Subgroups — C₃×C₄×#901 #11857249

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#901	C₂	1	2	yes	maximal
2	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5101	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4689	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₃×C₈	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×#131	—	3	1	no	maximal
10	C₄×#901	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₃×C₄×#67	C₄	1	4	yes	—
15	C₃×#926	C₂²	1	1	yes	characteristic
16	C₂×C₃×#208	C₂²	1	2	yes	—
17	C₃×#901	C₄	1	16	yes	direct product factor
18	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
19	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
20	C₃×C₄×D₁₂	C₄	1	2	yes	—
21	C₃×#872	C₂²	1	2	yes	—
22	C₃×C₄²×D₃	C₂²	1	2	yes	—
23	C₃×C₄×Dic₆	C₄	1	2	yes	—
24	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
25	C₃²×C₄×C₈	C₂²	1	2	yes	—
26	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
27	C₃×#815	C₂²	1	4	yes	—
28	C₃×C₈×Dic₃	C₂²	1	4	yes	—
29	C₃×#803	C₂²	1	2	yes	—
30	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
31	C₂×C₃×#131	—	3	2	no	—
32	C₃×C₄×#41	—	3	1	no	—
33	C₂×#901	C₂×C₃	1	2	yes	—
34	C₄×#235	C₂×C₃	1	1	yes	characteristic
35	C₃×#405	—	3	2	no	—
36	C₃×#405	—	3	4	no	—
37	C₃×C₄×M₁₆	—	3	1	no	—
38	C₃×C₄×M₁₆	—	3	2	no	—
39	C₂×C₃×C₄×C₈	—	2	1	no	—
40	C₂×C₃×C₄×C₈	—	3	2	no	—
41	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
42	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
43	#5101	C₂×C₃	1	2	yes	complemented
44	C₄×#208	C₂×C₃	1	1	yes	characteristic, complemented
45	#4689	C₂×C₃	1	4	yes	complemented
46	C₄×ΓL(1,𝔽₂₅)	C₂×C₃	1	2	yes	complemented
47	C₄×D₃×C₈	C₂×C₃	1	2	yes	complemented
48	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
49	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃×#67	C₂×C₄	1	2	yes	—
51	C₃×#235	C₂×C₄	1	8	yes	—
52	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
54	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
55	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃²×C₈	C₂×C₄	1	8	yes	complemented
57	C₂×C₃²×C₈	C₂³	1	2	yes	—
58	C₂×C₃²×C₈	C₂³	1	2	yes	—
59	C₃²×C₄²	C₂×C₄	1	2	yes	—
60	C₃²×C₄²	C₂³	1	1	yes	characteristic
61	C₃²×C₄²	C₂³	1	1	yes	characteristic
62	C₃×#217	C₂×C₄	1	2	yes	—
63	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
64	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
65	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
66	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
67	C₃×C₄×Dic₃	C₂³	1	2	yes	—
68	C₃×#208	C₂×C₄	1	8	yes	complemented
69	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
70	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	complemented
71	C₃×D₃×C₈	C₂×C₄	1	16	yes	complemented
72	C₄×#131	—	3	1	no	Sylow
73	C₂×C₃×#41	—	3	1	no	—
74	C₂×#235	C₂²×C₃	1	1	yes	characteristic
75	C₃×#131	—	3	16	no	—
76	C₂×C₃×M₁₆	—	3	2	no	—
77	C₂×C₃×M₁₆	—	3	4	no	—
78	C₂²×C₃×C₈	—	2	2	no	—
79	C₂²×C₃×C₈	—	3	4	no	—
80	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
81	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
82	C₃×C₄×Q₈	—	3	2	no	—
83	C₃×C₄×D₄	—	3	4	no	—
84	C₃×C₄×D₄	—	3	2	no	—
85	C₃×#117	—	3	1	no	—
86	C₃×#117	—	3	2	no	—
87	C₂×C₃×C₄²	—	2	1	no	—
88	C₂×C₃×C₄²	—	3	2	no	—
89	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
91	C₄×#67	C₃×C₄	1	4	yes	—
92	#926	C₂²×C₃	1	1	yes	characteristic
93	C₂×#208	C₂²×C₃	1	2	yes	—
94	#901	C₃×C₄	1	16	yes	direct product factor
95	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
96	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
97	C₄×D₁₂	C₃×C₄	1	2	yes	—
98	#872	C₂²×C₃	1	2	yes	—
99	C₄²×D₃	C₂²×C₃	1	2	yes	—
100	C₄×Dic₆	C₃×C₄	1	2	yes	—
101	C₃×#97	—	3	4	no	—
102	C₃×#97	—	3	2	no	—
103	C₃×C₄×C₈	—	2	1	no	—
104	C₃×C₄×C₈	—	2	2	no	—
105	C₃×C₄×C₈	—	2	1	no	—
106	C₃×C₄×C₈	—	3	4	no	—
107	C₃×C₄×C₈	—	3	2	no	—
108	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
109	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
110	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
111	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
112	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
114	#815	C₂²×C₃	1	4	yes	—
115	C₈×Dic₃	C₂²×C₃	1	4	yes	—
116	#803	C₂²×C₃	1	2	yes	—
117	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
118	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
120	C₂×C₃²×C₄	—	2	4	no	—
121	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
122	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
124	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
125	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
126	C₃×#67	C₄²	1	8	yes	—
127	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
128	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
129	C₃×D₁₂	C₄²	1	4	yes	—
130	C₃×C₄×D₃	—	2	8	no	—
131	C₃×C₄×D₃	C₂²×C₄	1	8	yes	—
132	C₃×Dic₆	C₄²	1	4	yes	—
133	C₃²×C₈	C₂²×C₄	1	4	yes	—
134	C₃²×C₈	C₂²×C₄	1	4	yes	—
135	C₃×C₃⋊C₈	C₂²×C₄	1	8	yes	—
136	C₂×#131	—	3	2	no	—
137	C₄×#41	—	3	1	no	—
138	#405	—	3	2	no	—
139	#405	—	3	4	no	—
140	C₄×M₁₆	—	3	1	no	—
141	C₄×M₁₆	—	3	2	no	—
142	C₂×C₄×C₈	—	3	2	no	—
143	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
144	C₃×#41	—	3	8	no	—
145	C₂×C₃×Q₈	—	3	1	no	—
146	C₂×C₃×D₄	—	3	2	no	—
147	C₂×C₃×D₄	—	3	1	no	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	—	2	1	no	—
150	C₂²×C₃×C₄	—	3	2	no	—
151	C₂²×C₃×C₄	—	3	4	no	—
152	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
153	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
154	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
156	C₂×#67	C₂×C₃×C₄	1	2	yes	—
157	#235	C₂×C₃×C₄	1	8	yes	—
158	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
159	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
160	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
161	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
162	C₃×M₁₆	—	3	8	no	—
163	C₃×M₁₆	—	3	16	no	—
164	C₂×C₃×C₈	—	2	8	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	2	2	no	—
167	C₂×C₃×C₈	—	3	4	no	—
168	C₂×C₃×C₈	—	3	16	no	—
169	C₂×C₃×C₈	C₄×D₃	1	8	yes	complemented
170	C₂×C₃×C₈	C₂×C₃×C₄	1	8	yes	complemented
171	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
172	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
173	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
174	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
175	C₃×C₄⋊C₄	—	3	4	no	—
176	C₃×C₄⋊C₄	—	3	2	no	—
177	C₃×C₂²⋊C₄	—	3	2	no	—
178	C₃×C₂²⋊C₄	—	3	4	no	—
179	C₃×C₄²	—	2	2	no	—
180	C₃×C₄²	—	2	1	no	—
181	C₃×C₄²	—	2	1	no	—
182	C₃×C₄²	—	3	4	no	—
183	C₃×C₄²	—	3	2	no	—
184	C₃×C₄²	C₄×D₃	1	2	yes	—
185	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
186	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
187	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
188	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
189	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
190	#217	C₂×C₃×C₄	1	2	yes	—
191	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
192	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
193	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
194	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
195	C₄×Dic₃	C₂³×C₃	1	2	yes	—
196	#208	C₂×C₃×C₄	1	8	yes	complemented
197	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
198	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	16	yes	complemented
199	D₃×C₈	C₂×C₃×C₄	1	16	yes	complemented
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	C₂×C₄²	1	2	yes	—
202	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₃×D₃	—	2	4	no	—
204	C₂×C₃×D₃	C₂×C₄²	1	4	yes	—
205	C₃²×C₄	—	2	2	no	—
206	C₃²×C₄	C₂×C₄²	1	2	yes	—
207	C₃²×C₄	#131	1	4	yes	complemented
208	C₃²×C₄	C₂³×C₄	1	2	yes	—
209	C₃×Dic₃	—	2	4	no	—
210	C₃×Dic₃	C₂×C₄²	1	4	yes	—
211	C₂×#41	—	3	1	no	—
212	#131	—	3	16	no	—
213	C₂×M₁₆	—	3	2	no	—
214	C₂×M₁₆	—	3	4	no	—
215	C₂²×C₈	—	3	4	no	—
216	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
217	C₄×Q₈	—	3	2	no	—
218	C₄×D₄	—	3	4	no	—
219	C₄×D₄	—	3	2	no	—
220	#117	—	3	1	no	—
221	#117	—	3	2	no	—
222	C₂×C₄²	—	3	2	no	—
223	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
224	#97	—	3	4	no	—
225	#97	—	3	2	no	—
226	C₄×C₈	—	3	4	no	—
227	C₄×C₈	—	3	2	no	—
228	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
229	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
230	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	—	3	2	no	—
233	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
235	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
236	C₃×Q₈	—	3	4	no	—
237	C₃×D₄	—	3	8	no	—
238	C₃×D₄	—	3	4	no	—
239	C₂×C₃×C₄	—	2	8	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	3	2	no	—
248	C₂×C₃×C₄	—	3	8	no	—
249	C₂×C₃×C₄	—	3	4	no	—
250	C₂×C₃×C₄	—	6	8	no	—
251	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
254	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
255	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
256	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
258	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
259	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
261	#67	C₃×C₄²	1	8	yes	—
262	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
263	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
264	D₁₂	C₃×C₄²	1	4	yes	—
265	C₄×D₃	—	2	8	no	—
266	C₄×D₃	C₂²×C₃×C₄	1	8	yes	—
267	Dic₆	C₃×C₄²	1	4	yes	—
268	C₃×C₈	—	2	4	no	—
269	C₃×C₈	—	2	4	no	—
270	C₃×C₈	—	3	8	no	—
271	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
272	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
273	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
274	C₃×C₈	C₂²×C₃×C₄	1	4	yes	—
275	C₃⋊C₈	C₂²×C₃×C₄	1	8	yes	—
276	C₂×C₃²	—	2	2	no	—
277	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
278	C₂×C₃²	C₂×#131	1	2	yes	—
279	C₃×D₃	—	2	4	no	—
280	#41	—	3	8	no	—
281	C₂×Q₈	—	3	1	no	—
282	C₂×D₄	—	3	2	no	—
283	C₂×D₄	—	3	1	no	—
284	C₂²×C₄	—	3	2	no	—
285	C₂²×C₄	—	3	4	no	—
286	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
287	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
288	M₁₆	—	3	8	no	—
289	M₁₆	—	3	16	no	—
290	C₂×C₈	—	3	4	no	—
291	C₂×C₈	—	3	16	no	—
292	C₂×C₈	C₃×C₄×D₃	1	8	yes	complemented
293	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
294	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
295	C₄⋊C₄	—	3	4	no	—
296	C₄⋊C₄	—	3	2	no	—
297	C₂²⋊C₄	—	3	2	no	—
298	C₂²⋊C₄	—	3	4	no	—
299	C₄²	—	3	2	no	—
300	C₄²	—	3	4	no	—
301	C₄²	C₃×C₄×D₃	1	2	yes	—
302	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
304	C₂²×C₃	—	2	4	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	2	no	—
307	C₂²×C₃	—	2	1	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	3	4	no	—
310	C₂²×C₃	—	6	4	no	—
311	C₂²×C₃	C₄²×D₃	1	2	yes	—
312	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
313	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
314	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
315	C₂×D₃	—	2	4	no	—
316	C₂×D₃	C₂×C₃×C₄²	1	4	yes	—
317	C₃×C₄	—	2	4	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	2	4	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	2	no	—
323	C₃×C₄	—	3	4	no	—
324	C₃×C₄	—	6	4	no	—
325	C₃×C₄	C₄²×D₃	1	2	yes	—
326	C₃×C₄	#901	1	4	yes	direct product factor
327	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
328	C₃×C₄	C₃×#131	1	4	yes	complemented
329	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
330	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
331	Dic₃	—	2	4	no	—
332	Dic₃	C₂×C₃×C₄²	1	4	yes	—
333	C₃²	C₄×#131	1	1	yes	characteristic, complemented, Sylow
334	C₂³	—	3	2	no	—
335	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
336	Q₈	—	3	4	no	—
337	D₄	—	3	8	no	—
338	D₄	—	3	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	3	2	no	—
341	C₂×C₄	—	3	8	no	—
342	C₂×C₄	—	3	4	no	—
343	C₂×C₄	—	6	8	no	—
344	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
345	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
346	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
347	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
348	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
349	C₈	—	3	8	no	—
350	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
351	C₈	C₂×C₃×C₄×D₃	1	4	yes	—
352	C₂×C₃	—	2	4	no	—
353	C₂×C₃	—	2	2	no	—
354	C₂×C₃	—	2	2	no	—
355	C₂×C₃	—	2	1	no	—
356	C₂×C₃	—	2	2	no	—
357	C₂×C₃	—	6	4	no	—
358	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
359	C₂×C₃	C₂×#901	1	2	yes	—
360	C₂×C₃	C₂²×C₃×C₄²	1	1	yes	characteristic
361	C₂×C₃	C₂×C₃×#131	1	2	yes	—
362	D₃	—	2	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	3	4	no	—
365	C₂²	—	6	4	no	—
366	C₂²	C₃×C₄²×D₃	1	2	yes	—
367	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	3	4	no	—
370	C₄	—	6	4	no	—
371	C₄	C₃×C₄²×D₃	1	2	yes	—
372	C₄	C₃×#901	1	4	yes	direct product factor
373	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
374	C₃	—	2	1	no	—
375	C₃	C₄×#901	1	1	yes	characteristic, direct product factor
376	C₃	C₃×C₄×#131	1	1	yes	characteristic, complemented
377	C₂	—	2	2	no	—
378	C₂	—	6	4	no	—
379	C₂	C₂×C₃×C₄²×D₃	1	1	yes	characteristic
380	C₂	C₂×C₃×#901	1	2	yes	—

	subgroup	G/H
center	C₃×C₄×C₈	C₂×D₃
commutator	C₂×C₃	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×C₄×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄×C₈ ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃²×C₄×C₈	C₂	semidirect
4. C₃×#5101	C₂	semidirect
5. C₃×C₄×#208	C₂	semidirect
6. C₃×#4689	C₂	semidirect
7. C₃×C₄×ΓL(1,𝔽₂₅)	C₂	semidirect
8. C₃×C₄×D₃×C₈	C₂	semidirect
10. C₄×#901	C₃	direct (N × H)
17. C₃×#901	C₄	direct (N × H)
41. C₂×C₃×C₄×C₈	D₃	semidirect
42. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
43. #5101	C₂×C₃	semidirect
44. C₄×#208	C₂×C₃	semidirect
45. #4689	C₂×C₃	semidirect
46. C₄×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
47. C₄×D₃×C₈	C₂×C₃	semidirect
56. C₂×C₃²×C₈	C₂×C₄	semidirect
68. C₃×#208	C₂×C₄	semidirect
70. C₃×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
71. C₃×D₃×C₈	C₂×C₄	semidirect
94. #901	C₃×C₄	direct (N × H)
143. C₂×C₄×C₈	C₃×D₃	semidirect
169. C₂×C₃×C₈	C₄×D₃	semidirect
170. C₂×C₃×C₈	C₂×C₃×C₄	semidirect
196. #208	C₂×C₃×C₄	semidirect
198. ΓL(1,𝔽₂₅)	C₂×C₃×C₄	semidirect
199. D₃×C₈	C₂×C₃×C₄	semidirect
207. C₃²×C₄	#131	semidirect
292. C₂×C₈	C₃×C₄×D₃	semidirect
326. C₃×C₄	#901	direct (N × H)
328. C₃×C₄	C₃×#131	semidirect
333. C₃²	C₄×#131	semidirect
372. C₄	C₃×#901	direct (N × H)
375. C₃	C₄×#901	direct (N × H)
376. C₃	C₃×C₄×#131	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#901	2
C₃×C₄×#235	2
C₂×C₃²×C₄×C₈	2
C₃×#5101	2
C₃×C₄×#208	2
C₃×#4689	2
C₃×C₄×ΓL(1,𝔽₂₅)	2
C₃×C₄×D₃×C₈	2
C₃×C₄×#131	3
C₄×#901	3

Subgroups — C3×C4×#901 #11857249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#901 #11857249