Subgroups — C₂²×#88668 #13164809

Order 1728.

4834 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₃×D₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×#611	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88668	C₂	1	24	yes	maximal, direct product factor
6	C₂²×#6195	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6192	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×(C₃⋊D₉)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#3811	—	3	1	no	maximal
10	C₂²×D₄×D₉	—	3	1	no	maximal
11	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic, complemented
12	C₂³×C₃⋊D₉	—	2	8	no	—
13	C₂³×C₃⋊D₉	C₂²	1	1	yes	characteristic
14	C₂³×C₃⋊D₉	C₂²	1	12	yes	complemented
15	C₂³×C₃⋊D₉	C₂²	1	1	yes	characteristic, complemented
16	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₃×D₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃×D₉	—	2	8	no	—
19	C₂²×D₃×D₉	C₂²	1	12	yes	complemented
20	C₂×C₉×#67	C₂²	1	12	yes	complemented
21	C₂×C₃×#611	C₂²	1	12	yes	complemented
22	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₃×Dic₉	C₂²	1	1	yes	characteristic, complemented
24	#88668	C₂²	1	64	yes	direct product factor
25	C₂×#6195	C₂²	1	12	yes	complemented
26	C₂×#6192	C₂²	1	12	yes	complemented
27	C₂×(C₃⋊D₉)⋊C₄	C₂²	1	12	yes	complemented
28	C₂⁴×C₃⋊D₃	—	3	1	no	—
29	C₂³×D₃²	—	3	1	no	—
30	C₂²×C₃×#67	—	3	1	no	—
31	C₂²×C₃×#67	D₃	1	1	yes	characteristic
32	C₂×#3811	—	3	24	no	—
33	C₂²×#626	—	3	1	no	—
34	C₂²×#626	—	3	1	no	—
35	C₂²×#624	—	3	1	no	—
36	C₂⁴×D₉	—	3	1	no	—
37	C₂⁴×D₉	—	3	1	no	—
38	C₂⁴×D₉	—	6	1	no	—
39	C₂²×D₄×C₉	—	3	1	no	—
40	C₂²×#611	—	3	1	no	—
41	C₂²×#611	D₃	1	1	yes	characteristic, complemented
42	C₂×D₄×D₉	—	3	24	no	—
43	C₂²×D₃₆	—	3	1	no	—
44	C₂²×C₄×D₉	—	3	1	no	—
45	C₂³×C₃×C₉	—	2	4	no	—
46	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
47	C₂³×C₃×C₉	C₂³	1	6	yes	complemented
48	C₂²×C₃⋊D₉	—	2	4	no	—
49	C₂²×C₃⋊D₉	—	2	48	no	—
50	C₂²×C₃⋊D₉	D₄	1	8	yes	complemented
51	C₂²×C₃⋊D₉	C₂³	1	6	yes	—
52	C₂²×C₃⋊D₉	C₂³	1	16	yes	complemented
53	C₂²×C₃⋊D₉	C₂³	1	6	yes	complemented
54	C₂²×D₃×C₉	—	2	4	no	—
55	C₂²×D₃×C₉	C₂³	1	6	yes	complemented
56	C₂²×C₃×D₉	—	2	4	no	—
57	C₂²×C₃×D₉	C₂³	1	6	yes	complemented
58	C₂×D₃×D₉	—	2	48	no	—
59	C₂×D₃×D₉	C₂³	1	16	yes	complemented
60	C₉×#67	C₂³	1	16	yes	complemented
61	C₃×#611	C₂³	1	16	yes	complemented
62	C₂×C₉×Dic₃	C₂³	1	6	yes	complemented
63	C₂×C₃×Dic₉	C₂³	1	6	yes	complemented
64	#6195	C₂³	1	16	yes	complemented
65	#6192	C₂³	1	16	yes	complemented
66	(C₃⋊D₉)⋊C₄	C₂³	1	16	yes	complemented
67	C₂²×D₃×D₄	—	9	1	no	—
68	C₂²×D₃×D₄	—	9	1	no	—
69	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
70	C₂³×C₃⋊D₃	—	3	1	no	—
71	C₂³×C₃⋊D₃	—	3	1	no	—
72	C₂³×C₃⋊D₃	—	3	12	no	—
73	C₂³×C₃⋊D₃	—	6	8	no	—
74	C₂³×C₃×D₃	—	3	1	no	—
75	C₂³×C₃×D₃	C₂×D₃	1	1	yes	characteristic
76	C₂²×D₃²	—	3	12	no	—
77	C₂²×D₃²	—	6	8	no	—
78	C₂×C₃×#67	—	3	12	no	—
79	C₂×C₃×#67	C₂×D₃	1	12	yes	—
80	C₂²×C₃×Dic₃	—	3	1	no	—
81	C₂²×C₃×Dic₃	C₂×D₃	1	1	yes	characteristic
82	#3811	—	3	64	no	—
83	C₂×#626	—	3	12	no	—
84	C₂×#626	—	3	12	no	—
85	C₂×#624	—	3	12	no	—
86	C₂⁴×C₉	—	2	1	no	—
87	C₂⁴×C₉	—	3	1	no	—
88	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic, complemented
89	C₂³×D₉	—	3	1	no	—
90	C₂³×D₉	—	3	1	no	—
91	C₂³×D₉	—	3	12	no	—
92	C₂³×D₉	—	3	12	no	—
93	C₂³×D₉	—	6	8	no	—
94	C₂³×D₉	—	6	8	no	—
95	C₂³×D₉	—	6	1	no	—
96	C₂³×D₉	—	6	12	no	—
97	C₂³×D₉	—	6	1	no	—
98	C₂³×D₉	—	6	16	no	—
99	C₂³×D₉	C₂×D₃	1	1	yes	characteristic, complemented
100	C₂×D₄×C₉	—	3	12	no	—
101	C₂²×C₄×C₉	—	3	1	no	—
102	C₂×#611	—	3	12	no	—
103	C₂×#611	C₂×D₃	1	12	yes	complemented
104	C₂²×Dic₉	C₂×D₃	1	1	yes	characteristic, complemented
105	D₄×D₉	—	3	64	no	—
106	C₂×D₃₆	—	3	12	no	—
107	C₂×C₄×D₉	—	3	12	no	—
108	C₂²×C₃×C₉	—	2	12	no	—
109	C₂²×C₃×C₉	C₂×D₄	1	4	yes	complemented
110	C₂²×C₃×C₉	C₂⁴	1	3	yes	—
111	C₂²×C₃×C₉	C₂⁴	1	4	yes	complemented
112	C₂×C₃⋊D₉	—	2	12	no	—
113	C₂×C₃⋊D₉	—	2	32	no	—
114	C₂×C₃⋊D₉	C₂×D₄	1	24	yes	complemented
115	C₂×C₃⋊D₉	C₂⁴	1	4	yes	—
116	C₂×C₃⋊D₉	C₂⁴	1	4	yes	complemented
117	C₂×D₃×C₉	—	2	12	no	—
118	C₂×D₃×C₉	C₂⁴	1	4	yes	complemented
119	C₂×C₃×D₉	—	2	12	no	—
120	C₂×C₃×D₉	C₂⁴	1	4	yes	complemented
121	D₃×D₉	—	2	32	no	—
122	C₉×Dic₃	C₂⁴	1	4	yes	complemented
123	C₃×Dic₉	C₂⁴	1	4	yes	complemented
124	C₂⁴×D₃	—	9	1	no	—
125	C₂⁴×D₃	—	9	1	no	—
126	C₂⁴×D₃	—	9	1	no	—
127	C₂⁴×D₃	—	9	1	no	—
128	C₂⁴×D₃	—	18	1	no	—
129	C₂²×C₃×D₄	—	3	1	no	—
130	C₂²×C₃×D₄	—	9	1	no	—
131	C₂²×#67	—	3	1	no	—
132	C₂²×#67	—	9	1	no	—
133	C₂²×#67	—	9	1	no	—
134	C₂²×#67	D₉	1	1	yes	characteristic, complemented
135	C₂×D₃×D₄	—	9	24	no	—
136	C₂×D₃×D₄	—	9	24	no	—
137	C₂²×D₁₂	—	9	1	no	—
138	C₂²×D₁₂	—	9	1	no	—
139	C₂²×C₄×D₃	—	9	1	no	—
140	C₂²×C₄×D₃	—	9	1	no	—
141	C₂³×C₃²	—	2	4	no	—
142	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
143	C₂³×C₃²	C₂²×D₃	1	6	yes	—
144	C₂²×C₃⋊D₃	—	3	8	no	—
145	C₂²×C₃⋊D₃	—	3	6	no	—
146	C₂²×C₃⋊D₃	—	3	6	no	—
147	C₂²×C₃⋊D₃	—	3	16	no	—
148	C₂²×C₃⋊D₃	—	6	48	no	—
149	C₂²×C₃⋊D₃	—	6	4	no	—
150	C₂²×C₃×D₃	—	2	4	no	—
151	C₂²×C₃×D₃	—	3	6	no	—
152	C₂²×C₃×D₃	—	6	4	no	—
153	C₂²×C₃×D₃	C₂²×D₃	1	6	yes	—
154	C₂×D₃²	—	3	16	no	—
155	C₂×D₃²	—	6	48	no	—
156	C₃×#67	—	3	16	no	—
157	C₃×#67	C₂²×D₃	1	16	yes	—
158	C₂×C₃×Dic₃	—	3	6	no	—
159	C₂×C₃×Dic₃	C₂²×D₃	1	6	yes	—
160	#626	—	3	16	no	—
161	#626	—	3	16	no	—
162	#624	—	3	16	no	—
163	C₂³×C₉	—	2	8	no	—
164	C₂³×C₉	—	2	4	no	—
165	C₂³×C₉	—	2	1	no	—
166	C₂³×C₉	—	2	6	no	—
167	C₂³×C₉	—	3	6	no	—
168	C₂³×C₉	—	6	4	no	—
169	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
170	C₂³×C₉	C₂²×D₃	1	6	yes	complemented
171	C₂²×D₉	—	2	4	no	—
172	C₂²×D₉	—	3	8	no	—
173	C₂²×D₉	—	3	6	no	—
174	C₂²×D₉	—	3	6	no	—
175	C₂²×D₉	—	3	16	no	—
176	C₂²×D₉	—	3	16	no	—
177	C₂²×D₉	—	6	8	no	—
178	C₂²×D₉	—	6	6	no	—
179	C₂²×D₉	—	6	6	no	—
180	C₂²×D₉	—	6	16	no	—
181	C₂²×D₉	—	6	48	no	—
182	C₂²×D₉	—	6	48	no	—
183	C₂²×D₉	—	6	96	no	—
184	C₂²×D₉	—	6	8	no	—
185	C₂²×D₉	—	6	4	no	—
186	C₂²×D₉	C₂²×D₃	1	6	yes	complemented
187	D₄×C₉	—	3	16	no	—
188	C₂×C₄×C₉	—	3	6	no	—
189	#611	—	3	16	no	—
190	#611	C₂²×D₃	1	16	yes	complemented
191	C₂×Dic₉	C₂²×D₃	1	6	yes	complemented
192	D₃₆	—	3	16	no	—
193	C₄×D₉	—	3	16	no	—
194	C₂³×D₄	—	27	1	no	Sylow
195	C₂×C₃×C₉	—	2	4	no	—
196	C₂×C₃×C₉	C₂²×D₄	1	6	yes	complemented
197	C₂×C₃×C₉	C₂⁵	1	1	yes	characteristic
198	C₃⋊D₉	—	2	4	no	—
199	C₃⋊D₉	C₂²×D₄	1	8	yes	complemented
200	D₃×C₉	—	2	4	no	—
201	C₃×D₉	—	2	4	no	—
202	C₂⁴×C₃	—	2	1	no	—
203	C₂⁴×C₃	—	3	1	no	—
204	C₂⁴×C₃	—	9	1	no	—
205	C₂⁴×C₃	C₂×D₉	1	1	yes	characteristic, complemented
206	C₂⁴×C₃	D₃²	1	1	yes	characteristic
207	C₂³×D₃	—	3	1	no	—
208	C₂³×D₃	—	9	12	no	—
209	C₂³×D₃	—	9	1	no	—
210	C₂³×D₃	—	9	1	no	—
211	C₂³×D₃	—	9	1	no	—
212	C₂³×D₃	—	9	12	no	—
213	C₂³×D₃	—	9	1	no	—
214	C₂³×D₃	—	9	12	no	—
215	C₂³×D₃	—	9	12	no	—
216	C₂³×D₃	—	18	1	no	—
217	C₂³×D₃	—	18	1	no	—
218	C₂³×D₃	—	18	12	no	—
219	C₂³×D₃	—	18	8	no	—
220	C₂³×D₃	—	18	8	no	—
221	C₂³×D₃	—	18	8	no	—
222	C₂³×D₃	—	18	8	no	—
223	C₂³×D₃	—	18	16	no	—
224	C₂³×D₃	C₂×D₉	1	1	yes	characteristic, complemented
225	C₂×C₃×D₄	—	3	12	no	—
226	C₂×C₃×D₄	—	9	12	no	—
227	C₂²×C₃×C₄	—	3	1	no	—
228	C₂²×C₃×C₄	—	9	1	no	—
229	C₂×#67	—	3	12	no	—
230	C₂×#67	—	9	12	no	—
231	C₂×#67	—	9	12	no	—
232	C₂×#67	C₂×D₉	1	12	yes	complemented
233	C₂²×Dic₃	—	3	1	no	—
234	C₂²×Dic₃	C₂×D₉	1	1	yes	characteristic, complemented
235	D₃×D₄	—	9	64	no	—
236	D₃×D₄	—	9	64	no	—
237	C₂×D₁₂	—	9	12	no	—
238	C₂×D₁₂	—	9	12	no	—
239	C₂×C₄×D₃	—	9	12	no	—
240	C₂×C₄×D₃	—	9	12	no	—
241	C₂²×C₃²	—	2	12	no	—
242	C₂²×C₃²	D₃×D₄	1	4	yes	—
243	C₂²×C₃²	C₂³×D₃	1	3	yes	—
244	C₂²×C₃²	C₂³×D₃	1	4	yes	—
245	C₂×C₃⋊D₃	—	3	24	no	—
246	C₂×C₃⋊D₃	—	3	4	no	—
247	C₂×C₃⋊D₃	—	3	4	no	—
248	C₂×C₃⋊D₃	—	6	32	no	—
249	C₂×C₃⋊D₃	—	6	12	no	—
250	C₂×C₃×D₃	—	2	12	no	—
251	C₂×C₃×D₃	—	3	4	no	—
252	C₂×C₃×D₃	—	6	12	no	—
253	C₂×C₃×D₃	C₂³×D₃	1	4	yes	—
254	D₃²	—	6	32	no	—
255	C₃×Dic₃	—	3	4	no	—
256	C₃×Dic₃	C₂³×D₃	1	4	yes	—
257	C₂²×C₉	—	2	24	no	—
258	C₂²×C₉	—	2	12	no	—
259	C₂²×C₉	—	2	3	no	—
260	C₂²×C₉	—	2	4	no	—
261	C₂²×C₉	—	2	4	no	—
262	C₂²×C₉	—	3	4	no	—
263	C₂²×C₉	—	6	12	no	—
264	C₂²×C₉	D₃×D₄	1	4	yes	complemented
265	C₂²×C₉	C₂³×D₃	1	3	yes	—
266	C₂²×C₉	C₂³×D₃	1	4	yes	complemented
267	C₂×D₉	—	2	12	no	—
268	C₂×D₉	—	3	24	no	—
269	C₂×D₉	—	3	4	no	—
270	C₂×D₉	—	3	4	no	—
271	C₂×D₉	—	6	24	no	—
272	C₂×D₉	—	6	4	no	—
273	C₂×D₉	—	6	4	no	—
274	C₂×D₉	—	6	32	no	—
275	C₂×D₉	—	6	32	no	—
276	C₂×D₉	—	6	64	no	—
277	C₂×D₉	—	6	24	no	—
278	C₂×D₉	—	6	12	no	—
279	C₂×D₉	C₂³×D₃	1	4	yes	complemented
280	C₄×C₉	—	3	4	no	—
281	Dic₉	C₂³×D₃	1	4	yes	complemented
282	C₂⁵	—	27	1	no	—
283	C₂⁵	—	27	1	no	—
284	C₂²×D₄	—	3	1	no	—
285	C₂²×D₄	—	9	1	no	—
286	C₂²×D₄	—	27	1	no	—
287	C₂²×D₄	—	27	1	no	—
288	C₂²×D₄	—	27	24	no	—
289	C₂³×C₄	—	27	1	no	—
290	C₃×C₉	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
291	C₂³×C₃	—	2	8	no	—
292	C₂³×C₃	—	2	4	no	—
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	2	1	no	—
295	C₂³×C₃	—	2	6	no	—
296	C₂³×C₃	—	3	6	no	—
297	C₂³×C₃	—	6	4	no	—
298	C₂³×C₃	—	9	6	no	—
299	C₂³×C₃	—	18	4	no	—
300	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
301	C₂³×C₃	C₂²×D₉	1	6	yes	complemented
302	C₂³×C₃	C₂×D₃²	1	1	yes	characteristic
303	C₂³×C₃	C₂×D₃²	1	6	yes	—
304	C₂²×D₃	—	2	4	no	—
305	C₂²×D₃	—	3	6	no	—
306	C₂²×D₃	—	6	4	no	—
307	C₂²×D₃	—	9	16	no	—
308	C₂²×D₃	—	9	6	no	—
309	C₂²×D₃	—	9	8	no	—
310	C₂²×D₃	—	9	6	no	—
311	C₂²×D₃	—	9	8	no	—
312	C₂²×D₃	—	9	6	no	—
313	C₂²×D₃	—	9	16	no	—
314	C₂²×D₃	—	9	6	no	—
315	C₂²×D₃	—	9	16	no	—
316	C₂²×D₃	—	9	16	no	—
317	C₂²×D₃	—	18	6	no	—
318	C₂²×D₃	—	18	8	no	—
319	C₂²×D₃	—	18	6	no	—
320	C₂²×D₃	—	18	16	no	—
321	C₂²×D₃	—	18	48	no	—
322	C₂²×D₃	—	18	48	no	—
323	C₂²×D₃	—	18	48	no	—
324	C₂²×D₃	—	18	48	no	—
325	C₂²×D₃	—	18	96	no	—
326	C₂²×D₃	—	18	8	no	—
327	C₂²×D₃	—	18	4	no	—
328	C₂²×D₃	—	18	4	no	—
329	C₂²×D₃	C₂²×D₉	1	6	yes	complemented
330	C₃×D₄	—	3	16	no	—
331	C₃×D₄	—	9	16	no	—
332	C₂×C₃×C₄	—	3	6	no	—
333	C₂×C₃×C₄	—	9	6	no	—
334	#67	—	3	16	no	—
335	#67	—	9	16	no	—
336	#67	—	9	16	no	—
337	#67	C₂²×D₉	1	16	yes	complemented
338	C₂×Dic₃	—	3	6	no	—
339	C₂×Dic₃	C₂²×D₉	1	6	yes	complemented
340	D₁₂	—	9	16	no	—
341	D₁₂	—	9	16	no	—
342	C₄×D₃	—	9	16	no	—
343	C₄×D₃	—	9	16	no	—
344	C₂×C₃²	—	2	4	no	—
345	C₂×C₃²	C₂×D₃×D₄	1	6	yes	—
346	C₂×C₃²	C₂⁴×D₃	1	1	yes	characteristic
347	C₃⋊D₃	—	3	8	no	—
348	C₃⋊D₃	—	6	4	no	—
349	C₃×D₃	—	2	4	no	—
350	C₃×D₃	—	6	4	no	—
351	C₂×C₉	—	2	8	no	—
352	C₂×C₉	—	2	4	no	—
353	C₂×C₉	—	2	6	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	6	4	no	—
356	C₂×C₉	C₂×D₃×D₄	1	6	yes	complemented
357	C₂×C₉	C₂⁴×D₃	1	1	yes	characteristic
358	D₉	—	2	4	no	—
359	D₉	—	3	8	no	—
360	D₉	—	6	8	no	—
361	D₉	—	6	8	no	—
362	D₉	—	6	4	no	—
363	C₂⁴	—	3	1	no	—
364	C₂⁴	—	9	1	no	—
365	C₂⁴	—	27	12	no	—
366	C₂⁴	—	27	1	no	—
367	C₂⁴	—	27	1	no	—
368	C₂⁴	—	27	12	no	—
369	C₂⁴	—	54	8	no	—
370	C₂⁴	—	54	8	no	—
371	C₂⁴	D₃×D₉	1	1	yes	characteristic, complemented
372	C₂×D₄	—	3	12	no	—
373	C₂×D₄	—	9	12	no	—
374	C₂×D₄	—	27	12	no	—
375	C₂×D₄	—	27	12	no	—
376	C₂×D₄	—	27	64	no	—
377	C₂²×C₄	—	3	1	no	—
378	C₂²×C₄	—	9	1	no	—
379	C₂²×C₄	—	27	12	no	—
380	C₂²×C₃	—	2	24	no	—
381	C₂²×C₃	—	2	12	no	—
382	C₂²×C₃	—	2	12	no	—
383	C₂²×C₃	—	2	3	no	—
384	C₂²×C₃	—	2	4	no	—
385	C₂²×C₃	—	2	4	no	—
386	C₂²×C₃	—	3	4	no	—
387	C₂²×C₃	—	6	12	no	—
388	C₂²×C₃	—	9	4	no	—
389	C₂²×C₃	—	18	12	no	—
390	C₂²×C₃	D₄×D₉	1	4	yes	complemented
391	C₂²×C₃	C₂³×D₉	1	3	yes	—
392	C₂²×C₃	C₂³×D₉	1	4	yes	complemented
393	C₂²×C₃	#3811	1	4	yes	—
394	C₂²×C₃	C₂²×D₃²	1	3	yes	—
395	C₂²×C₃	C₂²×D₃²	1	4	yes	—
396	C₂×D₃	—	2	12	no	—
397	C₂×D₃	—	3	4	no	—
398	C₂×D₃	—	6	12	no	—
399	C₂×D₃	—	9	24	no	—
400	C₂×D₃	—	9	4	no	—
401	C₂×D₃	—	9	4	no	—
402	C₂×D₃	—	9	24	no	—
403	C₂×D₃	—	9	4	no	—
404	C₂×D₃	—	9	4	no	—
405	C₂×D₃	—	18	4	no	—
406	C₂×D₃	—	18	24	no	—
407	C₂×D₃	—	18	4	no	—
408	C₂×D₃	—	18	32	no	—
409	C₂×D₃	—	18	32	no	—
410	C₂×D₃	—	18	32	no	—
411	C₂×D₃	—	18	32	no	—
412	C₂×D₃	—	18	64	no	—
413	C₂×D₃	—	18	24	no	—
414	C₂×D₃	—	18	12	no	—
415	C₂×D₃	—	18	12	no	—
416	C₂×D₃	C₂³×D₉	1	4	yes	complemented
417	C₃×C₄	—	3	4	no	—
418	C₃×C₄	—	9	4	no	—
419	Dic₃	—	3	4	no	—
420	Dic₃	C₂³×D₉	1	4	yes	complemented
421	C₃²	C₂²×D₃×D₄	1	1	yes	characteristic
422	C₉	—	2	1	no	—
423	C₉	C₂²×D₃×D₄	1	1	yes	characteristic, complemented
424	C₂³	—	2	4	no	—
425	C₂³	—	3	6	no	—
426	C₂³	—	6	4	no	—
427	C₂³	—	9	6	no	—
428	C₂³	—	18	4	no	—
429	C₂³	—	27	16	no	—
430	C₂³	—	27	6	no	—
431	C₂³	—	27	8	no	—
432	C₂³	—	27	6	no	—
433	C₂³	—	27	16	no	—
434	C₂³	—	54	48	no	—
435	C₂³	—	54	48	no	—
436	C₂³	—	54	4	no	—
437	C₂³	C₂×D₃×D₉	1	1	yes	characteristic
438	C₂³	C₂×D₃×D₉	1	6	yes	complemented
439	D₄	—	3	16	no	—
440	D₄	—	9	16	no	—
441	D₄	—	27	16	no	—
442	D₄	—	27	16	no	—
443	C₂×C₄	—	3	6	no	—
444	C₂×C₄	—	9	6	no	—
445	C₂×C₄	—	27	16	no	—
446	C₂×C₃	—	2	8	no	—
447	C₂×C₃	—	2	4	no	—
448	C₂×C₃	—	2	4	no	—
449	C₂×C₃	—	2	1	no	—
450	C₂×C₃	—	2	6	no	—
451	C₂×C₃	—	6	4	no	—
452	C₂×C₃	—	18	4	no	—
453	C₂×C₃	C₂×D₄×D₉	1	6	yes	complemented
454	C₂×C₃	C₂⁴×D₉	1	1	yes	characteristic
455	C₂×C₃	C₂×#3811	1	6	yes	—
456	C₂×C₃	C₂³×D₃²	1	1	yes	characteristic
457	D₃	—	2	4	no	—
458	D₃	—	6	4	no	—
459	D₃	—	9	8	no	—
460	D₃	—	9	8	no	—
461	D₃	—	18	8	no	—
462	D₃	—	18	8	no	—
463	D₃	—	18	4	no	—
464	D₃	—	18	4	no	—
465	C₂²	—	2	12	no	—
466	C₂²	—	3	4	no	—
467	C₂²	—	6	12	no	—
468	C₂²	—	9	4	no	—
469	C₂²	—	18	12	no	—
470	C₂²	—	27	4	no	—
471	C₂²	—	27	24	no	—
472	C₂²	—	27	4	no	—
473	C₂²	—	54	32	no	—
474	C₂²	—	54	32	no	—
475	C₂²	—	54	12	no	—
476	C₂²	#88668	1	4	yes	direct product factor
477	C₂²	C₂²×D₃×D₉	1	3	yes	—
478	C₂²	C₂²×D₃×D₉	1	4	yes	complemented
479	C₄	—	3	4	no	—
480	C₄	—	9	4	no	—
481	C₃	—	2	1	no	—
482	C₃	C₂²×D₄×D₉	1	1	yes	characteristic, complemented
483	C₃	C₂²×#3811	1	1	yes	characteristic
484	C₂	—	2	4	no	—
485	C₂	—	6	4	no	—
486	C₂	—	18	4	no	—
487	C₂	—	27	8	no	—
488	C₂	—	54	4	no	—
489	C₂	C₂×#88668	1	6	yes	direct product factor
490	C₂	C₂³×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃×D₉
commutator, cosocle	C₂×C₃×C₉	C₂⁵
Frattini	C₂×C₃	C₂³×D₃²
Fitting	C₂⁴×C₃×C₉	C₂²
socle	C₂³×C₃²	C₂²×D₃
hypercenter	C₂⁴	D₃×D₉
hypocenter	C₃×C₉	C₂³×D₄
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃⋊D₉	C₂	semidirect
2. C₂³×D₃×D₉	C₂	semidirect
3. C₂²×C₉×#67	C₂	semidirect
4. C₂²×C₃×#611	C₂	semidirect
5. C₂×#88668	C₂	direct (N × H)
6. C₂²×#6195	C₂	semidirect
7. C₂²×#6192	C₂	semidirect
8. C₂²×(C₃⋊D₉)⋊C₄	C₂	semidirect
11. C₂⁴×C₃×C₉	C₂²	semidirect
14. C₂³×C₃⋊D₉	C₂²	semidirect
15. C₂³×C₃⋊D₉	C₂²	semidirect
16. C₂³×D₃×C₉	C₂²	semidirect
17. C₂³×C₃×D₉	C₂²	semidirect
19. C₂²×D₃×D₉	C₂²	semidirect
20. C₂×C₉×#67	C₂²	semidirect
21. C₂×C₃×#611	C₂²	semidirect
22. C₂²×C₉×Dic₃	C₂²	semidirect
23. C₂²×C₃×Dic₉	C₂²	semidirect
24. #88668	C₂²	direct (N × H)
25. C₂×#6195	C₂²	semidirect
26. C₂×#6192	C₂²	semidirect
27. C₂×(C₃⋊D₉)⋊C₄	C₂²	semidirect
41. C₂²×#611	D₃	semidirect
47. C₂³×C₃×C₉	C₂³	semidirect
50. C₂²×C₃⋊D₉	D₄	semidirect
52. C₂²×C₃⋊D₉	C₂³	semidirect
53. C₂²×C₃⋊D₉	C₂³	semidirect
55. C₂²×D₃×C₉	C₂³	semidirect
57. C₂²×C₃×D₉	C₂³	semidirect
59. C₂×D₃×D₉	C₂³	semidirect
60. C₉×#67	C₂³	semidirect
61. C₃×#611	C₂³	semidirect
62. C₂×C₉×Dic₃	C₂³	semidirect
63. C₂×C₃×Dic₉	C₂³	semidirect
64. #6195	C₂³	semidirect
65. #6192	C₂³	semidirect
66. (C₃⋊D₉)⋊C₄	C₂³	semidirect
88. C₂⁴×C₉	C₂×D₃	semidirect
99. C₂³×D₉	C₂×D₃	semidirect
103. C₂×#611	C₂×D₃	semidirect
104. C₂²×Dic₉	C₂×D₃	semidirect
109. C₂²×C₃×C₉	C₂×D₄	semidirect
111. C₂²×C₃×C₉	C₂⁴	semidirect
114. C₂×C₃⋊D₉	C₂×D₄	semidirect
116. C₂×C₃⋊D₉	C₂⁴	semidirect
118. C₂×D₃×C₉	C₂⁴	semidirect
120. C₂×C₃×D₉	C₂⁴	semidirect
122. C₉×Dic₃	C₂⁴	semidirect
123. C₃×Dic₉	C₂⁴	semidirect
134. C₂²×#67	D₉	semidirect
170. C₂³×C₉	C₂²×D₃	semidirect
186. C₂²×D₉	C₂²×D₃	semidirect
190. #611	C₂²×D₃	semidirect
191. C₂×Dic₉	C₂²×D₃	semidirect
196. C₂×C₃×C₉	C₂²×D₄	semidirect
199. C₃⋊D₉	C₂²×D₄	semidirect
205. C₂⁴×C₃	C₂×D₉	semidirect
224. C₂³×D₃	C₂×D₉	semidirect
232. C₂×#67	C₂×D₉	semidirect
234. C₂²×Dic₃	C₂×D₉	semidirect
264. C₂²×C₉	D₃×D₄	semidirect
266. C₂²×C₉	C₂³×D₃	semidirect
279. C₂×D₉	C₂³×D₃	semidirect
281. Dic₉	C₂³×D₃	semidirect
290. C₃×C₉	C₂³×D₄	semidirect
301. C₂³×C₃	C₂²×D₉	semidirect
329. C₂²×D₃	C₂²×D₉	semidirect
337. #67	C₂²×D₉	semidirect
339. C₂×Dic₃	C₂²×D₉	semidirect
356. C₂×C₉	C₂×D₃×D₄	semidirect
371. C₂⁴	D₃×D₉	semidirect
390. C₂²×C₃	D₄×D₉	semidirect
392. C₂²×C₃	C₂³×D₉	semidirect
416. C₂×D₃	C₂³×D₉	semidirect
420. Dic₃	C₂³×D₉	semidirect
423. C₉	C₂²×D₃×D₄	semidirect
438. C₂³	C₂×D₃×D₉	semidirect
453. C₂×C₃	C₂×D₄×D₉	semidirect
476. C₂²	#88668	direct (N × H)
478. C₂²	C₂²×D₃×D₉	semidirect
482. C₃	C₂²×D₄×D₉	semidirect
489. C₂	C₂×#88668	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⋊D₉	2
C₂³×D₃×D₉	2
C₂²×C₉×#67	2
C₂²×C₃×#611	2
C₂×#88668	2
C₂²×#6195	2
C₂²×#6192	2
C₂²×(C₃⋊D₉)⋊C₄	2
C₂²×#3811	3
C₂²×D₄×D₉	3

Subgroups — C22×#88668 #13164809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#88668 #13164809