Subgroups — #10589683⋊C₃ #13152742

Order 1728.

677 conjugacy classes of subgroups.

The subgroup lattice has 460 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	#63508⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63508⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63456⋊C₃	C₂	1	2	yes	maximal
5	#63454⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
7	#63451⋊C₃	C₂	1	2	yes	maximal, complemented
8	#11721396	C₂	1	2	yes	maximal, complemented
9	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
10	#63434⋊C₃	C₂	1	2	yes	maximal, complemented
11	#63432⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5581	—	3	1	no	maximal
13	#10589683	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	1	yes	characteristic
16	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
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	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
20	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
21	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
22	C₄²×3₋¹⁺²	C₂²	1	2	yes	—
23	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
24	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
25	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
26	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
27	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
28	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
29	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
30	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
31	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
32	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
33	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
34	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
35	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
36	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
37	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
38	C₃×#946	—	3	1	no	—
39	C₃×#946	—	3	1	no	—
40	C₃×#894	—	3	2	no	—
41	C₃×#892	—	3	1	no	—
42	C₃×D₃×C₄⋊C₄	—	3	1	no	—
43	C₃×#889	—	3	2	no	—
44	C₃×#876	—	3	2	no	—
45	C₃×C₄×D₁₂	—	3	1	no	—
46	C₃×#872	—	3	2	no	—
47	C₃×#870	—	3	1	no	—
48	C₄×Q₈×C₉	—	2	1	no	—
49	C₄×Q₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
50	#63508	C₂×C₃	1	1	yes	characteristic, complemented
51	#63508	C₂×C₃	1	1	yes	characteristic, complemented
52	#63456	C₂×C₃	1	2	yes	—
53	#63454	C₂×C₃	1	1	yes	characteristic, complemented
54	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
55	#63451	C₂×C₃	1	2	yes	complemented
56	#63438	C₂×C₃	1	2	yes	complemented
57	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic
58	#63434	C₂×C₃	1	2	yes	complemented
59	#63432	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
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	2	yes	—
64	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	no	—
73	C₄×AGL(1,ℤ/9)	—	2	4	no	—
74	C₄×AGL(1,ℤ/9)	—	2	2	no	—
75	C₄×AGL(1,ℤ/9)	—	2	2	no	—
76	C₃×#552	—	9	1	no	—
77	#5581	—	3	1	no	—
78	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃×D₁₂	—	3	1	no	—
80	C₂×C₃×C₄×D₃	—	3	2	no	—
81	C₂×C₃×C₄×D₃	—	3	1	no	—
82	C₂×C₃×C₄×D₃	—	3	1	no	—
83	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
84	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
85	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₄²	C₂×D₃	1	2	yes	—
87	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
88	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
89	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
90	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
91	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
92	C₃×C₄⋊Dic₃	—	3	1	no	—
93	C₃×C₄⋊Dic₃	—	3	1	no	—
94	C₃×C₄⋊Dic₃	—	3	1	no	—
95	C₃×Dic₃⋊C₄	—	3	2	no	—
96	C₃×Dic₃⋊C₄	—	3	2	no	—
97	C₃×Dic₃⋊C₄	—	3	2	no	—
98	C₃×Dic₃⋊C₄	—	3	2	no	—
99	C₃×Dic₃⋊C₄	—	3	2	no	—
100	C₃×C₄×Dic₃	—	3	2	no	—
101	C₂×Q₈×C₉	—	2	1	no	—
102	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
103	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
107	C₉×C₄⋊C₄	—	2	2	no	—
108	C₉×C₄⋊C₄	—	2	1	no	—
109	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₄²×C₉	—	2	1	no	—
112	C₄²×C₉	—	2	2	no	—
113	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
114	C₄²×C₉	C₂²×C₃	1	2	yes	—
115	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
116	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
117	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
118	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
120	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
121	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
122	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
123	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
124	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
125	Dic₉⋊C₄	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	2	yes	—
129	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
130	C₂×AGL(1,ℤ/9)	—	2	1	no	—
131	C₂×AGL(1,ℤ/9)	—	2	1	no	—
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	1	no	—
135	C₂×AGL(1,ℤ/9)	#41	1	2	yes	—
136	C₄×3₋¹⁺²	—	2	2	no	—
137	C₄×3₋¹⁺²	—	2	2	no	—
138	C₄×3₋¹⁺²	—	2	1	no	—
139	C₄×3₋¹⁺²	—	2	1	no	—
140	C₄×3₋¹⁺²	#41	1	2	yes	—
141	3₋¹⁺²⋊C₄	—	2	1	no	—
142	3₋¹⁺²⋊C₄	—	2	1	no	—
143	3₋¹⁺²⋊C₄	—	2	2	no	—
144	3₋¹⁺²⋊C₄	—	2	2	no	—
145	C₃×#126	—	9	2	no	—
146	C₃×#125	—	9	1	no	—
147	C₃×#125	—	9	2	no	—
148	C₃×#123	—	9	2	no	—
149	C₃×C₂²⋊Q₈	—	9	1	no	—
150	C₃×C₂²⋊Q₈	—	9	1	no	—
151	C₃×C₄×Q₈	—	3	1	no	—
152	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
153	C₃×C₄×D₄	—	9	1	no	—
154	C₃×#117	—	9	2	no	—
155	C₃×#117	—	9	1	no	—
156	C₂×C₃×C₄⋊C₄	—	9	1	no	—
157	#946	—	3	1	no	—
158	#946	—	3	1	no	—
159	#894	—	3	2	no	—
160	#892	—	3	1	no	—
161	D₃×C₄⋊C₄	—	3	1	no	—
162	#889	—	3	2	no	—
163	#876	—	3	2	no	—
164	C₄×D₁₂	—	3	1	no	—
165	#872	—	3	2	no	—
166	#870	—	3	1	no	—
167	C₂²×C₃×D₃	—	3	1	no	—
168	C₂²×C₃×D₃	—	3	1	no	—
169	C₃²×Q₈	—	2	2	no	—
170	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
171	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
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	1	yes	characteristic
175	C₂×C₃×Dic₃	—	3	1	no	—
176	C₂×C₃×Dic₃	—	3	2	no	—
177	C₂×C₃×Dic₃	—	3	1	no	—
178	C₂×C₃×Dic₃	—	3	2	no	—
179	C₃×D₁₂	—	6	2	no	—
180	C₃×C₄×D₃	—	6	4	no	—
181	C₃×C₄×D₃	—	6	2	no	—
182	C₃×C₄×D₃	—	6	2	no	—
183	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
184	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
185	Q₈×C₉	—	2	4	no	—
186	Q₈×C₉	—	2	2	no	—
187	C₂×C₄×C₉	—	2	1	no	—
188	C₂×C₄×C₉	—	2	2	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	2	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
193	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
196	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
197	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
198	C₂×Dic₉	C₂³×C₃	1	2	yes	—
199	C₂×Dic₉	C₂³×C₃	1	2	yes	—
200	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
201	D₃₆	—	2	2	no	—
202	C₄×D₉	—	2	4	no	—
203	C₄×D₉	—	2	2	no	—
204	C₄×D₉	—	2	2	no	—
205	#552	—	9	1	no	Sylow
206	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
207	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
208	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
209	AGL(1,ℤ/9)	—	2	2	no	—
210	AGL(1,ℤ/9)	—	4	1	no	—
211	C₂×C₃×Q₈	—	3	1	no	—
212	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
213	C₂×C₃×D₄	—	9	1	no	—
214	C₂²×C₃×C₄	—	9	2	no	—
215	C₂²×C₃×C₄	—	9	1	no	—
216	C₂²×C₃×C₄	—	9	1	no	—
217	C₂×D₁₂	—	3	1	no	—
218	C₂×C₄×D₃	—	3	2	no	—
219	C₂×C₄×D₃	—	3	1	no	—
220	C₂×C₄×D₃	—	3	1	no	—
221	C₃×C₄⋊C₄	—	3	1	no	—
222	C₃×C₄⋊C₄	—	3	2	no	—
223	C₃×C₄⋊C₄	—	9	2	no	—
224	C₃×C₄⋊C₄	—	9	2	no	—
225	C₃×C₄⋊C₄	—	9	2	no	—
226	C₃×C₄⋊C₄	—	9	2	no	—
227	C₃×C₄⋊C₄	—	9	2	no	—
228	C₃×C₄⋊C₄	—	9	1	no	—
229	C₃×C₄⋊C₄	—	9	1	no	—
230	C₃×C₄⋊C₄	—	9	1	no	—
231	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
232	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
233	C₃×C₂²⋊C₄	—	9	1	no	—
234	C₃×C₂²⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	—	9	2	no	—
236	C₃×C₂²⋊C₄	—	9	1	no	—
237	C₃×C₂²⋊C₄	—	9	2	no	—
238	C₃×C₄²	—	3	2	no	—
239	C₃×C₄²	—	3	1	no	—
240	C₃×C₄²	—	9	2	no	—
241	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
242	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
243	(C₂×D₃)⋊C₄	—	3	1	no	—
244	(C₂×D₃)⋊C₄	—	3	2	no	—
245	(C₂×D₃)⋊C₄	—	3	1	no	—
246	(C₂×D₃)⋊C₄	—	3	2	no	—
247	(C₂×D₃)⋊C₄	—	3	2	no	—
248	C₄⋊Dic₃	—	3	1	no	—
249	C₄⋊Dic₃	—	3	1	no	—
250	C₄⋊Dic₃	—	3	1	no	—
251	Dic₃⋊C₄	—	3	2	no	—
252	Dic₃⋊C₄	—	3	2	no	—
253	Dic₃⋊C₄	—	3	2	no	—
254	Dic₃⋊C₄	—	3	2	no	—
255	Dic₃⋊C₄	—	3	2	no	—
256	C₄×Dic₃	—	3	2	no	—
257	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
258	C₂×C₃×D₃	—	3	2	no	—
259	C₂×C₃×D₃	—	6	1	no	—
260	C₂×C₃×D₃	—	6	1	no	—
261	C₂×C₃×D₃	—	6	1	no	—
262	C₂×C₃×D₃	—	6	1	no	—
263	C₂×C₃×D₃	—	6	1	no	—
264	C₃²×C₄	—	2	2	no	—
265	C₃²×C₄	—	2	1	no	—
266	C₃²×C₄	—	2	2	no	—
267	C₃²×C₄	—	2	1	no	—
268	C₃²×C₄	#235	1	2	yes	—
269	C₃×Dic₃	—	6	1	no	—
270	C₃×Dic₃	—	6	1	no	—
271	C₃×Dic₃	—	6	2	no	—
272	C₃×Dic₃	—	6	2	no	—
273	C₂²×C₉	—	2	1	no	—
274	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
275	C₂×D₉	—	2	1	no	—
276	C₂×D₉	—	2	1	no	—
277	C₂×D₉	—	2	1	no	—
278	C₂×D₉	—	2	1	no	—
279	C₂×D₉	—	2	1	no	—
280	C₂×D₉	C₃×#41	1	2	yes	—
281	C₄×C₉	—	2	2	no	—
282	C₄×C₉	—	2	4	no	—
283	C₄×C₉	—	2	2	no	—
284	C₄×C₉	—	2	1	no	—
285	C₄×C₉	—	2	2	no	—
286	C₄×C₉	—	2	1	no	—
287	C₄×C₉	—	2	2	no	—
288	C₄×C₉	—	4	2	no	—
289	C₄×C₉	—	4	1	no	—
290	C₄×C₉	C₃×#41	1	2	yes	—
291	Dic₉	—	2	1	no	—
292	Dic₉	—	2	1	no	—
293	Dic₉	—	2	2	no	—
294	Dic₉	—	2	2	no	—
295	#126	—	9	2	no	—
296	#125	—	9	2	no	—
297	#125	—	9	1	no	—
298	#123	—	9	2	no	—
299	C₂²⋊Q₈	—	9	1	no	—
300	C₂²⋊Q₈	—	9	1	no	—
301	C₄×Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
302	C₄×D₄	—	9	1	no	—
303	#117	—	9	1	no	—
304	#117	—	9	2	no	—
305	C₂×C₄⋊C₄	—	9	1	no	—
306	3₋¹⁺²	#552	1	1	yes	characteristic, complemented, Sylow
307	C₂³×C₃	—	9	1	no	—
308	C₂³×C₃	—	9	1	no	—
309	C₂²×D₃	—	3	1	no	—
310	C₂²×D₃	—	3	1	no	—
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	6	2	no	—
313	C₃×D₄	—	18	2	no	—
314	C₂×C₃×C₄	—	3	1	no	—
315	C₂×C₃×C₄	—	3	1	no	—
316	C₂×C₃×C₄	—	3	2	no	—
317	C₂×C₃×C₄	—	3	2	no	—
318	C₂×C₃×C₄	—	3	1	no	—
319	C₂×C₃×C₄	—	9	1	no	—
320	C₂×C₃×C₄	—	9	2	no	—
321	C₂×C₃×C₄	—	9	1	no	—
322	C₂×C₃×C₄	—	9	2	no	—
323	C₂×C₃×C₄	—	18	2	no	—
324	C₂×C₃×C₄	—	18	2	no	—
325	C₂×C₃×C₄	—	18	4	no	—
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
330	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
331	C₂×Dic₃	—	3	1	no	—
332	C₂×Dic₃	—	3	2	no	—
333	C₂×Dic₃	—	3	1	no	—
334	C₂×Dic₃	—	3	2	no	—
335	D₁₂	—	6	2	no	—
336	C₄×D₃	—	6	4	no	—
337	C₄×D₃	—	6	2	no	—
338	C₄×D₃	—	6	2	no	—
339	C₂×C₃²	C₂×#235	1	1	yes	characteristic
340	C₂×C₃²	#1007	1	1	yes	characteristic
341	C₂×C₃²	D₃×#41	1	1	yes	characteristic
342	C₃×D₃	—	6	2	no	—
343	C₃×D₃	—	12	1	no	—
344	C₂×C₉	—	2	1	no	—
345	C₂×C₉	—	2	1	no	—
346	C₂×C₉	—	2	1	no	—
347	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
348	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
349	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
350	D₉	—	2	2	no	—
351	D₉	—	4	1	no	—
352	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
353	C₂×D₄	—	9	1	no	—
354	C₂²×C₄	—	9	2	no	—
355	C₂²×C₄	—	9	1	no	—
356	C₂²×C₄	—	9	1	no	—
357	C₄⋊C₄	—	9	1	no	—
358	C₄⋊C₄	—	9	2	no	—
359	C₄⋊C₄	—	9	2	no	—
360	C₄⋊C₄	—	9	1	no	—
361	C₄⋊C₄	—	9	2	no	—
362	C₄⋊C₄	—	9	1	no	—
363	C₄⋊C₄	—	9	2	no	—
364	C₄⋊C₄	—	9	2	no	—
365	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
366	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
367	C₂²⋊C₄	—	9	1	no	—
368	C₂²⋊C₄	—	9	2	no	—
369	C₂²⋊C₄	—	9	2	no	—
370	C₂²⋊C₄	—	9	1	no	—
371	C₂²⋊C₄	—	9	2	no	—
372	C₄²	—	9	2	no	—
373	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
374	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
375	C₂²×C₃	—	3	1	no	—
376	C₂²×C₃	—	9	2	no	—
377	C₂²×C₃	—	18	1	no	—
378	C₂²×C₃	—	18	1	no	—
379	C₂²×C₃	—	18	1	no	—
380	C₂²×C₃	—	18	1	no	—
381	C₂²×C₃	—	18	1	no	—
382	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
383	C₂×D₃	—	3	2	no	—
384	C₂×D₃	—	6	1	no	—
385	C₂×D₃	—	6	1	no	—
386	C₂×D₃	—	6	1	no	—
387	C₂×D₃	—	6	1	no	—
388	C₂×D₃	—	6	1	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	3	2	no	—
394	C₃×C₄	—	6	2	no	—
395	C₃×C₄	—	6	1	no	—
396	C₃×C₄	—	6	2	no	—
397	C₃×C₄	—	6	1	no	—
398	C₃×C₄	—	18	1	no	—
399	C₃×C₄	—	18	1	no	—
400	C₃×C₄	—	18	2	no	—
401	C₃×C₄	—	18	2	no	—
402	C₃×C₄	C₃×#235	1	2	yes	—
403	Dic₃	—	6	1	no	—
404	Dic₃	—	6	1	no	—
405	Dic₃	—	6	2	no	—
406	Dic₃	—	6	2	no	—
407	C₃²	#5581	1	1	yes	characteristic
408	C₉	—	2	1	no	—
409	C₉	C₃×#552	1	1	yes	characteristic, complemented
410	C₂³	—	9	1	no	—
411	C₂³	—	9	1	no	—
412	Q₈	—	2	2	no	—
413	D₄	—	18	2	no	—
414	C₂×C₄	—	9	1	no	—
415	C₂×C₄	—	9	2	no	—
416	C₂×C₄	—	9	1	no	—
417	C₂×C₄	—	9	2	no	—
418	C₂×C₄	—	18	4	no	—
419	C₂×C₄	—	18	2	no	—
420	C₂×C₄	—	18	2	no	—
421	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
422	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
423	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
424	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
425	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
426	C₂×C₃	—	3	1	no	—
427	C₂×C₃	—	3	1	no	—
428	C₂×C₃	—	3	1	no	—
429	C₂×C₃	—	18	2	no	—
430	C₂×C₃	—	36	1	no	—
431	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
432	C₂×C₃	C₃×#1007	1	1	yes	characteristic
433	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
434	D₃	—	6	2	no	—
435	D₃	—	12	1	no	—
436	C₂²	—	9	2	no	—
437	C₂²	—	18	1	no	—
438	C₂²	—	18	1	no	—
439	C₂²	—	18	1	no	—
440	C₂²	—	18	1	no	—
441	C₂²	—	18	1	no	—
442	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	1	no	—
447	C₄	—	18	1	no	—
448	C₄	—	18	1	no	—
449	C₄	—	18	2	no	—
450	C₄	—	18	2	no	—
451	C₄	#3697⋊C₃	1	2	yes	—
452	C₃	—	3	1	no	—
453	C₃	C₃×#5581	1	1	yes	characteristic
454	C₂	—	18	2	no	—
455	C₂	—	36	1	no	—
456	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
457	C₂	#11722630	1	1	yes	characteristic
458	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×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	C₂×C₄⋊AGL(1,ℤ/9)	C₂²
hypercenter	C₄×Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#552
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ 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. #63508⋊C₃	C₂	semidirect
3. #63508⋊C₃	C₂	semidirect
5. #63454⋊C₃	C₂	semidirect
6. C₄⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
7. #63451⋊C₃	C₂	semidirect
8. #11721396	C₂	semidirect
10. #63434⋊C₃	C₂	semidirect
11. #63432⋊C₃	C₂	semidirect
13. #10589683	C₃	semidirect
49. C₄×Q₈×C₉	C₂×C₃	semidirect
50. #63508	C₂×C₃	semidirect
51. #63508	C₂×C₃	semidirect
53. #63454	C₂×C₃	semidirect
54. C₄⋊C₄×D₉	C₂×C₃	semidirect
55. #63451	C₂×C₃	semidirect
56. #63438	C₂×C₃	semidirect
58. #63434	C₂×C₃	semidirect
59. #63432	C₂×C₃	semidirect
301. C₄×Q₈	AGL(1,ℤ/9)	semidirect
306. 3₋¹⁺²	#552	semidirect
409. C₉	C₃×#552	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
#63508⋊C₃	2
#63456⋊C₃	2
#63454⋊C₃	2
C₄⋊C₄×AGL(1,ℤ/9)	2
#63451⋊C₃	2
#11721396	2
C₄×C₄⋊AGL(1,ℤ/9)	2
#63434⋊C₃	2
#63432⋊C₃	2
C₃×#5581	3
#10589683	3

Subgroups — #10589683⋊C3 #13152742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589683⋊C₃ #13152742