Subgroups — C₃×#10596245 #13179525

Order 1728.

1880 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#64366	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64159	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3753	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64125	C₂	1	2	yes	maximal, complemented
7	C₃×#64123	C₂	1	2	yes	maximal, complemented
8	C₃×#64120	C₂	1	2	yes	maximal, complemented
9	C₃×D₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
10	C₃×#64117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64116	C₂	1	1	yes	maximal, characteristic, complemented
12	#10596245	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×#5774	—	3	4	no	maximal
14	C₃³×#41	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×#638	—	2	2	no	—
17	C₃×#3832	C₂²	1	2	yes	complemented
18	C₃×#3830	—	2	1	no	—
19	C₃×#3830	C₂²	1	2	yes	complemented
20	C₃×D₄×C₃⋊D₃	—	2	2	no	—
21	C₃×D₄×C₃⋊D₃	—	2	1	no	—
22	C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	complemented
23	C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	complemented
24	C₃×#3828	—	2	1	no	—
25	C₃×#3828	C₂²	1	1	yes	characteristic
26	C₃×#3828	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
28	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
29	C₃³×SD₁₆	C₂²	1	2	yes	complemented
30	C₃³×D₈	C₂²	1	2	yes	complemented
31	C₃³×M₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₃×#3756	C₂²	1	1	yes	characteristic, complemented
33	C₃×#3755	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3754	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3753	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3753	C₂²	1	2	yes	complemented
37	C₃×#3753	C₂²	1	2	yes	complemented
38	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3745	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	#64366	C₂×C₃	1	1	yes	characteristic, complemented
44	#64361	C₂×C₃	1	1	yes	characteristic, complemented
45	C₃×#1009	—	3	4	no	—
46	C₃×#1004	—	3	4	no	—
47	C₃²×AGL(1,ℤ/8)	—	2	4	no	—
48	C₃²×AGL(1,ℤ/8)	D₃	1	4	yes	complemented
49	C₃²×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
50	#64159	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×#3753	C₂×C₃	1	1	yes	characteristic, complemented
52	#64125	C₂×C₃	1	2	yes	complemented
53	#64123	C₂×C₃	1	2	yes	complemented
54	#64120	C₂×C₃	1	2	yes	complemented
55	D₈×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
56	#64117	C₂×C₃	1	1	yes	characteristic, complemented
57	#64116	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃×#950	—	3	4	no	—
59	C₂×C₃×#213	—	3	4	no	—
60	C₃×#916	—	3	8	no	—
61	C₃×#914	—	3	8	no	—
62	C₃×#911	—	3	8	no	—
63	C₃×D₃×D₈	—	3	8	no	—
64	C₃×#908	—	3	4	no	—
65	C₃×#907	—	3	4	no	—
66	C₂³×C₃³	—	2	1	no	—
67	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
68	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
69	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
70	C₃³×Q₈	C₂³	1	1	yes	characteristic
71	C₃³×D₄	—	2	1	no	—
72	C₃³×D₄	—	2	1	no	—
73	C₃³×D₄	C₂³	1	2	yes	—
74	C₃³×D₄	C₂³	1	1	yes	characteristic
75	C₂×C₃³×C₄	—	2	1	no	—
76	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
77	C₃×#638	—	2	1	no	—
78	C₃×#638	—	2	2	no	—
79	C₃×#638	—	2	2	no	—
80	C₃×#638	—	2	2	no	—
81	C₃×#638	D₄	1	2	yes	—
82	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
83	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
84	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
85	C₃×C₄⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
86	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
87	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
88	C₃×C₄×C₃⋊D₃	—	2	1	no	—
89	C₃×C₄×C₃⋊D₃	—	2	2	no	—
90	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
91	C₃×#634	D₄	1	1	yes	characteristic
92	C₃×#634	C₂³	1	1	yes	characteristic
93	C₃³×C₈	C₂³	1	2	yes	—
94	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
95	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
96	C₃×#576	—	9	1	no	—
97	#5774	—	3	4	no	—
98	C₃²×#41	—	2	4	no	—
99	C₃²×#41	C₂×D₃	1	4	yes	complemented
100	C₃²×#41	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₂×C₃²×D₄	—	2	4	no	—
102	C₂×C₃²×D₄	C₂×D₃	1	4	yes	complemented
103	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂×#638	—	2	2	no	—
105	#3832	C₂²×C₃	1	2	yes	complemented
106	#3830	—	2	1	no	—
107	#3830	C₂²×C₃	1	2	yes	complemented
108	D₄×C₃⋊D₃	—	2	2	no	—
109	D₄×C₃⋊D₃	—	2	1	no	—
110	D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
111	D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
112	#3828	—	2	1	no	—
113	#3828	C₂²×C₃	1	1	yes	characteristic
114	#3828	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
116	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₂×C₃×#67	—	6	8	no	—
118	C₃×#239	—	3	8	no	—
119	C₃×#237	—	3	8	no	—
120	C₃×#237	—	6	4	no	—
121	C₃×D₃×D₄	—	3	8	no	—
122	C₃×D₃×D₄	—	3	8	no	—
123	C₃×D₃×D₄	—	6	4	no	—
124	C₃×D₃×D₄	—	6	8	no	—
125	C₃×#235	—	3	4	no	—
126	C₃×#235	—	3	4	no	—
127	C₃×#235	—	6	4	no	—
128	C₂×C₃×D₁₂	—	3	4	no	—
129	C₂×C₃×D₁₂	—	6	4	no	—
130	C₃²×SD₁₆	—	2	8	no	—
131	C₃²×SD₁₆	C₂×D₃	1	8	yes	complemented
132	C₃²×SD₁₆	C₂²×C₃	1	2	yes	complemented
133	C₃²×D₈	—	2	8	no	—
134	C₃²×D₈	C₂×D₃	1	8	yes	complemented
135	C₃²×D₈	C₂²×C₃	1	2	yes	complemented
136	C₃²×M₁₆	—	2	4	no	—
137	C₃²×M₁₆	C₂×D₃	1	4	yes	complemented
138	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
139	#3756	C₂²×C₃	1	1	yes	characteristic, complemented
140	#3755	C₂²×C₃	1	1	yes	characteristic, complemented
141	#3754	C₂²×C₃	1	1	yes	characteristic, complemented
142	#3753	C₂²×C₃	1	1	yes	characteristic, complemented
143	#3753	C₂²×C₃	1	2	yes	complemented
144	#3753	C₂²×C₃	1	2	yes	complemented
145	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
146	#3745	C₂²×C₃	1	2	yes	complemented
147	#3744	C₂²×C₃	1	2	yes	complemented
148	#3743	C₂²×C₃	1	2	yes	complemented
149	C₈×C₃⋊D₃	C₂²×C₃	1	2	yes	complemented
150	C₃×#216	—	3	4	no	—
151	C₃×#215	—	3	4	no	—
152	C₃×#214	—	3	4	no	—
153	C₃×#213	—	3	4	no	—
154	C₃×#213	—	3	8	no	—
155	C₃×#213	—	3	8	no	—
156	C₂×C₃×C₃⋊C₈	—	3	4	no	—
157	C₃×D₂₄	—	3	8	no	—
158	C₃×#204	—	3	8	no	—
159	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
160	C₃×D₃×C₈	—	3	8	no	—
161	C₂²×C₃³	—	2	2	no	—
162	C₂²×C₃³	—	2	1	no	—
163	C₂²×C₃³	—	8	1	no	—
164	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×C₃⋊D₃	—	2	2	no	—
166	C₂×C₃×C₃⋊D₃	—	2	1	no	—
167	C₂×C₃×C₃⋊D₃	—	8	2	no	—
168	C₂×C₃×C₃⋊D₃	—	8	2	no	—
169	C₂×C₃×C₃⋊D₃	—	8	1	no	—
170	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
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	1	no	—
175	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
176	C₃×H(5,𝔽₂)	—	9	1	no	—
177	C₃×H(5,𝔽₂)	—	9	1	no	—
178	#1009	—	3	4	no	—
179	#1004	—	3	4	no	—
180	C₃×AGL(1,ℤ/8)	—	2	4	no	—
181	C₃×AGL(1,ℤ/8)	—	9	2	no	—
182	C₃×AGL(1,ℤ/8)	—	9	2	no	—
183	C₃×AGL(1,ℤ/8)	—	9	1	no	—
184	C₃×AGL(1,ℤ/8)	C₃×D₃	1	4	yes	complemented
185	C₃×AGL(1,ℤ/8)	C₃⋊D₃	1	1	yes	characteristic, complemented
186	C₃×#135	—	9	1	no	—
187	C₃×#135	—	9	2	no	—
188	C₂×C₃×D₈	—	9	1	no	—
189	C₂×C₃×D₈	—	9	2	no	—
190	C₃×#131	—	9	1	no	—
191	#950	—	3	4	no	—
192	C₂×#213	—	3	4	no	—
193	#916	—	3	8	no	—
194	#914	—	3	8	no	—
195	#911	—	3	8	no	—
196	D₃×D₈	—	3	8	no	—
197	#908	—	3	4	no	—
198	#907	—	3	4	no	—
199	C₂³×C₃²	—	2	1	no	—
200	C₂³×C₃²	—	2	4	no	—
201	C₂³×C₃²	—	4	4	no	—
202	C₂²×C₃⋊D₃	—	2	1	no	—
203	C₂²×C₃⋊D₃	—	2	2	no	—
204	C₂²×C₃⋊D₃	—	2	2	no	—
205	C₂²×C₃×D₃	—	6	8	no	—
206	C₂²×C₃×D₃	—	6	8	no	—
207	C₂²×C₃×D₃	—	6	4	no	—
208	C₃²×Q₈	—	2	4	no	—
209	C₃²×Q₈	C₂²×D₃	1	4	yes	—
210	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic
211	C₃²×D₄	—	2	1	no	—
212	C₃²×D₄	—	2	1	no	—
213	C₃²×D₄	—	2	4	no	—
214	C₃²×D₄	—	2	8	no	—
215	C₃²×D₄	—	2	4	no	—
216	C₃²×D₄	—	2	4	no	—
217	C₃²×D₄	—	4	4	no	—
218	C₃²×D₄	—	4	4	no	—
219	C₃²×D₄	C₂²×D₃	1	8	yes	—
220	C₃²×D₄	C₂²×D₃	1	4	yes	—
221	C₃²×D₄	C₂³×C₃	1	2	yes	—
222	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₃²×C₄	—	2	1	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	C₂²×D₃	1	4	yes	—
228	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
229	#638	—	2	1	no	—
230	#638	—	2	2	no	—
231	#638	—	2	2	no	—
232	#638	—	2	2	no	—
233	#638	C₃×D₄	1	2	yes	—
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)	C₂³×C₃	1	1	yes	characteristic
240	C₄×C₃⋊D₃	—	2	1	no	—
241	C₄×C₃⋊D₃	—	2	2	no	—
242	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
243	#634	C₃×D₄	1	1	yes	characteristic
244	#634	C₂³×C₃	1	1	yes	characteristic
245	C₃×#67	—	3	8	no	—
246	C₃×#67	—	6	8	no	—
247	C₃×#67	—	6	8	no	—
248	C₃×#67	—	6	8	no	—
249	C₃×#67	—	6	4	no	—
250	C₂×C₃×Dic₃	—	6	8	no	—
251	C₃×D₁₂	—	3	4	no	—
252	C₃×D₁₂	—	3	8	no	—
253	C₃×D₁₂	—	3	4	no	—
254	C₃×D₁₂	—	6	8	no	—
255	C₃×D₁₂	—	6	4	no	—
256	C₃×C₄×D₃	—	3	8	no	—
257	C₃×C₄×D₃	—	6	8	no	—
258	C₃×C₄×D₃	—	6	4	no	—
259	C₃×Dic₆	—	3	4	no	—
260	C₃×Dic₆	—	3	4	no	—
261	C₃²×C₈	—	2	8	no	—
262	C₃²×C₈	C₂²×D₃	1	8	yes	—
263	C₃²×C₈	C₂³×C₃	1	2	yes	—
264	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
265	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
266	C₃×C₃⋊C₈	—	3	4	no	—
267	C₃×C₃⋊C₈	—	3	4	no	—
268	#576	—	9	1	no	Sylow
269	C₂×C₃³	—	2	1	no	—
270	C₂×C₃³	—	4	1	no	—
271	C₂×C₃³	—	4	2	no	—
272	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
273	C₃×C₃⋊D₃	—	2	2	no	—
274	C₃×C₃⋊D₃	—	4	2	no	—
275	C₃×C₃⋊D₃	—	4	1	no	—
276	C₃×#41	—	2	4	no	—
277	C₃×#41	—	9	1	no	—
278	C₃×#41	—	9	2	no	—
279	C₃×#41	—	9	2	no	—
280	C₃×#41	—	9	1	no	—
281	C₃×#41	—	18	1	no	—
282	C₃×#41	—	18	1	no	—
283	C₃×#41	C₂×C₃×D₃	1	4	yes	complemented
284	C₃×#41	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
285	C₂×C₃×D₄	—	2	4	no	—
286	C₂×C₃×D₄	—	9	2	no	—
287	C₂×C₃×D₄	—	9	2	no	—
288	C₂×C₃×D₄	—	9	1	no	—
289	C₂×C₃×D₄	—	18	1	no	—
290	C₂×C₃×D₄	—	18	2	no	—
291	C₂×C₃×D₄	—	18	1	no	—
292	C₂×C₃×D₄	—	18	2	no	—
293	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	complemented
294	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
295	C₂×#67	—	6	8	no	—
296	#239	—	3	8	no	—
297	#237	—	3	8	no	—
298	#237	—	6	4	no	—
299	D₃×D₄	—	3	8	no	—
300	D₃×D₄	—	3	8	no	—
301	D₃×D₄	—	6	4	no	—
302	D₃×D₄	—	6	8	no	—
303	#235	—	3	4	no	—
304	#235	—	3	4	no	—
305	#235	—	6	4	no	—
306	C₂×D₁₂	—	3	4	no	—
307	C₂×D₁₂	—	6	4	no	—
308	C₃×Q₁₆	—	9	1	no	—
309	C₃×SD₁₆	—	2	8	no	—
310	C₃×SD₁₆	—	9	1	no	—
311	C₃×SD₁₆	—	9	1	no	—
312	C₃×SD₁₆	—	9	2	no	—
313	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	complemented
314	C₃×SD₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
315	C₃×D₈	—	2	8	no	—
316	C₃×D₈	—	9	2	no	—
317	C₃×D₈	—	9	1	no	—
318	C₃×D₈	—	9	2	no	—
319	C₃×D₈	—	9	2	no	—
320	C₃×D₈	C₂×C₃×D₃	1	8	yes	complemented
321	C₃×D₈	C₂×C₃⋊D₃	1	2	yes	complemented
322	C₃×M₁₆	—	2	4	no	—
323	C₃×M₁₆	—	9	2	no	—
324	C₃×M₁₆	C₂×C₃×D₃	1	4	yes	complemented
325	C₃×M₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
326	C₂×C₃×C₈	—	9	1	no	—
327	C₂×C₃×C₈	—	9	2	no	—
328	#216	—	3	4	no	—
329	#215	—	3	4	no	—
330	#214	—	3	4	no	—
331	#213	—	3	4	no	—
332	#213	—	3	8	no	—
333	#213	—	3	8	no	—
334	C₂×C₃⋊C₈	—	3	4	no	—
335	D₂₄	—	3	8	no	—
336	#204	—	3	8	no	—
337	ΓL(1,𝔽₂₅)	—	3	8	no	—
338	D₃×C₈	—	3	8	no	—
339	C₂²×C₃²	—	2	2	no	—
340	C₂²×C₃²	—	2	1	no	—
341	C₂²×C₃²	—	2	4	no	—
342	C₂²×C₃²	—	2	8	no	—
343	C₂²×C₃²	—	2	4	no	—
344	C₂²×C₃²	—	4	4	no	—
345	C₂²×C₃²	—	4	8	no	—
346	C₂²×C₃²	—	8	1	no	—
347	C₂²×C₃²	—	8	4	no	—
348	C₂²×C₃²	—	8	8	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	—	2	1	no	—
353	C₂×C₃⋊D₃	—	8	2	no	—
354	C₂×C₃⋊D₃	—	8	2	no	—
355	C₂×C₃⋊D₃	—	8	1	no	—
356	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
357	C₂×C₃×D₃	—	3	8	no	—
358	C₂×C₃×D₃	—	6	8	no	—
359	C₂×C₃×D₃	—	6	4	no	—
360	C₂×C₃×D₃	—	24	8	no	—
361	C₂×C₃×D₃	—	24	8	no	—
362	C₂×C₃×D₃	—	24	4	no	—
363	C₃²×C₄	—	2	1	no	—
364	C₃²×C₄	—	2	4	no	—
365	C₃²×C₄	—	2	4	no	—
366	C₃²×C₄	—	2	4	no	—
367	C₃²×C₄	—	4	4	no	—
368	C₃²×C₄	D₃×D₄	1	4	yes	—
369	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
370	C₃²×C₄	C₂³×D₃	1	4	yes	—
371	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
372	C₃⋊Dic₃	—	2	1	no	—
373	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
374	C₃×Dic₃	—	3	8	no	—
375	C₃×Dic₃	—	6	4	no	—
376	H(5,𝔽₂)	—	9	1	no	—
377	H(5,𝔽₂)	—	9	1	no	—
378	AGL(1,ℤ/8)	—	9	2	no	—
379	AGL(1,ℤ/8)	—	9	2	no	—
380	AGL(1,ℤ/8)	—	9	1	no	—
381	AGL(1,ℤ/8)	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
382	#135	—	9	1	no	—
383	#135	—	9	2	no	—
384	C₂×D₈	—	9	1	no	—
385	C₂×D₈	—	9	2	no	—
386	#131	—	9	1	no	—
387	C₃³	#576	1	1	yes	characteristic, complemented, Sylow
388	C₂³×C₃	—	2	4	no	—
389	C₂³×C₃	—	2	1	no	—
390	C₂³×C₃	—	4	4	no	—
391	C₂³×C₃	—	18	2	no	—
392	C₂³×C₃	—	18	2	no	—
393	C₂³×C₃	—	18	1	no	—
394	C₂²×D₃	—	6	8	no	—
395	C₂²×D₃	—	6	8	no	—
396	C₂²×D₃	—	6	4	no	—
397	C₃×Q₈	—	2	4	no	—
398	C₃×Q₈	—	9	1	no	—
399	C₃×Q₈	—	9	1	no	—
400	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
401	C₃×Q₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
402	C₃×D₄	—	2	4	no	—
403	C₃×D₄	—	2	1	no	—
404	C₃×D₄	—	2	4	no	—
405	C₃×D₄	—	2	1	no	—
406	C₃×D₄	—	2	4	no	—
407	C₃×D₄	—	2	8	no	—
408	C₃×D₄	—	4	4	no	—
409	C₃×D₄	—	4	4	no	—
410	C₃×D₄	—	9	2	no	—
411	C₃×D₄	—	9	2	no	—
412	C₃×D₄	—	9	1	no	—
413	C₃×D₄	—	9	1	no	—
414	C₃×D₄	—	18	2	no	—
415	C₃×D₄	—	18	2	no	—
416	C₃×D₄	—	18	2	no	—
417	C₃×D₄	—	18	2	no	—
418	C₃×D₄	—	18	1	no	—
419	C₃×D₄	—	18	1	no	—
420	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
421	C₃×D₄	C₂²×C₃×D₃	1	4	yes	—
422	C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
423	C₃×D₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
424	C₂×C₃×C₄	—	2	4	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	4	no	—
427	C₂×C₃×C₄	—	4	4	no	—
428	C₂×C₃×C₄	—	9	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	#67	—	6	8	no	—
438	#67	—	6	4	no	—
439	C₂×Dic₃	—	6	8	no	—
440	D₁₂	—	3	8	no	—
441	D₁₂	—	3	4	no	—
442	D₁₂	—	3	4	no	—
443	D₁₂	—	6	8	no	—
444	D₁₂	—	6	4	no	—
445	C₄×D₃	—	3	8	no	—
446	C₄×D₃	—	6	8	no	—
447	C₄×D₃	—	6	4	no	—
448	Dic₆	—	3	4	no	—
449	Dic₆	—	3	4	no	—
450	C₃×C₈	—	2	8	no	—
451	C₃×C₈	—	9	1	no	—
452	C₃×C₈	—	9	1	no	—
453	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
454	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
455	C₃⋊C₈	—	3	4	no	—
456	C₃⋊C₈	—	3	4	no	—
457	C₂×C₃²	—	2	1	no	—
458	C₂×C₃²	—	2	4	no	—
459	C₂×C₃²	—	2	4	no	—
460	C₂×C₃²	—	4	4	no	—
461	C₂×C₃²	—	4	1	no	—
462	C₂×C₃²	—	4	2	no	—
463	C₂×C₃²	—	4	4	no	—
464	C₂×C₃²	—	4	8	no	—
465	C₂×C₃²	—	8	4	no	—
466	C₂×C₃²	—	8	8	no	—
467	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
468	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
469	C₃⋊D₃	—	2	2	no	—
470	C₃⋊D₃	—	4	2	no	—
471	C₃⋊D₃	—	4	1	no	—
472	C₃×D₃	—	6	8	no	—
473	C₃×D₃	—	12	8	no	—
474	C₃×D₃	—	12	4	no	—
475	#41	—	9	1	no	—
476	#41	—	9	2	no	—
477	#41	—	9	2	no	—
478	#41	—	9	1	no	—
479	#41	—	18	1	no	—
480	#41	—	18	1	no	—
481	#41	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
482	C₂×D₄	—	9	2	no	—
483	C₂×D₄	—	9	2	no	—
484	C₂×D₄	—	9	1	no	—
485	C₂×D₄	—	18	1	no	—
486	C₂×D₄	—	18	2	no	—
487	C₂×D₄	—	18	1	no	—
488	C₂×D₄	—	18	2	no	—
489	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
490	Q₁₆	—	9	1	no	—
491	SD₁₆	—	9	1	no	—
492	SD₁₆	—	9	1	no	—
493	SD₁₆	—	9	2	no	—
494	SD₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
495	D₈	—	9	2	no	—
496	D₈	—	9	1	no	—
497	D₈	—	9	2	no	—
498	D₈	—	9	2	no	—
499	D₈	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
500	M₁₆	—	9	2	no	—
501	M₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
502	C₂×C₈	—	9	1	no	—
503	C₂×C₈	—	9	2	no	—
504	C₂²×C₃	—	2	8	no	—
505	C₂²×C₃	—	2	4	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	2	4	no	—
509	C₂²×C₃	—	4	4	no	—
510	C₂²×C₃	—	4	8	no	—
511	C₂²×C₃	—	8	4	no	—
512	C₂²×C₃	—	8	1	no	—
513	C₂²×C₃	—	8	8	no	—
514	C₂²×C₃	—	9	2	no	—
515	C₂²×C₃	—	18	2	no	—
516	C₂²×C₃	—	18	1	no	—
517	C₂²×C₃	—	72	1	no	—
518	C₂²×C₃	—	72	2	no	—
519	C₂²×C₃	—	72	2	no	—
520	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
521	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
522	C₂×D₃	—	3	8	no	—
523	C₂×D₃	—	6	8	no	—
524	C₂×D₃	—	6	4	no	—
525	C₂×D₃	—	24	8	no	—
526	C₂×D₃	—	24	8	no	—
527	C₂×D₃	—	24	4	no	—
528	C₃×C₄	—	2	4	no	—
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	4	no	—
531	C₃×C₄	—	2	4	no	—
532	C₃×C₄	—	4	4	no	—
533	C₃×C₄	—	9	2	no	—
534	C₃×C₄	—	18	1	no	—
535	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
536	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
537	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
538	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
539	Dic₃	—	3	8	no	—
540	Dic₃	—	6	4	no	—
541	C₃²	—	2	4	no	—
542	C₃²	#5774	1	4	yes	complemented
543	C₃²	C₃×#576	1	1	yes	characteristic, complemented
544	C₂³	—	2	1	no	—
545	C₂³	—	18	2	no	—
546	C₂³	—	18	2	no	—
547	C₂³	—	18	1	no	—
548	Q₈	—	9	1	no	—
549	Q₈	—	9	1	no	—
550	Q₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
551	D₄	—	2	1	no	—
552	D₄	—	2	1	no	—
553	D₄	—	9	2	no	—
554	D₄	—	9	2	no	—
555	D₄	—	9	1	no	—
556	D₄	—	9	1	no	—
557	D₄	—	18	2	no	—
558	D₄	—	18	2	no	—
559	D₄	—	18	2	no	—
560	D₄	—	18	2	no	—
561	D₄	—	18	1	no	—
562	D₄	—	18	1	no	—
563	D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
564	D₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	9	2	no	—
567	C₂×C₄	—	18	2	no	—
568	C₂×C₄	—	18	2	no	—
569	C₂×C₄	—	18	1	no	—
570	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
571	C₈	—	9	1	no	—
572	C₈	—	9	1	no	—
573	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
574	C₂×C₃	—	2	4	no	—
575	C₂×C₃	—	2	1	no	—
576	C₂×C₃	—	2	4	no	—
577	C₂×C₃	—	4	4	no	—
578	C₂×C₃	—	4	4	no	—
579	C₂×C₃	—	4	8	no	—
580	C₂×C₃	—	4	2	no	—
581	C₂×C₃	—	4	1	no	—
582	C₂×C₃	—	8	8	no	—
583	C₂×C₃	—	8	4	no	—
584	C₂×C₃	—	18	2	no	—
585	C₂×C₃	—	36	2	no	—
586	C₂×C₃	—	36	1	no	—
587	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
588	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
589	D₃	—	6	8	no	—
590	D₃	—	12	8	no	—
591	D₃	—	12	4	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	9	2	no	—
596	C₂²	—	18	2	no	—
597	C₂²	—	18	1	no	—
598	C₂²	—	72	1	no	—
599	C₂²	—	72	2	no	—
600	C₂²	—	72	2	no	—
601	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
602	C₄	—	2	1	no	—
603	C₄	—	9	2	no	—
604	C₄	—	18	1	no	—
605	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
606	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
607	C₃	—	2	4	no	—
608	C₃	C₃×#5774	1	4	yes	complemented
609	C₃	#10596245	1	1	yes	characteristic, direct product factor
610	C₂	—	2	1	no	—
611	C₂	—	4	2	no	—
612	C₂	—	4	1	no	—
613	C₂	—	18	2	no	—
614	C₂	—	36	2	no	—
615	C₂	—	36	1	no	—
616	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×AGL(1,ℤ/8)	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	C₃×AGL(1,ℤ/8)	C₃⋊D₃
hypocenter	C₃²	C₃×#576
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₃×#64366	C₂	semidirect
2. C₃×#64361	C₂	semidirect
3. C₃³×AGL(1,ℤ/8)	C₂	semidirect
4. C₃×#64159	C₂	semidirect
5. C₂×C₃×#3753	C₂	semidirect
6. C₃×#64125	C₂	semidirect
7. C₃×#64123	C₂	semidirect
8. C₃×#64120	C₂	semidirect
9. C₃×D₈×C₃⋊D₃	C₂	semidirect
10. C₃×#64117	C₂	semidirect
11. C₃×#64116	C₂	semidirect
12. #10596245	C₃	direct (N × H)
14. C₃³×#41	C₂²	semidirect
15. C₂×C₃³×D₄	C₂²	semidirect
17. C₃×#3832	C₂²	semidirect
19. C₃×#3830	C₂²	semidirect
22. C₃×D₄×C₃⋊D₃	C₂²	semidirect
23. C₃×D₄×C₃⋊D₃	C₂²	semidirect
26. C₃×#3828	C₂²	semidirect
28. C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	semidirect
29. C₃³×SD₁₆	C₂²	semidirect
30. C₃³×D₈	C₂²	semidirect
31. C₃³×M₁₆	C₂²	semidirect
32. C₃×#3756	C₂²	semidirect
33. C₃×#3755	C₂²	semidirect
34. C₃×#3754	C₂²	semidirect
35. C₃×#3753	C₂²	semidirect
36. C₃×#3753	C₂²	semidirect
37. C₃×#3753	C₂²	semidirect
38. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
39. C₃×#3745	C₂²	semidirect
40. C₃×#3744	C₂²	semidirect
41. C₃×#3743	C₂²	semidirect
42. C₃×C₈×C₃⋊D₃	C₂²	semidirect
43. #64366	C₂×C₃	semidirect
44. #64361	C₂×C₃	semidirect
48. C₃²×AGL(1,ℤ/8)	D₃	semidirect
49. C₃²×AGL(1,ℤ/8)	C₂×C₃	semidirect
50. #64159	C₂×C₃	semidirect
51. C₂×#3753	C₂×C₃	semidirect
52. #64125	C₂×C₃	semidirect
53. #64123	C₂×C₃	semidirect
54. #64120	C₂×C₃	semidirect
55. D₈×C₃⋊D₃	C₂×C₃	semidirect
56. #64117	C₂×C₃	semidirect
57. #64116	C₂×C₃	semidirect
99. C₃²×#41	C₂×D₃	semidirect
100. C₃²×#41	C₂²×C₃	semidirect
102. C₂×C₃²×D₄	C₂×D₃	semidirect
103. C₂×C₃²×D₄	C₂²×C₃	semidirect
105. #3832	C₂²×C₃	semidirect
107. #3830	C₂²×C₃	semidirect
110. D₄×C₃⋊D₃	C₂²×C₃	semidirect
111. D₄×C₃⋊D₃	C₂²×C₃	semidirect
114. #3828	C₂²×C₃	semidirect
116. C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	semidirect
131. C₃²×SD₁₆	C₂×D₃	semidirect
132. C₃²×SD₁₆	C₂²×C₃	semidirect
134. C₃²×D₈	C₂×D₃	semidirect
135. C₃²×D₈	C₂²×C₃	semidirect
137. C₃²×M₁₆	C₂×D₃	semidirect
138. C₃²×M₁₆	C₂²×C₃	semidirect
139. #3756	C₂²×C₃	semidirect
140. #3755	C₂²×C₃	semidirect
141. #3754	C₂²×C₃	semidirect
142. #3753	C₂²×C₃	semidirect
143. #3753	C₂²×C₃	semidirect
144. #3753	C₂²×C₃	semidirect
145. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
146. #3745	C₂²×C₃	semidirect
147. #3744	C₂²×C₃	semidirect
148. #3743	C₂²×C₃	semidirect
149. C₈×C₃⋊D₃	C₂²×C₃	semidirect
184. C₃×AGL(1,ℤ/8)	C₃×D₃	semidirect
185. C₃×AGL(1,ℤ/8)	C₃⋊D₃	semidirect
283. C₃×#41	C₂×C₃×D₃	semidirect
284. C₃×#41	C₂×C₃⋊D₃	semidirect
293. C₂×C₃×D₄	C₂×C₃×D₃	semidirect
294. C₂×C₃×D₄	C₂×C₃⋊D₃	semidirect
313. C₃×SD₁₆	C₂×C₃×D₃	semidirect
314. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
320. C₃×D₈	C₂×C₃×D₃	semidirect
321. C₃×D₈	C₂×C₃⋊D₃	semidirect
324. C₃×M₁₆	C₂×C₃×D₃	semidirect
325. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
381. AGL(1,ℤ/8)	C₃×C₃⋊D₃	semidirect
387. C₃³	#576	semidirect
481. #41	C₂×C₃×C₃⋊D₃	semidirect
489. C₂×D₄	C₂×C₃×C₃⋊D₃	semidirect
494. SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
499. D₈	C₂×C₃×C₃⋊D₃	semidirect
501. M₁₆	C₂×C₃×C₃⋊D₃	semidirect
542. C₃²	#5774	semidirect
543. C₃²	C₃×#576	semidirect
608. C₃	C₃×#5774	semidirect
609. C₃	#10596245	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×#64366	2
C₃×#64361	2
C₃³×AGL(1,ℤ/8)	2
C₃×#64159	2
C₂×C₃×#3753	2
C₃×#64125	2
C₃×#64123	2
C₃×#64120	2
C₃×D₈×C₃⋊D₃	2
C₃×#64117	2
C₃×#64116	2
#10596245	3
C₃×#5774	3

Subgroups — C3×#10596245 #13179525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596245 #13179525