Subgroups — C₃×#10596241 #13179521

Order 1728.

1796 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64367	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64366	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64160	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64158	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64127	C₂	1	2	yes	maximal, complemented
7	C₃×#64125	C₂	1	2	yes	maximal, complemented
8	C₃×SD₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
9	C₃×#64120	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#3744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64110	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596241	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5770	—	3	4	no	maximal
14	C₃³×#41	C₂²	1	1	yes	characteristic
15	C₃³×#41	C₂²	1	1	yes	characteristic, complemented
16	C₃×#3832	C₂²	1	2	yes	—
17	C₃×Q₈×C₃⋊D₃	C₂²	1	2	yes	complemented
18	C₃×#3830	—	2	2	no	—
19	C₃×#3830	C₂²	1	2	yes	complemented
20	C₃×D₄×C₃⋊D₃	—	2	2	no	—
21	C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	—
22	C₃×#3828	—	2	1	no	—
23	C₃×#3828	—	2	1	no	—
24	C₃×#3828	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
26	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
27	C₂×C₃×#634	—	2	1	no	—
28	C₂×C₃×#634	C₂²	1	1	yes	characteristic, complemented
29	C₃³×Q₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₃³×SD₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₃³×SD₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₃³×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3756	C₂²	1	2	yes	complemented
35	C₃×#3755	C₂²	1	2	yes	complemented
36	C₃×#3754	C₂²	1	2	yes	complemented
37	C₃×#3753	C₂²	1	2	yes	complemented
38	C₃×#3748	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3744	C₂²	1	2	yes	complemented
40	C₃×#3744	C₂²	1	2	yes	complemented
41	C₃×#3743	C₂²	1	2	yes	complemented
42	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	complemented
43	#64367	C₂×C₃	1	1	yes	characteristic, complemented
44	#64366	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#1010	—	3	4	no	—
46	C₃×#1009	—	3	4	no	—
47	C₃²×#135	—	2	4	no	—
48	C₃²×#135	D₃	1	4	yes	complemented
49	C₃²×#135	C₂×C₃	1	1	yes	characteristic, complemented
50	#64160	C₂×C₃	1	1	yes	characteristic, complemented
51	#64158	C₂×C₃	1	1	yes	characteristic, complemented
52	#64127	C₂×C₃	1	2	yes	complemented
53	#64125	C₂×C₃	1	2	yes	complemented
54	SD₁₆×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
55	#64120	C₂×C₃	1	2	yes	complemented
56	C₂×#3744	C₂×C₃	1	1	yes	characteristic, complemented
57	#64110	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃×#951	—	3	4	no	—
59	C₃×#949	—	3	4	no	—
60	C₃×#918	—	3	8	no	—
61	C₃×#916	—	3	8	no	—
62	C₃×D₃×SD₁₆	—	3	8	no	—
63	C₃×#911	—	3	8	no	—
64	C₂×C₃×#204	—	3	4	no	—
65	C₃×#901	—	3	4	no	—
66	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
67	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
68	C₃³×Q₈	C₂³	1	1	yes	characteristic
69	C₃³×Q₈	C₂³	1	1	yes	characteristic
70	C₃³×D₄	—	2	1	no	—
71	C₃³×D₄	—	2	1	no	—
72	C₃³×D₄	C₂³	1	1	yes	characteristic
73	C₃³×D₄	C₂³	1	1	yes	characteristic
74	C₂×C₃³×C₄	—	2	1	no	—
75	C₂×C₃³×C₄	—	2	1	no	—
76	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
77	C₃×#638	—	2	2	no	—
78	C₃×#638	—	2	2	no	—
79	C₃×#638	D₄	1	2	yes	—
80	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
81	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
82	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
83	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
84	C₃×C₄⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
85	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
86	C₃×C₄×C₃⋊D₃	—	2	2	no	—
87	C₃×C₄×C₃⋊D₃	—	2	2	no	—
88	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
89	C₃×#634	—	2	1	no	—
90	C₃×#634	—	2	2	no	—
91	C₃×#634	D₄	1	1	yes	characteristic
92	C₃×#634	C₂³	1	2	yes	—
93	C₃³×C₈	C₂³	1	1	yes	characteristic
94	C₃³×C₈	C₂³	1	1	yes	characteristic
95	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
96	C₃×#577	—	9	1	no	—
97	#5770	—	3	4	no	—
98	C₃²×#41	—	2	4	no	—
99	C₃²×#41	—	2	4	no	—
100	C₃²×#41	C₂×D₃	1	4	yes	—
101	C₃²×#41	C₂×D₃	1	4	yes	complemented
102	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
103	C₃²×#41	C₂²×C₃	1	1	yes	characteristic, complemented
104	#3832	C₂²×C₃	1	2	yes	—
105	Q₈×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
106	#3830	—	2	2	no	—
107	#3830	C₂²×C₃	1	2	yes	complemented
108	D₄×C₃⋊D₃	—	2	2	no	—
109	D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
110	#3828	—	2	1	no	—
111	#3828	—	2	1	no	—
112	#3828	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
114	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
115	C₂×#634	—	2	1	no	—
116	C₂×#634	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₃×#239	—	3	8	no	—
118	C₃×D₃×Q₈	—	3	8	no	—
119	C₃×#237	—	3	8	no	—
120	C₃×#237	—	6	8	no	—
121	C₃×D₃×D₄	—	3	8	no	—
122	C₃×D₃×D₄	—	6	8	no	—
123	C₃×#235	—	3	4	no	—
124	C₃×#235	—	6	4	no	—
125	C₃×#235	—	6	4	no	—
126	C₂×C₃×D₁₂	—	3	4	no	—
127	C₂×C₃×D₁₂	—	6	4	no	—
128	C₂×C₃×Dic₆	—	3	4	no	—
129	C₂×C₃×Dic₆	—	6	4	no	—
130	C₃²×Q₁₆	—	2	4	no	—
131	C₃²×Q₁₆	C₂×D₃	1	4	yes	complemented
132	C₃²×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₃²×SD₁₆	—	2	4	no	—
134	C₃²×SD₁₆	—	2	4	no	—
135	C₃²×SD₁₆	C₂×D₃	1	4	yes	complemented
136	C₃²×SD₁₆	C₂×D₃	1	4	yes	complemented
137	C₃²×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₃²×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₃²×D₈	—	2	4	no	—
140	C₃²×D₈	C₂×D₃	1	4	yes	complemented
141	C₃²×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₂×C₃²×C₈	—	2	4	no	—
143	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
144	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
145	#3756	C₂²×C₃	1	2	yes	complemented
146	#3755	C₂²×C₃	1	2	yes	complemented
147	#3754	C₂²×C₃	1	2	yes	complemented
148	#3753	C₂²×C₃	1	2	yes	complemented
149	#3748	C₂²×C₃	1	1	yes	characteristic, complemented
150	#3744	C₂²×C₃	1	2	yes	complemented
151	#3744	C₂²×C₃	1	2	yes	complemented
152	#3743	C₂²×C₃	1	2	yes	complemented
153	C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
154	C₃×#216	—	3	8	no	—
155	C₃×#215	—	3	8	no	—
156	C₃×#214	—	3	8	no	—
157	C₃×#213	—	3	8	no	—
158	C₃×#208	—	3	4	no	—
159	C₃×#204	—	3	8	no	—
160	C₃×#204	—	3	8	no	—
161	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
162	C₃×D₃×C₈	—	3	8	no	—
163	C₂²×C₃³	—	2	1	no	—
164	C₂²×C₃³	—	2	1	no	—
165	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃×C₃⋊D₃	—	2	2	no	—
167	C₂×C₃×C₃⋊D₃	—	8	2	no	—
168	C₂×C₃×C₃⋊D₃	—	8	1	no	—
169	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
170	C₃³×C₄	—	2	1	no	—
171	C₃³×C₄	—	2	1	no	—
172	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
173	C₃³×C₄	C₂⁴	1	1	yes	characteristic
174	C₃×C₃⋊Dic₃	—	2	2	no	—
175	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
176	C₃×2₋¹⁺⁴	—	9	1	no	—
177	C₃×H(5,𝔽₂)	—	9	1	no	—
178	#1010	—	3	4	no	—
179	#1009	—	3	4	no	—
180	C₃×#137	—	9	1	no	—
181	C₃×#137	—	9	2	no	—
182	C₃×AGL(1,ℤ/8)	—	9	1	no	—
183	C₃×AGL(1,ℤ/8)	—	9	2	no	—
184	C₃×#135	—	2	4	no	—
185	C₃×#135	—	9	2	no	—
186	C₃×#135	C₃×D₃	1	4	yes	complemented
187	C₃×#135	C₃⋊D₃	1	1	yes	characteristic, complemented
188	C₂×C₃×SD₁₆	—	9	2	no	—
189	C₂×C₃×SD₁₆	—	9	1	no	—
190	C₃×#131	—	9	1	no	—
191	#951	—	3	4	no	—
192	#949	—	3	4	no	—
193	#918	—	3	8	no	—
194	#916	—	3	8	no	—
195	D₃×SD₁₆	—	3	8	no	—
196	#911	—	3	8	no	—
197	C₂×#204	—	3	4	no	—
198	#901	—	3	4	no	—
199	C₂²×C₃⋊D₃	—	2	1	no	—
200	C₂²×C₃⋊D₃	—	2	2	no	—
201	C₂²×C₃×D₃	—	6	8	no	—
202	C₂²×C₃×D₃	—	6	4	no	—
203	C₃²×Q₈	—	2	4	no	—
204	C₃²×Q₈	—	2	4	no	—
205	C₃²×Q₈	C₂²×D₃	1	4	yes	—
206	C₃²×Q₈	C₂²×D₃	1	4	yes	—
207	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic
208	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic
209	C₃²×D₄	—	2	1	no	—
210	C₃²×D₄	—	2	1	no	—
211	C₃²×D₄	—	2	4	no	—
212	C₃²×D₄	—	2	4	no	—
213	C₃²×D₄	—	2	4	no	—
214	C₃²×D₄	—	2	4	no	—
215	C₃²×D₄	—	4	4	no	—
216	C₃²×D₄	—	4	4	no	—
217	C₃²×D₄	C₂²×D₃	1	4	yes	—
218	C₃²×D₄	C₂²×D₃	1	4	yes	—
219	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
220	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₃²×C₄	—	2	1	no	—
222	C₂×C₃²×C₄	—	2	1	no	—
223	C₂×C₃²×C₄	—	2	4	no	—
224	C₂×C₃²×C₄	—	2	4	no	—
225	C₂×C₃²×C₄	—	2	4	no	—
226	C₂×C₃²×C₄	—	4	4	no	—
227	C₂×C₃²×C₄	—	4	4	no	—
228	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
229	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
230	#638	—	2	2	no	—
231	#638	—	2	2	no	—
232	#638	C₃×D₄	1	2	yes	—
233	C₂×C₃⋊Dic₃	—	2	1	no	—
234	C₂×C₃⋊Dic₃	—	2	2	no	—
235	C₄⋊(C₃⋊D₃)	—	2	2	no	—
236	C₄⋊(C₃⋊D₃)	—	2	1	no	—
237	C₄⋊(C₃⋊D₃)	C₃×D₄	1	1	yes	characteristic
238	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
239	C₄×C₃⋊D₃	—	2	2	no	—
240	C₄×C₃⋊D₃	—	2	2	no	—
241	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
242	#634	—	2	1	no	—
243	#634	—	2	2	no	—
244	#634	C₃×D₄	1	1	yes	characteristic
245	#634	C₂³×C₃	1	2	yes	—
246	C₃×#67	—	3	8	no	—
247	C₃×#67	—	6	8	no	—
248	C₃×#67	—	6	8	no	—
249	C₂×C₃×Dic₃	—	6	8	no	—
250	C₂×C₃×Dic₃	—	6	4	no	—
251	C₃×D₁₂	—	3	4	no	—
252	C₃×D₁₂	—	3	8	no	—
253	C₃×D₁₂	—	6	8	no	—
254	C₃×D₁₂	—	6	4	no	—
255	C₃×C₄×D₃	—	3	8	no	—
256	C₃×C₄×D₃	—	6	8	no	—
257	C₃×C₄×D₃	—	6	8	no	—
258	C₃×Dic₆	—	3	4	no	—
259	C₃×Dic₆	—	3	8	no	—
260	C₃×Dic₆	—	6	8	no	—
261	C₃×Dic₆	—	6	4	no	—
262	C₃²×C₈	—	2	4	no	—
263	C₃²×C₈	—	2	4	no	—
264	C₃²×C₈	C₂²×D₃	1	4	yes	—
265	C₃²×C₈	C₂²×D₃	1	4	yes	—
266	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
267	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
268	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	—
269	C₃×C₃⋊C₈	—	3	8	no	—
270	#577	—	9	1	no	Sylow
271	C₂×C₃³	—	2	1	no	—
272	C₂×C₃³	—	4	1	no	—
273	C₂×C₃³	—	4	1	no	—
274	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
275	C₃×C₃⋊D₃	—	2	2	no	—
276	C₃×C₃⋊D₃	—	4	2	no	—
277	C₃×#41	—	2	4	no	—
278	C₃×#41	—	2	4	no	—
279	C₃×#41	—	9	1	no	—
280	C₃×#41	—	9	2	no	—
281	C₃×#41	—	9	2	no	—
282	C₃×#41	—	18	1	no	—
283	C₃×#41	—	18	1	no	—
284	C₃×#41	—	18	2	no	—
285	C₃×#41	C₂×C₃×D₃	1	4	yes	—
286	C₃×#41	C₂×C₃×D₃	1	4	yes	complemented
287	C₃×#41	C₂×C₃⋊D₃	1	1	yes	characteristic
288	C₃×#41	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
289	C₂×C₃×Q₈	—	9	2	no	—
290	C₂×C₃×Q₈	—	9	1	no	—
291	C₂×C₃×Q₈	—	18	1	no	—
292	C₂×C₃×D₄	—	9	2	no	—
293	C₂×C₃×D₄	—	9	1	no	—
294	C₂×C₃×D₄	—	18	1	no	—
295	C₂×C₃×D₄	—	18	2	no	—
296	#239	—	3	8	no	—
297	D₃×Q₈	—	3	8	no	—
298	#237	—	3	8	no	—
299	#237	—	6	8	no	—
300	D₃×D₄	—	3	8	no	—
301	D₃×D₄	—	6	8	no	—
302	#235	—	3	4	no	—
303	#235	—	6	4	no	—
304	#235	—	6	4	no	—
305	C₂×D₁₂	—	3	4	no	—
306	C₂×D₁₂	—	6	4	no	—
307	C₂×Dic₆	—	3	4	no	—
308	C₂×Dic₆	—	6	4	no	—
309	C₃×Q₁₆	—	2	4	no	—
310	C₃×Q₁₆	—	9	2	no	—
311	C₃×Q₁₆	C₂×C₃×D₃	1	4	yes	complemented
312	C₃×Q₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
313	C₃×SD₁₆	—	2	4	no	—
314	C₃×SD₁₆	—	2	4	no	—
315	C₃×SD₁₆	—	9	2	no	—
316	C₃×SD₁₆	—	9	2	no	—
317	C₃×SD₁₆	—	9	2	no	—
318	C₃×SD₁₆	—	9	2	no	—
319	C₃×SD₁₆	C₂×C₃×D₃	1	4	yes	complemented
320	C₃×SD₁₆	C₂×C₃×D₃	1	4	yes	complemented
321	C₃×SD₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
322	C₃×SD₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
323	C₃×D₈	—	2	4	no	—
324	C₃×D₈	—	9	2	no	—
325	C₃×D₈	C₂×C₃×D₃	1	4	yes	complemented
326	C₃×D₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
327	C₃×M₁₆	—	9	1	no	—
328	C₃×M₁₆	—	9	2	no	—
329	C₂×C₃×C₈	—	2	4	no	—
330	C₂×C₃×C₈	—	9	2	no	—
331	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
332	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
333	#216	—	3	8	no	—
334	#215	—	3	8	no	—
335	#214	—	3	8	no	—
336	#213	—	3	8	no	—
337	#208	—	3	4	no	—
338	#204	—	3	8	no	—
339	#204	—	3	8	no	—
340	ΓL(1,𝔽₂₅)	—	3	8	no	—
341	D₃×C₈	—	3	8	no	—
342	C₂²×C₃²	—	2	1	no	—
343	C₂²×C₃²	—	2	1	no	—
344	C₂²×C₃²	—	2	4	no	—
345	C₂²×C₃²	—	2	4	no	—
346	C₂²×C₃²	—	2	4	no	—
347	C₂²×C₃²	—	4	4	no	—
348	C₂²×C₃²	—	4	4	no	—
349	C₂²×C₃²	D₃×D₄	1	4	yes	—
350	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂×C₃⋊D₃	—	2	2	no	—
352	C₂×C₃⋊D₃	—	8	2	no	—
353	C₂×C₃⋊D₃	—	8	1	no	—
354	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
355	C₂×C₃×D₃	—	3	8	no	—
356	C₂×C₃×D₃	—	6	8	no	—
357	C₂×C₃×D₃	—	24	8	no	—
358	C₂×C₃×D₃	—	24	4	no	—
359	C₃²×C₄	—	2	1	no	—
360	C₃²×C₄	—	2	1	no	—
361	C₃²×C₄	—	2	4	no	—
362	C₃²×C₄	—	2	4	no	—
363	C₃²×C₄	—	2	4	no	—
364	C₃²×C₄	—	2	4	no	—
365	C₃²×C₄	—	4	4	no	—
366	C₃²×C₄	—	4	4	no	—
367	C₃²×C₄	D₃×D₄	1	4	yes	—
368	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
369	C₃²×C₄	C₂³×D₃	1	4	yes	—
370	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
371	C₃⋊Dic₃	—	2	2	no	—
372	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
373	C₃×Dic₃	—	3	8	no	—
374	C₃×Dic₃	—	6	8	no	—
375	2₋¹⁺⁴	—	9	1	no	—
376	H(5,𝔽₂)	—	9	1	no	—
377	#137	—	9	1	no	—
378	#137	—	9	2	no	—
379	AGL(1,ℤ/8)	—	9	1	no	—
380	AGL(1,ℤ/8)	—	9	2	no	—
381	#135	—	9	2	no	—
382	#135	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
383	C₂×SD₁₆	—	9	2	no	—
384	C₂×SD₁₆	—	9	1	no	—
385	#131	—	9	1	no	—
386	C₃³	#577	1	1	yes	characteristic, complemented, Sylow
387	C₂³×C₃	—	18	2	no	—
388	C₂³×C₃	—	18	1	no	—
389	C₂²×D₃	—	6	8	no	—
390	C₂²×D₃	—	6	4	no	—
391	C₃×Q₈	—	2	4	no	—
392	C₃×Q₈	—	2	4	no	—
393	C₃×Q₈	—	9	1	no	—
394	C₃×Q₈	—	9	2	no	—
395	C₃×Q₈	—	18	2	no	—
396	C₃×Q₈	—	18	1	no	—
397	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
398	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
399	C₃×Q₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
400	C₃×Q₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
401	C₃×D₄	—	2	4	no	—
402	C₃×D₄	—	2	4	no	—
403	C₃×D₄	—	2	1	no	—
404	C₃×D₄	—	2	1	no	—
405	C₃×D₄	—	2	4	no	—
406	C₃×D₄	—	2	4	no	—
407	C₃×D₄	—	4	4	no	—
408	C₃×D₄	—	4	4	no	—
409	C₃×D₄	—	9	2	no	—
410	C₃×D₄	—	9	2	no	—
411	C₃×D₄	—	9	1	no	—
412	C₃×D₄	—	18	2	no	—
413	C₃×D₄	—	18	2	no	—
414	C₃×D₄	—	18	2	no	—
415	C₃×D₄	—	18	1	no	—
416	C₃×D₄	C₂²×C₃×D₃	1	4	yes	—
417	C₃×D₄	C₂²×C₃×D₃	1	4	yes	—
418	C₃×D₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
419	C₃×D₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
420	C₂×C₃×C₄	—	2	4	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	1	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	4	4	no	—
426	C₂×C₃×C₄	—	4	4	no	—
427	C₂×C₃×C₄	—	9	2	no	—
428	C₂×C₃×C₄	—	18	2	no	—
429	C₂×C₃×C₄	—	18	2	no	—
430	C₂×C₃×C₄	—	18	2	no	—
431	C₂×C₃×C₄	—	18	1	no	—
432	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
433	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
434	#67	—	3	8	no	—
435	#67	—	6	8	no	—
436	#67	—	6	8	no	—
437	C₂×Dic₃	—	6	8	no	—
438	C₂×Dic₃	—	6	4	no	—
439	D₁₂	—	3	8	no	—
440	D₁₂	—	3	4	no	—
441	D₁₂	—	6	8	no	—
442	D₁₂	—	6	4	no	—
443	C₄×D₃	—	3	8	no	—
444	C₄×D₃	—	6	8	no	—
445	C₄×D₃	—	6	8	no	—
446	Dic₆	—	3	4	no	—
447	Dic₆	—	3	8	no	—
448	Dic₆	—	6	8	no	—
449	Dic₆	—	6	4	no	—
450	C₃×C₈	—	2	4	no	—
451	C₃×C₈	—	2	4	no	—
452	C₃×C₈	—	9	2	no	—
453	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
454	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
455	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
456	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
457	C₃⋊C₈	—	3	8	no	—
458	C₂×C₃²	—	2	1	no	—
459	C₂×C₃²	—	2	4	no	—
460	C₂×C₃²	—	2	4	no	—
461	C₂×C₃²	—	4	4	no	—
462	C₂×C₃²	—	4	1	no	—
463	C₂×C₃²	—	4	1	no	—
464	C₂×C₃²	—	4	4	no	—
465	C₂×C₃²	—	4	4	no	—
466	C₂×C₃²	—	8	4	no	—
467	C₂×C₃²	—	8	4	no	—
468	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
469	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
470	C₃⋊D₃	—	2	2	no	—
471	C₃⋊D₃	—	4	2	no	—
472	C₃×D₃	—	6	8	no	—
473	C₃×D₃	—	12	8	no	—
474	#41	—	9	1	no	—
475	#41	—	9	2	no	—
476	#41	—	9	2	no	—
477	#41	—	18	1	no	—
478	#41	—	18	1	no	—
479	#41	—	18	2	no	—
480	#41	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
481	#41	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
482	C₂×Q₈	—	9	2	no	—
483	C₂×Q₈	—	9	1	no	—
484	C₂×Q₈	—	18	1	no	—
485	C₂×D₄	—	9	2	no	—
486	C₂×D₄	—	9	1	no	—
487	C₂×D₄	—	18	1	no	—
488	C₂×D₄	—	18	2	no	—
489	Q₁₆	—	9	2	no	—
490	Q₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
491	SD₁₆	—	9	2	no	—
492	SD₁₆	—	9	2	no	—
493	SD₁₆	—	9	2	no	—
494	SD₁₆	—	9	2	no	—
495	SD₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
496	SD₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
497	D₈	—	9	2	no	—
498	D₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
499	M₁₆	—	9	1	no	—
500	M₁₆	—	9	2	no	—
501	C₂×C₈	—	9	2	no	—
502	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
503	C₂²×C₃	—	2	4	no	—
504	C₂²×C₃	—	2	4	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	4	no	—
508	C₂²×C₃	—	4	4	no	—
509	C₂²×C₃	—	4	4	no	—
510	C₂²×C₃	—	9	2	no	—
511	C₂²×C₃	—	18	2	no	—
512	C₂²×C₃	—	72	1	no	—
513	C₂²×C₃	—	72	2	no	—
514	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
515	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
516	C₂×D₃	—	3	8	no	—
517	C₂×D₃	—	6	8	no	—
518	C₂×D₃	—	24	8	no	—
519	C₂×D₃	—	24	4	no	—
520	C₃×C₄	—	2	4	no	—
521	C₃×C₄	—	2	4	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	2	4	no	—
525	C₃×C₄	—	2	4	no	—
526	C₃×C₄	—	4	4	no	—
527	C₃×C₄	—	4	4	no	—
528	C₃×C₄	—	9	2	no	—
529	C₃×C₄	—	18	2	no	—
530	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
531	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
532	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
533	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
534	Dic₃	—	3	8	no	—
535	Dic₃	—	6	8	no	—
536	C₃²	—	2	4	no	—
537	C₃²	#5770	1	4	yes	complemented
538	C₃²	C₃×#577	1	1	yes	characteristic, complemented
539	C₂³	—	18	2	no	—
540	C₂³	—	18	1	no	—
541	Q₈	—	9	1	no	—
542	Q₈	—	9	2	no	—
543	Q₈	—	18	2	no	—
544	Q₈	—	18	1	no	—
545	Q₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
546	Q₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
547	D₄	—	2	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	9	2	no	—
550	D₄	—	9	2	no	—
551	D₄	—	9	1	no	—
552	D₄	—	18	2	no	—
553	D₄	—	18	2	no	—
554	D₄	—	18	2	no	—
555	D₄	—	18	1	no	—
556	D₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
557	D₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	9	2	no	—
561	C₂×C₄	—	18	2	no	—
562	C₂×C₄	—	18	2	no	—
563	C₂×C₄	—	18	2	no	—
564	C₂×C₄	—	18	1	no	—
565	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
566	C₈	—	9	2	no	—
567	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
568	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
569	C₂×C₃	—	2	4	no	—
570	C₂×C₃	—	2	1	no	—
571	C₂×C₃	—	2	4	no	—
572	C₂×C₃	—	4	4	no	—
573	C₂×C₃	—	4	4	no	—
574	C₂×C₃	—	4	4	no	—
575	C₂×C₃	—	4	1	no	—
576	C₂×C₃	—	4	1	no	—
577	C₂×C₃	—	8	4	no	—
578	C₂×C₃	—	8	4	no	—
579	C₂×C₃	—	18	2	no	—
580	C₂×C₃	—	36	2	no	—
581	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
582	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
583	D₃	—	6	8	no	—
584	D₃	—	12	8	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	9	2	no	—
588	C₂²	—	18	2	no	—
589	C₂²	—	72	1	no	—
590	C₂²	—	72	2	no	—
591	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	9	2	no	—
595	C₄	—	18	2	no	—
596	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
597	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
598	C₃	—	2	4	no	—
599	C₃	C₃×#5770	1	4	yes	complemented
600	C₃	#10596241	1	1	yes	characteristic, direct product factor
601	C₂	—	2	1	no	—
602	C₂	—	4	1	no	—
603	C₂	—	4	1	no	—
604	C₂	—	18	2	no	—
605	C₂	—	36	2	no	—
606	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#135	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₃×#135	C₃⋊D₃
hypocenter	C₃²	C₃×#577
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₃×#64367	C₂	semidirect
2. C₃×#64366	C₂	semidirect
3. C₃³×#135	C₂	semidirect
4. C₃×#64160	C₂	semidirect
5. C₃×#64158	C₂	semidirect
6. C₃×#64127	C₂	semidirect
7. C₃×#64125	C₂	semidirect
8. C₃×SD₁₆×C₃⋊D₃	C₂	semidirect
9. C₃×#64120	C₂	semidirect
10. C₂×C₃×#3744	C₂	semidirect
11. C₃×#64110	C₂	semidirect
12. #10596241	C₃	direct (N × H)
15. C₃³×#41	C₂²	semidirect
17. C₃×Q₈×C₃⋊D₃	C₂²	semidirect
19. C₃×#3830	C₂²	semidirect
28. C₂×C₃×#634	C₂²	semidirect
29. C₃³×Q₁₆	C₂²	semidirect
30. C₃³×SD₁₆	C₂²	semidirect
31. C₃³×SD₁₆	C₂²	semidirect
32. C₃³×D₈	C₂²	semidirect
33. C₂×C₃³×C₈	C₂²	semidirect
34. C₃×#3756	C₂²	semidirect
35. C₃×#3755	C₂²	semidirect
36. C₃×#3754	C₂²	semidirect
37. C₃×#3753	C₂²	semidirect
38. C₃×#3748	C₂²	semidirect
39. C₃×#3744	C₂²	semidirect
40. C₃×#3744	C₂²	semidirect
41. C₃×#3743	C₂²	semidirect
42. C₃×C₈×C₃⋊D₃	C₂²	semidirect
43. #64367	C₂×C₃	semidirect
44. #64366	C₂×C₃	semidirect
48. C₃²×#135	D₃	semidirect
49. C₃²×#135	C₂×C₃	semidirect
50. #64160	C₂×C₃	semidirect
51. #64158	C₂×C₃	semidirect
52. #64127	C₂×C₃	semidirect
53. #64125	C₂×C₃	semidirect
54. SD₁₆×C₃⋊D₃	C₂×C₃	semidirect
55. #64120	C₂×C₃	semidirect
56. C₂×#3744	C₂×C₃	semidirect
57. #64110	C₂×C₃	semidirect
101. C₃²×#41	C₂×D₃	semidirect
103. C₃²×#41	C₂²×C₃	semidirect
105. Q₈×C₃⋊D₃	C₂²×C₃	semidirect
107. #3830	C₂²×C₃	semidirect
116. C₂×#634	C₂²×C₃	semidirect
131. C₃²×Q₁₆	C₂×D₃	semidirect
132. C₃²×Q₁₆	C₂²×C₃	semidirect
135. C₃²×SD₁₆	C₂×D₃	semidirect
136. C₃²×SD₁₆	C₂×D₃	semidirect
137. C₃²×SD₁₆	C₂²×C₃	semidirect
138. C₃²×SD₁₆	C₂²×C₃	semidirect
140. C₃²×D₈	C₂×D₃	semidirect
141. C₃²×D₈	C₂²×C₃	semidirect
143. C₂×C₃²×C₈	C₂×D₃	semidirect
144. C₂×C₃²×C₈	C₂²×C₃	semidirect
145. #3756	C₂²×C₃	semidirect
146. #3755	C₂²×C₃	semidirect
147. #3754	C₂²×C₃	semidirect
148. #3753	C₂²×C₃	semidirect
149. #3748	C₂²×C₃	semidirect
150. #3744	C₂²×C₃	semidirect
151. #3744	C₂²×C₃	semidirect
152. #3743	C₂²×C₃	semidirect
153. C₈×C₃⋊D₃	C₂²×C₃	semidirect
186. C₃×#135	C₃×D₃	semidirect
187. C₃×#135	C₃⋊D₃	semidirect
286. C₃×#41	C₂×C₃×D₃	semidirect
288. C₃×#41	C₂×C₃⋊D₃	semidirect
311. C₃×Q₁₆	C₂×C₃×D₃	semidirect
312. C₃×Q₁₆	C₂×C₃⋊D₃	semidirect
319. C₃×SD₁₆	C₂×C₃×D₃	semidirect
320. C₃×SD₁₆	C₂×C₃×D₃	semidirect
321. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
322. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
325. C₃×D₈	C₂×C₃×D₃	semidirect
326. C₃×D₈	C₂×C₃⋊D₃	semidirect
331. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
332. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
382. #135	C₃×C₃⋊D₃	semidirect
386. C₃³	#577	semidirect
481. #41	C₂×C₃×C₃⋊D₃	semidirect
490. Q₁₆	C₂×C₃×C₃⋊D₃	semidirect
495. SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
496. SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
498. D₈	C₂×C₃×C₃⋊D₃	semidirect
502. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
537. C₃²	#5770	semidirect
538. C₃²	C₃×#577	semidirect
599. C₃	C₃×#5770	semidirect
600. C₃	#10596241	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#64367	2
C₃×#64366	2
C₃³×#135	2
C₃×#64160	2
C₃×#64158	2
C₃×#64127	2
C₃×#64125	2
C₃×SD₁₆×C₃⋊D₃	2
C₃×#64120	2
C₂×C₃×#3744	2
C₃×#64110	2
#10596241	3
C₃×#5770	3

Subgroups — C3×#10596241 #13179521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596241 #13179521