Subgroups — C₃×#79889 #11861132

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5768	C₂	1	1	yes	maximal, characteristic
2	C₃×#5750	C₂	1	2	yes	maximal, complemented
3	C₃²×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5197	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5145	C₂	1	2	yes	maximal, complemented
6	C₃×#4894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4824	C₂	1	2	yes	maximal, complemented
9	C₃×D₃×#104	C₂	1	2	yes	maximal, complemented
10	C₃×#4700	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2956	—	3	1	no	maximal
13	#79889	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃×D₃×#41	C₂²	1	2	yes	—
15	C₃²×#135	C₂²	1	1	yes	characteristic
16	C₃²×#131	C₂²	1	2	yes	complemented
17	C₃×#950	C₂²	1	2	yes	—
18	C₃×#948	C₂²	1	2	yes	complemented
19	C₃×#918	C₄	1	2	yes	complemented
20	C₃×#915	C₄	1	2	yes	complemented
21	C₃×#914	C₄	1	2	yes	complemented
22	C₃×#911	C₄	1	2	yes	complemented
23	C₃×#907	—	2	2	no	—
24	C₃×#907	C₂²	1	2	yes	complemented
25	C₃×D₃×M₁₆	—	2	2	no	—
26	C₃×D₃×M₁₆	C₂²	1	2	yes	—
27	C₃×#904	C₂²	1	1	yes	characteristic
28	C₃×#901	—	2	2	no	—
29	C₃×#901	C₂²	1	2	yes	complemented
30	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
31	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
32	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
33	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
34	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
35	C₃²×#104	C₂²	1	2	yes	complemented
36	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
37	C₃×#837	C₂²	1	2	yes	complemented
38	C₃×#825	C₂²	1	2	yes	complemented
39	C₃×#822	C₂²	1	2	yes	complemented
40	C₃×#819	C₂²	1	1	yes	characteristic, complemented
41	C₃×#815	C₂²	1	1	yes	characteristic, complemented
42	C₃×#815	C₂²	1	1	yes	characteristic, complemented
43	C₃×#805	C₂²	1	2	yes	complemented
44	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₃×#575	—	3	1	no	—
46	C₃×#568	—	3	2	no	—
47	#5768	C₂×C₃	1	1	yes	characteristic
48	#5750	C₂×C₃	1	2	yes	complemented
49	C₃×#444	—	3	1	no	—
50	C₃×#444	—	3	2	no	—
51	C₃×#444	—	3	1	no	—
52	C₃×#443	—	2	1	no	—
53	C₃×#443	—	3	2	no	—
54	C₃×#443	—	3	1	no	—
55	C₃×#443	D₃	1	1	yes	characteristic, complemented
56	C₃×#443	C₂×C₃	1	1	yes	characteristic, complemented
57	C₃×#430	—	3	1	no	—
58	C₂×C₃×#104	—	3	2	no	—
59	C₃×C₄×M₁₆	—	3	1	no	—
60	#5197	C₂×C₃	1	1	yes	characteristic, complemented
61	#5145	C₂×C₃	1	2	yes	complemented
62	#4894	C₂×C₃	1	1	yes	characteristic, complemented
63	#4893	C₂×C₃	1	1	yes	characteristic, complemented
64	#4824	C₂×C₃	1	2	yes	complemented
65	D₃×#104	C₂×C₃	1	2	yes	complemented
66	#4700	C₂×C₃	1	1	yes	characteristic, complemented
67	C₄×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic, complemented
68	C₃²×#41	C₂³	1	2	yes	—
69	C₃×#239	C₂×C₄	1	2	yes	—
70	C₃×D₃×Q₈	C₂×C₄	1	2	yes	—
71	C₃×#237	—	2	2	no	—
72	C₃×#237	C₂×C₄	1	2	yes	—
73	C₃×D₃×D₄	—	2	2	no	—
74	C₃×D₃×D₄	C₂×C₄	1	2	yes	—
75	C₃×#235	—	2	2	no	—
76	C₃×#235	C₂³	1	2	yes	—
77	C₂×C₃×C₄×D₃	—	2	2	no	—
78	C₂×C₃×C₄×D₃	—	2	1	no	—
79	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
80	C₃²×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
81	C₃²×SD₁₆	C₂×C₄	1	2	yes	complemented
82	C₃²×D₈	C₂×C₄	1	1	yes	characteristic, complemented
83	C₃²×M₁₆	—	2	2	no	—
84	C₃²×M₁₆	C₂³	1	2	yes	—
85	C₂×C₃²×C₈	—	2	2	no	—
86	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
87	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
88	C₃²×C₄²	C₂³	1	1	yes	characteristic
89	C₃×#216	C₂×C₄	1	2	yes	complemented
90	C₃×#215	C₂×C₄	1	2	yes	complemented
91	C₃×#214	C₂×C₄	1	2	yes	complemented
92	C₃×#213	C₂×C₄	1	2	yes	complemented
93	C₃×C₄×Dic₃	—	2	1	no	—
94	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
95	C₃×#208	—	2	2	no	—
96	C₃×#208	C₂³	1	2	yes	—
97	C₂×C₃×C₃⋊C₈	—	2	2	no	—
98	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
100	C₃×Dic₁₂	C₂×C₄	1	1	yes	characteristic, complemented
101	C₃×D₂₄	C₂×C₄	1	1	yes	characteristic, complemented
102	C₃×#204	C₂×C₄	1	2	yes	complemented
103	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
104	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
105	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
106	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
107	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
108	C₃×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
109	C₃×ΓL(1,𝔽₂₅)	D₄	1	2	yes	—
110	C₃×D₃×C₈	—	2	2	no	—
111	C₃×D₃×C₈	—	2	2	no	—
112	C₃×D₃×C₈	—	2	2	no	—
113	#2956	—	3	1	no	Sylow
114	C₂×C₃×#41	—	3	2	no	—
115	D₃×#41	C₂²×C₃	1	2	yes	—
116	C₃×#137	—	3	2	no	—
117	C₃×#137	—	3	2	no	—
118	C₃×AGL(1,ℤ/8)	—	3	2	no	—
119	C₃×AGL(1,ℤ/8)	—	3	2	no	—
120	C₃×#135	—	2	1	no	—
121	C₃×#135	—	3	2	no	—
122	C₃×#135	—	3	1	no	—
123	C₃×#135	C₂×D₃	1	1	yes	characteristic
124	C₃×#135	C₂²×C₃	1	1	yes	characteristic
125	C₃×#131	—	2	2	no	—
126	C₃×#131	—	3	2	no	—
127	C₃×#131	—	3	2	no	—
128	C₃×#131	—	3	2	no	—
129	C₃×#131	—	6	2	no	—
130	C₃×#131	—	6	2	no	—
131	C₃×#131	C₂×D₃	1	2	yes	complemented
132	C₃×#131	C₂²×C₃	1	2	yes	complemented
133	C₂×C₃×M₁₆	—	3	1	no	—
134	C₂×C₃×M₁₆	—	3	1	no	—
135	C₂×C₃×M₁₆	—	3	2	no	—
136	C₂×C₃×M₁₆	—	6	2	no	—
137	C₂×C₃×M₁₆	—	6	2	no	—
138	C₂×C₃×C₄²	—	3	1	no	—
139	#950	C₂²×C₃	1	2	yes	—
140	#948	C₂²×C₃	1	2	yes	complemented
141	#918	C₃×C₄	1	2	yes	complemented
142	#915	C₃×C₄	1	2	yes	complemented
143	#914	C₃×C₄	1	2	yes	complemented
144	#911	C₃×C₄	1	2	yes	complemented
145	#907	—	2	2	no	—
146	#907	C₂²×C₃	1	2	yes	complemented
147	D₃×M₁₆	—	2	2	no	—
148	D₃×M₁₆	C₂²×C₃	1	2	yes	—
149	#904	C₂²×C₃	1	1	yes	characteristic
150	#901	—	2	2	no	—
151	#901	C₂²×C₃	1	2	yes	complemented
152	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
153	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
154	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
155	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
156	C₃×#108	—	2	1	no	—
157	C₃×#108	—	3	2	no	—
158	C₃×#108	—	3	1	no	—
159	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
160	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₃×#104	—	2	2	no	—
162	C₃×#104	—	3	2	no	—
163	C₃×#104	—	3	2	no	—
164	C₃×#104	—	3	2	no	—
165	C₃×#104	C₂×D₃	1	2	yes	complemented
166	C₃×#104	C₂²×C₃	1	2	yes	complemented
167	C₃×#97	—	3	1	no	—
168	C₃×#97	—	3	1	no	—
169	C₃×C₄×C₈	—	2	1	no	—
170	C₃×C₄×C₈	—	3	1	no	—
171	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
172	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	#837	C₂²×C₃	1	2	yes	complemented
174	#825	C₂²×C₃	1	2	yes	complemented
175	#822	C₂²×C₃	1	2	yes	complemented
176	#819	C₂²×C₃	1	1	yes	characteristic, complemented
177	#815	C₂²×C₃	1	1	yes	characteristic, complemented
178	#815	C₂²×C₃	1	1	yes	characteristic, complemented
179	#805	C₂²×C₃	1	2	yes	complemented
180	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂²×C₃×D₃	—	2	2	no	—
182	C₂²×C₃×D₃	#41	1	1	yes	characteristic
183	C₃²×Q₈	C₂²×C₄	1	2	yes	—
184	C₃²×D₄	—	2	2	no	—
185	C₃²×D₄	C₂²×C₄	1	2	yes	—
186	C₂×C₃²×C₄	—	2	1	no	—
187	C₂×C₃²×C₄	—	2	2	no	—
188	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
189	C₃×#67	—	2	2	no	—
190	C₃×#67	—	2	2	no	—
191	C₃×#67	—	2	2	no	—
192	C₂×C₃×Dic₃	—	2	2	no	—
193	C₂×C₃×Dic₃	—	2	1	no	—
194	C₂×C₃×Dic₃	#41	1	1	yes	characteristic
195	C₃×D₁₂	—	2	2	no	—
196	C₃×D₁₂	C₂²×C₄	1	2	yes	—
197	C₃×C₄×D₃	—	2	2	no	—
198	C₃×C₄×D₃	—	2	2	no	—
199	C₃×C₄×D₃	—	2	2	no	—
200	C₃×C₄×D₃	—	4	2	no	—
201	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
202	C₃×C₄×D₃	C₂×D₄	1	2	yes	—
203	C₃×Dic₆	—	2	2	no	—
204	C₃×Dic₆	C₂²×C₄	1	2	yes	—
205	C₃²×C₈	—	2	2	no	—
206	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
207	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
208	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
209	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
210	C₃×C₃⋊C₈	—	2	2	no	—
211	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
212	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
213	#575	—	3	1	no	—
214	#568	—	3	2	no	—
215	#444	—	3	1	no	—
216	#444	—	3	2	no	—
217	#444	—	3	1	no	—
218	#443	—	3	2	no	—
219	#443	—	3	1	no	—
220	#443	C₃×D₃	1	1	yes	characteristic, complemented
221	#430	—	3	1	no	—
222	C₂×#104	—	3	2	no	—
223	C₄×M₁₆	—	3	1	no	—
224	C₃×#41	—	2	2	no	—
225	C₃×#41	—	3	2	no	—
226	C₃×#41	—	3	2	no	—
227	C₃×#41	—	3	2	no	—
228	C₃×#41	—	6	2	no	—
229	C₃×#41	—	6	2	no	—
230	C₃×#41	C₂²×D₃	1	2	yes	—
231	C₃×#41	C₂³×C₃	1	2	yes	—
232	C₂×C₃×Q₈	—	3	2	no	—
233	C₂×C₃×D₄	—	3	2	no	—
234	C₂×C₃×D₄	—	6	2	no	—
235	C₂²×C₃×C₄	—	3	1	no	—
236	C₂²×C₃×C₄	—	6	2	no	—
237	C₂²×C₃×C₄	—	6	1	no	—
238	#239	C₂×C₃×C₄	1	2	yes	—
239	D₃×Q₈	C₂×C₃×C₄	1	2	yes	—
240	#237	—	2	2	no	—
241	#237	C₂×C₃×C₄	1	2	yes	—
242	D₃×D₄	—	2	2	no	—
243	D₃×D₄	C₂×C₃×C₄	1	2	yes	—
244	#235	—	2	2	no	—
245	#235	C₂³×C₃	1	2	yes	—
246	C₂×C₄×D₃	—	2	2	no	—
247	C₂×C₄×D₃	—	2	1	no	—
248	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
249	C₃×Q₁₆	—	2	1	no	—
250	C₃×Q₁₆	—	3	2	no	—
251	C₃×Q₁₆	—	3	1	no	—
252	C₃×Q₁₆	C₄×D₃	1	1	yes	characteristic, complemented
253	C₃×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic, complemented
254	C₃×SD₁₆	—	2	2	no	—
255	C₃×SD₁₆	—	3	2	no	—
256	C₃×SD₁₆	—	3	2	no	—
257	C₃×SD₁₆	—	3	2	no	—
258	C₃×SD₁₆	C₄×D₃	1	2	yes	complemented
259	C₃×SD₁₆	C₂×C₃×C₄	1	2	yes	complemented
260	C₃×D₈	—	2	1	no	—
261	C₃×D₈	—	3	2	no	—
262	C₃×D₈	—	3	1	no	—
263	C₃×D₈	C₄×D₃	1	1	yes	characteristic, complemented
264	C₃×D₈	C₂×C₃×C₄	1	1	yes	characteristic, complemented
265	C₃×M₁₆	—	2	2	no	—
266	C₃×M₁₆	—	2	2	no	—
267	C₃×M₁₆	—	2	2	no	—
268	C₃×M₁₆	—	3	2	no	—
269	C₃×M₁₆	—	3	2	no	—
270	C₃×M₁₆	—	3	2	no	—
271	C₃×M₁₆	—	3	2	no	—
272	C₃×M₁₆	—	3	2	no	—
273	C₃×M₁₆	—	4	2	no	—
274	C₃×M₁₆	—	6	2	no	—
275	C₃×M₁₆	—	6	2	no	—
276	C₃×M₁₆	—	6	2	no	—
277	C₃×M₁₆	—	6	2	no	—
278	C₃×M₁₆	C₂²×D₃	1	2	yes	—
279	C₃×M₁₆	C₂³×C₃	1	2	yes	—
280	C₂×C₃×C₈	—	2	2	no	—
281	C₂×C₃×C₈	—	2	2	no	—
282	C₂×C₃×C₈	—	2	1	no	—
283	C₂×C₃×C₈	—	2	1	no	—
284	C₂×C₃×C₈	—	3	1	no	—
285	C₂×C₃×C₈	—	3	1	no	—
286	C₂×C₃×C₈	—	4	2	no	—
287	C₂×C₃×C₈	—	6	2	no	—
288	C₂×C₃×C₈	—	6	2	no	—
289	C₂×C₃×C₈	—	6	2	no	—
290	C₂×C₃×C₈	—	6	2	no	—
291	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
292	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
293	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
295	C₃×C₄²	—	2	1	no	—
296	C₃×C₄²	—	3	1	no	—
297	C₃×C₄²	—	6	1	no	—
298	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
299	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
300	#216	C₂×C₃×C₄	1	2	yes	complemented
301	#215	C₂×C₃×C₄	1	2	yes	complemented
302	#214	C₂×C₃×C₄	1	2	yes	complemented
303	#213	C₂×C₃×C₄	1	2	yes	complemented
304	C₄×Dic₃	—	2	1	no	—
305	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
306	#208	—	2	2	no	—
307	#208	C₂³×C₃	1	2	yes	—
308	C₂×C₃⋊C₈	—	2	2	no	—
309	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
311	Dic₁₂	C₂×C₃×C₄	1	1	yes	characteristic, complemented
312	D₂₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
313	#204	C₂×C₃×C₄	1	2	yes	complemented
314	ΓL(1,𝔽₂₅)	—	2	2	no	—
315	ΓL(1,𝔽₂₅)	—	2	2	no	—
316	ΓL(1,𝔽₂₅)	—	2	2	no	—
317	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	2	yes	—
318	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	2	yes	—
319	ΓL(1,𝔽₂₅)	C₃×D₄	1	2	yes	—
320	ΓL(1,𝔽₂₅)	C₃×D₄	1	2	yes	—
321	D₃×C₈	—	2	2	no	—
322	D₃×C₈	—	2	2	no	—
323	D₃×C₈	—	2	2	no	—
324	C₂²×C₃²	—	2	2	no	—
325	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
326	C₂×C₃×D₃	—	2	2	no	—
327	C₂×C₃×D₃	—	4	1	no	—
328	C₂×C₃×D₃	—	8	2	no	—
329	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
330	C₃²×C₄	—	2	2	no	—
331	C₃²×C₄	—	2	2	no	—
332	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
333	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₃×Dic₃	—	2	2	no	—
335	C₃×Dic₃	—	4	1	no	—
336	C₃×Dic₃	C₄×D₄	1	2	yes	—
337	C₂×#41	—	3	2	no	—
338	#137	—	3	2	no	—
339	#137	—	3	2	no	—
340	AGL(1,ℤ/8)	—	3	2	no	—
341	AGL(1,ℤ/8)	—	3	2	no	—
342	#135	—	3	2	no	—
343	#135	—	3	1	no	—
344	#135	C₂×C₃×D₃	1	1	yes	characteristic
345	#131	—	3	2	no	—
346	#131	—	3	2	no	—
347	#131	—	3	2	no	—
348	#131	—	6	2	no	—
349	#131	—	6	2	no	—
350	#131	C₂×C₃×D₃	1	2	yes	complemented
351	C₂×M₁₆	—	3	1	no	—
352	C₂×M₁₆	—	3	1	no	—
353	C₂×M₁₆	—	3	2	no	—
354	C₂×M₁₆	—	6	2	no	—
355	C₂×M₁₆	—	6	2	no	—
356	C₂×C₄²	—	3	1	no	—
357	#108	—	3	2	no	—
358	#108	—	3	1	no	—
359	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
360	#104	—	3	2	no	—
361	#104	—	3	2	no	—
362	#104	—	3	2	no	—
363	#104	C₂×C₃×D₃	1	2	yes	complemented
364	#97	—	3	1	no	—
365	#97	—	3	1	no	—
366	C₄×C₈	—	3	1	no	—
367	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
368	C₂³×C₃	—	3	1	no	—
369	C₂³×C₃	—	6	2	no	—
370	C₂²×D₃	—	2	2	no	—
371	C₂²×D₃	C₃×#41	1	1	yes	characteristic
372	C₃×Q₈	—	2	2	no	—
373	C₃×Q₈	—	3	2	no	—
374	C₃×Q₈	—	6	2	no	—
375	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
376	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	2	no	—
379	C₃×D₄	—	2	2	no	—
380	C₃×D₄	—	3	2	no	—
381	C₃×D₄	—	4	2	no	—
382	C₃×D₄	—	6	2	no	—
383	C₃×D₄	—	6	2	no	—
384	C₃×D₄	—	6	2	no	—
385	C₃×D₄	—	6	2	no	—
386	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
387	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	2	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	3	1	no	—
394	C₂×C₃×C₄	—	3	2	no	—
395	C₂×C₃×C₄	—	3	2	no	—
396	C₂×C₃×C₄	—	4	2	no	—
397	C₂×C₃×C₄	—	4	1	no	—
398	C₂×C₃×C₄	—	6	2	no	—
399	C₂×C₃×C₄	—	6	2	no	—
400	C₂×C₃×C₄	—	6	2	no	—
401	C₂×C₃×C₄	—	6	2	no	—
402	C₂×C₃×C₄	—	6	1	no	—
403	C₂×C₃×C₄	—	12	2	no	—
404	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
406	#67	—	2	2	no	—
407	#67	—	2	2	no	—
408	#67	—	2	2	no	—
409	C₂×Dic₃	—	2	2	no	—
410	C₂×Dic₃	—	2	1	no	—
411	C₂×Dic₃	C₃×#41	1	1	yes	characteristic
412	D₁₂	—	2	2	no	—
413	D₁₂	C₂²×C₃×C₄	1	2	yes	—
414	C₄×D₃	—	2	2	no	—
415	C₄×D₃	—	2	2	no	—
416	C₄×D₃	—	2	2	no	—
417	C₄×D₃	—	4	2	no	—
418	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
419	C₄×D₃	C₂×C₃×D₄	1	2	yes	—
420	Dic₆	—	2	2	no	—
421	Dic₆	C₂²×C₃×C₄	1	2	yes	—
422	C₃×C₈	—	2	2	no	—
423	C₃×C₈	—	2	2	no	—
424	C₃×C₈	—	2	1	no	—
425	C₃×C₈	—	2	1	no	—
426	C₃×C₈	—	2	1	no	—
427	C₃×C₈	—	2	1	no	—
428	C₃×C₈	—	3	2	no	—
429	C₃×C₈	—	3	2	no	—
430	C₃×C₈	—	4	2	no	—
431	C₃×C₈	—	6	2	no	—
432	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
433	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
434	C₃×C₈	D₃×D₄	1	1	yes	characteristic
435	C₃×C₈	D₃×D₄	1	1	yes	characteristic
436	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
437	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
438	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
439	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
440	C₃⋊C₈	—	2	2	no	—
441	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
442	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
443	C₂×C₃²	—	2	1	no	—
444	C₂×C₃²	—	4	2	no	—
445	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
446	C₃×D₃	—	2	2	no	—
447	C₃×D₃	—	4	2	no	—
448	#41	—	3	2	no	—
449	#41	—	3	2	no	—
450	#41	—	3	2	no	—
451	#41	—	6	2	no	—
452	#41	—	6	2	no	—
453	#41	C₂²×C₃×D₃	1	2	yes	—
454	C₂×Q₈	—	3	2	no	—
455	C₂×D₄	—	3	2	no	—
456	C₂×D₄	—	6	2	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	6	2	no	—
459	C₂²×C₄	—	6	1	no	—
460	Q₁₆	—	3	2	no	—
461	Q₁₆	—	3	1	no	—
462	Q₁₆	C₃×C₄×D₃	1	1	yes	characteristic, complemented
463	SD₁₆	—	3	2	no	—
464	SD₁₆	—	3	2	no	—
465	SD₁₆	—	3	2	no	—
466	SD₁₆	C₃×C₄×D₃	1	2	yes	complemented
467	D₈	—	3	2	no	—
468	D₈	—	3	1	no	—
469	D₈	C₃×C₄×D₃	1	1	yes	characteristic, complemented
470	M₁₆	—	2	2	no	—
471	M₁₆	—	3	2	no	—
472	M₁₆	—	3	2	no	—
473	M₁₆	—	3	2	no	—
474	M₁₆	—	3	2	no	—
475	M₁₆	—	3	2	no	—
476	M₁₆	—	6	2	no	—
477	M₁₆	—	6	2	no	—
478	M₁₆	—	6	2	no	—
479	M₁₆	—	6	2	no	—
480	M₁₆	C₂²×C₃×D₃	1	2	yes	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	3	1	no	—
483	C₂×C₈	—	3	1	no	—
484	C₂×C₈	—	6	2	no	—
485	C₂×C₈	—	6	2	no	—
486	C₂×C₈	—	6	2	no	—
487	C₂×C₈	—	6	2	no	—
488	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
489	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
490	C₄²	—	3	1	no	—
491	C₄²	—	6	1	no	—
492	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	3	2	no	—
497	C₂²×C₃	—	4	2	no	—
498	C₂²×C₃	—	6	2	no	—
499	C₂²×C₃	—	12	1	no	—
500	C₂²×C₃	—	24	2	no	—
501	C₂²×C₃	D₃×#41	1	1	yes	characteristic
502	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
503	C₂×D₃	—	2	2	no	—
504	C₂×D₃	—	4	1	no	—
505	C₂×D₃	—	8	2	no	—
506	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	2	2	no	—
509	C₃×C₄	—	2	2	no	—
510	C₃×C₄	—	2	2	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	3	2	no	—
514	C₃×C₄	—	4	2	no	—
515	C₃×C₄	—	4	2	no	—
516	C₃×C₄	—	6	2	no	—
517	C₃×C₄	—	12	1	no	—
518	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
519	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
520	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
521	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
522	Dic₃	—	2	2	no	—
523	Dic₃	—	4	1	no	—
524	Dic₃	C₃×C₄×D₄	1	2	yes	—
525	C₃²	#2956	1	1	yes	characteristic, complemented, Sylow
526	C₂³	—	3	1	no	—
527	C₂³	—	6	2	no	—
528	Q₈	—	3	2	no	—
529	Q₈	—	6	2	no	—
530	Q₈	C₂×C₃×C₄×D₃	1	2	yes	—
531	D₄	—	2	2	no	—
532	D₄	—	3	2	no	—
533	D₄	—	6	2	no	—
534	D₄	—	6	2	no	—
535	D₄	—	6	2	no	—
536	D₄	—	6	2	no	—
537	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	3	1	no	—
541	C₂×C₄	—	3	2	no	—
542	C₂×C₄	—	3	2	no	—
543	C₂×C₄	—	6	2	no	—
544	C₂×C₄	—	6	2	no	—
545	C₂×C₄	—	6	2	no	—
546	C₂×C₄	—	6	2	no	—
547	C₂×C₄	—	6	1	no	—
548	C₂×C₄	—	12	2	no	—
549	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
550	C₈	—	2	2	no	—
551	C₈	—	3	2	no	—
552	C₈	—	3	2	no	—
553	C₈	—	6	2	no	—
554	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
555	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
556	C₈	C₃×D₃×D₄	1	1	yes	characteristic
557	C₈	C₃×D₃×D₄	1	1	yes	characteristic
558	C₂×C₃	—	2	1	no	—
559	C₂×C₃	—	2	1	no	—
560	C₂×C₃	—	2	1	no	—
561	C₂×C₃	—	4	1	no	—
562	C₂×C₃	—	4	2	no	—
563	C₂×C₃	—	4	2	no	—
564	C₂×C₃	—	6	2	no	—
565	C₂×C₃	—	8	2	no	—
566	C₂×C₃	—	12	2	no	—
567	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
568	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
569	D₃	—	2	2	no	—
570	D₃	—	4	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	3	2	no	—
573	C₂²	—	6	2	no	—
574	C₂²	—	12	1	no	—
575	C₂²	—	24	2	no	—
576	C₂²	C₃×D₃×#41	1	1	yes	characteristic
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	3	2	no	—
580	C₄	—	6	2	no	—
581	C₄	—	12	1	no	—
582	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
583	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
584	C₃	—	2	1	no	—
585	C₃	#79889	1	1	yes	characteristic, direct product factor
586	C₃	C₃×#2956	1	1	yes	characteristic, complemented
587	C₂	—	2	1	no	—
588	C₂	—	4	2	no	—
589	C₂	—	6	2	no	—
590	C₂	—	12	2	no	—
591	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#443	C₂
socle	C₂×C₃²	C₂×C₄×D₄
prime radical	C₃×#5768	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#443	D₃
hypocenter	C₃	C₃×#2956
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#443

Complements

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

N	H ≅ G/N	type
2. C₃×#5750	C₂	semidirect
3. C₃²×#443	C₂	semidirect
4. C₃×#5197	C₂	semidirect
5. C₃×#5145	C₂	semidirect
6. C₃×#4894	C₂	semidirect
7. C₃×#4893	C₂	semidirect
8. C₃×#4824	C₂	semidirect
9. C₃×D₃×#104	C₂	semidirect
10. C₃×#4700	C₂	semidirect
11. C₃×C₄×ΓL(1,𝔽₂₅)	C₂	semidirect
13. #79889	C₃	direct (N × H)
16. C₃²×#131	C₂²	semidirect
18. C₃×#948	C₂²	semidirect
19. C₃×#918	C₄	semidirect
20. C₃×#915	C₄	semidirect
21. C₃×#914	C₄	semidirect
22. C₃×#911	C₄	semidirect
24. C₃×#907	C₂²	semidirect
29. C₃×#901	C₂²	semidirect
34. C₃²×#108	C₂²	semidirect
35. C₃²×#104	C₂²	semidirect
36. C₃²×C₄×C₈	C₂²	semidirect
37. C₃×#837	C₂²	semidirect
38. C₃×#825	C₂²	semidirect
39. C₃×#822	C₂²	semidirect
40. C₃×#819	C₂²	semidirect
41. C₃×#815	C₂²	semidirect
42. C₃×#815	C₂²	semidirect
43. C₃×#805	C₂²	semidirect
44. C₃×C₄×C₃⋊C₈	C₂²	semidirect
48. #5750	C₂×C₃	semidirect
55. C₃×#443	D₃	semidirect
56. C₃×#443	C₂×C₃	semidirect
60. #5197	C₂×C₃	semidirect
61. #5145	C₂×C₃	semidirect
62. #4894	C₂×C₃	semidirect
63. #4893	C₂×C₃	semidirect
64. #4824	C₂×C₃	semidirect
65. D₃×#104	C₂×C₃	semidirect
66. #4700	C₂×C₃	semidirect
67. C₄×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
80. C₃²×Q₁₆	C₂×C₄	semidirect
81. C₃²×SD₁₆	C₂×C₄	semidirect
82. C₃²×D₈	C₂×C₄	semidirect
89. C₃×#216	C₂×C₄	semidirect
90. C₃×#215	C₂×C₄	semidirect
91. C₃×#214	C₂×C₄	semidirect
92. C₃×#213	C₂×C₄	semidirect
100. C₃×Dic₁₂	C₂×C₄	semidirect
101. C₃×D₂₄	C₂×C₄	semidirect
102. C₃×#204	C₂×C₄	semidirect
131. C₃×#131	C₂×D₃	semidirect
132. C₃×#131	C₂²×C₃	semidirect
140. #948	C₂²×C₃	semidirect
141. #918	C₃×C₄	semidirect
142. #915	C₃×C₄	semidirect
143. #914	C₃×C₄	semidirect
144. #911	C₃×C₄	semidirect
146. #907	C₂²×C₃	semidirect
151. #901	C₂²×C₃	semidirect
159. C₃×#108	C₂×D₃	semidirect
160. C₃×#108	C₂²×C₃	semidirect
165. C₃×#104	C₂×D₃	semidirect
166. C₃×#104	C₂²×C₃	semidirect
171. C₃×C₄×C₈	C₂×D₃	semidirect
172. C₃×C₄×C₈	C₂²×C₃	semidirect
173. #837	C₂²×C₃	semidirect
174. #825	C₂²×C₃	semidirect
175. #822	C₂²×C₃	semidirect
176. #819	C₂²×C₃	semidirect
177. #815	C₂²×C₃	semidirect
178. #815	C₂²×C₃	semidirect
179. #805	C₂²×C₃	semidirect
180. C₄×C₃⋊C₈	C₂²×C₃	semidirect
220. #443	C₃×D₃	semidirect
252. C₃×Q₁₆	C₄×D₃	semidirect
253. C₃×Q₁₆	C₂×C₃×C₄	semidirect
258. C₃×SD₁₆	C₄×D₃	semidirect
259. C₃×SD₁₆	C₂×C₃×C₄	semidirect
263. C₃×D₈	C₄×D₃	semidirect
264. C₃×D₈	C₂×C₃×C₄	semidirect
300. #216	C₂×C₃×C₄	semidirect
301. #215	C₂×C₃×C₄	semidirect
302. #214	C₂×C₃×C₄	semidirect
303. #213	C₂×C₃×C₄	semidirect
311. Dic₁₂	C₂×C₃×C₄	semidirect
312. D₂₄	C₂×C₃×C₄	semidirect
313. #204	C₂×C₃×C₄	semidirect
350. #131	C₂×C₃×D₃	semidirect
359. #108	C₂×C₃×D₃	semidirect
363. #104	C₂×C₃×D₃	semidirect
367. C₄×C₈	C₂×C₃×D₃	semidirect
462. Q₁₆	C₃×C₄×D₃	semidirect
466. SD₁₆	C₃×C₄×D₃	semidirect
469. D₈	C₃×C₄×D₃	semidirect
525. C₃²	#2956	semidirect
585. C₃	#79889	direct (N × H)
586. C₃	C₃×#2956	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5768	2
C₃×#5750	2
C₃²×#443	2
C₃×#5197	2
C₃×#5145	2
C₃×#4894	2
C₃×#4893	2
C₃×#4824	2
C₃×D₃×#104	2
C₃×#4700	2
C₃×C₄×ΓL(1,𝔽₂₅)	2
C₃×#2956	3
#79889	3

Subgroups — C3×#79889 #11861132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79889 #11861132