Subgroups — #10589925⋊C₃ #13153731

Order 1728.

868 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₄	C₂×#611⋊C₃
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×#41×3₋¹⁺²	C₂
socle	C₂×C₃	C₂²×C₃×#67
hypercenter	C₂×#41	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#575
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×3₋¹⁺²	C₂	semidirect
2. C₂×#3697⋊C₃	C₂	semidirect
3. #63513⋊C₃	C₂	semidirect
4. #63512⋊C₃	C₂	semidirect
5. #63511⋊C₃	C₂	semidirect
6. #63505⋊C₃	C₂	semidirect
7. #63495⋊C₃	C₂	semidirect
8. C₂×#3667⋊C₃	C₂	semidirect
10. #10589925	C₃	semidirect
14. #41×3₋¹⁺²	C₂²	semidirect
15. C₂×Q₈×3₋¹⁺²	C₂²	semidirect
17. C₂×D₄×3₋¹⁺²	C₂²	semidirect
24. #3697⋊C₃	C₂²	semidirect
25. C₂×C₄⋊AGL(1,ℤ/9)	C₂²	semidirect
27. C₂×3₋¹⁺²⋊Q₈	C₂²	semidirect
28. #3675⋊C₃	C₂²	semidirect
29. #3674⋊C₃	C₂²	semidirect
30. #3673⋊C₃	C₂²	semidirect
31. #3672⋊C₃	C₂²	semidirect
32. #3667⋊C₃	C₂²	semidirect
33. #3667⋊C₃	C₂²	semidirect
34. C₂×3₋¹⁺²⋊C₈	C₂²	semidirect
44. C₂×C₉×#41	C₂×C₃	semidirect
45. C₂×#3697	C₂×C₃	semidirect
46. #63513	C₂×C₃	semidirect
47. #63512	C₂×C₃	semidirect
48. #63511	C₂×C₃	semidirect
49. #63505	C₂×C₃	semidirect
50. #63495	C₂×C₃	semidirect
51. C₂×#3667	C₂×C₃	semidirect
113. C₉×#41	C₂²×C₃	semidirect
115. C₂×Q₈×C₉	C₂²×C₃	semidirect
119. C₂×D₄×C₉	C₂²×C₃	semidirect
128. #3697	C₂²×C₃	semidirect
129. C₂×D₃₆	C₂²×C₃	semidirect
131. C₂×Dic₁₈	C₂²×C₃	semidirect
132. #3675	C₂²×C₃	semidirect
133. #3674	C₂²×C₃	semidirect
134. #3673	C₂²×C₃	semidirect
135. #3672	C₂²×C₃	semidirect
136. #3667	C₂²×C₃	semidirect
137. #3667	C₂²×C₃	semidirect
138. C₂×C₉⋊C₈	C₂²×C₃	semidirect
337. C₂×#41	AGL(1,ℤ/9)	semidirect
344. 3₋¹⁺²	#575	semidirect
425. #41	C₂×AGL(1,ℤ/9)	semidirect
427. C₂×Q₈	C₂×AGL(1,ℤ/9)	semidirect
431. C₂×D₄	C₂×AGL(1,ℤ/9)	semidirect
472. C₉	C₃×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×3₋¹⁺²	2
C₂×#3697⋊C₃	2
#63513⋊C₃	2
#63512⋊C₃	2
#63511⋊C₃	2
#63505⋊C₃	2
#63495⋊C₃	2
C₂×#3667⋊C₃	2
C₃×#5822	3
#10589925	3

Subgroups — #10589925⋊C3 #13153731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589925⋊C₃ #13153731