Subgroups — C₃²×#5762 #13179139

Order 1728.

1820 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#1007	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#1004	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃³×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#942	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×#932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#916	C₂	1	2	yes	maximal, complemented
7	C₃²×#915	C₂	1	2	yes	maximal, complemented
8	C₃²×#914	C₂	1	2	yes	maximal, complemented
9	C₃²×D₃×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₃²×#904	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×#901	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#577	—	3	1	no	maximal
13	C₃×#5762	C₃	1	4	yes	maximal, direct product factor
14	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃²×#67	—	2	2	no	—
17	C₃²×#239	—	2	1	no	—
18	C₃²×#239	C₂²	1	2	yes	complemented
19	C₃²×D₃×Q₈	—	2	1	no	—
20	C₃²×D₃×Q₈	C₂²	1	2	yes	complemented
21	C₃²×#237	—	2	1	no	—
22	C₃²×#237	C₂²	1	2	yes	—
23	C₃²×D₃×D₄	—	2	1	no	—
24	C₃²×D₃×D₄	C₂²	1	2	yes	—
25	C₃²×#235	—	2	2	no	—
26	C₃²×#235	C₂²	1	1	yes	characteristic
27	C₃²×#235	C₂²	1	1	yes	characteristic
28	C₃²×#235	C₂²	1	1	yes	characteristic, complemented
29	C₃³×SD₁₆	C₂²	1	2	yes	complemented
30	C₃³×SD₁₆	C₂²	1	2	yes	complemented
31	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#216	C₂²	1	2	yes	complemented
33	C₃²×#215	C₂²	1	2	yes	complemented
34	C₃²×#214	C₂²	1	2	yes	complemented
35	C₃²×#213	C₂²	1	2	yes	complemented
36	C₃²×#208	C₂²	1	1	yes	characteristic, complemented
37	C₃²×Dic₁₂	C₂²	1	1	yes	characteristic, complemented
38	C₃²×D₂₄	C₂²	1	1	yes	characteristic, complemented
39	C₃²×#204	C₂²	1	1	yes	characteristic, complemented
40	C₃²×#204	C₂²	1	1	yes	characteristic, complemented
41	C₃²×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
42	C₃²×D₃×C₈	C₂²	1	2	yes	complemented
43	C₃²×2₋¹⁺⁴	—	3	1	no	—
44	C₃²×H(5,𝔽₂)	—	3	1	no	—
45	C₃×#1007	C₂×C₃	1	4	yes	complemented
46	C₃×#1004	C₂×C₃	1	4	yes	complemented
47	C₃²×#137	—	3	1	no	—
48	C₃²×#137	—	3	2	no	—
49	C₃²×AGL(1,ℤ/8)	—	3	1	no	—
50	C₃²×AGL(1,ℤ/8)	—	3	2	no	—
51	C₃²×#135	—	3	2	no	—
52	C₃²×#135	—	3	1	no	—
53	C₂×C₃²×SD₁₆	—	2	4	no	—
54	C₂×C₃²×SD₁₆	—	3	2	no	—
55	C₂×C₃²×SD₁₆	D₃	1	1	yes	characteristic, complemented
56	C₂×C₃²×SD₁₆	C₂×C₃	1	4	yes	complemented
57	C₃²×#131	—	3	1	no	—
58	C₃×#942	C₂×C₃	1	4	yes	complemented
59	C₃×#932	C₂×C₃	1	4	yes	complemented
60	C₃×#916	C₂×C₃	1	8	yes	complemented
61	C₃×#915	C₂×C₃	1	8	yes	complemented
62	C₃×#914	C₂×C₃	1	8	yes	complemented
63	C₃×D₃×SD₁₆	C₂×C₃	1	8	yes	complemented
64	C₃×#904	C₂×C₃	1	4	yes	complemented
65	C₃×#901	C₂×C₃	1	4	yes	complemented
66	C₂³×C₃³	—	2	1	no	—
67	C₂²×C₃²×D₃	—	2	2	no	—
68	C₃³×Q₈	—	2	1	no	—
69	C₃³×Q₈	C₂³	1	2	yes	—
70	C₃³×D₄	—	2	1	no	—
71	C₃³×D₄	C₂³	1	2	yes	—
72	C₂×C₃³×C₄	—	2	1	no	—
73	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
74	C₃²×#67	—	2	1	no	—
75	C₃²×#67	—	2	1	no	—
76	C₃²×#67	—	2	2	no	—
77	C₃²×#67	—	2	2	no	—
78	C₃²×#67	D₄	1	2	yes	—
79	C₂×C₃²×Dic₃	—	2	2	no	—
80	C₃²×D₁₂	—	2	2	no	—
81	C₃²×D₁₂	D₄	1	1	yes	characteristic
82	C₃²×D₁₂	C₂³	1	1	yes	characteristic
83	C₃²×D₁₂	C₂³	1	1	yes	characteristic
84	C₃²×C₄×D₃	—	2	2	no	—
85	C₃²×C₄×D₃	—	2	1	no	—
86	C₃²×C₄×D₃	—	2	1	no	—
87	C₃²×C₄×D₃	—	2	2	no	—
88	C₃²×C₄×D₃	C₂³	1	2	yes	—
89	C₃²×Dic₆	—	2	2	no	—
90	C₃²×Dic₆	D₄	1	1	yes	characteristic
91	C₃²×Dic₆	C₂³	1	1	yes	characteristic
92	C₃²×Dic₆	C₂³	1	1	yes	characteristic
93	C₃³×C₈	C₂³	1	1	yes	characteristic
94	C₃³×C₈	C₂³	1	1	yes	characteristic
95	C₃²×C₃⋊C₈	C₂³	1	2	yes	—
96	C₃×#577	—	3	4	no	—
97	#5762	C₃²	1	1	yes	characteristic, direct product factor
98	C₃²×#41	—	3	1	no	—
99	C₃²×#41	—	3	2	no	—
100	C₃²×#41	—	3	2	no	—
101	C₃²×#41	—	3	1	no	—
102	C₃²×#41	—	3	1	no	—
103	C₃²×#41	—	6	2	no	—
104	C₃²×#41	—	6	1	no	—
105	C₃²×#41	—	6	1	no	—
106	C₂×C₃²×Q₈	—	2	4	no	—
107	C₂×C₃²×Q₈	—	3	2	no	—
108	C₂×C₃²×Q₈	—	6	1	no	—
109	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
110	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
111	C₂×C₃²×D₄	—	2	4	no	—
112	C₂×C₃²×D₄	—	3	2	no	—
113	C₂×C₃²×D₄	—	6	1	no	—
114	C₂×C₃²×D₄	—	6	2	no	—
115	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
116	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
117	C₂×C₃×#67	—	2	8	no	—
118	C₃×#239	—	2	4	no	—
119	C₃×#239	C₂²×C₃	1	8	yes	complemented
120	C₃×D₃×Q₈	—	2	4	no	—
121	C₃×D₃×Q₈	C₂²×C₃	1	8	yes	complemented
122	C₃×#237	—	2	4	no	—
123	C₃×#237	C₂²×C₃	1	8	yes	—
124	C₃×D₃×D₄	—	2	4	no	—
125	C₃×D₃×D₄	C₂²×C₃	1	8	yes	—
126	C₃×#235	—	2	8	no	—
127	C₃×#235	C₂²×C₃	1	4	yes	—
128	C₃×#235	C₂²×C₃	1	4	yes	—
129	C₃×#235	C₂²×C₃	1	4	yes	complemented
130	C₃²×Q₁₆	—	3	2	no	—
131	C₃²×Q₁₆	—	3	1	no	—
132	C₃²×SD₁₆	—	2	8	no	—
133	C₃²×SD₁₆	—	2	8	no	—
134	C₃²×SD₁₆	—	3	2	no	—
135	C₃²×SD₁₆	—	3	2	no	—
136	C₃²×SD₁₆	—	3	1	no	—
137	C₃²×SD₁₆	—	3	1	no	—
138	C₃²×SD₁₆	C₂×D₃	1	2	yes	complemented
139	C₃²×SD₁₆	C₂×D₃	1	2	yes	complemented
140	C₃²×SD₁₆	C₂²×C₃	1	8	yes	complemented
141	C₃²×SD₁₆	C₂²×C₃	1	8	yes	complemented
142	C₃²×D₈	—	3	2	no	—
143	C₃²×D₈	—	3	1	no	—
144	C₃²×M₁₆	—	3	1	no	—
145	C₃²×M₁₆	—	3	2	no	—
146	C₂×C₃²×C₈	—	2	4	no	—
147	C₂×C₃²×C₈	—	3	2	no	—
148	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic, complemented
149	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	complemented
150	C₃×#216	C₂²×C₃	1	8	yes	complemented
151	C₃×#215	C₂²×C₃	1	8	yes	complemented
152	C₃×#214	C₂²×C₃	1	8	yes	complemented
153	C₃×#213	C₂²×C₃	1	8	yes	complemented
154	C₃×#208	C₂²×C₃	1	4	yes	complemented
155	C₃×Dic₁₂	C₂²×C₃	1	4	yes	complemented
156	C₃×D₂₄	C₂²×C₃	1	4	yes	complemented
157	C₃×#204	C₂²×C₃	1	4	yes	complemented
158	C₃×#204	C₂²×C₃	1	4	yes	complemented
159	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	8	yes	complemented
160	C₃×D₃×C₈	C₂²×C₃	1	8	yes	complemented
161	C₂²×C₃³	—	2	2	no	—
162	C₂²×C₃³	—	8	1	no	—
163	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃²×D₃	—	2	1	no	—
165	C₂×C₃²×D₃	—	2	1	no	—
166	C₂×C₃²×D₃	—	8	2	no	—
167	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
168	C₃³×C₄	—	2	2	no	—
169	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
170	C₃³×C₄	C₂⁴	1	1	yes	characteristic
171	C₃²×Dic₃	—	2	1	no	—
172	C₃²×Dic₃	—	2	1	no	—
173	C₃²×Dic₃	C₂×D₄	1	2	yes	—
174	C₃×2₋¹⁺⁴	—	3	4	no	—
175	C₃×H(5,𝔽₂)	—	3	4	no	—
176	#1007	C₂×C₃²	1	1	yes	characteristic, complemented
177	#1004	C₂×C₃²	1	1	yes	characteristic, complemented
178	C₃×#137	—	3	4	no	—
179	C₃×#137	—	3	8	no	—
180	C₃×AGL(1,ℤ/8)	—	3	4	no	—
181	C₃×AGL(1,ℤ/8)	—	3	8	no	—
182	C₃×#135	—	3	8	no	—
183	C₃×#135	—	3	4	no	—
184	C₂×C₃×SD₁₆	—	2	4	no	—
185	C₂×C₃×SD₁₆	—	3	8	no	—
186	C₂×C₃×SD₁₆	C₃×D₃	1	4	yes	complemented
187	C₂×C₃×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
188	C₃×#131	—	3	4	no	—
189	#942	C₂×C₃²	1	1	yes	characteristic, complemented
190	#932	C₂×C₃²	1	1	yes	characteristic, complemented
191	#916	C₂×C₃²	1	2	yes	complemented
192	#915	C₂×C₃²	1	2	yes	complemented
193	#914	C₂×C₃²	1	2	yes	complemented
194	D₃×SD₁₆	C₂×C₃²	1	2	yes	complemented
195	#904	C₂×C₃²	1	1	yes	characteristic, complemented
196	#901	C₂×C₃²	1	1	yes	characteristic, complemented
197	C₂³×C₃²	—	2	1	no	—
198	C₂³×C₃²	—	2	4	no	—
199	C₂³×C₃²	—	4	4	no	—
200	C₂³×C₃²	—	6	2	no	—
201	C₂²×C₃×D₃	—	2	8	no	—
202	C₃²×Q₈	—	2	1	no	—
203	C₃²×Q₈	—	2	8	no	—
204	C₃²×Q₈	—	2	4	no	—
205	C₃²×Q₈	—	3	1	no	—
206	C₃²×Q₈	—	3	1	no	—
207	C₃²×Q₈	—	3	1	no	—
208	C₃²×Q₈	—	4	4	no	—
209	C₃²×Q₈	—	6	2	no	—
210	C₃²×Q₈	C₂²×D₃	1	2	yes	—
211	C₃²×Q₈	C₂³×C₃	1	8	yes	—
212	C₃²×D₄	—	2	1	no	—
213	C₃²×D₄	—	2	8	no	—
214	C₃²×D₄	—	2	4	no	—
215	C₃²×D₄	—	3	2	no	—
216	C₃²×D₄	—	3	1	no	—
217	C₃²×D₄	—	3	1	no	—
218	C₃²×D₄	—	3	1	no	—
219	C₃²×D₄	—	4	4	no	—
220	C₃²×D₄	—	6	2	no	—
221	C₃²×D₄	—	6	2	no	—
222	C₃²×D₄	—	6	2	no	—
223	C₃²×D₄	—	6	1	no	—
224	C₃²×D₄	—	6	1	no	—
225	C₃²×D₄	C₂²×D₃	1	2	yes	—
226	C₃²×D₄	C₂³×C₃	1	8	yes	—
227	C₂×C₃²×C₄	—	2	1	no	—
228	C₂×C₃²×C₄	—	2	4	no	—
229	C₂×C₃²×C₄	—	2	4	no	—
230	C₂×C₃²×C₄	—	3	2	no	—
231	C₂×C₃²×C₄	—	4	4	no	—
232	C₂×C₃²×C₄	—	6	2	no	—
233	C₂×C₃²×C₄	—	6	2	no	—
234	C₂×C₃²×C₄	—	6	2	no	—
235	C₂×C₃²×C₄	—	6	1	no	—
236	C₂×C₃²×C₄	—	6	1	no	—
237	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
239	C₃×#67	—	2	4	no	—
240	C₃×#67	—	2	4	no	—
241	C₃×#67	—	2	8	no	—
242	C₃×#67	—	2	8	no	—
243	C₃×#67	C₃×D₄	1	8	yes	—
244	C₂×C₃×Dic₃	—	2	8	no	—
245	C₃×D₁₂	—	2	8	no	—
246	C₃×D₁₂	C₃×D₄	1	4	yes	—
247	C₃×D₁₂	C₂³×C₃	1	4	yes	—
248	C₃×D₁₂	C₂³×C₃	1	4	yes	—
249	C₃×C₄×D₃	—	2	8	no	—
250	C₃×C₄×D₃	—	2	4	no	—
251	C₃×C₄×D₃	—	2	4	no	—
252	C₃×C₄×D₃	—	2	8	no	—
253	C₃×C₄×D₃	C₂³×C₃	1	8	yes	—
254	C₃×Dic₆	—	2	8	no	—
255	C₃×Dic₆	C₃×D₄	1	4	yes	—
256	C₃×Dic₆	C₂³×C₃	1	4	yes	—
257	C₃×Dic₆	C₂³×C₃	1	4	yes	—
258	C₃²×C₈	—	2	4	no	—
259	C₃²×C₈	—	2	4	no	—
260	C₃²×C₈	—	3	2	no	—
261	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
262	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
263	C₃²×C₈	C₂³×C₃	1	4	yes	—
264	C₃²×C₈	C₂³×C₃	1	4	yes	—
265	C₃×C₃⋊C₈	C₂³×C₃	1	8	yes	—
266	#577	—	3	1	no	Sylow
267	C₂×C₃³	—	2	1	no	—
268	C₂×C₃³	—	4	2	no	—
269	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
270	C₃²×D₃	—	2	2	no	—
271	C₃²×D₃	—	4	1	no	—
272	C₃²×D₃	—	4	1	no	—
273	C₃×#41	—	3	4	no	—
274	C₃×#41	—	3	8	no	—
275	C₃×#41	—	3	8	no	—
276	C₃×#41	—	3	4	no	—
277	C₃×#41	—	3	4	no	—
278	C₃×#41	—	6	8	no	—
279	C₃×#41	—	6	4	no	—
280	C₃×#41	—	6	4	no	—
281	C₂×C₃×Q₈	—	2	4	no	—
282	C₂×C₃×Q₈	—	3	8	no	—
283	C₂×C₃×Q₈	—	6	4	no	—
284	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
285	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
286	C₂×C₃×D₄	—	2	4	no	—
287	C₂×C₃×D₄	—	3	8	no	—
288	C₂×C₃×D₄	—	6	4	no	—
289	C₂×C₃×D₄	—	6	8	no	—
290	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
291	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
292	C₂×#67	—	2	2	no	—
293	#239	—	2	1	no	—
294	#239	C₂²×C₃²	1	2	yes	complemented
295	D₃×Q₈	—	2	1	no	—
296	D₃×Q₈	C₂²×C₃²	1	2	yes	complemented
297	#237	—	2	1	no	—
298	#237	C₂²×C₃²	1	2	yes	—
299	D₃×D₄	—	2	1	no	—
300	D₃×D₄	C₂²×C₃²	1	2	yes	—
301	#235	—	2	2	no	—
302	#235	C₂²×C₃²	1	1	yes	characteristic
303	#235	C₂²×C₃²	1	1	yes	characteristic
304	#235	C₂²×C₃²	1	1	yes	characteristic, complemented
305	C₃×Q₁₆	—	3	8	no	—
306	C₃×Q₁₆	—	3	4	no	—
307	C₃×SD₁₆	—	2	8	no	—
308	C₃×SD₁₆	—	2	8	no	—
309	C₃×SD₁₆	—	3	8	no	—
310	C₃×SD₁₆	—	3	8	no	—
311	C₃×SD₁₆	—	3	4	no	—
312	C₃×SD₁₆	—	3	4	no	—
313	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	complemented
314	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	complemented
315	C₃×SD₁₆	C₂²×C₃²	1	2	yes	complemented
316	C₃×SD₁₆	C₂²×C₃²	1	2	yes	complemented
317	C₃×D₈	—	3	8	no	—
318	C₃×D₈	—	3	4	no	—
319	C₃×M₁₆	—	3	4	no	—
320	C₃×M₁₆	—	3	8	no	—
321	C₂×C₃×C₈	—	2	4	no	—
322	C₂×C₃×C₈	—	3	8	no	—
323	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
324	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
325	#216	C₂²×C₃²	1	2	yes	complemented
326	#215	C₂²×C₃²	1	2	yes	complemented
327	#214	C₂²×C₃²	1	2	yes	complemented
328	#213	C₂²×C₃²	1	2	yes	complemented
329	#208	C₂²×C₃²	1	1	yes	characteristic, complemented
330	Dic₁₂	C₂²×C₃²	1	1	yes	characteristic, complemented
331	D₂₄	C₂²×C₃²	1	1	yes	characteristic, complemented
332	#204	C₂²×C₃²	1	1	yes	characteristic, complemented
333	#204	C₂²×C₃²	1	1	yes	characteristic, complemented
334	ΓL(1,𝔽₂₅)	C₂²×C₃²	1	2	yes	complemented
335	D₃×C₈	C₂²×C₃²	1	2	yes	complemented
336	C₂²×C₃²	—	2	2	no	—
337	C₂²×C₃²	—	2	4	no	—
338	C₂²×C₃²	—	2	8	no	—
339	C₂²×C₃²	—	3	2	no	—
340	C₂²×C₃²	—	4	8	no	—
341	C₂²×C₃²	—	6	1	no	—
342	C₂²×C₃²	—	6	1	no	—
343	C₂²×C₃²	—	8	1	no	—
344	C₂²×C₃²	—	8	4	no	—
345	C₂²×C₃²	—	8	8	no	—
346	C₂²×C₃²	—	24	2	no	—
347	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
348	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
349	C₂×C₃×D₃	—	2	4	no	—
350	C₂×C₃×D₃	—	2	4	no	—
351	C₂×C₃×D₃	—	8	8	no	—
352	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
353	C₃²×C₄	—	2	2	no	—
354	C₃²×C₄	—	2	4	no	—
355	C₃²×C₄	—	2	4	no	—
356	C₃²×C₄	—	2	8	no	—
357	C₃²×C₄	—	3	2	no	—
358	C₃²×C₄	—	4	8	no	—
359	C₃²×C₄	—	6	1	no	—
360	C₃²×C₄	—	6	1	no	—
361	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
362	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
363	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
364	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
365	C₃×Dic₃	—	2	4	no	—
366	C₃×Dic₃	—	2	4	no	—
367	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
368	2₋¹⁺⁴	—	3	1	no	—
369	H(5,𝔽₂)	—	3	1	no	—
370	#137	—	3	1	no	—
371	#137	—	3	2	no	—
372	AGL(1,ℤ/8)	—	3	1	no	—
373	AGL(1,ℤ/8)	—	3	2	no	—
374	#135	—	3	2	no	—
375	#135	—	3	1	no	—
376	C₂×SD₁₆	—	3	2	no	—
377	C₂×SD₁₆	C₃²×D₃	1	1	yes	characteristic, complemented
378	#131	—	3	1	no	—
379	C₃³	#577	1	1	yes	characteristic, complemented, Sylow
380	C₂³×C₃	—	2	4	no	—
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	4	4	no	—
383	C₂³×C₃	—	6	8	no	—
384	C₂²×D₃	—	2	2	no	—
385	C₃×Q₈	—	2	4	no	—
386	C₃×Q₈	—	2	1	no	—
387	C₃×Q₈	—	2	8	no	—
388	C₃×Q₈	—	3	4	no	—
389	C₃×Q₈	—	3	4	no	—
390	C₃×Q₈	—	3	4	no	—
391	C₃×Q₈	—	4	4	no	—
392	C₃×Q₈	—	6	8	no	—
393	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
394	C₃×Q₈	C₂³×C₃²	1	2	yes	—
395	C₃×D₄	—	2	4	no	—
396	C₃×D₄	—	2	1	no	—
397	C₃×D₄	—	2	8	no	—
398	C₃×D₄	—	3	8	no	—
399	C₃×D₄	—	3	4	no	—
400	C₃×D₄	—	3	4	no	—
401	C₃×D₄	—	3	4	no	—
402	C₃×D₄	—	4	4	no	—
403	C₃×D₄	—	6	8	no	—
404	C₃×D₄	—	6	8	no	—
405	C₃×D₄	—	6	8	no	—
406	C₃×D₄	—	6	4	no	—
407	C₃×D₄	—	6	4	no	—
408	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
409	C₃×D₄	C₂³×C₃²	1	2	yes	—
410	C₂×C₃×C₄	—	2	4	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	3	8	no	—
414	C₂×C₃×C₄	—	4	4	no	—
415	C₂×C₃×C₄	—	6	8	no	—
416	C₂×C₃×C₄	—	6	8	no	—
417	C₂×C₃×C₄	—	6	8	no	—
418	C₂×C₃×C₄	—	6	4	no	—
419	C₂×C₃×C₄	—	6	4	no	—
420	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
421	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
422	#67	—	2	1	no	—
423	#67	—	2	1	no	—
424	#67	—	2	2	no	—
425	#67	—	2	2	no	—
426	#67	C₃²×D₄	1	2	yes	—
427	C₂×Dic₃	—	2	2	no	—
428	D₁₂	—	2	2	no	—
429	D₁₂	C₃²×D₄	1	1	yes	characteristic
430	D₁₂	C₂³×C₃²	1	1	yes	characteristic
431	D₁₂	C₂³×C₃²	1	1	yes	characteristic
432	C₄×D₃	—	2	2	no	—
433	C₄×D₃	—	2	1	no	—
434	C₄×D₃	—	2	1	no	—
435	C₄×D₃	—	2	2	no	—
436	C₄×D₃	C₂³×C₃²	1	2	yes	—
437	Dic₆	—	2	2	no	—
438	Dic₆	C₃²×D₄	1	1	yes	characteristic
439	Dic₆	C₂³×C₃²	1	1	yes	characteristic
440	Dic₆	C₂³×C₃²	1	1	yes	characteristic
441	C₃×C₈	—	2	4	no	—
442	C₃×C₈	—	2	4	no	—
443	C₃×C₈	—	3	8	no	—
444	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
445	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
446	C₃×C₈	C₂³×C₃²	1	1	yes	characteristic
447	C₃×C₈	C₂³×C₃²	1	1	yes	characteristic
448	C₃⋊C₈	C₂³×C₃²	1	2	yes	—
449	C₂×C₃²	—	2	8	no	—
450	C₂×C₃²	—	2	4	no	—
451	C₂×C₃²	—	2	1	no	—
452	C₂×C₃²	—	2	4	no	—
453	C₂×C₃²	—	4	2	no	—
454	C₂×C₃²	—	4	8	no	—
455	C₂×C₃²	—	6	2	no	—
456	C₂×C₃²	—	8	8	no	—
457	C₂×C₃²	—	12	1	no	—
458	C₂×C₃²	—	12	1	no	—
459	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
460	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
461	C₃×D₃	—	2	8	no	—
462	C₃×D₃	—	4	4	no	—
463	C₃×D₃	—	4	4	no	—
464	#41	—	3	1	no	—
465	#41	—	3	2	no	—
466	#41	—	3	2	no	—
467	#41	—	3	1	no	—
468	#41	—	3	1	no	—
469	#41	—	6	2	no	—
470	#41	—	6	1	no	—
471	#41	—	6	1	no	—
472	C₂×Q₈	—	3	2	no	—
473	C₂×Q₈	—	6	1	no	—
474	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
475	C₂×D₄	—	3	2	no	—
476	C₂×D₄	—	6	1	no	—
477	C₂×D₄	—	6	2	no	—
478	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
479	Q₁₆	—	3	2	no	—
480	Q₁₆	—	3	1	no	—
481	SD₁₆	—	3	2	no	—
482	SD₁₆	—	3	2	no	—
483	SD₁₆	—	3	1	no	—
484	SD₁₆	—	3	1	no	—
485	SD₁₆	C₂×C₃²×D₃	1	2	yes	complemented
486	SD₁₆	C₂×C₃²×D₃	1	2	yes	complemented
487	D₈	—	3	2	no	—
488	D₈	—	3	1	no	—
489	M₁₆	—	3	1	no	—
490	M₁₆	—	3	2	no	—
491	C₂×C₈	—	3	2	no	—
492	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
493	C₂²×C₃	—	2	8	no	—
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	4	no	—
496	C₂²×C₃	—	3	8	no	—
497	C₂²×C₃	—	4	8	no	—
498	C₂²×C₃	—	6	4	no	—
499	C₂²×C₃	—	6	4	no	—
500	C₂²×C₃	—	8	4	no	—
501	C₂²×C₃	—	8	1	no	—
502	C₂²×C₃	—	8	8	no	—
503	C₂²×C₃	—	24	8	no	—
504	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
505	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
506	C₂×D₃	—	2	1	no	—
507	C₂×D₃	—	2	1	no	—
508	C₂×D₃	—	8	2	no	—
509	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
510	C₃×C₄	—	2	8	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	4	no	—
513	C₃×C₄	—	2	4	no	—
514	C₃×C₄	—	3	8	no	—
515	C₃×C₄	—	4	8	no	—
516	C₃×C₄	—	6	4	no	—
517	C₃×C₄	—	6	4	no	—
518	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
519	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
520	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
521	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
522	Dic₃	—	2	1	no	—
523	Dic₃	—	2	1	no	—
524	Dic₃	C₂×C₃²×D₄	1	2	yes	—
525	C₃²	—	2	4	no	—
526	C₃²	#5762	1	1	yes	characteristic, direct product factor
527	C₃²	C₃×#577	1	4	yes	complemented
528	C₂³	—	2	1	no	—
529	C₂³	—	6	2	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	3	1	no	—
532	Q₈	—	3	1	no	—
533	Q₈	—	3	1	no	—
534	Q₈	—	6	2	no	—
535	Q₈	C₂²×C₃²×D₃	1	2	yes	—
536	D₄	—	2	1	no	—
537	D₄	—	3	2	no	—
538	D₄	—	3	1	no	—
539	D₄	—	3	1	no	—
540	D₄	—	3	1	no	—
541	D₄	—	6	2	no	—
542	D₄	—	6	2	no	—
543	D₄	—	6	2	no	—
544	D₄	—	6	1	no	—
545	D₄	—	6	1	no	—
546	D₄	C₂²×C₃²×D₃	1	2	yes	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	3	2	no	—
549	C₂×C₄	—	6	2	no	—
550	C₂×C₄	—	6	2	no	—
551	C₂×C₄	—	6	2	no	—
552	C₂×C₄	—	6	1	no	—
553	C₂×C₄	—	6	1	no	—
554	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
555	C₈	—	3	2	no	—
556	C₈	C₂²×C₃²×D₃	1	1	yes	characteristic
557	C₈	C₂²×C₃²×D₃	1	1	yes	characteristic
558	C₂×C₃	—	2	8	no	—
559	C₂×C₃	—	2	4	no	—
560	C₂×C₃	—	2	1	no	—
561	C₂×C₃	—	2	4	no	—
562	C₂×C₃	—	4	8	no	—
563	C₂×C₃	—	4	2	no	—
564	C₂×C₃	—	6	8	no	—
565	C₂×C₃	—	8	8	no	—
566	C₂×C₃	—	12	4	no	—
567	C₂×C₃	—	12	4	no	—
568	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
569	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
570	D₃	—	2	2	no	—
571	D₃	—	4	1	no	—
572	D₃	—	4	1	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	3	2	no	—
575	C₂²	—	6	1	no	—
576	C₂²	—	6	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	24	2	no	—
579	C₂²	C₃²×D₃×D₄	1	1	yes	characteristic
580	C₄	—	2	2	no	—
581	C₄	—	3	2	no	—
582	C₄	—	6	1	no	—
583	C₄	—	6	1	no	—
584	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
585	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
586	C₃	—	2	4	no	—
587	C₃	C₃×#5762	1	4	yes	direct product factor
588	C₃	C₃²×#577	1	1	yes	characteristic, complemented
589	C₂	—	2	1	no	—
590	C₂	—	4	2	no	—
591	C₂	—	6	2	no	—
592	C₂	—	12	1	no	—
593	C₂	—	12	1	no	—
594	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	C₂×D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×SD₁₆	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₂×C₃²×SD₁₆	D₃
hypocenter	C₃	C₃²×#577
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₃²×#1007	C₂	semidirect
2. C₃²×#1004	C₂	semidirect
3. C₂×C₃³×SD₁₆	C₂	semidirect
4. C₃²×#942	C₂	semidirect
5. C₃²×#932	C₂	semidirect
6. C₃²×#916	C₂	semidirect
7. C₃²×#915	C₂	semidirect
8. C₃²×#914	C₂	semidirect
9. C₃²×D₃×SD₁₆	C₂	semidirect
10. C₃²×#904	C₂	semidirect
11. C₃²×#901	C₂	semidirect
13. C₃×#5762	C₃	direct (N × H)
14. C₂×C₃³×Q₈	C₂²	semidirect
18. C₃²×#239	C₂²	semidirect
20. C₃²×D₃×Q₈	C₂²	semidirect
28. C₃²×#235	C₂²	semidirect
29. C₃³×SD₁₆	C₂²	semidirect
30. C₃³×SD₁₆	C₂²	semidirect
31. C₂×C₃³×C₈	C₂²	semidirect
32. C₃²×#216	C₂²	semidirect
33. C₃²×#215	C₂²	semidirect
34. C₃²×#214	C₂²	semidirect
35. C₃²×#213	C₂²	semidirect
36. C₃²×#208	C₂²	semidirect
37. C₃²×Dic₁₂	C₂²	semidirect
38. C₃²×D₂₄	C₂²	semidirect
39. C₃²×#204	C₂²	semidirect
40. C₃²×#204	C₂²	semidirect
41. C₃²×ΓL(1,𝔽₂₅)	C₂²	semidirect
42. C₃²×D₃×C₈	C₂²	semidirect
45. C₃×#1007	C₂×C₃	semidirect
46. C₃×#1004	C₂×C₃	semidirect
55. C₂×C₃²×SD₁₆	D₃	semidirect
56. C₂×C₃²×SD₁₆	C₂×C₃	semidirect
58. C₃×#942	C₂×C₃	semidirect
59. C₃×#932	C₂×C₃	semidirect
60. C₃×#916	C₂×C₃	semidirect
61. C₃×#915	C₂×C₃	semidirect
62. C₃×#914	C₂×C₃	semidirect
63. C₃×D₃×SD₁₆	C₂×C₃	semidirect
64. C₃×#904	C₂×C₃	semidirect
65. C₃×#901	C₂×C₃	semidirect
97. #5762	C₃²	direct (N × H)
109. C₂×C₃²×Q₈	C₂×D₃	semidirect
110. C₂×C₃²×Q₈	C₂²×C₃	semidirect
119. C₃×#239	C₂²×C₃	semidirect
121. C₃×D₃×Q₈	C₂²×C₃	semidirect
129. C₃×#235	C₂²×C₃	semidirect
138. C₃²×SD₁₆	C₂×D₃	semidirect
139. C₃²×SD₁₆	C₂×D₃	semidirect
140. C₃²×SD₁₆	C₂²×C₃	semidirect
141. C₃²×SD₁₆	C₂²×C₃	semidirect
148. C₂×C₃²×C₈	C₂×D₃	semidirect
149. C₂×C₃²×C₈	C₂²×C₃	semidirect
150. C₃×#216	C₂²×C₃	semidirect
151. C₃×#215	C₂²×C₃	semidirect
152. C₃×#214	C₂²×C₃	semidirect
153. C₃×#213	C₂²×C₃	semidirect
154. C₃×#208	C₂²×C₃	semidirect
155. C₃×Dic₁₂	C₂²×C₃	semidirect
156. C₃×D₂₄	C₂²×C₃	semidirect
157. C₃×#204	C₂²×C₃	semidirect
158. C₃×#204	C₂²×C₃	semidirect
159. C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
160. C₃×D₃×C₈	C₂²×C₃	semidirect
176. #1007	C₂×C₃²	semidirect
177. #1004	C₂×C₃²	semidirect
186. C₂×C₃×SD₁₆	C₃×D₃	semidirect
187. C₂×C₃×SD₁₆	C₂×C₃²	semidirect
189. #942	C₂×C₃²	semidirect
190. #932	C₂×C₃²	semidirect
191. #916	C₂×C₃²	semidirect
192. #915	C₂×C₃²	semidirect
193. #914	C₂×C₃²	semidirect
194. D₃×SD₁₆	C₂×C₃²	semidirect
195. #904	C₂×C₃²	semidirect
196. #901	C₂×C₃²	semidirect
284. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
285. C₂×C₃×Q₈	C₂²×C₃²	semidirect
294. #239	C₂²×C₃²	semidirect
296. D₃×Q₈	C₂²×C₃²	semidirect
304. #235	C₂²×C₃²	semidirect
313. C₃×SD₁₆	C₂×C₃×D₃	semidirect
314. C₃×SD₁₆	C₂×C₃×D₃	semidirect
315. C₃×SD₁₆	C₂²×C₃²	semidirect
316. C₃×SD₁₆	C₂²×C₃²	semidirect
323. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
324. C₂×C₃×C₈	C₂²×C₃²	semidirect
325. #216	C₂²×C₃²	semidirect
326. #215	C₂²×C₃²	semidirect
327. #214	C₂²×C₃²	semidirect
328. #213	C₂²×C₃²	semidirect
329. #208	C₂²×C₃²	semidirect
330. Dic₁₂	C₂²×C₃²	semidirect
331. D₂₄	C₂²×C₃²	semidirect
332. #204	C₂²×C₃²	semidirect
333. #204	C₂²×C₃²	semidirect
334. ΓL(1,𝔽₂₅)	C₂²×C₃²	semidirect
335. D₃×C₈	C₂²×C₃²	semidirect
377. C₂×SD₁₆	C₃²×D₃	semidirect
379. C₃³	#577	semidirect
474. C₂×Q₈	C₂×C₃²×D₃	semidirect
485. SD₁₆	C₂×C₃²×D₃	semidirect
486. SD₁₆	C₂×C₃²×D₃	semidirect
492. C₂×C₈	C₂×C₃²×D₃	semidirect
526. C₃²	#5762	direct (N × H)
527. C₃²	C₃×#577	semidirect
587. C₃	C₃×#5762	direct (N × H)
588. C₃	C₃²×#577	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#1007	2
C₃²×#1004	2
C₂×C₃³×SD₁₆	2
C₃²×#942	2
C₃²×#932	2
C₃²×#916	2
C₃²×#915	2
C₃²×#914	2
C₃²×D₃×SD₁₆	2
C₃²×#904	2
C₃²×#901	2
C₃²×#577	3
C₃×#5762	3

Subgroups — C32×#5762 #13179139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5762 #13179139