Subgroups — C₂×C₃×#4685 #11858696

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×(C₂×D₃)⋊C₈	C₂	1	2	yes	maximal
4	C₂×C₃×Dic₃⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4685	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#431	—	3	1	no	maximal
8	C₂×#4685	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
10	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	2	yes	—
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₃	C₄	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₃	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
18	C₃×C₄²×D₃	C₄	1	4	yes	—
19	C₃×C₄²×D₃	C₂²	1	4	yes	—
20	C₃²×C₄×C₈	C₂²	1	4	yes	complemented
21	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
22	C₃×Dic₃⋊C₈	C₂²	1	8	yes	complemented
23	C₃×C₄×C₃⋊C₈	C₂²	1	4	yes	complemented
24	C₂²×C₃×C₄²	—	3	1	no	—
25	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
26	C₃×#431	—	3	8	no	—
27	C₂×C₃×C₄⋊C₈	—	3	2	no	—
28	C₂×C₃×C₂²⋊C₈	—	3	2	no	—
29	C₂×C₃×C₄×C₈	—	2	1	no	—
30	C₂×C₃×C₄×C₈	—	3	1	no	—
31	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
32	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×(C₂×D₃)⋊C₈	C₂×C₃	1	2	yes	—
34	C₂×Dic₃⋊C₈	C₂×C₃	1	2	yes	complemented
35	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
36	#4685	C₂×C₃	1	8	yes	direct product factor
37	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₃	—	2	4	no	—
45	C₂×C₃×C₄×D₃	—	2	4	no	—
46	C₂×C₃×C₄×D₃	C₈	1	8	yes	complemented
47	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
48	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	C₂×C₄	1	4	yes	—
50	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
51	C₂×C₃²×C₈	—	2	4	no	—
52	C₂×C₃²×C₈	C₂³	1	4	yes	—
53	C₃²×C₄²	C₂×C₄	1	2	yes	—
54	C₃²×C₄²	C₂³	1	2	yes	—
55	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
56	C₃×C₄×Dic₃	C₂×C₄	1	4	yes	—
57	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
58	C₃×C₄×Dic₃	C₂³	1	2	yes	—
59	C₂×C₃×C₃⋊C₈	—	2	4	no	—
60	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
61	C₂×#431	—	3	1	no	Sylow
62	C₂³×C₃×C₄	—	3	1	no	—
63	C₂³×C₃×C₄	—	3	1	no	—
64	C₂³×C₃×C₄	—	3	1	no	—
65	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
67	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
68	C₂²×C₃×C₈	—	2	2	no	—
69	C₂²×C₃×C₈	—	3	2	no	—
70	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
71	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
72	C₂×C₃×C₄²	—	2	1	no	—
73	C₂×C₃×C₄²	—	3	1	no	—
74	C₂×C₃×C₄²	—	3	1	no	—
75	C₂×C₃×C₄²	—	3	1	no	—
76	C₂×C₃×C₄²	—	3	4	no	—
77	C₂×C₃×C₄²	—	3	4	no	—
78	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄×Dic₃	C₃×C₄	1	1	yes	characteristic
81	C₂×C₄×Dic₃	C₃×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	—
84	C₄²×D₃	C₃×C₄	1	4	yes	—
85	C₄²×D₃	C₂²×C₃	1	4	yes	—
86	C₃×C₄⋊C₈	—	3	8	no	—
87	C₃×C₂²⋊C₈	—	3	8	no	—
88	C₃×C₄×C₈	—	2	4	no	—
89	C₃×C₄×C₈	—	3	4	no	—
90	C₃×C₄×C₈	C₂×D₃	1	4	yes	complemented
91	C₃×C₄×C₈	C₂²×C₃	1	4	yes	complemented
92	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	—
93	Dic₃⋊C₈	C₂²×C₃	1	8	yes	complemented
94	C₄×C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
95	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	2	2	no	—
97	C₂²×C₃×D₃	—	2	2	no	—
98	C₂²×C₃×D₃	C₂×C₈	1	4	yes	—
99	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
100	C₂×C₃²×C₄	C₂×C₈	1	4	yes	—
101	C₂×C₃²×C₄	M₁₆	1	4	yes	—
102	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
104	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
105	C₂×C₃²×C₄	#41	1	4	yes	—
106	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×Dic₃	—	2	2	no	—
108	C₂×C₃×Dic₃	—	2	2	no	—
109	C₂×C₃×Dic₃	C₂×C₈	1	4	yes	—
110	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
111	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
112	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
113	C₃×C₄×D₃	—	2	4	no	—
114	C₃×C₄×D₃	—	2	8	no	—
115	C₃×C₄×D₃	—	2	4	no	—
116	C₃×C₄×D₃	C₂×C₈	1	16	yes	complemented
117	C₃²×C₈	—	2	4	no	—
118	C₃×C₃⋊C₈	—	2	4	no	—
119	C₂²×C₄²	—	3	1	no	—
120	#431	—	3	8	no	—
121	C₂×C₄⋊C₈	—	3	2	no	—
122	C₂×C₂²⋊C₈	—	3	2	no	—
123	C₂×C₄×C₈	—	3	1	no	—
124	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
125	C₂⁴×C₃	—	3	1	no	—
126	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	1	no	—
129	C₂²×C₃×C₄	—	2	1	no	—
130	C₂²×C₃×C₄	—	3	1	no	—
131	C₂²×C₃×C₄	—	3	8	no	—
132	C₂²×C₃×C₄	—	3	4	no	—
133	C₂²×C₃×C₄	—	3	1	no	—
134	C₂²×C₃×C₄	—	3	1	no	—
135	C₂²×C₃×C₄	—	3	2	no	—
136	C₂²×C₃×C₄	—	3	4	no	—
137	C₂²×C₃×C₄	—	3	2	no	—
138	C₂²×C₃×C₄	—	6	4	no	—
139	C₂²×C₃×C₄	—	6	4	no	—
140	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
143	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
145	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
146	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂×C₄×D₃	—	2	4	no	—
150	C₂×C₄×D₃	—	2	4	no	—
151	C₂×C₄×D₃	C₃×C₈	1	8	yes	complemented
152	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
153	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
154	C₂×C₄×D₃	C₂×C₃×C₄	1	4	yes	—
155	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
156	C₂×C₃×C₈	—	2	8	no	—
157	C₂×C₃×C₈	—	2	4	no	—
158	C₂×C₃×C₈	—	2	4	no	—
159	C₂×C₃×C₈	—	2	4	no	—
160	C₂×C₃×C₈	—	3	4	no	—
161	C₂×C₃×C₈	—	6	4	no	—
162	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
163	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
164	C₃×C₄²	—	2	2	no	—
165	C₃×C₄²	—	2	2	no	—
166	C₃×C₄²	—	3	2	no	—
167	C₃×C₄²	—	3	4	no	—
168	C₃×C₄²	—	3	4	no	—
169	C₃×C₄²	—	3	2	no	—
170	C₃×C₄²	C₄×D₃	1	2	yes	—
171	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
172	C₃×C₄²	C₂²×D₃	1	2	yes	—
173	C₃×C₄²	C₂³×C₃	1	2	yes	—
174	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
175	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
176	C₄×Dic₃	C₂×C₃×C₄	1	4	yes	—
177	C₄×Dic₃	C₂³×C₃	1	2	yes	—
178	C₂×C₃⋊C₈	—	2	4	no	—
179	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
180	C₂²×C₃²	#117	1	2	yes	—
181	C₂²×C₃²	C₂²×C₈	1	2	yes	—
182	C₂²×C₃²	C₂×M₁₆	1	2	yes	—
183	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₃×D₃	—	2	2	no	—
185	C₂×C₃×D₃	—	2	2	no	—
186	C₂×C₃×D₃	—	2	8	no	—
187	C₂×C₃×D₃	C₂²×C₈	1	4	yes	—
188	C₃²×C₄	#117	1	2	yes	—
189	C₃²×C₄	C₂²×C₈	1	4	yes	—
190	C₃²×C₄	C₂×M₁₆	1	4	yes	—
191	C₃²×C₄	C₂×#41	1	2	yes	—
192	C₃×Dic₃	—	2	2	no	—
193	C₃×Dic₃	—	2	2	no	—
194	C₃×Dic₃	C₂²×C₈	1	4	yes	—
195	C₂³×C₄	—	3	1	no	—
196	C₂³×C₄	—	3	1	no	—
197	C₂³×C₄	—	3	1	no	—
198	C₂²×C₈	—	3	2	no	—
199	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
200	C₂×C₄²	—	3	1	no	—
201	C₂×C₄²	—	3	1	no	—
202	C₂×C₄²	—	3	1	no	—
203	C₂×C₄²	—	3	4	no	—
204	C₂×C₄²	—	3	4	no	—
205	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
206	C₄⋊C₈	—	3	8	no	—
207	C₂²⋊C₈	—	3	8	no	—
208	C₄×C₈	—	3	4	no	—
209	C₄×C₈	C₂×C₃×D₃	1	4	yes	complemented
210	C₂³×C₃	—	2	1	no	—
211	C₂³×C₃	—	3	4	no	—
212	C₂³×C₃	—	3	2	no	—
213	C₂³×C₃	—	6	2	no	—
214	C₂³×C₃	—	6	2	no	—
215	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
216	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂²×D₃	—	2	2	no	—
218	C₂²×D₃	—	2	2	no	—
219	C₂²×D₃	C₂×C₃×C₈	1	4	yes	—
220	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	4	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	3	4	no	—
229	C₂×C₃×C₄	—	3	2	no	—
230	C₂×C₃×C₄	—	3	16	no	—
231	C₂×C₃×C₄	—	3	2	no	—
232	C₂×C₃×C₄	—	3	2	no	—
233	C₂×C₃×C₄	—	6	2	no	—
234	C₂×C₃×C₄	—	6	2	no	—
235	C₂×C₃×C₄	—	6	4	no	—
236	C₂×C₃×C₄	—	6	8	no	—
237	C₂×C₃×C₄	—	6	4	no	—
238	C₂×C₃×C₄	D₃×C₈	1	4	yes	—
239	C₂×C₃×C₄	ΓL(1,𝔽₂₅)	1	4	yes	—
240	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	—
241	C₂×C₃×C₄	C₃×M₁₆	1	4	yes	—
242	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
244	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
245	C₂×C₃×C₄	#235	1	4	yes	—
246	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
248	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
249	C₂×C₃×C₄	C₃×#41	1	4	yes	—
250	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
252	C₂×Dic₃	—	2	2	no	—
253	C₂×Dic₃	—	2	2	no	—
254	C₂×Dic₃	C₂×C₃×C₈	1	4	yes	—
255	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
256	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
257	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
258	C₄×D₃	—	2	4	no	—
259	C₄×D₃	—	2	8	no	—
260	C₄×D₃	—	2	4	no	—
261	C₄×D₃	C₂×C₃×C₈	1	16	yes	complemented
262	C₃×C₈	—	2	8	no	—
263	C₃×C₈	—	2	4	no	—
264	C₃×C₈	—	2	4	no	—
265	C₃×C₈	—	6	4	no	—
266	C₃⋊C₈	—	2	4	no	—
267	C₂×C₃²	#431	1	4	yes	complemented
268	C₂×C₃²	C₂×#117	1	1	yes	characteristic
269	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
270	C₂×C₃²	C₂²×M₁₆	1	1	yes	characteristic
271	C₃×D₃	—	2	4	no	—
272	C₂⁴	—	3	1	no	—
273	C₂²×C₄	—	3	1	no	—
274	C₂²×C₄	—	3	8	no	—
275	C₂²×C₄	—	3	4	no	—
276	C₂²×C₄	—	3	1	no	—
277	C₂²×C₄	—	3	1	no	—
278	C₂²×C₄	—	3	2	no	—
279	C₂²×C₄	—	3	4	no	—
280	C₂²×C₄	—	3	2	no	—
281	C₂²×C₄	—	6	4	no	—
282	C₂²×C₄	—	6	4	no	—
283	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
284	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	3	4	no	—
288	C₂×C₈	—	6	4	no	—
289	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
290	C₄²	—	3	2	no	—
291	C₄²	—	3	4	no	—
292	C₄²	—	3	2	no	—
293	C₄²	—	3	4	no	—
294	C₄²	C₃×C₄×D₃	1	2	yes	—
295	C₄²	C₂²×C₃×D₃	1	2	yes	—
296	C₂²×C₃	—	2	2	no	—
297	C₂²×C₃	—	2	2	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	3	4	no	—
301	C₂²×C₃	—	6	8	no	—
302	C₂²×C₃	—	6	2	no	—
303	C₂²×C₃	—	6	2	no	—
304	C₂²×C₃	#872	1	2	yes	—
305	C₂²×C₃	C₂×D₃×C₈	1	2	yes	—
306	C₂²×C₃	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
307	C₂²×C₃	C₃×#117	1	2	yes	—
308	C₂²×C₃	C₂²×C₃×C₈	1	2	yes	—
309	C₂²×C₃	C₂×C₃×M₁₆	1	2	yes	—
310	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
311	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
312	C₂×D₃	—	2	2	no	—
313	C₂×D₃	—	2	8	no	—
314	C₂×D₃	—	2	2	no	—
315	C₂×D₃	C₂²×C₃×C₈	1	4	yes	—
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	—	2	4	no	—
318	C₃×C₄	—	2	2	no	—
319	C₃×C₄	—	2	2	no	—
320	C₃×C₄	—	3	4	no	—
321	C₃×C₄	—	6	2	no	—
322	C₃×C₄	—	6	2	no	—
323	C₃×C₄	#872	1	2	yes	—
324	C₃×C₄	C₂×D₃×C₈	1	4	yes	—
325	C₃×C₄	C₂×ΓL(1,𝔽₂₅)	1	4	yes	—
326	C₃×C₄	C₃×#117	1	2	yes	—
327	C₃×C₄	C₂²×C₃×C₈	1	4	yes	—
328	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	—
329	C₃×C₄	C₂×#235	1	2	yes	—
330	C₃×C₄	C₂×C₃×#41	1	2	yes	—
331	Dic₃	—	2	2	no	—
332	Dic₃	—	2	2	no	—
333	Dic₃	C₂²×C₃×C₈	1	4	yes	—
334	C₃²	C₂×#431	1	1	yes	characteristic, complemented, Sylow
335	C₂³	—	3	4	no	—
336	C₂³	—	3	2	no	—
337	C₂³	—	6	2	no	—
338	C₂³	—	6	2	no	—
339	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
340	C₂×C₄	—	3	4	no	—
341	C₂×C₄	—	3	2	no	—
342	C₂×C₄	—	3	16	no	—
343	C₂×C₄	—	3	2	no	—
344	C₂×C₄	—	3	2	no	—
345	C₂×C₄	—	6	2	no	—
346	C₂×C₄	—	6	2	no	—
347	C₂×C₄	—	6	8	no	—
348	C₂×C₄	—	6	4	no	—
349	C₂×C₄	—	6	4	no	—
350	C₂×C₄	C₃×D₃×C₈	1	4	yes	—
351	C₂×C₄	C₃×ΓL(1,𝔽₂₅)	1	4	yes	—
352	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
353	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
354	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
355	C₂×C₄	C₃×#235	1	4	yes	—
356	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	6	4	no	—
359	C₂×C₃	—	2	4	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	6	4	no	—
364	C₂×C₃	#4685	1	4	yes	direct product factor
365	C₂×C₃	C₃×#431	1	4	yes	complemented
366	C₂×C₃	C₂×#872	1	1	yes	characteristic
367	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
368	C₂×C₃	C₂²×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
369	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
370	C₂×C₃	C₂³×C₃×C₈	1	1	yes	characteristic
371	C₂×C₃	C₂²×C₃×M₁₆	1	1	yes	characteristic
372	D₃	—	2	4	no	—
373	C₂²	—	3	4	no	—
374	C₂²	—	6	8	no	—
375	C₂²	—	6	2	no	—
376	C₂²	—	6	2	no	—
377	C₂²	C₃×#872	1	2	yes	—
378	C₂²	C₂×C₃×D₃×C₈	1	2	yes	—
379	C₂²	C₂×C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
380	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
381	C₄	—	3	4	no	—
382	C₄	—	6	2	no	—
383	C₄	—	6	2	no	—
384	C₄	C₃×#872	1	2	yes	—
385	C₄	C₂×C₃×D₃×C₈	1	4	yes	—
386	C₄	C₂×C₃×ΓL(1,𝔽₂₅)	1	4	yes	—
387	C₄	C₂×C₃×#235	1	2	yes	—
388	C₃	—	2	1	no	—
389	C₃	C₂×#4685	1	1	yes	characteristic, direct product factor
390	C₃	C₂×C₃×#431	1	1	yes	characteristic, complemented
391	C₂	—	6	4	no	—
392	C₂	C₃×#4685	1	4	yes	direct product factor
393	C₂	C₂×C₃×#872	1	1	yes	characteristic
394	C₂	C₂²×C₃×D₃×C₈	1	1	yes	characteristic
395	C₂	C₂²×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄²	C₂×D₃
commutator	C₂×C₃	C₂³×C₃×C₈
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₂×C₃×#431
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×C₄×C₈	C₂	semidirect
4. C₂×C₃×Dic₃⋊C₈	C₂	semidirect
5. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
6. C₃×#4685	C₂	direct (N × H)
8. C₂×#4685	C₃	direct (N × H)
20. C₃²×C₄×C₈	C₂²	semidirect
22. C₃×Dic₃⋊C₈	C₂²	semidirect
23. C₃×C₄×C₃⋊C₈	C₂²	semidirect
31. C₂×C₃×C₄×C₈	D₃	semidirect
32. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
34. C₂×Dic₃⋊C₈	C₂×C₃	semidirect
35. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
36. #4685	C₂×C₃	direct (N × H)
46. C₂×C₃×C₄×D₃	C₈	semidirect
90. C₃×C₄×C₈	C₂×D₃	semidirect
91. C₃×C₄×C₈	C₂²×C₃	semidirect
93. Dic₃⋊C₈	C₂²×C₃	semidirect
94. C₄×C₃⋊C₈	C₂²×C₃	semidirect
116. C₃×C₄×D₃	C₂×C₈	semidirect
124. C₂×C₄×C₈	C₃×D₃	semidirect
151. C₂×C₄×D₃	C₃×C₈	semidirect
209. C₄×C₈	C₂×C₃×D₃	semidirect
261. C₄×D₃	C₂×C₃×C₈	semidirect
267. C₂×C₃²	#431	semidirect
334. C₃²	C₂×#431	semidirect
364. C₂×C₃	#4685	direct (N × H)
365. C₂×C₃	C₃×#431	semidirect
389. C₃	C₂×#4685	direct (N × H)
390. C₃	C₂×C₃×#431	semidirect
392. C₂	C₃×#4685	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×D₃	2
C₂×C₃²×C₄×C₈	2
C₂×C₃×(C₂×D₃)⋊C₈	2
C₂×C₃×Dic₃⋊C₈	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×#4685	2
C₂×C₃×#431	3
C₂×#4685	3

Subgroups — C2×C3×#4685 #11858696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4685 #11858696