Subgroups — #10588409⋊C₃ #13141634

Order 1728.

499 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3697⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#3663⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#63389⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×AGL(1,ℤ/9))⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	(C₂×AGL(1,ℤ/9))⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4727	—	3	1	no	maximal
9	#10588409	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
11	C₂×#611⋊C₃	C₄	1	1	yes	characteristic
12	C₂×#611⋊C₃	C₄	1	1	yes	characteristic
13	#3697⋊C₃	—	2	2	no	—
14	#3697⋊C₃	—	2	2	no	—
15	C₂×C₄⋊AGL(1,ℤ/9)	C₄	1	1	yes	characteristic
16	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
17	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
18	C₂×3₋¹⁺²⋊Q₈	C₄	1	1	yes	characteristic
19	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
21	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
23	#3663⋊C₃	—	2	2	no	—
24	C₈×AGL(1,ℤ/9)	—	2	2	no	—
25	C₂×C₃×#235	—	3	1	no	—
26	C₂×C₃×ΓL(1,𝔽₂₅)	—	3	1	no	—
27	C₂×C₃×D₃×C₈	—	3	1	no	—
28	C₂×#3697	C₂×C₃	1	1	yes	characteristic
29	C₃²×C₂²⋊C₈	D₃	1	1	yes	characteristic
30	C₃×#830	—	3	1	no	—
31	C₃×(C₂×D₃)⋊C₈	—	3	1	no	—
32	C₃×(C₂×D₃)⋊C₈	—	3	1	no	—
33	C₂×#3663	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₈×D₉	C₂×C₃	1	1	yes	characteristic, complemented
35	C₉×C₂²⋊C₈	—	2	1	no	—
36	C₉×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
37	#63389	C₂×C₃	1	1	yes	characteristic, complemented
38	(C₂×D₉)⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
39	(C₂×D₉)⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂³×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
41	C₂²×AGL(1,ℤ/9)	C₂×C₄	1	1	yes	characteristic
42	C₂²×AGL(1,ℤ/9)	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×3₋¹⁺²	—	2	1	no	—
44	C₂×C₄×3₋¹⁺²	—	2	1	no	—
45	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
47	#611⋊C₃	—	2	2	no	—
48	#611⋊C₃	—	2	2	no	—
49	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
52	C₄×AGL(1,ℤ/9)	—	2	1	no	—
53	C₄×AGL(1,ℤ/9)	—	2	1	no	—
54	C₄×AGL(1,ℤ/9)	D₄	1	2	yes	—
55	C₄×AGL(1,ℤ/9)	D₄	1	2	yes	—
56	3₋¹⁺²⋊Q₈	—	2	2	no	—
57	C₈×3₋¹⁺²	—	2	1	no	—
58	C₈×3₋¹⁺²	—	2	1	no	—
59	3₋¹⁺²⋊C₈	—	2	1	no	—
60	3₋¹⁺²⋊C₈	—	2	1	no	—
61	C₃×#408	—	9	1	no	—
62	#4727	—	3	1	no	—
63	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃×#67	—	3	1	no	—
65	C₂×C₃×#67	—	3	1	no	—
66	C₃×#235	—	6	2	no	—
67	C₃×#235	—	6	2	no	—
68	C₂×C₃×D₁₂	—	3	1	no	—
69	C₂×C₃×C₄×D₃	—	3	1	no	—
70	C₂×C₃×C₄×D₃	—	3	1	no	—
71	C₂×C₃×Dic₆	—	3	1	no	—
72	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃×C₃⋊C₈	—	3	1	no	—
75	C₂×C₃×C₃⋊C₈	—	3	1	no	—
76	C₃×ΓL(1,𝔽₂₅)	—	6	2	no	—
77	C₃×D₃×C₈	—	6	2	no	—
78	C₂²×C₄×C₉	—	2	1	no	—
79	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
80	C₂×#611	C₃×C₄	1	1	yes	characteristic
81	C₂×#611	C₃×C₄	1	1	yes	characteristic
82	#3697	—	2	2	no	—
83	#3697	—	2	2	no	—
84	C₂×D₃₆	C₃×C₄	1	1	yes	characteristic
85	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
87	C₂×Dic₁₈	C₃×C₄	1	1	yes	characteristic
88	C₂×C₈×C₉	—	2	1	no	—
89	C₂×C₈×C₉	—	2	1	no	—
90	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
94	#3663	—	2	2	no	—
95	C₈×D₉	—	2	2	no	—
96	C₂²×3₋¹⁺²	—	2	1	no	—
97	C₂²×3₋¹⁺²	—	2	1	no	—
98	C₂²×3₋¹⁺²	—	2	1	no	—
99	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
100	C₂×AGL(1,ℤ/9)	—	2	1	no	—
101	C₂×AGL(1,ℤ/9)	—	2	1	no	—
102	C₂×AGL(1,ℤ/9)	—	2	1	no	—
103	C₂×AGL(1,ℤ/9)	—	2	1	no	—
104	C₂×AGL(1,ℤ/9)	—	2	1	no	—
105	C₂×AGL(1,ℤ/9)	C₂²⋊C₄	1	2	yes	—
106	C₄×3₋¹⁺²	—	2	1	no	—
107	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
108	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
109	3₋¹⁺²⋊C₄	—	2	1	no	—
110	3₋¹⁺²⋊C₄	C₂²⋊C₄	1	2	yes	—
111	C₂×C₃×#41	—	9	1	no	—
112	C₂×#235	—	3	1	no	—
113	C₂×C₃×M₁₆	—	9	1	no	—
114	C₂²×C₃×C₈	—	9	1	no	—
115	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
116	C₂×D₃×C₈	—	3	1	no	—
117	C₃×C₂²⋊C₈	—	3	1	no	—
118	C₃×C₂²⋊C₈	—	9	1	no	—
119	C₃×C₂²⋊C₈	—	9	1	no	—
120	C₃×C₂²⋊C₈	—	9	1	no	—
121	C₃×C₂²⋊C₈	C₃×D₃	1	1	yes	characteristic
122	#830	—	3	1	no	—
123	(C₂×D₃)⋊C₈	—	3	1	no	—
124	(C₂×D₃)⋊C₈	—	3	1	no	—
125	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
126	C₂²×C₃×D₃	—	3	1	no	—
127	C₂²×C₃×D₃	—	3	1	no	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	—	2	1	no	—
130	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
132	C₃×#67	—	6	2	no	—
133	C₃×#67	—	6	2	no	—
134	C₂×C₃×Dic₃	—	3	1	no	—
135	C₂×C₃×Dic₃	—	3	1	no	—
136	C₃×D₁₂	—	6	2	no	—
137	C₃×C₄×D₃	—	3	2	no	—
138	C₃×C₄×D₃	—	3	2	no	—
139	C₃×C₄×D₃	—	6	1	no	—
140	C₃×C₄×D₃	—	6	1	no	—
141	C₃×Dic₆	—	6	2	no	—
142	C₂³×C₉	—	2	1	no	—
143	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
144	C₂²×D₉	C₂×C₃×C₄	1	1	yes	characteristic
145	C₂²×D₉	C₂×C₃×C₄	1	1	yes	characteristic
146	C₃²×C₈	—	2	1	no	—
147	C₃²×C₈	—	2	1	no	—
148	C₃×C₃⋊C₈	—	6	1	no	—
149	C₃×C₃⋊C₈	—	6	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	4	1	no	—
155	C₂×C₄×C₉	—	4	1	no	—
156	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
158	#611	—	2	2	no	—
159	#611	—	2	2	no	—
160	C₂×Dic₉	C₂×C₃×C₄	1	1	yes	characteristic
161	C₂×Dic₉	C₂×C₃×C₄	1	1	yes	characteristic
162	D₃₆	—	2	2	no	—
163	C₄×D₉	—	2	1	no	—
164	C₄×D₉	—	2	1	no	—
165	C₄×D₉	C₃×D₄	1	2	yes	—
166	C₄×D₉	C₃×D₄	1	2	yes	—
167	Dic₁₈	—	2	2	no	—
168	C₈×C₉	—	2	1	no	—
169	C₈×C₉	—	2	1	no	—
170	C₈×C₉	—	4	1	no	—
171	C₈×C₉	—	4	1	no	—
172	C₉⋊C₈	—	2	1	no	—
173	C₉⋊C₈	—	2	1	no	—
174	#408	—	9	1	no	Sylow
175	C₂×3₋¹⁺²	—	4	1	no	—
176	C₂×3₋¹⁺²	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×3₋¹⁺²	#131	1	1	yes	characteristic
178	C₂×3₋¹⁺²	#131	1	1	yes	characteristic
179	AGL(1,ℤ/9)	—	2	2	no	—
180	AGL(1,ℤ/9)	—	4	1	no	—
181	C₃×#41	—	18	2	no	—
182	C₃×#41	—	18	2	no	—
183	C₂×C₃×Q₈	—	9	1	no	—
184	C₂×C₃×D₄	—	9	1	no	—
185	C₂×C₃×D₄	—	9	1	no	—
186	C₂×C₃×D₄	—	9	1	no	—
187	C₂²×C₃×C₄	—	3	1	no	—
188	C₂²×C₃×C₄	—	9	1	no	—
189	C₂²×C₃×C₄	—	9	1	no	—
190	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
191	C₂×#67	—	3	1	no	—
192	C₂×#67	—	3	1	no	—
193	#235	—	6	2	no	—
194	#235	—	6	2	no	—
195	C₂×D₁₂	—	3	1	no	—
196	C₂×C₄×D₃	—	3	1	no	—
197	C₂×C₄×D₃	—	3	1	no	—
198	C₂×Dic₆	—	3	1	no	—
199	C₃×M₁₆	—	18	2	no	—
200	C₂×C₃×C₈	—	3	1	no	—
201	C₂×C₃×C₈	—	3	1	no	—
202	C₂×C₃×C₈	—	9	1	no	—
203	C₂×C₃×C₈	—	9	1	no	—
204	C₂×C₃×C₈	—	18	2	no	—
205	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
206	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
207	C₂×C₃⋊C₈	—	3	1	no	—
208	C₂×C₃⋊C₈	—	3	1	no	—
209	ΓL(1,𝔽₂₅)	—	6	2	no	—
210	D₃×C₈	—	6	2	no	—
211	C₂²×C₃²	—	2	1	no	—
212	C₂²×C₃²	—	2	1	no	—
213	C₂²×C₃²	—	2	1	no	—
214	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
215	C₂×C₃×D₃	—	3	2	no	—
216	C₂×C₃×D₃	—	6	1	no	—
217	C₂×C₃×D₃	—	6	1	no	—
218	C₂×C₃×D₃	—	6	1	no	—
219	C₂×C₃×D₃	—	6	1	no	—
220	C₂×C₃×D₃	—	6	1	no	—
221	C₃²×C₄	—	2	1	no	—
222	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
223	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
224	C₃×Dic₃	—	3	2	no	—
225	C₃×Dic₃	—	6	1	no	—
226	C₂²×C₉	—	2	2	no	—
227	C₂²×C₉	—	2	1	no	—
228	C₂²×C₉	—	2	1	no	—
229	C₂²×C₉	—	2	1	no	—
230	C₂²×C₉	—	2	1	no	—
231	C₂²×C₉	—	4	1	no	—
232	C₂²×C₉	—	4	1	no	—
233	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×D₉	—	2	1	no	—
235	C₂×D₉	—	2	1	no	—
236	C₂×D₉	—	2	1	no	—
237	C₂×D₉	—	2	1	no	—
238	C₂×D₉	—	2	1	no	—
239	C₂×D₉	C₃×C₂²⋊C₄	1	2	yes	—
240	C₄×C₉	—	2	1	no	—
241	C₄×C₉	—	2	1	no	—
242	C₄×C₉	—	2	1	no	—
243	C₄×C₉	—	4	1	no	—
244	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
245	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
246	Dic₉	—	2	1	no	—
247	Dic₉	C₃×C₂²⋊C₄	1	2	yes	—
248	C₂×#41	—	9	1	no	—
249	C₂×M₁₆	—	9	1	no	—
250	C₂²×C₈	—	9	1	no	—
251	C₂²⋊C₈	—	9	1	no	—
252	C₂²⋊C₈	—	9	1	no	—
253	C₂²⋊C₈	—	9	1	no	—
254	C₂²⋊C₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
255	3₋¹⁺²	#408	1	1	yes	characteristic, complemented, Sylow
256	C₂³×C₃	—	3	1	no	—
257	C₂³×C₃	—	9	1	no	—
258	C₂³×C₃	—	9	1	no	—
259	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
260	C₂²×D₃	—	3	1	no	—
261	C₂²×D₃	—	3	1	no	—
262	C₃×Q₈	—	18	2	no	—
263	C₃×D₄	—	18	2	no	—
264	C₃×D₄	—	18	2	no	—
265	C₃×D₄	—	18	2	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	3	1	no	—
269	C₂×C₃×C₄	—	3	1	no	—
270	C₂×C₃×C₄	—	6	1	no	—
271	C₂×C₃×C₄	—	6	1	no	—
272	C₂×C₃×C₄	—	9	2	no	—
273	C₂×C₃×C₄	—	9	2	no	—
274	C₂×C₃×C₄	—	9	1	no	—
275	C₂×C₃×C₄	—	9	1	no	—
276	C₂×C₃×C₄	—	18	1	no	—
277	C₂×C₃×C₄	—	18	1	no	—
278	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
280	#67	—	6	2	no	—
281	#67	—	6	2	no	—
282	C₂×Dic₃	—	3	1	no	—
283	C₂×Dic₃	—	3	1	no	—
284	D₁₂	—	6	2	no	—
285	C₄×D₃	—	3	2	no	—
286	C₄×D₃	—	3	2	no	—
287	C₄×D₃	—	6	1	no	—
288	C₄×D₃	—	6	1	no	—
289	Dic₆	—	6	2	no	—
290	C₃×C₈	—	2	1	no	—
291	C₃×C₈	—	2	1	no	—
292	C₃×C₈	—	6	1	no	—
293	C₃×C₈	—	6	1	no	—
294	C₃×C₈	—	18	1	no	—
295	C₃×C₈	—	18	1	no	—
296	C₃⋊C₈	—	6	1	no	—
297	C₃⋊C₈	—	6	1	no	—
298	C₂×C₃²	—	4	1	no	—
299	C₂×C₃²	D₃×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₃²	#901	1	1	yes	characteristic
301	C₂×C₃²	#907	1	1	yes	characteristic
302	C₃×D₃	—	6	2	no	—
303	C₃×D₃	—	12	1	no	—
304	C₂×C₉	—	2	1	no	—
305	C₂×C₉	—	2	1	no	—
306	C₂×C₉	—	2	1	no	—
307	C₂×C₉	—	4	2	no	—
308	C₂×C₉	—	4	1	no	—
309	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₉	C₃×#131	1	1	yes	characteristic
311	C₂×C₉	C₃×#131	1	1	yes	characteristic
312	D₉	—	2	2	no	—
313	D₉	—	4	1	no	—
314	#41	—	18	2	no	—
315	#41	—	18	2	no	—
316	C₂×Q₈	—	9	1	no	—
317	C₂×D₄	—	9	1	no	—
318	C₂×D₄	—	9	1	no	—
319	C₂×D₄	—	9	1	no	—
320	C₂²×C₄	—	9	1	no	—
321	C₂²×C₄	—	9	1	no	—
322	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
323	M₁₆	—	18	2	no	—
324	C₂×C₈	—	9	1	no	—
325	C₂×C₈	—	9	1	no	—
326	C₂×C₈	—	18	2	no	—
327	C₂×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
328	C₂×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	3	1	no	—
333	C₂²×C₃	—	6	1	no	—
334	C₂²×C₃	—	6	1	no	—
335	C₂²×C₃	—	6	1	no	—
336	C₂²×C₃	—	9	2	no	—
337	C₂²×C₃	—	18	1	no	—
338	C₂²×C₃	—	18	1	no	—
339	C₂²×C₃	—	18	1	no	—
340	C₂²×C₃	—	18	1	no	—
341	C₂²×C₃	—	18	1	no	—
342	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
343	C₂×D₃	—	3	2	no	—
344	C₂×D₃	—	6	1	no	—
345	C₂×D₃	—	6	1	no	—
346	C₂×D₃	—	6	1	no	—
347	C₂×D₃	—	6	1	no	—
348	C₂×D₃	—	6	1	no	—
349	C₃×C₄	—	2	1	no	—
350	C₃×C₄	—	3	1	no	—
351	C₃×C₄	—	3	1	no	—
352	C₃×C₄	—	6	1	no	—
353	C₃×C₄	—	9	2	no	—
354	C₃×C₄	—	18	1	no	—
355	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
356	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
357	Dic₃	—	3	2	no	—
358	Dic₃	—	6	1	no	—
359	C₃²	#4727	1	1	yes	characteristic
360	C₉	—	2	1	no	—
361	C₉	C₃×#408	1	1	yes	characteristic, complemented
362	C₂³	—	9	1	no	—
363	C₂³	—	9	1	no	—
364	C₂³	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
365	Q₈	—	18	2	no	—
366	D₄	—	18	2	no	—
367	D₄	—	18	2	no	—
368	D₄	—	18	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	9	1	no	—
372	C₂×C₄	—	9	2	no	—
373	C₂×C₄	—	9	2	no	—
374	C₂×C₄	—	9	1	no	—
375	C₂×C₄	—	18	1	no	—
376	C₂×C₄	—	18	1	no	—
377	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
378	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	18	1	no	—
382	C₈	—	18	1	no	—
383	C₂×C₃	—	3	1	no	—
384	C₂×C₃	—	3	1	no	—
385	C₂×C₃	—	3	1	no	—
386	C₂×C₃	—	4	1	no	—
387	C₂×C₃	—	12	1	no	—
388	C₂×C₃	—	18	2	no	—
389	C₂×C₃	—	36	1	no	—
390	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
391	C₂×C₃	C₃×#901	1	1	yes	characteristic
392	C₂×C₃	C₃×#907	1	1	yes	characteristic
393	D₃	—	6	2	no	—
394	D₃	—	12	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	9	2	no	—
399	C₂²	—	18	1	no	—
400	C₂²	—	18	1	no	—
401	C₂²	—	18	1	no	—
402	C₂²	—	18	1	no	—
403	C₂²	—	18	1	no	—
404	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	9	2	no	—
407	C₄	—	18	1	no	—
408	C₄	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
409	C₄	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
410	C₃	—	3	1	no	—
411	C₃	C₃×#4727	1	1	yes	characteristic
412	C₂	—	4	1	no	—
413	C₂	—	18	2	no	—
414	C₂	—	36	1	no	—
415	C₂	C₂²⋊C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
416	C₂	#63464⋊C₃	1	1	yes	characteristic
417	C₂	#63469⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×AGL(1,ℤ/9)
commutator	C₂²×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	3₋¹⁺²×C₂²⋊C₈	C₂
socle	C₂²×C₃	C₂×C₃×C₄×D₃
prime radical	C₂×#3697⋊C₃	C₂
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	C₂²⋊C₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#408
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#3663⋊C₃	C₂	semidirect
3. C₂×C₈×AGL(1,ℤ/9)	C₂	semidirect
4. 3₋¹⁺²×C₂²⋊C₈	C₂	semidirect
5. #63389⋊C₃	C₂	semidirect
6. (C₂×AGL(1,ℤ/9))⋊C₈	C₂	semidirect
7. (C₂×AGL(1,ℤ/9))⋊C₈	C₂	semidirect
9. #10588409	C₃	semidirect
33. C₂×#3663	C₂×C₃	semidirect
34. C₂×C₈×D₉	C₂×C₃	semidirect
36. C₉×C₂²⋊C₈	C₂×C₃	semidirect
37. #63389	C₂×C₃	semidirect
38. (C₂×D₉)⋊C₈	C₂×C₃	semidirect
39. (C₂×D₉)⋊C₈	C₂×C₃	semidirect
254. C₂²⋊C₈	AGL(1,ℤ/9)	semidirect
255. 3₋¹⁺²	#408	semidirect
361. C₉	C₃×#408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3697⋊C₃	2
C₂×#3663⋊C₃	2
C₂×C₈×AGL(1,ℤ/9)	2
3₋¹⁺²×C₂²⋊C₈	2
#63389⋊C₃	2
(C₂×AGL(1,ℤ/9))⋊C₈	2
C₃×#4727	3
#10588409	3

Subgroups — #10588409⋊C3 #13141634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588409⋊C₃ #13141634