Subgroups — C₃⋊C₈×#237 #11861553

Order 1152.

979 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#237	C₂	1	1	yes	maximal, characteristic
2	D₄×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#67⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
5	C₃⋊C₈×#67	C₂	1	2	yes	maximal, complemented
6	#10591053	C₂	1	2	yes	maximal, complemented
7	C₂×Dic₃×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₄×D₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#10590250	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃⋊C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#10590248	C₂	1	1	yes	maximal, characteristic, complemented
12	#41×C₃⋊C₈	—	3	1	no	maximal
13	C₈×#237	—	3	1	no	maximal
14	C₂×C₃×#237	C₄	1	1	yes	characteristic
15	C₃²×C₄×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
17	C₃×D₄×Dic₃	C₄	1	1	yes	characteristic
18	C₃×C₄×#67	C₂²	1	2	yes	—
19	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
20	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
21	C₃×#892	C₄	1	1	yes	characteristic
22	C₃×#887	C₄	1	1	yes	characteristic
23	C₃×#67⋊C₄	C₄	1	2	yes	—
24	C₃×#877	C₄	1	2	yes	—
25	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
27	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×D₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
29	#63657	C₂²	1	2	yes	—
30	C₄⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
31	C₄×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
32	C₃×#830	C₂²	1	2	yes	—
33	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
35	Dic₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
36	Dic₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
37	(C₂×D₃)⋊(C₃⋊C₈)	C₂²	1	2	yes	—
38	Dic₃×C₃⋊C₈	C₂²	1	2	yes	—
39	Dic₃×C₃⋊C₈	C₂²	1	2	yes	—
40	Dic₃×C₃⋊C₈	C₂²	1	2	yes	—
41	Dic₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	Dic₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₄×#41	—	3	1	no	—
44	C₄×#237	D₃	1	1	yes	characteristic
45	C₃×C₈×D₄	—	3	1	no	—
46	C₈×#67	—	3	2	no	—
47	C₂×C₈×Dic₃	—	3	2	no	—
48	Q₈×C₃⋊C₈	—	3	1	no	—
49	Q₈×C₃⋊C₈	—	3	1	no	—
50	D₄×C₃⋊C₈	—	3	1	no	—
51	D₄×C₃⋊C₈	—	3	1	no	—
52	D₄×C₃⋊C₈	—	3	2	no	—
53	D₄×C₃⋊C₈	—	3	2	no	—
54	D₄×C₃⋊C₈	—	6	1	no	—
55	D₄×C₃⋊C₈	D₃	1	1	yes	characteristic, complemented
56	#4925	—	3	2	no	—
57	#4925	—	3	1	no	—
58	C₂×C₄×C₃⋊C₈	—	3	2	no	—
59	C₂×C₄×C₃⋊C₈	—	3	1	no	—
60	#4833	—	3	1	no	—
61	#4830	—	3	1	no	—
62	#67⋊C₈	—	3	2	no	—
63	#4718	—	3	2	no	—
64	C₄×D₃×C₈	—	3	1	no	—
65	C₈×Dic₆	—	3	1	no	—
66	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₃²×C₄	C₂³	1	2	yes	—
68	C₂×C₃×#67	C₂×C₄	1	2	yes	—
69	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
70	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
71	C₃×#237	C₈	1	8	yes	complemented
72	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
75	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
76	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₃²×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₃²×C₄²	C₂³	1	1	yes	characteristic
79	C₂×C₃⋊(C₃⋊C₈)	—	2	4	no	—
80	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
81	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
82	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	1	yes	characteristic
83	C₃×#217	C₂×C₄	1	2	yes	—
84	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
85	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
86	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
87	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
88	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
89	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
90	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
91	C₃×C₄×Dic₃	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
93	C₃×C₄×Dic₃	C₂³	1	2	yes	—
94	C₂×C₃×C₃⋊C₈	—	2	4	no	—
95	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
96	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
98	D₃×C₃⋊C₈	—	2	2	no	—
99	D₃×C₃⋊C₈	—	2	2	no	—
100	C₈×#41	—	9	1	no	Sylow
101	C₂×C₃×#41	—	3	1	no	—
102	C₂×#237	Dic₃	1	1	yes	characteristic
103	C₂²×C₃×C₈	—	3	2	no	—
104	C₃×C₄×Q₈	—	3	1	no	—
105	C₃×C₄×Q₈	—	3	1	no	—
106	C₃×C₄×D₄	—	2	1	no	—
107	C₃×C₄×D₄	—	3	1	no	—
108	C₃×C₄×D₄	—	3	2	no	—
109	C₃×C₄×D₄	—	3	2	no	—
110	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
111	C₃×C₄×D₄	C₂×D₃	1	1	yes	characteristic
112	C₃×#117	—	3	1	no	—
113	C₃×#117	—	3	2	no	—
114	C₂×C₃×C₄²	—	3	2	no	—
115	C₂×C₃×C₄²	—	3	1	no	—
116	D₄×Dic₃	Dic₃	1	1	yes	characteristic
117	C₄×#67	C₂×D₃	1	2	yes	—
118	C₂×C₄×Dic₃	C₂×D₃	1	2	yes	—
119	C₂²×C₃⋊C₈	—	3	2	no	—
120	C₂²×C₃⋊C₈	—	3	2	no	—
121	C₂²×C₃⋊C₈	—	3	1	no	—
122	C₂²×C₃⋊C₈	—	3	1	no	—
123	C₂²×C₃⋊C₈	—	6	2	no	—
124	C₂²×C₃⋊C₈	C₂×D₃	1	2	yes	—
125	C₂×D₃×C₈	—	3	1	no	—
126	C₂×D₃×C₈	—	3	1	no	—
127	#892	Dic₃	1	1	yes	characteristic
128	#887	Dic₃	1	1	yes	characteristic
129	#67⋊C₄	Dic₃	1	2	yes	—
130	#877	Dic₃	1	2	yes	—
131	C₄²×D₃	C₂×D₃	1	1	yes	characteristic
132	C₄×Dic₆	C₂×D₃	1	1	yes	characteristic
133	C₃×C₄⋊C₈	—	3	1	no	—
134	C₃×C₂²⋊C₈	—	3	2	no	—
135	C₃×C₄×C₈	—	3	1	no	—
136	#830	—	3	2	no	—
137	#830	—	3	2	no	—
138	#830	—	3	2	no	—
139	#830	—	6	2	no	—
140	#830	C₂×D₃	1	2	yes	—
141	(C₂×D₃)⋊C₈	—	3	2	no	—
142	Dic₃⋊C₈	—	3	2	no	—
143	Dic₃⋊C₈	—	3	2	no	—
144	C₈×Dic₃	—	3	2	no	—
145	C₈×Dic₃	—	3	1	no	—
146	C₈×Dic₃	—	3	1	no	—
147	C₈×Dic₃	—	3	2	no	—
148	C₈×Dic₃	—	3	2	no	—
149	C₄⋊(C₃⋊C₈)	—	3	1	no	—
150	C₄⋊(C₃⋊C₈)	—	3	1	no	—
151	C₄⋊(C₃⋊C₈)	—	3	2	no	—
152	C₄⋊(C₃⋊C₈)	—	3	2	no	—
153	C₄⋊(C₃⋊C₈)	—	6	1	no	—
154	C₄⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
155	C₄×C₃⋊C₈	—	3	1	no	—
156	C₄×C₃⋊C₈	—	3	1	no	—
157	C₄×C₃⋊C₈	—	3	1	no	—
158	C₄×C₃⋊C₈	—	3	2	no	—
159	C₄×C₃⋊C₈	—	3	1	no	—
160	C₄×C₃⋊C₈	—	3	2	no	—
161	C₄×C₃⋊C₈	—	3	2	no	—
162	C₄×C₃⋊C₈	—	6	1	no	—
163	C₄×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
164	C₂³×C₃²	C₂²×C₄	1	2	yes	—
165	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
166	C₃²×D₄	C₂×C₈	1	4	yes	complemented
167	C₂×C₃²×C₄	—	2	2	no	—
168	C₂×C₃²×C₄	—	2	2	no	—
169	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
170	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
173	C₃×#67	C₂×C₈	1	8	yes	complemented
174	C₂×C₃×Dic₃	—	2	4	no	—
175	C₂×C₃×Dic₃	C₂×C₈	1	8	yes	complemented
176	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
178	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
180	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
181	C₃×C₄×D₃	—	2	1	no	—
182	C₃×C₄×D₃	—	2	1	no	—
183	C₃×C₄×D₃	—	2	2	no	—
184	C₃×C₄×D₃	C₂×C₈	1	4	yes	complemented
185	C₃×Dic₆	C₂×C₈	1	4	yes	complemented
186	C₃⋊(C₃⋊C₈)	—	2	1	no	—
187	C₃⋊(C₃⋊C₈)	—	2	2	no	—
188	C₃⋊(C₃⋊C₈)	#41	1	2	yes	complemented
189	C₃×C₃⋊C₈	—	2	1	no	—
190	C₃×C₃⋊C₈	—	2	2	no	—
191	C₃×C₃⋊C₈	#41	1	2	yes	complemented
192	C₄×#41	—	3	1	no	—
193	C₈×Q₈	—	9	1	no	—
194	C₈×Q₈	—	9	1	no	—
195	C₈×D₄	—	3	1	no	—
196	C₈×D₄	—	9	2	no	—
197	C₈×D₄	—	9	2	no	—
198	C₈×D₄	—	9	1	no	—
199	#431	—	9	2	no	—
200	#431	—	9	1	no	—
201	C₂×C₄×C₈	—	9	1	no	—
202	C₂×C₄×C₈	—	9	2	no	—
203	C₃×#41	—	3	8	no	—
204	C₂×C₃×Q₈	—	3	1	no	—
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	—	3	2	no	—
207	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
208	C₂×C₃×D₄	C₂×Dic₃	1	1	yes	characteristic
209	C₂²×C₃×C₄	—	2	2	no	—
210	C₂²×C₃×C₄	—	3	2	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	—	3	2	no	—
213	C₂²×C₃×C₄	—	3	1	no	—
214	C₂²×C₃×C₄	—	3	1	no	—
215	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
216	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
217	C₂×#67	C₂×Dic₃	1	2	yes	—
218	C₂²×Dic₃	C₂×Dic₃	1	2	yes	—
219	C₂²×Dic₃	C₂×Dic₃	1	2	yes	—
220	#237	C₃⋊C₈	1	8	yes	direct product factor
221	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
222	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
223	C₂×C₄×D₃	C₂²×D₃	1	1	yes	characteristic
224	C₂×Dic₆	C₂×Dic₃	1	1	yes	characteristic
225	C₂×C₃×C₈	—	3	1	no	—
226	C₂×C₃×C₈	—	3	2	no	—
227	C₂×C₃×C₈	—	3	1	no	—
228	C₂×C₃×C₈	—	6	4	no	—
229	C₃×C₄⋊C₄	—	2	1	no	—
230	C₃×C₄⋊C₄	—	3	2	no	—
231	C₃×C₄⋊C₄	—	3	2	no	—
232	C₃×C₄⋊C₄	—	3	1	no	—
233	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
234	C₃×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
235	C₃×C₂²⋊C₄	—	2	2	no	—
236	C₃×C₂²⋊C₄	—	3	2	no	—
237	C₃×C₂²⋊C₄	—	3	2	no	—
238	C₃×C₂²⋊C₄	C₄×D₃	1	2	yes	—
239	C₃×C₂²⋊C₄	C₂×Dic₃	1	2	yes	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	—	3	2	no	—
242	C₃×C₄²	—	3	1	no	—
243	C₃×C₄²	—	3	2	no	—
244	C₃×C₄²	—	3	1	no	—
245	C₃×C₄²	—	3	1	no	—
246	C₃×C₄²	—	3	2	no	—
247	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
248	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
249	#217	C₂×Dic₃	1	2	yes	—
250	(C₂×D₃)⋊C₄	C₂×Dic₃	1	2	yes	—
251	C₄⋊Dic₃	C₂×Dic₃	1	1	yes	characteristic
252	Dic₃⋊C₄	C₂×Dic₃	1	2	yes	—
253	Dic₃⋊C₄	C₂×Dic₃	1	2	yes	—
254	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
255	C₄×Dic₃	C₂×Dic₃	1	1	yes	characteristic
256	C₄×Dic₃	C₂×Dic₃	1	2	yes	—
257	C₄×Dic₃	C₂×Dic₃	1	2	yes	—
258	C₄×Dic₃	C₂²×D₃	1	1	yes	characteristic
259	C₄×Dic₃	C₂²×D₃	1	2	yes	—
260	C₂×C₃⋊C₈	—	2	4	no	—
261	C₂×C₃⋊C₈	—	3	1	no	—
262	C₂×C₃⋊C₈	—	3	1	no	—
263	C₂×C₃⋊C₈	—	3	1	no	—
264	C₂×C₃⋊C₈	—	3	2	no	—
265	C₂×C₃⋊C₈	—	3	1	no	—
266	C₂×C₃⋊C₈	—	3	2	no	—
267	C₂×C₃⋊C₈	—	6	1	no	—
268	C₂×C₃⋊C₈	—	6	1	no	—
269	C₂×C₃⋊C₈	—	6	2	no	—
270	C₂×C₃⋊C₈	—	6	2	no	—
271	C₂×C₃⋊C₈	—	6	4	no	—
272	C₂×C₃⋊C₈	—	6	4	no	—
273	C₂×C₃⋊C₈	—	6	2	no	—
274	C₂×C₃⋊C₈	—	12	4	no	—
275	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
276	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
277	C₂×C₃⋊C₈	C₂²×D₃	1	1	yes	characteristic
278	D₃×C₈	—	6	2	no	—
279	D₃×C₈	—	6	2	no	—
280	C₂²×C₃²	—	2	2	no	—
281	C₂²×C₃²	—	2	2	no	—
282	C₂²×C₃²	C₂²×C₈	1	4	yes	—
283	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₃×D₃	—	2	1	no	—
285	C₂×C₃×D₃	—	2	1	no	—
286	C₂×C₃×D₃	C₂²×C₈	1	2	yes	—
287	C₃²×C₄	—	2	2	no	—
288	C₃²×C₄	—	2	1	no	—
289	C₃²×C₄	C₂²×C₈	1	2	yes	—
290	C₃²×C₄	C₂×#41	1	1	yes	characteristic
291	C₃²×C₄	C₂×#41	1	1	yes	characteristic
292	C₃×Dic₃	—	2	1	no	—
293	C₃×Dic₃	—	2	2	no	—
294	C₃×Dic₃	C₂²×C₈	1	4	yes	—
295	C₃×Dic₃	C₂²×C₈	1	2	yes	—
296	C₃×Dic₃	#131	1	2	yes	—
297	C₂×#41	—	3	1	no	—
298	C₂²×C₈	—	3	2	no	—
299	C₂²×C₈	—	9	1	no	—
300	C₂²×C₈	—	9	1	no	—
301	C₂²×C₈	—	9	2	no	—
302	C₄×Q₈	—	3	1	no	—
303	C₄×Q₈	—	3	1	no	—
304	C₄×D₄	—	3	1	no	—
305	C₄×D₄	—	3	2	no	—
306	C₄×D₄	—	3	2	no	—
307	C₄×D₄	D₃²	1	1	yes	characteristic
308	#117	—	3	1	no	—
309	#117	—	3	2	no	—
310	C₂×C₄²	—	3	2	no	—
311	C₂×C₄²	—	3	1	no	—
312	C₄⋊C₈	—	3	1	no	—
313	C₄⋊C₈	—	9	2	no	—
314	C₄⋊C₈	—	9	2	no	—
315	C₄⋊C₈	—	9	1	no	—
316	C₂²⋊C₈	—	3	2	no	—
317	C₂²⋊C₈	—	9	2	no	—
318	C₂²⋊C₈	—	9	2	no	—
319	C₄×C₈	—	3	1	no	—
320	C₄×C₈	—	9	1	no	—
321	C₄×C₈	—	9	1	no	—
322	C₄×C₈	—	9	2	no	—
323	C₄×C₈	—	9	2	no	—
324	C₄×C₈	—	9	2	no	—
325	C₄×C₈	—	9	1	no	—
326	C₂³×C₃	—	2	2	no	—
327	C₂³×C₃	—	3	1	no	—
328	C₂³×C₃	C₂×C₄×D₃	1	2	yes	—
329	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
330	C₂²×D₃	C₂²×Dic₃	1	1	yes	characteristic
331	C₃×Q₈	—	3	4	no	—
332	C₃×D₄	—	2	4	no	—
333	C₃×D₄	—	3	8	no	—
334	C₃×D₄	D₃×C₈	1	4	yes	complemented
335	C₃×D₄	C₂×C₃⋊C₈	1	4	yes	complemented
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	3	8	no	—
345	C₂×C₃×C₄	—	3	1	no	—
346	C₂×C₃×C₄	—	3	1	no	—
347	C₂×C₃×C₄	—	3	2	no	—
348	C₂×C₃×C₄	—	3	4	no	—
349	C₂×C₃×C₄	—	3	2	no	—
350	C₂×C₃×C₄	—	3	1	no	—
351	C₂×C₃×C₄	—	4	2	no	—
352	C₂×C₃×C₄	—	4	2	no	—
353	C₂×C₃×C₄	—	6	2	no	—
354	C₂×C₃×C₄	—	6	4	no	—
355	C₂×C₃×C₄	—	6	1	no	—
356	C₂×C₃×C₄	—	6	1	no	—
357	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
358	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂²×Dic₃	1	2	yes	—
361	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
365	#67	C₂×C₃⋊C₈	1	8	yes	complemented
366	C₂×Dic₃	—	2	4	no	—
367	C₂×Dic₃	C₂×C₃⋊C₈	1	8	yes	complemented
368	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
369	C₂×Dic₃	C₂²×Dic₃	1	2	yes	—
370	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
371	C₂×Dic₃	C₂²×Dic₃	1	2	yes	—
372	C₂×Dic₃	C₂²×Dic₃	1	1	yes	characteristic
373	C₄×D₃	—	2	1	no	—
374	C₄×D₃	—	2	1	no	—
375	C₄×D₃	—	2	2	no	—
376	C₄×D₃	C₂×C₃⋊C₈	1	4	yes	complemented
377	Dic₆	C₂×C₃⋊C₈	1	4	yes	complemented
378	C₃×C₈	—	3	2	no	—
379	C₃×C₈	—	6	1	no	—
380	C₃×C₈	—	6	2	no	—
381	C₃⋊C₈	—	2	2	no	—
382	C₃⋊C₈	—	2	1	no	—
383	C₃⋊C₈	—	3	2	no	—
384	C₃⋊C₈	—	3	2	no	—
385	C₃⋊C₈	—	6	2	no	—
386	C₃⋊C₈	—	6	1	no	—
387	C₃⋊C₈	—	6	1	no	—
388	C₃⋊C₈	—	6	2	no	—
389	C₃⋊C₈	—	6	2	no	—
390	C₃⋊C₈	—	12	1	no	—
391	C₃⋊C₈	—	12	2	no	—
392	C₃⋊C₈	#237	1	2	yes	direct product factor
393	C₂×C₃²	—	2	4	no	—
394	C₂×C₃²	C₄×#41	1	1	yes	characteristic
395	C₂×C₃²	C₂³×C₈	1	1	yes	characteristic
396	C₂×C₃²	C₂×#131	1	1	yes	characteristic
397	C₃×D₃	—	2	2	no	—
398	#41	—	3	8	no	—
399	C₂×Q₈	—	3	1	no	—
400	C₂×D₄	—	3	2	no	—
401	C₂×D₄	D₃×Dic₃	1	1	yes	characteristic
402	C₂²×C₄	—	3	2	no	—
403	C₂²×C₄	—	3	1	no	—
404	C₂²×C₄	—	3	2	no	—
405	C₂²×C₄	—	3	1	no	—
406	C₂²×C₄	—	3	1	no	—
407	C₂²×C₄	C₂×D₃²	1	2	yes	—
408	C₂×C₈	—	3	1	no	—
409	C₂×C₈	—	3	1	no	—
410	C₂×C₈	—	3	2	no	—
411	C₂×C₈	—	6	4	no	—
412	C₂×C₈	—	9	1	no	—
413	C₂×C₈	—	9	1	no	—
414	C₂×C₈	—	9	2	no	—
415	C₂×C₈	—	18	2	no	—
416	C₂×C₈	—	18	2	no	—
417	C₂×C₈	—	18	4	no	—
418	C₄⋊C₄	—	3	2	no	—
419	C₄⋊C₄	—	3	2	no	—
420	C₄⋊C₄	—	3	1	no	—
421	C₄⋊C₄	D₃×Dic₃	1	1	yes	characteristic
422	C₂²⋊C₄	—	3	2	no	—
423	C₂²⋊C₄	—	3	2	no	—
424	C₂²⋊C₄	D₃×Dic₃	1	2	yes	—
425	C₄²	—	3	1	no	—
426	C₄²	—	3	2	no	—
427	C₄²	—	3	2	no	—
428	C₄²	—	3	1	no	—
429	C₄²	—	3	2	no	—
430	C₄²	—	3	1	no	—
431	C₄²	C₂×D₃²	1	1	yes	characteristic
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	2	2	no	—
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	1	no	—
437	C₂²×C₃	—	2	4	no	—
438	C₂²×C₃	—	3	2	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	—	4	2	no	—
441	C₂²×C₃	—	6	1	no	—
442	C₂²×C₃	—	6	1	no	—
443	C₂²×C₃	C₂×D₃×C₈	1	4	yes	—
444	C₂²×C₃	C₂²×C₃⋊C₈	1	4	yes	—
445	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
446	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
447	C₂×D₃	—	2	1	no	—
448	C₂×D₃	—	2	1	no	—
449	C₂×D₃	C₂²×C₃⋊C₈	1	2	yes	—
450	C₃×C₄	—	2	1	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	1	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	2	1	no	—
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	3	2	no	—
458	C₃×C₄	—	3	4	no	—
459	C₃×C₄	—	3	2	no	—
460	C₃×C₄	—	4	2	no	—
461	C₃×C₄	—	4	1	no	—
462	C₃×C₄	—	6	2	no	—
463	C₃×C₄	—	6	1	no	—
464	C₃×C₄	C₂×D₃×C₈	1	2	yes	—
465	C₃×C₄	C₂²×C₃⋊C₈	1	2	yes	—
466	C₃×C₄	C₂×#237	1	1	yes	characteristic
467	C₃×C₄	D₃×#41	1	1	yes	characteristic
468	C₃×C₄	D₃×#41	1	1	yes	characteristic
469	C₃×C₄	D₃×#41	1	1	yes	characteristic
470	Dic₃	—	2	2	no	—
471	Dic₃	—	2	1	no	—
472	Dic₃	C₂²×C₃⋊C₈	1	4	yes	—
473	Dic₃	C₂²×C₃⋊C₈	1	2	yes	—
474	Dic₃	#948	1	2	yes	—
475	C₃²	C₈×#41	1	1	yes	characteristic, complemented, Sylow
476	C₂³	—	3	1	no	—
477	C₂³	C₂×D₃×Dic₃	1	2	yes	—
478	Q₈	—	3	4	no	—
479	D₄	—	3	8	no	—
480	D₄	D₃×C₃⋊C₈	1	4	yes	complemented
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	3	1	no	—
484	C₂×C₄	—	3	1	no	—
485	C₂×C₄	—	3	2	no	—
486	C₂×C₄	—	3	8	no	—
487	C₂×C₄	—	3	4	no	—
488	C₂×C₄	—	3	2	no	—
489	C₂×C₄	—	3	1	no	—
490	C₂×C₄	—	6	2	no	—
491	C₂×C₄	—	6	4	no	—
492	C₂×C₄	—	6	1	no	—
493	C₂×C₄	—	6	1	no	—
494	C₂×C₄	C₂×D₃×Dic₃	1	2	yes	—
495	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
496	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
498	C₈	—	3	2	no	—
499	C₈	—	6	2	no	—
500	C₈	—	6	1	no	—
501	C₈	—	9	2	no	—
502	C₈	—	18	1	no	—
503	C₈	—	18	2	no	—
504	C₂×C₃	—	2	4	no	—
505	C₂×C₃	—	2	4	no	—
506	C₂×C₃	—	2	1	no	—
507	C₂×C₃	—	2	1	no	—
508	C₂×C₃	—	2	1	no	—
509	C₂×C₃	—	4	4	no	—
510	C₂×C₃	—	6	2	no	—
511	C₂×C₃	C₄×#237	1	1	yes	characteristic
512	C₂×C₃	C₂²×D₃×C₈	1	1	yes	characteristic
513	C₂×C₃	D₃×#131	1	1	yes	characteristic
514	C₂×C₃	C₂³×C₃⋊C₈	1	1	yes	characteristic
515	C₂×C₃	C₂×#948	1	1	yes	characteristic
516	C₂×C₃	Dic₃×#41	1	1	yes	characteristic
517	D₃	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	3	2	no	—
521	C₂²	—	6	1	no	—
522	C₂²	—	6	1	no	—
523	C₂²	C₂×D₃×C₃⋊C₈	1	4	yes	—
524	C₂²	C₂²×D₃×Dic₃	1	1	yes	characteristic
525	C₄	—	2	1	no	—
526	C₄	—	2	2	no	—
527	C₄	—	3	2	no	—
528	C₄	—	3	2	no	—
529	C₄	—	3	4	no	—
530	C₄	—	6	2	no	—
531	C₄	—	6	1	no	—
532	C₄	C₂×D₃×C₃⋊C₈	1	2	yes	—
533	C₄	D₃×#237	1	1	yes	characteristic
534	C₄	#64312	1	1	yes	characteristic
535	C₃	—	2	1	no	—
536	C₃	C₈×#237	1	1	yes	characteristic, complemented
537	C₃	#41×C₃⋊C₈	1	1	yes	characteristic, complemented
538	C₂	—	2	4	no	—
539	C₂	—	6	2	no	—
540	C₂	C₂²×D₃×C₃⋊C₈	1	1	yes	characteristic
541	C₂	Dic₃×#237	1	1	yes	characteristic
542	C₂	D₃×#948	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃²
commutator	C₂×C₃²	C₂³×C₈
Fitting	C₃²×C₄×D₄	C₂²
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂×C₃×#237	C₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₄×D₄	D₃²
hypocenter	C₃²	C₈×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. D₄×C₃⋊(C₃⋊C₈)	C₂	semidirect
3. C₃×D₄×C₃⋊C₈	C₂	semidirect
4. #67⋊(C₃⋊C₈)	C₂	semidirect
5. C₃⋊C₈×#67	C₂	semidirect
6. #10591053	C₂	semidirect
7. C₂×Dic₃×C₃⋊C₈	C₂	semidirect
8. C₄×D₃×C₃⋊C₈	C₂	semidirect
9. #10590250	C₂	semidirect
10. C₃⋊C₈×Dic₆	C₂	semidirect
11. #10590248	C₂	semidirect
55. D₄×C₃⋊C₈	D₃	semidirect
71. C₃×#237	C₈	semidirect
166. C₃²×D₄	C₂×C₈	semidirect
173. C₃×#67	C₂×C₈	semidirect
175. C₂×C₃×Dic₃	C₂×C₈	semidirect
184. C₃×C₄×D₃	C₂×C₈	semidirect
185. C₃×Dic₆	C₂×C₈	semidirect
188. C₃⋊(C₃⋊C₈)	#41	semidirect
191. C₃×C₃⋊C₈	#41	semidirect
220. #237	C₃⋊C₈	direct (N × H)
334. C₃×D₄	D₃×C₈	semidirect
335. C₃×D₄	C₂×C₃⋊C₈	semidirect
365. #67	C₂×C₃⋊C₈	semidirect
367. C₂×Dic₃	C₂×C₃⋊C₈	semidirect
376. C₄×D₃	C₂×C₃⋊C₈	semidirect
377. Dic₆	C₂×C₃⋊C₈	semidirect
392. C₃⋊C₈	#237	direct (N × H)
475. C₃²	C₈×#41	semidirect
480. D₄	D₃×C₃⋊C₈	semidirect
536. C₃	C₈×#237	semidirect
537. C₃	#41×C₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#237	2
D₄×C₃⋊(C₃⋊C₈)	2
C₃×D₄×C₃⋊C₈	2
#67⋊(C₃⋊C₈)	2
C₃⋊C₈×#67	2
#10591053	2
C₂×Dic₃×C₃⋊C₈	2
C₄×D₃×C₃⋊C₈	2
#10590250	2
C₃⋊C₈×Dic₆	2
#10590248	2
#41×C₃⋊C₈	3
C₈×#237	3

Subgroups — C3⋊C8×#237 #11861553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊C₈×#237 #11861553