Subgroups — C₃×#79538 #11859461

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#907	C₂	1	2	yes	maximal, complemented
2	C₃×#5548	C₂	1	1	yes	maximal, characteristic
3	C₃²×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5128	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4837	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4834	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4727	C₂	1	2	yes	maximal, complemented
9	C₃×#67⋊C₈	C₂	1	2	yes	maximal, complemented
10	C₃×#4688	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2931	—	3	1	no	maximal
13	#79538	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#235	C₂²	1	2	yes	—
15	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
16	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
17	C₃×#940	C₄	1	1	yes	characteristic
18	C₃×#938	C₄	1	1	yes	characteristic
19	C₃×C₄×#67	C₂²	1	2	yes	—
20	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
21	C₃×#907	—	2	8	no	—
22	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
23	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
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	C₃×#895	C₄	1	1	yes	characteristic
28	C₃×#888	C₄	1	1	yes	characteristic
29	C₃×#885	C₄	1	2	yes	—
30	C₃×#884	C₄	1	2	yes	—
31	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
32	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
33	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃²×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
36	C₃×#830	C₂²	1	2	yes	—
37	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
38	C₃×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
39	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
40	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
41	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
42	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₃×#131	—	3	2	no	—
45	C₃×#532	—	3	1	no	—
46	C₂×#907	C₂×C₃	1	2	yes	complemented
47	#5548	C₂×C₃	1	1	yes	characteristic
48	C₃×#436	—	2	1	no	—
49	C₃×#436	—	3	2	no	—
50	C₃×#436	—	3	1	no	—
51	C₃×#436	D₃	1	1	yes	characteristic, complemented
52	C₃×#436	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×C₈×D₄	—	3	1	no	—
54	C₃×C₈×D₄	—	3	1	no	—
55	C₃×C₈×D₄	—	3	2	no	—
56	C₃×#423	—	3	1	no	—
57	C₃×#408	—	3	2	no	—
58	C₂×C₃×C₄×C₈	—	3	1	no	—
59	#5128	C₂×C₃	1	2	yes	complemented
60	D₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
61	#4837	C₂×C₃	1	1	yes	characteristic, complemented
62	#4834	C₂×C₃	1	1	yes	characteristic, complemented
63	#4727	C₂×C₃	1	2	yes	complemented
64	#67⋊C₈	C₂×C₃	1	2	yes	complemented
65	#4688	C₂×C₃	1	1	yes	characteristic, complemented
66	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic, complemented
67	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₃²×C₄	C₂³	1	2	yes	—
69	C₂×C₃×#67	C₂×C₄	1	2	yes	—
70	C₂×C₃×#67	C₂×C₄	1	2	yes	—
71	C₂×C₃×#67	C₂×C₄	1	2	yes	—
72	C₃×#235	—	2	4	no	—
73	C₃×#235	—	2	4	no	—
74	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
75	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
79	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
81	C₃²×M₁₆	—	2	4	no	—
82	C₂×C₃²×C₈	C₂³	1	2	yes	—
83	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
84	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
85	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
87	C₃²×C₄²	C₂³	1	1	yes	characteristic
88	C₃×#217	C₂×C₄	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
91	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
92	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
93	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
94	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
95	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₃⋊C₈	—	2	4	no	—
97	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
99	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
101	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
102	C₃×D₃×C₈	—	2	2	no	—
103	C₃×D₃×C₈	—	2	4	no	—
104	C₃×D₃×C₈	D₄	1	4	yes	complemented
105	#2931	—	3	1	no	Sylow
106	C₂×C₃×#41	—	3	2	no	—
107	C₂×#235	C₂²×C₃	1	2	yes	—
108	C₃×#131	—	6	8	no	—
109	C₂×C₃×M₁₆	—	2	2	no	—
110	C₂×C₃×M₁₆	—	3	2	no	—
111	C₂×C₃×M₁₆	—	3	2	no	—
112	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
113	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
114	C₂²×C₃×C₈	—	3	1	no	—
115	C₂²×C₃×C₈	—	3	2	no	—
116	C₂²×C₃×C₈	—	3	2	no	—
117	C₂²×C₃×C₈	—	3	1	no	—
118	C₃×C₄⋊Q₈	—	3	1	no	—
119	C₃×#127	—	3	1	no	—
120	C₃×#124	—	3	2	no	—
121	C₃×#121	—	3	1	no	—
122	C₃×#121	—	3	1	no	—
123	C₃×#121	—	3	2	no	—
124	C₃×C₄×D₄	—	2	1	no	—
125	C₃×C₄×D₄	—	3	2	no	—
126	C₃×C₄×D₄	—	3	1	no	—
127	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
128	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄²	—	3	1	no	—
130	#940	C₃×C₄	1	1	yes	characteristic
131	#938	C₃×C₄	1	1	yes	characteristic
132	C₄×#67	C₂²×C₃	1	2	yes	—
133	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
134	#907	—	2	8	no	—
135	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
136	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
137	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
138	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
139	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
140	#895	C₃×C₄	1	1	yes	characteristic
141	#888	C₃×C₄	1	1	yes	characteristic
142	#885	C₃×C₄	1	2	yes	—
143	#884	C₃×C₄	1	2	yes	—
144	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
145	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
146	C₃×C₄⋊C₈	—	2	1	no	—
147	C₃×C₄⋊C₈	—	3	2	no	—
148	C₃×C₄⋊C₈	—	3	1	no	—
149	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
150	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
151	C₃×C₂²⋊C₈	—	2	2	no	—
152	C₃×C₂²⋊C₈	—	3	2	no	—
153	C₃×C₂²⋊C₈	—	3	2	no	—
154	C₃×C₂²⋊C₈	—	3	2	no	—
155	C₃×C₂²⋊C₈	C₂×D₃	1	2	yes	—
156	C₃×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
157	C₃×C₄×C₈	—	2	1	no	—
158	C₃×C₄×C₈	—	3	1	no	—
159	C₃×C₄×C₈	—	3	1	no	—
160	C₃×C₄×C₈	—	3	1	no	—
161	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
162	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
163	#830	C₂²×C₃	1	2	yes	—
164	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
165	(C₂×D₃)⋊C₈	C₂²×C₃	1	2	yes	—
166	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
167	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
168	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
169	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
170	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	C₂³×C₃²	C₂²×C₄	1	2	yes	—
172	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
173	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
174	C₃²×D₄	—	2	2	no	—
175	C₂×C₃²×C₄	—	2	2	no	—
176	C₂×C₃²×C₄	—	2	2	no	—
177	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
179	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
181	C₃×#67	—	2	4	no	—
182	C₃×#67	—	2	4	no	—
183	C₃×#67	—	2	4	no	—
184	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
186	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
188	C₃×D₁₂	—	2	4	no	—
189	C₃×D₁₂	—	2	2	no	—
190	C₃×C₄×D₃	—	2	2	no	—
191	C₃×C₄×D₃	—	2	2	no	—
192	C₃×C₄×D₃	—	2	2	no	—
193	C₃×C₄×D₃	—	2	2	no	—
194	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
195	C₃×C₄×D₃	#41	1	2	yes	—
196	C₃×Dic₆	—	2	4	no	—
197	C₃²×C₈	—	2	2	no	—
198	C₃²×C₈	—	2	1	no	—
199	C₃²×C₈	C₂×D₄	1	2	yes	—
200	C₃×C₃⋊C₈	—	2	2	no	—
201	C₃×C₃⋊C₈	—	2	1	no	—
202	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
203	C₂×#131	—	3	2	no	—
204	#532	—	3	1	no	—
205	#436	—	3	2	no	—
206	#436	—	3	1	no	—
207	#436	C₃×D₃	1	1	yes	characteristic, complemented
208	C₈×D₄	—	3	1	no	—
209	C₈×D₄	—	3	1	no	—
210	C₈×D₄	—	3	2	no	—
211	#423	—	3	1	no	—
212	#408	—	3	2	no	—
213	C₂×C₄×C₈	—	3	1	no	—
214	C₃×#41	—	6	4	no	—
215	C₃×#41	—	6	4	no	—
216	C₂×C₃×Q₈	—	3	2	no	—
217	C₂×C₃×D₄	—	2	1	no	—
218	C₂×C₃×D₄	—	3	2	no	—
219	C₂×C₃×D₄	—	3	2	no	—
220	C₂×C₃×D₄	—	3	2	no	—
221	C₂×C₃×D₄	—	3	1	no	—
222	C₂×C₃×D₄	—	3	2	no	—
223	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
224	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	—	3	1	no	—
227	C₂²×C₃×C₄	—	3	1	no	—
228	C₂²×C₃×C₄	—	3	1	no	—
229	C₂²×C₃×C₄	—	3	2	no	—
230	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
231	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
232	C₂×#67	C₂×C₃×C₄	1	2	yes	—
233	C₂×#67	C₂×C₃×C₄	1	2	yes	—
234	C₂×#67	C₂×C₃×C₄	1	2	yes	—
235	#235	—	2	4	no	—
236	#235	—	2	4	no	—
237	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
238	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
239	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
240	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
241	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
242	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
243	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
244	C₃×M₁₆	—	2	4	no	—
245	C₃×M₁₆	—	2	4	no	—
246	C₃×M₁₆	—	4	4	no	—
247	C₃×M₁₆	—	6	4	no	—
248	C₃×M₁₆	—	6	4	no	—
249	C₂×C₃×C₈	—	2	1	no	—
250	C₂×C₃×C₈	—	2	1	no	—
251	C₂×C₃×C₈	—	2	2	no	—
252	C₂×C₃×C₈	—	3	1	no	—
253	C₂×C₃×C₈	—	3	4	no	—
254	C₂×C₃×C₈	—	3	1	no	—
255	C₂×C₃×C₈	—	3	2	no	—
256	C₂×C₃×C₈	—	6	4	no	—
257	C₂×C₃×C₈	—	6	2	no	—
258	C₂×C₃×C₈	—	6	4	no	—
259	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
261	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
262	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
264	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
265	C₃×C₄⋊C₄	—	2	1	no	—
266	C₃×C₄⋊C₄	—	3	2	no	—
267	C₃×C₄⋊C₄	—	3	1	no	—
268	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
269	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
270	C₃×C₂²⋊C₄	—	2	2	no	—
271	C₃×C₂²⋊C₄	—	3	2	no	—
272	C₃×C₂²⋊C₄	—	3	2	no	—
273	C₃×C₂²⋊C₄	—	3	2	no	—
274	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
275	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
276	C₃×C₄²	—	2	1	no	—
277	C₃×C₄²	—	3	1	no	—
278	C₃×C₄²	—	3	1	no	—
279	C₃×C₄²	—	3	1	no	—
280	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
281	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
282	#217	C₂×C₃×C₄	1	2	yes	—
283	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
284	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
285	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
286	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
287	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
288	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
289	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₃⋊C₈	—	2	4	no	—
291	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
293	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
294	ΓL(1,𝔽₂₅)	—	2	4	no	—
295	ΓL(1,𝔽₂₅)	—	2	4	no	—
296	D₃×C₈	—	2	2	no	—
297	D₃×C₈	—	2	4	no	—
298	D₃×C₈	C₃×D₄	1	4	yes	complemented
299	C₂²×C₃²	—	2	2	no	—
300	C₂²×C₃²	—	2	2	no	—
301	C₂²×C₃²	—	2	2	no	—
302	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
303	C₂×C₃×D₃	—	2	1	no	—
304	C₂×C₃×D₃	—	2	1	no	—
305	C₂×C₃×D₃	—	2	2	no	—
306	C₂×C₃×D₃	—	2	2	no	—
307	C₂×C₃×D₃	—	2	2	no	—
308	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
309	C₃²×C₄	—	2	2	no	—
310	C₃²×C₄	—	2	1	no	—
311	C₃²×C₄	#131	1	2	yes	complemented
312	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₃²×C₄	C₂×#41	1	1	yes	characteristic
314	C₃×Dic₃	—	2	2	no	—
315	C₃×Dic₃	—	2	1	no	—
316	C₃×Dic₃	C₄×D₄	1	2	yes	—
317	C₃×Dic₃	#131	1	2	yes	complemented
318	C₂×#41	—	3	2	no	—
319	#131	—	6	8	no	—
320	C₂×M₁₆	—	3	2	no	—
321	C₂×M₁₆	—	3	2	no	—
322	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
323	C₂²×C₈	—	3	1	no	—
324	C₂²×C₈	—	3	2	no	—
325	C₂²×C₈	—	3	2	no	—
326	C₂²×C₈	—	3	1	no	—
327	C₄⋊Q₈	—	3	1	no	—
328	#127	—	3	1	no	—
329	#124	—	3	2	no	—
330	#121	—	3	1	no	—
331	#121	—	3	1	no	—
332	#121	—	3	2	no	—
333	C₄×D₄	—	3	2	no	—
334	C₄×D₄	—	3	1	no	—
335	C₄×D₄	C₂×C₃×D₃	1	1	yes	characteristic
336	C₂×C₄²	—	3	1	no	—
337	C₄⋊C₈	—	3	2	no	—
338	C₄⋊C₈	—	3	1	no	—
339	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
340	C₂²⋊C₈	—	3	2	no	—
341	C₂²⋊C₈	—	3	2	no	—
342	C₂²⋊C₈	—	3	2	no	—
343	C₂²⋊C₈	C₂×C₃×D₃	1	2	yes	—
344	C₄×C₈	—	3	1	no	—
345	C₄×C₈	—	3	1	no	—
346	C₄×C₈	—	3	1	no	—
347	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
348	C₂³×C₃	—	2	2	no	—
349	C₂³×C₃	—	3	1	no	—
350	C₂³×C₃	—	3	2	no	—
351	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
352	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
353	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
354	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
355	C₃×Q₈	—	6	4	no	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	2	2	no	—
358	C₃×D₄	—	4	2	no	—
359	C₃×D₄	—	6	4	no	—
360	C₃×D₄	—	6	4	no	—
361	C₃×D₄	—	6	4	no	—
362	C₃×D₄	—	6	4	no	—
363	C₃×D₄	—	6	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	3	1	no	—
373	C₂×C₃×C₄	—	3	1	no	—
374	C₂×C₃×C₄	—	3	2	no	—
375	C₂×C₃×C₄	—	3	2	no	—
376	C₂×C₃×C₄	—	3	1	no	—
377	C₂×C₃×C₄	—	3	2	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	4	2	no	—
380	C₂×C₃×C₄	—	6	2	no	—
381	C₂×C₃×C₄	—	6	2	no	—
382	C₂×C₃×C₄	—	6	2	no	—
383	C₂×C₃×C₄	—	6	2	no	—
384	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
386	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
389	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
392	#67	—	2	4	no	—
393	#67	—	2	4	no	—
394	#67	—	2	4	no	—
395	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
396	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
397	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
398	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
399	D₁₂	—	2	4	no	—
400	D₁₂	—	2	2	no	—
401	C₄×D₃	—	2	2	no	—
402	C₄×D₃	—	2	2	no	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
406	C₄×D₃	C₃×#41	1	2	yes	—
407	Dic₆	—	2	4	no	—
408	C₃×C₈	—	2	2	no	—
409	C₃×C₈	—	2	1	no	—
410	C₃×C₈	—	2	2	no	—
411	C₃×C₈	—	2	1	no	—
412	C₃×C₈	—	2	2	no	—
413	C₃×C₈	—	3	2	no	—
414	C₃×C₈	—	4	1	no	—
415	C₃×C₈	—	4	2	no	—
416	C₃×C₈	—	6	2	no	—
417	C₃×C₈	—	6	1	no	—
418	C₃×C₈	D₃×D₄	1	2	yes	—
419	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
420	C₃⋊C₈	—	2	2	no	—
421	C₃⋊C₈	—	2	1	no	—
422	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
423	C₂×C₃²	—	4	2	no	—
424	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
425	C₂×C₃²	C₂×#131	1	1	yes	characteristic
426	C₂×C₃²	C₂×#131	1	1	yes	characteristic
427	C₃×D₃	—	2	2	no	—
428	C₃×D₃	—	4	2	no	—
429	#41	—	6	4	no	—
430	#41	—	6	4	no	—
431	C₂×Q₈	—	3	2	no	—
432	C₂×D₄	—	3	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	3	2	no	—
435	C₂×D₄	—	3	1	no	—
436	C₂×D₄	—	3	2	no	—
437	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
438	C₂²×C₄	—	3	1	no	—
439	C₂²×C₄	—	3	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	3	1	no	—
442	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
443	M₁₆	—	2	4	no	—
444	M₁₆	—	6	4	no	—
445	M₁₆	—	6	4	no	—
446	C₂×C₈	—	3	1	no	—
447	C₂×C₈	—	3	4	no	—
448	C₂×C₈	—	3	1	no	—
449	C₂×C₈	—	3	2	no	—
450	C₂×C₈	—	6	4	no	—
451	C₂×C₈	—	6	2	no	—
452	C₂×C₈	—	6	4	no	—
453	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
454	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
455	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
456	C₄⋊C₄	—	3	2	no	—
457	C₄⋊C₄	—	3	1	no	—
458	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
459	C₂²⋊C₄	—	3	2	no	—
460	C₂²⋊C₄	—	3	2	no	—
461	C₂²⋊C₄	—	3	2	no	—
462	C₂²⋊C₄	C₃×C₄×D₃	1	2	yes	—
463	C₄²	—	3	1	no	—
464	C₄²	—	3	1	no	—
465	C₄²	—	3	1	no	—
466	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
467	C₂²×C₃	—	2	2	no	—
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	1	no	—
474	C₂²×C₃	—	3	2	no	—
475	C₂²×C₃	—	4	2	no	—
476	C₂²×C₃	—	4	2	no	—
477	C₂²×C₃	—	4	2	no	—
478	C₂²×C₃	—	6	1	no	—
479	C₂²×C₃	—	6	1	no	—
480	C₂²×C₃	—	6	2	no	—
481	C₂²×C₃	—	6	2	no	—
482	C₂²×C₃	—	6	2	no	—
483	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
484	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
485	C₂×D₃	—	2	1	no	—
486	C₂×D₃	—	2	1	no	—
487	C₂×D₃	—	2	2	no	—
488	C₂×D₃	—	2	2	no	—
489	C₂×D₃	—	2	2	no	—
490	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
491	C₃×C₄	—	2	1	no	—
492	C₃×C₄	—	2	1	no	—
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	3	2	no	—
499	C₃×C₄	—	3	2	no	—
500	C₃×C₄	—	4	2	no	—
501	C₃×C₄	—	4	1	no	—
502	C₃×C₄	—	6	1	no	—
503	C₃×C₄	—	6	2	no	—
504	C₃×C₄	#907	1	2	yes	complemented
505	C₃×C₄	C₃×#131	1	2	yes	complemented
506	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
507	C₃×C₄	D₃×#41	1	1	yes	characteristic
508	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
509	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
510	Dic₃	—	2	1	no	—
511	Dic₃	—	2	2	no	—
512	Dic₃	C₃×C₄×D₄	1	2	yes	—
513	Dic₃	C₃×#131	1	2	yes	complemented
514	C₃²	#2931	1	1	yes	characteristic, complemented, Sylow
515	C₂³	—	3	1	no	—
516	C₂³	—	3	2	no	—
517	C₂³	C₂×C₃×C₄×D₃	1	2	yes	—
518	Q₈	—	6	4	no	—
519	D₄	—	2	2	no	—
520	D₄	—	6	4	no	—
521	D₄	—	6	4	no	—
522	D₄	—	6	4	no	—
523	D₄	—	6	4	no	—
524	D₄	—	6	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	3	1	no	—
528	C₂×C₄	—	3	1	no	—
529	C₂×C₄	—	3	2	no	—
530	C₂×C₄	—	3	2	no	—
531	C₂×C₄	—	3	1	no	—
532	C₂×C₄	—	3	2	no	—
533	C₂×C₄	—	6	2	no	—
534	C₂×C₄	—	6	2	no	—
535	C₂×C₄	—	6	2	no	—
536	C₂×C₄	—	6	2	no	—
537	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
538	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
539	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
540	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	2	1	no	—
543	C₈	—	3	2	no	—
544	C₈	—	6	2	no	—
545	C₈	—	6	1	no	—
546	C₈	C₃×D₃×D₄	1	2	yes	—
547	C₂×C₃	—	2	1	no	—
548	C₂×C₃	—	2	1	no	—
549	C₂×C₃	—	2	1	no	—
550	C₂×C₃	—	4	2	no	—
551	C₂×C₃	—	4	2	no	—
552	C₂×C₃	—	6	2	no	—
553	C₂×C₃	—	8	2	no	—
554	C₂×C₃	—	12	2	no	—
555	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
556	C₂×C₃	C₂×#907	1	1	yes	characteristic
557	C₂×C₃	D₃×#131	1	1	yes	characteristic
558	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
559	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
560	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
561	D₃	—	2	2	no	—
562	D₃	—	4	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	3	2	no	—
567	C₂²	—	6	1	no	—
568	C₂²	—	6	1	no	—
569	C₂²	—	6	2	no	—
570	C₂²	—	6	2	no	—
571	C₂²	—	6	2	no	—
572	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	3	2	no	—
576	C₄	—	3	2	no	—
577	C₄	—	6	1	no	—
578	C₄	—	6	2	no	—
579	C₄	C₃×#907	1	2	yes	complemented
580	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
581	C₄	C₃×D₃×#41	1	1	yes	characteristic
582	C₃	—	2	1	no	—
583	C₃	#79538	1	1	yes	characteristic, direct product factor
584	C₃	C₃×#2931	1	1	yes	characteristic, complemented
585	C₂	—	4	2	no	—
586	C₂	—	6	2	no	—
587	C₂	—	12	2	no	—
588	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
589	C₂	C₂×C₃×#907	1	1	yes	characteristic
590	C₂	C₃×D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#436	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₃×#5548	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#436	D₃
hypocenter	C₃	C₃×#2931
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#436

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#907	C₂	semidirect
3. C₃²×#436	C₂	semidirect
4. C₃×#5128	C₂	semidirect
5. C₃×D₄×C₃⋊C₈	C₂	semidirect
6. C₃×#4837	C₂	semidirect
7. C₃×#4834	C₂	semidirect
8. C₃×#4727	C₂	semidirect
9. C₃×#67⋊C₈	C₂	semidirect
10. C₃×#4688	C₂	semidirect
11. C₃×C₄×D₃×C₈	C₂	semidirect
13. #79538	C₃	direct (N × H)
46. C₂×#907	C₂×C₃	semidirect
51. C₃×#436	D₃	semidirect
52. C₃×#436	C₂×C₃	semidirect
59. #5128	C₂×C₃	semidirect
60. D₄×C₃⋊C₈	C₂×C₃	semidirect
61. #4837	C₂×C₃	semidirect
62. #4834	C₂×C₃	semidirect
63. #4727	C₂×C₃	semidirect
64. #67⋊C₈	C₂×C₃	semidirect
65. #4688	C₂×C₃	semidirect
66. C₄×D₃×C₈	C₂×C₃	semidirect
104. C₃×D₃×C₈	D₄	semidirect
207. #436	C₃×D₃	semidirect
298. D₃×C₈	C₃×D₄	semidirect
311. C₃²×C₄	#131	semidirect
317. C₃×Dic₃	#131	semidirect
504. C₃×C₄	#907	semidirect
505. C₃×C₄	C₃×#131	semidirect
513. Dic₃	C₃×#131	semidirect
514. C₃²	#2931	semidirect
579. C₄	C₃×#907	semidirect
583. C₃	#79538	direct (N × H)
584. C₃	C₃×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#907	2
C₃×#5548	2
C₃²×#436	2
C₃×#5128	2
C₃×D₄×C₃⋊C₈	2
C₃×#4837	2
C₃×#4834	2
C₃×#4727	2
C₃×#67⋊C₈	2
C₃×#4688	2
C₃×C₄×D₃×C₈	2
C₃×#2931	3
#79538	3

Subgroups — C3×#79538 #11859461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79538 #11859461