Subgroups — D₃×#4559 #11783455

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	D₃×#926	C₂	1	1	yes	maximal, characteristic
3	C₂×D₃×#208	C₂	1	1	yes	maximal, characteristic
4	#10589425	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4559	C₂	1	1	yes	maximal, characteristic, complemented
6	#10589171	C₂	1	1	yes	maximal, characteristic, complemented
7	#10589170	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#4559	—	3	1	no	maximal
9	D₃×#344	—	3	1	no	maximal
10	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
12	#64135	C₂²	1	1	yes	characteristic
13	C₂×#3748	C₂²	1	1	yes	characteristic
14	C₃×#926	C₂²	1	1	yes	characteristic
15	C₂×C₃×#208	C₂²	1	1	yes	characteristic
16	C₂×C₃×#208	C₂²	1	1	yes	characteristic
17	C₃×D₃×M₁₆	—	2	1	no	—
18	C₃×D₃×M₁₆	—	2	1	no	—
19	C₃×D₃×M₁₆	C₄	1	2	yes	complemented
20	C₃×D₃×M₁₆	C₄	1	2	yes	complemented
21	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
22	C₂×C₃×D₃×C₈	—	2	1	no	—
23	D₃×#217	C₄	1	2	yes	—
24	#63955	C₄	1	2	yes	—
25	D₃×C₄⋊Dic₃	—	2	1	no	—
26	C₄×D₃×Dic₃	—	2	1	no	—
27	#63855	—	2	1	no	—
28	#63841	—	2	1	no	—
29	C₂×#3711	C₄	1	2	yes	complemented
30	D₃×#208	—	2	1	no	—
31	D₃×#208	—	2	1	no	—
32	D₃×#208	—	2	1	no	—
33	D₃×#208	—	2	1	no	—
34	C₂×D₃×C₃⋊C₈	C₄	1	2	yes	complemented
35	C₂²×C₃×M₁₆	—	3	1	no	—
36	C₂×#926	—	3	1	no	—
37	C₂²×#208	—	3	1	no	—
38	C₂×D₃×M₁₆	—	3	1	no	—
39	C₂×D₃×M₁₆	D₃	1	1	yes	characteristic
40	D₃×#117	—	3	1	no	—
41	C₃×#344	—	3	1	no	—
42	#4559	—	3	1	no	—
43	#4559	—	3	1	no	—
44	#4559	—	3	1	no	—
45	#4559	—	3	1	no	—
46	#4559	—	6	1	no	—
47	#4559	D₃	1	1	yes	characteristic, direct product factor
48	#4556	—	3	1	no	—
49	#4533	—	3	1	no	—
50	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
52	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₃	Q₈	1	1	yes	characteristic
64	C₂×C₃×C₄×D₃	Q₈	1	1	yes	characteristic
65	C₂×D₃×Dic₃	—	2	2	no	—
66	C₃²×M₁₆	—	2	1	no	—
67	C₃²×M₁₆	C₂×C₄	1	2	yes	complemented
68	C₂×C₃²×C₈	—	2	1	no	—
69	#3757	C₂×C₄	1	2	yes	—
70	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
71	C₄×C₃⋊Dic₃	—	2	1	no	—
72	#3748	—	2	1	no	—
73	#3748	—	2	1	no	—
74	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	complemented
75	C₃×#217	C₂×C₄	1	2	yes	—
76	C₃×C₄⋊Dic₃	—	2	1	no	—
77	C₃×C₄×Dic₃	—	2	1	no	—
78	C₃×#208	—	2	1	no	—
79	C₃×#208	—	2	1	no	—
80	C₃×#208	—	2	1	no	—
81	C₃×#208	C₂×C₄	1	2	yes	complemented
82	C₂×C₃×C₃⋊C₈	—	2	1	no	—
83	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
84	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
85	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
86	C₃×D₃×C₈	—	2	2	no	—
87	C₃×D₃×C₈	—	2	2	no	—
88	Dic₃⋊Dic₃	—	2	2	no	—
89	(C₂×D₃)⋊Dic₃	—	2	2	no	—
90	Dic₃²	—	2	2	no	—
91	#3711	—	2	2	no	—
92	#3711	—	2	2	no	—
93	D₃×C₃⋊C₈	—	2	2	no	—
94	D₃×C₃⋊C₈	—	2	2	no	—
95	C₂×#344	—	9	1	no	Sylow
96	C₂³×C₃×C₄	—	3	1	no	—
97	C₂²×C₄×D₃	C₂×D₃	1	1	yes	characteristic
98	C₂×C₃×M₁₆	—	2	1	no	—
99	C₂×C₃×M₁₆	—	3	1	no	—
100	C₂×C₃×M₁₆	—	3	1	no	—
101	C₂×C₃×M₁₆	—	3	2	no	—
102	C₂×C₃×M₁₆	—	3	2	no	—
103	C₂×C₃×M₁₆	—	6	1	no	—
104	C₂×C₃×M₁₆	—	6	1	no	—
105	C₂×C₃×M₁₆	—	6	1	no	—
106	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	—	6	1	no	—
109	C₃×#117	—	3	1	no	—
110	C₂×#217	—	3	2	no	—
111	#926	—	3	1	no	—
112	#926	—	3	1	no	—
113	#926	—	3	2	no	—
114	#926	—	6	1	no	—
115	#926	—	6	1	no	—
116	#926	—	6	1	no	—
117	#926	C₂×D₃	1	1	yes	characteristic
118	C₂×C₄⋊Dic₃	—	6	1	no	—
119	C₂×C₄×Dic₃	—	6	1	no	—
120	C₂×#208	—	3	1	no	—
121	C₂×#208	—	3	1	no	—
122	C₂×#208	—	3	2	no	—
123	C₂×#208	—	6	1	no	—
124	C₂×#208	—	6	1	no	—
125	C₂×#208	—	6	1	no	—
126	C₂×#208	—	6	1	no	—
127	C₂×#208	—	6	1	no	—
128	C₂×#208	C₂×D₃	1	1	yes	characteristic
129	C₂×#208	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₃⋊C₈	—	3	2	no	—
131	D₃×M₁₆	—	2	1	no	—
132	D₃×M₁₆	—	2	1	no	—
133	D₃×M₁₆	—	6	1	no	—
134	D₃×M₁₆	—	6	1	no	—
135	D₃×M₁₆	—	6	1	no	—
136	D₃×M₁₆	—	6	1	no	—
137	D₃×M₁₆	Dic₃	1	2	yes	complemented
138	D₃×M₁₆	Dic₃	1	2	yes	complemented
139	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
140	C₂×ΓL(1,𝔽₂₅)	—	3	2	no	—
141	C₂×D₃×C₈	—	2	1	no	—
142	C₂×D₃×C₈	—	3	2	no	—
143	#892	—	6	1	no	—
144	D₃×C₄⋊C₄	—	6	1	no	—
145	D₃×C₂²⋊C₄	—	3	2	no	—
146	#877	—	3	2	no	—
147	#872	—	6	1	no	—
148	C₄²×D₃	—	6	1	no	—
149	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₃×D₃	—	4	2	no	—
151	C₂²×C₃×D₃	C₄²	1	1	yes	characteristic
152	C₂²×C₃×D₃	C₄²	1	1	yes	characteristic
153	C₂²×C₃×D₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₃×D₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₃×D₃	C₄⋊C₄	1	1	yes	characteristic
156	C₂²×C₃×D₃	C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
163	C₂×C₃⋊Dic₃	—	2	2	no	—
164	C₂×C₃×Dic₃	—	2	2	no	—
165	C₂×C₃×Dic₃	C₄²	1	1	yes	characteristic
166	C₂×C₃×Dic₃	C₄²	1	1	yes	characteristic
167	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₃×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₃×Dic₃	C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₃×Dic₃	C₄⋊C₄	1	1	yes	characteristic
171	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
180	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
181	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
182	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
183	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
184	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
185	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
186	C₃×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
187	D₃×Dic₃	—	4	4	no	—
188	C₃²×C₈	—	2	2	no	—
189	C₃⋊(C₃⋊C₈)	—	2	2	no	—
190	C₃×C₃⋊C₈	—	2	2	no	—
191	C₃×C₃⋊C₈	—	2	2	no	—
192	C₂²×M₁₆	—	3	1	no	—
193	C₂²×M₁₆	—	9	1	no	—
194	C₂×#117	—	9	1	no	—
195	#344	—	3	1	no	—
196	#344	—	9	1	no	—
197	#344	—	9	1	no	—
198	#344	—	9	1	no	—
199	C₂⁴×C₃	—	3	1	no	—
200	C₂³×D₃	C₄×D₃	1	1	yes	characteristic
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	3	1	no	—
204	C₂²×C₃×C₄	—	3	1	no	—
205	C₂²×C₃×C₄	—	3	1	no	—
206	C₂²×C₃×C₄	—	3	1	no	—
207	C₂²×C₃×C₄	—	3	1	no	—
208	C₂²×C₃×C₄	—	3	1	no	—
209	C₂²×C₃×C₄	—	3	1	no	—
210	C₂²×C₃×C₄	—	3	1	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂²×C₃×C₄	—	3	1	no	—
213	C₂²×C₃×C₄	—	3	1	no	—
214	C₂²×C₃×C₄	—	3	1	no	—
215	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
217	C₂²×Dic₃	—	6	2	no	—
218	C₂²×Dic₃	C₄×D₃	1	1	yes	characteristic
219	C₂×C₄×D₃	—	6	2	no	—
220	C₂×C₄×D₃	Dic₆	1	1	yes	characteristic
221	C₂×C₄×D₃	Dic₆	1	1	yes	characteristic
222	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
223	C₂×C₄×D₃	C₄×D₃	1	1	yes	characteristic
224	C₂×C₄×D₃	D₁₂	1	1	yes	characteristic
225	C₂×C₄×D₃	D₁₂	1	1	yes	characteristic
226	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
227	C₂×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
228	C₂×C₄×D₃	#67	1	1	yes	characteristic
229	C₂×C₄×D₃	#67	1	1	yes	characteristic
230	C₂×C₄×D₃	#67	1	1	yes	characteristic
231	C₂×C₄×D₃	#67	1	1	yes	characteristic
232	C₃×M₁₆	—	2	1	no	—
233	C₃×M₁₆	—	2	1	no	—
234	C₃×M₁₆	—	2	2	no	—
235	C₃×M₁₆	—	3	2	no	—
236	C₃×M₁₆	—	4	1	no	—
237	C₃×M₁₆	—	6	2	no	—
238	C₃×M₁₆	—	6	2	no	—
239	C₃×M₁₆	—	6	1	no	—
240	C₃×M₁₆	—	6	1	no	—
241	C₃×M₁₆	—	6	1	no	—
242	C₃×M₁₆	C₄×D₃	1	2	yes	complemented
243	C₃×M₁₆	C₂×Dic₃	1	2	yes	complemented
244	C₂×C₃×C₈	—	2	1	no	—
245	C₂×C₃×C₈	—	2	1	no	—
246	C₂×C₃×C₈	—	3	2	no	—
247	C₂×C₃×C₈	—	4	1	no	—
248	C₂×C₃×C₈	—	6	2	no	—
249	C₂×C₃×C₈	—	6	2	no	—
250	C₂×C₃×C₈	—	6	1	no	—
251	C₃×C₄⋊C₄	—	6	1	no	—
252	C₃×C₂²⋊C₄	—	3	2	no	—
253	C₃×C₄²	—	6	1	no	—
254	#217	—	3	2	no	—
255	#217	—	3	2	no	—
256	#217	—	6	2	no	—
257	#217	—	6	2	no	—
258	#217	C₄×D₃	1	2	yes	—
259	(C₂×D₃)⋊C₄	—	6	2	no	—
260	C₄⋊Dic₃	—	2	1	no	—
261	C₄⋊Dic₃	—	6	2	no	—
262	C₄⋊Dic₃	—	6	1	no	—
263	C₄⋊Dic₃	—	6	1	no	—
264	C₄⋊Dic₃	—	12	1	no	—
265	Dic₃⋊C₄	—	6	2	no	—
266	C₄×Dic₃	—	2	1	no	—
267	C₄×Dic₃	—	6	2	no	—
268	C₄×Dic₃	—	6	1	no	—
269	C₄×Dic₃	—	6	1	no	—
270	C₄×Dic₃	—	6	2	no	—
271	C₄×Dic₃	—	12	1	no	—
272	#208	—	2	1	no	—
273	#208	—	2	1	no	—
274	#208	—	2	1	no	—
275	#208	—	6	2	no	—
276	#208	—	6	2	no	—
277	#208	—	6	1	no	—
278	#208	—	6	1	no	—
279	#208	—	6	1	no	—
280	#208	—	6	1	no	—
281	#208	—	12	1	no	—
282	#208	—	12	1	no	—
283	#208	C₂×Dic₃	1	2	yes	complemented
284	C₂×C₃⋊C₈	—	2	1	no	—
285	C₂×C₃⋊C₈	—	3	2	no	—
286	C₂×C₃⋊C₈	—	3	2	no	—
287	C₂×C₃⋊C₈	—	6	2	no	—
288	C₂×C₃⋊C₈	—	6	2	no	—
289	C₂×C₃⋊C₈	—	6	2	no	—
290	C₂×C₃⋊C₈	C₄×D₃	1	2	yes	complemented
291	ΓL(1,𝔽₂₅)	—	2	2	no	—
292	ΓL(1,𝔽₂₅)	—	2	2	no	—
293	ΓL(1,𝔽₂₅)	—	6	2	no	—
294	ΓL(1,𝔽₂₅)	—	6	2	no	—
295	D₃×C₈	—	2	2	no	—
296	D₃×C₈	—	2	2	no	—
297	D₃×C₈	—	6	2	no	—
298	D₃×C₈	—	6	2	no	—
299	C₂²×C₃²	—	4	1	no	—
300	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
301	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
303	C₂×C₃×D₃	—	2	2	no	—
304	C₂×C₃×D₃	—	2	2	no	—
305	C₂×C₃×D₃	—	2	2	no	—
306	C₂×C₃×D₃	—	4	1	no	—
307	C₂×C₃×D₃	—	4	1	no	—
308	C₂×C₃×D₃	—	4	1	no	—
309	C₂×C₃×D₃	#95	1	1	yes	characteristic
310	C₂×C₃×D₃	#95	1	1	yes	characteristic
311	C₂×C₃×D₃	#95	1	1	yes	characteristic
312	C₂×C₃×D₃	#95	1	1	yes	characteristic
313	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
316	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
317	C₃⋊Dic₃	—	4	2	no	—
318	C₃×Dic₃	—	4	2	no	—
319	C₃×Dic₃	#95	1	1	yes	characteristic
320	C₃×Dic₃	#95	1	1	yes	characteristic
321	C₃×Dic₃	#95	1	1	yes	characteristic
322	C₃×Dic₃	#95	1	1	yes	characteristic
323	C₂³×C₄	—	3	1	no	—
324	C₂×M₁₆	—	3	1	no	—
325	C₂×M₁₆	—	3	1	no	—
326	C₂×M₁₆	—	3	2	no	—
327	C₂×M₁₆	—	3	2	no	—
328	C₂×M₁₆	—	6	1	no	—
329	C₂×M₁₆	—	6	1	no	—
330	C₂×M₁₆	—	6	1	no	—
331	C₂×M₁₆	—	9	2	no	—
332	C₂×M₁₆	—	9	1	no	—
333	C₂×M₁₆	—	18	1	no	—
334	C₂×M₁₆	—	18	1	no	—
335	C₂×M₁₆	—	18	1	no	—
336	C₂×M₁₆	—	18	1	no	—
337	C₂×M₁₆	D₃²	1	1	yes	characteristic
338	C₂²×C₈	—	6	1	no	—
339	C₂²×C₈	—	9	2	no	—
340	#117	—	3	1	no	—
341	#117	—	9	2	no	—
342	#117	—	9	1	no	—
343	#117	—	18	1	no	—
344	#117	—	18	1	no	—
345	C₂×C₄⋊C₄	—	18	1	no	—
346	C₂×C₂²⋊C₄	—	9	2	no	—
347	C₂×C₄²	—	18	1	no	—
348	C₂³×C₃	—	2	1	no	—
349	C₂³×C₃	—	3	1	no	—
350	C₂³×C₃	—	3	1	no	—
351	C₂³×C₃	—	3	1	no	—
352	C₂³×C₃	—	3	1	no	—
353	C₂³×C₃	—	3	1	no	—
354	C₂³×C₃	—	3	1	no	—
355	C₂³×C₃	—	12	2	no	—
356	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
357	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
358	C₂²×D₃	—	4	2	no	—
359	C₂²×D₃	C₄×Dic₃	1	1	yes	characteristic
360	C₂²×D₃	C₄×Dic₃	1	1	yes	characteristic
361	C₂²×D₃	Dic₃⋊C₄	1	1	yes	characteristic
362	C₂²×D₃	Dic₃⋊C₄	1	1	yes	characteristic
363	C₂²×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
364	C₂²×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	3	1	no	—
372	C₂×C₃×C₄	—	3	1	no	—
373	C₂×C₃×C₄	—	3	1	no	—
374	C₂×C₃×C₄	—	3	1	no	—
375	C₂×C₃×C₄	—	3	1	no	—
376	C₂×C₃×C₄	—	3	1	no	—
377	C₂×C₃×C₄	—	3	1	no	—
378	C₂×C₃×C₄	—	3	1	no	—
379	C₂×C₃×C₄	—	3	1	no	—
380	C₂×C₃×C₄	—	3	1	no	—
381	C₂×C₃×C₄	—	3	1	no	—
382	C₂×C₃×C₄	—	3	1	no	—
383	C₂×C₃×C₄	—	3	1	no	—
384	C₂×C₃×C₄	—	3	1	no	—
385	C₂×C₃×C₄	—	3	1	no	—
386	C₂×C₃×C₄	—	3	1	no	—
387	C₂×C₃×C₄	—	3	1	no	—
388	C₂×C₃×C₄	—	3	1	no	—
389	C₂×C₃×C₄	—	3	1	no	—
390	C₂×C₃×C₄	—	3	1	no	—
391	C₂×C₃×C₄	—	3	1	no	—
392	C₂×C₃×C₄	—	3	1	no	—
393	C₂×C₃×C₄	—	6	2	no	—
394	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
399	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
400	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
401	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
402	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
406	C₂×Dic₃	—	2	2	no	—
407	C₂×Dic₃	—	6	2	no	—
408	C₂×Dic₃	—	6	2	no	—
409	C₂×Dic₃	—	12	2	no	—
410	C₂×Dic₃	—	12	4	no	—
411	C₂×Dic₃	C₄×Dic₃	1	1	yes	characteristic
412	C₂×Dic₃	C₄×Dic₃	1	1	yes	characteristic
413	C₂×Dic₃	Dic₃⋊C₄	1	1	yes	characteristic
414	C₂×Dic₃	Dic₃⋊C₄	1	1	yes	characteristic
415	C₂×Dic₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
416	C₂×Dic₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
417	C₄×D₃	—	12	4	no	—
418	C₄×D₃	Dic₃⋊C₄	1	1	yes	characteristic
419	C₄×D₃	Dic₃⋊C₄	1	1	yes	characteristic
420	C₄×D₃	Dic₃⋊C₄	1	1	yes	characteristic
421	C₄×D₃	Dic₃⋊C₄	1	1	yes	characteristic
422	C₄×D₃	C₄⋊Dic₃	1	1	yes	characteristic
423	C₄×D₃	C₄⋊Dic₃	1	1	yes	characteristic
424	C₄×D₃	C₄⋊Dic₃	1	1	yes	characteristic
425	C₄×D₃	C₄⋊Dic₃	1	1	yes	characteristic
426	C₄×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
427	C₄×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
428	C₄×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
429	C₄×D₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
430	C₄×D₃	#217	1	1	yes	characteristic
431	C₄×D₃	#217	1	1	yes	characteristic
432	C₄×D₃	#217	1	1	yes	characteristic
433	C₄×D₃	#217	1	1	yes	characteristic
434	C₃×C₈	—	2	2	no	—
435	C₃×C₈	—	2	2	no	—
436	C₃×C₈	—	4	2	no	—
437	C₃×C₈	—	6	2	no	—
438	C₃×C₈	—	6	2	no	—
439	C₃⋊C₈	—	2	2	no	—
440	C₃⋊C₈	—	2	2	no	—
441	C₃⋊C₈	—	6	2	no	—
442	C₃⋊C₈	—	6	2	no	—
443	C₃⋊C₈	—	12	2	no	—
444	C₂×C₃²	—	2	1	no	—
445	C₂×C₃²	—	2	1	no	—
446	C₂×C₃²	—	2	1	no	—
447	C₂×C₃²	C₂×#95	1	1	yes	characteristic
448	C₃×D₃	—	2	1	no	—
449	C₃×D₃	—	2	1	no	—
450	C₃×D₃	—	2	1	no	—
451	C₃×D₃	#344	1	2	yes	complemented
452	C₂⁴	—	3	1	no	—
453	C₂²×C₄	—	3	1	no	—
454	C₂²×C₄	—	3	1	no	—
455	C₂²×C₄	—	3	1	no	—
456	C₂²×C₄	—	3	1	no	—
457	C₂²×C₄	—	3	1	no	—
458	C₂²×C₄	—	3	1	no	—
459	C₂²×C₄	—	3	1	no	—
460	C₂²×C₄	—	3	1	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	1	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	3	1	no	—
465	C₂²×C₄	—	3	1	no	—
466	C₂²×C₄	—	18	2	no	—
467	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
468	M₁₆	—	2	1	no	—
469	M₁₆	—	3	2	no	—
470	M₁₆	—	6	2	no	—
471	M₁₆	—	6	2	no	—
472	M₁₆	—	6	1	no	—
473	M₁₆	—	6	1	no	—
474	M₁₆	—	6	1	no	—
475	M₁₆	—	18	2	no	—
476	M₁₆	—	18	2	no	—
477	M₁₆	—	18	1	no	—
478	M₁₆	—	18	1	no	—
479	M₁₆	D₃×Dic₃	1	2	yes	complemented
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	3	2	no	—
482	C₂×C₈	—	6	2	no	—
483	C₂×C₈	—	6	2	no	—
484	C₂×C₈	—	6	1	no	—
485	C₂×C₈	—	9	2	no	—
486	C₂×C₈	—	18	2	no	—
487	C₂×C₈	—	18	2	no	—
488	C₄⋊C₄	—	6	1	no	—
489	C₄⋊C₄	—	18	2	no	—
490	C₄⋊C₄	—	18	1	no	—
491	C₂²⋊C₄	—	3	2	no	—
492	C₂²⋊C₄	—	9	2	no	—
493	C₂²⋊C₄	—	18	2	no	—
494	C₄²	—	6	1	no	—
495	C₄²	—	18	2	no	—
496	C₄²	—	18	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	1	no	—
500	C₂²×C₃	—	3	1	no	—
501	C₂²×C₃	—	3	1	no	—
502	C₂²×C₃	—	3	1	no	—
503	C₂²×C₃	—	3	1	no	—
504	C₂²×C₃	—	4	1	no	—
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	6	2	no	—
507	C₂²×C₃	—	6	2	no	—
508	C₂²×C₃	—	6	2	no	—
509	C₂²×C₃	—	8	1	no	—
510	C₂²×C₃	—	12	1	no	—
511	C₂²×C₃	—	12	1	no	—
512	C₂²×C₃	—	12	1	no	—
513	C₂²×C₃	C₄²×D₃	1	1	yes	characteristic
514	C₂²×C₃	D₃×C₂²⋊C₄	1	1	yes	characteristic
515	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
516	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
517	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
518	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
519	C₂×D₃	—	2	2	no	—
520	C₂×D₃	—	2	2	no	—
521	C₂×D₃	—	2	2	no	—
522	C₂×D₃	—	4	1	no	—
523	C₂×D₃	—	4	1	no	—
524	C₂×D₃	—	4	1	no	—
525	C₂×D₃	C₃⋊#95	1	1	yes	characteristic
526	C₂×D₃	C₃⋊#95	1	1	yes	characteristic
527	C₂×D₃	C₃⋊#95	1	1	yes	characteristic
528	C₂×D₃	C₃⋊#95	1	1	yes	characteristic
529	C₃×C₄	—	2	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	3	1	no	—
534	C₃×C₄	—	3	1	no	—
535	C₃×C₄	—	3	1	no	—
536	C₃×C₄	—	3	1	no	—
537	C₃×C₄	—	12	2	no	—
538	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
539	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
540	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
541	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
542	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
543	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
544	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
545	C₃×C₄	C₂×#217	1	1	yes	characteristic
546	Dic₃	—	4	2	no	—
547	Dic₃	—	12	2	no	—
548	Dic₃	—	12	2	no	—
549	Dic₃	—	24	2	no	—
550	Dic₃	C₃⋊#95	1	1	yes	characteristic
551	Dic₃	C₃⋊#95	1	1	yes	characteristic
552	Dic₃	C₃⋊#95	1	1	yes	characteristic
553	Dic₃	C₃⋊#95	1	1	yes	characteristic
554	C₃²	C₂×#344	1	1	yes	characteristic, complemented, Sylow
555	C₂³	—	3	1	no	—
556	C₂³	—	3	1	no	—
557	C₂³	—	3	1	no	—
558	C₂³	—	3	1	no	—
559	C₂³	—	3	1	no	—
560	C₂³	—	3	1	no	—
561	C₂³	—	12	2	no	—
562	C₂³	C₄×D₃²	1	1	yes	characteristic
563	C₂×C₄	—	3	1	no	—
564	C₂×C₄	—	3	1	no	—
565	C₂×C₄	—	3	1	no	—
566	C₂×C₄	—	3	1	no	—
567	C₂×C₄	—	3	1	no	—
568	C₂×C₄	—	3	1	no	—
569	C₂×C₄	—	3	1	no	—
570	C₂×C₄	—	3	1	no	—
571	C₂×C₄	—	3	1	no	—
572	C₂×C₄	—	3	1	no	—
573	C₂×C₄	—	3	1	no	—
574	C₂×C₄	—	3	1	no	—
575	C₂×C₄	—	3	1	no	—
576	C₂×C₄	—	3	1	no	—
577	C₂×C₄	—	3	1	no	—
578	C₂×C₄	—	3	1	no	—
579	C₂×C₄	—	3	1	no	—
580	C₂×C₄	—	3	1	no	—
581	C₂×C₄	—	3	1	no	—
582	C₂×C₄	—	3	1	no	—
583	C₂×C₄	—	3	1	no	—
584	C₂×C₄	—	3	1	no	—
585	C₂×C₄	—	6	2	no	—
586	C₂×C₄	—	18	2	no	—
587	C₂×C₄	—	36	4	no	—
588	C₂×C₄	D₃×Dic₆	1	1	yes	characteristic
589	C₂×C₄	C₄×D₃²	1	1	yes	characteristic
590	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
591	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
592	C₂×C₄	D₃×#67	1	1	yes	characteristic
593	C₂×C₄	D₃×#67	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	6	2	no	—
596	C₈	—	6	2	no	—
597	C₈	—	18	2	no	—
598	C₂×C₃	—	2	1	no	—
599	C₂×C₃	—	2	1	no	—
600	C₂×C₃	—	2	1	no	—
601	C₂×C₃	—	2	1	no	—
602	C₂×C₃	—	2	1	no	—
603	C₂×C₃	—	2	1	no	—
604	C₂×C₃	—	2	1	no	—
605	C₂×C₃	—	3	2	no	—
606	C₂×C₃	—	4	1	no	—
607	C₂×C₃	—	4	1	no	—
608	C₂×C₃	—	4	1	no	—
609	C₂×C₃	—	6	1	no	—
610	C₂×C₃	—	6	1	no	—
611	C₂×C₃	—	6	1	no	—
612	C₂×C₃	D₃×#95	1	1	yes	characteristic
613	C₂×C₃	C₂×C₃⋊#95	1	1	yes	characteristic
614	D₃	—	2	1	no	—
615	D₃	—	2	1	no	—
616	D₃	—	2	1	no	—
617	D₃	#4559	1	2	yes	direct product factor
618	C₂²	—	3	1	no	—
619	C₂²	—	3	1	no	—
620	C₂²	—	3	1	no	—
621	C₂²	—	3	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	6	2	no	—
624	C₂²	—	6	2	no	—
625	C₂²	—	6	2	no	—
626	C₂²	—	12	1	no	—
627	C₂²	—	12	1	no	—
628	C₂²	—	12	1	no	—
629	C₂²	C₄×D₃×Dic₃	1	1	yes	characteristic
630	C₂²	D₃×Dic₃⋊C₄	1	1	yes	characteristic
631	C₂²	D₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
632	C₄	—	3	1	no	—
633	C₄	—	3	1	no	—
634	C₄	—	3	1	no	—
635	C₄	—	3	1	no	—
636	C₄	—	12	2	no	—
637	C₄	—	36	2	no	—
638	C₄	D₃×Dic₃⋊C₄	1	1	yes	characteristic
639	C₄	D₃×C₄⋊Dic₃	1	1	yes	characteristic
640	C₄	D₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
641	C₄	D₃×#217	1	1	yes	characteristic
642	C₃	—	2	1	no	—
643	C₃	D₃×#344	1	1	yes	characteristic, complemented
644	C₃	C₂×#4559	1	1	yes	characteristic, complemented
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	3	2	no	—
649	C₂	—	6	1	no	—
650	C₂	—	6	1	no	—
651	C₂	—	6	1	no	—
652	C₂	D₃×C₃⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃×(C₂×D₃)⋊C₄
commutator	C₂²×C₃²	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×M₁₆	C₂²
socle	C₂×C₃²	C₂×#95
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂×M₁₆	D₃²
hypocenter	C₃²	C₂×#344
LCS	G ▷ C₂²×C₃² ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #10589425	C₂	semidirect
5. C₃×#4559	C₂	semidirect
6. #10589171	C₂	semidirect
7. #10589170	C₂	semidirect
19. C₃×D₃×M₁₆	C₄	semidirect
20. C₃×D₃×M₁₆	C₄	semidirect
29. C₂×#3711	C₄	semidirect
34. C₂×D₃×C₃⋊C₈	C₄	semidirect
47. #4559	D₃	direct (N × H)
67. C₃²×M₁₆	C₂×C₄	semidirect
74. C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	semidirect
81. C₃×#208	C₂×C₄	semidirect
83. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
137. D₃×M₁₆	Dic₃	semidirect
138. D₃×M₁₆	Dic₃	semidirect
242. C₃×M₁₆	C₄×D₃	semidirect
243. C₃×M₁₆	C₂×Dic₃	semidirect
283. #208	C₂×Dic₃	semidirect
290. C₂×C₃⋊C₈	C₄×D₃	semidirect
451. C₃×D₃	#344	semidirect
479. M₁₆	D₃×Dic₃	semidirect
554. C₃²	C₂×#344	semidirect
617. D₃	#4559	direct (N × H)
643. C₃	D₃×#344	semidirect
644. C₃	C₂×#4559	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×M₁₆	2
D₃×#926	2
C₂×D₃×#208	2
#10589425	2
C₃×#4559	2
#10589171	2
#10589170	2
C₂×#4559	3
D₃×#344	3

Subgroups — D3×#4559 #11783455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#4559 #11783455