Subgroups — #10589685⋊C₃ #13152744

Order 1728.

611 conjugacy classes of subgroups.

The subgroup lattice has 430 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
3	#63506⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63460⋊C₃	C₂	1	2	yes	maximal
5	#63459⋊C₃	C₂	1	1	yes	maximal, characteristic
6	#63452⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63451⋊C₃	C₂	1	2	yes	maximal, complemented
8	#11721396	C₂	1	2	yes	maximal
9	#63434⋊C₃	C₂	1	1	yes	maximal, characteristic
10	#63432⋊C₃	C₂	1	2	yes	maximal, complemented
11	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5583	—	3	1	no	maximal
13	#10589685	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	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
18	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₄²×3₋¹⁺²	C₂²	1	2	yes	—
21	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
22	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
23	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
24	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
25	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
26	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
27	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
28	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
29	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
30	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
35	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
36	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
37	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
38	C₃×#946	—	3	1	no	—
39	C₃×#944	—	3	1	no	—
40	C₃×#898	—	3	2	no	—
41	C₃×#897	—	3	1	no	—
42	C₃×#890	—	3	1	no	—
43	C₃×#889	—	3	2	no	—
44	C₃×#876	—	3	2	no	—
45	C₃×#872	—	3	1	no	—
46	C₃×#870	—	3	2	no	—
47	C₃×C₄×Dic₆	—	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
51	#63506	C₂×C₃	1	1	yes	characteristic, complemented
52	#63460	C₂×C₃	1	2	yes	—
53	#63459	C₂×C₃	1	1	yes	characteristic
54	#63452	C₂×C₃	1	1	yes	characteristic, complemented
55	#63451	C₂×C₃	1	2	yes	complemented
56	#63438	C₂×C₃	1	2	yes	—
57	#63434	C₂×C₃	1	1	yes	characteristic
58	#63432	C₂×C₃	1	2	yes	complemented
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
61	Q₈×3₋¹⁺²	—	2	2	no	—
62	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
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	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
71	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
72	C₄×AGL(1,ℤ/9)	—	2	2	no	—
73	3₋¹⁺²⋊Q₈	—	2	2	no	—
74	C₃×#541	—	9	1	no	—
75	#5583	—	3	1	no	—
76	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
77	C₂×C₃×C₄×D₃	—	3	1	no	—
78	C₂×C₃×Dic₆	—	3	1	no	—
79	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
80	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
81	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
82	C₃²×C₄²	C₂×D₃	1	2	yes	—
83	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
84	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
85	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
86	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
87	C₃×C₄⋊Dic₃	—	3	2	no	—
88	C₃×C₄⋊Dic₃	—	3	2	no	—
89	C₃×C₄⋊Dic₃	—	3	1	no	—
90	C₃×Dic₃⋊C₄	—	3	1	no	—
91	C₃×Dic₃⋊C₄	—	3	2	no	—
92	C₃×Dic₃⋊C₄	—	3	2	no	—
93	C₃×Dic₃⋊C₄	—	3	2	no	—
94	C₃×Dic₃⋊C₄	—	3	2	no	—
95	C₃×Dic₃⋊C₄	—	3	2	no	—
96	C₃×Dic₃⋊C₄	—	3	1	no	—
97	C₃×C₄×Dic₃	—	3	2	no	—
98	C₃×C₄×Dic₃	—	3	1	no	—
99	C₂×Q₈×C₉	—	2	1	no	—
100	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
102	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
103	C₉×C₄⋊C₄	—	2	2	no	—
104	C₉×C₄⋊C₄	—	2	1	no	—
105	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₄²×C₉	—	2	1	no	—
108	C₄²×C₉	—	2	2	no	—
109	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
110	C₄²×C₉	C₂²×C₃	1	2	yes	—
111	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
112	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
115	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
116	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
117	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
118	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
119	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
120	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
125	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
126	C₄×Dic₉	C₂²×C₃	1	2	yes	—
127	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
128	C₂×AGL(1,ℤ/9)	—	2	1	no	—
129	C₂×AGL(1,ℤ/9)	—	2	1	no	—
130	C₂×AGL(1,ℤ/9)	—	2	1	no	—
131	C₄×3₋¹⁺²	—	2	2	no	—
132	C₄×3₋¹⁺²	—	2	1	no	—
133	C₄×3₋¹⁺²	—	2	1	no	—
134	C₄×3₋¹⁺²	—	2	2	no	—
135	C₄×3₋¹⁺²	#41	1	2	yes	—
136	3₋¹⁺²⋊C₄	—	2	2	no	—
137	3₋¹⁺²⋊C₄	—	2	1	no	—
138	3₋¹⁺²⋊C₄	—	2	2	no	—
139	3₋¹⁺²⋊C₄	—	2	1	no	—
140	3₋¹⁺²⋊C₄	—	2	1	no	—
141	C₃×C₄⋊Q₈	—	9	1	no	—
142	C₃×#126	—	9	2	no	—
143	C₃×#126	—	9	2	no	—
144	C₃×#125	—	9	2	no	—
145	C₃×#125	—	9	2	no	—
146	C₃×#125	—	9	1	no	—
147	C₃×C₂²⋊Q₈	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	1	no	—
149	C₃×C₄×Q₈	—	3	1	no	—
150	C₃×C₄×Q₈	—	9	1	no	—
151	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
152	C₃×#117	—	9	1	no	—
153	#946	—	3	1	no	—
154	#944	—	3	1	no	—
155	#898	—	3	2	no	—
156	#897	—	3	1	no	—
157	#890	—	3	1	no	—
158	#889	—	3	2	no	—
159	#876	—	3	2	no	—
160	#872	—	3	1	no	—
161	#870	—	3	2	no	—
162	C₄×Dic₆	—	3	1	no	—
163	C₂²×C₃×D₃	—	3	1	no	—
164	C₃²×Q₈	—	2	2	no	—
165	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
167	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
168	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
169	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₃×Dic₃	—	3	1	no	—
171	C₂×C₃×Dic₃	—	3	2	no	—
172	C₂×C₃×Dic₃	—	3	1	no	—
173	C₂×C₃×Dic₃	—	3	2	no	—
174	C₂×C₃×Dic₃	—	3	1	no	—
175	C₃×C₄×D₃	—	6	2	no	—
176	C₃×Dic₆	—	6	2	no	—
177	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
178	Q₈×C₉	—	2	4	no	—
179	Q₈×C₉	—	2	2	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	2	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	2	no	—
185	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
188	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
189	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
190	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
191	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
192	C₂×Dic₉	C₂³×C₃	1	2	yes	—
193	C₂×Dic₉	C₂³×C₃	1	2	yes	—
194	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
195	C₄×D₉	—	2	2	no	—
196	Dic₁₈	—	2	2	no	—
197	#541	—	9	1	no	Sylow
198	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
199	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
201	AGL(1,ℤ/9)	—	4	1	no	—
202	C₂×C₃×Q₈	—	3	1	no	—
203	C₂×C₃×Q₈	—	9	1	no	—
204	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
205	C₂²×C₃×C₄	—	9	1	no	—
206	C₂×C₄×D₃	—	3	1	no	—
207	C₂×Dic₆	—	3	1	no	—
208	C₃×C₄⋊C₄	—	3	1	no	—
209	C₃×C₄⋊C₄	—	3	2	no	—
210	C₃×C₄⋊C₄	—	9	1	no	—
211	C₃×C₄⋊C₄	—	9	1	no	—
212	C₃×C₄⋊C₄	—	9	2	no	—
213	C₃×C₄⋊C₄	—	9	2	no	—
214	C₃×C₄⋊C₄	—	9	2	no	—
215	C₃×C₄⋊C₄	—	9	2	no	—
216	C₃×C₄⋊C₄	—	9	2	no	—
217	C₃×C₄⋊C₄	—	9	1	no	—
218	C₃×C₄⋊C₄	—	9	2	no	—
219	C₃×C₄⋊C₄	—	9	2	no	—
220	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
221	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
222	C₃×C₂²⋊C₄	—	9	1	no	—
223	C₃×C₂²⋊C₄	—	9	1	no	—
224	C₃×C₂²⋊C₄	—	9	2	no	—
225	C₃×C₂²⋊C₄	—	9	2	no	—
226	C₃×C₄²	—	3	1	no	—
227	C₃×C₄²	—	3	2	no	—
228	C₃×C₄²	—	9	1	no	—
229	C₃×C₄²	—	9	2	no	—
230	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
231	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
232	(C₂×D₃)⋊C₄	—	3	1	no	—
233	(C₂×D₃)⋊C₄	—	3	1	no	—
234	(C₂×D₃)⋊C₄	—	3	2	no	—
235	(C₂×D₃)⋊C₄	—	3	2	no	—
236	C₄⋊Dic₃	—	3	1	no	—
237	C₄⋊Dic₃	—	3	2	no	—
238	C₄⋊Dic₃	—	3	2	no	—
239	Dic₃⋊C₄	—	3	2	no	—
240	Dic₃⋊C₄	—	3	1	no	—
241	Dic₃⋊C₄	—	3	2	no	—
242	Dic₃⋊C₄	—	3	2	no	—
243	Dic₃⋊C₄	—	3	1	no	—
244	Dic₃⋊C₄	—	3	2	no	—
245	Dic₃⋊C₄	—	3	2	no	—
246	C₄×Dic₃	—	3	2	no	—
247	C₄×Dic₃	—	3	1	no	—
248	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
249	C₂×C₃×D₃	—	6	1	no	—
250	C₂×C₃×D₃	—	6	1	no	—
251	C₂×C₃×D₃	—	6	1	no	—
252	C₃²×C₄	—	2	2	no	—
253	C₃²×C₄	—	2	1	no	—
254	C₃²×C₄	—	2	1	no	—
255	C₃²×C₄	—	2	2	no	—
256	C₃²×C₄	#235	1	2	yes	—
257	C₃×Dic₃	—	6	2	no	—
258	C₃×Dic₃	—	6	1	no	—
259	C₃×Dic₃	—	6	2	no	—
260	C₃×Dic₃	—	6	1	no	—
261	C₃×Dic₃	—	6	1	no	—
262	C₂²×C₉	—	2	1	no	—
263	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
264	C₂×D₉	—	2	1	no	—
265	C₂×D₉	—	2	1	no	—
266	C₂×D₉	—	2	1	no	—
267	C₄×C₉	—	2	2	no	—
268	C₄×C₉	—	2	4	no	—
269	C₄×C₉	—	2	2	no	—
270	C₄×C₉	—	2	1	no	—
271	C₄×C₉	—	2	1	no	—
272	C₄×C₉	—	2	2	no	—
273	C₄×C₉	—	2	2	no	—
274	C₄×C₉	—	4	1	no	—
275	C₄×C₉	—	4	2	no	—
276	C₄×C₉	C₃×#41	1	2	yes	—
277	Dic₉	—	2	2	no	—
278	Dic₉	—	2	1	no	—
279	Dic₉	—	2	1	no	—
280	Dic₉	—	2	2	no	—
281	Dic₉	—	2	1	no	—
282	C₄⋊Q₈	—	9	1	no	—
283	#126	—	9	2	no	—
284	#126	—	9	2	no	—
285	#125	—	9	2	no	—
286	#125	—	9	1	no	—
287	#125	—	9	2	no	—
288	C₂²⋊Q₈	—	9	1	no	—
289	C₂²⋊Q₈	—	9	1	no	—
290	C₄×Q₈	—	9	1	no	—
291	C₄×Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
292	#117	—	9	1	no	—
293	3₋¹⁺²	#541	1	1	yes	characteristic, complemented, Sylow
294	C₂³×C₃	—	9	1	no	—
295	C₂²×D₃	—	3	1	no	—
296	C₃×Q₈	—	2	2	no	—
297	C₃×Q₈	—	6	2	no	—
298	C₃×Q₈	—	18	2	no	—
299	C₂×C₃×C₄	—	3	1	no	—
300	C₂×C₃×C₄	—	3	1	no	—
301	C₂×C₃×C₄	—	3	1	no	—
302	C₂×C₃×C₄	—	3	2	no	—
303	C₂×C₃×C₄	—	3	2	no	—
304	C₂×C₃×C₄	—	9	1	no	—
305	C₂×C₃×C₄	—	9	1	no	—
306	C₂×C₃×C₄	—	9	2	no	—
307	C₂×C₃×C₄	—	9	2	no	—
308	C₂×C₃×C₄	—	9	1	no	—
309	C₂×C₃×C₄	—	18	2	no	—
310	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
313	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
314	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
315	C₂×Dic₃	—	3	1	no	—
316	C₂×Dic₃	—	3	2	no	—
317	C₂×Dic₃	—	3	1	no	—
318	C₂×Dic₃	—	3	2	no	—
319	C₂×Dic₃	—	3	1	no	—
320	C₄×D₃	—	6	2	no	—
321	Dic₆	—	6	2	no	—
322	C₂×C₃²	C₂×#235	1	1	yes	characteristic
323	C₂×C₃²	#1007	1	1	yes	characteristic
324	C₂×C₃²	#1010	1	1	yes	characteristic
325	C₃×D₃	—	12	1	no	—
326	C₂×C₉	—	2	1	no	—
327	C₂×C₉	—	2	1	no	—
328	C₂×C₉	—	2	1	no	—
329	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
330	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
332	D₉	—	4	1	no	—
333	C₂×Q₈	—	9	1	no	—
334	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
335	C₂²×C₄	—	9	1	no	—
336	C₄⋊C₄	—	9	1	no	—
337	C₄⋊C₄	—	9	1	no	—
338	C₄⋊C₄	—	9	1	no	—
339	C₄⋊C₄	—	9	2	no	—
340	C₄⋊C₄	—	9	2	no	—
341	C₄⋊C₄	—	9	2	no	—
342	C₄⋊C₄	—	9	2	no	—
343	C₄⋊C₄	—	9	2	no	—
344	C₄⋊C₄	—	9	2	no	—
345	C₄⋊C₄	—	9	2	no	—
346	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
347	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
348	C₂²⋊C₄	—	9	1	no	—
349	C₂²⋊C₄	—	9	1	no	—
350	C₂²⋊C₄	—	9	2	no	—
351	C₂²⋊C₄	—	9	2	no	—
352	C₄²	—	9	1	no	—
353	C₄²	—	9	2	no	—
354	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
355	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
356	C₂²×C₃	—	3	1	no	—
357	C₂²×C₃	—	18	1	no	—
358	C₂²×C₃	—	18	1	no	—
359	C₂²×C₃	—	18	1	no	—
360	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
361	C₂×D₃	—	6	1	no	—
362	C₂×D₃	—	6	1	no	—
363	C₂×D₃	—	6	1	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	3	2	no	—
369	C₃×C₄	—	6	2	no	—
370	C₃×C₄	—	6	1	no	—
371	C₃×C₄	—	6	1	no	—
372	C₃×C₄	—	6	2	no	—
373	C₃×C₄	—	18	1	no	—
374	C₃×C₄	—	18	2	no	—
375	C₃×C₄	—	18	1	no	—
376	C₃×C₄	—	18	2	no	—
377	C₃×C₄	—	18	1	no	—
378	C₃×C₄	C₃×#235	1	2	yes	—
379	Dic₃	—	6	2	no	—
380	Dic₃	—	6	1	no	—
381	Dic₃	—	6	2	no	—
382	Dic₃	—	6	1	no	—
383	Dic₃	—	6	1	no	—
384	C₃²	#5583	1	1	yes	characteristic
385	C₉	—	2	1	no	—
386	C₉	C₃×#541	1	1	yes	characteristic, complemented
387	C₂³	—	9	1	no	—
388	Q₈	—	2	2	no	—
389	Q₈	—	18	2	no	—
390	C₂×C₄	—	9	1	no	—
391	C₂×C₄	—	9	2	no	—
392	C₂×C₄	—	9	1	no	—
393	C₂×C₄	—	9	2	no	—
394	C₂×C₄	—	9	1	no	—
395	C₂×C₄	—	18	2	no	—
396	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
397	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
398	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
399	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
400	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
401	C₂×C₃	—	3	1	no	—
402	C₂×C₃	—	3	1	no	—
403	C₂×C₃	—	3	1	no	—
404	C₂×C₃	—	36	1	no	—
405	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
406	C₂×C₃	C₃×#1007	1	1	yes	characteristic
407	C₂×C₃	C₃×#1010	1	1	yes	characteristic
408	D₃	—	12	1	no	—
409	C₂²	—	18	1	no	—
410	C₂²	—	18	1	no	—
411	C₂²	—	18	1	no	—
412	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	2	no	—
417	C₄	—	18	1	no	—
418	C₄	—	18	2	no	—
419	C₄	—	18	1	no	—
420	C₄	—	18	2	no	—
421	C₄	—	18	1	no	—
422	C₄	#3697⋊C₃	1	2	yes	—
423	C₃	—	3	1	no	—
424	C₃	C₃×#5583	1	1	yes	characteristic
425	C₂	—	36	1	no	—
426	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
427	C₂	#11722630	1	1	yes	characteristic
428	C₂	#11722642	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	C₂²×AGL(1,ℤ/9)	C₂³
hypercenter	C₄×Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#541
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
3. #63506⋊C₃	C₂	semidirect
6. #63452⋊C₃	C₂	semidirect
7. #63451⋊C₃	C₂	semidirect
10. #63432⋊C₃	C₂	semidirect
11. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
13. #10589685	C₃	semidirect
49. C₄×Q₈×C₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
54. #63452	C₂×C₃	semidirect
55. #63451	C₂×C₃	semidirect
58. #63432	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
291. C₄×Q₈	AGL(1,ℤ/9)	semidirect
293. 3₋¹⁺²	#541	semidirect
386. C₉	C₃×#541	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
#63506⋊C₃	2
#63460⋊C₃	2
#63459⋊C₃	2
#63452⋊C₃	2
#63451⋊C₃	2
#11721396	2
#63434⋊C₃	2
#63432⋊C₃	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5583	3
#10589685	3

Subgroups — #10589685⋊C3 #13152744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589685⋊C₃ #13152744