Subgroups — C₃×C₈×(C₂×D₃)⋊C₄ #11783634

Order 1152.

849 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	C₂²×C₃×D₃×C₈	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	1	yes	maximal, characteristic
4	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₃×#4550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4524	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₈×C₂²⋊C₄	—	3	1	no	maximal
9	C₈×(C₂×D₃)⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
15	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×D₃×C₈	—	2	2	no	—
19	C₂×C₃×D₃×C₈	—	2	2	no	—
20	C₂×C₃×D₃×C₈	C₄	1	4	yes	complemented
21	C₃²×C₄×C₈	—	2	2	no	—
22	C₃×C₃⋊#95	C₄	1	2	yes	—
23	C₃×(C₂×D₃)⋊C₈	C₄	1	4	yes	complemented
24	C₃×C₈×Dic₃	—	2	2	no	—
25	C₂³×C₃×C₈	—	3	1	no	—
26	C₂²×D₃×C₈	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊C₈	—	3	1	no	—
28	C₂×C₃×C₄×C₈	—	2	1	no	—
29	C₂×C₃×C₄×C₈	—	3	1	no	—
30	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₃×C₄×C₂²⋊C₄	—	3	1	no	—
33	C₂×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
34	C₂×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
35	C₄×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
36	C₃×#336	—	3	1	no	—
37	C₃×#336	—	3	1	no	—
38	#4550	C₂×C₃	1	1	yes	characteristic, complemented
39	#4524	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
42	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
43	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₃	—	2	1	no	—
46	C₂×C₃×C₄×D₃	—	2	1	no	—
47	C₂×C₃×C₄×D₃	—	2	1	no	—
48	C₂×C₃×C₄×D₃	—	2	1	no	—
49	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
51	C₂×C₃²×C₈	—	2	1	no	—
52	C₂×C₃²×C₈	—	2	1	no	—
53	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
54	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
55	C₂×C₃²×C₈	D₄	1	2	yes	—
56	C₂×C₃²×C₈	D₄	1	2	yes	—
57	C₃²×C₄²	—	2	1	no	—
58	C₃²×C₄²	—	2	1	no	—
59	C₃×(C₂×D₃)⋊C₄	C₈	1	8	yes	direct product factor
60	C₃×C₄×Dic₃	—	2	1	no	—
61	C₃×C₄×Dic₃	—	2	1	no	—
62	C₂×C₃×C₃⋊C₈	—	2	1	no	—
63	C₂×C₃×C₃⋊C₈	—	2	1	no	—
64	C₂×C₃×C₃⋊C₈	—	2	1	no	—
65	C₂×C₃×C₃⋊C₈	—	2	1	no	—
66	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
67	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
68	C₃×D₃×C₈	—	2	8	no	—
69	C₈×C₂²⋊C₄	—	3	1	no	Sylow
70	C₂³×C₃×C₄	—	3	1	no	—
71	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	—	2	1	no	—
73	C₂²×C₃×C₈	—	2	1	no	—
74	C₂²×C₃×C₈	—	3	1	no	—
75	C₂²×C₃×C₈	—	3	1	no	—
76	C₂²×C₃×C₈	—	3	4	no	—
77	C₂²×C₃×C₈	—	6	2	no	—
78	C₂²×C₃×C₈	—	6	2	no	—
79	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
80	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
84	C₂×C₃×C₄²	—	2	1	no	—
85	C₂×C₃×C₄²	—	3	1	no	—
86	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
87	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
88	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
89	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
92	C₂×D₃×C₈	—	2	2	no	—
93	C₂×D₃×C₈	—	2	2	no	—
94	C₂×D₃×C₈	C₃×C₄	1	4	yes	complemented
95	C₃×C₂²⋊C₈	—	3	4	no	—
96	C₃×C₄×C₈	—	2	4	no	—
97	C₃×C₄×C₈	—	2	2	no	—
98	C₃×C₄×C₈	—	2	2	no	—
99	C₃×C₄×C₈	—	6	2	no	—
100	C₃×#95	—	3	2	no	—
101	C₃⋊#95	C₃×C₄	1	2	yes	—
102	(C₂×D₃)⋊C₈	C₃×C₄	1	4	yes	complemented
103	C₈×Dic₃	—	2	2	no	—
104	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₃×D₃	—	2	1	no	—
106	C₂²×C₃×D₃	—	2	1	no	—
107	C₂²×C₃×D₃	—	2	2	no	—
108	C₂²×C₃×D₃	C₄²	1	2	yes	—
109	C₂²×C₃×D₃	C₂×C₈	1	4	yes	—
110	C₂×C₃²×C₄	—	2	2	no	—
111	C₂×C₃²×C₄	—	2	2	no	—
112	C₂×C₃²×C₄	C₂×C₈	1	4	yes	complemented
113	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃²×C₄	#41	1	1	yes	characteristic
118	C₂×C₃²×C₄	#41	1	1	yes	characteristic
119	C₂×C₃×Dic₃	—	2	2	no	—
120	C₂×C₃×Dic₃	—	2	1	no	—
121	C₂×C₃×Dic₃	—	2	1	no	—
122	C₂×C₃×Dic₃	—	2	2	no	—
123	C₂×C₃×Dic₃	C₄²	1	2	yes	—
124	C₂×C₃×Dic₃	C₂×C₈	1	4	yes	complemented
125	C₃×C₄×D₃	—	2	2	no	—
126	C₃×C₄×D₃	—	2	2	no	—
127	C₃×C₄×D₃	—	2	2	no	—
128	C₃×C₄×D₃	—	2	2	no	—
129	C₃²×C₈	—	2	2	no	—
130	C₃²×C₈	C₂²⋊C₄	1	4	yes	complemented
131	C₃×C₃⋊C₈	—	2	2	no	—
132	C₃×C₃⋊C₈	—	2	2	no	—
133	C₂³×C₈	—	3	1	no	—
134	C₂×C₂²⋊C₈	—	3	1	no	—
135	C₂×C₄×C₈	—	3	1	no	—
136	C₂×C₄×C₈	C₃×D₃	1	1	yes	characteristic, complemented
137	C₄×C₂²⋊C₄	—	3	1	no	—
138	#336	—	3	1	no	—
139	#336	—	3	1	no	—
140	C₂⁴×C₃	—	3	1	no	—
141	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
142	C₂²×C₃×C₄	—	2	2	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	3	1	no	—
145	C₂²×C₃×C₄	—	3	2	no	—
146	C₂²×C₃×C₄	—	3	2	no	—
147	C₂²×C₃×C₄	—	3	2	no	—
148	C₂²×C₃×C₄	—	6	1	no	—
149	C₂²×C₃×C₄	—	6	1	no	—
150	C₂²×C₃×C₄	—	6	1	no	—
151	C₂²×C₃×C₄	—	6	1	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	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
158	C₂×C₄×D₃	—	2	1	no	—
159	C₂×C₄×D₃	—	2	1	no	—
160	C₂×C₄×D₃	—	2	1	no	—
161	C₂×C₄×D₃	—	2	1	no	—
162	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
163	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
164	C₂×C₃×C₈	—	2	2	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	—	2	1	no	—
168	C₂×C₃×C₈	—	2	1	no	—
169	C₂×C₃×C₈	—	2	1	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₂×C₃×C₈	—	2	2	no	—
172	C₂×C₃×C₈	—	2	2	no	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	—	3	2	no	—
175	C₂×C₃×C₈	—	3	2	no	—
176	C₂×C₃×C₈	—	6	1	no	—
177	C₂×C₃×C₈	—	6	1	no	—
178	C₂×C₃×C₈	—	6	1	no	—
179	C₂×C₃×C₈	—	6	1	no	—
180	C₂×C₃×C₈	—	6	8	no	—
181	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
182	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
183	C₂×C₃×C₈	D₁₂	1	2	yes	—
184	C₂×C₃×C₈	#67	1	2	yes	—
185	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
186	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
187	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
188	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
189	C₃×C₂²⋊C₄	—	3	8	no	—
190	C₃×C₄²	—	2	2	no	—
191	C₃×C₄²	—	2	2	no	—
192	C₃×C₄²	—	2	1	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	—	2	1	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	—	6	1	no	—
197	C₃×C₄²	—	6	1	no	—
198	(C₂×D₃)⋊C₄	C₃×C₈	1	8	yes	direct product factor
199	C₄×Dic₃	—	2	1	no	—
200	C₄×Dic₃	—	2	1	no	—
201	C₂×C₃⋊C₈	—	2	1	no	—
202	C₂×C₃⋊C₈	—	2	1	no	—
203	C₂×C₃⋊C₈	—	2	1	no	—
204	C₂×C₃⋊C₈	—	2	1	no	—
205	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
206	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
207	D₃×C₈	—	2	8	no	—
208	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
209	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
210	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
211	C₂²×C₃²	C₂²×C₈	1	2	yes	—
212	C₂²×C₃²	#131	1	2	yes	—
213	C₂×C₃×D₃	—	2	2	no	—
214	C₂×C₃×D₃	—	2	2	no	—
215	C₂×C₃×D₃	—	2	4	no	—
216	C₂×C₃×D₃	—	2	4	no	—
217	C₂×C₃×D₃	C₄×C₈	1	4	yes	complemented
218	C₃²×C₄	—	2	4	no	—
219	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₃²×C₄	#117	1	1	yes	characteristic
221	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
222	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
223	C₃×Dic₃	—	2	2	no	—
224	C₃×Dic₃	—	2	4	no	—
225	C₂³×C₄	—	3	1	no	—
226	C₂²×C₈	—	3	1	no	—
227	C₂²×C₈	—	3	1	no	—
228	C₂²×C₈	—	3	4	no	—
229	C₂²×C₈	—	6	2	no	—
230	C₂²×C₈	—	6	2	no	—
231	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	—	3	2	no	—
234	C₂×C₄²	—	3	1	no	—
235	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
236	C₂²⋊C₈	—	3	4	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	—	6	2	no	—
239	#95	—	3	2	no	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	—	3	2	no	—
242	C₂³×C₃	—	3	4	no	—
243	C₂³×C₃	—	6	1	no	—
244	C₂³×C₃	—	6	2	no	—
245	C₂³×C₃	—	6	1	no	—
246	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
248	C₂²×D₃	—	2	1	no	—
249	C₂²×D₃	—	2	1	no	—
250	C₂²×D₃	—	2	2	no	—
251	C₂²×D₃	C₃×C₄²	1	2	yes	—
252	C₂²×D₃	C₂×C₃×C₈	1	4	yes	—
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	4	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	3	2	no	—
267	C₂×C₃×C₄	—	3	4	no	—
268	C₂×C₃×C₄	—	6	2	no	—
269	C₂×C₃×C₄	—	6	1	no	—
270	C₂×C₃×C₄	—	6	2	no	—
271	C₂×C₃×C₄	—	6	1	no	—
272	C₂×C₃×C₄	—	6	2	no	—
273	C₂×C₃×C₄	—	6	2	no	—
274	C₂×C₃×C₄	—	6	2	no	—
275	C₂×C₃×C₄	—	6	2	no	—
276	C₂×C₃×C₄	D₃×C₈	1	4	yes	complemented
277	C₂×C₃×C₄	C₂×C₃×C₈	1	4	yes	complemented
278	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
281	C₂×C₃×C₄	#235	1	1	yes	characteristic
282	C₂×C₃×C₄	#235	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
289	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
290	C₂×Dic₃	—	2	2	no	—
291	C₂×Dic₃	—	2	1	no	—
292	C₂×Dic₃	—	2	1	no	—
293	C₂×Dic₃	—	2	2	no	—
294	C₂×Dic₃	C₃×C₄²	1	2	yes	—
295	C₂×Dic₃	C₂×C₃×C₈	1	4	yes	complemented
296	C₄×D₃	—	2	2	no	—
297	C₄×D₃	—	2	2	no	—
298	C₄×D₃	—	2	2	no	—
299	C₄×D₃	—	2	2	no	—
300	C₃×C₈	—	2	4	no	—
301	C₃×C₈	—	2	2	no	—
302	C₃×C₈	—	2	2	no	—
303	C₃×C₈	—	2	4	no	—
304	C₃×C₈	—	6	2	no	—
305	C₃×C₈	—	6	2	no	—
306	C₃×C₈	(C₂×D₃)⋊C₄	1	4	yes	direct product factor
307	C₃×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
308	C₃⋊C₈	—	2	2	no	—
309	C₃⋊C₈	—	2	2	no	—
310	C₂×C₃²	C₄×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
312	C₂×C₃²	#405	1	1	yes	characteristic
313	C₂×C₃²	C₈×D₄	1	2	yes	—
314	C₂×C₃²	C₈×D₄	1	2	yes	—
315	C₃×D₃	—	2	4	no	—
316	C₂⁴	—	3	1	no	—
317	C₂²×C₄	—	3	1	no	—
318	C₂²×C₄	—	3	2	no	—
319	C₂²×C₄	—	3	2	no	—
320	C₂²×C₄	—	3	2	no	—
321	C₂²×C₄	—	6	1	no	—
322	C₂²×C₄	—	6	1	no	—
323	C₂²×C₄	—	6	1	no	—
324	C₂²×C₄	—	6	1	no	—
325	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
326	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	3	2	no	—
330	C₂×C₈	—	3	2	no	—
331	C₂×C₈	—	6	1	no	—
332	C₂×C₈	—	6	1	no	—
333	C₂×C₈	—	6	1	no	—
334	C₂×C₈	—	6	1	no	—
335	C₂×C₈	—	6	8	no	—
336	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
337	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
338	C₂×C₈	C₃×D₁₂	1	2	yes	—
339	C₂×C₈	C₃×#67	1	2	yes	—
340	C₂²⋊C₄	—	3	8	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	6	1	no	—
344	C₄²	—	6	1	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	2	1	no	—
350	C₂²×C₃	—	3	4	no	—
351	C₂²×C₃	—	6	2	no	—
352	C₂²×C₃	—	6	4	no	—
353	C₂²×C₃	—	6	2	no	—
354	C₂²×C₃	—	6	4	no	—
355	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
356	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
357	C₂²×C₃	C₂×D₃×C₈	1	2	yes	—
358	C₂²×C₃	#901	1	2	yes	—
359	C₂²×C₃	C₄×#67	1	1	yes	characteristic
360	C₂²×C₃	C₂×C₃×C₄²	1	1	yes	characteristic
361	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
362	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
363	C₂²×C₃	C₂²×C₃×C₈	1	2	yes	—
364	C₂²×C₃	C₃×#131	1	2	yes	—
365	C₂×D₃	—	2	2	no	—
366	C₂×D₃	—	2	2	no	—
367	C₂×D₃	—	2	4	no	—
368	C₂×D₃	—	2	4	no	—
369	C₂×D₃	C₃×C₄×C₈	1	4	yes	complemented
370	C₃×C₄	—	2	8	no	—
371	C₃×C₄	—	2	4	no	—
372	C₃×C₄	—	2	4	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	6	2	no	—
378	C₃×C₄	—	6	4	no	—
379	C₃×C₄	#872	1	1	yes	characteristic
380	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
381	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
382	C₃×C₄	C₄×#67	1	1	yes	characteristic
383	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
384	C₃×C₄	C₃×#117	1	1	yes	characteristic
385	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
386	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
387	Dic₃	—	2	2	no	—
388	Dic₃	—	2	4	no	—
389	C₃²	C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
390	C₂³	—	3	4	no	—
391	C₂³	—	3	2	no	—
392	C₂³	—	6	2	no	—
393	C₂³	—	6	1	no	—
394	C₂³	—	6	1	no	—
395	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	3	4	no	—
399	C₂×C₄	—	3	2	no	—
400	C₂×C₄	—	6	2	no	—
401	C₂×C₄	—	6	1	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	6	1	no	—
404	C₂×C₄	—	6	2	no	—
405	C₂×C₄	—	6	2	no	—
406	C₂×C₄	—	6	2	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	C₃×D₃×C₈	1	4	yes	complemented
409	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
410	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
411	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
412	C₂×C₄	C₃×#235	1	1	yes	characteristic
413	C₂×C₄	C₃×#235	1	1	yes	characteristic
414	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	6	2	no	—
417	C₈	—	6	2	no	—
418	C₈	C₃×(C₂×D₃)⋊C₄	1	4	yes	direct product factor
419	C₂×C₃	—	2	1	no	—
420	C₂×C₃	—	2	1	no	—
421	C₂×C₃	—	2	2	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	2	2	no	—
424	C₂×C₃	—	6	4	no	—
425	C₂×C₃	C₄×D₃×C₈	1	1	yes	characteristic
426	C₂×C₃	C₈×D₁₂	1	2	yes	—
427	C₂×C₃	#4689	1	1	yes	characteristic
428	C₂×C₃	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
429	C₂×C₃	C₈×#67	1	2	yes	—
430	C₂×C₃	C₃×C₄×C₂²⋊C₄	1	1	yes	characteristic
431	C₂×C₃	C₂×C₃×C₄×C₈	1	1	yes	characteristic
432	C₂×C₃	C₃×#405	1	1	yes	characteristic
433	C₂×C₃	C₃×C₈×D₄	1	2	yes	—
434	C₂×C₃	C₃×C₈×D₄	1	2	yes	—
435	D₃	—	2	4	no	—
436	C₂²	—	3	4	no	—
437	C₂²	—	6	2	no	—
438	C₂²	—	6	4	no	—
439	C₂²	—	6	2	no	—
440	C₂²	—	6	4	no	—
441	C₂²	C₃×C₄²×D₃	1	1	yes	characteristic
442	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
443	C₂²	C₂×C₃×D₃×C₈	1	2	yes	—
444	C₂²	C₃×#901	1	2	yes	—
445	C₂²	C₃×C₄×#67	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	6	2	no	—
448	C₄	—	6	4	no	—
449	C₄	C₃×#872	1	1	yes	characteristic
450	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
451	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
452	C₄	C₃×C₄×#67	1	1	yes	characteristic
453	C₃	—	2	1	no	—
454	C₃	C₈×(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor
455	C₃	C₃×C₈×C₂²⋊C₄	1	1	yes	characteristic, complemented
456	C₂	—	6	4	no	—
457	C₂	C₃×C₄×D₃×C₈	1	1	yes	characteristic
458	C₂	C₃×C₈×D₁₂	1	2	yes	—
459	C₂	C₃×#4689	1	1	yes	characteristic
460	C₂	C₃×C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
461	C₂	C₃×C₈×#67	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₈	C₂×D₃
commutator	C₂×C₃	C₂×C₃×C₄×C₈
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×C₈×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×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
4. C₂×C₃×C₈×Dic₃	C₂	semidirect
6. C₃×#4550	C₂	semidirect
7. C₃×#4524	C₂	semidirect
9. C₈×(C₂×D₃)⋊C₄	C₃	direct (N × H)
20. C₂×C₃×D₃×C₈	C₄	semidirect
23. C₃×(C₂×D₃)⋊C₈	C₄	semidirect
30. C₂×C₃×C₄×C₈	D₃	semidirect
31. C₂×C₃×C₄×C₈	C₂×C₃	semidirect
34. C₂×C₈×Dic₃	C₂×C₃	semidirect
38. #4550	C₂×C₃	semidirect
39. #4524	C₂×C₃	semidirect
59. C₃×(C₂×D₃)⋊C₄	C₈	direct (N × H)
94. C₂×D₃×C₈	C₃×C₄	semidirect
102. (C₂×D₃)⋊C₈	C₃×C₄	semidirect
112. C₂×C₃²×C₄	C₂×C₈	semidirect
124. C₂×C₃×Dic₃	C₂×C₈	semidirect
130. C₃²×C₈	C₂²⋊C₄	semidirect
136. C₂×C₄×C₈	C₃×D₃	semidirect
198. (C₂×D₃)⋊C₄	C₃×C₈	direct (N × H)
217. C₂×C₃×D₃	C₄×C₈	semidirect
276. C₂×C₃×C₄	D₃×C₈	semidirect
277. C₂×C₃×C₄	C₂×C₃×C₈	semidirect
295. C₂×Dic₃	C₂×C₃×C₈	semidirect
306. C₃×C₈	(C₂×D₃)⋊C₄	direct (N × H)
307. C₃×C₈	C₃×C₂²⋊C₄	semidirect
369. C₂×D₃	C₃×C₄×C₈	semidirect
389. C₃²	C₈×C₂²⋊C₄	semidirect
408. C₂×C₄	C₃×D₃×C₈	semidirect
418. C₈	C₃×(C₂×D₃)⋊C₄	direct (N × H)
454. C₃	C₈×(C₂×D₃)⋊C₄	direct (N × H)
455. C₃	C₃×C₈×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₃×C₈	2
C₂×C₃²×C₄×C₈	2
C₂×C₃×(C₂×D₃)⋊C₈	2
C₂×C₃×C₈×Dic₃	2
C₃×C₄×(C₂×D₃)⋊C₄	2
C₃×#4550	2
C₃×#4524	2
C₃×C₈×C₂²⋊C₄	3
C₈×(C₂×D₃)⋊C₄	3

Subgroups — C3×C8×(C2×D3)⋊C4 #11783634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×(C₂×D₃)⋊C₄ #11783634