Subgroups — C₃×#70756 #11774301

Order 1152.

683 conjugacy classes of subgroups.

The subgroup lattice has 393 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4483	C₂	1	4	yes	maximal, complemented
5	C₃×#1478	—	3	1	no	maximal
6	#70756	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂²×C₃×D₁₂	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₄×D₃	—	2	1	no	—
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₂×C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
11	C₂×C₃×C₄⋊Dic₃	C₄	1	1	yes	characteristic
12	C₃×C₄×D₁₂	—	2	1	no	—
13	C₃×C₄×D₁₂	—	2	1	no	—
14	C₃×C₄×D₁₂	C₄	1	2	yes	—
15	C₃×C₄×D₁₂	C₂²	1	2	yes	—
16	C₃²×C₄⋊C₈	C₂²	1	2	yes	complemented
17	C₃²×C₂²⋊C₈	—	2	1	no	—
18	C₃²×C₄×C₈	—	2	1	no	—
19	C₃×#830	—	2	1	no	—
20	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
21	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₃×C₄×D₄	—	3	1	no	—
23	C₂×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
24	C₃×#431	—	2	1	no	—
25	C₃×#431	—	3	1	no	—
26	C₃×#431	D₃	1	1	yes	characteristic, complemented
27	C₃×#431	C₂×C₃	1	1	yes	characteristic, complemented
28	#4925	C₂×C₃	1	1	yes	characteristic, complemented
29	C₃×D₄⋊C₈	—	3	4	no	—
30	#4483	C₂×C₃	1	4	yes	complemented
31	C₂³×C₃×D₃	—	2	1	no	—
32	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
35	C₂²×C₃×Dic₃	—	2	1	no	—
36	C₂×C₃×D₁₂	—	2	1	no	—
37	C₂×C₃×D₁₂	—	2	2	no	—
38	C₂×C₃×D₁₂	C₈	1	4	yes	complemented
39	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₄×D₃	—	2	2	no	—
41	C₂×C₃×C₄×D₃	—	2	2	no	—
42	C₂×C₃×C₄×D₃	—	4	4	no	—
43	C₂×C₃²×C₈	—	2	2	no	—
44	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
45	C₃²×C₄²	D₄	1	1	yes	characteristic
46	C₃²×C₄²	D₄	1	1	yes	characteristic
47	C₃²×C₄²	C₂³	1	1	yes	characteristic
48	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
49	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
50	C₃×C₄⋊Dic₃	—	2	1	no	—
51	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
52	C₂×C₃×C₃⋊C₈	—	2	2	no	—
53	#1478	—	3	1	no	Sylow
54	C₂²×C₃×D₄	—	3	1	no	—
55	C₂³×C₃×C₄	—	6	1	no	—
56	C₂²×D₁₂	C₃×C₄	1	1	yes	characteristic
57	C₂²×C₄×D₃	—	2	1	no	—
58	C₃×C₄×D₄	—	3	2	no	—
59	C₃×C₄×D₄	—	3	2	no	—
60	C₃×C₄×D₄	—	6	1	no	—
61	C₃×C₄×D₄	—	6	1	no	—
62	C₂×C₃×C₄⋊C₄	—	3	1	no	—
63	C₂×C₃×C₂²⋊C₄	—	6	1	no	—
64	C₂×C₃×C₄²	—	2	1	no	—
65	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
66	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
67	C₂×(C₂×D₃)⋊C₄	—	2	1	no	—
68	C₂×C₄⋊Dic₃	C₃×C₄	1	1	yes	characteristic
69	C₄×D₁₂	—	2	1	no	—
70	C₄×D₁₂	—	2	1	no	—
71	C₄×D₁₂	C₃×C₄	1	2	yes	—
72	C₄×D₁₂	C₂²×C₃	1	2	yes	—
73	C₃×C₄⋊C₈	—	2	2	no	—
74	C₃×C₄⋊C₈	—	6	1	no	—
75	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
76	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
77	C₃×C₂²⋊C₈	—	2	2	no	—
78	C₃×C₂²⋊C₈	—	2	1	no	—
79	C₃×C₂²⋊C₈	—	2	1	no	—
80	C₃×C₂²⋊C₈	—	6	1	no	—
81	C₃×C₄×C₈	—	2	2	no	—
82	C₃×C₄×C₈	—	2	1	no	—
83	C₃×C₄×C₈	—	2	1	no	—
84	C₃×C₄×C₈	—	3	2	no	—
85	#830	—	2	1	no	—
86	C₄⋊(C₃⋊C₈)	—	2	1	no	—
87	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
88	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₃×D₃	—	2	4	no	—
90	C₂²×C₃×D₃	—	2	2	no	—
91	C₂²×C₃×D₃	—	4	2	no	—
92	C₂²×C₃×D₃	—	4	2	no	—
93	C₂×C₃²×C₄	—	2	2	no	—
94	C₂×C₃²×C₄	—	4	1	no	—
95	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
99	C₂×C₃²×C₄	M₁₆	1	2	yes	—
100	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×Dic₃	—	2	2	no	—
104	C₂×C₃×Dic₃	—	4	2	no	—
105	C₃×D₁₂	—	2	4	no	—
106	C₃×D₁₂	—	2	2	no	—
107	C₃×D₁₂	C₂×C₈	1	4	yes	—
108	C₃×C₄×D₃	—	4	4	no	—
109	C₃×C₄×D₃	—	4	4	no	—
110	C₃²×C₈	—	4	2	no	—
111	C₃×C₃⋊C₈	—	4	2	no	—
112	C₂×C₄×D₄	—	3	1	no	—
113	#431	—	3	1	no	—
114	#431	C₃×D₃	1	1	yes	characteristic, complemented
115	D₄⋊C₈	—	3	4	no	—
116	C₂⁴×C₃	—	6	1	no	—
117	C₂³×D₃	—	2	1	no	—
118	C₂×C₃×D₄	—	3	4	no	—
119	C₂×C₃×D₄	—	3	2	no	—
120	C₂×C₃×D₄	—	6	2	no	—
121	C₂×C₃×D₄	—	6	1	no	—
122	C₂²×C₃×C₄	—	2	1	no	—
123	C₂²×C₃×C₄	—	2	1	no	—
124	C₂²×C₃×C₄	—	2	1	no	—
125	C₂²×C₃×C₄	—	6	1	no	—
126	C₂²×C₃×C₄	—	6	2	no	—
127	C₂²×C₃×C₄	—	6	2	no	—
128	C₂²×C₃×C₄	—	12	4	no	—
129	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
130	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
131	C₂²×C₃×C₄	#67	1	1	yes	characteristic
132	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
135	C₂²×Dic₃	—	2	1	no	—
136	C₂×D₁₂	—	2	1	no	—
137	C₂×D₁₂	—	2	2	no	—
138	C₂×D₁₂	C₃×C₈	1	4	yes	complemented
139	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
140	C₂×C₄×D₃	—	2	2	no	—
141	C₂×C₄×D₃	—	2	2	no	—
142	C₂×C₄×D₃	—	4	4	no	—
143	C₂×C₃×C₈	—	2	4	no	—
144	C₂×C₃×C₈	—	2	2	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	6	2	no	—
147	C₃×C₄⋊C₄	—	3	2	no	—
148	C₃×C₄⋊C₄	—	6	1	no	—
149	C₃×C₂²⋊C₄	—	6	2	no	—
150	C₃×C₂²⋊C₄	—	6	2	no	—
151	C₃×C₄²	—	2	1	no	—
152	C₃×C₄²	—	2	1	no	—
153	C₃×C₄²	—	2	1	no	—
154	C₃×C₄²	—	2	1	no	—
155	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
156	C₃×C₄²	D₁₂	1	1	yes	characteristic
157	C₃×C₄²	#67	1	1	yes	characteristic
158	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
159	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
160	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
161	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
162	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
163	(C₂×D₃)⋊C₄	—	2	2	no	—
164	(C₂×D₃)⋊C₄	—	2	2	no	—
165	C₄⋊Dic₃	—	2	1	no	—
166	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
167	C₂×C₃⋊C₈	—	2	2	no	—
168	C₂²×C₃²	—	2	1	no	—
169	C₂²×C₃²	—	2	1	no	—
170	C₂²×C₃²	C₂²⋊C₈	1	2	yes	—
171	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₃×D₃	—	2	4	no	—
173	C₂×C₃×D₃	—	4	8	no	—
174	C₂×C₃×D₃	—	4	2	no	—
175	C₂×C₃×D₃	—	4	2	no	—
176	C₃²×C₄	—	2	1	no	—
177	C₃²×C₄	—	2	1	no	—
178	C₃²×C₄	—	2	1	no	—
179	C₃²×C₄	C₂²⋊C₈	1	2	yes	—
180	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
181	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
182	C₃²×C₄	AGL(1,ℤ/8)	1	2	yes	—
183	C₃×Dic₃	—	4	2	no	—
184	C₂²×D₄	—	3	1	no	—
185	C₂³×C₄	—	6	1	no	—
186	C₄×D₄	—	3	2	no	—
187	C₄×D₄	—	3	2	no	—
188	C₄×D₄	—	6	1	no	—
189	C₄×D₄	—	6	1	no	—
190	C₂×C₄⋊C₄	—	3	1	no	—
191	C₂×C₂²⋊C₄	—	6	1	no	—
192	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
193	C₄⋊C₈	—	6	1	no	—
194	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	complemented
195	C₂²⋊C₈	—	2	1	no	—
196	C₂²⋊C₈	—	6	1	no	—
197	C₄×C₈	—	2	1	no	—
198	C₄×C₈	—	3	2	no	—
199	C₂³×C₃	—	2	1	no	—
200	C₂³×C₃	—	6	4	no	—
201	C₂³×C₃	—	6	2	no	—
202	C₂³×C₃	—	12	2	no	—
203	C₂³×C₃	—	12	2	no	—
204	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
205	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
206	C₂²×D₃	—	2	4	no	—
207	C₂²×D₃	—	2	2	no	—
208	C₂²×D₃	—	4	2	no	—
209	C₂²×D₃	—	4	2	no	—
210	C₃×D₄	—	3	4	no	—
211	C₃×D₄	—	6	4	no	—
212	C₃×D₄	—	6	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	4	2	no	—
224	C₂×C₃×C₄	—	4	1	no	—
225	C₂×C₃×C₄	—	4	1	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	—	6	2	no	—
228	C₂×C₃×C₄	—	12	4	no	—
229	C₂×C₃×C₄	—	12	2	no	—
230	C₂×C₃×C₄	—	12	4	no	—
231	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
232	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	2	yes	—
233	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
234	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
235	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
240	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
241	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂×Dic₃	—	2	2	no	—
248	C₂×Dic₃	—	4	2	no	—
249	D₁₂	—	2	4	no	—
250	D₁₂	—	2	2	no	—
251	D₁₂	C₂×C₃×C₈	1	4	yes	—
252	C₄×D₃	—	4	4	no	—
253	C₄×D₃	—	4	4	no	—
254	C₃×C₈	—	4	4	no	—
255	C₃×C₈	—	4	2	no	—
256	C₃×C₈	—	4	2	no	—
257	C₃×C₈	—	12	2	no	—
258	C₃⋊C₈	—	4	2	no	—
259	C₂×C₃²	—	2	2	no	—
260	C₂×C₃²	C₂×C₂²⋊C₈	1	1	yes	characteristic
261	C₂×C₃²	#418	1	1	yes	characteristic
262	C₂×C₃²	#421	1	1	yes	characteristic
263	C₃×D₃	—	4	4	no	—
264	C₂⁴	—	6	1	no	—
265	C₂×D₄	—	3	4	no	—
266	C₂×D₄	—	3	2	no	—
267	C₂×D₄	—	6	2	no	—
268	C₂×D₄	—	6	1	no	—
269	C₂²×C₄	—	6	1	no	—
270	C₂²×C₄	—	6	2	no	—
271	C₂²×C₄	—	6	2	no	—
272	C₂²×C₄	—	12	4	no	—
273	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
274	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
275	C₂²×C₄	C₃×#67	1	1	yes	characteristic
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	6	2	no	—
278	C₄⋊C₄	—	3	2	no	—
279	C₄⋊C₄	—	6	1	no	—
280	C₂²⋊C₄	—	6	2	no	—
281	C₂²⋊C₄	—	6	2	no	—
282	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
283	C₄²	C₃×D₁₂	1	1	yes	characteristic
284	C₄²	C₃×#67	1	1	yes	characteristic
285	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	4	1	no	—
293	C₂²×C₃	—	4	1	no	—
294	C₂²×C₃	—	6	4	no	—
295	C₂²×C₃	—	12	8	no	—
296	C₂²×C₃	—	12	2	no	—
297	C₂²×C₃	—	12	2	no	—
298	C₂²×C₃	(C₂×D₃)⋊C₈	1	2	yes	—
299	C₂²×C₃	C₃×C₂²⋊C₈	1	2	yes	—
300	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×D₃	—	2	4	no	—
303	C₂×D₃	—	4	8	no	—
304	C₂×D₃	—	4	2	no	—
305	C₂×D₃	—	4	2	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	2	1	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	4	1	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	12	2	no	—
320	C₃×C₄	(C₂×D₃)⋊C₈	1	2	yes	—
321	C₃×C₄	C₃×C₂²⋊C₈	1	2	yes	—
322	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
323	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
324	C₃×C₄	#949	1	2	yes	—
325	C₃×C₄	C₂²×C₃×C₈	1	1	yes	characteristic
326	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
327	C₃×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
328	Dic₃	—	4	2	no	—
329	C₃²	#1478	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	6	2	no	—
331	C₂³	—	6	4	no	—
332	C₂³	—	12	2	no	—
333	C₂³	—	12	2	no	—
334	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
335	D₄	—	3	4	no	—
336	D₄	—	6	2	no	—
337	D₄	—	6	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	6	2	no	—
341	C₂×C₄	—	12	4	no	—
342	C₂×C₄	—	12	2	no	—
343	C₂×C₄	—	12	4	no	—
344	C₂×C₄	C₃×D₃×C₈	1	2	yes	—
345	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
346	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
347	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
350	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
351	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
352	C₈	—	4	2	no	—
353	C₈	—	12	2	no	—
354	C₂×C₃	—	2	2	no	—
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	4	2	no	—
360	C₂×C₃	—	12	4	no	—
361	C₂×C₃	#5001	1	1	yes	characteristic
362	C₂×C₃	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
363	C₂×C₃	#5139	1	1	yes	characteristic
364	C₂×C₃	C₂×C₃×C₂²⋊C₈	1	1	yes	characteristic
365	C₂×C₃	C₃×#418	1	1	yes	characteristic
366	C₂×C₃	C₃×#421	1	1	yes	characteristic
367	D₃	—	4	4	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	6	4	no	—
371	C₂²	—	12	8	no	—
372	C₂²	—	12	2	no	—
373	C₂²	—	12	2	no	—
374	C₂²	C₃×(C₂×D₃)⋊C₈	1	2	yes	—
375	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	12	2	no	—
380	C₄	C₃×(C₂×D₃)⋊C₈	1	2	yes	—
381	C₄	C₂×C₃×D₃×C₈	1	1	yes	characteristic
382	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
383	C₄	C₃×#949	1	2	yes	—
384	C₃	—	2	1	no	—
385	C₃	#70756	1	1	yes	characteristic, direct product factor
386	C₃	C₃×#1478	1	1	yes	characteristic, complemented
387	C₂	—	2	2	no	—
388	C₂	—	12	4	no	—
389	C₂	C₃×#5001	1	1	yes	characteristic
390	C₂	C₂×C₃×(C₂×D₃)⋊C₈	1	1	yes	characteristic
391	C₂	C₃×#5139	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×#67
commutator	C₃×C₄	C₂²×C₃×C₈
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×#431	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₁₂	C₄
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×#431	D₃
hypocenter	C₃	C₃×#1478
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃²×#431	C₂	semidirect
3. C₃×#4925	C₂	semidirect
4. C₃×#4483	C₂	semidirect
6. #70756	C₃	direct (N × H)
16. C₃²×C₄⋊C₈	C₂²	semidirect
21. C₃×C₄×C₃⋊C₈	C₂²	semidirect
26. C₃×#431	D₃	semidirect
27. C₃×#431	C₂×C₃	semidirect
28. #4925	C₂×C₃	semidirect
30. #4483	C₂×C₃	semidirect
38. C₂×C₃×D₁₂	C₈	semidirect
75. C₃×C₄⋊C₈	C₂×D₃	semidirect
76. C₃×C₄⋊C₈	C₂²×C₃	semidirect
87. C₄×C₃⋊C₈	C₂²×C₃	semidirect
114. #431	C₃×D₃	semidirect
138. C₂×D₁₂	C₃×C₈	semidirect
194. C₄⋊C₈	C₂×C₃×D₃	semidirect
329. C₃²	#1478	semidirect
385. C₃	#70756	direct (N × H)
386. C₃	C₃×#1478	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₁₂	2
C₃²×#431	2
C₃×#4925	2
C₃×#4483	2
C₃×#1478	3
#70756	3

Subgroups — C3×#70756 #11774301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70756 #11774301