Subgroups — C₃×#79890 #11861186

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×#135	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×#5196	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5145	C₂	1	2	yes	maximal, complemented
6	C₃×#4895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×D₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4823	C₂	1	2	yes	maximal, complemented
9	C₃×#4821	C₂	1	2	yes	maximal, complemented
10	C₃×#4700	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#2957	—	3	1	no	maximal
13	#79890	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×#919	C₄	1	1	yes	characteristic, complemented
20	C₃×D₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
21	C₃×#916	C₄	1	2	yes	complemented
22	C₃×D₃×SD₁₆	C₄	1	2	yes	complemented
23	C₃×#912	C₄	1	1	yes	characteristic, complemented
24	C₃×D₃×D₈	C₄	1	1	yes	characteristic, complemented
25	C₃×#907	—	2	2	no	—
26	C₃×#907	C₂²	1	2	yes	complemented
27	C₃×D₃×M₁₆	—	2	2	no	—
28	C₃×D₃×M₁₆	C₂²	1	2	yes	—
29	C₃×#904	C₂²	1	1	yes	characteristic
30	C₃×#901	—	2	2	no	—
31	C₃×#901	C₂²	1	2	yes	complemented
32	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
33	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
34	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
35	C₃×#872	C₂²	1	1	yes	characteristic
36	C₃²×#108	C₂²	1	1	yes	characteristic, complemented
37	C₃²×#104	C₂²	1	2	yes	complemented
38	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic, complemented
39	C₃×#837	C₂²	1	2	yes	complemented
40	C₃×#825	C₂²	1	2	yes	complemented
41	C₃×#822	C₂²	1	2	yes	complemented
42	C₃×#819	C₂²	1	1	yes	characteristic, complemented
43	C₃×#815	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₃×#805	C₂²	1	2	yes	complemented
46	C₃×#803	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#135	—	3	1	no	—
48	C₃×#568	—	3	2	no	—
49	D₃×#135	C₂×C₃	1	1	yes	characteristic
50	#5750	C₂×C₃	1	2	yes	complemented
51	C₃×#444	—	3	2	no	—
52	C₃×#444	—	3	2	no	—
53	C₃×#443	—	2	1	no	—
54	C₃×#443	—	3	1	no	—
55	C₃×#443	—	3	1	no	—
56	C₃×#443	—	3	1	no	—
57	C₃×#443	D₃	1	1	yes	characteristic, complemented
58	C₃×#443	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×#108	—	3	1	no	—
60	C₃×#421	—	3	2	no	—
61	C₃×#405	—	3	1	no	—
62	#5196	C₂×C₃	1	1	yes	characteristic, complemented
63	#5145	C₂×C₃	1	2	yes	complemented
64	#4895	C₂×C₃	1	1	yes	characteristic, complemented
65	D₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
66	#4823	C₂×C₃	1	2	yes	complemented
67	#4821	C₂×C₃	1	2	yes	complemented
68	#4700	C₂×C₃	1	1	yes	characteristic, complemented
69	#4689	C₂×C₃	1	1	yes	characteristic, complemented
70	C₃²×#41	C₂³	1	2	yes	—
71	C₃×#239	C₂×C₄	1	2	yes	—
72	C₃×D₃×Q₈	C₂×C₄	1	2	yes	—
73	C₃×#237	—	2	2	no	—
74	C₃×#237	C₂×C₄	1	2	yes	—
75	C₃×D₃×D₄	—	2	2	no	—
76	C₃×D₃×D₄	C₂×C₄	1	2	yes	—
77	C₃×#235	—	2	2	no	—
78	C₃×#235	C₂³	1	2	yes	—
79	C₂×C₃×C₄×D₃	—	2	2	no	—
80	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
81	C₃²×Q₁₆	C₂×C₄	1	1	yes	characteristic
82	C₃²×SD₁₆	C₂×C₄	1	2	yes	—
83	C₃²×D₈	C₂×C₄	1	1	yes	characteristic
84	C₃²×M₁₆	—	2	2	no	—
85	C₃²×M₁₆	C₂³	1	2	yes	—
86	C₂×C₃²×C₈	—	2	2	no	—
87	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
88	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
89	C₃²×C₄²	C₂³	1	1	yes	characteristic
90	C₃×#216	C₂×C₄	1	2	yes	—
91	C₃×#215	C₂×C₄	1	2	yes	—
92	C₃×#214	C₂×C₄	1	2	yes	—
93	C₃×#213	C₂×C₄	1	2	yes	—
94	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
95	C₃×Dic₃⋊C₄	—	2	1	no	—
96	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
97	C₃×#208	—	2	2	no	—
98	C₃×#208	C₂³	1	2	yes	—
99	C₂×C₃×C₃⋊C₈	—	2	2	no	—
100	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
102	C₃×Dic₁₂	C₂×C₄	1	1	yes	characteristic
103	C₃×D₂₄	C₂×C₄	1	1	yes	characteristic
104	C₃×#204	C₂×C₄	1	2	yes	—
105	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
106	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
107	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
108	C₃×ΓL(1,𝔽₂₅)	D₄	1	1	yes	characteristic
109	C₃×ΓL(1,𝔽₂₅)	D₄	1	1	yes	characteristic
110	C₃×ΓL(1,𝔽₂₅)	D₄	1	1	yes	characteristic
111	C₃×ΓL(1,𝔽₂₅)	D₄	1	1	yes	characteristic
112	C₃×D₃×C₈	—	2	2	no	—
113	C₃×D₃×C₈	—	2	2	no	—
114	C₃×D₃×C₈	—	2	2	no	—
115	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
116	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
117	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
118	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
119	#2957	—	3	1	no	Sylow
120	C₂×C₃×#41	—	3	2	no	—
121	D₃×#41	C₂²×C₃	1	2	yes	—
122	C₃×#135	—	2	1	no	—
123	C₃×#135	—	3	2	no	—
124	C₃×#135	—	3	1	no	—
125	C₃×#135	—	3	2	no	—
126	C₃×#135	—	3	1	no	—
127	C₃×#135	—	3	1	no	—
128	C₃×#135	C₂×D₃	1	1	yes	characteristic
129	C₃×#135	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×Q₁₆	—	3	1	no	—
131	C₂×C₃×SD₁₆	—	3	2	no	—
132	C₂×C₃×D₈	—	3	1	no	—
133	C₃×#131	—	2	2	no	—
134	C₃×#131	—	3	2	no	—
135	C₃×#131	—	3	2	no	—
136	C₃×#131	—	3	2	no	—
137	C₃×#131	—	6	2	no	—
138	C₃×#131	—	6	2	no	—
139	C₃×#131	C₂×D₃	1	2	yes	complemented
140	C₃×#131	C₂²×C₃	1	2	yes	complemented
141	C₂×C₃×M₁₆	—	3	1	no	—
142	C₂×C₃×M₁₆	—	3	2	no	—
143	C₂×C₃×M₁₆	—	6	2	no	—
144	C₂×C₃×M₁₆	—	6	2	no	—
145	C₂²×C₃×C₈	—	3	1	no	—
146	C₃×#117	—	3	1	no	—
147	#950	C₂²×C₃	1	2	yes	—
148	#948	C₂²×C₃	1	2	yes	complemented
149	#919	C₃×C₄	1	1	yes	characteristic, complemented
150	D₃×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
151	#916	C₃×C₄	1	2	yes	complemented
152	D₃×SD₁₆	C₃×C₄	1	2	yes	complemented
153	#912	C₃×C₄	1	1	yes	characteristic, complemented
154	D₃×D₈	C₃×C₄	1	1	yes	characteristic, complemented
155	#907	—	2	2	no	—
156	#907	C₂²×C₃	1	2	yes	complemented
157	D₃×M₁₆	—	2	2	no	—
158	D₃×M₁₆	C₂²×C₃	1	2	yes	—
159	#904	C₂²×C₃	1	1	yes	characteristic
160	#901	—	2	2	no	—
161	#901	C₂²×C₃	1	2	yes	complemented
162	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
163	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	1	yes	characteristic
164	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
165	#872	C₂²×C₃	1	1	yes	characteristic
166	C₃×#108	—	2	1	no	—
167	C₃×#108	—	3	2	no	—
168	C₃×#108	—	3	1	no	—
169	C₃×#108	C₂×D₃	1	1	yes	characteristic, complemented
170	C₃×#108	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₃×#104	—	2	2	no	—
172	C₃×#104	—	3	2	no	—
173	C₃×#104	—	3	2	no	—
174	C₃×#104	—	3	2	no	—
175	C₃×#104	C₂×D₃	1	2	yes	complemented
176	C₃×#104	C₂²×C₃	1	2	yes	complemented
177	C₃×#97	—	3	1	no	—
178	C₃×#97	—	3	1	no	—
179	C₃×C₄×C₈	—	2	1	no	—
180	C₃×C₄×C₈	—	3	1	no	—
181	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic, complemented
182	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
183	#837	C₂²×C₃	1	2	yes	complemented
184	#825	C₂²×C₃	1	2	yes	complemented
185	#822	C₂²×C₃	1	2	yes	complemented
186	#819	C₂²×C₃	1	1	yes	characteristic, complemented
187	#815	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic, complemented
189	#805	C₂²×C₃	1	2	yes	complemented
190	#803	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂²×C₃×D₃	—	2	2	no	—
192	C₂²×C₃×D₃	#41	1	1	yes	characteristic
193	C₃²×Q₈	C₂²×C₄	1	2	yes	—
194	C₃²×D₄	—	2	2	no	—
195	C₃²×D₄	C₂²×C₄	1	2	yes	—
196	C₂×C₃²×C₄	—	2	2	no	—
197	C₂×C₃²×C₄	—	2	1	no	—
198	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
199	C₃×#67	—	2	2	no	—
200	C₃×#67	—	2	2	no	—
201	C₃×#67	—	2	2	no	—
202	C₂×C₃×Dic₃	—	2	2	no	—
203	C₂×C₃×Dic₃	—	2	1	no	—
204	C₂×C₃×Dic₃	#41	1	1	yes	characteristic
205	C₃×D₁₂	—	2	2	no	—
206	C₃×D₁₂	C₂²×C₄	1	2	yes	—
207	C₃×C₄×D₃	—	2	2	no	—
208	C₃×C₄×D₃	—	2	2	no	—
209	C₃×C₄×D₃	—	2	2	no	—
210	C₃×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
211	C₃×C₄×D₃	C₂²×C₄	1	1	yes	characteristic
212	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
213	C₃×C₄×D₃	C₂×D₄	1	1	yes	characteristic
214	C₃×Dic₆	—	2	2	no	—
215	C₃×Dic₆	C₂²×C₄	1	2	yes	—
216	C₃²×C₈	—	2	2	no	—
217	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
218	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
219	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
220	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
221	C₃×C₃⋊C₈	—	2	2	no	—
222	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
223	C₃×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
224	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
225	C₃×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
226	C₂×#135	—	3	1	no	—
227	#568	—	3	2	no	—
228	#444	—	3	2	no	—
229	#444	—	3	2	no	—
230	#443	—	3	1	no	—
231	#443	—	3	1	no	—
232	#443	—	3	1	no	—
233	#443	C₃×D₃	1	1	yes	characteristic, complemented
234	C₂×#108	—	3	1	no	—
235	#421	—	3	2	no	—
236	#405	—	3	1	no	—
237	C₃×#41	—	2	2	no	—
238	C₃×#41	—	3	2	no	—
239	C₃×#41	—	3	2	no	—
240	C₃×#41	—	3	2	no	—
241	C₃×#41	—	6	2	no	—
242	C₃×#41	—	6	2	no	—
243	C₃×#41	C₂²×D₃	1	2	yes	—
244	C₃×#41	C₂³×C₃	1	2	yes	—
245	C₂×C₃×Q₈	—	3	2	no	—
246	C₂×C₃×D₄	—	3	2	no	—
247	C₂×C₃×D₄	—	6	2	no	—
248	C₂²×C₃×C₄	—	3	1	no	—
249	C₂²×C₃×C₄	—	6	2	no	—
250	#239	C₂×C₃×C₄	1	2	yes	—
251	D₃×Q₈	C₂×C₃×C₄	1	2	yes	—
252	#237	—	2	2	no	—
253	#237	C₂×C₃×C₄	1	2	yes	—
254	D₃×D₄	—	2	2	no	—
255	D₃×D₄	C₂×C₃×C₄	1	2	yes	—
256	#235	—	2	2	no	—
257	#235	C₂³×C₃	1	2	yes	—
258	C₂×C₄×D₃	—	2	2	no	—
259	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
260	C₃×Q₁₆	—	2	1	no	—
261	C₃×Q₁₆	—	3	2	no	—
262	C₃×Q₁₆	—	3	1	no	—
263	C₃×Q₁₆	C₄×D₃	1	1	yes	characteristic
264	C₃×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
265	C₃×SD₁₆	—	2	2	no	—
266	C₃×SD₁₆	—	3	2	no	—
267	C₃×SD₁₆	—	3	2	no	—
268	C₃×SD₁₆	—	3	2	no	—
269	C₃×SD₁₆	C₄×D₃	1	2	yes	—
270	C₃×SD₁₆	C₂×C₃×C₄	1	2	yes	—
271	C₃×D₈	—	2	1	no	—
272	C₃×D₈	—	3	2	no	—
273	C₃×D₈	—	3	1	no	—
274	C₃×D₈	C₄×D₃	1	1	yes	characteristic
275	C₃×D₈	C₂×C₃×C₄	1	1	yes	characteristic
276	C₃×M₁₆	—	2	2	no	—
277	C₃×M₁₆	—	2	2	no	—
278	C₃×M₁₆	—	2	2	no	—
279	C₃×M₁₆	—	3	1	no	—
280	C₃×M₁₆	—	3	1	no	—
281	C₃×M₁₆	—	3	1	no	—
282	C₃×M₁₆	—	3	1	no	—
283	C₃×M₁₆	—	3	2	no	—
284	C₃×M₁₆	—	4	2	no	—
285	C₃×M₁₆	—	6	2	no	—
286	C₃×M₁₆	—	6	2	no	—
287	C₃×M₁₆	—	6	2	no	—
288	C₃×M₁₆	—	6	2	no	—
289	C₃×M₁₆	C₂²×D₃	1	2	yes	—
290	C₃×M₁₆	C₂³×C₃	1	2	yes	—
291	C₂×C₃×C₈	—	2	2	no	—
292	C₂×C₃×C₈	—	2	2	no	—
293	C₂×C₃×C₈	—	2	1	no	—
294	C₂×C₃×C₈	—	2	1	no	—
295	C₂×C₃×C₈	—	3	1	no	—
296	C₂×C₃×C₈	—	3	1	no	—
297	C₂×C₃×C₈	—	3	1	no	—
298	C₂×C₃×C₈	—	3	1	no	—
299	C₂×C₃×C₈	—	3	1	no	—
300	C₂×C₃×C₈	—	3	1	no	—
301	C₂×C₃×C₈	—	4	2	no	—
302	C₂×C₃×C₈	—	6	2	no	—
303	C₂×C₃×C₈	—	6	2	no	—
304	C₂×C₃×C₈	—	6	2	no	—
305	C₂×C₃×C₈	—	6	2	no	—
306	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
307	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
308	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
310	C₃×C₄⋊C₄	—	6	1	no	—
311	C₃×C₂²⋊C₄	—	6	1	no	—
312	C₃×C₄²	—	2	1	no	—
313	C₃×C₄²	—	3	1	no	—
314	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
315	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
316	#216	C₂×C₃×C₄	1	2	yes	—
317	#215	C₂×C₃×C₄	1	2	yes	—
318	#214	C₂×C₃×C₄	1	2	yes	—
319	#213	C₂×C₃×C₄	1	2	yes	—
320	(C₂×D₃)⋊C₄	—	2	1	no	—
321	Dic₃⋊C₄	—	2	1	no	—
322	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
323	#208	—	2	2	no	—
324	#208	C₂³×C₃	1	2	yes	—
325	C₂×C₃⋊C₈	—	2	2	no	—
326	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
327	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
328	Dic₁₂	C₂×C₃×C₄	1	1	yes	characteristic
329	D₂₄	C₂×C₃×C₄	1	1	yes	characteristic
330	#204	C₂×C₃×C₄	1	2	yes	—
331	ΓL(1,𝔽₂₅)	—	2	2	no	—
332	ΓL(1,𝔽₂₅)	—	2	2	no	—
333	ΓL(1,𝔽₂₅)	—	2	2	no	—
334	ΓL(1,𝔽₂₅)	C₃×D₄	1	1	yes	characteristic
335	ΓL(1,𝔽₂₅)	C₃×D₄	1	1	yes	characteristic
336	ΓL(1,𝔽₂₅)	C₃×D₄	1	1	yes	characteristic
337	ΓL(1,𝔽₂₅)	C₃×D₄	1	1	yes	characteristic
338	D₃×C₈	—	2	2	no	—
339	D₃×C₈	—	2	2	no	—
340	D₃×C₈	—	2	2	no	—
341	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
342	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
343	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
344	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
345	C₂²×C₃²	—	2	2	no	—
346	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
347	C₂×C₃×D₃	—	2	2	no	—
348	C₂×C₃×D₃	—	4	1	no	—
349	C₂×C₃×D₃	—	8	2	no	—
350	C₂×C₃×D₃	C₄×D₄	1	1	yes	characteristic
351	C₂×C₃×D₃	C₄×D₄	1	1	yes	characteristic
352	C₃²×C₄	—	2	2	no	—
353	C₃²×C₄	—	4	1	no	—
354	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
355	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
356	C₃×Dic₃	—	2	2	no	—
357	C₃×Dic₃	—	4	1	no	—
358	C₃×Dic₃	C₄×D₄	1	1	yes	characteristic
359	C₃×Dic₃	C₄×D₄	1	1	yes	characteristic
360	C₂×#41	—	3	2	no	—
361	#135	—	3	2	no	—
362	#135	—	3	1	no	—
363	#135	—	3	2	no	—
364	#135	—	3	1	no	—
365	#135	—	3	1	no	—
366	#135	C₂×C₃×D₃	1	1	yes	characteristic
367	C₂×Q₁₆	—	3	1	no	—
368	C₂×SD₁₆	—	3	2	no	—
369	C₂×D₈	—	3	1	no	—
370	#131	—	3	2	no	—
371	#131	—	3	2	no	—
372	#131	—	3	2	no	—
373	#131	—	6	2	no	—
374	#131	—	6	2	no	—
375	#131	C₂×C₃×D₃	1	2	yes	complemented
376	C₂×M₁₆	—	3	1	no	—
377	C₂×M₁₆	—	3	2	no	—
378	C₂×M₁₆	—	6	2	no	—
379	C₂×M₁₆	—	6	2	no	—
380	C₂²×C₈	—	3	1	no	—
381	#117	—	3	1	no	—
382	#108	—	3	2	no	—
383	#108	—	3	1	no	—
384	#108	C₂×C₃×D₃	1	1	yes	characteristic, complemented
385	#104	—	3	2	no	—
386	#104	—	3	2	no	—
387	#104	—	3	2	no	—
388	#104	C₂×C₃×D₃	1	2	yes	complemented
389	#97	—	3	1	no	—
390	#97	—	3	1	no	—
391	C₄×C₈	—	3	1	no	—
392	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
393	C₂³×C₃	—	3	1	no	—
394	C₂³×C₃	—	6	2	no	—
395	C₂²×D₃	—	2	2	no	—
396	C₂²×D₃	C₃×#41	1	1	yes	characteristic
397	C₃×Q₈	—	2	2	no	—
398	C₃×Q₈	—	3	2	no	—
399	C₃×Q₈	—	6	2	no	—
400	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
401	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	—
402	C₃×D₄	—	2	2	no	—
403	C₃×D₄	—	2	2	no	—
404	C₃×D₄	—	2	2	no	—
405	C₃×D₄	—	3	2	no	—
406	C₃×D₄	—	4	2	no	—
407	C₃×D₄	—	6	2	no	—
408	C₃×D₄	—	6	2	no	—
409	C₃×D₄	—	6	2	no	—
410	C₃×D₄	—	6	2	no	—
411	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
412	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
413	C₂×C₃×C₄	—	2	2	no	—
414	C₂×C₃×C₄	—	2	2	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	3	1	no	—
419	C₂×C₃×C₄	—	3	1	no	—
420	C₂×C₃×C₄	—	3	1	no	—
421	C₂×C₃×C₄	—	3	1	no	—
422	C₂×C₃×C₄	—	3	1	no	—
423	C₂×C₃×C₄	—	4	2	no	—
424	C₂×C₃×C₄	—	4	1	no	—
425	C₂×C₃×C₄	—	6	2	no	—
426	C₂×C₃×C₄	—	6	2	no	—
427	C₂×C₃×C₄	—	6	2	no	—
428	C₂×C₃×C₄	—	6	2	no	—
429	C₂×C₃×C₄	—	6	1	no	—
430	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
432	#67	—	2	2	no	—
433	#67	—	2	2	no	—
434	#67	—	2	2	no	—
435	C₂×Dic₃	—	2	2	no	—
436	C₂×Dic₃	—	2	1	no	—
437	C₂×Dic₃	C₃×#41	1	1	yes	characteristic
438	D₁₂	—	2	2	no	—
439	D₁₂	C₂²×C₃×C₄	1	2	yes	—
440	C₄×D₃	—	2	2	no	—
441	C₄×D₃	—	2	2	no	—
442	C₄×D₃	—	2	2	no	—
443	C₄×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
444	C₄×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
445	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
446	C₄×D₃	C₂×C₃×D₄	1	1	yes	characteristic
447	Dic₆	—	2	2	no	—
448	Dic₆	C₂²×C₃×C₄	1	2	yes	—
449	C₃×C₈	—	2	2	no	—
450	C₃×C₈	—	2	2	no	—
451	C₃×C₈	—	2	1	no	—
452	C₃×C₈	—	2	1	no	—
453	C₃×C₈	—	2	1	no	—
454	C₃×C₈	—	2	1	no	—
455	C₃×C₈	—	3	1	no	—
456	C₃×C₈	—	3	1	no	—
457	C₃×C₈	—	3	1	no	—
458	C₃×C₈	—	3	1	no	—
459	C₃×C₈	—	4	2	no	—
460	C₃×C₈	—	6	2	no	—
461	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
462	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
463	C₃×C₈	D₃×D₄	1	1	yes	characteristic
464	C₃×C₈	D₃×D₄	1	1	yes	characteristic
465	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
466	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
467	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
468	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
469	C₃⋊C₈	—	2	2	no	—
470	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
471	C₃⋊C₈	C₂²×C₃×C₄	1	1	yes	characteristic
472	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
473	C₃⋊C₈	C₂×C₃×D₄	1	1	yes	characteristic
474	C₂×C₃²	—	2	1	no	—
475	C₂×C₃²	—	4	2	no	—
476	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
477	C₃×D₃	—	2	1	no	—
478	C₃×D₃	—	2	1	no	—
479	C₃×D₃	—	4	2	no	—
480	#41	—	3	2	no	—
481	#41	—	3	2	no	—
482	#41	—	3	2	no	—
483	#41	—	6	2	no	—
484	#41	—	6	2	no	—
485	#41	C₂²×C₃×D₃	1	2	yes	—
486	C₂×Q₈	—	3	2	no	—
487	C₂×D₄	—	3	2	no	—
488	C₂×D₄	—	6	2	no	—
489	C₂²×C₄	—	3	1	no	—
490	C₂²×C₄	—	6	2	no	—
491	Q₁₆	—	3	2	no	—
492	Q₁₆	—	3	1	no	—
493	Q₁₆	C₃×C₄×D₃	1	1	yes	characteristic
494	SD₁₆	—	3	2	no	—
495	SD₁₆	—	3	2	no	—
496	SD₁₆	—	3	2	no	—
497	SD₁₆	C₃×C₄×D₃	1	2	yes	—
498	D₈	—	3	2	no	—
499	D₈	—	3	1	no	—
500	D₈	C₃×C₄×D₃	1	1	yes	characteristic
501	M₁₆	—	2	2	no	—
502	M₁₆	—	3	1	no	—
503	M₁₆	—	3	1	no	—
504	M₁₆	—	3	1	no	—
505	M₁₆	—	3	1	no	—
506	M₁₆	—	3	2	no	—
507	M₁₆	—	6	2	no	—
508	M₁₆	—	6	2	no	—
509	M₁₆	—	6	2	no	—
510	M₁₆	—	6	2	no	—
511	M₁₆	C₂²×C₃×D₃	1	2	yes	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	3	1	no	—
514	C₂×C₈	—	3	1	no	—
515	C₂×C₈	—	3	1	no	—
516	C₂×C₈	—	3	1	no	—
517	C₂×C₈	—	3	1	no	—
518	C₂×C₈	—	3	1	no	—
519	C₂×C₈	—	6	2	no	—
520	C₂×C₈	—	6	2	no	—
521	C₂×C₈	—	6	2	no	—
522	C₂×C₈	—	6	2	no	—
523	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
524	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
525	C₄⋊C₄	—	6	1	no	—
526	C₂²⋊C₄	—	6	1	no	—
527	C₄²	—	3	1	no	—
528	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	2	2	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	—	3	1	no	—
533	C₂²×C₃	—	3	1	no	—
534	C₂²×C₃	—	4	2	no	—
535	C₂²×C₃	—	6	2	no	—
536	C₂²×C₃	—	12	1	no	—
537	C₂²×C₃	—	24	2	no	—
538	C₂²×C₃	D₃×#41	1	1	yes	characteristic
539	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
540	C₂×D₃	—	2	2	no	—
541	C₂×D₃	—	4	1	no	—
542	C₂×D₃	—	8	2	no	—
543	C₂×D₃	C₃×C₄×D₄	1	1	yes	characteristic
544	C₂×D₃	C₃×C₄×D₄	1	1	yes	characteristic
545	C₃×C₄	—	2	2	no	—
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	—	2	1	no	—
548	C₃×C₄	—	2	1	no	—
549	C₃×C₄	—	3	1	no	—
550	C₃×C₄	—	3	1	no	—
551	C₃×C₄	—	4	2	no	—
552	C₃×C₄	—	4	1	no	—
553	C₃×C₄	—	4	1	no	—
554	C₃×C₄	—	4	2	no	—
555	C₃×C₄	—	6	2	no	—
556	C₃×C₄	—	12	1	no	—
557	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
558	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
559	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
560	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
561	Dic₃	—	2	2	no	—
562	Dic₃	—	4	1	no	—
563	Dic₃	C₃×C₄×D₄	1	1	yes	characteristic
564	Dic₃	C₃×C₄×D₄	1	1	yes	characteristic
565	C₃²	#2957	1	1	yes	characteristic, complemented, Sylow
566	C₂³	—	3	1	no	—
567	C₂³	—	6	2	no	—
568	Q₈	—	3	2	no	—
569	Q₈	—	6	2	no	—
570	Q₈	C₂×C₃×C₄×D₃	1	2	yes	—
571	D₄	—	2	2	no	—
572	D₄	—	3	2	no	—
573	D₄	—	6	2	no	—
574	D₄	—	6	2	no	—
575	D₄	—	6	2	no	—
576	D₄	—	6	2	no	—
577	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	1	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	1	no	—
585	C₂×C₄	—	6	2	no	—
586	C₂×C₄	—	6	2	no	—
587	C₂×C₄	—	6	2	no	—
588	C₂×C₄	—	6	2	no	—
589	C₂×C₄	—	6	1	no	—
590	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
591	C₈	—	2	2	no	—
592	C₈	—	3	1	no	—
593	C₈	—	3	1	no	—
594	C₈	—	3	1	no	—
595	C₈	—	3	1	no	—
596	C₈	—	6	2	no	—
597	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
598	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
599	C₈	C₃×D₃×D₄	1	1	yes	characteristic
600	C₈	C₃×D₃×D₄	1	1	yes	characteristic
601	C₂×C₃	—	2	1	no	—
602	C₂×C₃	—	2	1	no	—
603	C₂×C₃	—	2	1	no	—
604	C₂×C₃	—	4	1	no	—
605	C₂×C₃	—	4	2	no	—
606	C₂×C₃	—	4	2	no	—
607	C₂×C₃	—	6	1	no	—
608	C₂×C₃	—	6	1	no	—
609	C₂×C₃	—	8	2	no	—
610	C₂×C₃	—	12	2	no	—
611	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
612	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
613	D₃	—	2	1	no	—
614	D₃	—	2	1	no	—
615	D₃	—	4	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	3	1	no	—
618	C₂²	—	3	1	no	—
619	C₂²	—	6	2	no	—
620	C₂²	—	12	1	no	—
621	C₂²	—	24	2	no	—
622	C₂²	C₃×D₃×#41	1	1	yes	characteristic
623	C₄	—	2	2	no	—
624	C₄	—	3	1	no	—
625	C₄	—	3	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	6	2	no	—
628	C₄	—	12	1	no	—
629	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
630	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
631	C₃	—	2	1	no	—
632	C₃	#79890	1	1	yes	characteristic, direct product factor
633	C₃	C₃×#2957	1	1	yes	characteristic, complemented
634	C₂	—	2	1	no	—
635	C₂	—	4	2	no	—
636	C₂	—	6	1	no	—
637	C₂	—	6	1	no	—
638	C₂	—	12	2	no	—
639	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×D₃×#135	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#443	D₃
hypocenter	C₃	C₃×#2957
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×#5196	C₂	semidirect
5. C₃×#5145	C₂	semidirect
6. C₃×#4895	C₂	semidirect
7. C₃×D₃×#108	C₂	semidirect
8. C₃×#4823	C₂	semidirect
9. C₃×#4821	C₂	semidirect
10. C₃×#4700	C₂	semidirect
11. C₃×#4689	C₂	semidirect
13. #79890	C₃	direct (N × H)
16. C₃²×#131	C₂²	semidirect
18. C₃×#948	C₂²	semidirect
19. C₃×#919	C₄	semidirect
20. C₃×D₃×Q₁₆	C₄	semidirect
21. C₃×#916	C₄	semidirect
22. C₃×D₃×SD₁₆	C₄	semidirect
23. C₃×#912	C₄	semidirect
24. C₃×D₃×D₈	C₄	semidirect
26. C₃×#907	C₂²	semidirect
31. C₃×#901	C₂²	semidirect
36. C₃²×#108	C₂²	semidirect
37. C₃²×#104	C₂²	semidirect
38. C₃²×C₄×C₈	C₂²	semidirect
39. C₃×#837	C₂²	semidirect
40. C₃×#825	C₂²	semidirect
41. C₃×#822	C₂²	semidirect
42. C₃×#819	C₂²	semidirect
43. C₃×#815	C₂²	semidirect
44. C₃×C₈×Dic₃	C₂²	semidirect
45. C₃×#805	C₂²	semidirect
46. C₃×#803	C₂²	semidirect
50. #5750	C₂×C₃	semidirect
57. C₃×#443	D₃	semidirect
58. C₃×#443	C₂×C₃	semidirect
62. #5196	C₂×C₃	semidirect
63. #5145	C₂×C₃	semidirect
64. #4895	C₂×C₃	semidirect
65. D₃×#108	C₂×C₃	semidirect
66. #4823	C₂×C₃	semidirect
67. #4821	C₂×C₃	semidirect
68. #4700	C₂×C₃	semidirect
69. #4689	C₂×C₃	semidirect
139. C₃×#131	C₂×D₃	semidirect
140. C₃×#131	C₂²×C₃	semidirect
148. #948	C₂²×C₃	semidirect
149. #919	C₃×C₄	semidirect
150. D₃×Q₁₆	C₃×C₄	semidirect
151. #916	C₃×C₄	semidirect
152. D₃×SD₁₆	C₃×C₄	semidirect
153. #912	C₃×C₄	semidirect
154. D₃×D₈	C₃×C₄	semidirect
156. #907	C₂²×C₃	semidirect
161. #901	C₂²×C₃	semidirect
169. C₃×#108	C₂×D₃	semidirect
170. C₃×#108	C₂²×C₃	semidirect
175. C₃×#104	C₂×D₃	semidirect
176. C₃×#104	C₂²×C₃	semidirect
181. C₃×C₄×C₈	C₂×D₃	semidirect
182. C₃×C₄×C₈	C₂²×C₃	semidirect
183. #837	C₂²×C₃	semidirect
184. #825	C₂²×C₃	semidirect
185. #822	C₂²×C₃	semidirect
186. #819	C₂²×C₃	semidirect
187. #815	C₂²×C₃	semidirect
188. C₈×Dic₃	C₂²×C₃	semidirect
189. #805	C₂²×C₃	semidirect
190. #803	C₂²×C₃	semidirect
233. #443	C₃×D₃	semidirect
375. #131	C₂×C₃×D₃	semidirect
384. #108	C₂×C₃×D₃	semidirect
388. #104	C₂×C₃×D₃	semidirect
392. C₄×C₈	C₂×C₃×D₃	semidirect
565. C₃²	#2957	semidirect
632. C₃	#79890	direct (N × H)
633. C₃	C₃×#2957	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×#135	2
C₃×#5750	2
C₃²×#443	2
C₃×#5196	2
C₃×#5145	2
C₃×#4895	2
C₃×D₃×#108	2
C₃×#4823	2
C₃×#4821	2
C₃×#4700	2
C₃×#4689	2
C₃×#2957	3
#79890	3

Subgroups — C3×#79890 #11861186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79890 #11861186