Subgroups — C₃×D₃×#497 #11874371

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×Q₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₃×SD₁₆	C₂	1	2	yes	maximal
3	C₃×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₃×#124	C₂	1	1	yes	maximal, characteristic
5	C₃²×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5190	C₂	1	2	yes	maximal, complemented
7	C₃×#5167	C₂	1	2	yes	maximal, complemented
8	C₃×#5086	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4715	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#497	—	3	1	no	maximal
13	D₃×#497	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
15	C₂×C₃×D₃×Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₃×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃²×Q₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃²×SD₁₆	C₂²	1	2	yes	—
19	C₃²×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃²×#124	C₂²	1	1	yes	characteristic
21	C₃×#947	C₂²	1	1	yes	characteristic
22	C₃×#944	C₂²	1	2	yes	complemented
23	C₂×C₃×#216	C₂²	1	2	yes	complemented
24	C₂×C₃×#216	C₂²	1	2	yes	complemented
25	C₂×C₃×#215	C₂²	1	2	yes	—
26	C₃×#936	C₂²	1	1	yes	characteristic
27	C₂×C₃×#214	C₂²	1	2	yes	—
28	C₃×D₃×Q₁₆	—	2	8	no	—
29	C₃×D₃×SD₁₆	—	2	8	no	—
30	C₂×C₃×Dic₁₂	C₂²	1	2	yes	complemented
31	C₂×C₃×#204	C₂²	1	2	yes	—
32	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
33	C₃×D₃×C₄⋊C₄	—	2	2	no	—
34	C₃×#888	—	2	2	no	—
35	C₃×#885	—	2	2	no	—
36	C₃×D₃×C₂²⋊C₄	—	2	2	no	—
37	C₃×#875	C₂²	1	1	yes	characteristic
38	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
39	C₃×#869	C₂²	1	1	yes	characteristic, complemented
40	C₃²×#97	C₂²	1	1	yes	characteristic, complemented
41	C₃×#815	C₂²	1	2	yes	complemented
42	C₃×#803	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₃×Q₁₆	—	3	2	no	—
44	C₂²×C₃×SD₁₆	—	3	2	no	—
45	C₂×C₃×C₄⋊Q₈	—	3	1	no	—
46	C₂×C₃×#124	—	3	1	no	—
47	C₂×D₃×Q₁₆	C₂×C₃	1	2	yes	complemented
48	C₂×D₃×SD₁₆	C₂×C₃	1	2	yes	—
49	D₃×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
50	D₃×#124	C₂×C₃	1	1	yes	characteristic
51	C₃×#497	—	2	1	no	—
52	C₃×#497	—	3	2	no	—
53	C₃×#497	—	3	2	no	—
54	C₃×#497	—	3	1	no	—
55	C₃×#497	—	3	1	no	—
56	C₃×#497	—	3	1	no	—
57	C₃×#497	D₃	1	1	yes	characteristic, direct product factor
58	C₃×#497	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×#97	—	3	1	no	—
60	#5190	C₂×C₃	1	2	yes	complemented
61	#5167	C₂×C₃	1	2	yes	complemented
62	#5086	C₂×C₃	1	1	yes	characteristic, complemented
63	#5060	C₂×C₃	1	1	yes	characteristic, complemented
64	#4715	C₂×C₃	1	1	yes	characteristic, complemented
65	D₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂³×C₃×D₃	—	2	1	no	—
67	C₂×C₃²×Q₈	C₂³	1	2	yes	—
68	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
69	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
70	C₂×C₃×#67	—	2	1	no	—
71	C₃×D₃×Q₈	—	2	4	no	—
72	C₃×D₃×Q₈	—	2	4	no	—
73	C₃×D₃×Q₈	—	2	4	no	—
74	C₃×D₃×D₄	—	2	4	no	—
75	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×D₃	—	2	1	no	—
77	C₂×C₃×C₄×D₃	—	2	2	no	—
78	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
79	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₆	—	2	1	no	—
81	C₂×C₃×Dic₆	—	2	2	no	—
82	C₂×C₃×Dic₆	C₂³	1	2	yes	—
83	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
84	C₃²×Q₁₆	—	2	4	no	—
85	C₃²×SD₁₆	—	2	4	no	—
86	C₂×C₃²×C₈	C₂³	1	2	yes	—
87	C₃²×C₄⋊C₄	—	2	2	no	—
88	C₃²×C₂²⋊C₄	—	2	2	no	—
89	C₃²×C₄²	C₂³	1	1	yes	characteristic
90	C₃×#217	—	2	2	no	—
91	C₃×#216	—	2	4	no	—
92	C₃×#216	—	2	4	no	—
93	C₃×#215	—	2	4	no	—
94	C₃×#214	—	2	4	no	—
95	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
96	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
97	C₃×C₄⋊Dic₃	—	2	2	no	—
98	C₃×Dic₃⋊C₄	—	2	4	no	—
99	C₃×C₄×Dic₃	D₄	1	2	yes	—
100	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
102	C₃×Dic₁₂	—	2	4	no	—
103	C₃×#204	—	2	4	no	—
104	C₃×D₃×C₈	D₄	1	8	yes	—
105	C₂×#497	—	3	1	no	Sylow
106	C₂²×C₃×Q₈	—	3	2	no	—
107	C₂²×C₃×Q₈	—	3	1	no	—
108	C₂²×C₃×D₄	—	3	1	no	—
109	C₂×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
111	C₂×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×Q₁₆	—	2	2	no	—
113	C₂×C₃×Q₁₆	—	3	2	no	—
114	C₂×C₃×Q₁₆	—	3	2	no	—
115	C₂×C₃×Q₁₆	—	3	2	no	—
116	C₂×C₃×Q₁₆	—	6	8	no	—
117	C₂×C₃×Q₁₆	C₂×D₃	1	2	yes	complemented
118	C₂×C₃×Q₁₆	C₂²×C₃	1	2	yes	complemented
119	C₂×C₃×SD₁₆	—	2	2	no	—
120	C₂×C₃×SD₁₆	—	3	2	no	—
121	C₂×C₃×SD₁₆	—	3	2	no	—
122	C₂×C₃×SD₁₆	—	3	2	no	—
123	C₂×C₃×SD₁₆	—	6	8	no	—
124	C₂×C₃×SD₁₆	C₂×D₃	1	2	yes	—
125	C₂×C₃×SD₁₆	C₂²×C₃	1	2	yes	—
126	C₂²×C₃×C₈	—	3	2	no	—
127	C₃×C₄⋊Q₈	—	2	1	no	—
128	C₃×C₄⋊Q₈	—	3	2	no	—
129	C₃×C₄⋊Q₈	—	3	1	no	—
130	C₃×C₄⋊Q₈	—	6	2	no	—
131	C₃×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
132	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
133	C₃×#124	—	2	1	no	—
134	C₃×#124	—	3	1	no	—
135	C₃×#124	—	3	1	no	—
136	C₃×#124	—	3	1	no	—
137	C₃×#124	—	6	2	no	—
138	C₃×#124	C₂×D₃	1	1	yes	characteristic
139	C₃×#124	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	—	6	2	no	—
141	C₂×C₃×C₂²⋊C₄	—	6	2	no	—
142	C₂×C₃×C₄²	—	3	1	no	—
143	#947	C₂²×C₃	1	1	yes	characteristic
144	#944	C₂²×C₃	1	2	yes	complemented
145	C₂×#216	C₂²×C₃	1	2	yes	complemented
146	C₂×#216	C₂²×C₃	1	2	yes	complemented
147	C₂×#215	C₂²×C₃	1	2	yes	—
148	#936	C₂²×C₃	1	1	yes	characteristic
149	C₂×#214	C₂²×C₃	1	2	yes	—
150	D₃×Q₁₆	—	2	8	no	—
151	D₃×SD₁₆	—	2	8	no	—
152	C₂×Dic₁₂	C₂²×C₃	1	2	yes	complemented
153	C₂×#204	C₂²×C₃	1	2	yes	—
154	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
155	D₃×C₄⋊C₄	—	2	2	no	—
156	#888	—	2	2	no	—
157	#885	—	2	2	no	—
158	D₃×C₂²⋊C₄	—	2	2	no	—
159	#875	C₂²×C₃	1	1	yes	characteristic
160	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
161	#869	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₃×#97	—	2	1	no	—
163	C₃×#97	—	3	2	no	—
164	C₃×#97	—	3	1	no	—
165	C₃×#97	C₂×D₃	1	1	yes	characteristic, complemented
166	C₃×#97	C₂²×C₃	1	1	yes	characteristic, complemented
167	#815	C₂²×C₃	1	2	yes	complemented
168	#803	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂³×C₃²	—	2	1	no	—
170	C₂²×C₃×D₃	—	2	1	no	—
171	C₂²×C₃×D₃	—	4	2	no	—
172	C₂²×C₃×D₃	—	4	4	no	—
173	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
174	C₃²×Q₈	—	2	2	no	—
175	C₃²×Q₈	—	2	2	no	—
176	C₃²×Q₈	—	2	2	no	—
177	C₃²×D₄	—	2	2	no	—
178	C₂×C₃²×C₄	—	2	2	no	—
179	C₂×C₃²×C₄	—	2	1	no	—
180	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
181	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
182	C₃×#67	—	4	2	no	—
183	C₂×C₃×Dic₃	—	2	2	no	—
184	C₂×C₃×Dic₃	—	2	1	no	—
185	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
186	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
187	C₃×D₁₂	—	2	2	no	—
188	C₃×C₄×D₃	—	2	4	no	—
189	C₃×C₄×D₃	—	4	2	no	—
190	C₃×C₄×D₃	—	4	4	no	—
191	C₃×C₄×D₃	C₂×D₄	1	4	yes	—
192	C₃×Dic₆	—	2	2	no	—
193	C₃×Dic₆	—	2	2	no	—
194	C₃×Dic₆	—	2	2	no	—
195	C₃×Dic₆	—	4	2	no	—
196	C₃×Dic₆	—	4	4	no	—
197	C₃²×C₈	C₂×D₄	1	4	yes	—
198	C₃×C₃⋊C₈	C₂×D₄	1	4	yes	—
199	C₂²×Q₁₆	—	3	2	no	—
200	C₂²×SD₁₆	—	3	2	no	—
201	C₂×C₄⋊Q₈	—	3	1	no	—
202	C₂×#124	—	3	1	no	—
203	#497	—	3	2	no	—
204	#497	—	3	2	no	—
205	#497	—	3	1	no	—
206	#497	—	3	1	no	—
207	#497	—	3	1	no	—
208	#497	C₃×D₃	1	1	yes	characteristic, direct product factor
209	C₂×#97	—	3	1	no	—
210	C₂⁴×C₃	—	6	1	no	—
211	C₂³×D₃	—	2	1	no	—
212	C₂×C₃×Q₈	—	2	1	no	—
213	C₂×C₃×Q₈	—	2	2	no	—
214	C₂×C₃×Q₈	—	3	1	no	—
215	C₂×C₃×Q₈	—	3	2	no	—
216	C₂×C₃×Q₈	—	6	1	no	—
217	C₂×C₃×Q₈	—	6	2	no	—
218	C₂×C₃×Q₈	—	6	4	no	—
219	C₂×C₃×Q₈	—	6	4	no	—
220	C₂×C₃×Q₈	—	6	4	no	—
221	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
222	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
223	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
224	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₃×D₄	—	2	1	no	—
226	C₂×C₃×D₄	—	3	1	no	—
227	C₂×C₃×D₄	—	6	4	no	—
228	C₂×C₃×D₄	—	6	1	no	—
229	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
230	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₃×C₄	—	3	1	no	—
232	C₂²×C₃×C₄	—	3	2	no	—
233	C₂²×C₃×C₄	—	6	1	no	—
234	C₂²×C₃×C₄	—	6	2	no	—
235	C₂×#67	—	2	1	no	—
236	D₃×Q₈	—	2	4	no	—
237	D₃×Q₈	—	2	4	no	—
238	D₃×Q₈	—	2	4	no	—
239	D₃×D₄	—	2	4	no	—
240	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₄×D₃	—	2	1	no	—
242	C₂×C₄×D₃	—	2	2	no	—
243	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
244	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
245	C₂×Dic₆	—	2	1	no	—
246	C₂×Dic₆	—	2	2	no	—
247	C₂×Dic₆	C₂³×C₃	1	2	yes	—
248	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
249	C₃×Q₁₆	—	2	4	no	—
250	C₃×Q₁₆	—	2	4	no	—
251	C₃×Q₁₆	—	4	4	no	—
252	C₃×Q₁₆	—	6	4	no	—
253	C₃×Q₁₆	—	6	4	no	—
254	C₃×Q₁₆	—	6	4	no	—
255	C₃×SD₁₆	—	2	4	no	—
256	C₃×SD₁₆	—	2	4	no	—
257	C₃×SD₁₆	—	4	4	no	—
258	C₃×SD₁₆	—	6	4	no	—
259	C₃×SD₁₆	—	6	4	no	—
260	C₃×SD₁₆	—	6	4	no	—
261	C₂×C₃×C₈	—	2	2	no	—
262	C₂×C₃×C₈	—	3	2	no	—
263	C₂×C₃×C₈	—	3	8	no	—
264	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
265	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
266	C₃×C₄⋊C₄	—	2	2	no	—
267	C₃×C₄⋊C₄	—	2	2	no	—
268	C₃×C₄⋊C₄	—	4	2	no	—
269	C₃×C₄⋊C₄	—	6	4	no	—
270	C₃×C₄⋊C₄	—	6	2	no	—
271	C₃×C₂²⋊C₄	—	2	2	no	—
272	C₃×C₂²⋊C₄	—	2	2	no	—
273	C₃×C₂²⋊C₄	—	4	2	no	—
274	C₃×C₂²⋊C₄	—	6	2	no	—
275	C₃×C₂²⋊C₄	—	6	2	no	—
276	C₃×C₂²⋊C₄	—	6	2	no	—
277	C₃×C₄²	—	2	1	no	—
278	C₃×C₄²	—	3	2	no	—
279	C₃×C₄²	—	3	1	no	—
280	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
281	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
282	#217	—	2	2	no	—
283	#216	—	2	4	no	—
284	#216	—	2	4	no	—
285	#215	—	2	4	no	—
286	#214	—	2	4	no	—
287	(C₂×D₃)⋊C₄	—	2	2	no	—
288	(C₂×D₃)⋊C₄	—	2	2	no	—
289	C₄⋊Dic₃	—	2	2	no	—
290	Dic₃⋊C₄	—	2	4	no	—
291	C₄×Dic₃	C₃×D₄	1	2	yes	—
292	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
294	Dic₁₂	—	2	4	no	—
295	#204	—	2	4	no	—
296	D₃×C₈	C₃×D₄	1	8	yes	—
297	C₂²×C₃²	—	4	1	no	—
298	C₂²×C₃²	—	4	2	no	—
299	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
300	C₂×C₃×D₃	—	4	1	no	—
301	C₂×C₃×D₃	—	4	2	no	—
302	C₂×C₃×D₃	—	8	4	no	—
303	C₂×C₃×D₃	#127	1	2	yes	—
304	C₂×C₃×D₃	#137	1	4	yes	—
305	C₃²×C₄	—	2	2	no	—
306	C₃²×C₄	—	4	2	no	—
307	C₃²×C₄	—	4	1	no	—
308	C₃²×C₄	C₂²×D₄	1	2	yes	—
309	C₃×Dic₃	—	2	2	no	—
310	C₃×Dic₃	—	4	2	no	—
311	C₃×Dic₃	—	4	1	no	—
312	C₃×Dic₃	#127	1	2	yes	—
313	C₂²×Q₈	—	3	1	no	—
314	C₂²×Q₈	—	3	2	no	—
315	C₂²×D₄	—	3	1	no	—
316	C₂×Q₁₆	—	3	2	no	—
317	C₂×Q₁₆	—	3	2	no	—
318	C₂×Q₁₆	—	3	2	no	—
319	C₂×Q₁₆	—	6	8	no	—
320	C₂×Q₁₆	C₂×C₃×D₃	1	2	yes	complemented
321	C₂×SD₁₆	—	3	2	no	—
322	C₂×SD₁₆	—	3	2	no	—
323	C₂×SD₁₆	—	3	2	no	—
324	C₂×SD₁₆	—	6	8	no	—
325	C₂×SD₁₆	C₂×C₃×D₃	1	2	yes	—
326	C₂²×C₈	—	3	2	no	—
327	C₄⋊Q₈	—	3	2	no	—
328	C₄⋊Q₈	—	3	1	no	—
329	C₄⋊Q₈	—	6	2	no	—
330	C₄⋊Q₈	C₂×C₃×D₃	1	1	yes	characteristic, complemented
331	#124	—	3	1	no	—
332	#124	—	3	1	no	—
333	#124	—	3	1	no	—
334	#124	—	6	2	no	—
335	#124	C₂×C₃×D₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	—	6	2	no	—
337	C₂×C₂²⋊C₄	—	6	2	no	—
338	C₂×C₄²	—	3	1	no	—
339	#97	—	3	2	no	—
340	#97	—	3	1	no	—
341	#97	C₂×C₃×D₃	1	1	yes	characteristic, complemented
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	3	1	no	—
345	C₂³×C₃	—	4	1	no	—
346	C₂³×C₃	—	6	1	no	—
347	C₂³×C₃	—	12	2	no	—
348	C₂³×C₃	—	12	4	no	—
349	C₂²×D₃	—	2	1	no	—
350	C₂²×D₃	—	4	2	no	—
351	C₂²×D₃	—	4	4	no	—
352	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
353	C₃×Q₈	—	2	2	no	—
354	C₃×Q₈	—	2	2	no	—
355	C₃×Q₈	—	2	2	no	—
356	C₃×Q₈	—	2	2	no	—
357	C₃×Q₈	—	2	2	no	—
358	C₃×Q₈	—	2	2	no	—
359	C₃×Q₈	—	4	2	no	—
360	C₃×Q₈	—	4	2	no	—
361	C₃×Q₈	—	4	2	no	—
362	C₃×Q₈	—	6	2	no	—
363	C₃×Q₈	—	6	2	no	—
364	C₃×Q₈	—	6	2	no	—
365	C₃×Q₈	—	12	2	no	—
366	C₃×Q₈	—	12	4	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	4	2	no	—
370	C₃×D₄	—	6	2	no	—
371	C₃×D₄	—	12	2	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	3	1	no	—
379	C₂×C₃×C₄	—	3	4	no	—
380	C₂×C₃×C₄	—	3	2	no	—
381	C₂×C₃×C₄	—	4	1	no	—
382	C₂×C₃×C₄	—	4	2	no	—
383	C₂×C₃×C₄	—	6	4	no	—
384	C₂×C₃×C₄	—	6	1	no	—
385	C₂×C₃×C₄	—	6	2	no	—
386	C₂×C₃×C₄	—	12	2	no	—
387	C₂×C₃×C₄	—	12	4	no	—
388	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
389	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
390	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
392	#67	—	4	2	no	—
393	C₂×Dic₃	—	2	2	no	—
394	C₂×Dic₃	—	2	1	no	—
395	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
396	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
397	D₁₂	—	2	2	no	—
398	C₄×D₃	—	2	4	no	—
399	C₄×D₃	—	4	2	no	—
400	C₄×D₃	—	4	4	no	—
401	C₄×D₃	C₂×C₃×D₄	1	4	yes	—
402	Dic₆	—	2	2	no	—
403	Dic₆	—	2	2	no	—
404	Dic₆	—	2	2	no	—
405	Dic₆	—	4	2	no	—
406	Dic₆	—	4	4	no	—
407	C₃×C₈	—	2	4	no	—
408	C₃×C₈	—	3	4	no	—
409	C₃×C₈	D₃×D₄	1	4	yes	—
410	C₃×C₈	C₂×C₃×D₄	1	4	yes	—
411	C₃⋊C₈	C₂×C₃×D₄	1	4	yes	—
412	C₂×C₃²	—	8	1	no	—
413	C₂×C₃²	C₂×#127	1	1	yes	characteristic
414	C₂×C₃²	C₂×#137	1	2	yes	—
415	C₃×D₃	—	8	1	no	—
416	C₃×D₃	#497	1	4	yes	direct product factor
417	C₂⁴	—	6	1	no	—
418	C₂×Q₈	—	3	1	no	—
419	C₂×Q₈	—	3	2	no	—
420	C₂×Q₈	—	6	1	no	—
421	C₂×Q₈	—	6	2	no	—
422	C₂×Q₈	—	6	4	no	—
423	C₂×Q₈	—	6	4	no	—
424	C₂×Q₈	—	6	4	no	—
425	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
426	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
427	C₂×D₄	—	3	1	no	—
428	C₂×D₄	—	6	4	no	—
429	C₂×D₄	—	6	1	no	—
430	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	6	1	no	—
434	C₂²×C₄	—	6	2	no	—
435	Q₁₆	—	2	4	no	—
436	Q₁₆	—	6	4	no	—
437	Q₁₆	—	6	4	no	—
438	Q₁₆	—	6	4	no	—
439	SD₁₆	—	2	4	no	—
440	SD₁₆	—	6	4	no	—
441	SD₁₆	—	6	4	no	—
442	SD₁₆	—	6	4	no	—
443	C₂×C₈	—	3	2	no	—
444	C₂×C₈	—	3	8	no	—
445	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	6	4	no	—
448	C₄⋊C₄	—	6	2	no	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	6	2	no	—
451	C₂²⋊C₄	—	6	2	no	—
452	C₂²⋊C₄	—	6	2	no	—
453	C₄²	—	3	1	no	—
454	C₄²	—	3	2	no	—
455	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	—	3	2	no	—
458	C₂²×C₃	—	3	4	no	—
459	C₂²×C₃	—	4	2	no	—
460	C₂²×C₃	—	4	1	no	—
461	C₂²×C₃	—	4	2	no	—
462	C₂²×C₃	—	4	1	no	—
463	C₂²×C₃	—	8	1	no	—
464	C₂²×C₃	—	8	2	no	—
465	C₂²×C₃	—	12	1	no	—
466	C₂²×C₃	—	12	2	no	—
467	C₂²×C₃	—	24	4	no	—
468	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
469	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
470	C₂×D₃	—	4	2	no	—
471	C₂×D₃	—	4	1	no	—
472	C₂×D₃	—	8	4	no	—
473	C₂×D₃	C₃×#127	1	2	yes	—
474	C₂×D₃	C₃×#137	1	4	yes	—
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	2	2	no	—
478	C₃×C₄	—	3	2	no	—
479	C₃×C₄	—	4	2	no	—
480	C₃×C₄	—	4	1	no	—
481	C₃×C₄	—	4	2	no	—
482	C₃×C₄	—	4	2	no	—
483	C₃×C₄	—	4	1	no	—
484	C₃×C₄	—	6	2	no	—
485	C₃×C₄	—	8	1	no	—
486	C₃×C₄	—	8	2	no	—
487	C₃×C₄	—	12	1	no	—
488	C₃×C₄	—	12	2	no	—
489	C₃×C₄	C₂×D₃×D₄	1	2	yes	—
490	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
491	Dic₃	—	2	2	no	—
492	Dic₃	—	4	2	no	—
493	Dic₃	—	4	1	no	—
494	Dic₃	C₃×#127	1	2	yes	—
495	C₃²	C₂×#497	1	1	yes	characteristic, complemented, Sylow
496	C₂³	—	2	1	no	—
497	C₂³	—	3	1	no	—
498	C₂³	—	6	1	no	—
499	C₂³	—	12	2	no	—
500	C₂³	—	12	4	no	—
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	2	2	no	—
504	Q₈	—	6	2	no	—
505	Q₈	—	6	2	no	—
506	Q₈	—	6	2	no	—
507	Q₈	—	12	2	no	—
508	Q₈	—	12	4	no	—
509	D₄	—	2	2	no	—
510	D₄	—	6	2	no	—
511	D₄	—	12	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	3	4	no	—
516	C₂×C₄	—	3	2	no	—
517	C₂×C₄	—	6	4	no	—
518	C₂×C₄	—	6	1	no	—
519	C₂×C₄	—	6	2	no	—
520	C₂×C₄	—	12	2	no	—
521	C₂×C₄	—	12	4	no	—
522	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
523	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
524	C₈	—	3	4	no	—
525	C₈	C₃×D₃×D₄	1	4	yes	—
526	C₂×C₃	—	2	2	no	—
527	C₂×C₃	—	2	1	no	—
528	C₂×C₃	—	3	4	no	—
529	C₂×C₃	—	8	1	no	—
530	C₂×C₃	—	8	1	no	—
531	C₂×C₃	—	16	1	no	—
532	C₂×C₃	—	24	1	no	—
533	C₂×C₃	D₃×#127	1	1	yes	characteristic
534	C₂×C₃	D₃×#137	1	2	yes	—
535	C₂×C₃	C₂×C₃×#127	1	1	yes	characteristic
536	C₂×C₃	C₂×C₃×#137	1	2	yes	—
537	D₃	—	8	1	no	—
538	D₃	C₃×#497	1	4	yes	direct product factor
539	C₂²	—	3	4	no	—
540	C₂²	—	3	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	12	2	no	—
544	C₂²	—	12	1	no	—
545	C₂²	—	24	4	no	—
546	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	3	2	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	2	no	—
551	C₄	—	6	2	no	—
552	C₄	—	12	1	no	—
553	C₄	—	12	2	no	—
554	C₄	C₂×C₃×D₃×D₄	1	2	yes	—
555	C₃	—	2	1	no	—
556	C₃	D₃×#497	1	1	yes	characteristic, direct product factor
557	C₃	C₂×C₃×#497	1	1	yes	characteristic, complemented
558	C₂	—	3	4	no	—
559	C₂	—	8	1	no	—
560	C₂	—	24	1	no	—
561	C₂	C₃×D₃×#127	1	1	yes	characteristic
562	C₂	C₃×D₃×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#497	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₃×D₄	C₂²
hypercenter	C₃×#497	D₃
hypocenter	C₃	C₂×C₃×#497
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×Q₁₆	C₂	semidirect
3. C₃×D₃×C₄⋊Q₈	C₂	semidirect
5. C₃²×#497	C₂	semidirect
6. C₃×#5190	C₂	semidirect
7. C₃×#5167	C₂	semidirect
8. C₃×#5086	C₂	semidirect
9. C₃×#5060	C₂	semidirect
10. C₃×#4715	C₂	semidirect
11. C₃×D₃×#97	C₂	semidirect
13. D₃×#497	C₃	direct (N × H)
17. C₂×C₃²×Q₁₆	C₂²	semidirect
19. C₃²×C₄⋊Q₈	C₂²	semidirect
22. C₃×#944	C₂²	semidirect
23. C₂×C₃×#216	C₂²	semidirect
24. C₂×C₃×#216	C₂²	semidirect
30. C₂×C₃×Dic₁₂	C₂²	semidirect
39. C₃×#869	C₂²	semidirect
40. C₃²×#97	C₂²	semidirect
41. C₃×#815	C₂²	semidirect
42. C₃×#803	C₂²	semidirect
47. C₂×D₃×Q₁₆	C₂×C₃	semidirect
49. D₃×C₄⋊Q₈	C₂×C₃	semidirect
57. C₃×#497	D₃	direct (N × H)
58. C₃×#497	C₂×C₃	semidirect
60. #5190	C₂×C₃	semidirect
61. #5167	C₂×C₃	semidirect
62. #5086	C₂×C₃	semidirect
63. #5060	C₂×C₃	semidirect
64. #4715	C₂×C₃	semidirect
65. D₃×#97	C₂×C₃	semidirect
117. C₂×C₃×Q₁₆	C₂×D₃	semidirect
118. C₂×C₃×Q₁₆	C₂²×C₃	semidirect
131. C₃×C₄⋊Q₈	C₂×D₃	semidirect
132. C₃×C₄⋊Q₈	C₂²×C₃	semidirect
144. #944	C₂²×C₃	semidirect
145. C₂×#216	C₂²×C₃	semidirect
146. C₂×#216	C₂²×C₃	semidirect
152. C₂×Dic₁₂	C₂²×C₃	semidirect
161. #869	C₂²×C₃	semidirect
165. C₃×#97	C₂×D₃	semidirect
166. C₃×#97	C₂²×C₃	semidirect
167. #815	C₂²×C₃	semidirect
168. #803	C₂²×C₃	semidirect
208. #497	C₃×D₃	direct (N × H)
320. C₂×Q₁₆	C₂×C₃×D₃	semidirect
330. C₄⋊Q₈	C₂×C₃×D₃	semidirect
341. #97	C₂×C₃×D₃	semidirect
416. C₃×D₃	#497	direct (N × H)
495. C₃²	C₂×#497	semidirect
538. D₃	C₃×#497	direct (N × H)
556. C₃	D₃×#497	direct (N × H)
557. C₃	C₂×C₃×#497	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×Q₁₆	2
C₂×C₃×D₃×SD₁₆	2
C₃×D₃×C₄⋊Q₈	2
C₃×D₃×#124	2
C₃²×#497	2
C₃×#5190	2
C₃×#5167	2
C₃×#5086	2
C₃×#5060	2
C₃×#4715	2
C₃×D₃×#97	2
C₂×C₃×#497	3
D₃×#497	3

Subgroups — C3×D3×#497 #11874371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#497 #11874371