊C₁₆	C₂²×C₃	semidirect
162. #800	C₂²×C₃	semidirect
163. D₄₈	C₂²×C₃	semidirect
164. #798	C₂²×C₃	semidirect
165. D₃×C₁₆	C₂²×C₃	semidirect
201. #509	C₃×D₃	semidirect
312. #135	C₂×C₃×D₃	semidirect
316. C₂×D₈	C₂×C₃×D₃	semidirect
322. SD₃₂	C₂×C₃×D₃	semidirect
327. D₁₆	C₂×C₃×D₃	semidirect
329. M₃₂	C₂×C₃×D₃	semidirect
482. C₃²	#3415	semidirect
547. C₃	#82036	direct (N × H)
548. C₃	C₃×#3415	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5769	2
C₃×#5757	2
C₃²×#509	2
C₃×#5194	2
C₂×C₃×#826	2
C₃×#4916	2
C₃×#4914	2
C₃×#4911	2
C₃×D₃×D₁₆	2
C₃×#4908	2
C₃×#4907	2
C₃×#3415	3
#82036	3

Subgroups — C3×#82036 #11899672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#82036 #11899672