Subgroups — C₃×#83275 #11859470

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#948	C₂	1	2	yes	maximal, complemented
3	C₃×#5234	C₂	1	2	yes	maximal, complemented
4	C₃×#5012	C₂	1	4	yes	maximal, complemented
5	C₃×D₄×C₃⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#2931	—	3	1	no	maximal
9	#83275	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃²×#41	C₂²	1	2	yes	—
11	C₃²×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₃²×#127	C₄	1	1	yes	characteristic
13	C₃²×#124	C₄	1	2	yes	—
14	C₃²×#121	C₄	1	4	yes	—
15	C₃²×C₄×D₄	C₂²	1	4	yes	—
16	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
17	C₃×#948	—	2	8	no	—
18	C₂×C₃×#208	C₂²	1	2	yes	—
19	C₂×C₃×#208	C₂²	1	4	yes	—
20	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₃⋊C₈	C₂²	1	4	yes	—
22	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×#830	C₂²	1	8	yes	—
24	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	—
25	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
26	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
27	C₂×C₃×#131	—	3	2	no	—
28	C₃×#532	—	2	1	no	—
29	C₃×#532	D₃	1	1	yes	characteristic
30	C₃×#532	C₂×C₃	1	1	yes	characteristic
31	C₂×#948	C₂×C₃	1	2	yes	complemented
32	C₃×#436	—	3	4	no	—
33	C₃×C₈×D₄	—	3	4	no	—
34	C₃×#423	—	3	1	no	—
35	C₃×#408	—	3	2	no	—
36	C₂×C₃×C₄×C₈	—	3	1	no	—
37	#5234	C₂×C₃	1	2	yes	complemented
38	#5012	C₂×C₃	1	4	yes	complemented
39	D₄×C₃⋊C₈	C₂×C₃	1	4	yes	complemented
40	#4924	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₃²×#41	—	2	4	no	—
43	C₃²×#41	—	2	4	no	—
44	C₂×C₃²×Q₈	C₂×C₄	1	2	yes	—
45	C₂×C₃²×D₄	C₂×C₄	1	4	yes	—
46	C₂×C₃²×D₄	C₂×C₄	1	2	yes	—
47	C₂×C₃²×D₄	C₂×C₄	1	4	yes	—
48	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
49	C₂²×C₃²×C₄	C₂³	1	4	yes	—
50	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
51	C₃²×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₃²×C₂²⋊C₄	C₂×C₄	1	8	yes	—
53	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
54	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
55	C₃²×C₄²	C₂³	1	2	yes	—
56	C₃×#208	—	2	4	no	—
57	C₃×#208	—	2	8	no	—
58	C₂×C₃×C₃⋊C₈	—	2	2	no	—
59	C₂×C₃×C₃⋊C₈	—	2	8	no	—
60	C₂×C₃×C₃⋊C₈	D₄	1	4	yes	complemented
61	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
62	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
65	#2931	—	3	1	no	Sylow
66	C₂×C₃×#41	—	2	2	no	—
67	C₂×C₃×#41	C₂×D₃	1	2	yes	—
68	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
69	C₃×#131	—	6	8	no	—
70	C₂×C₃×M₁₆	—	3	2	no	—
71	C₂×C₃×M₁₆	—	3	4	no	—
72	C₂²×C₃×C₈	—	3	1	no	—
73	C₂²×C₃×C₈	—	3	4	no	—
74	C₂²×C₃×C₈	—	3	1	no	—
75	C₃×C₄⋊Q₈	—	2	1	no	—
76	C₃×C₄⋊Q₈	Dic₃	1	1	yes	characteristic
77	C₃×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
78	C₃×#127	—	2	1	no	—
79	C₃×#127	Dic₃	1	1	yes	characteristic
80	C₃×#127	C₃×C₄	1	1	yes	characteristic
81	C₃×#124	—	2	2	no	—
82	C₃×#124	Dic₃	1	2	yes	—
83	C₃×#124	C₃×C₄	1	2	yes	—
84	C₃×#121	—	2	4	no	—
85	C₃×#121	Dic₃	1	4	yes	—
86	C₃×#121	C₃×C₄	1	4	yes	—
87	C₃×C₄×D₄	—	2	4	no	—
88	C₃×C₄×D₄	C₂×D₃	1	4	yes	—
89	C₃×C₄×D₄	C₂²×C₃	1	4	yes	—
90	C₂×C₃×C₄²	—	2	1	no	—
91	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
92	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
93	#948	—	2	8	no	—
94	C₂×#208	C₂²×C₃	1	2	yes	—
95	C₂×#208	C₂²×C₃	1	4	yes	—
96	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
97	C₂²×C₃⋊C₈	C₂²×C₃	1	4	yes	—
98	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
99	C₃×C₄⋊C₈	—	3	4	no	—
100	C₃×C₂²⋊C₈	—	3	8	no	—
101	C₃×C₄×C₈	—	3	2	no	—
102	C₃×C₄×C₈	—	3	2	no	—
103	#830	C₂²×C₃	1	8	yes	—
104	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	—
105	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
106	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
107	C₂³×C₃²	C₂²×C₄	1	4	yes	—
108	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
109	C₃²×Q₈	—	2	4	no	—
110	C₃²×D₄	—	2	8	no	—
111	C₃²×D₄	—	2	4	no	—
112	C₃²×D₄	—	2	8	no	—
113	C₂×C₃²×C₄	—	2	4	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	—	2	4	no	—
116	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
117	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
118	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
120	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
121	C₂×C₃²×C₄	#41	1	2	yes	—
122	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
123	C₃×C₃⋊C₈	—	2	4	no	—
124	C₃×C₃⋊C₈	—	2	2	no	—
125	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
126	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
127	C₂×#131	—	3	2	no	—
128	#532	C₃×D₃	1	1	yes	characteristic
129	#436	—	3	4	no	—
130	C₈×D₄	—	3	4	no	—
131	#423	—	3	1	no	—
132	#408	—	3	2	no	—
133	C₂×C₄×C₈	—	3	1	no	—
134	C₃×#41	—	2	4	no	—
135	C₃×#41	—	2	4	no	—
136	C₃×#41	—	2	4	no	—
137	C₃×#41	—	2	4	no	—
138	C₃×#41	—	4	4	no	—
139	C₃×#41	—	4	4	no	—
140	C₂×C₃×Q₈	—	2	2	no	—
141	C₂×C₃×Q₈	C₂×Dic₃	1	2	yes	—
142	C₂×C₃×Q₈	C₂×C₃×C₄	1	2	yes	—
143	C₂×C₃×D₄	—	2	4	no	—
144	C₂×C₃×D₄	—	2	4	no	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	C₂×Dic₃	1	4	yes	—
147	C₂×C₃×D₄	C₂×Dic₃	1	4	yes	—
148	C₂×C₃×D₄	C₂×Dic₃	1	2	yes	—
149	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
150	C₂×C₃×D₄	C₂×C₃×C₄	1	4	yes	—
151	C₂×C₃×D₄	C₂×C₃×C₄	1	2	yes	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	2	1	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
156	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
157	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
158	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₃×M₁₆	—	6	8	no	—
162	C₃×M₁₆	—	6	4	no	—
163	C₂×C₃×C₈	—	3	4	no	—
164	C₂×C₃×C₈	—	3	1	no	—
165	C₂×C₃×C₈	—	3	1	no	—
166	C₂×C₃×C₈	—	3	2	no	—
167	C₂×C₃×C₈	—	3	4	no	—
168	C₂×C₃×C₈	—	6	8	no	—
169	C₂×C₃×C₈	—	6	2	no	—
170	C₃×C₄⋊C₄	—	2	4	no	—
171	C₃×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
172	C₃×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
173	C₃×C₂²⋊C₄	—	2	8	no	—
174	C₃×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
175	C₃×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
176	C₃×C₄²	—	2	1	no	—
177	C₃×C₄²	—	2	1	no	—
178	C₃×C₄²	—	2	2	no	—
179	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
180	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
181	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
182	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
183	C₃×C₄²	C₂²×D₃	1	2	yes	—
184	C₃×C₄²	C₂³×C₃	1	2	yes	—
185	#208	—	2	4	no	—
186	#208	—	2	8	no	—
187	C₂×C₃⋊C₈	—	2	2	no	—
188	C₂×C₃⋊C₈	—	2	8	no	—
189	C₂×C₃⋊C₈	C₃×D₄	1	4	yes	complemented
190	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
191	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
192	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₃²	—	2	2	no	—
195	C₂²×C₃²	—	2	4	no	—
196	C₂²×C₃²	—	2	8	no	—
197	C₂²×C₃²	C₄×D₄	1	2	yes	—
198	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
199	C₃²×C₄	—	2	4	no	—
200	C₃²×C₄	—	2	2	no	—
201	C₃²×C₄	C₄×D₄	1	2	yes	—
202	C₃²×C₄	#131	1	4	yes	complemented
203	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
204	C₃²×C₄	C₂×#41	1	1	yes	characteristic
205	C₂×#41	C₂×C₃×D₃	1	2	yes	—
206	#131	—	6	8	no	—
207	C₂×M₁₆	—	3	2	no	—
208	C₂×M₁₆	—	3	4	no	—
209	C₂²×C₈	—	3	1	no	—
210	C₂²×C₈	—	3	4	no	—
211	C₂²×C₈	—	3	1	no	—
212	C₄⋊Q₈	C₃×Dic₃	1	1	yes	characteristic
213	#127	C₃×Dic₃	1	1	yes	characteristic
214	#124	C₃×Dic₃	1	2	yes	—
215	#121	C₃×Dic₃	1	4	yes	—
216	C₄×D₄	C₂×C₃×D₃	1	4	yes	—
217	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
218	C₄⋊C₈	—	3	4	no	—
219	C₂²⋊C₈	—	3	8	no	—
220	C₄×C₈	—	3	2	no	—
221	C₄×C₈	—	3	2	no	—
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	2	4	no	—
224	C₂³×C₃	C₂²×Dic₃	1	4	yes	—
225	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
226	C₂³×C₃	C₂²×C₃×C₄	1	4	yes	—
227	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
228	C₃×Q₈	—	2	4	no	—
229	C₃×Q₈	—	2	4	no	—
230	C₃×Q₈	—	4	4	no	—
231	C₃×D₄	—	2	8	no	—
232	C₃×D₄	—	2	8	no	—
233	C₃×D₄	—	2	4	no	—
234	C₃×D₄	—	2	8	no	—
235	C₃×D₄	—	2	4	no	—
236	C₃×D₄	—	2	8	no	—
237	C₃×D₄	—	4	8	no	—
238	C₃×D₄	—	4	4	no	—
239	C₃×D₄	—	4	8	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	2	no	—
249	C₂×C₃×C₄	—	2	2	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	4	4	no	—
254	C₂×C₃×C₄	—	4	4	no	—
255	C₂×C₃×C₄	—	4	4	no	—
256	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
257	C₂×C₃×C₄	#237	1	2	yes	—
258	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
259	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
260	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
262	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
263	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
264	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
266	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
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	C₃×C₈	—	3	2	no	—
271	C₃×C₈	—	3	2	no	—
272	C₃×C₈	—	6	4	no	—
273	C₃×C₈	—	6	2	no	—
274	C₃⋊C₈	—	2	4	no	—
275	C₃⋊C₈	—	2	2	no	—
276	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
277	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
278	C₂×C₃²	—	2	2	no	—
279	C₂×C₃²	—	4	4	no	—
280	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
281	C₂×C₃²	C₂×#131	1	2	yes	—
282	#41	—	2	4	no	—
283	#41	—	2	4	no	—
284	C₂×Q₈	C₂×C₃×Dic₃	1	2	yes	—
285	C₂×D₄	C₂×C₃×Dic₃	1	4	yes	—
286	C₂×D₄	C₂×C₃×Dic₃	1	4	yes	—
287	C₂×D₄	C₂×C₃×Dic₃	1	2	yes	—
288	C₂²×C₄	C₂×C₃×Dic₃	1	2	yes	—
289	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
290	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
291	M₁₆	—	6	8	no	—
292	M₁₆	—	6	4	no	—
293	C₂×C₈	—	3	1	no	—
294	C₂×C₈	—	3	1	no	—
295	C₂×C₈	—	3	4	no	—
296	C₂×C₈	—	3	2	no	—
297	C₂×C₈	—	3	4	no	—
298	C₂×C₈	—	6	8	no	—
299	C₂×C₈	—	6	2	no	—
300	C₄⋊C₄	C₂×C₃×Dic₃	1	4	yes	—
301	C₂²⋊C₄	C₂×C₃×Dic₃	1	8	yes	—
302	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
303	C₄²	C₂×C₃×Dic₃	1	1	yes	characteristic
304	C₄²	C₂²×C₃×D₃	1	2	yes	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	8	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	8	no	—
310	C₂²×C₃	—	2	4	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	1	no	—
313	C₂²×C₃	—	4	2	no	—
314	C₂²×C₃	—	4	4	no	—
315	C₂²×C₃	—	4	8	no	—
316	C₂²×C₃	D₄×Dic₃	1	2	yes	—
317	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
318	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
319	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
320	C₃×C₄	—	2	2	no	—
321	C₃×C₄	—	2	4	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	2	no	—
325	C₃×C₄	—	2	4	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	4	4	no	—
329	C₃×C₄	—	4	2	no	—
330	C₃×C₄	D₄×Dic₃	1	2	yes	—
331	C₃×C₄	#948	1	4	yes	complemented
332	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
333	C₃×C₄	C₃×#131	1	4	yes	complemented
334	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
335	C₃×C₄	C₂×#237	1	1	yes	characteristic
336	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
337	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
338	C₃²	#2931	1	1	yes	characteristic, complemented, Sylow
339	C₂³	C₂²×C₃×Dic₃	1	4	yes	—
340	C₂³	C₂²×C₃×Dic₃	1	1	yes	characteristic
341	Q₈	—	2	4	no	—
342	D₄	—	2	8	no	—
343	D₄	—	2	4	no	—
344	D₄	—	2	8	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
349	C₂×C₄	C₃×#237	1	2	yes	—
350	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
351	C₂×C₄	C₂²×C₃×Dic₃	1	4	yes	—
352	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₃×Dic₃	1	2	yes	—
354	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
355	C₈	—	3	2	no	—
356	C₈	—	3	2	no	—
357	C₈	—	6	4	no	—
358	C₈	—	6	2	no	—
359	C₂×C₃	—	2	2	no	—
360	C₂×C₃	—	2	2	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	4	2	no	—
364	C₂×C₃	—	4	4	no	—
365	C₂×C₃	—	4	4	no	—
366	C₂×C₃	—	8	4	no	—
367	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
368	C₂×C₃	C₂×#948	1	2	yes	—
369	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
370	C₂×C₃	C₂×C₃×#131	1	2	yes	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	8	no	—
374	C₂²	C₃×D₄×Dic₃	1	2	yes	—
375	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
376	C₄	—	2	4	no	—
377	C₄	—	2	2	no	—
378	C₄	C₃×D₄×Dic₃	1	2	yes	—
379	C₄	C₃×#948	1	4	yes	complemented
380	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
381	C₄	C₂×C₃×#237	1	1	yes	characteristic
382	C₃	—	2	1	no	—
383	C₃	#83275	1	1	yes	characteristic, direct product factor
384	C₃	C₃×#2931	1	1	yes	characteristic, complemented
385	C₂	—	2	2	no	—
386	C₂	—	4	4	no	—
387	C₂	C₂×C₃×D₄×Dic₃	1	1	yes	characteristic
388	C₂	C₂×C₃×#948	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting, prime radical	C₃²×#532	C₂
socle	C₂²×C₃²	C₂³×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#532	D₃
hypocenter	C₃	C₃×#2931
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#948	C₂	semidirect
3. C₃×#5234	C₂	semidirect
4. C₃×#5012	C₂	semidirect
5. C₃×D₄×C₃⋊C₈	C₂	semidirect
6. C₃×#4924	C₂	semidirect
7. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
9. #83275	C₃	direct (N × H)
31. C₂×#948	C₂×C₃	semidirect
37. #5234	C₂×C₃	semidirect
38. #5012	C₂×C₃	semidirect
39. D₄×C₃⋊C₈	C₂×C₃	semidirect
40. #4924	C₂×C₃	semidirect
41. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
60. C₂×C₃×C₃⋊C₈	D₄	semidirect
189. C₂×C₃⋊C₈	C₃×D₄	semidirect
202. C₃²×C₄	#131	semidirect
331. C₃×C₄	#948	semidirect
333. C₃×C₄	C₃×#131	semidirect
338. C₃²	#2931	semidirect
379. C₄	C₃×#948	semidirect
383. C₃	#83275	direct (N × H)
384. C₃	C₃×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#532	2
C₂×C₃×#948	2
C₃×#5234	2
C₃×#5012	2
C₃×D₄×C₃⋊C₈	2
C₃×#4924	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×#2931	3
#83275	3

Subgroups — C3×#83275 #11859470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#83275 #11859470