Subgroups — C₃×#79165 #11859974

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
2	C₃×#5522	C₂	1	2	yes	maximal, complemented
3	C₃²×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5002	C₂	1	2	yes	maximal, complemented
6	C₃×#4873	C₂	1	2	yes	maximal, complemented
7	C₃×#4872	C₂	1	2	yes	maximal, complemented
8	C₃×#4852	C₂	1	4	yes	maximal, complemented
9	C₃×C₄×#135	—	3	1	no	maximal
10	#79165	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	2	yes	—
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₃²×#117	C₂²	1	2	yes	—
14	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
17	C₃×#904	C₄	1	8	yes	complemented
18	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×#204	C₂²	1	2	yes	—
20	C₃×#893	C₂²	1	4	yes	—
21	C₃×#887	C₂²	1	4	yes	—
22	C₃×#67⋊C₄	—	2	4	no	—
23	C₃×#872	—	2	2	no	—
24	C₃×C₄²×D₃	—	2	2	no	—
25	C₃²×#107	C₂²	1	2	yes	—
26	C₃²×#106	C₂²	1	2	yes	—
27	C₃×C₈×Dic₃	C₂²	1	2	yes	—
28	C₃×C₈×Dic₃	C₂²	1	2	yes	—
29	C₃×#810	C₂²	1	4	yes	—
30	C₃×#809	C₂²	1	4	yes	—
31	C₂×C₃×#135	—	3	1	no	—
32	C₃×C₄×#41	—	3	2	no	—
33	C₂×#904	C₂×C₃	1	1	yes	characteristic
34	#5522	C₂×C₃	1	2	yes	complemented
35	C₃×C₄×Q₁₆	—	3	2	no	—
36	C₃×C₄×SD₁₆	—	3	4	no	—
37	C₃×C₄×D₈	—	3	2	no	—
38	C₃×#427	—	2	1	no	—
39	C₃×#427	D₃	1	1	yes	characteristic, complemented
40	C₃×#427	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×#416	—	3	2	no	—
42	C₂×C₃×C₄×C₈	—	3	1	no	—
43	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
44	#5002	C₂×C₃	1	2	yes	complemented
45	#4873	C₂×C₃	1	2	yes	complemented
46	#4872	C₂×C₃	1	2	yes	complemented
47	#4852	C₂×C₃	1	4	yes	complemented
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃×#67	—	2	2	no	—
50	C₂²×C₃×Dic₃	D₄	1	2	yes	—
51	C₃×#235	—	2	4	no	—
52	C₃×#235	C₂×C₄	1	8	yes	complemented
53	C₂×C₃×D₁₂	C₂³	1	2	yes	—
54	C₂×C₃×C₄×D₃	—	2	2	no	—
55	C₂×C₃×C₄×D₃	—	2	4	no	—
56	C₂×C₃×Dic₆	C₂³	1	2	yes	—
57	C₂×C₃²×C₈	C₂×C₄	1	4	yes	complemented
58	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
59	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
60	C₃²×C₄⋊C₄	C₂³	1	4	yes	—
61	C₃²×C₂²⋊C₄	—	2	2	no	—
62	C₃²×C₄²	—	2	2	no	—
63	C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₃×Dic₃⋊C₄	—	2	4	no	—
65	C₃×C₄×Dic₃	—	2	4	no	—
66	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
67	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
68	C₃×C₄×Dic₃	C₂³	1	2	yes	—
69	C₂×C₃×C₃⋊C₈	—	2	2	no	—
70	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
71	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
72	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
73	C₃×#204	C₂×C₄	1	8	yes	complemented
74	C₄×#135	—	3	1	no	Sylow
75	C₂×C₃×#41	—	3	2	no	—
76	C₂×#235	C₂²×C₃	1	2	yes	—
77	C₃×#135	—	3	8	no	—
78	C₂×C₃×Q₁₆	—	3	1	no	—
79	C₂×C₃×SD₁₆	—	3	2	no	—
80	C₂×C₃×D₈	—	3	1	no	—
81	C₂²×C₃×C₈	—	2	1	no	—
82	C₂²×C₃×C₈	—	3	1	no	—
83	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
85	C₃×C₄×Q₈	—	3	4	no	—
86	C₃×C₄×D₄	—	3	4	no	—
87	C₃×C₄×D₄	—	6	4	no	—
88	C₃×#117	—	2	2	no	—
89	C₃×#117	—	6	2	no	—
90	C₃×#117	C₂×D₃	1	2	yes	—
91	C₃×#117	C₂²×C₃	1	2	yes	—
92	C₂×C₃×C₄²	—	3	1	no	—
93	C₂×C₃×C₄²	—	6	2	no	—
94	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
96	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
97	#904	C₃×C₄	1	8	yes	complemented
98	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×#204	C₂²×C₃	1	2	yes	—
100	#893	C₂²×C₃	1	4	yes	—
101	#887	C₂²×C₃	1	4	yes	—
102	#67⋊C₄	—	2	4	no	—
103	#872	—	2	2	no	—
104	C₄²×D₃	—	2	2	no	—
105	C₃×#107	—	2	2	no	—
106	C₃×#107	C₂×D₃	1	2	yes	—
107	C₃×#107	C₂²×C₃	1	2	yes	—
108	C₃×#106	—	2	2	no	—
109	C₃×#106	C₂×D₃	1	2	yes	—
110	C₃×#106	C₂²×C₃	1	2	yes	—
111	C₃×#103	—	3	4	no	—
112	C₃×#102	—	3	4	no	—
113	C₃×C₄×C₈	—	3	2	no	—
114	C₃×C₄×C₈	—	3	2	no	—
115	C₈×Dic₃	C₂²×C₃	1	2	yes	—
116	C₈×Dic₃	C₂²×C₃	1	2	yes	—
117	#810	C₂²×C₃	1	4	yes	—
118	#809	C₂²×C₃	1	4	yes	—
119	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃×D₃	—	2	2	no	—
121	C₂×C₃²×C₄	—	2	4	no	—
122	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
123	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃²×C₄	#41	1	2	yes	—
125	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
126	C₃×#67	—	2	8	no	—
127	C₂×C₃×Dic₃	—	2	2	no	—
128	C₂×C₃×Dic₃	—	2	4	no	—
129	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
130	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
131	C₃×D₁₂	—	2	2	no	—
132	C₃×D₁₂	C₂²×C₄	1	4	yes	—
133	C₃×C₄×D₃	—	2	8	no	—
134	C₃×C₄×D₃	—	4	8	no	—
135	C₃×Dic₆	—	2	2	no	—
136	C₃×Dic₆	C₂²×C₄	1	4	yes	—
137	C₃²×C₈	C₂²×C₄	1	2	yes	—
138	C₃²×C₈	C₂²×C₄	1	2	yes	—
139	C₃×C₃⋊C₈	—	2	2	no	—
140	C₂×#135	—	3	1	no	—
141	C₄×#41	—	3	2	no	—
142	C₄×Q₁₆	—	3	2	no	—
143	C₄×SD₁₆	—	3	4	no	—
144	C₄×D₈	—	3	2	no	—
145	#427	C₃×D₃	1	1	yes	characteristic, complemented
146	#416	—	3	2	no	—
147	C₂×C₄×C₈	—	3	1	no	—
148	C₃×#41	—	3	8	no	—
149	C₃×#41	—	6	4	no	—
150	C₂×C₃×Q₈	—	3	2	no	—
151	C₂×C₃×D₄	—	3	2	no	—
152	C₂×C₃×D₄	—	6	2	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	3	2	no	—
155	C₂²×C₃×C₄	—	6	4	no	—
156	C₂²×C₃×C₄	—	6	2	no	—
157	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
159	C₂×#67	—	2	2	no	—
160	C₂²×Dic₃	C₃×D₄	1	2	yes	—
161	#235	—	2	4	no	—
162	#235	C₂×C₃×C₄	1	8	yes	complemented
163	C₂×D₁₂	C₂³×C₃	1	2	yes	—
164	C₂×C₄×D₃	—	2	2	no	—
165	C₂×C₄×D₃	—	2	4	no	—
166	C₂×Dic₆	C₂³×C₃	1	2	yes	—
167	C₃×Q₁₆	—	3	4	no	—
168	C₃×SD₁₆	—	3	8	no	—
169	C₃×D₈	—	3	4	no	—
170	C₂×C₃×C₈	—	2	4	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	2	1	no	—
173	C₂×C₃×C₈	—	3	2	no	—
174	C₂×C₃×C₈	—	6	2	no	—
175	C₂×C₃×C₈	C₄×D₃	1	4	yes	complemented
176	C₂×C₃×C₈	C₂×C₃×C₄	1	4	yes	complemented
177	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
181	C₃×C₄⋊C₄	—	2	4	no	—
182	C₃×C₄⋊C₄	—	6	4	no	—
183	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
184	C₃×C₄⋊C₄	C₂³×C₃	1	4	yes	—
185	C₃×C₂²⋊C₄	—	2	2	no	—
186	C₃×C₂²⋊C₄	—	2	2	no	—
187	C₃×C₂²⋊C₄	—	4	2	no	—
188	C₃×C₂²⋊C₄	—	6	4	no	—
189	C₃×C₄²	—	2	2	no	—
190	C₃×C₄²	—	2	2	no	—
191	C₃×C₄²	—	3	1	no	—
192	C₃×C₄²	—	3	1	no	—
193	C₃×C₄²	—	3	2	no	—
194	C₃×C₄²	—	4	2	no	—
195	C₃×C₄²	—	6	4	no	—
196	(C₂×D₃)⋊C₄	—	2	4	no	—
197	Dic₃⋊C₄	—	2	4	no	—
198	C₄×Dic₃	—	2	4	no	—
199	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
200	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
201	C₄×Dic₃	C₂³×C₃	1	2	yes	—
202	C₂×C₃⋊C₈	—	2	2	no	—
203	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
204	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
205	D₂₄	C₂×C₃×C₄	1	4	yes	complemented
206	#204	C₂×C₃×C₄	1	8	yes	complemented
207	C₂²×C₃²	—	2	2	no	—
208	C₂²×C₃²	C₄×D₄	1	2	yes	—
209	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₃×D₃	—	2	4	no	—
211	C₂×C₃×D₃	—	4	4	no	—
212	C₃²×C₄	—	4	4	no	—
213	C₃²×C₄	C₄×D₄	1	2	yes	—
214	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
215	C₃²×C₄	C₂×#41	1	1	yes	characteristic
216	C₃×Dic₃	—	2	4	no	—
217	C₃×Dic₃	—	2	2	no	—
218	C₃×Dic₃	#135	1	4	yes	complemented
219	C₂×#41	—	3	2	no	—
220	#135	—	3	8	no	—
221	C₂×Q₁₆	—	3	1	no	—
222	C₂×SD₁₆	—	3	2	no	—
223	C₂×D₈	—	3	1	no	—
224	C₂²×C₈	—	3	1	no	—
225	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
226	C₄×Q₈	—	3	4	no	—
227	C₄×D₄	—	3	4	no	—
228	C₄×D₄	—	6	4	no	—
229	#117	—	6	2	no	—
230	#117	C₂×C₃×D₃	1	2	yes	—
231	C₂×C₄²	—	3	1	no	—
232	C₂×C₄²	—	6	2	no	—
233	#107	C₂×C₃×D₃	1	2	yes	—
234	#106	C₂×C₃×D₃	1	2	yes	—
235	#103	—	3	4	no	—
236	#102	—	3	4	no	—
237	C₄×C₈	—	3	2	no	—
238	C₄×C₈	—	3	2	no	—
239	C₂³×C₃	—	2	1	no	—
240	C₂³×C₃	—	6	2	no	—
241	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
242	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂²×D₃	—	2	2	no	—
244	C₃×Q₈	—	3	4	no	—
245	C₃×Q₈	—	6	2	no	—
246	C₃×D₄	—	3	4	no	—
247	C₃×D₄	—	6	8	no	—
248	C₃×D₄	—	6	2	no	—
249	C₂×C₃×C₄	—	2	4	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	2	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	3	2	no	—
256	C₂×C₃×C₄	—	3	2	no	—
257	C₂×C₃×C₄	—	4	4	no	—
258	C₂×C₃×C₄	—	6	4	no	—
259	C₂×C₃×C₄	—	6	2	no	—
260	C₂×C₃×C₄	—	6	8	no	—
261	C₂×C₃×C₄	—	12	8	no	—
262	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
263	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	#239	1	2	yes	—
265	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₃×#41	1	2	yes	—
268	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
270	#67	—	2	8	no	—
271	C₂×Dic₃	—	2	2	no	—
272	C₂×Dic₃	—	2	4	no	—
273	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
274	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
275	D₁₂	—	2	2	no	—
276	D₁₂	C₂²×C₃×C₄	1	4	yes	—
277	C₄×D₃	—	2	8	no	—
278	C₄×D₃	—	4	8	no	—
279	Dic₆	—	2	2	no	—
280	Dic₆	C₂²×C₃×C₄	1	4	yes	—
281	C₃×C₈	—	2	2	no	—
282	C₃×C₈	—	2	2	no	—
283	C₃×C₈	—	6	2	no	—
284	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
285	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
286	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
287	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
288	C₃⋊C₈	—	2	2	no	—
289	C₂×C₃²	—	2	2	no	—
290	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×C₃²	C₂×#135	1	2	yes	—
292	C₃×D₃	—	4	4	no	—
293	#41	—	3	8	no	—
294	#41	—	6	4	no	—
295	C₂×Q₈	—	3	2	no	—
296	C₂×D₄	—	3	2	no	—
297	C₂×D₄	—	6	2	no	—
298	C₂²×C₄	—	3	2	no	—
299	C₂²×C₄	—	6	4	no	—
300	C₂²×C₄	—	6	2	no	—
301	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
302	Q₁₆	—	3	4	no	—
303	SD₁₆	—	3	8	no	—
304	D₈	—	3	4	no	—
305	C₂×C₈	—	3	2	no	—
306	C₂×C₈	—	6	2	no	—
307	C₂×C₈	C₃×C₄×D₃	1	4	yes	complemented
308	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
309	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
310	C₄⋊C₄	—	6	4	no	—
311	C₄⋊C₄	C₂²×C₃×D₃	1	4	yes	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	6	4	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	3	2	no	—
316	C₄²	—	3	1	no	—
317	C₄²	—	3	1	no	—
318	C₄²	—	6	4	no	—
319	C₂²×C₃	—	2	2	no	—
320	C₂²×C₃	—	2	2	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	6	4	no	—
325	C₂²×C₃	—	12	4	no	—
326	C₂²×C₃	#893	1	2	yes	—
327	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
328	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
329	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
330	C₂×D₃	—	2	4	no	—
331	C₂×D₃	—	4	4	no	—
332	C₃×C₄	—	2	2	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	3	4	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	—	4	4	no	—
338	C₃×C₄	—	6	4	no	—
339	C₃×C₄	—	6	2	no	—
340	C₃×C₄	—	8	4	no	—
341	C₃×C₄	#893	1	2	yes	—
342	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
343	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
344	C₃×C₄	C₂×#239	1	1	yes	characteristic
345	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
346	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
347	Dic₃	—	2	2	no	—
348	Dic₃	—	2	4	no	—
349	Dic₃	C₃×#135	1	4	yes	complemented
350	C₃²	C₄×#135	1	1	yes	characteristic, complemented, Sylow
351	C₂³	—	6	2	no	—
352	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
353	Q₈	—	3	4	no	—
354	Q₈	—	6	2	no	—
355	D₄	—	3	4	no	—
356	D₄	—	6	8	no	—
357	D₄	—	6	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	3	2	no	—
360	C₂×C₄	—	3	2	no	—
361	C₂×C₄	—	6	4	no	—
362	C₂×C₄	—	6	2	no	—
363	C₂×C₄	—	6	8	no	—
364	C₂×C₄	—	12	8	no	—
365	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
366	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
367	C₂×C₄	C₃×#239	1	2	yes	—
368	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
369	C₈	—	6	2	no	—
370	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
371	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	4	2	no	—
377	C₂×C₃	—	12	4	no	—
378	C₂×C₃	C₂×#893	1	1	yes	characteristic
379	C₂×C₃	D₃×#135	1	2	yes	—
380	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
381	C₂×C₃	C₂×C₃×#135	1	2	yes	—
382	D₃	—	4	4	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	6	4	no	—
385	C₂²	—	12	4	no	—
386	C₂²	C₃×#893	1	2	yes	—
387	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
388	C₄	—	3	4	no	—
389	C₄	—	4	4	no	—
390	C₄	—	6	4	no	—
391	C₄	—	6	2	no	—
392	C₄	C₃×#893	1	2	yes	—
393	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
394	C₄	C₂×C₃×#239	1	1	yes	characteristic
395	C₃	—	2	1	no	—
396	C₃	#79165	1	1	yes	characteristic, direct product factor
397	C₃	C₃×C₄×#135	1	1	yes	characteristic, complemented
398	C₂	—	2	2	no	—
399	C₂	—	12	4	no	—
400	C₂	C₂×C₃×#893	1	1	yes	characteristic
401	C₂	C₃×D₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#427	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#427	D₃
hypocenter	C₃	C₃×C₄×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#427

Complements

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

N	H ≅ G/N	type
2. C₃×#5522	C₂	semidirect
3. C₃²×#427	C₂	semidirect
4. C₂×C₃×C₈×Dic₃	C₂	semidirect
5. C₃×#5002	C₂	semidirect
6. C₃×#4873	C₂	semidirect
7. C₃×#4872	C₂	semidirect
8. C₃×#4852	C₂	semidirect
10. #79165	C₃	direct (N × H)
17. C₃×#904	C₄	semidirect
34. #5522	C₂×C₃	semidirect
39. C₃×#427	D₃	semidirect
40. C₃×#427	C₂×C₃	semidirect
43. C₂×C₈×Dic₃	C₂×C₃	semidirect
44. #5002	C₂×C₃	semidirect
45. #4873	C₂×C₃	semidirect
46. #4872	C₂×C₃	semidirect
47. #4852	C₂×C₃	semidirect
52. C₃×#235	C₂×C₄	semidirect
57. C₂×C₃²×C₈	C₂×C₄	semidirect
71. C₃×Dic₁₂	C₂×C₄	semidirect
72. C₃×D₂₄	C₂×C₄	semidirect
73. C₃×#204	C₂×C₄	semidirect
97. #904	C₃×C₄	semidirect
145. #427	C₃×D₃	semidirect
162. #235	C₂×C₃×C₄	semidirect
175. C₂×C₃×C₈	C₄×D₃	semidirect
176. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
204. Dic₁₂	C₂×C₃×C₄	semidirect
205. D₂₄	C₂×C₃×C₄	semidirect
206. #204	C₂×C₃×C₄	semidirect
218. C₃×Dic₃	#135	semidirect
307. C₂×C₈	C₃×C₄×D₃	semidirect
349. Dic₃	C₃×#135	semidirect
350. C₃²	C₄×#135	semidirect
396. C₃	#79165	direct (N × H)
397. C₃	C₃×C₄×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#904	2
C₃×#5522	2
C₃²×#427	2
C₂×C₃×C₈×Dic₃	2
C₃×#5002	2
C₃×#4873	2
C₃×#4872	2
C₃×#4852	2
C₃×C₄×#135	3
#79165	3

Subgroups — C3×#79165 #11859974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79165 #11859974