Subgroups — #13150110

Order 1728.

950 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88736	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3667	C₂	1	1	yes	maximal, characteristic, complemented
4	#11720895	C₂	1	2	yes	maximal, complemented
5	#11720891	C₂	1	2	yes	maximal, complemented
6	#11720890	C₂	1	2	yes	maximal, complemented
7	#11720889	C₂	1	4	yes	maximal, complemented
8	#11720885	C₂	1	2	yes	maximal, complemented
9	#10594795	—	3	1	no	maximal
10	#10589925	—	3	1	no	maximal
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×#6233	—	2	1	no	—
13	#88736	—	2	1	no	—
14	#88736	—	2	1	no	—
15	#88736	C₂²	1	2	yes	—
16	#88736	C₂²	1	2	yes	complemented
17	C₂×C₄⋊(C₃⋊D₉)	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₄×C₃⋊D₉	—	2	1	no	—
19	C₂×#6226	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₉×#67	—	2	1	no	—
21	C₉×#235	—	2	1	no	—
22	C₉×#235	—	2	1	no	—
23	C₉×#235	C₂²	1	2	yes	—
24	C₉×#235	C₂²	1	2	yes	complemented
25	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₃×C₉	—	2	1	no	—
27	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×#3667	C₂²	1	2	yes	complemented
29	C₃×#3667	C₂²	1	2	yes	complemented
30	C₂×C₃×C₉⋊C₈	C₂²	1	2	yes	complemented
31	#88428	C₂²	1	4	yes	complemented
32	#88426	C₂²	1	4	yes	complemented
33	#88424	C₂²	1	4	yes	complemented
34	#88422	C₂²	1	4	yes	complemented
35	C₂×#3828	—	3	1	no	—
36	C₂×C₃×#235	D₃	1	1	yes	characteristic
37	C₂×C₃×#208	—	3	1	no	—
38	#63833	—	3	2	no	—
39	#63831	—	3	2	no	—
40	#63830	—	3	2	no	—
41	#63829	—	3	4	no	—
42	#63825	—	3	2	no	—
43	C₂×C₉×#41	—	3	1	no	—
44	C₂×#3697	—	3	1	no	—
45	C₂×#3697	—	6	1	no	—
46	#63513	—	3	4	no	—
47	#63512	—	3	2	no	—
48	#63511	—	3	2	no	—
49	#63505	—	3	2	no	—
50	#63495	—	3	2	no	—
51	C₂×#3667	D₃	1	1	yes	characteristic, complemented
52	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
53	C₂²×C₃⋊D₉	—	2	1	no	—
54	C₂²×D₃×C₉	—	2	1	no	—
55	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
56	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
57	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
58	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
61	#6233	—	2	2	no	—
62	#6233	—	2	2	no	—
63	C₂×C₃⋊Dic₉	—	2	1	no	—
64	C₄⋊(C₃⋊D₉)	—	2	1	no	—
65	C₄⋊(C₃⋊D₉)	C₂³	1	2	yes	—
66	C₄×C₃⋊D₉	—	2	2	no	—
67	C₄×C₃⋊D₉	—	2	2	no	—
68	#6226	—	2	1	no	—
69	#6226	C₂³	1	2	yes	—
70	C₉×#67	—	2	2	no	—
71	C₉×#67	—	2	2	no	—
72	C₂×C₉×Dic₃	—	2	1	no	—
73	C₉×D₁₂	—	2	1	no	—
74	C₉×D₁₂	C₂³	1	2	yes	—
75	C₄×D₃×C₉	—	2	2	no	—
76	C₄×D₃×C₉	—	2	2	no	—
77	C₉×Dic₆	—	2	1	no	—
78	C₉×Dic₆	C₂³	1	2	yes	—
79	C₃×C₉⋊C₈	C₂³	1	4	yes	—
80	#5822	—	9	1	no	—
81	#5748	—	9	1	no	—
82	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
83	C₂×#638	—	6	1	no	—
84	#3828	—	3	2	no	—
85	#3828	—	3	2	no	—
86	#3828	—	6	1	no	—
87	#3828	—	6	1	no	—
88	C₂×C₄⋊(C₃⋊D₃)	—	3	1	no	—
89	C₂×C₄×C₃⋊D₃	—	6	1	no	—
90	C₂×#634	—	3	1	no	—
91	C₂×C₃×#67	—	2	1	no	—
92	C₃×#235	—	2	1	no	—
93	C₃×#235	—	2	1	no	—
94	C₃×#235	C₂×D₃	1	2	yes	—
95	C₃×#235	C₂×D₃	1	2	yes	—
96	C₂×C₃×D₁₂	C₂×D₃	1	1	yes	characteristic
97	C₂×C₃×C₄×D₃	—	2	1	no	—
98	C₂×C₃×Dic₆	C₂×D₃	1	1	yes	characteristic
99	C₃×#208	—	3	2	no	—
100	C₃×#208	—	3	2	no	—
101	C₂×C₃×C₃⋊C₈	—	3	2	no	—
102	#3719	—	3	4	no	—
103	#3717	—	3	4	no	—
104	#3716	—	3	4	no	—
105	#3714	—	3	4	no	—
106	C₉×#41	—	3	2	no	—
107	C₉×#41	—	3	2	no	—
108	C₉×#41	—	6	1	no	—
109	C₉×#41	—	6	1	no	—
110	C₂×Q₈×C₉	—	3	1	no	—
111	C₂×D₄×C₉	—	3	1	no	—
112	C₂×D₄×C₉	—	6	1	no	—
113	C₂²×C₄×C₉	—	2	1	no	—
114	C₂²×C₄×C₉	—	6	1	no	—
115	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
116	C₂×#611	—	6	2	no	—
117	C₂×#611	—	6	1	no	—
118	#3697	—	3	2	no	—
119	#3697	—	3	2	no	—
120	#3697	—	6	2	no	—
121	#3697	—	6	2	no	—
122	#3697	—	6	2	no	—
123	#3697	—	6	2	no	—
124	#3697	—	6	1	no	—
125	#3697	—	6	1	no	—
126	C₂×D₃₆	—	3	1	no	—
127	C₂×D₃₆	—	6	1	no	—
128	C₂×C₄×D₉	—	6	2	no	—
129	C₂×C₄×D₉	—	6	1	no	—
130	C₂×Dic₁₈	—	3	1	no	—
131	C₂×Dic₁₈	—	6	1	no	—
132	#3675	—	3	4	no	—
133	#3674	—	3	4	no	—
134	#3673	—	3	4	no	—
135	#3672	—	3	4	no	—
136	#3667	C₂×D₃	1	2	yes	complemented
137	#3667	C₂×D₃	1	2	yes	complemented
138	C₂×C₉⋊C₈	C₂×D₃	1	2	yes	complemented
139	C₂²×C₃×C₉	—	4	1	no	—
140	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃⋊D₉	—	2	2	no	—
144	C₂×C₃⋊D₉	—	4	2	no	—
145	C₂×D₃×C₉	—	2	2	no	—
146	C₂×D₃×C₉	—	4	2	no	—
147	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
148	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
149	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
150	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
151	C₃⋊Dic₉	—	2	2	no	—
152	C₉×Dic₃	—	2	2	no	—
153	C₂×C₃×#41	—	3	1	no	—
154	C₂×#235	—	9	1	no	—
155	C₂×#235	—	9	1	no	—
156	C₂×#235	—	18	1	no	—
157	C₂×#235	D₉	1	1	yes	characteristic, complemented
158	C₂×C₃×M₁₆	—	9	1	no	—
159	#951	—	9	2	no	—
160	#950	—	9	4	no	—
161	#949	—	9	2	no	—
162	#942	—	9	2	no	—
163	#932	—	9	2	no	—
164	C₂×#208	—	3	1	no	—
165	#909	—	9	2	no	—
166	#909	—	9	2	no	—
167	#908	—	9	2	no	—
168	#908	—	9	2	no	—
169	#904	—	9	4	no	—
170	C₂³×C₃²	#67	1	1	yes	characteristic
171	C₂²×C₃⋊D₃	—	6	1	no	—
172	C₂²×C₃×D₃	—	2	1	no	—
173	C₂×C₃²×C₄	#67	1	1	yes	characteristic
174	C₂×C₃²×C₄	#67	1	1	yes	characteristic
175	C₂×C₃²×C₄	#67	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
179	#638	—	6	2	no	—
180	#638	—	6	2	no	—
181	C₂×C₃⋊Dic₃	—	6	1	no	—
182	C₄⋊(C₃⋊D₃)	—	3	2	no	—
183	C₄⋊(C₃⋊D₃)	—	6	1	no	—
184	C₄×C₃⋊D₃	—	6	2	no	—
185	C₄×C₃⋊D₃	—	6	2	no	—
186	#634	—	3	2	no	—
187	#634	—	6	1	no	—
188	C₃×#67	—	2	2	no	—
189	C₃×#67	—	2	2	no	—
190	C₂×C₃×Dic₃	—	2	1	no	—
191	C₃×D₁₂	—	2	1	no	—
192	C₃×D₁₂	C₂²×D₃	1	2	yes	—
193	C₃×C₄×D₃	—	2	2	no	—
194	C₃×C₄×D₃	—	2	2	no	—
195	C₃×Dic₆	—	2	1	no	—
196	C₃×Dic₆	C₂²×D₃	1	2	yes	—
197	C₂³×C₉	—	2	1	no	—
198	C₂³×C₉	—	6	1	no	—
199	C₂³×C₉	D₁₂	1	1	yes	characteristic
200	C₂²×D₉	—	6	2	no	—
201	C₂²×D₉	—	6	1	no	—
202	C₃×C₃⋊C₈	—	3	4	no	—
203	Q₈×C₉	—	3	2	no	—
204	Q₈×C₉	—	6	1	no	—
205	D₄×C₉	—	3	2	no	—
206	D₄×C₉	—	6	2	no	—
207	D₄×C₉	—	6	2	no	—
208	D₄×C₉	—	6	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	2	1	no	—
215	C₂×C₄×C₉	—	6	1	no	—
216	C₂×C₄×C₉	—	6	2	no	—
217	C₂×C₄×C₉	—	6	2	no	—
218	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
219	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
220	C₂×C₄×C₉	D₁₂	1	1	yes	characteristic
221	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
222	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
223	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
224	#611	—	6	4	no	—
225	#611	—	6	4	no	—
226	#611	—	6	2	no	—
227	#611	—	6	2	no	—
228	C₂×Dic₉	—	6	2	no	—
229	C₂×Dic₉	—	6	1	no	—
230	D₃₆	—	3	2	no	—
231	D₃₆	—	6	2	no	—
232	D₃₆	—	6	2	no	—
233	D₃₆	—	6	1	no	—
234	C₄×D₉	—	6	4	no	—
235	C₄×D₉	—	6	4	no	—
236	C₄×D₉	—	6	2	no	—
237	C₄×D₉	—	6	2	no	—
238	Dic₁₈	—	3	2	no	—
239	Dic₁₈	—	6	2	no	—
240	Dic₁₈	—	6	2	no	—
241	Dic₁₈	—	6	1	no	—
242	C₉⋊C₈	C₂²×D₃	1	4	yes	—
243	#575	—	27	1	no	Sylow
244	C₂×C₃×C₉	—	2	1	no	—
245	C₂×C₃×C₉	—	2	1	no	—
246	C₂×C₃×C₉	—	2	1	no	—
247	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
248	C₃⋊D₉	—	4	2	no	—
249	D₃×C₉	—	4	2	no	—
250	C₃×#41	—	3	2	no	—
251	C₃×#41	—	3	2	no	—
252	C₃×#41	—	6	1	no	—
253	C₃×#41	—	6	1	no	—
254	C₂×C₃×Q₈	—	3	1	no	—
255	C₂×C₃×D₄	—	3	1	no	—
256	C₂×C₃×D₄	—	6	1	no	—
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	6	1	no	—
259	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
260	C₂²×C₃×C₄	D₃²	1	1	yes	characteristic
261	C₂×#67	—	2	1	no	—
262	C₂×#67	—	18	2	no	—
263	C₂×#67	—	18	1	no	—
264	C₂×#67	—	18	1	no	—
265	#235	—	2	1	no	—
266	#235	—	2	1	no	—
267	#235	—	9	2	no	—
268	#235	—	9	2	no	—
269	#235	—	9	2	no	—
270	#235	—	9	2	no	—
271	#235	—	18	2	no	—
272	#235	—	18	2	no	—
273	#235	—	18	2	no	—
274	#235	—	18	2	no	—
275	#235	—	18	1	no	—
276	#235	—	18	1	no	—
277	#235	—	18	1	no	—
278	#235	—	18	1	no	—
279	#235	C₂×D₉	1	2	yes	—
280	#235	C₂×D₉	1	2	yes	complemented
281	C₂×D₁₂	—	9	1	no	—
282	C₂×D₁₂	—	9	1	no	—
283	C₂×D₁₂	—	18	1	no	—
284	C₂×D₁₂	C₂×D₉	1	1	yes	characteristic, complemented
285	C₂×C₄×D₃	—	2	1	no	—
286	C₂×C₄×D₃	—	18	2	no	—
287	C₂×C₄×D₃	—	18	1	no	—
288	C₂×C₄×D₃	—	18	1	no	—
289	C₂×Dic₆	—	9	1	no	—
290	C₂×Dic₆	—	9	1	no	—
291	C₂×Dic₆	—	18	1	no	—
292	C₂×Dic₆	C₂×D₉	1	1	yes	characteristic, complemented
293	C₃×M₁₆	—	9	2	no	—
294	C₃×M₁₆	—	9	2	no	—
295	C₂×C₃×C₈	—	9	2	no	—
296	#216	—	9	4	no	—
297	#215	—	9	4	no	—
298	#214	—	9	4	no	—
299	#213	—	9	4	no	—
300	#208	—	3	2	no	—
301	#208	—	3	2	no	—
302	C₂×C₃⋊C₈	—	3	2	no	—
303	Dic₁₂	—	9	4	no	—
304	D₂₄	—	9	4	no	—
305	#204	—	9	4	no	—
306	#204	—	9	4	no	—
307	C₂²×C₃²	—	4	1	no	—
308	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
309	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
310	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
311	C₂×C₃⋊D₃	—	6	2	no	—
312	C₂×C₃⋊D₃	—	12	2	no	—
313	C₂×C₃×D₃	—	2	2	no	—
314	C₂×C₃×D₃	—	4	2	no	—
315	C₃²×C₄	C₂×#67	1	1	yes	characteristic
316	C₃²×C₄	C₂×#67	1	1	yes	characteristic
317	C₃²×C₄	C₂×#67	1	1	yes	characteristic
318	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
319	C₃⋊Dic₃	—	6	2	no	—
320	C₃×Dic₃	—	2	2	no	—
321	C₂²×C₉	—	2	1	no	—
322	C₂²×C₉	—	2	1	no	—
323	C₂²×C₉	—	2	1	no	—
324	C₂²×C₉	—	4	1	no	—
325	C₂²×C₉	—	4	2	no	—
326	C₂²×C₉	—	6	2	no	—
327	C₂²×C₉	—	12	2	no	—
328	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
329	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
330	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
331	C₂×D₉	—	6	4	no	—
332	C₂×D₉	—	6	2	no	—
333	C₂×D₉	—	12	4	no	—
334	C₂×D₉	—	12	2	no	—
335	C₄×C₉	—	2	1	no	—
336	C₄×C₉	—	2	1	no	—
337	C₄×C₉	—	2	1	no	—
338	C₄×C₉	—	2	1	no	—
339	C₄×C₉	—	6	2	no	—
340	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
341	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
342	C₄×C₉	C₂×D₁₂	1	1	yes	characteristic
343	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
344	Dic₉	—	6	4	no	—
345	Dic₉	—	6	2	no	—
346	C₂×#41	—	3	1	no	—
347	C₂×#41	—	27	1	no	—
348	#137	—	27	2	no	—
349	#137	—	27	2	no	—
350	AGL(1,ℤ/8)	—	27	2	no	—
351	AGL(1,ℤ/8)	—	27	2	no	—
352	#135	—	27	4	no	—
353	C₂×M₁₆	—	9	1	no	—
354	C₃×C₉	#575	1	1	yes	characteristic, complemented, Sylow
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	—	6	1	no	—
357	C₂³×C₃	#611	1	1	yes	characteristic
358	C₂³×C₃	#626	1	1	yes	characteristic
359	C₂²×D₃	—	2	1	no	—
360	C₂²×D₃	—	18	2	no	—
361	C₂²×D₃	—	18	1	no	—
362	C₂²×D₃	—	18	1	no	—
363	C₃×Q₈	—	3	2	no	—
364	C₃×Q₈	—	6	1	no	—
365	C₃×D₄	—	3	2	no	—
366	C₃×D₄	—	6	2	no	—
367	C₃×D₄	—	6	2	no	—
368	C₃×D₄	—	6	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	6	1	no	—
376	C₂×C₃×C₄	—	6	2	no	—
377	C₂×C₃×C₄	—	6	2	no	—
378	C₂×C₃×C₄	#611	1	1	yes	characteristic
379	C₂×C₃×C₄	#611	1	1	yes	characteristic
380	C₂×C₃×C₄	#611	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
384	C₂×C₃×C₄	#626	1	1	yes	characteristic
385	C₂×C₃×C₄	#626	1	1	yes	characteristic
386	C₂×C₃×C₄	#626	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
390	#67	—	2	2	no	—
391	#67	—	2	2	no	—
392	#67	—	18	4	no	—
393	#67	—	18	4	no	—
394	#67	—	18	2	no	—
395	#67	—	18	2	no	—
396	#67	—	18	2	no	—
397	#67	—	18	2	no	—
398	C₂×Dic₃	—	2	1	no	—
399	C₂×Dic₃	—	18	2	no	—
400	C₂×Dic₃	—	18	1	no	—
401	C₂×Dic₃	—	18	1	no	—
402	D₁₂	—	2	1	no	—
403	D₁₂	—	9	2	no	—
404	D₁₂	—	9	2	no	—
405	D₁₂	—	18	2	no	—
406	D₁₂	—	18	2	no	—
407	D₁₂	—	18	1	no	—
408	D₁₂	—	18	1	no	—
409	D₁₂	C₂²×D₉	1	2	yes	—
410	C₄×D₃	—	2	2	no	—
411	C₄×D₃	—	2	2	no	—
412	C₄×D₃	—	18	4	no	—
413	C₄×D₃	—	18	4	no	—
414	C₄×D₃	—	18	2	no	—
415	C₄×D₃	—	18	2	no	—
416	C₄×D₃	—	18	2	no	—
417	C₄×D₃	—	18	2	no	—
418	Dic₆	—	2	1	no	—
419	Dic₆	—	9	2	no	—
420	Dic₆	—	9	2	no	—
421	Dic₆	—	18	2	no	—
422	Dic₆	—	18	2	no	—
423	Dic₆	—	18	1	no	—
424	Dic₆	—	18	1	no	—
425	Dic₆	C₂²×D₉	1	2	yes	—
426	C₃×C₈	—	9	4	no	—
427	C₃⋊C₈	—	3	4	no	—
428	C₂×C₃²	—	2	1	no	—
429	C₂×C₃²	—	2	1	no	—
430	C₂×C₃²	—	2	1	no	—
431	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
432	C₃⋊D₃	—	12	2	no	—
433	C₃×D₃	—	4	2	no	—
434	C₂×C₉	—	2	2	no	—
435	C₂×C₉	—	2	1	no	—
436	C₂×C₉	—	2	1	no	—
437	C₂×C₉	—	2	1	no	—
438	C₂×C₉	—	2	1	no	—
439	C₂×C₉	—	4	1	no	—
440	C₂×C₉	—	4	1	no	—
441	C₂×C₉	—	12	2	no	—
442	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
443	D₉	—	12	4	no	—
444	D₉	—	12	2	no	—
445	#41	—	3	2	no	—
446	#41	—	3	2	no	—
447	#41	—	6	1	no	—
448	#41	—	6	1	no	—
449	#41	—	27	2	no	—
450	#41	—	27	2	no	—
451	#41	—	54	1	no	—
452	#41	—	54	1	no	—
453	C₂×Q₈	—	3	1	no	—
454	C₂×Q₈	—	27	1	no	—
455	C₂×D₄	—	3	1	no	—
456	C₂×D₄	—	6	1	no	—
457	C₂×D₄	—	27	1	no	—
458	C₂×D₄	—	54	1	no	—
459	C₂²×C₄	—	6	1	no	—
460	C₂²×C₄	—	54	1	no	—
461	C₂²×C₄	D₃×D₉	1	1	yes	characteristic
462	Q₁₆	—	27	4	no	—
463	SD₁₆	—	27	4	no	—
464	SD₁₆	—	27	4	no	—
465	D₈	—	27	4	no	—
466	M₁₆	—	9	2	no	—
467	M₁₆	—	9	2	no	—
468	C₂×C₈	—	9	2	no	—
469	C₂²×C₃	—	2	1	no	—
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	4	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	—	4	2	no	—
475	C₂²×C₃	—	6	2	no	—
476	C₂²×C₃	—	12	2	no	—
477	C₂²×C₃	C₂×#611	1	1	yes	characteristic
478	C₂²×C₃	C₂×#611	1	1	yes	characteristic
479	C₂²×C₃	C₂×#611	1	1	yes	characteristic
480	C₂²×C₃	C₂×#626	1	1	yes	characteristic
481	C₂²×C₃	C₂×#626	1	1	yes	characteristic
482	C₂²×C₃	C₂×#626	1	1	yes	characteristic
483	C₂×D₃	—	2	2	no	—
484	C₂×D₃	—	4	2	no	—
485	C₂×D₃	—	18	4	no	—
486	C₂×D₃	—	18	2	no	—
487	C₂×D₃	—	18	2	no	—
488	C₂×D₃	—	36	2	no	—
489	C₂×D₃	—	36	4	no	—
490	C₂×D₃	—	36	2	no	—
491	C₃×C₄	—	2	1	no	—
492	C₃×C₄	—	2	1	no	—
493	C₃×C₄	—	2	1	no	—
494	C₃×C₄	—	2	1	no	—
495	C₃×C₄	—	6	2	no	—
496	C₃×C₄	C₂×#611	1	1	yes	characteristic
497	C₃×C₄	C₂×#611	1	1	yes	characteristic
498	C₃×C₄	C₂×#611	1	1	yes	characteristic
499	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
500	C₃×C₄	C₂×#626	1	1	yes	characteristic
501	C₃×C₄	C₂×#626	1	1	yes	characteristic
502	C₃×C₄	C₂×#626	1	1	yes	characteristic
503	C₃×C₄	C₂²×D₃²	1	1	yes	characteristic
504	Dic₃	—	2	2	no	—
505	Dic₃	—	18	4	no	—
506	Dic₃	—	18	2	no	—
507	Dic₃	—	18	2	no	—
508	C₃²	#5822	1	1	yes	characteristic
509	C₉	—	2	1	no	—
510	C₉	#5748	1	1	yes	characteristic, complemented
511	C₂³	—	6	1	no	—
512	C₂³	—	54	1	no	—
513	C₂³	#6195	1	1	yes	characteristic
514	Q₈	—	3	2	no	—
515	Q₈	—	6	1	no	—
516	Q₈	—	27	2	no	—
517	Q₈	—	54	1	no	—
518	D₄	—	3	2	no	—
519	D₄	—	6	2	no	—
520	D₄	—	6	2	no	—
521	D₄	—	6	1	no	—
522	D₄	—	27	2	no	—
523	D₄	—	54	2	no	—
524	D₄	—	54	2	no	—
525	D₄	—	54	1	no	—
526	C₂×C₄	—	6	1	no	—
527	C₂×C₄	—	6	2	no	—
528	C₂×C₄	—	6	2	no	—
529	C₂×C₄	—	54	1	no	—
530	C₂×C₄	—	54	2	no	—
531	C₂×C₄	—	54	2	no	—
532	C₂×C₄	#6195	1	1	yes	characteristic
533	C₂×C₄	#6195	1	1	yes	characteristic
534	C₂×C₄	#6195	1	1	yes	characteristic
535	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
536	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
537	C₂×C₄	C₂×D₃×D₉	1	1	yes	characteristic
538	C₈	—	9	4	no	—
539	C₂×C₃	—	2	2	no	—
540	C₂×C₃	—	2	1	no	—
541	C₂×C₃	—	2	1	no	—
542	C₂×C₃	—	2	1	no	—
543	C₂×C₃	—	2	1	no	—
544	C₂×C₃	—	2	1	no	—
545	C₂×C₃	—	2	1	no	—
546	C₂×C₃	—	2	1	no	—
547	C₂×C₃	—	4	1	no	—
548	C₂×C₃	—	4	1	no	—
549	C₂×C₃	—	12	2	no	—
550	C₂×C₃	C₂²×#611	1	1	yes	characteristic
551	C₂×C₃	C₂²×#626	1	1	yes	characteristic
552	D₃	—	4	2	no	—
553	D₃	—	36	4	no	—
554	D₃	—	36	2	no	—
555	D₃	—	36	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	6	2	no	—
558	C₂²	—	12	2	no	—
559	C₂²	—	54	2	no	—
560	C₂²	—	108	2	no	—
561	C₂²	C₂×#6195	1	1	yes	characteristic
562	C₂²	C₂×#6195	1	1	yes	characteristic
563	C₂²	C₂×#6195	1	1	yes	characteristic
564	C₄	—	6	2	no	—
565	C₄	—	54	2	no	—
566	C₄	C₂×#6195	1	1	yes	characteristic
567	C₄	C₂×#6195	1	1	yes	characteristic
568	C₄	C₂×#6195	1	1	yes	characteristic
569	C₄	C₂²×D₃×D₉	1	1	yes	characteristic
570	C₃	—	2	1	no	—
571	C₃	#10589925	1	1	yes	characteristic, complemented
572	C₃	#10594795	1	1	yes	characteristic
573	C₂	—	2	1	no	—
574	C₂	—	2	1	no	—
575	C₂	—	2	1	no	—
576	C₂	—	12	2	no	—
577	C₂	—	108	2	no	—
578	C₂	C₂²×#6195	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#6195
commutator, cosocle	C₃×C₄×C₉	C₂⁴
Frattini	C₃×C₄	C₂²×D₃²
Fitting	C₂²×C₃×C₄×C₉	C₂²
socle	C₂×C₃²	C₂²×#67
hypercenter	C₂²×C₄	D₃×D₉
hypocenter	C₃×C₉	#575
LCS	G ▷ C₃×C₄×C₉ ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#88736	C₂	semidirect
2. C₂×C₉×#235	C₂	semidirect
3. C₂×C₃×#3667	C₂	semidirect
4. #11720895	C₂	semidirect
5. #11720891	C₂	semidirect
6. #11720890	C₂	semidirect
7. #11720889	C₂	semidirect
8. #11720885	C₂	semidirect
16. #88736	C₂²	semidirect
17. C₂×C₄⋊(C₃⋊D₉)	C₂²	semidirect
19. C₂×#6226	C₂²	semidirect
24. C₉×#235	C₂²	semidirect
25. C₂×C₉×D₁₂	C₂²	semidirect
27. C₂×C₉×Dic₆	C₂²	semidirect
28. C₃×#3667	C₂²	semidirect
29. C₃×#3667	C₂²	semidirect
30. C₂×C₃×C₉⋊C₈	C₂²	semidirect
31. #88428	C₂²	semidirect
32. #88426	C₂²	semidirect
33. #88424	C₂²	semidirect
34. #88422	C₂²	semidirect
51. C₂×#3667	D₃	semidirect
136. #3667	C₂×D₃	semidirect
137. #3667	C₂×D₃	semidirect
138. C₂×C₉⋊C₈	C₂×D₃	semidirect
157. C₂×#235	D₉	semidirect
280. #235	C₂×D₉	semidirect
284. C₂×D₁₂	C₂×D₉	semidirect
292. C₂×Dic₆	C₂×D₉	semidirect
354. C₃×C₉	#575	semidirect
510. C₉	#5748	semidirect
571. C₃	#10589925	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88736	2
C₂×C₉×#235	2
C₂×C₃×#3667	2
#11720895	2
#11720891	2
#11720890	2
#11720889	2
#11720885	2
#10594795	3
#10589925	3