Subgroups — #10589682⋊C₃ #13152741

Order 1728.

737 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	#63509⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63508⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63460⋊C₃	C₂	1	2	yes	maximal, complemented
5	#63457⋊C₃	C₂	1	1	yes	maximal, characteristic
6	#63456⋊C₃	C₂	1	2	yes	maximal, complemented
7	#63452⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
9	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
10	#63434⋊C₃	C₂	1	2	yes	maximal, complemented
11	C₄²×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5580	—	3	1	no	maximal
13	#10589682	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	2	yes	—
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×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
19	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
20	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
21	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
23	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
24	C₄²×3₋¹⁺²	C₂²	1	2	yes	—
25	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
26	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
27	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
28	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
29	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
30	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
31	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
32	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
33	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
34	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
38	C₃×#947	—	3	1	no	—
39	C₃×#946	—	3	1	no	—
40	C₃×#898	—	3	2	no	—
41	C₃×#895	—	3	1	no	—
42	C₃×#894	—	3	2	no	—
43	C₃×#890	—	3	1	no	—
44	C₃×C₄×D₁₂	—	3	2	no	—
45	C₃×C₄×D₁₂	—	3	1	no	—
46	C₃×#872	—	3	2	no	—
47	C₃×C₄²×D₃	—	3	1	no	—
48	C₄×Q₈×C₉	—	2	1	no	—
49	C₄×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
50	#63509	C₂×C₃	1	1	yes	characteristic, complemented
51	#63508	C₂×C₃	1	1	yes	characteristic, complemented
52	#63460	C₂×C₃	1	2	yes	complemented
53	#63457	C₂×C₃	1	1	yes	characteristic
54	#63456	C₂×C₃	1	2	yes	complemented
55	#63452	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
57	C₄×D₃₆	C₂×C₃	1	2	yes	complemented
58	#63434	C₂×C₃	1	2	yes	complemented
59	C₄²×D₉	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×AGL(1,ℤ/9)	C₂³	1	2	yes	—
61	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
62	Q₈×3₋¹⁺²	—	2	2	no	—
63	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
64	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
65	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
66	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
67	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
68	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
72	C₄⋊AGL(1,ℤ/9)	—	2	4	no	—
73	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
74	C₄×AGL(1,ℤ/9)	—	2	2	no	—
75	C₄×AGL(1,ℤ/9)	—	2	2	no	—
76	C₄×AGL(1,ℤ/9)	—	2	2	no	—
77	C₄×AGL(1,ℤ/9)	—	2	4	no	—
78	C₃×#529	—	9	1	no	—
79	#5580	—	3	1	no	—
80	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
81	C₂×C₃×D₁₂	—	3	2	no	—
82	C₂×C₃×D₁₂	—	3	1	no	—
83	C₂×C₃×C₄×D₃	—	3	1	no	—
84	C₂×C₃×C₄×D₃	—	3	1	no	—
85	C₂×C₃×C₄×D₃	—	3	1	no	—
86	C₂×C₃×C₄×D₃	—	3	2	no	—
87	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
89	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
90	C₃²×C₄²	C₂×D₃	1	2	yes	—
91	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
92	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
93	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
94	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
95	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
96	C₃×C₄⋊Dic₃	—	3	2	no	—
97	C₃×C₄⋊Dic₃	—	3	1	no	—
98	C₃×Dic₃⋊C₄	—	3	2	no	—
99	C₃×Dic₃⋊C₄	—	3	2	no	—
100	C₃×C₄×Dic₃	—	3	1	no	—
101	C₃×C₄×Dic₃	—	3	1	no	—
102	C₃×C₄×Dic₃	—	3	1	no	—
103	C₂×Q₈×C₉	—	2	1	no	—
104	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
105	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
106	C₂×D₃₆	C₂²×C₃	1	2	yes	—
107	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
111	C₉×C₄⋊C₄	—	2	1	no	—
112	C₉×C₄⋊C₄	—	2	2	no	—
113	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
115	C₄²×C₉	—	2	1	no	—
116	C₄²×C₉	—	2	2	no	—
117	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
118	C₄²×C₉	C₂²×C₃	1	2	yes	—
119	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
120	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
121	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
122	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
123	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
124	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
125	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
126	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
127	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
128	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
129	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
130	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
131	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
132	C₂×AGL(1,ℤ/9)	—	2	1	no	—
133	C₂×AGL(1,ℤ/9)	—	2	1	no	—
134	C₂×AGL(1,ℤ/9)	—	2	2	no	—
135	C₂×AGL(1,ℤ/9)	—	2	2	no	—
136	C₂×AGL(1,ℤ/9)	—	2	2	no	—
137	C₂×AGL(1,ℤ/9)	#41	1	2	yes	—
138	C₄×3₋¹⁺²	—	2	2	no	—
139	C₄×3₋¹⁺²	—	2	1	no	—
140	C₄×3₋¹⁺²	—	2	2	no	—
141	C₄×3₋¹⁺²	#41	1	2	yes	—
142	C₄×3₋¹⁺²	#41	1	2	yes	—
143	3₋¹⁺²⋊C₄	—	2	1	no	—
144	3₋¹⁺²⋊C₄	—	2	1	no	—
145	3₋¹⁺²⋊C₄	—	2	2	no	—
146	3₋¹⁺²⋊C₄	—	2	1	no	—
147	C₃×#126	—	9	2	no	—
148	C₃×#125	—	9	1	no	—
149	C₃×#124	—	9	1	no	—
150	C₃×#123	—	9	2	no	—
151	C₃×C₂²⋊Q₈	—	9	1	no	—
152	C₃×#121	—	9	1	no	—
153	C₃×C₄×Q₈	—	3	1	no	—
154	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
155	C₃×C₄×D₄	—	9	1	no	—
156	C₃×C₄×D₄	—	9	2	no	—
157	C₃×#117	—	9	2	no	—
158	C₂×C₃×C₄²	—	9	1	no	—
159	#947	—	3	1	no	—
160	#946	—	3	1	no	—
161	#898	—	3	2	no	—
162	#895	—	3	1	no	—
163	#894	—	3	2	no	—
164	#890	—	3	1	no	—
165	C₄×D₁₂	—	3	2	no	—
166	C₄×D₁₂	—	3	1	no	—
167	#872	—	3	2	no	—
168	C₄²×D₃	—	3	1	no	—
169	C₂²×C₃×D₃	—	3	1	no	—
170	C₂²×C₃×D₃	—	3	2	no	—
171	C₃²×Q₈	—	2	2	no	—
172	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
174	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
175	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
176	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	—	3	1	no	—
178	C₂×C₃×Dic₃	—	3	1	no	—
179	C₂×C₃×Dic₃	—	3	1	no	—
180	C₂×C₃×Dic₃	—	3	2	no	—
181	C₃×D₁₂	—	6	4	no	—
182	C₃×D₁₂	—	6	2	no	—
183	C₃×C₄×D₃	—	6	2	no	—
184	C₃×C₄×D₃	—	6	2	no	—
185	C₃×C₄×D₃	—	6	2	no	—
186	C₃×C₄×D₃	—	6	4	no	—
187	C₂²×D₉	C₂³×C₃	1	2	yes	—
188	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
189	Q₈×C₉	—	2	4	no	—
190	Q₈×C₉	—	2	2	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	2	no	—
196	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
198	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
199	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
201	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
202	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
203	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
204	C₂×Dic₉	C₂³×C₃	1	2	yes	—
205	D₃₆	—	2	4	no	—
206	D₃₆	—	2	2	no	—
207	C₄×D₉	—	2	2	no	—
208	C₄×D₉	—	2	2	no	—
209	C₄×D₉	—	2	2	no	—
210	C₄×D₉	—	2	4	no	—
211	#529	—	9	1	no	Sylow
212	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
213	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
214	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
215	AGL(1,ℤ/9)	—	2	2	no	—
216	AGL(1,ℤ/9)	—	4	2	no	—
217	C₂×C₃×Q₈	—	3	1	no	—
218	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
219	C₂×C₃×D₄	—	9	2	no	—
220	C₂×C₃×D₄	—	9	1	no	—
221	C₂²×C₃×C₄	—	9	1	no	—
222	C₂²×C₃×C₄	—	9	1	no	—
223	C₂²×C₃×C₄	—	9	1	no	—
224	C₂²×C₃×C₄	—	9	2	no	—
225	C₂×D₁₂	—	3	2	no	—
226	C₂×D₁₂	—	3	1	no	—
227	C₂×C₄×D₃	—	3	1	no	—
228	C₂×C₄×D₃	—	3	1	no	—
229	C₂×C₄×D₃	—	3	1	no	—
230	C₂×C₄×D₃	—	3	2	no	—
231	C₃×C₄⋊C₄	—	3	1	no	—
232	C₃×C₄⋊C₄	—	3	2	no	—
233	C₃×C₄⋊C₄	—	9	2	no	—
234	C₃×C₄⋊C₄	—	9	2	no	—
235	C₃×C₄⋊C₄	—	9	1	no	—
236	C₃×C₄⋊C₄	—	9	2	no	—
237	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
238	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
239	C₃×C₂²⋊C₄	—	9	2	no	—
240	C₃×C₂²⋊C₄	—	9	2	no	—
241	C₃×C₂²⋊C₄	—	9	2	no	—
242	C₃×C₂²⋊C₄	—	9	2	no	—
243	C₃×C₂²⋊C₄	—	9	2	no	—
244	C₃×C₄²	—	3	1	no	—
245	C₃×C₄²	—	3	2	no	—
246	C₃×C₄²	—	9	1	no	—
247	C₃×C₄²	—	9	1	no	—
248	C₃×C₄²	—	9	1	no	—
249	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
250	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
251	(C₂×D₃)⋊C₄	—	3	2	no	—
252	(C₂×D₃)⋊C₄	—	3	2	no	—
253	(C₂×D₃)⋊C₄	—	3	2	no	—
254	(C₂×D₃)⋊C₄	—	3	2	no	—
255	(C₂×D₃)⋊C₄	—	3	2	no	—
256	C₄⋊Dic₃	—	3	2	no	—
257	C₄⋊Dic₃	—	3	1	no	—
258	Dic₃⋊C₄	—	3	2	no	—
259	Dic₃⋊C₄	—	3	2	no	—
260	C₄×Dic₃	—	3	1	no	—
261	C₄×Dic₃	—	3	1	no	—
262	C₄×Dic₃	—	3	1	no	—
263	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
264	C₂×C₃×D₃	—	3	2	no	—
265	C₂×C₃×D₃	—	6	1	no	—
266	C₂×C₃×D₃	—	6	1	no	—
267	C₂×C₃×D₃	—	6	2	no	—
268	C₂×C₃×D₃	—	6	2	no	—
269	C₂×C₃×D₃	—	6	2	no	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	—	2	1	no	—
272	C₃²×C₄	—	2	2	no	—
273	C₃²×C₄	#235	1	2	yes	—
274	C₃²×C₄	#239	1	2	yes	—
275	C₃×Dic₃	—	6	1	no	—
276	C₃×Dic₃	—	6	1	no	—
277	C₃×Dic₃	—	6	2	no	—
278	C₃×Dic₃	—	6	1	no	—
279	C₂²×C₉	—	2	1	no	—
280	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
281	C₂×D₉	—	2	1	no	—
282	C₂×D₉	—	2	1	no	—
283	C₂×D₉	—	2	2	no	—
284	C₂×D₉	—	2	2	no	—
285	C₂×D₉	—	2	2	no	—
286	C₂×D₉	C₃×#41	1	2	yes	—
287	C₄×C₉	—	2	4	no	—
288	C₄×C₉	—	2	1	no	—
289	C₄×C₉	—	2	2	no	—
290	C₄×C₉	—	2	2	no	—
291	C₄×C₉	—	2	2	no	—
292	C₄×C₉	—	2	2	no	—
293	C₄×C₉	—	4	1	no	—
294	C₄×C₉	—	4	2	no	—
295	C₄×C₉	C₃×#41	1	2	yes	—
296	C₄×C₉	C₃×#41	1	2	yes	—
297	Dic₉	—	2	1	no	—
298	Dic₉	—	2	1	no	—
299	Dic₉	—	2	2	no	—
300	Dic₉	—	2	1	no	—
301	#126	—	9	2	no	—
302	#125	—	9	1	no	—
303	#124	—	9	1	no	—
304	#123	—	9	2	no	—
305	C₂²⋊Q₈	—	9	1	no	—
306	#121	—	9	1	no	—
307	C₄×Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
308	C₄×D₄	—	9	1	no	—
309	C₄×D₄	—	9	2	no	—
310	#117	—	9	2	no	—
311	C₂×C₄²	—	9	1	no	—
312	3₋¹⁺²	#529	1	1	yes	characteristic, complemented, Sylow
313	C₂³×C₃	—	9	1	no	—
314	C₂³×C₃	—	9	2	no	—
315	C₂²×D₃	—	3	1	no	—
316	C₂²×D₃	—	3	2	no	—
317	C₃×Q₈	—	2	2	no	—
318	C₃×Q₈	—	6	2	no	—
319	C₃×D₄	—	18	2	no	—
320	C₃×D₄	—	18	4	no	—
321	C₂×C₃×C₄	—	3	1	no	—
322	C₂×C₃×C₄	—	3	1	no	—
323	C₂×C₃×C₄	—	3	2	no	—
324	C₂×C₃×C₄	—	3	2	no	—
325	C₂×C₃×C₄	—	3	1	no	—
326	C₂×C₃×C₄	—	9	1	no	—
327	C₂×C₃×C₄	—	9	1	no	—
328	C₂×C₃×C₄	—	9	1	no	—
329	C₂×C₃×C₄	—	9	2	no	—
330	C₂×C₃×C₄	—	18	2	no	—
331	C₂×C₃×C₄	—	18	2	no	—
332	C₂×C₃×C₄	—	18	4	no	—
333	C₂×C₃×C₄	—	18	2	no	—
334	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
336	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
337	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂×Dic₃	—	3	1	no	—
340	C₂×Dic₃	—	3	1	no	—
341	C₂×Dic₃	—	3	1	no	—
342	C₂×Dic₃	—	3	2	no	—
343	D₁₂	—	6	4	no	—
344	D₁₂	—	6	2	no	—
345	C₄×D₃	—	6	2	no	—
346	C₄×D₃	—	6	2	no	—
347	C₄×D₃	—	6	2	no	—
348	C₄×D₃	—	6	4	no	—
349	C₂×C₃²	C₂×#235	1	1	yes	characteristic
350	C₂×C₃²	C₂×#239	1	1	yes	characteristic
351	C₂×C₃²	D₃×#41	1	1	yes	characteristic
352	C₃×D₃	—	6	2	no	—
353	C₃×D₃	—	12	2	no	—
354	C₂×C₉	—	2	1	no	—
355	C₂×C₉	—	2	1	no	—
356	C₂×C₉	—	2	1	no	—
357	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
358	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
359	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
360	D₉	—	2	2	no	—
361	D₉	—	4	2	no	—
362	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
363	C₂×D₄	—	9	2	no	—
364	C₂×D₄	—	9	1	no	—
365	C₂²×C₄	—	9	1	no	—
366	C₂²×C₄	—	9	1	no	—
367	C₂²×C₄	—	9	1	no	—
368	C₂²×C₄	—	9	2	no	—
369	C₄⋊C₄	—	9	2	no	—
370	C₄⋊C₄	—	9	2	no	—
371	C₄⋊C₄	—	9	1	no	—
372	C₄⋊C₄	—	9	2	no	—
373	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
374	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
375	C₂²⋊C₄	—	9	2	no	—
376	C₂²⋊C₄	—	9	2	no	—
377	C₂²⋊C₄	—	9	2	no	—
378	C₂²⋊C₄	—	9	2	no	—
379	C₂²⋊C₄	—	9	2	no	—
380	C₄²	—	9	1	no	—
381	C₄²	—	9	1	no	—
382	C₄²	—	9	1	no	—
383	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
384	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
385	C₂²×C₃	—	3	1	no	—
386	C₂²×C₃	—	9	2	no	—
387	C₂²×C₃	—	18	1	no	—
388	C₂²×C₃	—	18	1	no	—
389	C₂²×C₃	—	18	2	no	—
390	C₂²×C₃	—	18	2	no	—
391	C₂²×C₃	—	18	2	no	—
392	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
393	C₂×D₃	—	3	2	no	—
394	C₂×D₃	—	6	1	no	—
395	C₂×D₃	—	6	1	no	—
396	C₂×D₃	—	6	2	no	—
397	C₂×D₃	—	6	2	no	—
398	C₂×D₃	—	6	2	no	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	1	no	—
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	3	2	no	—
403	C₃×C₄	—	3	2	no	—
404	C₃×C₄	—	6	1	no	—
405	C₃×C₄	—	6	2	no	—
406	C₃×C₄	—	6	2	no	—
407	C₃×C₄	—	18	1	no	—
408	C₃×C₄	—	18	1	no	—
409	C₃×C₄	—	18	2	no	—
410	C₃×C₄	—	18	1	no	—
411	C₃×C₄	C₃×#235	1	2	yes	—
412	C₃×C₄	C₃×#239	1	2	yes	—
413	Dic₃	—	6	1	no	—
414	Dic₃	—	6	1	no	—
415	Dic₃	—	6	2	no	—
416	Dic₃	—	6	1	no	—
417	C₃²	#5580	1	1	yes	characteristic
418	C₉	—	2	1	no	—
419	C₉	C₃×#529	1	1	yes	characteristic, complemented
420	C₂³	—	9	1	no	—
421	C₂³	—	9	2	no	—
422	Q₈	—	2	2	no	—
423	D₄	—	18	4	no	—
424	D₄	—	18	2	no	—
425	C₂×C₄	—	9	1	no	—
426	C₂×C₄	—	9	1	no	—
427	C₂×C₄	—	9	1	no	—
428	C₂×C₄	—	9	2	no	—
429	C₂×C₄	—	18	2	no	—
430	C₂×C₄	—	18	2	no	—
431	C₂×C₄	—	18	2	no	—
432	C₂×C₄	—	18	4	no	—
433	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
434	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
435	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
436	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
437	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
438	C₂×C₃	—	3	1	no	—
439	C₂×C₃	—	3	1	no	—
440	C₂×C₃	—	3	1	no	—
441	C₂×C₃	—	18	2	no	—
442	C₂×C₃	—	36	2	no	—
443	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
444	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
445	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
446	D₃	—	6	2	no	—
447	D₃	—	12	2	no	—
448	C₂²	—	9	2	no	—
449	C₂²	—	18	1	no	—
450	C₂²	—	18	1	no	—
451	C₂²	—	18	2	no	—
452	C₂²	—	18	2	no	—
453	C₂²	—	18	2	no	—
454	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	2	no	—
458	C₄	—	18	1	no	—
459	C₄	—	18	1	no	—
460	C₄	—	18	2	no	—
461	C₄	—	18	1	no	—
462	C₄	#3697⋊C₃	1	2	yes	—
463	C₄	#88724	1	2	yes	—
464	C₃	—	3	1	no	—
465	C₃	C₃×#5580	1	1	yes	characteristic
466	C₂	—	18	2	no	—
467	C₂	—	36	2	no	—
468	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
469	C₂	C₂×#88724	1	1	yes	characteristic
470	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×AGL(1,ℤ/9)
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini, socle	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₄×Q₈×3₋¹⁺²	C₂
prime radical	#63457⋊C₃	C₂
hypercenter	C₄×Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#529
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₄×Q₈×3₋¹⁺²	C₂	semidirect
2. #63509⋊C₃	C₂	semidirect
3. #63508⋊C₃	C₂	semidirect
4. #63460⋊C₃	C₂	semidirect
6. #63456⋊C₃	C₂	semidirect
7. #63452⋊C₃	C₂	semidirect
8. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
9. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
10. #63434⋊C₃	C₂	semidirect
11. C₄²×AGL(1,ℤ/9)	C₂	semidirect
13. #10589682	C₃	semidirect
49. C₄×Q₈×C₉	C₂×C₃	semidirect
50. #63509	C₂×C₃	semidirect
51. #63508	C₂×C₃	semidirect
52. #63460	C₂×C₃	semidirect
54. #63456	C₂×C₃	semidirect
55. #63452	C₂×C₃	semidirect
56. C₄×D₃₆	C₂×C₃	semidirect
57. C₄×D₃₆	C₂×C₃	semidirect
58. #63434	C₂×C₃	semidirect
59. C₄²×D₉	C₂×C₃	semidirect
307. C₄×Q₈	AGL(1,ℤ/9)	semidirect
312. 3₋¹⁺²	#529	semidirect
419. C₉	C₃×#529	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×3₋¹⁺²	2
#63509⋊C₃	2
#63508⋊C₃	2
#63460⋊C₃	2
#63457⋊C₃	2
#63456⋊C₃	2
#63452⋊C₃	2
C₄×C₄⋊AGL(1,ℤ/9)	2
#63434⋊C₃	2
C₄²×AGL(1,ℤ/9)	2
C₃×#5580	3
#10589682	3

Subgroups — #10589682⋊C3 #13152741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589682⋊C₃ #13152741