Subgroups — C₃×C₈×#235 #11861540

Order 1152.

993 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₈×#67	C₂	1	4	yes	maximal, complemented
4	C₃×#4925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₈×D₁₂	C₂	1	2	yes	maximal, complemented
6	C₃×#4685	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×D₃×C₈	C₂	1	2	yes	maximal, complemented
8	C₃×C₈×Dic₆	C₂	1	2	yes	maximal, complemented
9	C₃×C₈×#41	—	3	1	no	maximal
10	C₈×#235	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#235	C₄	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	2	yes	—
15	C₃×C₄×#67	C₂²	1	2	yes	—
16	C₃×#926	C₄	1	1	yes	characteristic
17	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
18	C₃×C₄×D₁₂	C₄	1	1	yes	characteristic
19	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
20	C₃×#872	C₄	1	2	yes	—
21	C₃×C₄²×D₃	C₂²	1	2	yes	—
22	C₃×C₄×Dic₆	C₄	1	1	yes	characteristic
23	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
24	C₃²×C₄×C₈	C₂²	1	2	yes	—
25	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
26	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
27	C₃×#830	C₂²	1	2	yes	—
28	C₃×(C₂×D₃)⋊C₈	C₂²	1	4	yes	—
29	C₃×Dic₃⋊C₈	C₂²	1	4	yes	—
30	C₃×C₈×Dic₃	C₂²	1	4	yes	—
31	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
32	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
33	C₃×C₄×#41	—	3	1	no	—
34	C₄×#235	C₂×C₃	1	1	yes	characteristic
35	C₃×C₈×Q₈	—	3	2	no	—
36	C₃×C₈×D₄	—	3	4	no	—
37	C₃×C₈×D₄	—	3	2	no	—
38	C₃×#431	—	3	1	no	—
39	C₃×#431	—	3	2	no	—
40	C₂×C₃×C₄×C₈	—	2	1	no	—
41	C₂×C₃×C₄×C₈	—	3	2	no	—
42	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
43	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₈×#67	C₂×C₃	1	4	yes	complemented
45	#4925	C₂×C₃	1	1	yes	characteristic, complemented
46	C₈×D₁₂	C₂×C₃	1	2	yes	complemented
47	#4685	C₂×C₃	1	2	yes	complemented
48	C₄×D₃×C₈	C₂×C₃	1	2	yes	complemented
49	C₈×Dic₆	C₂×C₃	1	2	yes	complemented
50	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
53	C₂×C₃×#67	C₂×C₄	1	2	yes	—
54	C₃×#235	C₈	1	8	yes	direct product factor
55	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
57	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
59	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃²×C₈	—	2	4	no	—
61	C₂×C₃²×C₈	C₂³	1	2	yes	—
62	C₂×C₃²×C₈	C₂³	1	2	yes	—
63	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
64	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
65	C₃²×C₄²	C₂³	1	1	yes	characteristic
66	C₃²×C₄²	C₂³	1	1	yes	characteristic
67	C₃×#217	C₂×C₄	1	2	yes	—
68	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
70	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
73	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
74	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
75	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₃	C₂³	1	2	yes	—
77	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
78	C₃×D₃×C₈	—	2	8	no	—
79	C₈×#41	—	3	1	no	Sylow
80	C₂×C₃×#41	—	3	1	no	—
81	C₂×#235	C₃×C₄	1	1	yes	characteristic
82	C₂²×C₃×C₈	—	2	2	no	—
83	C₂²×C₃×C₈	—	3	4	no	—
84	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
85	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	—
86	C₃×C₄×Q₈	—	3	1	no	—
87	C₃×C₄×Q₈	—	3	1	no	—
88	C₃×C₄×D₄	—	3	2	no	—
89	C₃×C₄×D₄	—	3	2	no	—
90	C₃×C₄×D₄	—	3	1	no	—
91	C₃×C₄×D₄	—	3	1	no	—
92	C₃×#117	—	3	1	no	—
93	C₃×#117	—	3	2	no	—
94	C₂×C₃×C₄²	—	2	1	no	—
95	C₂×C₃×C₄²	—	3	2	no	—
96	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
97	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
98	C₄×#67	C₃×C₄	1	2	yes	—
99	C₄×#67	C₂²×C₃	1	2	yes	—
100	#926	C₃×C₄	1	1	yes	characteristic
101	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
102	C₄×D₁₂	C₃×C₄	1	1	yes	characteristic
103	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
104	#872	C₃×C₄	1	2	yes	—
105	C₄²×D₃	C₂²×C₃	1	2	yes	—
106	C₄×Dic₆	C₃×C₄	1	1	yes	characteristic
107	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
108	C₃×C₄⋊C₈	—	3	4	no	—
109	C₃×C₄⋊C₈	—	3	2	no	—
110	C₃×C₂²⋊C₈	—	3	2	no	—
111	C₃×C₂²⋊C₈	—	3	4	no	—
112	C₃×C₄×C₈	—	2	1	no	—
113	C₃×C₄×C₈	—	2	2	no	—
114	C₃×C₄×C₈	—	2	1	no	—
115	C₃×C₄×C₈	—	3	4	no	—
116	C₃×C₄×C₈	—	3	2	no	—
117	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
118	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
119	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
120	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
121	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
122	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
123	#830	C₂²×C₃	1	2	yes	—
124	(C₂×D₃)⋊C₈	C₂²×C₃	1	4	yes	—
125	Dic₃⋊C₈	C₂²×C₃	1	4	yes	—
126	C₈×Dic₃	C₂²×C₃	1	4	yes	—
127	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
128	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
129	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
131	C₂×C₃²×C₄	—	2	2	no	—
132	C₂×C₃²×C₄	—	2	2	no	—
133	C₂×C₃²×C₄	C₂×C₈	1	4	yes	complemented
134	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
140	C₃×#67	C₂×C₈	1	8	yes	complemented
141	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
142	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
143	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
144	C₃×D₁₂	C₂×C₈	1	4	yes	complemented
145	C₃×C₄×D₃	—	2	4	no	—
146	C₃×C₄×D₃	—	2	4	no	—
147	C₃×C₄×D₃	C₂×C₈	1	8	yes	complemented
148	C₃×Dic₆	C₂×C₈	1	4	yes	complemented
149	C₃²×C₈	—	2	2	no	—
150	C₃²×C₈	#41	1	4	yes	complemented
151	C₃×C₃⋊C₈	—	2	4	no	—
152	C₄×#41	—	3	1	no	—
153	C₈×Q₈	—	3	2	no	—
154	C₈×D₄	—	3	4	no	—
155	C₈×D₄	—	3	2	no	—
156	#431	—	3	1	no	—
157	#431	—	3	2	no	—
158	C₂×C₄×C₈	—	3	2	no	—
159	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
160	C₃×#41	—	3	8	no	—
161	C₂×C₃×Q₈	—	3	1	no	—
162	C₂×C₃×D₄	—	3	2	no	—
163	C₂×C₃×D₄	—	3	1	no	—
164	C₂²×C₃×C₄	—	2	1	no	—
165	C₂²×C₃×C₄	—	2	1	no	—
166	C₂²×C₃×C₄	—	2	1	no	—
167	C₂²×C₃×C₄	—	3	2	no	—
168	C₂²×C₃×C₄	—	3	2	no	—
169	C₂²×C₃×C₄	—	3	2	no	—
170	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×#67	C₂×C₃×C₄	1	2	yes	—
177	#235	C₃×C₈	1	8	yes	direct product factor
178	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
179	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
180	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
181	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
182	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
183	C₂×C₃×C₈	—	2	8	no	—
184	C₂×C₃×C₈	—	2	4	no	—
185	C₂×C₃×C₈	—	2	4	no	—
186	C₂×C₃×C₈	—	2	2	no	—
187	C₂×C₃×C₈	—	2	2	no	—
188	C₂×C₃×C₈	—	3	4	no	—
189	C₂×C₃×C₈	—	6	8	no	—
190	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
191	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
192	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
193	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
194	C₃×C₄⋊C₄	—	3	2	no	—
195	C₃×C₄⋊C₄	—	3	2	no	—
196	C₃×C₄⋊C₄	—	3	1	no	—
197	C₃×C₄⋊C₄	—	3	1	no	—
198	C₃×C₂²⋊C₄	—	3	2	no	—
199	C₃×C₂²⋊C₄	—	3	2	no	—
200	C₃×C₂²⋊C₄	—	3	2	no	—
201	C₃×C₄²	—	2	1	no	—
202	C₃×C₄²	—	2	1	no	—
203	C₃×C₄²	—	2	1	no	—
204	C₃×C₄²	—	2	1	no	—
205	C₃×C₄²	—	3	2	no	—
206	C₃×C₄²	—	3	2	no	—
207	C₃×C₄²	—	3	2	no	—
208	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
209	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
210	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
211	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
212	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
213	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
214	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
215	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
216	#217	C₂×C₃×C₄	1	2	yes	—
217	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
218	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
219	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
220	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
221	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
222	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
223	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
224	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
225	C₄×Dic₃	C₂³×C₃	1	2	yes	—
226	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
227	D₃×C₈	—	2	8	no	—
228	C₂²×C₃²	—	2	1	no	—
229	C₂²×C₃²	—	2	1	no	—
230	C₂²×C₃²	C₂²×C₈	1	2	yes	—
231	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₃×D₃	—	2	2	no	—
233	C₂×C₃×D₃	—	2	2	no	—
234	C₂×C₃×D₃	C₂²×C₈	1	4	yes	—
235	C₃²×C₄	—	2	1	no	—
236	C₃²×C₄	—	2	1	no	—
237	C₃²×C₄	C₂²×C₈	1	2	yes	—
238	C₃²×C₄	C₂²×C₈	1	2	yes	—
239	C₃²×C₄	#131	1	2	yes	—
240	C₃²×C₄	C₂×#41	1	2	yes	—
241	C₃×Dic₃	—	2	2	no	—
242	C₃×Dic₃	—	2	2	no	—
243	C₃×Dic₃	C₂²×C₈	1	4	yes	—
244	C₂×#41	—	3	1	no	—
245	C₂²×C₈	—	3	4	no	—
246	C₂²×C₈	C₂×C₃×D₃	1	2	yes	—
247	C₄×Q₈	—	3	1	no	—
248	C₄×Q₈	—	3	1	no	—
249	C₄×D₄	—	3	2	no	—
250	C₄×D₄	—	3	2	no	—
251	C₄×D₄	—	3	1	no	—
252	C₄×D₄	—	3	1	no	—
253	#117	—	3	1	no	—
254	#117	—	3	2	no	—
255	C₂×C₄²	—	3	2	no	—
256	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
257	C₄⋊C₈	—	3	4	no	—
258	C₄⋊C₈	—	3	2	no	—
259	C₂²⋊C₈	—	3	2	no	—
260	C₂²⋊C₈	—	3	4	no	—
261	C₄×C₈	—	3	4	no	—
262	C₄×C₈	—	3	2	no	—
263	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
264	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
265	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
266	C₂³×C₃	—	2	1	no	—
267	C₂³×C₃	—	3	2	no	—
268	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
269	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
270	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
271	C₃×Q₈	—	3	4	no	—
272	C₃×D₄	—	3	8	no	—
273	C₃×D₄	—	3	4	no	—
274	C₂×C₃×C₄	—	2	4	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	1	no	—
281	C₂×C₃×C₄	—	2	4	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	3	2	no	—
288	C₂×C₃×C₄	—	3	8	no	—
289	C₂×C₃×C₄	—	3	2	no	—
290	C₂×C₃×C₄	—	3	2	no	—
291	C₂×C₃×C₄	—	6	4	no	—
292	C₂×C₃×C₄	—	6	4	no	—
293	C₂×C₃×C₄	D₃×C₈	1	4	yes	complemented
294	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	complemented
295	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
307	#67	C₂×C₃×C₈	1	8	yes	complemented
308	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
309	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
310	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
311	D₁₂	C₂×C₃×C₈	1	4	yes	complemented
312	C₄×D₃	—	2	4	no	—
313	C₄×D₃	—	2	4	no	—
314	C₄×D₃	C₂×C₃×C₈	1	8	yes	complemented
315	Dic₆	C₂×C₃×C₈	1	4	yes	complemented
316	C₃×C₈	—	2	4	no	—
317	C₃×C₈	—	2	2	no	—
318	C₃×C₈	—	2	2	no	—
319	C₃×C₈	—	2	4	no	—
320	C₃×C₈	—	6	4	no	—
321	C₃×C₈	#235	1	4	yes	direct product factor
322	C₃×C₈	C₃×#41	1	4	yes	complemented
323	C₃⋊C₈	—	2	4	no	—
324	C₂×C₃²	—	2	2	no	—
325	C₂×C₃²	C₄×#41	1	1	yes	characteristic
326	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
327	C₂×C₃²	C₂×#131	1	1	yes	characteristic
328	C₃×D₃	—	2	4	no	—
329	#41	—	3	8	no	—
330	C₂×Q₈	—	3	1	no	—
331	C₂×D₄	—	3	2	no	—
332	C₂×D₄	—	3	1	no	—
333	C₂²×C₄	—	3	2	no	—
334	C₂²×C₄	—	3	2	no	—
335	C₂²×C₄	—	3	2	no	—
336	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
337	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	3	4	no	—
341	C₂×C₈	—	6	8	no	—
342	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
343	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
344	C₄⋊C₄	—	3	2	no	—
345	C₄⋊C₄	—	3	2	no	—
346	C₄⋊C₄	—	3	1	no	—
347	C₄⋊C₄	—	3	1	no	—
348	C₂²⋊C₄	—	3	2	no	—
349	C₂²⋊C₄	—	3	2	no	—
350	C₂²⋊C₄	—	3	2	no	—
351	C₄²	—	3	2	no	—
352	C₄²	—	3	2	no	—
353	C₄²	—	3	2	no	—
354	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
355	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
356	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
357	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
358	C₂²×C₃	—	2	2	no	—
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	3	4	no	—
367	C₂²×C₃	—	6	2	no	—
368	C₂²×C₃	—	6	2	no	—
369	C₂²×C₃	C₂×D₃×C₈	1	2	yes	—
370	C₂²×C₃	C₂²×C₃×C₈	1	2	yes	—
371	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
372	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
373	C₂×D₃	—	2	2	no	—
374	C₂×D₃	—	2	2	no	—
375	C₂×D₃	C₂²×C₃×C₈	1	4	yes	—
376	C₃×C₄	—	2	2	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	2	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	2	no	—
386	C₃×C₄	—	3	4	no	—
387	C₃×C₄	—	6	2	no	—
388	C₃×C₄	—	6	2	no	—
389	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
390	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
391	C₃×C₄	#901	1	2	yes	—
392	C₃×C₄	C₂²×C₃×C₈	1	2	yes	—
393	C₃×C₄	C₂²×C₃×C₈	1	2	yes	—
394	C₃×C₄	C₃×#131	1	2	yes	—
395	C₃×C₄	C₂×#235	1	2	yes	—
396	C₃×C₄	C₂×C₃×#41	1	2	yes	—
397	Dic₃	—	2	2	no	—
398	Dic₃	—	2	2	no	—
399	Dic₃	C₂²×C₃×C₈	1	4	yes	—
400	C₃²	C₈×#41	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	3	2	no	—
402	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
403	Q₈	—	3	4	no	—
404	D₄	—	3	8	no	—
405	D₄	—	3	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	3	2	no	—
409	C₂×C₄	—	3	8	no	—
410	C₂×C₄	—	3	2	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	6	4	no	—
413	C₂×C₄	—	6	4	no	—
414	C₂×C₄	C₃×D₃×C₈	1	4	yes	complemented
415	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
417	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
418	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
419	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
420	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	6	4	no	—
423	C₈	C₃×#235	1	4	yes	direct product factor
424	C₂×C₃	—	2	4	no	—
425	C₂×C₃	—	2	2	no	—
426	C₂×C₃	—	2	2	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	—	2	1	no	—
430	C₂×C₃	—	6	4	no	—
431	C₂×C₃	C₄×#235	1	1	yes	characteristic
432	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
433	C₂×C₃	C₂×#901	1	1	yes	characteristic
434	C₂×C₃	C₃×C₄×#41	1	1	yes	characteristic
435	C₂×C₃	C₂³×C₃×C₈	1	1	yes	characteristic
436	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
437	D₃	—	2	4	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	3	4	no	—
441	C₂²	—	6	2	no	—
442	C₂²	—	6	2	no	—
443	C₂²	C₂×C₃×D₃×C₈	1	2	yes	—
444	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	3	4	no	—
448	C₄	—	6	2	no	—
449	C₄	—	6	2	no	—
450	C₄	C₂×C₃×D₃×C₈	1	2	yes	—
451	C₄	C₂×C₃×D₃×C₈	1	2	yes	—
452	C₄	C₃×#901	1	2	yes	—
453	C₄	C₂×C₃×#235	1	2	yes	—
454	C₃	—	2	1	no	—
455	C₃	C₈×#235	1	1	yes	characteristic, direct product factor
456	C₃	C₃×C₈×#41	1	1	yes	characteristic, complemented
457	C₂	—	2	2	no	—
458	C₂	—	6	4	no	—
459	C₂	C₃×C₄×#235	1	1	yes	characteristic
460	C₂	C₂²×C₃×D₃×C₈	1	1	yes	characteristic
461	C₂	C₂×C₃×#901	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₈	C₂×D₃
commutator	C₂×C₃	C₂³×C₃×C₈
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#235	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×C₈×#41
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
2. C₂×C₃²×C₄×C₈	C₂	semidirect
3. C₃×C₈×#67	C₂	semidirect
4. C₃×#4925	C₂	semidirect
5. C₃×C₈×D₁₂	C₂	semidirect
6. C₃×#4685	C₂	semidirect
7. C₃×C₄×D₃×C₈	C₂	semidirect
8. C₃×C₈×Dic₆	C₂	semidirect
10. C₈×#235	C₃	direct (N × H)
42. C₂×C₃×C₄×C₈	D₃	semidirect
43. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
44. C₈×#67	C₂×C₃	semidirect
45. #4925	C₂×C₃	semidirect
46. C₈×D₁₂	C₂×C₃	semidirect
47. #4685	C₂×C₃	semidirect
48. C₄×D₃×C₈	C₂×C₃	semidirect
49. C₈×Dic₆	C₂×C₃	semidirect
54. C₃×#235	C₈	direct (N × H)
133. C₂×C₃²×C₄	C₂×C₈	semidirect
140. C₃×#67	C₂×C₈	semidirect
144. C₃×D₁₂	C₂×C₈	semidirect
147. C₃×C₄×D₃	C₂×C₈	semidirect
148. C₃×Dic₆	C₂×C₈	semidirect
150. C₃²×C₈	#41	semidirect
159. C₂×C₄×C₈	C₃×D₃	semidirect
177. #235	C₃×C₈	direct (N × H)
293. C₂×C₃×C₄	D₃×C₈	semidirect
294. C₂×C₃×C₄	C₂×C₃×C₈	semidirect
307. #67	C₂×C₃×C₈	semidirect
311. D₁₂	C₂×C₃×C₈	semidirect
314. C₄×D₃	C₂×C₃×C₈	semidirect
315. Dic₆	C₂×C₃×C₈	semidirect
321. C₃×C₈	#235	direct (N × H)
322. C₃×C₈	C₃×#41	semidirect
400. C₃²	C₈×#41	semidirect
414. C₂×C₄	C₃×D₃×C₈	semidirect
423. C₈	C₃×#235	direct (N × H)
455. C₃	C₈×#235	direct (N × H)
456. C₃	C₃×C₈×#41	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#235	2
C₂×C₃²×C₄×C₈	2
C₃×C₈×#67	2
C₃×#4925	2
C₃×C₈×D₁₂	2
C₃×#4685	2
C₃×C₄×D₃×C₈	2
C₃×C₈×Dic₆	2
C₃×C₈×#41	3
C₈×#235	3

Subgroups — C3×C8×#235 #11861540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×#235 #11861540