Subgroups — C₂²×#89049 #13181694

Order 1728.

6802 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#1113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#638	C₂	1	2	yes	maximal, complemented
4	C₂×#89049	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#6295	C₂	1	2	yes	maximal, complemented
6	C₂²×#6294	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#3811	—	3	1	no	maximal
8	C₂²×D₃×#67	—	3	2	no	maximal
9	C₂⁴×C₃³	C₂²	1	1	yes	characteristic, complemented
10	C₂³×C₃×C₃⋊D₃	—	2	8	no	—
11	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₃⋊D₃	C₂²	1	12	yes	complemented
13	C₂³×C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	complemented
15	C₂²×#1113	—	2	8	no	—
16	C₂²×#1113	C₂²	1	12	yes	complemented
17	C₂×C₃×#638	C₂²	1	24	yes	complemented
18	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	complemented
19	#89049	C₂²	1	64	yes	direct product factor
20	C₂×#6295	C₂²	1	24	yes	complemented
21	C₂×#6294	C₂²	1	12	yes	complemented
22	C₂⁴×C₃⋊D₃	D₃	1	1	yes	characteristic, complemented
23	C₂⁴×C₃×D₃	—	3	2	no	—
24	C₂⁴×C₃×D₃	—	6	1	no	—
25	C₂³×D₃²	—	3	1	no	—
26	C₂³×D₃²	—	3	2	no	—
27	C₂²×#638	D₃	1	2	yes	complemented
28	C₂²×C₃×#67	—	3	2	no	—
29	C₂²×C₃×#67	—	3	2	no	—
30	C₂²×C₃×#67	—	6	2	no	—
31	C₂×#3811	—	3	24	no	—
32	C₂×D₃×#67	—	3	48	no	—
33	C₂²×#626	—	3	2	no	—
34	C₂²×#626	—	3	2	no	—
35	C₂²×#625	—	3	2	no	—
36	C₂²×#624	—	3	1	no	—
37	C₂²×D₃×Dic₃	—	3	2	no	—
38	C₂³×C₃³	—	2	4	no	—
39	C₂³×C₃³	C₂³	1	1	yes	characteristic
40	C₂³×C₃³	C₂³	1	6	yes	complemented
41	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
42	C₂²×C₃×C₃⋊D₃	—	2	8	no	—
43	C₂²×C₃×C₃⋊D₃	—	2	48	no	—
44	C₂²×C₃×C₃⋊D₃	D₄	1	8	yes	complemented
45	C₂²×C₃×C₃⋊D₃	C₂³	1	6	yes	—
46	C₂²×C₃×C₃⋊D₃	C₂³	1	16	yes	complemented
47	C₂²×C₃×C₃⋊D₃	C₂³	1	12	yes	complemented
48	C₂²×C₃×C₃⋊D₃	C₂³	1	6	yes	complemented
49	C₂×#1113	—	2	48	no	—
50	C₂×#1113	C₂³	1	16	yes	complemented
51	C₃×#638	C₂³	1	32	yes	complemented
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	12	yes	complemented
53	#6295	C₂³	1	32	yes	complemented
54	#6294	C₂³	1	16	yes	complemented
55	C₂³×#67	—	9	1	no	—
56	C₂²×D₃×D₄	—	9	2	no	—
57	C₂⁴×C₃²	—	2	1	no	—
58	C₂⁴×C₃²	—	2	2	no	—
59	C₂⁴×C₃²	—	4	1	no	—
60	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃²	C₂×D₃	1	2	yes	complemented
62	C₂³×C₃⋊D₃	—	2	8	no	—
63	C₂³×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
64	C₂³×C₃⋊D₃	C₂×D₃	1	12	yes	complemented
65	C₂³×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic, complemented
66	C₂³×C₃⋊D₃	C₂×D₃	1	2	yes	complemented
67	C₂³×C₃×D₃	—	3	2	no	—
68	C₂³×C₃×D₃	—	3	2	no	—
69	C₂³×C₃×D₃	—	3	2	no	—
70	C₂³×C₃×D₃	—	3	2	no	—
71	C₂³×C₃×D₃	—	3	24	no	—
72	C₂³×C₃×D₃	—	6	16	no	—
73	C₂³×C₃×D₃	—	6	1	no	—
74	C₂³×C₃×D₃	—	6	12	no	—
75	C₂³×C₃×D₃	—	6	1	no	—
76	C₂³×C₃×D₃	—	6	16	no	—
77	C₂³×C₃×D₃	—	6	2	no	—
78	C₂²×D₃²	—	3	12	no	—
79	C₂²×D₃²	—	3	24	no	—
80	C₂²×D₃²	—	6	16	no	—
81	C₂²×D₃²	—	6	8	no	—
82	C₂×#638	C₂×D₃	1	24	yes	complemented
83	C₂²×C₃⋊Dic₃	C₂×D₃	1	2	yes	complemented
84	C₂×C₃×#67	—	3	24	no	—
85	C₂×C₃×#67	—	3	24	no	—
86	C₂×C₃×#67	—	6	24	no	—
87	C₂²×C₃×Dic₃	—	3	2	no	—
88	C₂²×C₃×Dic₃	—	3	2	no	—
89	C₂²×C₃×Dic₃	—	6	2	no	—
90	#3811	—	3	64	no	—
91	D₃×#67	—	3	128	no	—
92	C₂×#626	—	3	24	no	—
93	C₂×#626	—	3	24	no	—
94	C₂×#625	—	3	24	no	—
95	C₂×#624	—	3	12	no	—
96	C₂×D₃×Dic₃	—	3	24	no	—
97	C₂²×C₃³	—	2	12	no	—
98	C₂²×C₃³	C₂×D₄	1	4	yes	complemented
99	C₂²×C₃³	C₂⁴	1	3	yes	—
100	C₂²×C₃³	C₂⁴	1	4	yes	complemented
101	C₂×C₃×C₃⋊D₃	—	2	12	no	—
102	C₂×C₃×C₃⋊D₃	—	2	24	no	—
103	C₂×C₃×C₃⋊D₃	—	2	32	no	—
104	C₂×C₃×C₃⋊D₃	C₂×D₄	1	24	yes	complemented
105	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	—
106	C₂×C₃×C₃⋊D₃	C₂⁴	1	4	yes	complemented
107	C₂×C₃×C₃⋊D₃	C₂⁴	1	8	yes	complemented
108	#1113	—	2	32	no	—
109	C₃×C₃⋊Dic₃	C₂⁴	1	8	yes	complemented
110	C₂⁵×C₃	—	9	1	no	—
111	C₂⁴×D₃	—	3	2	no	—
112	C₂⁴×D₃	—	6	1	no	—
113	C₂⁴×D₃	—	9	2	no	—
114	C₂⁴×D₃	—	9	1	no	—
115	C₂²×C₃×D₄	—	9	2	no	—
116	C₂²×#67	—	3	2	no	—
117	C₂²×#67	—	3	2	no	—
118	C₂²×#67	—	6	2	no	—
119	C₂²×#67	—	9	2	no	—
120	C₂²×#67	—	9	2	no	—
121	C₂²×#67	—	9	24	no	—
122	C₂³×Dic₃	—	9	1	no	—
123	C₂×D₃×D₄	—	9	48	no	—
124	C₂²×D₁₂	—	9	2	no	—
125	C₂²×C₄×D₃	—	9	2	no	—
126	C₂³×C₃²	—	2	4	no	—
127	C₂³×C₃²	—	2	8	no	—
128	C₂³×C₃²	—	2	8	no	—
129	C₂³×C₃²	—	2	1	no	—
130	C₂³×C₃²	—	2	2	no	—
131	C₂³×C₃²	—	2	6	no	—
132	C₂³×C₃²	—	2	12	no	—
133	C₂³×C₃²	—	4	1	no	—
134	C₂³×C₃²	—	4	6	no	—
135	C₂³×C₃²	—	4	8	no	—
136	C₂³×C₃²	—	4	8	no	—
137	C₂³×C₃²	C₂²×D₃	1	2	yes	—
138	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
139	C₂³×C₃²	C₂²×D₃	1	12	yes	complemented
140	C₂³×C₃²	C₂²×D₃	1	6	yes	complemented
141	C₂²×C₃⋊D₃	—	2	4	no	—
142	C₂²×C₃⋊D₃	—	2	48	no	—
143	C₂²×C₃⋊D₃	—	2	8	no	—
144	C₂²×C₃⋊D₃	#67	1	8	yes	complemented
145	C₂²×C₃⋊D₃	C₂²×D₃	1	6	yes	—
146	C₂²×C₃⋊D₃	C₂²×D₃	1	16	yes	complemented
147	C₂²×C₃⋊D₃	C₂²×D₃	1	12	yes	complemented
148	C₂²×C₃⋊D₃	C₂²×D₃	1	6	yes	complemented
149	C₂²×C₃×D₃	—	3	16	no	—
150	C₂²×C₃×D₃	—	3	12	no	—
151	C₂²×C₃×D₃	—	3	12	no	—
152	C₂²×C₃×D₃	—	3	12	no	—
153	C₂²×C₃×D₃	—	3	12	no	—
154	C₂²×C₃×D₃	—	3	32	no	—
155	C₂²×C₃×D₃	—	6	8	no	—
156	C₂²×C₃×D₃	—	6	6	no	—
157	C₂²×C₃×D₃	—	6	6	no	—
158	C₂²×C₃×D₃	—	6	16	no	—
159	C₂²×C₃×D₃	—	6	12	no	—
160	C₂²×C₃×D₃	—	6	96	no	—
161	C₂²×C₃×D₃	—	6	96	no	—
162	C₂²×C₃×D₃	—	6	8	no	—
163	C₂²×C₃×D₃	—	6	8	no	—
164	C₂²×C₃×D₃	—	6	8	no	—
165	C₂²×C₃×D₃	—	6	8	no	—
166	C₂²×C₃×D₃	—	12	8	no	—
167	C₂×D₃²	—	3	16	no	—
168	C₂×D₃²	—	3	32	no	—
169	C₂×D₃²	—	6	96	no	—
170	C₂×D₃²	—	6	48	no	—
171	#638	C₂²×D₃	1	32	yes	complemented
172	C₂×C₃⋊Dic₃	C₂²×D₃	1	12	yes	complemented
173	C₃×#67	—	3	32	no	—
174	C₃×#67	—	3	32	no	—
175	C₃×#67	—	6	32	no	—
176	C₂×C₃×Dic₃	—	3	12	no	—
177	C₂×C₃×Dic₃	—	3	12	no	—
178	C₂×C₃×Dic₃	—	6	12	no	—
179	#626	—	3	32	no	—
180	#626	—	3	32	no	—
181	#625	—	3	32	no	—
182	#624	—	3	16	no	—
183	D₃×Dic₃	—	3	32	no	—
184	C₂³×D₄	—	27	1	no	Sylow
185	C₂×C₃³	—	2	4	no	—
186	C₂×C₃³	C₂²×D₄	1	6	yes	complemented
187	C₂×C₃³	C₂⁵	1	1	yes	characteristic
188	C₃×C₃⋊D₃	—	2	4	no	—
189	C₃×C₃⋊D₃	—	2	8	no	—
190	C₃×C₃⋊D₃	C₂²×D₄	1	8	yes	complemented
191	C₂⁴×C₃	—	2	1	no	—
192	C₂⁴×C₃	—	2	2	no	—
193	C₂⁴×C₃	—	4	1	no	—
194	C₂⁴×C₃	—	9	1	no	—
195	C₂⁴×C₃	—	9	1	no	—
196	C₂⁴×C₃	—	9	2	no	—
197	C₂⁴×C₃	—	9	12	no	—
198	C₂⁴×C₃	—	18	8	no	—
199	C₂⁴×C₃	D₃²	1	1	yes	characteristic, complemented
200	C₂⁴×C₃	D₃²	1	2	yes	complemented
201	C₂³×D₃	—	3	2	no	—
202	C₂³×D₃	—	3	2	no	—
203	C₂³×D₃	—	3	2	no	—
204	C₂³×D₃	—	3	2	no	—
205	C₂³×D₃	—	3	24	no	—
206	C₂³×D₃	—	6	1	no	—
207	C₂³×D₃	—	6	1	no	—
208	C₂³×D₃	—	6	12	no	—
209	C₂³×D₃	—	6	2	no	—
210	C₂³×D₃	—	6	16	no	—
211	C₂³×D₃	—	6	16	no	—
212	C₂³×D₃	—	9	24	no	—
213	C₂³×D₃	—	9	12	no	—
214	C₂³×D₃	—	18	16	no	—
215	C₂³×D₃	—	18	8	no	—
216	C₂×C₃×D₄	—	9	24	no	—
217	C₂²×C₃×C₄	—	9	2	no	—
218	C₂×#67	—	3	24	no	—
219	C₂×#67	—	3	24	no	—
220	C₂×#67	—	6	24	no	—
221	C₂×#67	—	9	24	no	—
222	C₂×#67	—	9	24	no	—
223	C₂×#67	—	9	64	no	—
224	C₂²×Dic₃	—	3	2	no	—
225	C₂²×Dic₃	—	3	2	no	—
226	C₂²×Dic₃	—	6	2	no	—
227	C₂²×Dic₃	—	9	12	no	—
228	D₃×D₄	—	9	128	no	—
229	C₂×D₁₂	—	9	24	no	—
230	C₂×C₄×D₃	—	9	24	no	—
231	C₂²×C₃²	—	2	12	no	—
232	C₂²×C₃²	—	2	24	no	—
233	C₂²×C₃²	—	2	24	no	—
234	C₂²×C₃²	—	2	6	no	—
235	C₂²×C₃²	—	2	3	no	—
236	C₂²×C₃²	—	2	4	no	—
237	C₂²×C₃²	—	2	8	no	—
238	C₂²×C₃²	—	2	8	no	—
239	C₂²×C₃²	—	2	4	no	—
240	C₂²×C₃²	—	4	4	no	—
241	C₂²×C₃²	—	4	3	no	—
242	C₂²×C₃²	—	4	4	no	—
243	C₂²×C₃²	—	4	24	no	—
244	C₂²×C₃²	—	4	24	no	—
245	C₂²×C₃²	D₃×D₄	1	8	yes	complemented
246	C₂²×C₃²	C₂×#67	1	4	yes	complemented
247	C₂²×C₃²	C₂³×D₃	1	6	yes	—
248	C₂²×C₃²	C₂³×D₃	1	3	yes	—
249	C₂²×C₃²	C₂³×D₃	1	4	yes	complemented
250	C₂²×C₃²	C₂³×D₃	1	8	yes	complemented
251	C₂×C₃⋊D₃	—	2	12	no	—
252	C₂×C₃⋊D₃	—	2	32	no	—
253	C₂×C₃⋊D₃	—	2	24	no	—
254	C₂×C₃⋊D₃	C₂×#67	1	24	yes	complemented
255	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	—
256	C₂×C₃⋊D₃	C₂³×D₃	1	4	yes	complemented
257	C₂×C₃⋊D₃	C₂³×D₃	1	8	yes	complemented
258	C₂×C₃×D₃	—	3	48	no	—
259	C₂×C₃×D₃	—	3	8	no	—
260	C₂×C₃×D₃	—	3	8	no	—
261	C₂×C₃×D₃	—	3	8	no	—
262	C₂×C₃×D₃	—	3	8	no	—
263	C₂×C₃×D₃	—	6	24	no	—
264	C₂×C₃×D₃	—	6	4	no	—
265	C₂×C₃×D₃	—	6	4	no	—
266	C₂×C₃×D₃	—	6	8	no	—
267	C₂×C₃×D₃	—	6	64	no	—
268	C₂×C₃×D₃	—	6	64	no	—
269	C₂×C₃×D₃	—	6	24	no	—
270	C₂×C₃×D₃	—	6	24	no	—
271	C₂×C₃×D₃	—	6	24	no	—
272	C₂×C₃×D₃	—	6	24	no	—
273	C₂×C₃×D₃	—	12	24	no	—
274	D₃²	—	6	64	no	—
275	D₃²	—	6	32	no	—
276	C₃⋊Dic₃	C₂³×D₃	1	8	yes	complemented
277	C₃×Dic₃	—	3	8	no	—
278	C₃×Dic₃	—	3	8	no	—
279	C₃×Dic₃	—	6	8	no	—
280	C₂⁵	—	9	1	no	—
281	C₂⁵	—	27	1	no	—
282	C₂²×D₄	—	9	2	no	—
283	C₂²×D₄	—	27	2	no	—
284	C₂²×D₄	—	27	24	no	—
285	C₂³×C₄	—	27	1	no	—
286	C₃³	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
287	C₂³×C₃	—	2	8	no	—
288	C₂³×C₃	—	2	8	no	—
289	C₂³×C₃	—	2	4	no	—
290	C₂³×C₃	—	2	2	no	—
291	C₂³×C₃	—	2	1	no	—
292	C₂³×C₃	—	2	6	no	—
293	C₂³×C₃	—	2	12	no	—
294	C₂³×C₃	—	4	8	no	—
295	C₂³×C₃	—	4	8	no	—
296	C₂³×C₃	—	4	1	no	—
297	C₂³×C₃	—	4	6	no	—
298	C₂³×C₃	—	9	6	no	—
299	C₂³×C₃	—	9	8	no	—
300	C₂³×C₃	—	9	6	no	—
301	C₂³×C₃	—	9	12	no	—
302	C₂³×C₃	—	9	16	no	—
303	C₂³×C₃	—	18	48	no	—
304	C₂³×C₃	—	18	8	no	—
305	C₂³×C₃	—	18	4	no	—
306	C₂³×C₃	C₂×D₃²	1	2	yes	—
307	C₂³×C₃	C₂×D₃²	1	1	yes	characteristic
308	C₂³×C₃	C₂×D₃²	1	6	yes	complemented
309	C₂³×C₃	C₂×D₃²	1	12	yes	complemented
310	C₂²×D₃	—	3	12	no	—
311	C₂²×D₃	—	3	16	no	—
312	C₂²×D₃	—	3	12	no	—
313	C₂²×D₃	—	3	12	no	—
314	C₂²×D₃	—	3	12	no	—
315	C₂²×D₃	—	3	32	no	—
316	C₂²×D₃	—	6	8	no	—
317	C₂²×D₃	—	6	6	no	—
318	C₂²×D₃	—	6	6	no	—
319	C₂²×D₃	—	6	16	no	—
320	C₂²×D₃	—	6	12	no	—
321	C₂²×D₃	—	6	96	no	—
322	C₂²×D₃	—	6	96	no	—
323	C₂²×D₃	—	6	8	no	—
324	C₂²×D₃	—	6	8	no	—
325	C₂²×D₃	—	6	8	no	—
326	C₂²×D₃	—	6	8	no	—
327	C₂²×D₃	—	9	32	no	—
328	C₂²×D₃	—	9	16	no	—
329	C₂²×D₃	—	12	8	no	—
330	C₂²×D₃	—	18	96	no	—
331	C₂²×D₃	—	18	48	no	—
332	C₃×D₄	—	9	32	no	—
333	C₂×C₃×C₄	—	9	12	no	—
334	#67	—	3	32	no	—
335	#67	—	3	32	no	—
336	#67	—	6	32	no	—
337	#67	—	9	32	no	—
338	#67	—	9	32	no	—
339	C₂×Dic₃	—	3	12	no	—
340	C₂×Dic₃	—	3	12	no	—
341	C₂×Dic₃	—	6	12	no	—
342	C₂×Dic₃	—	9	16	no	—
343	D₁₂	—	9	32	no	—
344	C₄×D₃	—	9	32	no	—
345	C₂×C₃²	—	2	4	no	—
346	C₂×C₃²	—	2	8	no	—
347	C₂×C₃²	—	2	8	no	—
348	C₂×C₃²	—	2	12	no	—
349	C₂×C₃²	—	2	6	no	—
350	C₂×C₃²	—	2	2	no	—
351	C₂×C₃²	—	2	1	no	—
352	C₂×C₃²	—	4	6	no	—
353	C₂×C₃²	—	4	1	no	—
354	C₂×C₃²	—	4	8	no	—
355	C₂×C₃²	—	4	8	no	—
356	C₂×C₃²	C₂×D₃×D₄	1	12	yes	complemented
357	C₂×C₃²	C₂²×#67	1	6	yes	complemented
358	C₂×C₃²	C₂⁴×D₃	1	2	yes	—
359	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
360	C₃⋊D₃	—	2	4	no	—
361	C₃⋊D₃	—	2	8	no	—
362	C₃⋊D₃	C₂²×#67	1	8	yes	complemented
363	C₃×D₃	—	3	16	no	—
364	C₃×D₃	—	6	8	no	—
365	C₃×D₃	—	6	8	no	—
366	C₃×D₃	—	6	8	no	—
367	C₃×D₃	—	6	8	no	—
368	C₃×D₃	—	6	8	no	—
369	C₃×D₃	—	12	8	no	—
370	C₂⁴	—	9	1	no	—
371	C₂⁴	—	9	2	no	—
372	C₂⁴	—	9	1	no	—
373	C₂⁴	—	9	12	no	—
374	C₂⁴	—	18	8	no	—
375	C₂⁴	—	27	12	no	—
376	C₂⁴	—	54	8	no	—
377	C₂⁴	#1113	1	1	yes	characteristic, complemented
378	C₂×D₄	—	9	24	no	—
379	C₂×D₄	—	27	24	no	—
380	C₂×D₄	—	27	64	no	—
381	C₂²×C₄	—	9	2	no	—
382	C₂²×C₄	—	27	12	no	—
383	C₂²×C₃	—	2	24	no	—
384	C₂²×C₃	—	2	24	no	—
385	C₂²×C₃	—	2	12	no	—
386	C₂²×C₃	—	2	6	no	—
387	C₂²×C₃	—	2	3	no	—
388	C₂²×C₃	—	2	4	no	—
389	C₂²×C₃	—	2	8	no	—
390	C₂²×C₃	—	2	4	no	—
391	C₂²×C₃	—	2	8	no	—
392	C₂²×C₃	—	4	24	no	—
393	C₂²×C₃	—	4	24	no	—
394	C₂²×C₃	—	4	3	no	—
395	C₂²×C₃	—	4	4	no	—
396	C₂²×C₃	—	4	4	no	—
397	C₂²×C₃	—	9	24	no	—
398	C₂²×C₃	—	9	4	no	—
399	C₂²×C₃	—	9	4	no	—
400	C₂²×C₃	—	9	8	no	—
401	C₂²×C₃	—	18	32	no	—
402	C₂²×C₃	—	18	24	no	—
403	C₂²×C₃	—	18	12	no	—
404	C₂²×C₃	D₃×#67	1	8	yes	complemented
405	C₂²×C₃	#3811	1	4	yes	complemented
406	C₂²×C₃	C₂²×D₃²	1	6	yes	—
407	C₂²×C₃	C₂²×D₃²	1	3	yes	—
408	C₂²×C₃	C₂²×D₃²	1	4	yes	complemented
409	C₂²×C₃	C₂²×D₃²	1	8	yes	complemented
410	C₂×D₃	—	3	48	no	—
411	C₂×D₃	—	3	8	no	—
412	C₂×D₃	—	3	8	no	—
413	C₂×D₃	—	3	8	no	—
414	C₂×D₃	—	3	8	no	—
415	C₂×D₃	—	6	24	no	—
416	C₂×D₃	—	6	4	no	—
417	C₂×D₃	—	6	4	no	—
418	C₂×D₃	—	6	8	no	—
419	C₂×D₃	—	6	64	no	—
420	C₂×D₃	—	6	64	no	—
421	C₂×D₃	—	6	24	no	—
422	C₂×D₃	—	6	24	no	—
423	C₂×D₃	—	6	24	no	—
424	C₂×D₃	—	6	24	no	—
425	C₂×D₃	—	12	24	no	—
426	C₂×D₃	—	18	64	no	—
427	C₂×D₃	—	18	32	no	—
428	C₃×C₄	—	9	8	no	—
429	Dic₃	—	3	8	no	—
430	Dic₃	—	3	8	no	—
431	Dic₃	—	6	8	no	—
432	C₃²	—	2	2	no	—
433	C₃²	—	2	1	no	—
434	C₃²	—	4	1	no	—
435	C₃²	C₂²×D₃×D₄	1	2	yes	complemented
436	C₃²	C₂³×#67	1	1	yes	characteristic, complemented
437	C₂³	—	2	4	no	—
438	C₂³	—	9	6	no	—
439	C₂³	—	9	8	no	—
440	C₂³	—	9	12	no	—
441	C₂³	—	9	6	no	—
442	C₂³	—	9	16	no	—
443	C₂³	—	18	48	no	—
444	C₂³	—	18	4	no	—
445	C₂³	—	18	8	no	—
446	C₂³	—	27	16	no	—
447	C₂³	—	54	48	no	—
448	C₂³	C₂×#1113	1	1	yes	characteristic
449	C₂³	C₂×#1113	1	6	yes	complemented
450	D₄	—	9	32	no	—
451	D₄	—	27	32	no	—
452	C₂×C₄	—	9	12	no	—
453	C₂×C₄	—	27	16	no	—
454	C₂×C₃	—	2	8	no	—
455	C₂×C₃	—	2	8	no	—
456	C₂×C₃	—	2	4	no	—
457	C₂×C₃	—	2	6	no	—
458	C₂×C₃	—	2	12	no	—
459	C₂×C₃	—	2	2	no	—
460	C₂×C₃	—	2	1	no	—
461	C₂×C₃	—	4	8	no	—
462	C₂×C₃	—	4	8	no	—
463	C₂×C₃	—	4	6	no	—
464	C₂×C₃	—	4	1	no	—
465	C₂×C₃	—	9	8	no	—
466	C₂×C₃	—	18	8	no	—
467	C₂×C₃	—	18	4	no	—
468	C₂×C₃	C₂×D₃×#67	1	12	yes	complemented
469	C₂×C₃	C₂×#3811	1	6	yes	complemented
470	C₂×C₃	C₂³×D₃²	1	2	yes	—
471	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
472	D₃	—	3	16	no	—
473	D₃	—	6	8	no	—
474	D₃	—	6	8	no	—
475	D₃	—	6	8	no	—
476	D₃	—	6	8	no	—
477	D₃	—	6	8	no	—
478	D₃	—	12	8	no	—
479	C₂²	—	2	12	no	—
480	C₂²	—	9	24	no	—
481	C₂²	—	9	4	no	—
482	C₂²	—	9	8	no	—
483	C₂²	—	9	4	no	—
484	C₂²	—	18	32	no	—
485	C₂²	—	18	12	no	—
486	C₂²	—	18	24	no	—
487	C₂²	—	54	32	no	—
488	C₂²	#89049	1	4	yes	direct product factor
489	C₂²	C₂²×#1113	1	3	yes	—
490	C₂²	C₂²×#1113	1	4	yes	complemented
491	C₄	—	9	8	no	—
492	C₃	—	2	1	no	—
493	C₃	—	2	2	no	—
494	C₃	—	4	1	no	—
495	C₃	C₂²×D₃×#67	1	2	yes	complemented
496	C₃	C₂²×#3811	1	1	yes	characteristic, complemented
497	C₂	—	2	4	no	—
498	C₂	—	9	8	no	—
499	C₂	—	18	4	no	—
500	C₂	—	18	8	no	—
501	C₂	C₂×#89049	1	6	yes	direct product factor
502	C₂	C₂³×#1113	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#1113
commutator, cosocle	C₂×C₃³	C₂⁵
Frattini	C₂	C₂³×#1113
Fitting	C₂⁴×C₃³	C₂²
socle	C₂³×C₃³	C₂³
hypercenter	C₂⁴	#1113
hypocenter	C₃³	C₂³×D₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₃⋊D₃	C₂	semidirect
2. C₂³×#1113	C₂	semidirect
3. C₂²×C₃×#638	C₂	semidirect
4. C₂×#89049	C₂	direct (N × H)
5. C₂²×#6295	C₂	semidirect
6. C₂²×#6294	C₂	semidirect
9. C₂⁴×C₃³	C₂²	semidirect
12. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
13. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
14. C₂³×C₃×C₃⋊D₃	C₂²	semidirect
16. C₂²×#1113	C₂²	semidirect
17. C₂×C₃×#638	C₂²	semidirect
18. C₂²×C₃×C₃⋊Dic₃	C₂²	semidirect
19. #89049	C₂²	direct (N × H)
20. C₂×#6295	C₂²	semidirect
21. C₂×#6294	C₂²	semidirect
22. C₂⁴×C₃⋊D₃	D₃	semidirect
27. C₂²×#638	D₃	semidirect
40. C₂³×C₃³	C₂³	semidirect
44. C₂²×C₃×C₃⋊D₃	D₄	semidirect
46. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
47. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
48. C₂²×C₃×C₃⋊D₃	C₂³	semidirect
50. C₂×#1113	C₂³	semidirect
51. C₃×#638	C₂³	semidirect
52. C₂×C₃×C₃⋊Dic₃	C₂³	semidirect
53. #6295	C₂³	semidirect
54. #6294	C₂³	semidirect
60. C₂⁴×C₃²	C₂×D₃	semidirect
61. C₂⁴×C₃²	C₂×D₃	semidirect
64. C₂³×C₃⋊D₃	C₂×D₃	semidirect
65. C₂³×C₃⋊D₃	C₂×D₃	semidirect
66. C₂³×C₃⋊D₃	C₂×D₃	semidirect
82. C₂×#638	C₂×D₃	semidirect
83. C₂²×C₃⋊Dic₃	C₂×D₃	semidirect
98. C₂²×C₃³	C₂×D₄	semidirect
100. C₂²×C₃³	C₂⁴	semidirect
104. C₂×C₃×C₃⋊D₃	C₂×D₄	semidirect
106. C₂×C₃×C₃⋊D₃	C₂⁴	semidirect
107. C₂×C₃×C₃⋊D₃	C₂⁴	semidirect
109. C₃×C₃⋊Dic₃	C₂⁴	semidirect
139. C₂³×C₃²	C₂²×D₃	semidirect
140. C₂³×C₃²	C₂²×D₃	semidirect
144. C₂²×C₃⋊D₃	#67	semidirect
146. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
147. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
148. C₂²×C₃⋊D₃	C₂²×D₃	semidirect
171. #638	C₂²×D₃	semidirect
172. C₂×C₃⋊Dic₃	C₂²×D₃	semidirect
186. C₂×C₃³	C₂²×D₄	semidirect
190. C₃×C₃⋊D₃	C₂²×D₄	semidirect
199. C₂⁴×C₃	D₃²	semidirect
200. C₂⁴×C₃	D₃²	semidirect
245. C₂²×C₃²	D₃×D₄	semidirect
246. C₂²×C₃²	C₂×#67	semidirect
249. C₂²×C₃²	C₂³×D₃	semidirect
250. C₂²×C₃²	C₂³×D₃	semidirect
254. C₂×C₃⋊D₃	C₂×#67	semidirect
256. C₂×C₃⋊D₃	C₂³×D₃	semidirect
257. C₂×C₃⋊D₃	C₂³×D₃	semidirect
276. C₃⋊Dic₃	C₂³×D₃	semidirect
286. C₃³	C₂³×D₄	semidirect
308. C₂³×C₃	C₂×D₃²	semidirect
309. C₂³×C₃	C₂×D₃²	semidirect
356. C₂×C₃²	C₂×D₃×D₄	semidirect
357. C₂×C₃²	C₂²×#67	semidirect
362. C₃⋊D₃	C₂²×#67	semidirect
377. C₂⁴	#1113	semidirect
404. C₂²×C₃	D₃×#67	semidirect
405. C₂²×C₃	#3811	semidirect
408. C₂²×C₃	C₂²×D₃²	semidirect
409. C₂²×C₃	C₂²×D₃²	semidirect
435. C₃²	C₂²×D₃×D₄	semidirect
436. C₃²	C₂³×#67	semidirect
449. C₂³	C₂×#1113	semidirect
468. C₂×C₃	C₂×D₃×#67	semidirect
469. C₂×C₃	C₂×#3811	semidirect
488. C₂²	#89049	direct (N × H)
490. C₂²	C₂²×#1113	semidirect
495. C₃	C₂²×D₃×#67	semidirect
496. C₃	C₂²×#3811	semidirect
501. C₂	C₂×#89049	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₃⋊D₃	2
C₂³×#1113	2
C₂²×C₃×#638	2
C₂×#89049	2
C₂²×#6295	2
C₂²×#6294	2
C₂²×#3811	3
C₂²×D₃×#67	3

Subgroups — C22×#89049 #13181694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#89049 #13181694