Subgroups — C₃×#87203 #11918955

Order 1152.

2982 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5966	C₂	1	2	yes	maximal, complemented
2	C₃²×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5836	C₂	1	2	yes	maximal, complemented
4	C₃×#5775	C₂	1	6	yes	maximal, complemented
5	C₃×#5773	C₂	1	6	yes	maximal, complemented
6	C₃×#5771	C₂	1	3	yes	maximal, complemented
7	C₃×D₃×#135	C₂	1	3	yes	maximal, complemented
8	C₃×#5757	C₂	1	3	yes	maximal, complemented
9	C₂×C₃×#912	C₂	1	3	yes	maximal, complemented
10	C₃×#5753	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3584	—	3	1	no	maximal
13	#87203	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃²×H(5,𝔽₂)	C₂²	1	2	yes	complemented
15	C₃×#1010	—	2	2	no	—
16	C₃×#1010	C₂²	1	6	yes	complemented
17	C₃×#1010	C₂²	1	2	yes	complemented
18	C₃×D₃×#41	—	2	2	no	—
19	C₃×D₃×#41	C₂²	1	1	yes	characteristic
20	C₃×D₃×#41	C₂²	1	6	yes	complemented
21	C₃×#1004	—	2	6	no	—
22	C₃×#1004	C₂²	1	6	yes	complemented
23	C₂×C₃×#237	—	2	6	no	—
24	C₂×C₃×#237	C₂²	1	6	yes	complemented
25	C₃²×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
26	C₃²×#135	C₂²	1	3	yes	complemented
27	C₂×C₃²×D₈	C₂²	1	3	yes	complemented
28	C₃²×#131	C₂²	1	1	yes	characteristic, complemented
29	C₃×#951	C₂²	1	6	yes	complemented
30	C₃×#950	C₂²	1	6	yes	complemented
31	C₃×#948	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×#214	C₂²	1	6	yes	complemented
33	C₃×#932	C₂²	1	6	yes	complemented
34	C₃×#919	C₂²	1	1	yes	characteristic, complemented
35	C₃×D₃×Q₁₆	C₂²	1	3	yes	complemented
36	C₃×#916	C₂²	1	6	yes	complemented
37	C₃×#915	C₂²	1	12	yes	complemented
38	C₃×D₃×SD₁₆	C₂²	1	6	yes	complemented
39	C₃×#912	C₂²	1	3	yes	complemented
40	C₃×#912	C₂²	1	6	yes	complemented
41	C₃×#912	C₂²	1	6	yes	complemented
42	C₃×#912	C₂²	1	6	yes	complemented
43	C₃×#911	C₂²	1	12	yes	complemented
44	C₃×D₃×D₈	C₂²	1	3	yes	complemented
45	C₃×#909	C₂²	1	6	yes	complemented
46	C₃×#907	C₂²	1	3	yes	complemented
47	C₃×D₃×M₁₆	C₂²	1	3	yes	complemented
48	C₂×C₃×Dic₁₂	C₂²	1	3	yes	complemented
49	C₃×#904	C₂²	1	3	yes	complemented
50	C₃×#901	C₂²	1	3	yes	complemented
51	C₂×C₃×D₃×C₈	C₂²	1	3	yes	complemented
52	C₃×#585	—	3	2	no	—
53	#5966	C₂×C₃	1	2	yes	complemented
54	C₃×#578	—	3	3	no	—
55	C₃×#578	—	3	1	no	—
56	C₃×#577	—	3	2	no	—
57	C₃×#577	—	3	6	no	—
58	C₃×#576	—	2	1	no	—
59	C₃×#576	—	3	3	no	—
60	C₃×#576	D₃	1	1	yes	characteristic, complemented
61	C₃×#576	C₂×C₃	1	1	yes	characteristic, complemented
62	C₃×#575	—	3	6	no	—
63	C₂×C₃×#135	—	3	3	no	—
64	C₂×C₃×#135	—	3	3	no	—
65	C₂×C₃×#131	—	3	1	no	—
66	#5836	C₂×C₃	1	2	yes	complemented
67	#5775	C₂×C₃	1	6	yes	complemented
68	#5773	C₂×C₃	1	6	yes	complemented
69	#5771	C₂×C₃	1	3	yes	complemented
70	D₃×#135	C₂×C₃	1	3	yes	complemented
71	#5757	C₂×C₃	1	3	yes	complemented
72	C₂×#912	C₂×C₃	1	3	yes	complemented
73	#5753	C₂×C₃	1	1	yes	characteristic, complemented
74	D₃×#131	C₂×C₃	1	1	yes	characteristic, complemented
75	C₃²×#41	—	2	2	no	—
76	C₃²×#41	C₂³	1	6	yes	—
77	C₃²×#41	C₂³	1	1	yes	characteristic
78	C₂×C₃²×D₄	—	2	6	no	—
79	C₂×C₃²×D₄	C₂³	1	6	yes	—
80	C₂×C₃×#67	—	2	6	no	—
81	C₂×C₃×#67	—	2	12	no	—
82	C₂²×C₃×Dic₃	—	2	6	no	—
83	C₃×#239	D₄	1	1	yes	characteristic
84	C₃×#239	C₂³	1	2	yes	—
85	C₃×D₃×Q₈	—	2	2	no	—
86	C₃×D₃×Q₈	D₄	1	1	yes	characteristic
87	C₃×D₃×Q₈	C₂³	1	6	yes	—
88	C₃×#237	—	2	6	no	—
89	C₃×#237	—	2	12	no	—
90	C₃×#237	—	2	6	no	—
91	C₃×#237	—	2	6	no	—
92	C₃×#237	—	2	6	no	—
93	C₃×#237	—	2	6	no	—
94	C₃×#237	D₄	1	3	yes	—
95	C₃×#237	C₂³	1	12	yes	—
96	C₃×#237	C₂³	1	6	yes	—
97	C₃×D₃×D₄	—	2	6	no	—
98	C₃×D₃×D₄	—	2	6	no	—
99	C₃×D₃×D₄	D₄	1	3	yes	—
100	C₃×D₃×D₄	C₂³	1	6	yes	—
101	C₃×#235	—	2	6	no	—
102	C₃×#235	—	2	6	no	—
103	C₃×#235	C₂³	1	3	yes	—
104	C₃×#235	C₂³	1	6	yes	—
105	C₂×C₃×C₄×D₃	—	2	6	no	—
106	C₂×C₃×C₄×D₃	C₂³	1	3	yes	—
107	C₂×C₃×Dic₆	—	2	6	no	—
108	C₂×C₃×Dic₆	C₂³	1	6	yes	—
109	C₃²×Q₁₆	C₂³	1	1	yes	characteristic
110	C₃²×SD₁₆	C₂³	1	6	yes	—
111	C₃²×D₈	C₂³	1	3	yes	—
112	C₃²×D₈	C₂³	1	6	yes	—
113	C₃²×M₁₆	C₂³	1	3	yes	—
114	C₂×C₃²×C₈	C₂³	1	3	yes	—
115	C₃×#216	C₂³	1	6	yes	—
116	C₃×#215	C₂³	1	2	yes	—
117	C₃×#214	C₂³	1	12	yes	—
118	C₃×#214	C₂³	1	6	yes	—
119	C₃×#213	C₂³	1	6	yes	—
120	C₃×#208	C₂³	1	3	yes	—
121	C₂×C₃×C₃⋊C₈	C₂³	1	3	yes	—
122	C₃×Dic₁₂	C₂³	1	3	yes	—
123	C₃×Dic₁₂	C₂³	1	6	yes	—
124	C₃×D₂₄	C₂³	1	1	yes	characteristic
125	C₃×#204	C₂³	1	6	yes	—
126	C₃×ΓL(1,𝔽₂₅)	C₂³	1	6	yes	—
127	C₃×D₃×C₈	C₂³	1	1	yes	characteristic
128	C₃×D₃×C₈	C₂³	1	3	yes	—
129	C₃×D₃×C₈	C₂³	1	3	yes	—
130	C₃×D₃×C₈	C₂³	1	3	yes	—
131	#3584	—	3	1	no	Sylow
132	C₃×2₋¹⁺⁴	—	3	6	no	—
133	C₃×2₋¹⁺⁴	—	3	2	no	—
134	C₃×2₋¹⁺⁴	—	6	2	no	—
135	C₃×H(5,𝔽₂)	—	2	2	no	—
136	C₃×H(5,𝔽₂)	—	3	6	no	—
137	C₃×H(5,𝔽₂)	—	6	6	no	—
138	C₃×H(5,𝔽₂)	C₂×D₃	1	2	yes	complemented
139	C₃×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
140	C₂×C₃×#41	—	3	1	no	—
141	C₂×C₃×#41	—	3	6	no	—
142	C₂×C₃×#41	—	3	6	no	—
143	C₂×C₃×#41	—	6	6	no	—
144	C₂×C₃×#41	—	6	2	no	—
145	#1010	—	2	2	no	—
146	#1010	C₂²×C₃	1	6	yes	complemented
147	#1010	C₂²×C₃	1	2	yes	complemented
148	D₃×#41	—	2	2	no	—
149	D₃×#41	C₂²×C₃	1	1	yes	characteristic
150	D₃×#41	C₂²×C₃	1	6	yes	complemented
151	#1004	—	2	6	no	—
152	#1004	C₂²×C₃	1	6	yes	complemented
153	C₂×#237	—	2	6	no	—
154	C₂×#237	C₂²×C₃	1	6	yes	complemented
155	C₃×#137	—	3	6	no	—
156	C₃×#137	—	3	12	no	—
157	C₃×#137	—	3	6	no	—
158	C₃×AGL(1,ℤ/8)	—	2	6	no	—
159	C₃×AGL(1,ℤ/8)	—	3	6	no	—
160	C₃×AGL(1,ℤ/8)	—	3	12	no	—
161	C₃×AGL(1,ℤ/8)	C₂×D₃	1	6	yes	complemented
162	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	6	yes	complemented
163	C₃×#135	—	2	3	no	—
164	C₃×#135	—	3	6	no	—
165	C₃×#135	—	3	1	no	—
166	C₃×#135	—	3	6	no	—
167	C₃×#135	—	3	3	no	—
168	C₃×#135	—	3	6	no	—
169	C₃×#135	—	3	6	no	—
170	C₃×#135	—	3	6	no	—
171	C₃×#135	—	3	3	no	—
172	C₃×#135	C₂×D₃	1	3	yes	complemented
173	C₃×#135	C₂²×C₃	1	3	yes	complemented
174	C₂×C₃×Q₁₆	—	3	3	no	—
175	C₂×C₃×Q₁₆	—	3	3	no	—
176	C₂×C₃×SD₁₆	—	3	6	no	—
177	C₂×C₃×SD₁₆	—	3	6	no	—
178	C₂×C₃×D₈	—	2	3	no	—
179	C₂×C₃×D₈	—	3	3	no	—
180	C₂×C₃×D₈	C₂×D₃	1	3	yes	complemented
181	C₂×C₃×D₈	C₂²×C₃	1	3	yes	complemented
182	C₃×#131	—	2	1	no	—
183	C₃×#131	—	3	1	no	—
184	C₃×#131	—	3	3	no	—
185	C₃×#131	—	3	3	no	—
186	C₃×#131	C₂×D₃	1	1	yes	characteristic, complemented
187	C₃×#131	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂×C₃×M₁₆	—	3	3	no	—
189	C₂²×C₃×C₈	—	3	3	no	—
190	#951	C₂²×C₃	1	6	yes	complemented
191	#950	C₂²×C₃	1	6	yes	complemented
192	#948	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂×#214	C₂²×C₃	1	6	yes	complemented
194	#932	C₂²×C₃	1	6	yes	complemented
195	#919	C₂²×C₃	1	1	yes	characteristic, complemented
196	D₃×Q₁₆	C₂²×C₃	1	3	yes	complemented
197	#916	C₂²×C₃	1	6	yes	complemented
198	#915	C₂²×C₃	1	12	yes	complemented
199	D₃×SD₁₆	C₂²×C₃	1	6	yes	complemented
200	#912	C₂²×C₃	1	3	yes	complemented
201	#912	C₂²×C₃	1	6	yes	complemented
202	#912	C₂²×C₃	1	6	yes	complemented
203	#912	C₂²×C₃	1	6	yes	complemented
204	#911	C₂²×C₃	1	12	yes	complemented
205	D₃×D₈	C₂²×C₃	1	3	yes	complemented
206	#909	C₂²×C₃	1	6	yes	complemented
207	#907	C₂²×C₃	1	3	yes	complemented
208	D₃×M₁₆	C₂²×C₃	1	3	yes	complemented
209	C₂×Dic₁₂	C₂²×C₃	1	3	yes	complemented
210	#904	C₂²×C₃	1	3	yes	complemented
211	#901	C₂²×C₃	1	3	yes	complemented
212	C₂×D₃×C₈	C₂²×C₃	1	3	yes	complemented
213	C₂³×C₃²	—	2	6	no	—
214	C₂²×C₃×D₃	—	2	6	no	—
215	C₂²×C₃×D₃	C₂×D₄	1	3	yes	—
216	C₃²×Q₈	C₂×D₄	1	1	yes	characteristic
217	C₃²×Q₈	C₂⁴	1	2	yes	—
218	C₃²×D₄	—	2	6	no	—
219	C₃²×D₄	—	2	6	no	—
220	C₃²×D₄	C₂×D₄	1	3	yes	—
221	C₃²×D₄	C₂⁴	1	6	yes	—
222	C₂×C₃²×C₄	—	2	6	no	—
223	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
224	C₃×#67	—	2	6	no	—
225	C₃×#67	—	2	12	no	—
226	C₃×#67	—	2	6	no	—
227	C₃×#67	—	2	6	no	—
228	C₃×#67	C₂×D₄	1	6	yes	—
229	C₂×C₃×Dic₃	—	2	6	no	—
230	C₂×C₃×Dic₃	—	2	12	no	—
231	C₂×C₃×Dic₃	—	2	6	no	—
232	C₂×C₃×Dic₃	C₂×D₄	1	3	yes	—
233	C₃×D₁₂	—	2	2	no	—
234	C₃×D₁₂	C₂×D₄	1	3	yes	—
235	C₃×D₁₂	C₂⁴	1	2	yes	—
236	C₃×C₄×D₃	—	2	6	no	—
237	C₃×C₄×D₃	—	2	6	no	—
238	C₃×C₄×D₃	—	2	2	no	—
239	C₃×C₄×D₃	C₂×D₄	1	3	yes	—
240	C₃×C₄×D₃	C₂×D₄	1	3	yes	—
241	C₃×C₄×D₃	C₂⁴	1	1	yes	characteristic
242	C₃×C₄×D₃	C₂⁴	1	3	yes	—
243	C₃×Dic₆	—	2	6	no	—
244	C₃×Dic₆	—	2	6	no	—
245	C₃×Dic₆	C₂×D₄	1	3	yes	—
246	C₃×Dic₆	C₂⁴	1	6	yes	—
247	C₃²×C₈	C₂⁴	1	1	yes	characteristic
248	C₃²×C₈	C₂⁴	1	3	yes	—
249	C₃×C₃⋊C₈	C₂⁴	1	1	yes	characteristic
250	C₃×C₃⋊C₈	C₂⁴	1	3	yes	—
251	#585	—	3	2	no	—
252	#578	—	3	3	no	—
253	#578	—	3	1	no	—
254	#577	—	3	2	no	—
255	#577	—	3	6	no	—
256	#576	—	3	3	no	—
257	#576	C₃×D₃	1	1	yes	characteristic, complemented
258	#575	—	3	6	no	—
259	C₂×#135	—	3	3	no	—
260	C₂×#135	—	3	3	no	—
261	C₂×#131	—	3	1	no	—
262	C₃×#41	—	2	2	no	—
263	C₃×#41	—	2	2	no	—
264	C₃×#41	—	2	1	no	—
265	C₃×#41	—	2	6	no	—
266	C₃×#41	—	3	1	no	—
267	C₃×#41	—	3	3	no	—
268	C₃×#41	—	3	3	no	—
269	C₃×#41	—	3	2	no	—
270	C₃×#41	—	3	6	no	—
271	C₃×#41	—	3	12	no	—
272	C₃×#41	—	3	6	no	—
273	C₃×#41	—	4	2	no	—
274	C₃×#41	—	6	6	no	—
275	C₃×#41	—	6	6	no	—
276	C₃×#41	—	6	6	no	—
277	C₃×#41	—	6	6	no	—
278	C₃×#41	—	6	6	no	—
279	C₃×#41	—	6	12	no	—
280	C₃×#41	—	6	6	no	—
281	C₃×#41	—	6	6	no	—
282	C₃×#41	C₂²×D₃	1	6	yes	—
283	C₃×#41	C₂²×D₃	1	1	yes	characteristic
284	C₃×#41	C₂³×C₃	1	6	yes	—
285	C₃×#41	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₃×Q₈	—	3	1	no	—
287	C₂×C₃×Q₈	—	3	6	no	—
288	C₂×C₃×Q₈	—	3	6	no	—
289	C₂×C₃×Q₈	—	6	6	no	—
290	C₂×C₃×Q₈	—	6	2	no	—
291	C₂×C₃×D₄	—	2	6	no	—
292	C₂×C₃×D₄	—	2	6	no	—
293	C₂×C₃×D₄	—	2	6	no	—
294	C₂×C₃×D₄	—	3	3	no	—
295	C₂×C₃×D₄	—	3	6	no	—
296	C₂×C₃×D₄	—	4	6	no	—
297	C₂×C₃×D₄	—	6	6	no	—
298	C₂×C₃×D₄	—	6	6	no	—
299	C₂×C₃×D₄	—	6	12	no	—
300	C₂×C₃×D₄	—	6	6	no	—
301	C₂×C₃×D₄	C₂²×D₃	1	6	yes	—
302	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
303	C₂²×C₃×C₄	—	3	3	no	—
304	C₂²×C₃×C₄	—	6	6	no	—
305	C₂²×C₃×C₄	—	6	6	no	—
306	C₂×#67	—	2	6	no	—
307	C₂×#67	—	2	12	no	—
308	C₂²×Dic₃	—	2	6	no	—
309	#239	C₃×D₄	1	1	yes	characteristic
310	#239	C₂³×C₃	1	2	yes	—
311	D₃×Q₈	—	2	2	no	—
312	D₃×Q₈	C₃×D₄	1	1	yes	characteristic
313	D₃×Q₈	C₂³×C₃	1	6	yes	—
314	#237	—	2	6	no	—
315	#237	—	2	12	no	—
316	#237	—	2	6	no	—
317	#237	—	2	6	no	—
318	#237	—	2	6	no	—
319	#237	—	2	6	no	—
320	#237	C₃×D₄	1	3	yes	—
321	#237	C₂³×C₃	1	12	yes	—
322	#237	C₂³×C₃	1	6	yes	—
323	D₃×D₄	—	2	6	no	—
324	D₃×D₄	—	2	6	no	—
325	D₃×D₄	C₃×D₄	1	3	yes	—
326	D₃×D₄	C₂³×C₃	1	6	yes	—
327	#235	—	2	6	no	—
328	#235	—	2	6	no	—
329	#235	C₂³×C₃	1	3	yes	—
330	#235	C₂³×C₃	1	6	yes	—
331	C₂×C₄×D₃	—	2	6	no	—
332	C₂×C₄×D₃	C₂³×C₃	1	3	yes	—
333	C₂×Dic₆	—	2	6	no	—
334	C₂×Dic₆	C₂³×C₃	1	6	yes	—
335	C₃×Q₁₆	—	2	1	no	—
336	C₃×Q₁₆	—	3	6	no	—
337	C₃×Q₁₆	—	3	3	no	—
338	C₃×Q₁₆	—	3	6	no	—
339	C₃×Q₁₆	C₂²×D₃	1	1	yes	characteristic
340	C₃×Q₁₆	C₂³×C₃	1	1	yes	characteristic
341	C₃×SD₁₆	—	2	6	no	—
342	C₃×SD₁₆	—	3	2	no	—
343	C₃×SD₁₆	—	3	6	no	—
344	C₃×SD₁₆	—	3	12	no	—
345	C₃×SD₁₆	—	3	6	no	—
346	C₃×SD₁₆	C₂²×D₃	1	6	yes	—
347	C₃×SD₁₆	C₂³×C₃	1	6	yes	—
348	C₃×D₈	—	2	3	no	—
349	C₃×D₈	—	2	6	no	—
350	C₃×D₈	—	3	6	no	—
351	C₃×D₈	—	3	1	no	—
352	C₃×D₈	C₂²×D₃	1	3	yes	—
353	C₃×D₈	C₂²×D₃	1	6	yes	—
354	C₃×D₈	C₂³×C₃	1	3	yes	—
355	C₃×D₈	C₂³×C₃	1	6	yes	—
356	C₃×M₁₆	—	2	3	no	—
357	C₃×M₁₆	—	3	3	no	—
358	C₃×M₁₆	—	3	6	no	—
359	C₃×M₁₆	C₂²×D₃	1	3	yes	—
360	C₃×M₁₆	C₂³×C₃	1	3	yes	—
361	C₂×C₃×C₈	—	2	3	no	—
362	C₂×C₃×C₈	—	3	3	no	—
363	C₂×C₃×C₈	—	3	1	no	—
364	C₂×C₃×C₈	—	3	3	no	—
365	C₂×C₃×C₈	—	3	3	no	—
366	C₂×C₃×C₈	—	3	3	no	—
367	C₂×C₃×C₈	C₂²×D₃	1	3	yes	—
368	C₂×C₃×C₈	C₂³×C₃	1	3	yes	—
369	#216	C₂³×C₃	1	6	yes	—
370	#215	C₂³×C₃	1	2	yes	—
371	#214	C₂³×C₃	1	12	yes	—
372	#214	C₂³×C₃	1	6	yes	—
373	#213	C₂³×C₃	1	6	yes	—
374	#208	C₂³×C₃	1	3	yes	—
375	C₂×C₃⋊C₈	C₂³×C₃	1	3	yes	—
376	Dic₁₂	C₂³×C₃	1	3	yes	—
377	Dic₁₂	C₂³×C₃	1	6	yes	—
378	D₂₄	C₂³×C₃	1	1	yes	characteristic
379	#204	C₂³×C₃	1	6	yes	—
380	ΓL(1,𝔽₂₅)	C₂³×C₃	1	6	yes	—
381	D₃×C₈	C₂³×C₃	1	1	yes	characteristic
382	D₃×C₈	C₂³×C₃	1	3	yes	—
383	D₃×C₈	C₂³×C₃	1	3	yes	—
384	D₃×C₈	C₂³×C₃	1	3	yes	—
385	C₂²×C₃²	—	2	6	no	—
386	C₂²×C₃²	—	8	6	no	—
387	C₂²×C₃²	C₂²×D₄	1	3	yes	—
388	C₂×C₃×D₃	—	2	2	no	—
389	C₂×C₃×D₃	—	4	3	no	—
390	C₂×C₃×D₃	—	8	6	no	—
391	C₂×C₃×D₃	C₂²×D₄	1	3	yes	—
392	C₂×C₃×D₃	C₂²×D₄	1	1	yes	characteristic
393	C₃²×C₄	—	2	2	no	—
394	C₃²×C₄	C₂²×D₄	1	3	yes	—
395	C₃²×C₄	C₂⁵	1	1	yes	characteristic
396	C₃×Dic₃	—	2	6	no	—
397	C₃×Dic₃	C₂²×D₄	1	3	yes	—
398	C₃×Dic₃	C₂²×D₄	1	1	yes	characteristic
399	2₋¹⁺⁴	—	3	6	no	—
400	2₋¹⁺⁴	—	3	2	no	—
401	2₋¹⁺⁴	—	6	2	no	—
402	H(5,𝔽₂)	—	3	6	no	—
403	H(5,𝔽₂)	—	6	6	no	—
404	H(5,𝔽₂)	C₂×C₃×D₃	1	2	yes	complemented
405	C₂×#41	—	3	1	no	—
406	C₂×#41	—	3	6	no	—
407	C₂×#41	—	3	6	no	—
408	C₂×#41	—	6	6	no	—
409	C₂×#41	—	6	2	no	—
410	#137	—	3	6	no	—
411	#137	—	3	12	no	—
412	#137	—	3	6	no	—
413	AGL(1,ℤ/8)	—	3	6	no	—
414	AGL(1,ℤ/8)	—	3	12	no	—
415	AGL(1,ℤ/8)	C₂×C₃×D₃	1	6	yes	complemented
416	#135	—	3	6	no	—
417	#135	—	3	1	no	—
418	#135	—	3	6	no	—
419	#135	—	3	3	no	—
420	#135	—	3	6	no	—
421	#135	—	3	6	no	—
422	#135	—	3	6	no	—
423	#135	—	3	3	no	—
424	#135	C₂×C₃×D₃	1	3	yes	complemented
425	C₂×Q₁₆	—	3	3	no	—
426	C₂×Q₁₆	—	3	3	no	—
427	C₂×SD₁₆	—	3	6	no	—
428	C₂×SD₁₆	—	3	6	no	—
429	C₂×D₈	—	3	3	no	—
430	C₂×D₈	C₂×C₃×D₃	1	3	yes	complemented
431	#131	—	3	1	no	—
432	#131	—	3	3	no	—
433	#131	—	3	3	no	—
434	#131	C₂×C₃×D₃	1	1	yes	characteristic, complemented
435	C₂×M₁₆	—	3	3	no	—
436	C₂²×C₈	—	3	3	no	—
437	C₂³×C₃	—	2	6	no	—
438	C₂³×C₃	—	2	6	no	—
439	C₂³×C₃	—	3	3	no	—
440	C₂³×C₃	—	4	6	no	—
441	C₂³×C₃	—	6	6	no	—
442	C₂²×D₃	—	2	6	no	—
443	C₂²×D₃	C₂×C₃×D₄	1	3	yes	—
444	C₃×Q₈	—	2	2	no	—
445	C₃×Q₈	—	2	1	no	—
446	C₃×Q₈	—	3	3	no	—
447	C₃×Q₈	—	3	6	no	—
448	C₃×Q₈	—	6	6	no	—
449	C₃×Q₈	—	6	6	no	—
450	C₃×Q₈	D₃×D₄	1	1	yes	characteristic
451	C₃×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
452	C₃×Q₈	C₂³×D₃	1	2	yes	—
453	C₃×Q₈	C₂⁴×C₃	1	2	yes	—
454	C₃×D₄	—	2	6	no	—
455	C₃×D₄	—	2	6	no	—
456	C₃×D₄	—	2	6	no	—
457	C₃×D₄	—	2	6	no	—
458	C₃×D₄	—	2	6	no	—
459	C₃×D₄	—	2	3	no	—
460	C₃×D₄	—	3	6	no	—
461	C₃×D₄	—	3	3	no	—
462	C₃×D₄	—	3	2	no	—
463	C₃×D₄	—	4	6	no	—
464	C₃×D₄	—	4	6	no	—
465	C₃×D₄	—	6	2	no	—
466	C₃×D₄	—	6	6	no	—
467	C₃×D₄	—	6	6	no	—
468	C₃×D₄	—	6	12	no	—
469	C₃×D₄	—	6	6	no	—
470	C₃×D₄	D₃×D₄	1	3	yes	—
471	C₃×D₄	C₂×C₃×D₄	1	3	yes	—
472	C₃×D₄	C₂³×D₃	1	6	yes	—
473	C₃×D₄	C₂⁴×C₃	1	6	yes	—
474	C₂×C₃×C₄	—	2	6	no	—
475	C₂×C₃×C₄	—	2	6	no	—
476	C₂×C₃×C₄	—	2	3	no	—
477	C₂×C₃×C₄	—	3	3	no	—
478	C₂×C₃×C₄	—	3	3	no	—
479	C₂×C₃×C₄	—	3	3	no	—
480	C₂×C₃×C₄	—	3	1	no	—
481	C₂×C₃×C₄	—	3	3	no	—
482	C₂×C₃×C₄	—	4	6	no	—
483	C₂×C₃×C₄	—	6	2	no	—
484	C₂×C₃×C₄	—	6	6	no	—
485	C₂×C₃×C₄	—	6	6	no	—
486	C₂×C₃×C₄	—	6	12	no	—
487	C₂×C₃×C₄	—	6	6	no	—
488	C₂×C₃×C₄	—	6	6	no	—
489	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
490	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
491	#67	—	2	6	no	—
492	#67	—	2	12	no	—
493	#67	—	2	6	no	—
494	#67	—	2	6	no	—
495	#67	C₂×C₃×D₄	1	6	yes	—
496	C₂×Dic₃	—	2	6	no	—
497	C₂×Dic₃	—	2	12	no	—
498	C₂×Dic₃	—	2	6	no	—
499	C₂×Dic₃	C₂×C₃×D₄	1	3	yes	—
500	D₁₂	—	2	2	no	—
501	D₁₂	C₂×C₃×D₄	1	3	yes	—
502	D₁₂	C₂⁴×C₃	1	2	yes	—
503	C₄×D₃	—	2	6	no	—
504	C₄×D₃	—	2	6	no	—
505	C₄×D₃	—	2	2	no	—
506	C₄×D₃	C₂×C₃×D₄	1	3	yes	—
507	C₄×D₃	C₂×C₃×D₄	1	3	yes	—
508	C₄×D₃	C₂⁴×C₃	1	1	yes	characteristic
509	C₄×D₃	C₂⁴×C₃	1	3	yes	—
510	Dic₆	—	2	6	no	—
511	Dic₆	—	2	6	no	—
512	Dic₆	C₂×C₃×D₄	1	3	yes	—
513	Dic₆	C₂⁴×C₃	1	6	yes	—
514	C₃×C₈	—	2	1	no	—
515	C₃×C₈	—	2	3	no	—
516	C₃×C₈	—	3	1	no	—
517	C₃×C₈	—	3	3	no	—
518	C₃×C₈	C₂³×D₃	1	1	yes	characteristic
519	C₃×C₈	C₂³×D₃	1	3	yes	—
520	C₃×C₈	C₂⁴×C₃	1	1	yes	characteristic
521	C₃×C₈	C₂⁴×C₃	1	3	yes	—
522	C₃⋊C₈	C₂⁴×C₃	1	1	yes	characteristic
523	C₃⋊C₈	C₂⁴×C₃	1	3	yes	—
524	C₂×C₃²	—	2	3	no	—
525	C₂×C₃²	—	4	6	no	—
526	C₂×C₃²	C₂³×D₄	1	1	yes	characteristic
527	C₃×D₃	—	2	1	no	—
528	C₃×D₃	—	2	3	no	—
529	C₃×D₃	—	4	2	no	—
530	#41	—	2	2	no	—
531	#41	—	3	1	no	—
532	#41	—	3	3	no	—
533	#41	—	3	3	no	—
534	#41	—	3	2	no	—
535	#41	—	3	6	no	—
536	#41	—	3	12	no	—
537	#41	—	3	6	no	—
538	#41	—	6	6	no	—
539	#41	—	6	6	no	—
540	#41	—	6	6	no	—
541	#41	—	6	6	no	—
542	#41	—	6	6	no	—
543	#41	—	6	12	no	—
544	#41	—	6	6	no	—
545	#41	—	6	6	no	—
546	#41	C₂²×C₃×D₃	1	6	yes	—
547	#41	C₂²×C₃×D₃	1	1	yes	characteristic
548	C₂×Q₈	—	3	1	no	—
549	C₂×Q₈	—	3	6	no	—
550	C₂×Q₈	—	3	6	no	—
551	C₂×Q₈	—	6	6	no	—
552	C₂×Q₈	—	6	2	no	—
553	C₂×D₄	—	2	6	no	—
554	C₂×D₄	—	3	3	no	—
555	C₂×D₄	—	3	6	no	—
556	C₂×D₄	—	6	6	no	—
557	C₂×D₄	—	6	6	no	—
558	C₂×D₄	—	6	12	no	—
559	C₂×D₄	—	6	6	no	—
560	C₂×D₄	C₂²×C₃×D₃	1	6	yes	—
561	C₂²×C₄	—	3	3	no	—
562	C₂²×C₄	—	6	6	no	—
563	C₂²×C₄	—	6	6	no	—
564	Q₁₆	—	3	6	no	—
565	Q₁₆	—	3	3	no	—
566	Q₁₆	—	3	6	no	—
567	Q₁₆	C₂²×C₃×D₃	1	1	yes	characteristic
568	SD₁₆	—	3	2	no	—
569	SD₁₆	—	3	6	no	—
570	SD₁₆	—	3	12	no	—
571	SD₁₆	—	3	6	no	—
572	SD₁₆	C₂²×C₃×D₃	1	6	yes	—
573	D₈	—	3	6	no	—
574	D₈	—	3	1	no	—
575	D₈	C₂²×C₃×D₃	1	3	yes	—
576	D₈	C₂²×C₃×D₃	1	6	yes	—
577	M₁₆	—	3	3	no	—
578	M₁₆	—	3	6	no	—
579	M₁₆	C₂²×C₃×D₃	1	3	yes	—
580	C₂×C₈	—	3	3	no	—
581	C₂×C₈	—	3	1	no	—
582	C₂×C₈	—	3	3	no	—
583	C₂×C₈	—	3	3	no	—
584	C₂×C₈	—	3	3	no	—
585	C₂×C₈	C₂²×C₃×D₃	1	3	yes	—
586	C₂²×C₃	—	2	6	no	—
587	C₂²×C₃	—	2	6	no	—
588	C₂²×C₃	—	2	3	no	—
589	C₂²×C₃	—	3	1	no	—
590	C₂²×C₃	—	3	3	no	—
591	C₂²×C₃	—	4	6	no	—
592	C₂²×C₃	—	6	2	no	—
593	C₂²×C₃	—	8	6	no	—
594	C₂²×C₃	—	8	6	no	—
595	C₂²×C₃	—	12	3	no	—
596	C₂²×C₃	—	16	6	no	—
597	C₂²×C₃	—	24	6	no	—
598	C₂²×C₃	C₂×D₃×D₄	1	3	yes	—
599	C₂²×C₃	C₂²×C₃×D₄	1	3	yes	—
600	C₂×D₃	—	2	2	no	—
601	C₂×D₃	—	4	3	no	—
602	C₂×D₃	—	8	6	no	—
603	C₂×D₃	C₂²×C₃×D₄	1	3	yes	—
604	C₂×D₃	C₂²×C₃×D₄	1	1	yes	characteristic
605	C₃×C₄	—	2	2	no	—
606	C₃×C₄	—	2	2	no	—
607	C₃×C₄	—	2	3	no	—
608	C₃×C₄	—	2	1	no	—
609	C₃×C₄	—	3	1	no	—
610	C₃×C₄	—	3	3	no	—
611	C₃×C₄	—	4	2	no	—
612	C₃×C₄	—	6	6	no	—
613	C₃×C₄	C₂×D₃×D₄	1	3	yes	—
614	C₃×C₄	C₂²×C₃×D₄	1	3	yes	—
615	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
616	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
617	Dic₃	—	2	6	no	—
618	Dic₃	C₂²×C₃×D₄	1	3	yes	—
619	Dic₃	C₂²×C₃×D₄	1	1	yes	characteristic
620	C₃²	#3584	1	1	yes	characteristic, complemented, Sylow
621	C₂³	—	2	6	no	—
622	C₂³	—	3	3	no	—
623	C₂³	—	6	6	no	—
624	Q₈	—	3	3	no	—
625	Q₈	—	3	6	no	—
626	Q₈	—	6	6	no	—
627	Q₈	—	6	6	no	—
628	Q₈	C₃×D₃×D₄	1	1	yes	characteristic
629	Q₈	C₂³×C₃×D₃	1	2	yes	—
630	D₄	—	2	6	no	—
631	D₄	—	2	6	no	—
632	D₄	—	3	6	no	—
633	D₄	—	3	3	no	—
634	D₄	—	3	2	no	—
635	D₄	—	6	2	no	—
636	D₄	—	6	6	no	—
637	D₄	—	6	6	no	—
638	D₄	—	6	12	no	—
639	D₄	—	6	6	no	—
640	D₄	C₃×D₃×D₄	1	3	yes	—
641	D₄	C₂³×C₃×D₃	1	6	yes	—
642	C₂×C₄	—	2	6	no	—
643	C₂×C₄	—	3	3	no	—
644	C₂×C₄	—	3	3	no	—
645	C₂×C₄	—	3	3	no	—
646	C₂×C₄	—	3	1	no	—
647	C₂×C₄	—	3	3	no	—
648	C₂×C₄	—	6	2	no	—
649	C₂×C₄	—	6	6	no	—
650	C₂×C₄	—	6	6	no	—
651	C₂×C₄	—	6	12	no	—
652	C₂×C₄	—	6	6	no	—
653	C₂×C₄	—	6	6	no	—
654	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
655	C₈	—	3	1	no	—
656	C₈	—	3	3	no	—
657	C₈	C₂³×C₃×D₃	1	1	yes	characteristic
658	C₈	C₂³×C₃×D₃	1	3	yes	—
659	C₂×C₃	—	2	3	no	—
660	C₂×C₃	—	2	3	no	—
661	C₂×C₃	—	2	1	no	—
662	C₂×C₃	—	4	3	no	—
663	C₂×C₃	—	4	6	no	—
664	C₂×C₃	—	4	6	no	—
665	C₂×C₃	—	6	1	no	—
666	C₂×C₃	—	6	3	no	—
667	C₂×C₃	—	8	6	no	—
668	C₂×C₃	—	12	2	no	—
669	C₂×C₃	C₂²×D₃×D₄	1	1	yes	characteristic
670	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
671	D₃	—	2	1	no	—
672	D₃	—	2	3	no	—
673	D₃	—	4	2	no	—
674	C₂²	—	2	6	no	—
675	C₂²	—	3	1	no	—
676	C₂²	—	3	3	no	—
677	C₂²	—	6	2	no	—
678	C₂²	—	8	6	no	—
679	C₂²	—	12	3	no	—
680	C₂²	—	24	6	no	—
681	C₂²	C₂×C₃×D₃×D₄	1	3	yes	—
682	C₄	—	2	2	no	—
683	C₄	—	3	1	no	—
684	C₄	—	3	3	no	—
685	C₄	—	6	6	no	—
686	C₄	C₂×C₃×D₃×D₄	1	3	yes	—
687	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
688	C₃	—	2	1	no	—
689	C₃	#87203	1	1	yes	characteristic, direct product factor
690	C₃	C₃×#3584	1	1	yes	characteristic, complemented
691	C₂	—	2	3	no	—
692	C₂	—	4	6	no	—
693	C₂	—	6	1	no	—
694	C₂	—	6	3	no	—
695	C₂	—	12	2	no	—
696	C₂	C₂²×C₃×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁵×C₃
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₃²×#576	C₂
socle	C₂×C₃²	C₂³×D₄
hypercenter	C₃×#576	D₃
hypocenter	C₃	C₃×#3584
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41 ◁ C₃×#576

Complements

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

N	H ≅ G/N	type
1. C₃×#5966	C₂	semidirect
2. C₃²×#576	C₂	semidirect
3. C₃×#5836	C₂	semidirect
4. C₃×#5775	C₂	semidirect
5. C₃×#5773	C₂	semidirect
6. C₃×#5771	C₂	semidirect
7. C₃×D₃×#135	C₂	semidirect
8. C₃×#5757	C₂	semidirect
9. C₂×C₃×#912	C₂	semidirect
10. C₃×#5753	C₂	semidirect
11. C₃×D₃×#131	C₂	semidirect
13. #87203	C₃	direct (N × H)
14. C₃²×H(5,𝔽₂)	C₂²	semidirect
16. C₃×#1010	C₂²	semidirect
17. C₃×#1010	C₂²	semidirect
20. C₃×D₃×#41	C₂²	semidirect
22. C₃×#1004	C₂²	semidirect
24. C₂×C₃×#237	C₂²	semidirect
25. C₃²×AGL(1,ℤ/8)	C₂²	semidirect
26. C₃²×#135	C₂²	semidirect
27. C₂×C₃²×D₈	C₂²	semidirect
28. C₃²×#131	C₂²	semidirect
29. C₃×#951	C₂²	semidirect
30. C₃×#950	C₂²	semidirect
31. C₃×#948	C₂²	semidirect
32. C₂×C₃×#214	C₂²	semidirect
33. C₃×#932	C₂²	semidirect
34. C₃×#919	C₂²	semidirect
35. C₃×D₃×Q₁₆	C₂²	semidirect
36. C₃×#916	C₂²	semidirect
37. C₃×#915	C₂²	semidirect
38. C₃×D₃×SD₁₆	C₂²	semidirect
39. C₃×#912	C₂²	semidirect
40. C₃×#912	C₂²	semidirect
41. C₃×#912	C₂²	semidirect
42. C₃×#912	C₂²	semidirect
43. C₃×#911	C₂²	semidirect
44. C₃×D₃×D₈	C₂²	semidirect
45. C₃×#909	C₂²	semidirect
46. C₃×#907	C₂²	semidirect
47. C₃×D₃×M₁₆	C₂²	semidirect
48. C₂×C₃×Dic₁₂	C₂²	semidirect
49. C₃×#904	C₂²	semidirect
50. C₃×#901	C₂²	semidirect
51. C₂×C₃×D₃×C₈	C₂²	semidirect
53. #5966	C₂×C₃	semidirect
60. C₃×#576	D₃	semidirect
61. C₃×#576	C₂×C₃	semidirect
66. #5836	C₂×C₃	semidirect
67. #5775	C₂×C₃	semidirect
68. #5773	C₂×C₃	semidirect
69. #5771	C₂×C₃	semidirect
70. D₃×#135	C₂×C₃	semidirect
71. #5757	C₂×C₃	semidirect
72. C₂×#912	C₂×C₃	semidirect
73. #5753	C₂×C₃	semidirect
74. D₃×#131	C₂×C₃	semidirect
138. C₃×H(5,𝔽₂)	C₂×D₃	semidirect
139. C₃×H(5,𝔽₂)	C₂²×C₃	semidirect
146. #1010	C₂²×C₃	semidirect
147. #1010	C₂²×C₃	semidirect
150. D₃×#41	C₂²×C₃	semidirect
152. #1004	C₂²×C₃	semidirect
154. C₂×#237	C₂²×C₃	semidirect
161. C₃×AGL(1,ℤ/8)	C₂×D₃	semidirect
162. C₃×AGL(1,ℤ/8)	C₂²×C₃	semidirect
172. C₃×#135	C₂×D₃	semidirect
173. C₃×#135	C₂²×C₃	semidirect
180. C₂×C₃×D₈	C₂×D₃	semidirect
181. C₂×C₃×D₈	C₂²×C₃	semidirect
186. C₃×#131	C₂×D₃	semidirect
187. C₃×#131	C₂²×C₃	semidirect
190. #951	C₂²×C₃	semidirect
191. #950	C₂²×C₃	semidirect
192. #948	C₂²×C₃	semidirect
193. C₂×#214	C₂²×C₃	semidirect
194. #932	C₂²×C₃	semidirect
195. #919	C₂²×C₃	semidirect
196. D₃×Q₁₆	C₂²×C₃	semidirect
197. #916	C₂²×C₃	semidirect
198. #915	C₂²×C₃	semidirect
199. D₃×SD₁₆	C₂²×C₃	semidirect
200. #912	C₂²×C₃	semidirect
201. #912	C₂²×C₃	semidirect
202. #912	C₂²×C₃	semidirect
203. #912	C₂²×C₃	semidirect
204. #911	C₂²×C₃	semidirect
205. D₃×D₈	C₂²×C₃	semidirect
206. #909	C₂²×C₃	semidirect
207. #907	C₂²×C₃	semidirect
208. D₃×M₁₆	C₂²×C₃	semidirect
209. C₂×Dic₁₂	C₂²×C₃	semidirect
210. #904	C₂²×C₃	semidirect
211. #901	C₂²×C₃	semidirect
212. C₂×D₃×C₈	C₂²×C₃	semidirect
257. #576	C₃×D₃	semidirect
404. H(5,𝔽₂)	C₂×C₃×D₃	semidirect
415. AGL(1,ℤ/8)	C₂×C₃×D₃	semidirect
424. #135	C₂×C₃×D₃	semidirect
430. C₂×D₈	C₂×C₃×D₃	semidirect
434. #131	C₂×C₃×D₃	semidirect
620. C₃²	#3584	semidirect
689. C₃	#87203	direct (N × H)
690. C₃	C₃×#3584	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5966	2
C₃²×#576	2
C₃×#5836	2
C₃×#5775	2
C₃×#5773	2
C₃×#5771	2
C₃×D₃×#135	2
C₃×#5757	2
C₂×C₃×#912	2
C₃×#5753	2
C₃×D₃×#131	2
C₃×#3584	3
#87203	3

Subgroups — C3×#87203 #11918955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#87203 #11918955