Subgroups — C₃×#79917 #11861320

Order 1152.

779 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5578	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4839	C₂	1	2	yes	maximal
5	C₃×#4837	C₂	1	1	yes	maximal, characteristic
6	C₃×#4831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4828	C₂	1	2	yes	maximal, complemented
8	C₃×#4689	C₂	1	2	yes	maximal
9	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic
10	C₃×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×Dic₆	C₂	1	2	yes	maximal, complemented
12	C₃×#2960	—	3	1	no	maximal
13	#79917	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
15	C₃×#946	C₄	1	1	yes	characteristic
16	C₃×#944	C₄	1	1	yes	characteristic
17	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
18	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
20	C₃×#897	C₄	1	1	yes	characteristic
21	C₃×#896	C₄	1	2	yes	—
22	C₃×#889	C₄	1	2	yes	—
23	C₃×#888	C₄	1	1	yes	characteristic
24	C₃×#872	C₂²	1	2	yes	—
25	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄×Dic₆	C₂²	1	2	yes	—
27	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
28	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
29	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
31	C₃²×C₄×C₈	C₂²	1	2	yes	—
32	C₃×#815	C₂²	1	2	yes	—
33	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
34	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
35	C₃×Dic₃⋊C₈	C₂²	1	2	yes	—
36	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
37	C₃×C₈×Dic₃	C₂²	1	2	yes	—
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
41	C₃×#803	C₂²	1	2	yes	—
42	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×#533	—	3	1	no	—
44	#5578	C₂×C₃	1	1	yes	characteristic
45	C₃×#446	—	3	1	no	—
46	C₃×#446	—	3	2	no	—
47	C₃×#446	—	3	1	no	—
48	C₃×C₈×Q₈	—	2	1	no	—
49	C₃×C₈×Q₈	—	3	2	no	—
50	C₃×C₈×Q₈	—	3	1	no	—
51	C₃×C₈×Q₈	D₃	1	1	yes	characteristic, complemented
52	C₃×C₈×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃×#424	—	3	2	no	—
54	C₃×#423	—	3	1	no	—
55	C₃×#405	—	3	2	no	—
56	C₂×C₃×C₄×C₈	—	3	1	no	—
57	#5024	C₂×C₃	1	1	yes	characteristic, complemented
58	#4839	C₂×C₃	1	2	yes	—
59	#4837	C₂×C₃	1	1	yes	characteristic
60	#4831	C₂×C₃	1	1	yes	characteristic, complemented
61	#4828	C₂×C₃	1	2	yes	complemented
62	#4689	C₂×C₃	1	2	yes	—
63	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic
64	C₈×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
65	C₈×Dic₆	C₂×C₃	1	2	yes	complemented
66	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
71	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂³	1	2	yes	—
74	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
75	C₃²×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
77	C₃²×C₄²	C₂³	1	1	yes	characteristic
78	C₃²×C₄²	C₂³	1	2	yes	—
79	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
80	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
81	C₃×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
83	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
84	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
85	C₃×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
90	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
91	C₃×C₄×Dic₃	C₂³	1	2	yes	—
92	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
94	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
96	C₃×D₃×C₈	—	2	2	no	—
97	C₃×D₃×C₈	Q₈	1	4	yes	complemented
98	#2960	—	3	1	no	Sylow
99	C₂×C₃×M₁₆	—	3	2	no	—
100	C₂²×C₃×C₈	—	3	1	no	—
101	C₂²×C₃×C₈	—	3	1	no	—
102	C₃×C₄⋊Q₈	—	3	1	no	—
103	C₃×C₄⋊Q₈	—	3	1	no	—
104	C₃×#125	—	3	2	no	—
105	C₃×C₂²⋊Q₈	—	3	1	no	—
106	C₃×C₂²⋊Q₈	—	3	2	no	—
107	C₃×C₂²⋊Q₈	—	3	1	no	—
108	C₃×C₄×Q₈	—	2	1	no	—
109	C₃×C₄×Q₈	—	3	2	no	—
110	C₃×C₄×Q₈	—	3	1	no	—
111	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×#117	—	3	2	no	—
114	C₂×C₃×C₄²	—	3	1	no	—
115	#946	C₃×C₄	1	1	yes	characteristic
116	#944	C₃×C₄	1	1	yes	characteristic
117	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
118	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
119	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
120	#897	C₃×C₄	1	1	yes	characteristic
121	#896	C₃×C₄	1	2	yes	—
122	#889	C₃×C₄	1	2	yes	—
123	#888	C₃×C₄	1	1	yes	characteristic
124	#872	C₂²×C₃	1	2	yes	—
125	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₆	C₂²×C₃	1	2	yes	—
127	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
128	C₃×C₄⋊C₈	—	2	1	no	—
129	C₃×C₄⋊C₈	—	2	2	no	—
130	C₃×C₄⋊C₈	—	3	2	no	—
131	C₃×C₄⋊C₈	—	3	2	no	—
132	C₃×C₄⋊C₈	—	3	2	no	—
133	C₃×C₄⋊C₈	—	3	1	no	—
134	C₃×C₄⋊C₈	—	3	2	no	—
135	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
136	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
137	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
138	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
139	C₃×#97	—	3	2	no	—
140	C₃×#97	—	3	2	no	—
141	C₃×C₄×C₈	—	2	1	no	—
142	C₃×C₄×C₈	—	2	2	no	—
143	C₃×C₄×C₈	—	3	1	no	—
144	C₃×C₄×C₈	—	3	1	no	—
145	C₃×C₄×C₈	—	3	2	no	—
146	C₃×C₄×C₈	—	3	1	no	—
147	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
148	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
149	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
150	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
151	#815	C₂²×C₃	1	2	yes	—
152	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
153	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
154	Dic₃⋊C₈	C₂²×C₃	1	2	yes	—
155	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
156	C₈×Dic₃	C₂²×C₃	1	2	yes	—
157	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
158	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
159	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
160	#803	C₂²×C₃	1	2	yes	—
161	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
162	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
163	C₃²×Q₈	—	2	2	no	—
164	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
166	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
167	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
169	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
171	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
172	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
174	C₃×C₄×D₃	—	2	2	no	—
175	C₃×C₄×D₃	—	2	2	no	—
176	C₃×C₄×D₃	C₂×Q₈	1	2	yes	—
177	C₃×C₄×D₃	#41	1	2	yes	—
178	C₃×Dic₆	—	2	2	no	—
179	C₃×Dic₆	—	2	4	no	—
180	C₃²×C₈	—	2	1	no	—
181	C₃²×C₈	—	2	2	no	—
182	C₃²×C₈	C₂×Q₈	1	2	yes	—
183	C₃×C₃⋊C₈	—	2	1	no	—
184	C₃×C₃⋊C₈	—	2	2	no	—
185	C₃×C₃⋊C₈	C₂×Q₈	1	2	yes	—
186	#533	—	3	1	no	—
187	#446	—	3	1	no	—
188	#446	—	3	2	no	—
189	#446	—	3	1	no	—
190	C₈×Q₈	—	3	2	no	—
191	C₈×Q₈	—	3	1	no	—
192	C₈×Q₈	C₃×D₃	1	1	yes	characteristic, complemented
193	#424	—	3	2	no	—
194	#423	—	3	1	no	—
195	#405	—	3	2	no	—
196	C₂×C₄×C₈	—	3	1	no	—
197	C₂×C₃×Q₈	—	2	1	no	—
198	C₂×C₃×Q₈	—	3	2	no	—
199	C₂×C₃×Q₈	—	3	1	no	—
200	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
201	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
202	C₂²×C₃×C₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	3	1	no	—
204	C₂²×C₃×C₄	—	3	1	no	—
205	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
206	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
207	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
208	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
209	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
210	C₃×M₁₆	—	6	4	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₂×C₃×C₈	—	2	2	no	—
214	C₂×C₃×C₈	—	3	1	no	—
215	C₂×C₃×C₈	—	3	4	no	—
216	C₂×C₃×C₈	—	3	1	no	—
217	C₂×C₃×C₈	—	3	2	no	—
218	C₂×C₃×C₈	—	6	2	no	—
219	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
220	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
221	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
222	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
224	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
225	C₃×C₄⋊C₄	—	2	2	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	3	2	no	—
228	C₃×C₄⋊C₄	—	3	2	no	—
229	C₃×C₄⋊C₄	—	3	2	no	—
230	C₃×C₄⋊C₄	—	3	2	no	—
231	C₃×C₄⋊C₄	—	3	2	no	—
232	C₃×C₄⋊C₄	—	3	2	no	—
233	C₃×C₄⋊C₄	—	3	1	no	—
234	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
235	C₃×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
238	C₃×C₂²⋊C₄	—	3	2	no	—
239	C₃×C₂²⋊C₄	—	3	2	no	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	3	1	no	—
243	C₃×C₄²	—	3	1	no	—
244	C₃×C₄²	—	3	1	no	—
245	C₃×C₄²	—	3	2	no	—
246	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
247	C₃×C₄²	C₂²×D₃	1	2	yes	—
248	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
249	C₃×C₄²	C₂³×C₃	1	2	yes	—
250	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	2	yes	—
252	C₄⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
253	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
254	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
255	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
256	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
257	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
258	Dic₃⋊C₄	C₂×C₃×C₄	1	2	yes	—
259	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
260	C₄×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
261	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
262	C₄×Dic₃	C₂³×C₃	1	2	yes	—
263	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
265	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
266	ΓL(1,𝔽₂₅)	—	2	4	no	—
267	D₃×C₈	—	2	2	no	—
268	D₃×C₈	C₃×Q₈	1	4	yes	complemented
269	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
270	C₂×C₃×D₃	—	2	1	no	—
271	C₂×C₃×D₃	—	2	1	no	—
272	C₂×C₃×D₃	C₄×Q₈	1	2	yes	—
273	C₃²×C₄	—	2	2	no	—
274	C₃²×C₄	—	2	2	no	—
275	C₃²×C₄	—	2	1	no	—
276	C₃²×C₄	#131	1	2	yes	—
277	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
278	C₃²×C₄	C₂×#41	1	1	yes	characteristic
279	C₃×Dic₃	—	2	2	no	—
280	C₃×Dic₃	—	2	2	no	—
281	C₃×Dic₃	—	2	1	no	—
282	C₃×Dic₃	C₄×Q₈	1	2	yes	—
283	C₃×Dic₃	#131	1	2	yes	—
284	C₂×M₁₆	—	3	2	no	—
285	C₂²×C₈	—	3	1	no	—
286	C₂²×C₈	—	3	1	no	—
287	C₄⋊Q₈	—	3	1	no	—
288	C₄⋊Q₈	—	3	1	no	—
289	#125	—	3	2	no	—
290	C₂²⋊Q₈	—	3	1	no	—
291	C₂²⋊Q₈	—	3	2	no	—
292	C₂²⋊Q₈	—	3	1	no	—
293	C₄×Q₈	—	3	2	no	—
294	C₄×Q₈	—	3	1	no	—
295	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
296	#117	—	3	2	no	—
297	C₂×C₄²	—	3	1	no	—
298	C₄⋊C₈	—	3	2	no	—
299	C₄⋊C₈	—	3	2	no	—
300	C₄⋊C₈	—	3	2	no	—
301	C₄⋊C₈	—	3	1	no	—
302	C₄⋊C₈	—	3	2	no	—
303	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
304	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
305	#97	—	3	2	no	—
306	#97	—	3	2	no	—
307	C₄×C₈	—	3	1	no	—
308	C₄×C₈	—	3	1	no	—
309	C₄×C₈	—	3	2	no	—
310	C₄×C₈	—	3	1	no	—
311	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
312	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
313	C₂³×C₃	—	3	1	no	—
314	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₃×Q₈	—	2	4	no	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	2	2	no	—
318	C₃×Q₈	—	6	4	no	—
319	C₃×Q₈	—	6	2	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	3	1	no	—
326	C₂×C₃×C₄	—	3	1	no	—
327	C₂×C₃×C₄	—	3	2	no	—
328	C₂×C₃×C₄	—	3	2	no	—
329	C₂×C₃×C₄	—	3	1	no	—
330	C₂×C₃×C₄	—	3	2	no	—
331	C₂×C₃×C₄	—	3	2	no	—
332	C₂×C₃×C₄	—	6	2	no	—
333	C₂×C₃×C₄	—	6	2	no	—
334	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
336	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
337	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
340	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
341	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
344	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
345	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
346	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
347	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
348	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
349	C₄×D₃	—	2	2	no	—
350	C₄×D₃	—	2	2	no	—
351	C₄×D₃	C₂×C₃×Q₈	1	2	yes	—
352	C₄×D₃	C₃×#41	1	2	yes	—
353	Dic₆	—	2	2	no	—
354	Dic₆	—	2	4	no	—
355	C₃×C₈	—	2	1	no	—
356	C₃×C₈	—	2	2	no	—
357	C₃×C₈	—	2	1	no	—
358	C₃×C₈	—	2	2	no	—
359	C₃×C₈	—	2	2	no	—
360	C₃×C₈	—	3	2	no	—
361	C₃×C₈	—	4	1	no	—
362	C₃×C₈	—	4	2	no	—
363	C₃×C₈	—	6	1	no	—
364	C₃×C₈	—	6	2	no	—
365	C₃×C₈	D₃×Q₈	1	2	yes	—
366	C₃×C₈	C₂×C₃×Q₈	1	2	yes	—
367	C₃⋊C₈	—	2	1	no	—
368	C₃⋊C₈	—	2	2	no	—
369	C₃⋊C₈	C₂×C₃×Q₈	1	2	yes	—
370	C₂×C₃²	C₂×C₄×Q₈	1	1	yes	characteristic
371	C₂×C₃²	C₂×#131	1	1	yes	characteristic
372	C₂×C₃²	C₂×#131	1	1	yes	characteristic
373	C₃×D₃	—	2	2	no	—
374	C₂×Q₈	—	3	2	no	—
375	C₂×Q₈	—	3	1	no	—
376	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	3	1	no	—
379	C₂²×C₄	—	3	1	no	—
380	M₁₆	—	6	4	no	—
381	C₂×C₈	—	3	1	no	—
382	C₂×C₈	—	3	4	no	—
383	C₂×C₈	—	3	1	no	—
384	C₂×C₈	—	3	2	no	—
385	C₂×C₈	—	6	2	no	—
386	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
387	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
388	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
389	C₄⋊C₄	—	3	2	no	—
390	C₄⋊C₄	—	3	2	no	—
391	C₄⋊C₄	—	3	2	no	—
392	C₄⋊C₄	—	3	2	no	—
393	C₄⋊C₄	—	3	2	no	—
394	C₄⋊C₄	—	3	2	no	—
395	C₄⋊C₄	—	3	1	no	—
396	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
397	C₄⋊C₄	C₃×C₄×D₃	1	1	yes	characteristic
398	C₂²⋊C₄	—	3	2	no	—
399	C₂²⋊C₄	—	3	2	no	—
400	C₄²	—	3	1	no	—
401	C₄²	—	3	2	no	—
402	C₄²	—	3	1	no	—
403	C₄²	—	3	1	no	—
404	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
405	C₄²	C₂²×C₃×D₃	1	2	yes	—
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	3	2	no	—
408	C₂²×C₃	—	6	1	no	—
409	C₂²×C₃	—	6	1	no	—
410	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
411	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
412	C₂×D₃	—	2	1	no	—
413	C₂×D₃	—	2	1	no	—
414	C₂×D₃	C₃×C₄×Q₈	1	2	yes	—
415	C₃×C₄	—	2	4	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	1	no	—
418	C₃×C₄	—	2	2	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	3	2	no	—
426	C₃×C₄	—	3	2	no	—
427	C₃×C₄	—	4	1	no	—
428	C₃×C₄	—	4	2	no	—
429	C₃×C₄	—	6	1	no	—
430	C₃×C₄	—	6	2	no	—
431	C₃×C₄	—	6	2	no	—
432	C₃×C₄	#901	1	2	yes	—
433	C₃×C₄	C₃×#131	1	2	yes	—
434	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
435	C₃×C₄	D₃×#41	1	1	yes	characteristic
436	C₃×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
437	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
438	Dic₃	—	2	2	no	—
439	Dic₃	—	2	2	no	—
440	Dic₃	—	2	1	no	—
441	Dic₃	C₃×C₄×Q₈	1	2	yes	—
442	Dic₃	C₃×#131	1	2	yes	—
443	C₃²	#2960	1	1	yes	characteristic, complemented, Sylow
444	C₂³	—	3	1	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	6	4	no	—
447	Q₈	—	6	2	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	3	2	no	—
451	C₂×C₄	—	3	2	no	—
452	C₂×C₄	—	3	1	no	—
453	C₂×C₄	—	3	2	no	—
454	C₂×C₄	—	3	2	no	—
455	C₂×C₄	—	6	2	no	—
456	C₂×C₄	—	6	2	no	—
457	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
458	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
459	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
460	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
462	C₈	—	2	1	no	—
463	C₈	—	2	2	no	—
464	C₈	—	3	2	no	—
465	C₈	—	6	1	no	—
466	C₈	—	6	2	no	—
467	C₈	C₃×D₃×Q₈	1	2	yes	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	6	2	no	—
472	C₂×C₃	C₄×D₃×Q₈	1	1	yes	characteristic
473	C₂×C₃	C₂×#901	1	1	yes	characteristic
474	C₂×C₃	D₃×#131	1	1	yes	characteristic
475	C₂×C₃	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
476	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
477	C₂×C₃	C₂×C₃×#131	1	1	yes	characteristic
478	D₃	—	2	2	no	—
479	C₂²	—	3	2	no	—
480	C₂²	—	6	1	no	—
481	C₂²	—	6	1	no	—
482	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	3	2	no	—
487	C₄	—	3	2	no	—
488	C₄	—	6	2	no	—
489	C₄	—	6	1	no	—
490	C₄	—	6	2	no	—
491	C₄	C₃×#901	1	2	yes	—
492	C₄	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
493	C₄	C₃×D₃×#41	1	1	yes	characteristic
494	C₃	—	2	1	no	—
495	C₃	#79917	1	1	yes	characteristic, direct product factor
496	C₃	C₃×#2960	1	1	yes	characteristic, complemented
497	C₂	—	6	2	no	—
498	C₂	C₃×C₄×D₃×Q₈	1	1	yes	characteristic
499	C₂	C₂×C₃×#901	1	1	yes	characteristic
500	C₂	C₃×D₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₈×Q₈	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂²×C₃×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₈×Q₈	D₃
hypocenter	C₃	C₃×#2960
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₃×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. C₃²×C₈×Q₈	C₂	semidirect
3. C₃×#5024	C₂	semidirect
6. C₃×#4831	C₂	semidirect
7. C₃×#4828	C₂	semidirect
10. C₃×C₈×Dic₆	C₂	semidirect
11. C₃×C₈×Dic₆	C₂	semidirect
13. #79917	C₃	direct (N × H)
51. C₃×C₈×Q₈	D₃	semidirect
52. C₃×C₈×Q₈	C₂×C₃	semidirect
57. #5024	C₂×C₃	semidirect
60. #4831	C₂×C₃	semidirect
61. #4828	C₂×C₃	semidirect
64. C₈×Dic₆	C₂×C₃	semidirect
65. C₈×Dic₆	C₂×C₃	semidirect
97. C₃×D₃×C₈	Q₈	semidirect
192. C₈×Q₈	C₃×D₃	semidirect
268. D₃×C₈	C₃×Q₈	semidirect
443. C₃²	#2960	semidirect
495. C₃	#79917	direct (N × H)
496. C₃	C₃×#2960	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5578	2
C₃²×C₈×Q₈	2
C₃×#5024	2
C₃×#4839	2
C₃×#4837	2
C₃×#4831	2
C₃×#4828	2
C₃×#4689	2
C₃×C₄×D₃×C₈	2
C₃×C₈×Dic₆	2
C₃×#2960	3
#79917	3

Subgroups — C3×#79917 #11861320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79917 #11861320