Subgroups — C₃×C₃⋊D₃×#135 #13179518

Order 1728.

1844 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
2	C₃³×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64159	C₂	1	2	yes	maximal, complemented
4	C₃×#64128	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Q₁₆×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64125	C₂	1	2	yes	maximal, complemented
7	C₃×SD₁₆×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
8	C₃×#64121	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#64113	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃⋊D₃×#135	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₃×D₃×#135	—	3	4	no	maximal
14	C₃³×#41	C₂²	1	2	yes	complemented
15	C₃×#3832	C₂²	1	2	yes	complemented
16	C₃×Q₈×C₃⋊D₃	C₂²	1	2	yes	—
17	C₃×#3830	—	2	2	no	—
18	C₃×#3830	C₂²	1	2	yes	complemented
19	C₃×D₄×C₃⋊D₃	—	2	2	no	—
20	C₃×D₄×C₃⋊D₃	C₂²	1	2	yes	—
21	C₃×#3828	—	2	2	no	—
22	C₃×#3828	C₂²	1	2	yes	complemented
23	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
24	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
25	C₃³×Q₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₃³×SD₁₆	C₂²	1	2	yes	complemented
27	C₃³×D₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×#3756	C₂²	1	2	yes	complemented
30	C₃×#3755	C₂²	1	2	yes	complemented
31	C₃×#3754	C₂²	1	2	yes	complemented
32	C₃×#3753	C₂²	1	2	yes	complemented
33	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3746	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3745	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3744	C₂²	1	2	yes	complemented
37	C₃×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
38	C₃×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
39	C₃×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
41	#41×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
42	C₃×D₃×#41	—	3	8	no	—
43	C₃²×#135	—	2	4	no	—
44	C₃²×#135	D₃	1	4	yes	complemented
45	C₃²×#135	C₂×C₃	1	1	yes	characteristic, complemented
46	#64159	C₂×C₃	1	2	yes	complemented
47	#64128	C₂×C₃	1	1	yes	characteristic, complemented
48	Q₁₆×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
49	#64125	C₂×C₃	1	2	yes	complemented
50	SD₁₆×C₃⋊D₃	C₂×C₃	1	2	yes	complemented
51	#64121	C₂×C₃	1	1	yes	characteristic, complemented
52	D₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
53	#64113	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#950	—	3	8	no	—
56	C₃×#919	—	3	4	no	—
57	C₃×D₃×Q₁₆	—	3	4	no	—
58	C₃×#916	—	3	8	no	—
59	C₃×D₃×SD₁₆	—	3	8	no	—
60	C₃×#912	—	3	4	no	—
61	C₃×D₃×D₈	—	3	4	no	—
62	C₃×#904	—	3	4	no	—
63	C₂×C₃×D₃×C₈	—	3	4	no	—
64	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
65	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
66	C₃³×Q₈	C₂³	1	2	yes	—
67	C₃³×D₄	—	2	2	no	—
68	C₃³×D₄	C₂³	1	2	yes	—
69	C₂×C₃³×C₄	—	2	2	no	—
70	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
71	C₃×#638	—	2	2	no	—
72	C₃×#638	—	2	2	no	—
73	C₃×#638	—	2	2	no	—
74	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
75	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
76	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
77	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	2	yes	—
78	C₃×C₄×C₃⋊D₃	—	2	2	no	—
79	C₃×C₄×C₃⋊D₃	—	2	2	no	—
80	C₃×C₄×C₃⋊D₃	—	2	2	no	—
81	C₃×C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
82	C₃×C₄×C₃⋊D₃	D₄	1	1	yes	characteristic
83	C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
84	C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
85	C₃×#634	—	2	2	no	—
86	C₃×#634	C₂³	1	2	yes	—
87	C₃³×C₈	C₂³	1	1	yes	characteristic
88	C₃³×C₈	C₂³	1	1	yes	characteristic
89	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
90	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
91	C₂×C₃×#135	—	9	1	no	—
92	D₃×#135	—	3	4	no	—
93	C₃²×#41	—	2	8	no	—
94	C₃²×#41	C₂×D₃	1	8	yes	complemented
95	C₃²×#41	C₂²×C₃	1	2	yes	complemented
96	#3832	C₂²×C₃	1	2	yes	complemented
97	Q₈×C₃⋊D₃	C₂²×C₃	1	2	yes	—
98	#3830	—	2	2	no	—
99	#3830	C₂²×C₃	1	2	yes	complemented
100	D₄×C₃⋊D₃	—	2	2	no	—
101	D₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
102	#3828	—	2	2	no	—
103	#3828	C₂²×C₃	1	2	yes	complemented
104	C₂×C₄×C₃⋊D₃	—	2	2	no	—
105	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
106	C₃×#239	—	3	8	no	—
107	C₃×D₃×Q₈	—	3	8	no	—
108	C₃×#237	—	3	8	no	—
109	C₃×#237	—	6	8	no	—
110	C₃×D₃×D₄	—	3	8	no	—
111	C₃×D₃×D₄	—	6	8	no	—
112	C₃×#235	—	3	8	no	—
113	C₃×#235	—	6	8	no	—
114	C₂×C₃×C₄×D₃	—	3	4	no	—
115	C₂×C₃×C₄×D₃	—	6	8	no	—
116	C₃²×Q₁₆	—	2	4	no	—
117	C₃²×Q₁₆	C₂×D₃	1	4	yes	complemented
118	C₃²×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₃²×SD₁₆	—	2	8	no	—
120	C₃²×SD₁₆	C₂×D₃	1	8	yes	complemented
121	C₃²×SD₁₆	C₂²×C₃	1	2	yes	complemented
122	C₃²×D₈	—	2	4	no	—
123	C₃²×D₈	C₂×D₃	1	4	yes	complemented
124	C₃²×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×C₃²×C₈	—	2	4	no	—
126	C₂×C₃²×C₈	C₂×D₃	1	4	yes	complemented
127	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
128	#3756	C₂²×C₃	1	2	yes	complemented
129	#3755	C₂²×C₃	1	2	yes	complemented
130	#3754	C₂²×C₃	1	2	yes	complemented
131	#3753	C₂²×C₃	1	2	yes	complemented
132	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic, complemented
133	#3746	C₂²×C₃	1	1	yes	characteristic, complemented
134	#3745	C₂²×C₃	1	1	yes	characteristic, complemented
135	#3744	C₂²×C₃	1	2	yes	complemented
136	C₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
137	C₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
138	C₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
139	C₈×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₃×#216	—	3	8	no	—
141	C₃×#215	—	3	8	no	—
142	C₃×#214	—	3	8	no	—
143	C₃×#213	—	3	8	no	—
144	C₂×C₃×C₃⋊C₈	—	3	4	no	—
145	C₃×Dic₁₂	—	3	4	no	—
146	C₃×D₂₄	—	3	4	no	—
147	C₃×#204	—	3	8	no	—
148	C₃×D₃×C₈	—	3	4	no	—
149	C₃×D₃×C₈	—	3	4	no	—
150	C₃×D₃×C₈	—	3	4	no	—
151	C₃×D₃×C₈	—	3	4	no	—
152	C₂²×C₃³	—	2	2	no	—
153	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₃⋊D₃	—	2	2	no	—
155	C₂×C₃×C₃⋊D₃	—	2	2	no	—
156	C₂×C₃×C₃⋊D₃	—	4	4	no	—
157	C₂×C₃×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
159	C₃³×C₄	—	2	2	no	—
160	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
161	C₃³×C₄	C₂⁴	1	1	yes	characteristic
162	C₃×C₃⋊Dic₃	—	2	2	no	—
163	C₃×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
164	C₃×C₃⋊Dic₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₃×#41	—	9	2	no	—
166	D₃×#41	—	3	8	no	—
167	C₃×#135	—	2	4	no	—
168	C₃×#135	—	9	2	no	—
169	C₃×#135	—	9	1	no	—
170	C₃×#135	—	9	2	no	—
171	C₃×#135	—	9	1	no	—
172	C₃×#135	—	9	1	no	—
173	C₃×#135	C₃×D₃	1	4	yes	complemented
174	C₃×#135	C₃⋊D₃	1	1	yes	characteristic, direct product factor
175	C₂×C₃×Q₁₆	—	9	1	no	—
176	C₂×C₃×SD₁₆	—	9	2	no	—
177	C₂×C₃×D₈	—	9	1	no	—
178	C₂²×C₃×C₈	—	9	1	no	—
179	#950	—	3	8	no	—
180	#919	—	3	4	no	—
181	D₃×Q₁₆	—	3	4	no	—
182	#916	—	3	8	no	—
183	D₃×SD₁₆	—	3	8	no	—
184	#912	—	3	4	no	—
185	D₃×D₈	—	3	4	no	—
186	#904	—	3	4	no	—
187	C₂×D₃×C₈	—	3	4	no	—
188	C₂²×C₃⋊D₃	—	2	2	no	—
189	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
190	C₂²×C₃×D₃	—	3	4	no	—
191	C₂²×C₃×D₃	—	6	8	no	—
192	C₃²×Q₈	—	2	8	no	—
193	C₃²×Q₈	C₂²×D₃	1	8	yes	—
194	C₃²×Q₈	C₂³×C₃	1	2	yes	—
195	C₃²×D₄	—	2	2	no	—
196	C₃²×D₄	—	2	8	no	—
197	C₃²×D₄	—	2	8	no	—
198	C₃²×D₄	—	4	8	no	—
199	C₃²×D₄	C₂²×D₃	1	8	yes	—
200	C₃²×D₄	C₂³×C₃	1	2	yes	—
201	C₂×C₃²×C₄	—	2	2	no	—
202	C₂×C₃²×C₄	—	2	4	no	—
203	C₂×C₃²×C₄	—	2	8	no	—
204	C₂×C₃²×C₄	—	4	8	no	—
205	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
206	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
207	#638	—	2	2	no	—
208	#638	—	2	2	no	—
209	#638	—	2	2	no	—
210	C₂×C₃⋊Dic₃	—	2	2	no	—
211	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
212	C₄⋊(C₃⋊D₃)	—	2	2	no	—
213	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	2	yes	—
214	C₄×C₃⋊D₃	—	2	2	no	—
215	C₄×C₃⋊D₃	—	2	2	no	—
216	C₄×C₃⋊D₃	—	2	2	no	—
217	C₄×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
218	C₄×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
219	C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
220	C₄×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
221	#634	—	2	2	no	—
222	#634	C₂³×C₃	1	2	yes	—
223	C₃×#67	—	6	8	no	—
224	C₃×#67	—	6	8	no	—
225	C₃×#67	—	6	8	no	—
226	C₂×C₃×Dic₃	—	3	4	no	—
227	C₂×C₃×Dic₃	—	6	8	no	—
228	C₃×D₁₂	—	3	8	no	—
229	C₃×D₁₂	—	6	8	no	—
230	C₃×C₄×D₃	—	3	4	no	—
231	C₃×C₄×D₃	—	3	4	no	—
232	C₃×C₄×D₃	—	3	4	no	—
233	C₃×C₄×D₃	—	3	4	no	—
234	C₃×C₄×D₃	—	6	8	no	—
235	C₃×C₄×D₃	—	6	8	no	—
236	C₃×C₄×D₃	—	6	8	no	—
237	C₃×Dic₆	—	3	8	no	—
238	C₃×Dic₆	—	6	8	no	—
239	C₃²×C₈	—	2	4	no	—
240	C₃²×C₈	—	2	4	no	—
241	C₃²×C₈	C₂²×D₃	1	4	yes	—
242	C₃²×C₈	C₂²×D₃	1	4	yes	—
243	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
244	C₃²×C₈	C₂³×C₃	1	1	yes	characteristic
245	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
246	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	1	yes	characteristic
247	C₃×C₃⋊C₈	—	3	4	no	—
248	C₃×C₃⋊C₈	—	3	4	no	—
249	C₂×#135	—	9	1	no	Sylow
250	C₂×C₃³	—	2	1	no	—
251	C₂×C₃³	—	4	2	no	—
252	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
253	C₃×C₃⋊D₃	—	2	1	no	—
254	C₃×C₃⋊D₃	—	4	2	no	—
255	C₃×C₃⋊D₃	#135	1	2	yes	direct product factor
256	C₃×#41	—	2	8	no	—
257	C₃×#41	—	9	2	no	—
258	C₃×#41	—	9	2	no	—
259	C₃×#41	—	9	2	no	—
260	C₃×#41	—	18	2	no	—
261	C₃×#41	—	18	2	no	—
262	C₃×#41	C₂×C₃×D₃	1	8	yes	complemented
263	C₃×#41	C₂×C₃⋊D₃	1	2	yes	complemented
264	C₂×C₃×Q₈	—	9	2	no	—
265	C₂×C₃×D₄	—	9	2	no	—
266	C₂×C₃×D₄	—	18	2	no	—
267	C₂²×C₃×C₄	—	9	1	no	—
268	C₂²×C₃×C₄	—	18	2	no	—
269	#239	—	3	8	no	—
270	D₃×Q₈	—	3	8	no	—
271	#237	—	3	8	no	—
272	#237	—	6	8	no	—
273	D₃×D₄	—	3	8	no	—
274	D₃×D₄	—	6	8	no	—
275	#235	—	3	8	no	—
276	#235	—	6	8	no	—
277	C₂×C₄×D₃	—	3	4	no	—
278	C₂×C₄×D₃	—	6	8	no	—
279	C₃×Q₁₆	—	2	4	no	—
280	C₃×Q₁₆	—	9	2	no	—
281	C₃×Q₁₆	—	9	1	no	—
282	C₃×Q₁₆	C₂×C₃×D₃	1	4	yes	complemented
283	C₃×Q₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
284	C₃×SD₁₆	—	2	8	no	—
285	C₃×SD₁₆	—	9	2	no	—
286	C₃×SD₁₆	—	9	2	no	—
287	C₃×SD₁₆	—	9	2	no	—
288	C₃×SD₁₆	C₂×C₃×D₃	1	8	yes	complemented
289	C₃×SD₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
290	C₃×D₈	—	2	4	no	—
291	C₃×D₈	—	9	2	no	—
292	C₃×D₈	—	9	1	no	—
293	C₃×D₈	C₂×C₃×D₃	1	4	yes	complemented
294	C₃×D₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
295	C₂×C₃×C₈	—	2	4	no	—
296	C₂×C₃×C₈	—	9	1	no	—
297	C₂×C₃×C₈	—	9	1	no	—
298	C₂×C₃×C₈	—	9	1	no	—
299	C₂×C₃×C₈	—	9	1	no	—
300	C₂×C₃×C₈	—	9	1	no	—
301	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
302	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
303	#216	—	3	8	no	—
304	#215	—	3	8	no	—
305	#214	—	3	8	no	—
306	#213	—	3	8	no	—
307	C₂×C₃⋊C₈	—	3	4	no	—
308	Dic₁₂	—	3	4	no	—
309	D₂₄	—	3	4	no	—
310	#204	—	3	8	no	—
311	D₃×C₈	—	3	4	no	—
312	D₃×C₈	—	3	4	no	—
313	D₃×C₈	—	3	4	no	—
314	D₃×C₈	—	3	4	no	—
315	C₂²×C₃²	—	2	2	no	—
316	C₂²×C₃²	—	2	4	no	—
317	C₂²×C₃²	—	2	8	no	—
318	C₂²×C₃²	—	4	8	no	—
319	C₂²×C₃²	D₃×D₄	1	4	yes	—
320	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂×C₃⋊D₃	—	2	2	no	—
322	C₂×C₃⋊D₃	—	2	2	no	—
323	C₂×C₃⋊D₃	—	4	4	no	—
324	C₂×C₃⋊D₃	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₃⋊D₃	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₃×D₃	—	3	4	no	—
327	C₂×C₃×D₃	—	3	4	no	—
328	C₂×C₃×D₃	—	6	8	no	—
329	C₂×C₃×D₃	—	6	8	no	—
330	C₂×C₃×D₃	—	12	16	no	—
331	C₃²×C₄	—	2	2	no	—
332	C₃²×C₄	—	2	4	no	—
333	C₃²×C₄	—	2	4	no	—
334	C₃²×C₄	—	2	8	no	—
335	C₃²×C₄	—	4	8	no	—
336	C₃²×C₄	D₃×D₄	1	4	yes	—
337	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
338	C₃²×C₄	C₂³×D₃	1	4	yes	—
339	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
340	C₃⋊Dic₃	—	2	2	no	—
341	C₃⋊Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
342	C₃⋊Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
343	C₃×Dic₃	—	3	4	no	—
344	C₃×Dic₃	—	3	4	no	—
345	C₃×Dic₃	—	6	8	no	—
346	C₂×#41	—	9	2	no	—
347	#135	—	9	2	no	—
348	#135	—	9	1	no	—
349	#135	—	9	2	no	—
350	#135	—	9	1	no	—
351	#135	—	9	1	no	—
352	#135	C₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
353	C₂×Q₁₆	—	9	1	no	—
354	C₂×SD₁₆	—	9	2	no	—
355	C₂×D₈	—	9	1	no	—
356	C₂²×C₈	—	9	1	no	—
357	C₃³	C₂×#135	1	1	yes	characteristic, complemented, Sylow
358	C₂³×C₃	—	9	1	no	—
359	C₂³×C₃	—	18	2	no	—
360	C₂²×D₃	—	3	4	no	—
361	C₂²×D₃	—	6	8	no	—
362	C₃×Q₈	—	2	8	no	—
363	C₃×Q₈	—	9	2	no	—
364	C₃×Q₈	—	18	2	no	—
365	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	—
366	C₃×Q₈	C₂²×C₃⋊D₃	1	2	yes	—
367	C₃×D₄	—	2	8	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	2	8	no	—
370	C₃×D₄	—	4	8	no	—
371	C₃×D₄	—	9	2	no	—
372	C₃×D₄	—	18	2	no	—
373	C₃×D₄	—	18	2	no	—
374	C₃×D₄	—	18	2	no	—
375	C₃×D₄	—	18	2	no	—
376	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
377	C₃×D₄	C₂²×C₃⋊D₃	1	2	yes	—
378	C₂×C₃×C₄	—	2	8	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	4	no	—
381	C₂×C₃×C₄	—	4	8	no	—
382	C₂×C₃×C₄	—	9	1	no	—
383	C₂×C₃×C₄	—	9	1	no	—
384	C₂×C₃×C₄	—	9	1	no	—
385	C₂×C₃×C₄	—	9	1	no	—
386	C₂×C₃×C₄	—	9	1	no	—
387	C₂×C₃×C₄	—	18	2	no	—
388	C₂×C₃×C₄	—	18	2	no	—
389	C₂×C₃×C₄	—	18	2	no	—
390	C₂×C₃×C₄	—	18	2	no	—
391	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
392	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
393	#67	—	6	8	no	—
394	#67	—	6	8	no	—
395	#67	—	6	8	no	—
396	C₂×Dic₃	—	3	4	no	—
397	C₂×Dic₃	—	6	8	no	—
398	D₁₂	—	3	8	no	—
399	D₁₂	—	6	8	no	—
400	C₄×D₃	—	3	4	no	—
401	C₄×D₃	—	3	4	no	—
402	C₄×D₃	—	3	4	no	—
403	C₄×D₃	—	3	4	no	—
404	C₄×D₃	—	6	8	no	—
405	C₄×D₃	—	6	8	no	—
406	C₄×D₃	—	6	8	no	—
407	Dic₆	—	3	8	no	—
408	Dic₆	—	6	8	no	—
409	C₃×C₈	—	2	4	no	—
410	C₃×C₈	—	2	4	no	—
411	C₃×C₈	—	9	1	no	—
412	C₃×C₈	—	9	1	no	—
413	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
414	C₃×C₈	C₂²×C₃×D₃	1	4	yes	—
415	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
416	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
417	C₃⋊C₈	—	3	4	no	—
418	C₃⋊C₈	—	3	4	no	—
419	C₂×C₃²	—	2	1	no	—
420	C₂×C₃²	—	2	4	no	—
421	C₂×C₃²	—	2	4	no	—
422	C₂×C₃²	—	4	4	no	—
423	C₂×C₃²	—	4	2	no	—
424	C₂×C₃²	—	4	8	no	—
425	C₂×C₃²	—	8	8	no	—
426	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
427	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
428	C₃⋊D₃	—	2	1	no	—
429	C₃⋊D₃	—	4	2	no	—
430	C₃⋊D₃	C₃×#135	1	2	yes	direct product factor
431	C₃×D₃	—	3	8	no	—
432	C₃×D₃	—	6	4	no	—
433	C₃×D₃	—	12	8	no	—
434	#41	—	9	2	no	—
435	#41	—	9	2	no	—
436	#41	—	9	2	no	—
437	#41	—	18	2	no	—
438	#41	—	18	2	no	—
439	#41	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
440	C₂×Q₈	—	9	2	no	—
441	C₂×D₄	—	9	2	no	—
442	C₂×D₄	—	18	2	no	—
443	C₂²×C₄	—	9	1	no	—
444	C₂²×C₄	—	18	2	no	—
445	Q₁₆	—	9	2	no	—
446	Q₁₆	—	9	1	no	—
447	Q₁₆	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
448	SD₁₆	—	9	2	no	—
449	SD₁₆	—	9	2	no	—
450	SD₁₆	—	9	2	no	—
451	SD₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
452	D₈	—	9	2	no	—
453	D₈	—	9	1	no	—
454	D₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
455	C₂×C₈	—	9	1	no	—
456	C₂×C₈	—	9	1	no	—
457	C₂×C₈	—	9	1	no	—
458	C₂×C₈	—	9	1	no	—
459	C₂×C₈	—	9	1	no	—
460	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
461	C₂²×C₃	—	2	8	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	4	no	—
464	C₂²×C₃	—	4	8	no	—
465	C₂²×C₃	—	9	1	no	—
466	C₂²×C₃	—	9	1	no	—
467	C₂²×C₃	—	18	2	no	—
468	C₂²×C₃	—	18	2	no	—
469	C₂²×C₃	—	36	4	no	—
470	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
471	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
472	C₂×D₃	—	3	4	no	—
473	C₂×D₃	—	3	4	no	—
474	C₂×D₃	—	6	8	no	—
475	C₂×D₃	—	6	8	no	—
476	C₂×D₃	—	12	16	no	—
477	C₃×C₄	—	2	8	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	4	no	—
480	C₃×C₄	—	2	4	no	—
481	C₃×C₄	—	4	8	no	—
482	C₃×C₄	—	9	1	no	—
483	C₃×C₄	—	9	1	no	—
484	C₃×C₄	—	18	2	no	—
485	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
486	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
487	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
488	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
489	Dic₃	—	3	4	no	—
490	Dic₃	—	3	4	no	—
491	Dic₃	—	6	8	no	—
492	C₃²	—	2	4	no	—
493	C₃²	D₃×#135	1	4	yes	complemented
494	C₃²	C₂×C₃×#135	1	1	yes	characteristic, complemented
495	C₂³	—	9	1	no	—
496	C₂³	—	18	2	no	—
497	Q₈	—	9	2	no	—
498	Q₈	—	18	2	no	—
499	Q₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
500	D₄	—	2	2	no	—
501	D₄	—	9	2	no	—
502	D₄	—	18	2	no	—
503	D₄	—	18	2	no	—
504	D₄	—	18	2	no	—
505	D₄	—	18	2	no	—
506	D₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	9	1	no	—
509	C₂×C₄	—	9	1	no	—
510	C₂×C₄	—	9	1	no	—
511	C₂×C₄	—	9	1	no	—
512	C₂×C₄	—	9	1	no	—
513	C₂×C₄	—	18	2	no	—
514	C₂×C₄	—	18	2	no	—
515	C₂×C₄	—	18	2	no	—
516	C₂×C₄	—	18	2	no	—
517	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
518	C₈	—	9	1	no	—
519	C₈	—	9	1	no	—
520	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
521	C₈	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
522	C₂×C₃	—	2	4	no	—
523	C₂×C₃	—	2	1	no	—
524	C₂×C₃	—	2	4	no	—
525	C₂×C₃	—	4	4	no	—
526	C₂×C₃	—	4	8	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	—	8	8	no	—
529	C₂×C₃	—	9	2	no	—
530	C₂×C₃	—	18	1	no	—
531	C₂×C₃	—	36	2	no	—
532	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
533	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
534	D₃	—	3	8	no	—
535	D₃	—	6	4	no	—
536	D₃	—	12	8	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	9	1	no	—
539	C₂²	—	9	1	no	—
540	C₂²	—	18	2	no	—
541	C₂²	—	18	2	no	—
542	C₂²	—	36	4	no	—
543	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
544	C₄	—	2	2	no	—
545	C₄	—	9	1	no	—
546	C₄	—	9	1	no	—
547	C₄	—	18	2	no	—
548	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
549	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
550	C₃	—	2	4	no	—
551	C₃	C₃×D₃×#135	1	4	yes	complemented
552	C₃	C₃⋊D₃×#135	1	1	yes	characteristic, direct product factor
553	C₂	—	2	1	no	—
554	C₂	—	4	2	no	—
555	C₂	—	9	2	no	—
556	C₂	—	18	1	no	—
557	C₂	—	36	2	no	—
558	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	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	C₂×C₃×#135
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×#135

Complements

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

N	H ≅ G/N	type
1. C₃×#41×C₃⋊D₃	C₂	semidirect
2. C₃³×#135	C₂	semidirect
3. C₃×#64159	C₂	semidirect
4. C₃×#64128	C₂	semidirect
5. C₃×Q₁₆×C₃⋊D₃	C₂	semidirect
6. C₃×#64125	C₂	semidirect
7. C₃×SD₁₆×C₃⋊D₃	C₂	semidirect
8. C₃×#64121	C₂	semidirect
9. C₃×D₈×C₃⋊D₃	C₂	semidirect
10. C₃×#64113	C₂	semidirect
11. C₂×C₃×C₈×C₃⋊D₃	C₂	semidirect
12. C₃⋊D₃×#135	C₃	direct (N × H)
14. C₃³×#41	C₂²	semidirect
15. C₃×#3832	C₂²	semidirect
18. C₃×#3830	C₂²	semidirect
22. C₃×#3828	C₂²	semidirect
25. C₃³×Q₁₆	C₂²	semidirect
26. C₃³×SD₁₆	C₂²	semidirect
27. C₃³×D₈	C₂²	semidirect
28. C₂×C₃³×C₈	C₂²	semidirect
29. C₃×#3756	C₂²	semidirect
30. C₃×#3755	C₂²	semidirect
31. C₃×#3754	C₂²	semidirect
32. C₃×#3753	C₂²	semidirect
33. C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
34. C₃×#3746	C₂²	semidirect
35. C₃×#3745	C₂²	semidirect
36. C₃×#3744	C₂²	semidirect
39. C₃×C₈×C₃⋊D₃	C₂²	semidirect
40. C₃×C₈×C₃⋊D₃	C₂²	semidirect
41. #41×C₃⋊D₃	C₂×C₃	semidirect
44. C₃²×#135	D₃	semidirect
45. C₃²×#135	C₂×C₃	semidirect
46. #64159	C₂×C₃	semidirect
47. #64128	C₂×C₃	semidirect
48. Q₁₆×C₃⋊D₃	C₂×C₃	semidirect
49. #64125	C₂×C₃	semidirect
50. SD₁₆×C₃⋊D₃	C₂×C₃	semidirect
51. #64121	C₂×C₃	semidirect
52. D₈×C₃⋊D₃	C₂×C₃	semidirect
53. #64113	C₂×C₃	semidirect
54. C₂×C₈×C₃⋊D₃	C₂×C₃	semidirect
94. C₃²×#41	C₂×D₃	semidirect
95. C₃²×#41	C₂²×C₃	semidirect
96. #3832	C₂²×C₃	semidirect
99. #3830	C₂²×C₃	semidirect
103. #3828	C₂²×C₃	semidirect
117. C₃²×Q₁₆	C₂×D₃	semidirect
118. C₃²×Q₁₆	C₂²×C₃	semidirect
120. C₃²×SD₁₆	C₂×D₃	semidirect
121. C₃²×SD₁₆	C₂²×C₃	semidirect
123. C₃²×D₈	C₂×D₃	semidirect
124. C₃²×D₈	C₂²×C₃	semidirect
126. C₂×C₃²×C₈	C₂×D₃	semidirect
127. C₂×C₃²×C₈	C₂²×C₃	semidirect
128. #3756	C₂²×C₃	semidirect
129. #3755	C₂²×C₃	semidirect
130. #3754	C₂²×C₃	semidirect
131. #3753	C₂²×C₃	semidirect
132. C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	semidirect
133. #3746	C₂²×C₃	semidirect
134. #3745	C₂²×C₃	semidirect
135. #3744	C₂²×C₃	semidirect
138. C₈×C₃⋊D₃	C₂²×C₃	semidirect
139. C₈×C₃⋊D₃	C₂²×C₃	semidirect
173. C₃×#135	C₃×D₃	semidirect
174. C₃×#135	C₃⋊D₃	direct (N × H)
255. C₃×C₃⋊D₃	#135	direct (N × H)
262. C₃×#41	C₂×C₃×D₃	semidirect
263. C₃×#41	C₂×C₃⋊D₃	semidirect
282. C₃×Q₁₆	C₂×C₃×D₃	semidirect
283. C₃×Q₁₆	C₂×C₃⋊D₃	semidirect
288. C₃×SD₁₆	C₂×C₃×D₃	semidirect
289. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
293. C₃×D₈	C₂×C₃×D₃	semidirect
294. C₃×D₈	C₂×C₃⋊D₃	semidirect
301. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
302. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
352. #135	C₃×C₃⋊D₃	direct (N × H)
357. C₃³	C₂×#135	semidirect
430. C₃⋊D₃	C₃×#135	direct (N × H)
439. #41	C₂×C₃×C₃⋊D₃	semidirect
447. Q₁₆	C₂×C₃×C₃⋊D₃	semidirect
451. SD₁₆	C₂×C₃×C₃⋊D₃	semidirect
454. D₈	C₂×C₃×C₃⋊D₃	semidirect
460. C₂×C₈	C₂×C₃×C₃⋊D₃	semidirect
493. C₃²	D₃×#135	semidirect
494. C₃²	C₂×C₃×#135	semidirect
551. C₃	C₃×D₃×#135	semidirect
552. C₃	C₃⋊D₃×#135	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×#41×C₃⋊D₃	2
C₃³×#135	2
C₃×#64159	2
C₃×#64128	2
C₃×Q₁₆×C₃⋊D₃	2
C₃×#64125	2
C₃×SD₁₆×C₃⋊D₃	2
C₃×#64121	2
C₃×D₈×C₃⋊D₃	2
C₃×#64113	2
C₂×C₃×C₈×C₃⋊D₃	2
C₃⋊D₃×#135	3
C₃×D₃×#135	3

Subgroups — C3×C3⋊D3×#135 #13179518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃⋊D₃×#135 #13179518