Subgroups — C₃×#79588 #11860660

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×D₈	C₂	1	1	yes	maximal, characteristic
2	C₃×#5545	C₂	1	2	yes	maximal, complemented
3	C₃²×C₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5014	C₂	1	2	yes	maximal, complemented
6	C₃×#4880	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4872	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4785	C₂	1	2	yes	maximal, complemented
9	C₃×#4770	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2948	—	3	1	no	maximal
13	#79588	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
15	C₂×C₃²×D₈	C₂²	1	1	yes	characteristic
16	C₃²×C₄×D₄	C₂²	1	2	yes	complemented
17	C₃×D₄×Dic₃	C₂²	1	2	yes	complemented
18	C₂×C₃×#213	C₂²	1	2	yes	—
19	C₃×C₄×#67	—	2	2	no	—
20	C₂×C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
21	C₃×D₃×D₈	C₄	1	8	yes	complemented
22	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
24	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
25	C₃×#893	C₂²	1	2	yes	complemented
26	C₃×#892	C₂²	1	2	yes	—
27	C₃×#67⋊C₄	—	2	2	no	—
28	C₃×D₃×C₂²⋊C₄	—	2	2	no	—
29	C₃×C₄×D₁₂	C₂²	1	2	yes	complemented
30	C₃×#872	C₂²	1	1	yes	characteristic
31	C₃²×#107	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#102	C₂²	1	2	yes	complemented
33	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#832	C₂²	1	2	yes	complemented
35	C₃×#821	C₂²	1	2	yes	complemented
36	C₃×#818	C₂²	1	1	yes	characteristic, complemented
37	C₃×#815	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
39	C₃×#809	C₂²	1	2	yes	complemented
40	C₃×#808	C₂²	1	2	yes	complemented
41	C₃×#803	C₂²	1	1	yes	characteristic, complemented
42	C₂²×C₃×D₈	—	3	1	no	—
43	C₃×#518	—	3	2	no	—
44	C₂×D₃×D₈	C₂×C₃	1	1	yes	characteristic
45	#5545	C₂×C₃	1	2	yes	complemented
46	C₃×#442	—	3	2	no	—
47	C₃×#442	—	3	2	no	—
48	C₃×C₄×D₈	—	2	1	no	—
49	C₃×C₄×D₈	—	3	1	no	—
50	C₃×C₄×D₈	—	3	1	no	—
51	C₃×C₄×D₈	—	3	1	no	—
52	C₃×C₄×D₈	D₃	1	1	yes	characteristic, complemented
53	C₃×C₄×D₈	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×#427	—	3	1	no	—
55	C₃×#418	—	3	2	no	—
56	C₃×#405	—	3	1	no	—
57	Dic₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
58	#5014	C₂×C₃	1	2	yes	complemented
59	#4880	C₂×C₃	1	1	yes	characteristic, complemented
60	#4872	C₂×C₃	1	1	yes	characteristic, complemented
61	#4785	C₂×C₃	1	2	yes	complemented
62	#4770	C₂×C₃	1	2	yes	complemented
63	C₄×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
64	#4689	C₂×C₃	1	1	yes	characteristic, complemented
65	C₂³×C₃×D₃	—	2	2	no	—
66	C₂×C₃²×D₄	C₂³	1	2	yes	—
67	C₂²×C₃²×C₄	—	2	2	no	—
68	C₂×C₃×#67	—	2	2	no	—
69	C₂²×C₃×Dic₃	—	2	2	no	—
70	C₃×D₃×D₄	—	2	4	no	—
71	C₃×D₃×D₄	C₂×C₄	1	8	yes	complemented
72	C₂×C₃×D₁₂	C₂³	1	2	yes	—
73	C₂×C₃×C₄×D₃	—	2	2	no	—
74	C₂×C₃×C₄×D₃	—	2	2	no	—
75	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
76	C₃²×D₈	C₂×C₄	1	4	yes	complemented
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
79	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃²×C₂²⋊C₄	—	2	2	no	—
81	C₃²×C₄²	C₂³	1	1	yes	characteristic
82	C₃×#217	—	2	2	no	—
83	C₃×#213	C₂×C₄	1	8	yes	complemented
84	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
85	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
87	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
88	C₃×(C₂×D₃)⋊C₄	D₄	1	1	yes	characteristic
89	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
90	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
91	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
92	C₃×C₄×Dic₃	—	2	2	no	—
93	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
97	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
98	C₃×D₃×C₈	C₂×C₄	1	4	yes	complemented
99	#2948	—	3	1	no	Sylow
100	C₂²×C₃×D₄	—	3	2	no	—
101	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
102	C₂×C₃×D₈	—	2	1	no	—
103	C₂×C₃×D₈	—	3	2	no	—
104	C₂×C₃×D₈	—	3	8	no	—
105	C₂×C₃×D₈	—	3	1	no	—
106	C₂×C₃×D₈	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×M₁₆	—	3	1	no	—
109	C₂²×C₃×C₈	—	3	1	no	—
110	C₃×C₄×D₄	—	2	2	no	—
111	C₃×C₄×D₄	—	3	2	no	—
112	C₃×C₄×D₄	—	3	2	no	—
113	C₃×C₄×D₄	—	3	2	no	—
114	C₃×C₄×D₄	—	6	2	no	—
115	C₃×C₄×D₄	—	6	2	no	—
116	C₃×C₄×D₄	C₂×D₃	1	2	yes	complemented
117	C₃×C₄×D₄	C₂²×C₃	1	2	yes	complemented
118	C₃×#117	—	3	1	no	—
119	C₃×#117	—	3	2	no	—
120	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
121	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
122	D₄×Dic₃	C₂²×C₃	1	2	yes	complemented
123	C₂×#213	C₂²×C₃	1	2	yes	—
124	C₄×#67	—	2	2	no	—
125	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
126	D₃×D₈	C₃×C₄	1	8	yes	complemented
127	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
129	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
130	#893	C₂²×C₃	1	2	yes	complemented
131	#892	C₂²×C₃	1	2	yes	—
132	#67⋊C₄	—	2	2	no	—
133	D₃×C₂²⋊C₄	—	2	2	no	—
134	C₄×D₁₂	C₂²×C₃	1	2	yes	complemented
135	#872	C₂²×C₃	1	1	yes	characteristic
136	C₃×#107	—	2	1	no	—
137	C₃×#107	—	3	1	no	—
138	C₃×#107	C₂×D₃	1	1	yes	characteristic, complemented
139	C₃×#107	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₃×#106	—	3	2	no	—
141	C₃×#102	—	2	2	no	—
142	C₃×#102	—	3	2	no	—
143	C₃×#102	—	3	2	no	—
144	C₃×#102	—	3	2	no	—
145	C₃×#102	C₂×D₃	1	2	yes	complemented
146	C₃×#102	C₂²×C₃	1	2	yes	complemented
147	C₃×#97	—	3	1	no	—
148	C₃×#97	—	3	1	no	—
149	C₃×C₄×C₈	—	2	1	no	—
150	C₃×C₄×C₈	—	3	1	no	—
151	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
152	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
153	#832	C₂²×C₃	1	2	yes	complemented
154	#821	C₂²×C₃	1	2	yes	complemented
155	#818	C₂²×C₃	1	1	yes	characteristic, complemented
156	#815	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
158	#809	C₂²×C₃	1	2	yes	complemented
159	#808	C₂²×C₃	1	2	yes	complemented
160	#803	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂³×C₃²	—	2	2	no	—
162	C₂²×C₃×D₃	—	2	2	no	—
163	C₂²×C₃×D₃	—	2	8	no	—
164	C₂²×C₃×D₃	—	8	2	no	—
165	C₂²×C₃×D₃	—	8	2	no	—
166	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
167	C₃²×D₄	—	2	2	no	—
168	C₃²×D₄	C₂²×C₄	1	4	yes	—
169	C₂×C₃²×C₄	—	2	2	no	—
170	C₂×C₃²×C₄	—	8	2	no	—
171	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
174	C₃×#67	—	2	8	no	—
175	C₂×C₃×Dic₃	—	2	2	no	—
176	C₂×C₃×Dic₃	—	8	2	no	—
177	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
180	C₃×D₁₂	—	2	2	no	—
181	C₃×D₁₂	C₂²×C₄	1	4	yes	—
182	C₃×C₄×D₃	—	8	2	no	—
183	C₃×C₄×D₃	—	8	2	no	—
184	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
185	C₃×C₄×D₃	#41	1	2	yes	—
186	C₃²×C₈	—	2	1	no	—
187	C₃²×C₈	C₂²×C₄	1	2	yes	—
188	C₃×C₃⋊C₈	—	2	1	no	—
189	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
190	C₂²×D₈	—	3	1	no	—
191	#518	—	3	2	no	—
192	#442	—	3	2	no	—
193	#442	—	3	2	no	—
194	C₄×D₈	—	3	1	no	—
195	C₄×D₈	—	3	1	no	—
196	C₄×D₈	—	3	1	no	—
197	C₄×D₈	C₃×D₃	1	1	yes	characteristic, complemented
198	#427	—	3	1	no	—
199	#418	—	3	2	no	—
200	#405	—	3	1	no	—
201	C₂⁴×C₃	—	6	2	no	—
202	C₂³×D₃	—	2	2	no	—
203	C₂×C₃×D₄	—	2	2	no	—
204	C₂×C₃×D₄	—	3	8	no	—
205	C₂×C₃×D₄	—	3	2	no	—
206	C₂×C₃×D₄	—	6	4	no	—
207	C₂×C₃×D₄	—	6	2	no	—
208	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
209	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
210	C₂²×C₃×C₄	—	2	2	no	—
211	C₂²×C₃×C₄	—	2	2	no	—
212	C₂²×C₃×C₄	—	3	1	no	—
213	C₂²×C₃×C₄	—	4	2	no	—
214	C₂²×C₃×C₄	—	6	2	no	—
215	C₂²×C₃×C₄	—	6	2	no	—
216	C₂²×C₃×C₄	—	6	2	no	—
217	C₂×#67	—	2	2	no	—
218	C₂²×Dic₃	—	2	2	no	—
219	D₃×D₄	—	2	4	no	—
220	D₃×D₄	C₂×C₃×C₄	1	8	yes	complemented
221	C₂×D₁₂	C₂³×C₃	1	2	yes	—
222	C₂×C₄×D₃	—	2	2	no	—
223	C₂×C₄×D₃	—	2	2	no	—
224	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
225	C₃×D₈	—	2	4	no	—
226	C₃×D₈	—	3	8	no	—
227	C₃×D₈	—	3	4	no	—
228	C₃×D₈	C₄×D₃	1	4	yes	complemented
229	C₃×D₈	C₂×C₃×C₄	1	4	yes	complemented
230	C₃×M₁₆	—	6	2	no	—
231	C₂×C₃×C₈	—	2	1	no	—
232	C₂×C₃×C₈	—	2	1	no	—
233	C₂×C₃×C₈	—	3	1	no	—
234	C₂×C₃×C₈	—	3	4	no	—
235	C₂×C₃×C₈	—	3	1	no	—
236	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
240	C₃×C₄⋊C₄	—	2	2	no	—
241	C₃×C₄⋊C₄	—	3	1	no	—
242	C₃×C₄⋊C₄	—	3	1	no	—
243	C₃×C₄⋊C₄	—	3	2	no	—
244	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
245	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
246	C₃×C₂²⋊C₄	—	2	2	no	—
247	C₃×C₂²⋊C₄	—	2	2	no	—
248	C₃×C₂²⋊C₄	—	3	1	no	—
249	C₃×C₂²⋊C₄	—	3	1	no	—
250	C₃×C₂²⋊C₄	—	4	2	no	—
251	C₃×C₂²⋊C₄	—	6	2	no	—
252	C₃×C₂²⋊C₄	—	6	2	no	—
253	C₃×C₂²⋊C₄	—	6	2	no	—
254	C₃×C₂²⋊C₄	—	6	2	no	—
255	C₃×C₄²	—	2	1	no	—
256	C₃×C₄²	—	3	1	no	—
257	C₃×C₄²	—	6	2	no	—
258	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
259	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
260	#217	—	2	2	no	—
261	#213	C₂×C₃×C₄	1	8	yes	complemented
262	(C₂×D₃)⋊C₄	—	2	2	no	—
263	(C₂×D₃)⋊C₄	—	2	2	no	—
264	(C₂×D₃)⋊C₄	—	2	2	no	—
265	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
266	(C₂×D₃)⋊C₄	C₃×D₄	1	1	yes	characteristic
267	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
268	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
269	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
270	C₄×Dic₃	—	2	2	no	—
271	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
274	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
275	ΓL(1,𝔽₂₅)	—	2	2	no	—
276	D₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
277	C₂²×C₃²	—	2	4	no	—
278	C₂²×C₃²	—	4	2	no	—
279	C₂²×C₃²	—	4	2	no	—
280	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₃×D₃	—	2	1	no	—
282	C₂×C₃×D₃	—	2	1	no	—
283	C₂×C₃×D₃	—	2	4	no	—
284	C₂×C₃×D₃	—	4	2	no	—
285	C₂×C₃×D₃	—	4	2	no	—
286	C₂×C₃×D₃	—	8	8	no	—
287	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
288	C₃²×C₄	—	2	1	no	—
289	C₃²×C₄	—	2	1	no	—
290	C₃²×C₄	—	4	2	no	—
291	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
292	C₃²×C₄	C₂×#41	1	1	yes	characteristic
293	C₃×Dic₃	—	2	1	no	—
294	C₃×Dic₃	—	2	1	no	—
295	C₃×Dic₃	—	4	2	no	—
296	C₃×Dic₃	C₄×D₄	1	2	yes	—
297	C₂²×D₄	—	3	2	no	—
298	C₂×D₈	—	3	2	no	—
299	C₂×D₈	—	3	8	no	—
300	C₂×D₈	—	3	1	no	—
301	C₂×D₈	C₂×C₃×D₃	1	1	yes	characteristic
302	C₂×M₁₆	—	3	1	no	—
303	C₂²×C₈	—	3	1	no	—
304	C₄×D₄	—	3	2	no	—
305	C₄×D₄	—	3	2	no	—
306	C₄×D₄	—	3	2	no	—
307	C₄×D₄	—	6	2	no	—
308	C₄×D₄	—	6	2	no	—
309	C₄×D₄	C₂×C₃×D₃	1	2	yes	complemented
310	#117	—	3	1	no	—
311	#117	—	3	2	no	—
312	C₂×C₂²⋊C₄	—	6	2	no	—
313	C₂×C₂²⋊C₄	—	6	2	no	—
314	#107	—	3	1	no	—
315	#107	C₂×C₃×D₃	1	1	yes	characteristic, complemented
316	#106	—	3	2	no	—
317	#102	—	3	2	no	—
318	#102	—	3	2	no	—
319	#102	—	3	2	no	—
320	#102	C₂×C₃×D₃	1	2	yes	complemented
321	#97	—	3	1	no	—
322	#97	—	3	1	no	—
323	C₄×C₈	—	3	1	no	—
324	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
325	C₂³×C₃	—	2	2	no	—
326	C₂³×C₃	—	2	2	no	—
327	C₂³×C₃	—	3	1	no	—
328	C₂³×C₃	—	4	2	no	—
329	C₂³×C₃	—	6	8	no	—
330	C₂³×C₃	—	6	2	no	—
331	C₂³×C₃	—	24	2	no	—
332	C₂³×C₃	—	24	2	no	—
333	C₂²×D₃	—	2	2	no	—
334	C₂²×D₃	—	2	8	no	—
335	C₂²×D₃	—	8	2	no	—
336	C₂²×D₃	—	8	2	no	—
337	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	—	2	2	no	—
340	C₃×D₄	—	2	4	no	—
341	C₃×D₄	—	3	4	no	—
342	C₃×D₄	—	4	2	no	—
343	C₃×D₄	—	6	8	no	—
344	C₃×D₄	—	6	2	no	—
345	C₃×D₄	C₂×C₄×D₃	1	4	yes	—
346	C₃×D₄	C₂²×C₃×C₄	1	4	yes	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	2	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	3	1	no	—
353	C₂×C₃×C₄	—	3	2	no	—
354	C₂×C₃×C₄	—	3	2	no	—
355	C₂×C₃×C₄	—	3	1	no	—
356	C₂×C₃×C₄	—	3	1	no	—
357	C₂×C₃×C₄	—	4	2	no	—
358	C₂×C₃×C₄	—	6	2	no	—
359	C₂×C₃×C₄	—	8	2	no	—
360	C₂×C₃×C₄	—	8	2	no	—
361	C₂×C₃×C₄	—	8	4	no	—
362	C₂×C₃×C₄	—	24	2	no	—
363	C₂×C₃×C₄	—	24	2	no	—
364	C₂×C₃×C₄	—	24	2	no	—
365	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
366	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
371	#67	—	2	8	no	—
372	C₂×Dic₃	—	2	2	no	—
373	C₂×Dic₃	—	8	2	no	—
374	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
375	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
376	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
377	D₁₂	—	2	2	no	—
378	D₁₂	C₂²×C₃×C₄	1	4	yes	—
379	C₄×D₃	—	8	2	no	—
380	C₄×D₃	—	8	2	no	—
381	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
382	C₄×D₃	C₃×#41	1	2	yes	—
383	C₃×C₈	—	2	1	no	—
384	C₃×C₈	—	2	1	no	—
385	C₃×C₈	—	2	2	no	—
386	C₃×C₈	—	3	2	no	—
387	C₃×C₈	—	4	1	no	—
388	C₃×C₈	—	6	1	no	—
389	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
390	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
391	C₃⋊C₈	—	2	1	no	—
392	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
393	C₂×C₃²	—	4	4	no	—
394	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
395	C₂×C₃²	#576	1	1	yes	characteristic
396	C₂×C₃²	#576	1	1	yes	characteristic
397	C₃×D₃	—	2	2	no	—
398	C₃×D₃	—	4	4	no	—
399	C₂⁴	—	6	2	no	—
400	C₂×D₄	—	3	8	no	—
401	C₂×D₄	—	3	2	no	—
402	C₂×D₄	—	6	4	no	—
403	C₂×D₄	—	6	2	no	—
404	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	3	1	no	—
407	C₂²×C₄	—	6	2	no	—
408	C₂²×C₄	—	6	2	no	—
409	C₂²×C₄	—	6	2	no	—
410	D₈	—	3	8	no	—
411	D₈	—	3	4	no	—
412	D₈	C₃×C₄×D₃	1	4	yes	complemented
413	M₁₆	—	6	2	no	—
414	C₂×C₈	—	3	1	no	—
415	C₂×C₈	—	3	4	no	—
416	C₂×C₈	—	3	1	no	—
417	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
418	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
419	C₄⋊C₄	—	3	1	no	—
420	C₄⋊C₄	—	3	1	no	—
421	C₄⋊C₄	—	3	2	no	—
422	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	3	1	no	—
425	C₂²⋊C₄	—	3	1	no	—
426	C₂²⋊C₄	—	6	2	no	—
427	C₂²⋊C₄	—	6	2	no	—
428	C₂²⋊C₄	—	6	2	no	—
429	C₂²⋊C₄	—	6	2	no	—
430	C₄²	—	3	1	no	—
431	C₄²	—	6	2	no	—
432	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
433	C₂²×C₃	—	2	4	no	—
434	C₂²×C₃	—	2	4	no	—
435	C₂²×C₃	—	2	1	no	—
436	C₂²×C₃	—	3	2	no	—
437	C₂²×C₃	—	4	4	no	—
438	C₂²×C₃	—	4	2	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	—	4	2	no	—
441	C₂²×C₃	—	4	2	no	—
442	C₂²×C₃	—	6	1	no	—
443	C₂²×C₃	—	6	1	no	—
444	C₂²×C₃	—	6	4	no	—
445	C₂²×C₃	—	8	2	no	—
446	C₂²×C₃	—	8	2	no	—
447	C₂²×C₃	—	12	2	no	—
448	C₂²×C₃	—	12	2	no	—
449	C₂²×C₃	—	24	8	no	—
450	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
451	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
452	C₂×D₃	—	2	1	no	—
453	C₂×D₃	—	2	1	no	—
454	C₂×D₃	—	2	4	no	—
455	C₂×D₃	—	4	2	no	—
456	C₂×D₃	—	4	2	no	—
457	C₂×D₃	—	8	8	no	—
458	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
459	C₃×C₄	—	2	2	no	—
460	C₃×C₄	—	2	1	no	—
461	C₃×C₄	—	2	1	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	3	2	no	—
467	C₃×C₄	—	4	1	no	—
468	C₃×C₄	—	4	2	no	—
469	C₃×C₄	—	4	2	no	—
470	C₃×C₄	—	6	1	no	—
471	C₃×C₄	—	6	1	no	—
472	C₃×C₄	—	8	2	no	—
473	C₃×C₄	—	12	2	no	—
474	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
475	C₃×C₄	D₃×#41	1	1	yes	characteristic
476	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
477	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
478	Dic₃	—	2	1	no	—
479	Dic₃	—	2	1	no	—
480	Dic₃	—	4	2	no	—
481	Dic₃	C₃×C₄×D₄	1	2	yes	—
482	C₃²	#2948	1	1	yes	characteristic, complemented, Sylow
483	C₂³	—	2	2	no	—
484	C₂³	—	3	1	no	—
485	C₂³	—	6	8	no	—
486	C₂³	—	6	2	no	—
487	C₂³	—	24	2	no	—
488	C₂³	—	24	2	no	—
489	D₄	—	2	2	no	—
490	D₄	—	3	4	no	—
491	D₄	—	6	8	no	—
492	D₄	—	6	2	no	—
493	D₄	C₂×C₃×C₄×D₃	1	4	yes	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	3	1	no	—
496	C₂×C₄	—	3	2	no	—
497	C₂×C₄	—	3	2	no	—
498	C₂×C₄	—	3	1	no	—
499	C₂×C₄	—	3	1	no	—
500	C₂×C₄	—	6	2	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	24	2	no	—
503	C₂×C₄	—	24	2	no	—
504	C₂×C₄	—	24	2	no	—
505	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
506	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
508	C₈	—	2	1	no	—
509	C₈	—	3	2	no	—
510	C₈	—	6	1	no	—
511	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
512	C₂×C₃	—	2	1	no	—
513	C₂×C₃	—	2	1	no	—
514	C₂×C₃	—	2	1	no	—
515	C₂×C₃	—	4	4	no	—
516	C₂×C₃	—	4	4	no	—
517	C₂×C₃	—	6	2	no	—
518	C₂×C₃	—	8	4	no	—
519	C₂×C₃	—	12	4	no	—
520	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
521	C₂×C₃	#5757	1	1	yes	characteristic
522	C₂×C₃	#5769	1	1	yes	characteristic
523	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
524	C₂×C₃	C₃×#576	1	1	yes	characteristic
525	C₂×C₃	C₃×#576	1	1	yes	characteristic
526	D₃	—	2	2	no	—
527	D₃	—	4	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	3	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	6	1	no	—
533	C₂²	—	6	1	no	—
534	C₂²	—	6	4	no	—
535	C₂²	—	12	2	no	—
536	C₂²	—	12	2	no	—
537	C₂²	—	24	8	no	—
538	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	3	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	6	1	no	—
544	C₄	—	6	1	no	—
545	C₄	—	12	2	no	—
546	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
547	C₄	C₃×D₃×#41	1	1	yes	characteristic
548	C₃	—	2	1	no	—
549	C₃	#79588	1	1	yes	characteristic, direct product factor
550	C₃	C₃×#2948	1	1	yes	characteristic, complemented
551	C₂	—	4	4	no	—
552	C₂	—	6	2	no	—
553	C₂	—	12	4	no	—
554	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
555	C₂	C₃×#5757	1	1	yes	characteristic
556	C₂	C₃×#5769	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×D₈	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₃×D₈	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×D₈	D₃
hypocenter	C₃	C₃×#2948
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₃×#5545	C₂	semidirect
3. C₃²×C₄×D₈	C₂	semidirect
4. C₃×Dic₃×D₈	C₂	semidirect
5. C₃×#5014	C₂	semidirect
6. C₃×#4880	C₂	semidirect
7. C₃×#4872	C₂	semidirect
8. C₃×#4785	C₂	semidirect
9. C₃×#4770	C₂	semidirect
10. C₃×C₄×D₂₄	C₂	semidirect
11. C₃×#4689	C₂	semidirect
13. #79588	C₃	direct (N × H)
16. C₃²×C₄×D₄	C₂²	semidirect
17. C₃×D₄×Dic₃	C₂²	semidirect
21. C₃×D₃×D₈	C₄	semidirect
25. C₃×#893	C₂²	semidirect
29. C₃×C₄×D₁₂	C₂²	semidirect
31. C₃²×#107	C₂²	semidirect
32. C₃²×#102	C₂²	semidirect
33. C₃²×C₄×C₈	C₂²	semidirect
34. C₃×#832	C₂²	semidirect
35. C₃×#821	C₂²	semidirect
36. C₃×#818	C₂²	semidirect
37. C₃×#815	C₂²	semidirect
38. C₃×C₈×Dic₃	C₂²	semidirect
39. C₃×#809	C₂²	semidirect
40. C₃×#808	C₂²	semidirect
41. C₃×#803	C₂²	semidirect
45. #5545	C₂×C₃	semidirect
52. C₃×C₄×D₈	D₃	semidirect
53. C₃×C₄×D₈	C₂×C₃	semidirect
57. Dic₃×D₈	C₂×C₃	semidirect
58. #5014	C₂×C₃	semidirect
59. #4880	C₂×C₃	semidirect
60. #4872	C₂×C₃	semidirect
61. #4785	C₂×C₃	semidirect
62. #4770	C₂×C₃	semidirect
63. C₄×D₂₄	C₂×C₃	semidirect
64. #4689	C₂×C₃	semidirect
71. C₃×D₃×D₄	C₂×C₄	semidirect
76. C₃²×D₈	C₂×C₄	semidirect
83. C₃×#213	C₂×C₄	semidirect
96. C₃×D₂₄	C₂×C₄	semidirect
98. C₃×D₃×C₈	C₂×C₄	semidirect
116. C₃×C₄×D₄	C₂×D₃	semidirect
117. C₃×C₄×D₄	C₂²×C₃	semidirect
122. D₄×Dic₃	C₂²×C₃	semidirect
126. D₃×D₈	C₃×C₄	semidirect
130. #893	C₂²×C₃	semidirect
134. C₄×D₁₂	C₂²×C₃	semidirect
138. C₃×#107	C₂×D₃	semidirect
139. C₃×#107	C₂²×C₃	semidirect
145. C₃×#102	C₂×D₃	semidirect
146. C₃×#102	C₂²×C₃	semidirect
151. C₃×C₄×C₈	C₂×D₃	semidirect
152. C₃×C₄×C₈	C₂²×C₃	semidirect
153. #832	C₂²×C₃	semidirect
154. #821	C₂²×C₃	semidirect
155. #818	C₂²×C₃	semidirect
156. #815	C₂²×C₃	semidirect
157. C₈×Dic₃	C₂²×C₃	semidirect
158. #809	C₂²×C₃	semidirect
159. #808	C₂²×C₃	semidirect
160. #803	C₂²×C₃	semidirect
197. C₄×D₈	C₃×D₃	semidirect
220. D₃×D₄	C₂×C₃×C₄	semidirect
228. C₃×D₈	C₄×D₃	semidirect
229. C₃×D₈	C₂×C₃×C₄	semidirect
261. #213	C₂×C₃×C₄	semidirect
274. D₂₄	C₂×C₃×C₄	semidirect
276. D₃×C₈	C₂×C₃×C₄	semidirect
309. C₄×D₄	C₂×C₃×D₃	semidirect
315. #107	C₂×C₃×D₃	semidirect
320. #102	C₂×C₃×D₃	semidirect
324. C₄×C₈	C₂×C₃×D₃	semidirect
412. D₈	C₃×C₄×D₃	semidirect
482. C₃²	#2948	semidirect
549. C₃	#79588	direct (N × H)
550. C₃	C₃×#2948	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×D₈	2
C₃×#5545	2
C₃²×C₄×D₈	2
C₃×Dic₃×D₈	2
C₃×#5014	2
C₃×#4880	2
C₃×#4872	2
C₃×#4785	2
C₃×#4770	2
C₃×C₄×D₂₄	2
C₃×#4689	2
C₃×#2948	3
#79588	3

Subgroups — C3×#79588 #11860660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79588 #11860660