Subgroups — C₃×#79710 #11898350

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5568	C₂	1	2	yes	maximal, complemented
2	C₃²×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5191	C₂	1	1	yes	maximal, characteristic
4	C₃×#5183	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5028	C₂	1	2	yes	maximal, complemented
6	C₃×#4873	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4872	C₂	1	1	yes	maximal, characteristic
8	C₃×#4818	C₂	1	2	yes	maximal, complemented
9	C₃×#4798	C₂	1	2	yes	maximal, complemented
10	C₃×#4696	C₂	1	1	yes	maximal, characteristic
11	C₃×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3393	—	3	1	no	maximal
13	#79710	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃²×C₄×Q₈	C₂²	1	2	yes	—
16	C₃×#947	C₂²	1	2	yes	—
17	C₃×#944	C₂²	1	2	yes	—
18	C₂×C₃×#216	C₂²	1	2	yes	—
19	C₂×C₃×#215	C₂²	1	2	yes	—
20	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₂₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×#204	C₂²	1	2	yes	—
23	C₃×#898	—	2	2	no	—
24	C₃×#896	—	2	2	no	—
25	C₃×#893	C₂²	1	2	yes	—
26	C₃×#887	C₂²	1	2	yes	—
27	C₃×#876	—	2	2	no	—
28	C₃×#875	C₂²	1	2	yes	—
29	C₃×#872	—	2	2	no	—
30	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
31	C₃²×#107	C₂²	1	1	yes	characteristic
32	C₃²×#103	C₂²	1	2	yes	—
33	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
37	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₃×#810	C₂²	1	2	yes	—
39	C₃×#809	C₂²	1	2	yes	—
40	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
41	C₃×#556	—	3	2	no	—
42	#5568	C₂×C₃	1	2	yes	complemented
43	C₃×#495	—	3	1	no	—
44	C₃×#495	—	3	1	no	—
45	C₃×#494	—	3	1	no	—
46	C₃×#464	—	3	2	no	—
47	C₃×#464	—	3	2	no	—
48	C₃×#461	—	3	2	no	—
49	C₃×C₈×Q₈	—	3	1	no	—
50	C₃×C₄×Q₁₆	—	2	1	no	—
51	C₃×C₄×Q₁₆	—	3	1	no	—
52	C₃×C₄×Q₁₆	D₃	1	1	yes	characteristic, complemented
53	C₃×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×C₄×D₈	—	3	1	no	—
55	#5191	C₂×C₃	1	1	yes	characteristic
56	#5183	C₂×C₃	1	1	yes	characteristic, complemented
57	#5028	C₂×C₃	1	2	yes	complemented
58	#4873	C₂×C₃	1	1	yes	characteristic, complemented
59	#4872	C₂×C₃	1	1	yes	characteristic
60	#4818	C₂×C₃	1	2	yes	complemented
61	#4798	C₂×C₃	1	2	yes	complemented
62	#4696	C₂×C₃	1	1	yes	characteristic
63	C₈×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×C₃²×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×D₁₂	C₂³	1	2	yes	—
66	C₂×C₃×C₄×D₃	—	2	2	no	—
67	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
68	C₂×C₃×Dic₆	C₂³	1	2	yes	—
69	C₃²×Q₁₆	—	2	2	no	—
70	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
72	C₃²×C₄⋊C₄	—	2	2	no	—
73	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃²×C₄²	—	2	2	no	—
75	C₃²×C₄²	C₂³	1	1	yes	characteristic
76	C₃×#216	—	4	2	no	—
77	C₃×#215	—	4	2	no	—
78	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
79	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
81	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
84	C₃×Dic₃⋊C₄	—	2	2	no	—
85	C₃×Dic₃⋊C₄	—	2	2	no	—
86	C₃×Dic₃⋊C₄	—	2	2	no	—
87	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
88	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
89	C₃×C₄×Dic₃	—	2	2	no	—
90	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
91	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₃×Dic₁₂	—	2	2	no	—
95	C₃×D₂₄	—	2	2	no	—
96	C₃×#204	—	4	2	no	—
97	#3393	—	3	1	no	Sylow
98	C₂×C₃×Q₁₆	—	2	1	no	—
99	C₂×C₃×Q₁₆	—	3	2	no	—
100	C₂×C₃×Q₁₆	—	3	1	no	—
101	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
102	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×SD₁₆	—	3	2	no	—
104	C₂×C₃×SD₁₆	—	3	2	no	—
105	C₂×C₃×D₈	—	3	1	no	—
106	C₃×C₄⋊Q₈	—	3	2	no	—
107	C₃×#126	—	6	2	no	—
108	C₃×#126	—	6	2	no	—
109	C₃×#124	—	3	2	no	—
110	C₃×#124	—	3	2	no	—
111	C₃×C₂²⋊Q₈	—	6	2	no	—
112	C₃×C₄×Q₈	—	2	2	no	—
113	C₃×C₄×Q₈	—	3	1	no	—
114	C₃×C₄×Q₈	—	3	2	no	—
115	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
116	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
117	C₃×C₄×D₄	—	3	2	no	—
118	C₃×#117	—	6	2	no	—
119	#947	C₂²×C₃	1	2	yes	—
120	#944	C₂²×C₃	1	2	yes	—
121	C₂×#216	C₂²×C₃	1	2	yes	—
122	C₂×#215	C₂²×C₃	1	2	yes	—
123	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
124	C₂×D₂₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×#204	C₂²×C₃	1	2	yes	—
126	#898	—	2	2	no	—
127	#896	—	2	2	no	—
128	#893	C₂²×C₃	1	2	yes	—
129	#887	C₂²×C₃	1	2	yes	—
130	#876	—	2	2	no	—
131	#875	C₂²×C₃	1	2	yes	—
132	#872	—	2	2	no	—
133	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
134	C₃×#107	—	2	1	no	—
135	C₃×#107	C₂×D₃	1	1	yes	characteristic
136	C₃×#107	C₂²×C₃	1	1	yes	characteristic
137	C₃×C₄⋊C₈	—	3	1	no	—
138	C₃×C₄⋊C₈	—	3	1	no	—
139	C₃×C₄⋊C₈	—	3	1	no	—
140	C₃×#103	—	2	2	no	—
141	C₃×#103	—	3	2	no	—
142	C₃×#103	C₂×D₃	1	2	yes	—
143	C₃×#103	C₂²×C₃	1	2	yes	—
144	C₃×#102	—	3	2	no	—
145	C₃×C₄×C₈	—	2	1	no	—
146	C₃×C₄×C₈	—	3	1	no	—
147	C₃×C₄×C₈	—	3	1	no	—
148	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
149	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
150	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
151	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
152	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
153	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
154	#810	C₂²×C₃	1	2	yes	—
155	#809	C₂²×C₃	1	2	yes	—
156	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
157	C₂²×C₃×D₃	—	2	2	no	—
158	C₃²×Q₈	—	2	2	no	—
159	C₃²×Q₈	—	2	2	no	—
160	C₂×C₃²×C₄	—	2	2	no	—
161	C₂×C₃²×C₄	—	2	2	no	—
162	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
164	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
165	C₂×C₃×Dic₃	—	2	2	no	—
166	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
170	C₃×D₁₂	—	2	2	no	—
171	C₃×D₁₂	—	2	2	no	—
172	C₃×C₄×D₃	—	4	4	no	—
173	C₃×Dic₆	—	2	2	no	—
174	C₃×Dic₆	—	2	2	no	—
175	C₃×Dic₆	—	2	2	no	—
176	C₃²×C₈	—	2	1	no	—
177	C₃²×C₈	#41	1	2	yes	—
178	C₃×C₃⋊C₈	—	2	1	no	—
179	C₃×C₃⋊C₈	—	2	1	no	—
180	#556	—	3	2	no	—
181	#495	—	3	1	no	—
182	#495	—	3	1	no	—
183	#494	—	3	1	no	—
184	#464	—	3	2	no	—
185	#464	—	3	2	no	—
186	#461	—	3	2	no	—
187	C₈×Q₈	—	3	1	no	—
188	C₄×Q₁₆	—	3	1	no	—
189	C₄×Q₁₆	C₃×D₃	1	1	yes	characteristic, complemented
190	C₄×D₈	—	3	1	no	—
191	C₂×C₃×Q₈	—	2	2	no	—
192	C₂×C₃×Q₈	—	3	1	no	—
193	C₂×C₃×Q₈	—	3	2	no	—
194	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
195	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
196	C₂×C₃×D₄	—	3	2	no	—
197	C₂²×C₃×C₄	—	6	2	no	—
198	C₂×D₁₂	C₂³×C₃	1	2	yes	—
199	C₂×C₄×D₃	—	2	2	no	—
200	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
201	C₂×Dic₆	C₂³×C₃	1	2	yes	—
202	C₃×Q₁₆	—	2	4	no	—
203	C₃×Q₁₆	—	2	2	no	—
204	C₃×Q₁₆	—	2	2	no	—
205	C₃×Q₁₆	—	6	2	no	—
206	C₃×Q₁₆	—	12	2	no	—
207	C₃×SD₁₆	—	12	2	no	—
208	C₃×SD₁₆	—	12	2	no	—
209	C₃×D₈	—	6	2	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	3	1	no	—
213	C₂×C₃×C₈	—	3	1	no	—
214	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	—	2	2	no	—
221	C₃×C₄⋊C₄	—	3	1	no	—
222	C₃×C₄⋊C₄	—	3	1	no	—
223	C₃×C₄⋊C₄	—	3	1	no	—
224	C₃×C₄⋊C₄	—	4	2	no	—
225	C₃×C₄⋊C₄	—	6	2	no	—
226	C₃×C₄⋊C₄	—	6	2	no	—
227	C₃×C₄⋊C₄	—	6	2	no	—
228	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
229	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
230	C₃×C₂²⋊C₄	—	6	2	no	—
231	C₃×C₂²⋊C₄	—	6	2	no	—
232	C₃×C₂²⋊C₄	—	6	2	no	—
233	C₃×C₂²⋊C₄	—	6	2	no	—
234	C₃×C₂²⋊C₄	—	6	2	no	—
235	C₃×C₄²	—	2	2	no	—
236	C₃×C₄²	—	2	2	no	—
237	C₃×C₄²	—	2	1	no	—
238	C₃×C₄²	—	3	1	no	—
239	C₃×C₄²	—	3	1	no	—
240	C₃×C₄²	—	4	2	no	—
241	C₃×C₄²	—	6	2	no	—
242	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
243	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
244	#216	—	4	2	no	—
245	#215	—	4	2	no	—
246	(C₂×D₃)⋊C₄	—	2	2	no	—
247	(C₂×D₃)⋊C₄	—	2	2	no	—
248	(C₂×D₃)⋊C₄	—	2	2	no	—
249	(C₂×D₃)⋊C₄	—	2	2	no	—
250	(C₂×D₃)⋊C₄	—	2	2	no	—
251	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
252	Dic₃⋊C₄	—	2	2	no	—
253	Dic₃⋊C₄	—	2	2	no	—
254	Dic₃⋊C₄	—	2	2	no	—
255	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
256	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
257	C₄×Dic₃	—	2	2	no	—
258	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
259	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
262	Dic₁₂	—	2	2	no	—
263	D₂₄	—	2	2	no	—
264	#204	—	4	2	no	—
265	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₃×D₃	—	4	2	no	—
267	C₂×C₃×D₃	—	4	2	no	—
268	C₂×C₃×D₃	—	4	2	no	—
269	C₃²×C₄	—	2	1	no	—
270	C₃²×C₄	—	2	1	no	—
271	C₃²×C₄	—	4	2	no	—
272	C₃²×C₄	—	4	2	no	—
273	C₃²×C₄	C₂×#41	1	1	yes	characteristic
274	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
275	C₃×Dic₃	—	2	1	no	—
276	C₃×Dic₃	—	2	1	no	—
277	C₃×Dic₃	—	2	1	no	—
278	C₃×Dic₃	—	4	2	no	—
279	C₃×Dic₃	#135	1	2	yes	—
280	C₂×Q₁₆	—	3	2	no	—
281	C₂×Q₁₆	—	3	1	no	—
282	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
283	C₂×SD₁₆	—	3	2	no	—
284	C₂×SD₁₆	—	3	2	no	—
285	C₂×D₈	—	3	1	no	—
286	C₄⋊Q₈	—	3	2	no	—
287	#126	—	6	2	no	—
288	#126	—	6	2	no	—
289	#124	—	3	2	no	—
290	#124	—	3	2	no	—
291	C₂²⋊Q₈	—	6	2	no	—
292	C₄×Q₈	—	3	1	no	—
293	C₄×Q₈	—	3	2	no	—
294	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
295	C₄×D₄	—	3	2	no	—
296	#117	—	6	2	no	—
297	#107	C₂×C₃×D₃	1	1	yes	characteristic
298	C₄⋊C₈	—	3	1	no	—
299	C₄⋊C₈	—	3	1	no	—
300	C₄⋊C₈	—	3	1	no	—
301	#103	—	3	2	no	—
302	#103	C₂×C₃×D₃	1	2	yes	—
303	#102	—	3	2	no	—
304	C₄×C₈	—	3	1	no	—
305	C₄×C₈	—	3	1	no	—
306	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
307	C₂³×C₃	—	6	2	no	—
308	C₂²×D₃	—	2	2	no	—
309	C₃×Q₈	—	2	4	no	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	2	2	no	—
313	C₃×Q₈	—	2	2	no	—
314	C₃×Q₈	—	4	2	no	—
315	C₃×Q₈	—	6	2	no	—
316	C₃×Q₈	—	6	2	no	—
317	C₃×Q₈	—	6	2	no	—
318	C₃×D₄	—	6	2	no	—
319	C₃×D₄	—	6	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	3	1	no	—
328	C₂×C₃×C₄	—	3	1	no	—
329	C₂×C₃×C₄	—	3	1	no	—
330	C₂×C₃×C₄	—	3	1	no	—
331	C₂×C₃×C₄	—	4	2	no	—
332	C₂×C₃×C₄	—	4	2	no	—
333	C₂×C₃×C₄	—	6	2	no	—
334	C₂×C₃×C₄	—	12	4	no	—
335	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
336	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
341	C₂×Dic₃	—	2	2	no	—
342	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
343	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
344	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
346	D₁₂	—	2	2	no	—
347	D₁₂	—	2	2	no	—
348	C₄×D₃	—	4	4	no	—
349	Dic₆	—	2	2	no	—
350	Dic₆	—	2	2	no	—
351	Dic₆	—	2	2	no	—
352	C₃×C₈	—	2	1	no	—
353	C₃×C₈	—	2	1	no	—
354	C₃×C₈	—	2	2	no	—
355	C₃×C₈	—	4	1	no	—
356	C₃×C₈	—	6	1	no	—
357	C₃×C₈	—	6	1	no	—
358	C₃×C₈	#235	1	2	yes	—
359	C₃×C₈	C₃×#41	1	2	yes	—
360	C₃⋊C₈	—	2	1	no	—
361	C₃⋊C₈	—	2	1	no	—
362	C₂×C₃²	#550	1	1	yes	characteristic
363	C₂×C₃²	C₂×#135	1	1	yes	characteristic
364	C₂×C₃²	#578	1	1	yes	characteristic
365	C₃×D₃	—	8	2	no	—
366	C₂×Q₈	—	3	1	no	—
367	C₂×Q₈	—	3	2	no	—
368	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
369	C₂×D₄	—	3	2	no	—
370	C₂²×C₄	—	6	2	no	—
371	Q₁₆	—	2	2	no	—
372	Q₁₆	—	6	2	no	—
373	Q₁₆	—	12	2	no	—
374	SD₁₆	—	12	2	no	—
375	SD₁₆	—	12	2	no	—
376	D₈	—	6	2	no	—
377	C₂×C₈	—	3	1	no	—
378	C₂×C₈	—	3	1	no	—
379	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
380	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	3	1	no	—
383	C₄⋊C₄	—	3	1	no	—
384	C₄⋊C₄	—	3	1	no	—
385	C₄⋊C₄	—	6	2	no	—
386	C₄⋊C₄	—	6	2	no	—
387	C₄⋊C₄	—	6	2	no	—
388	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
389	C₂²⋊C₄	—	6	2	no	—
390	C₂²⋊C₄	—	6	2	no	—
391	C₂²⋊C₄	—	6	2	no	—
392	C₂²⋊C₄	—	6	2	no	—
393	C₂²⋊C₄	—	6	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	3	1	no	—
396	C₄²	—	3	1	no	—
397	C₄²	—	6	2	no	—
398	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
399	C₂²×C₃	—	2	1	no	—
400	C₂²×C₃	—	12	2	no	—
401	C₂²×C₃	—	12	2	no	—
402	C₂²×C₃	—	12	2	no	—
403	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
404	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
405	C₂×D₃	—	4	2	no	—
406	C₂×D₃	—	4	2	no	—
407	C₂×D₃	—	4	2	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	3	2	no	—
416	C₃×C₄	—	4	1	no	—
417	C₃×C₄	—	4	4	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	—	4	2	no	—
420	C₃×C₄	—	4	2	no	—
421	C₃×C₄	—	4	2	no	—
422	C₃×C₄	—	6	1	no	—
423	C₃×C₄	—	6	1	no	—
424	C₃×C₄	—	6	1	no	—
425	C₃×C₄	—	8	2	no	—
426	C₃×C₄	—	12	2	no	—
427	C₃×C₄	C₂×#235	1	1	yes	characteristic
428	C₃×C₄	#1009	1	1	yes	characteristic
429	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
430	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
431	Dic₃	—	2	1	no	—
432	Dic₃	—	2	1	no	—
433	Dic₃	—	2	1	no	—
434	Dic₃	—	4	2	no	—
435	Dic₃	C₃×#135	1	2	yes	—
436	C₃²	#3393	1	1	yes	characteristic, complemented, Sylow
437	C₂³	—	6	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	6	2	no	—
441	Q₈	—	6	2	no	—
442	Q₈	—	6	2	no	—
443	D₄	—	6	2	no	—
444	D₄	—	6	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	3	1	no	—
448	C₂×C₄	—	3	1	no	—
449	C₂×C₄	—	3	1	no	—
450	C₂×C₄	—	3	1	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	12	4	no	—
453	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
454	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
455	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
456	C₈	—	2	1	no	—
457	C₈	—	6	1	no	—
458	C₈	—	6	1	no	—
459	C₈	C₃×#235	1	2	yes	—
460	C₂×C₃	—	2	1	no	—
461	C₂×C₃	—	2	1	no	—
462	C₂×C₃	—	2	1	no	—
463	C₂×C₃	—	24	2	no	—
464	C₂×C₃	#5553	1	1	yes	characteristic
465	C₂×C₃	#5766	1	1	yes	characteristic
466	C₂×C₃	D₃×#135	1	1	yes	characteristic
467	C₂×C₃	C₃×#550	1	1	yes	characteristic
468	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
469	C₂×C₃	C₃×#578	1	1	yes	characteristic
470	D₃	—	8	2	no	—
471	C₂²	—	12	2	no	—
472	C₂²	—	12	2	no	—
473	C₂²	—	12	2	no	—
474	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	3	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	6	1	no	—
481	C₄	—	6	1	no	—
482	C₄	—	6	1	no	—
483	C₄	—	12	2	no	—
484	C₄	C₂×C₃×#235	1	1	yes	characteristic
485	C₄	C₃×#1009	1	1	yes	characteristic
486	C₃	—	2	1	no	—
487	C₃	#79710	1	1	yes	characteristic, direct product factor
488	C₃	C₃×#3393	1	1	yes	characteristic, complemented
489	C₂	—	24	2	no	—
490	C₂	C₃×#5553	1	1	yes	characteristic
491	C₂	C₃×#5766	1	1	yes	characteristic
492	C₂	C₃×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×Q₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₂₄	C₂²
hypercenter	C₃×C₄×Q₁₆	D₃
hypocenter	C₃	C₃×#3393
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#5568	C₂	semidirect
2. C₃²×C₄×Q₁₆	C₂	semidirect
4. C₃×#5183	C₂	semidirect
5. C₃×#5028	C₂	semidirect
6. C₃×#4873	C₂	semidirect
8. C₃×#4818	C₂	semidirect
9. C₃×#4798	C₂	semidirect
11. C₃×C₈×Dic₆	C₂	semidirect
13. #79710	C₃	direct (N × H)
42. #5568	C₂×C₃	semidirect
52. C₃×C₄×Q₁₆	D₃	semidirect
53. C₃×C₄×Q₁₆	C₂×C₃	semidirect
56. #5183	C₂×C₃	semidirect
57. #5028	C₂×C₃	semidirect
58. #4873	C₂×C₃	semidirect
60. #4818	C₂×C₃	semidirect
61. #4798	C₂×C₃	semidirect
63. C₈×Dic₆	C₂×C₃	semidirect
189. C₄×Q₁₆	C₃×D₃	semidirect
436. C₃²	#3393	semidirect
487. C₃	#79710	direct (N × H)
488. C₃	C₃×#3393	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5568	2
C₃²×C₄×Q₁₆	2
C₃×#5191	2
C₃×#5183	2
C₃×#5028	2
C₃×#4873	2
C₃×#4872	2
C₃×#4818	2
C₃×#4798	2
C₃×#4696	2
C₃×C₈×Dic₆	2
C₃×#3393	3
#79710	3

Subgroups — C3×#79710 #11898350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79710 #11898350