Subgroups — #10589670⋊C₃ #13152729

Order 1728.

671 conjugacy classes of subgroups.

The subgroup lattice has 442 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
3	#63506⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63460⋊C₃	C₂	1	2	yes	maximal, complemented
5	#63458⋊C₃	C₂	1	2	yes	maximal, complemented
6	#63455⋊C₃	C₂	1	1	yes	maximal, characteristic
7	#63449⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#11721396	C₂	1	2	yes	maximal, complemented
9	#63437⋊C₃	C₂	1	1	yes	maximal, characteristic
10	#63434⋊C₃	C₂	1	2	yes	maximal, complemented
11	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5568	—	3	1	no	maximal
13	#10589670	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	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
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	2	yes	—
27	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
28	C₄⋊(3₋¹⁺²⋊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	1	yes	characteristic
33	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
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×#944	—	3	1	no	—
40	C₃×#898	—	3	2	no	—
41	C₃×#896	—	3	2	no	—
42	C₃×#893	—	3	1	no	—
43	C₃×#887	—	3	1	no	—
44	C₃×#876	—	3	2	no	—
45	C₃×#875	—	3	1	no	—
46	C₃×#872	—	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	#63509	C₂×C₃	1	1	yes	characteristic
51	#63506	C₂×C₃	1	1	yes	characteristic, complemented
52	#63460	C₂×C₃	1	2	yes	complemented
53	#63458	C₂×C₃	1	2	yes	complemented
54	#63455	C₂×C₃	1	1	yes	characteristic
55	#63449	C₂×C₃	1	1	yes	characteristic, complemented
56	#63438	C₂×C₃	1	2	yes	complemented
57	#63437	C₂×C₃	1	1	yes	characteristic
58	#63434	C₂×C₃	1	2	yes	complemented
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×AGL(1,ℤ/9)	C₂³	1	2	yes	—
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	2	yes	—
65	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
71	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
72	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
73	C₄×AGL(1,ℤ/9)	—	2	4	no	—
74	3₋¹⁺²⋊Q₈	—	2	2	no	—
75	3₋¹⁺²⋊Q₈	—	2	2	no	—
76	C₃×#556	—	9	1	no	—
77	#5568	—	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×Dic₆	—	3	1	no	—
82	C₂×C₃×Dic₆	—	3	1	no	—
83	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
84	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
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	2	no	—
91	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
92	C₃×C₄⋊Dic₃	—	3	1	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×Dic₃⋊C₄	—	3	1	no	—
98	C₃×C₄×Dic₃	—	3	2	no	—
99	C₃×C₄×Dic₃	—	3	1	no	—
100	C₃×C₄×Dic₃	—	3	1	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	2	yes	—
105	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
106	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	—	2	2	no	—
109	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
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	2	yes	—
118	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
119	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
120	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
123	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
126	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
127	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
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	2	no	—
131	C₂×AGL(1,ℤ/9)	—	2	2	no	—
132	C₂×AGL(1,ℤ/9)	—	2	2	no	—
133	C₄×3₋¹⁺²	—	2	2	no	—
134	C₄×3₋¹⁺²	—	2	1	no	—
135	C₄×3₋¹⁺²	—	2	2	no	—
136	C₄×3₋¹⁺²	—	2	1	no	—
137	C₄×3₋¹⁺²	#41	1	2	yes	—
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	3₋¹⁺²⋊C₄	—	2	1	no	—
142	3₋¹⁺²⋊C₄	#41	1	2	yes	—
143	C₃×C₄⋊Q₈	—	9	1	no	—
144	C₃×#126	—	9	2	no	—
145	C₃×#126	—	9	2	no	—
146	C₃×#124	—	9	1	no	—
147	C₃×#124	—	9	1	no	—
148	C₃×C₂²⋊Q₈	—	9	2	no	—
149	C₃×C₄×Q₈	—	3	1	no	—
150	C₃×C₄×Q₈	—	9	1	no	—
151	C₃×C₄×Q₈	—	9	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	#947	—	3	1	no	—
156	#944	—	3	1	no	—
157	#898	—	3	2	no	—
158	#896	—	3	2	no	—
159	#893	—	3	1	no	—
160	#887	—	3	1	no	—
161	#876	—	3	2	no	—
162	#875	—	3	1	no	—
163	#872	—	3	2	no	—
164	C₄×Dic₆	—	3	1	no	—
165	C₂²×C₃×D₃	—	3	2	no	—
166	C₃²×Q₈	—	2	2	no	—
167	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
168	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
170	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
171	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₃×Dic₃	—	3	1	no	—
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	1	no	—
175	C₂×C₃×Dic₃	—	3	2	no	—
176	C₂×C₃×Dic₃	—	3	1	no	—
177	C₃×D₁₂	—	6	2	no	—
178	C₃×C₄×D₃	—	6	4	no	—
179	C₃×Dic₆	—	6	2	no	—
180	C₃×Dic₆	—	6	2	no	—
181	C₂²×D₉	C₂³×C₃	1	2	yes	—
182	Q₈×C₉	—	2	4	no	—
183	Q₈×C₉	—	2	2	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	2	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	2	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
190	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
192	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
194	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
196	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
197	C₂×Dic₉	C₂³×C₃	1	2	yes	—
198	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
199	D₃₆	—	2	2	no	—
200	C₄×D₉	—	2	4	no	—
201	Dic₁₈	—	2	2	no	—
202	Dic₁₈	—	2	2	no	—
203	#556	—	9	1	no	Sylow
204	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
205	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
206	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
207	AGL(1,ℤ/9)	—	4	2	no	—
208	C₂×C₃×Q₈	—	3	1	no	—
209	C₂×C₃×Q₈	—	9	1	no	—
210	C₂×C₃×Q₈	—	9	1	no	—
211	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
212	C₂×C₃×D₄	—	9	1	no	—
213	C₂²×C₃×C₄	—	9	2	no	—
214	C₂×D₁₂	—	3	1	no	—
215	C₂×C₄×D₃	—	3	2	no	—
216	C₂×Dic₆	—	3	1	no	—
217	C₂×Dic₆	—	3	1	no	—
218	C₃×C₄⋊C₄	—	3	1	no	—
219	C₃×C₄⋊C₄	—	3	2	no	—
220	C₃×C₄⋊C₄	—	9	1	no	—
221	C₃×C₄⋊C₄	—	9	2	no	—
222	C₃×C₄⋊C₄	—	9	2	no	—
223	C₃×C₄⋊C₄	—	9	1	no	—
224	C₃×C₄⋊C₄	—	9	2	no	—
225	C₃×C₄⋊C₄	—	9	1	no	—
226	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
227	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
228	C₃×C₂²⋊C₄	—	9	2	no	—
229	C₃×C₂²⋊C₄	—	9	2	no	—
230	C₃×C₂²⋊C₄	—	9	2	no	—
231	C₃×C₂²⋊C₄	—	9	2	no	—
232	C₃×C₂²⋊C₄	—	9	2	no	—
233	C₃×C₄²	—	3	2	no	—
234	C₃×C₄²	—	3	1	no	—
235	C₃×C₄²	—	9	2	no	—
236	C₃×C₄²	—	9	1	no	—
237	C₃×C₄²	—	9	1	no	—
238	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
239	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
240	(C₂×D₃)⋊C₄	—	3	2	no	—
241	(C₂×D₃)⋊C₄	—	3	2	no	—
242	(C₂×D₃)⋊C₄	—	3	2	no	—
243	(C₂×D₃)⋊C₄	—	3	2	no	—
244	(C₂×D₃)⋊C₄	—	3	2	no	—
245	C₄⋊Dic₃	—	3	1	no	—
246	Dic₃⋊C₄	—	3	1	no	—
247	Dic₃⋊C₄	—	3	1	no	—
248	Dic₃⋊C₄	—	3	2	no	—
249	Dic₃⋊C₄	—	3	2	no	—
250	Dic₃⋊C₄	—	3	2	no	—
251	C₄×Dic₃	—	3	1	no	—
252	C₄×Dic₃	—	3	1	no	—
253	C₄×Dic₃	—	3	2	no	—
254	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
255	C₂×C₃×D₃	—	6	2	no	—
256	C₂×C₃×D₃	—	6	2	no	—
257	C₂×C₃×D₃	—	6	2	no	—
258	C₃²×C₄	—	2	2	no	—
259	C₃²×C₄	—	2	1	no	—
260	C₃²×C₄	—	2	1	no	—
261	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	#235	1	2	yes	—
263	C₃×Dic₃	—	3	2	no	—
264	C₃×Dic₃	—	6	2	no	—
265	C₃×Dic₃	—	6	1	no	—
266	C₃×Dic₃	—	6	1	no	—
267	C₃×Dic₃	—	6	1	no	—
268	C₂²×C₉	—	2	1	no	—
269	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
270	C₂×D₉	—	2	2	no	—
271	C₂×D₉	—	2	2	no	—
272	C₂×D₉	—	2	2	no	—
273	C₄×C₉	—	2	2	no	—
274	C₄×C₉	—	2	4	no	—
275	C₄×C₉	—	2	1	no	—
276	C₄×C₉	—	2	2	no	—
277	C₄×C₉	—	2	2	no	—
278	C₄×C₉	—	2	1	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	4	1	no	—
281	C₄×C₉	—	4	2	no	—
282	C₄×C₉	C₃×#41	1	2	yes	—
283	Dic₉	—	2	2	no	—
284	Dic₉	—	2	1	no	—
285	Dic₉	—	2	1	no	—
286	Dic₉	—	2	1	no	—
287	Dic₉	C₃×#41	1	2	yes	—
288	C₄⋊Q₈	—	9	1	no	—
289	#126	—	9	2	no	—
290	#126	—	9	2	no	—
291	#124	—	9	1	no	—
292	#124	—	9	1	no	—
293	C₂²⋊Q₈	—	9	2	no	—
294	C₄×Q₈	—	9	1	no	—
295	C₄×Q₈	—	9	1	no	—
296	C₄×Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
297	C₄×D₄	—	9	1	no	—
298	#117	—	9	2	no	—
299	3₋¹⁺²	#556	1	1	yes	characteristic, complemented, Sylow
300	C₂³×C₃	—	9	2	no	—
301	C₂²×D₃	—	3	2	no	—
302	C₃×Q₈	—	2	2	no	—
303	C₃×Q₈	—	6	2	no	—
304	C₃×Q₈	—	18	2	no	—
305	C₃×Q₈	—	18	2	no	—
306	C₃×D₄	—	18	2	no	—
307	C₂×C₃×C₄	—	3	1	no	—
308	C₂×C₃×C₄	—	3	1	no	—
309	C₂×C₃×C₄	—	3	2	no	—
310	C₂×C₃×C₄	—	3	1	no	—
311	C₂×C₃×C₄	—	3	2	no	—
312	C₂×C₃×C₄	—	9	1	no	—
313	C₂×C₃×C₄	—	9	1	no	—
314	C₂×C₃×C₄	—	9	1	no	—
315	C₂×C₃×C₄	—	9	2	no	—
316	C₂×C₃×C₄	—	9	1	no	—
317	C₂×C₃×C₄	—	18	4	no	—
318	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
319	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
321	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
323	C₂×Dic₃	—	3	1	no	—
324	C₂×Dic₃	—	3	1	no	—
325	C₂×Dic₃	—	3	1	no	—
326	C₂×Dic₃	—	3	2	no	—
327	C₂×Dic₃	—	3	1	no	—
328	D₁₂	—	6	2	no	—
329	C₄×D₃	—	6	4	no	—
330	Dic₆	—	6	2	no	—
331	Dic₆	—	6	2	no	—
332	C₂×C₃²	C₂×#235	1	1	yes	characteristic
333	C₂×C₃²	#1007	1	1	yes	characteristic
334	C₂×C₃²	D₃×#41	1	1	yes	characteristic
335	C₃×D₃	—	12	2	no	—
336	C₂×C₉	—	2	1	no	—
337	C₂×C₉	—	2	1	no	—
338	C₂×C₉	—	2	1	no	—
339	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
340	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
341	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
342	D₉	—	4	2	no	—
343	C₂×Q₈	—	9	1	no	—
344	C₂×Q₈	—	9	1	no	—
345	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
346	C₂×D₄	—	9	1	no	—
347	C₂²×C₄	—	9	2	no	—
348	C₄⋊C₄	—	9	1	no	—
349	C₄⋊C₄	—	9	2	no	—
350	C₄⋊C₄	—	9	2	no	—
351	C₄⋊C₄	—	9	1	no	—
352	C₄⋊C₄	—	9	1	no	—
353	C₄⋊C₄	—	9	2	no	—
354	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
355	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
356	C₂²⋊C₄	—	9	2	no	—
357	C₂²⋊C₄	—	9	2	no	—
358	C₂²⋊C₄	—	9	2	no	—
359	C₂²⋊C₄	—	9	2	no	—
360	C₂²⋊C₄	—	9	2	no	—
361	C₄²	—	9	2	no	—
362	C₄²	—	9	1	no	—
363	C₄²	—	9	1	no	—
364	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
365	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
366	C₂²×C₃	—	3	1	no	—
367	C₂²×C₃	—	18	2	no	—
368	C₂²×C₃	—	18	2	no	—
369	C₂²×C₃	—	18	2	no	—
370	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
371	C₂×D₃	—	6	2	no	—
372	C₂×D₃	—	6	2	no	—
373	C₂×D₃	—	6	2	no	—
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	2	no	—
378	C₃×C₄	—	3	2	no	—
379	C₃×C₄	—	6	2	no	—
380	C₃×C₄	—	6	2	no	—
381	C₃×C₄	—	6	1	no	—
382	C₃×C₄	—	6	1	no	—
383	C₃×C₄	—	9	2	no	—
384	C₃×C₄	—	18	2	no	—
385	C₃×C₄	—	18	1	no	—
386	C₃×C₄	—	18	1	no	—
387	C₃×C₄	—	18	1	no	—
388	C₃×C₄	C₃×#235	1	2	yes	—
389	Dic₃	—	3	2	no	—
390	Dic₃	—	6	2	no	—
391	Dic₃	—	6	1	no	—
392	Dic₃	—	6	1	no	—
393	Dic₃	—	6	1	no	—
394	C₃²	#5568	1	1	yes	characteristic
395	C₉	—	2	1	no	—
396	C₉	C₃×#556	1	1	yes	characteristic, complemented
397	C₂³	—	9	2	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	18	2	no	—
400	Q₈	—	18	2	no	—
401	D₄	—	18	2	no	—
402	C₂×C₄	—	9	1	no	—
403	C₂×C₄	—	9	1	no	—
404	C₂×C₄	—	9	1	no	—
405	C₂×C₄	—	9	2	no	—
406	C₂×C₄	—	9	1	no	—
407	C₂×C₄	—	18	4	no	—
408	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
409	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
410	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
411	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
412	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
413	C₂×C₃	—	3	1	no	—
414	C₂×C₃	—	3	1	no	—
415	C₂×C₃	—	3	1	no	—
416	C₂×C₃	—	36	2	no	—
417	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
418	C₂×C₃	C₃×#1007	1	1	yes	characteristic
419	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
420	D₃	—	12	2	no	—
421	C₂²	—	18	2	no	—
422	C₂²	—	18	2	no	—
423	C₂²	—	18	2	no	—
424	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
425	C₄	—	2	2	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	1	no	—
429	C₄	—	9	2	no	—
430	C₄	—	18	2	no	—
431	C₄	—	18	1	no	—
432	C₄	—	18	1	no	—
433	C₄	—	18	1	no	—
434	C₄	#3697⋊C₃	1	2	yes	—
435	C₃	—	3	1	no	—
436	C₃	C₃×#5568	1	1	yes	characteristic
437	C₂	—	36	2	no	—
438	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
439	C₂	#11722630	1	1	yes	characteristic
440	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×#556
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
4. #63460⋊C₃	C₂	semidirect
5. #63458⋊C₃	C₂	semidirect
7. #63449⋊C₃	C₂	semidirect
8. #11721396	C₂	semidirect
10. #63434⋊C₃	C₂	semidirect
11. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
13. #10589670	C₃	semidirect
49. C₄×Q₈×C₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
52. #63460	C₂×C₃	semidirect
53. #63458	C₂×C₃	semidirect
55. #63449	C₂×C₃	semidirect
56. #63438	C₂×C₃	semidirect
58. #63434	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
296. C₄×Q₈	AGL(1,ℤ/9)	semidirect
299. 3₋¹⁺²	#556	semidirect
396. C₉	C₃×#556	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
#63506⋊C₃	2
#63460⋊C₃	2
#63458⋊C₃	2
#63455⋊C₃	2
#63449⋊C₃	2
#11721396	2
#63437⋊C₃	2
#63434⋊C₃	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5568	3
#10589670	3

Subgroups — #10589670⋊C3 #13152729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589670⋊C₃ #13152729