Subgroups — #10589680⋊C₃ #13152739

Order 1728.

701 conjugacy classes of subgroups.

The subgroup lattice has 448 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	#63459⋊C₃	C₂	1	1	yes	maximal, characteristic
5	#63458⋊C₃	C₂	1	2	yes	maximal
6	#63451⋊C₃	C₂	1	2	yes	maximal, complemented
7	#63450⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63434⋊C₃	C₂	1	2	yes	maximal
9	C₄²×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
10	C₄×3₋¹⁺²⋊Q₈	C₂	1	2	yes	maximal, complemented
11	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5578	—	3	1	no	maximal
13	#10589680	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	1	yes	characteristic
17	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
18	C₂×3₋¹⁺²⋊Q₈	C₂²	1	2	yes	—
19	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
22	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
23	C₄²×3₋¹⁺²	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	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
27	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
28	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
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	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
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	2	yes	—
37	C₃²×C₄×Q₈	D₃	1	1	yes	characteristic
38	C₃×#946	—	3	1	no	—
39	C₃×#944	—	3	1	no	—
40	C₃×#897	—	3	1	no	—
41	C₃×#896	—	3	2	no	—
42	C₃×#889	—	3	2	no	—
43	C₃×#888	—	3	1	no	—
44	C₃×#872	—	3	2	no	—
45	C₃×C₄²×D₃	—	3	1	no	—
46	C₃×C₄×Dic₆	—	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	#63459	C₂×C₃	1	1	yes	characteristic
53	#63458	C₂×C₃	1	2	yes	—
54	#63451	C₂×C₃	1	2	yes	complemented
55	#63450	C₂×C₃	1	1	yes	characteristic, complemented
56	#63434	C₂×C₃	1	2	yes	—
57	C₄²×D₉	C₂×C₃	1	1	yes	characteristic
58	C₄×Dic₁₈	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	2	yes	—
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	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	2	yes	—
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	2	no	—
74	C₄×AGL(1,ℤ/9)	Q₈	1	4	yes	complemented
75	3₋¹⁺²⋊Q₈	—	2	2	no	—
76	3₋¹⁺²⋊Q₈	—	2	4	no	—
77	C₃×#533	—	9	1	no	—
78	#5578	—	3	1	no	—
79	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	—	3	1	no	—
81	C₂×C₃×C₄×D₃	—	3	1	no	—
82	C₂×C₃×C₄×D₃	—	3	1	no	—
83	C₂×C₃×Dic₆	—	3	2	no	—
84	C₂×C₃×Dic₆	—	3	1	no	—
85	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
86	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
87	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
88	C₃²×C₄²	C₂×D₃	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
90	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
91	C₃×C₄⋊Dic₃	—	3	1	no	—
92	C₃×C₄⋊Dic₃	—	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	2	no	—
97	C₃×Dic₃⋊C₄	—	3	2	no	—
98	C₃×C₄×Dic₃	—	3	1	no	—
99	C₃×C₄×Dic₃	—	3	1	no	—
100	C₃×C₄×Dic₃	—	3	1	no	—
101	C₃×C₄×Dic₃	—	3	2	no	—
102	C₂×Q₈×C₉	—	2	1	no	—
103	C₂×Q₈×C₉	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	1	yes	characteristic
107	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
108	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	2	no	—
111	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
113	C₄²×C₉	—	2	1	no	—
114	C₄²×C₉	—	2	2	no	—
115	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
116	C₄²×C₉	C₂²×C₃	1	2	yes	—
117	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
118	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
119	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
120	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
121	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
122	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
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	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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
130	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
131	C₂×AGL(1,ℤ/9)	—	2	1	no	—
132	C₂×AGL(1,ℤ/9)	—	2	1	no	—
133	C₂×AGL(1,ℤ/9)	C₂×Q₈	1	2	yes	—
134	C₄×3₋¹⁺²	—	2	2	no	—
135	C₄×3₋¹⁺²	—	2	2	no	—
136	C₄×3₋¹⁺²	—	2	1	no	—
137	C₄×3₋¹⁺²	C₂×Q₈	1	2	yes	—
138	C₄×3₋¹⁺²	#41	1	2	yes	—
139	3₋¹⁺²⋊C₄	—	2	2	no	—
140	3₋¹⁺²⋊C₄	—	2	2	no	—
141	3₋¹⁺²⋊C₄	—	2	1	no	—
142	3₋¹⁺²⋊C₄	C₂×Q₈	1	2	yes	—
143	3₋¹⁺²⋊C₄	#41	1	2	yes	—
144	C₃×C₄⋊Q₈	—	9	1	no	—
145	C₃×C₄⋊Q₈	—	9	1	no	—
146	C₃×#125	—	9	2	no	—
147	C₃×C₂²⋊Q₈	—	9	2	no	—
148	C₃×C₂²⋊Q₈	—	9	1	no	—
149	C₃×C₂²⋊Q₈	—	9	1	no	—
150	C₃×C₄×Q₈	—	3	1	no	—
151	C₃×C₄×Q₈	—	9	1	no	—
152	C₃×C₄×Q₈	—	9	2	no	—
153	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
154	C₃×#117	—	9	2	no	—
155	C₂×C₃×C₄²	—	9	1	no	—
156	#946	—	3	1	no	—
157	#944	—	3	1	no	—
158	#897	—	3	1	no	—
159	#896	—	3	2	no	—
160	#889	—	3	2	no	—
161	#888	—	3	1	no	—
162	#872	—	3	2	no	—
163	C₄²×D₃	—	3	1	no	—
164	C₄×Dic₆	—	3	2	no	—
165	C₄×Dic₆	—	3	1	no	—
166	C₂²×C₃×D₃	—	3	1	no	—
167	C₃²×Q₈	—	2	2	no	—
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	2	yes	—
171	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	1	no	—
175	C₂×C₃×Dic₃	—	3	1	no	—
176	C₂×C₃×Dic₃	—	3	2	no	—
177	C₂×C₃×Dic₃	—	3	2	no	—
178	C₃×C₄×D₃	—	3	4	no	—
179	C₃×C₄×D₃	—	6	2	no	—
180	C₃×C₄×D₃	—	6	2	no	—
181	C₃×Dic₆	—	6	4	no	—
182	C₃×Dic₆	—	6	2	no	—
183	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
184	Q₈×C₉	—	2	4	no	—
185	Q₈×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	—	2	1	no	—
190	C₂×C₄×C₉	—	2	2	no	—
191	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
193	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
194	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₄×C₉	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	2	yes	—
199	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
200	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
201	C₄×D₉	—	2	2	no	—
202	C₄×D₉	—	2	2	no	—
203	C₄×D₉	C₃×Q₈	1	4	yes	complemented
204	Dic₁₈	—	2	2	no	—
205	Dic₁₈	—	2	4	no	—
206	#533	—	9	1	no	Sylow
207	C₂×3₋¹⁺²	C₂²×Q₈	1	1	yes	characteristic
208	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
209	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
210	AGL(1,ℤ/9)	—	2	2	no	—
211	C₂×C₃×Q₈	—	3	1	no	—
212	C₂×C₃×Q₈	—	9	1	no	—
213	C₂×C₃×Q₈	—	9	2	no	—
214	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
215	C₂²×C₃×C₄	—	9	1	no	—
216	C₂²×C₃×C₄	—	9	1	no	—
217	C₂²×C₃×C₄	—	9	1	no	—
218	C₂×C₄×D₃	—	3	1	no	—
219	C₂×C₄×D₃	—	3	1	no	—
220	C₂×C₄×D₃	—	3	1	no	—
221	C₂×Dic₆	—	3	2	no	—
222	C₂×Dic₆	—	3	1	no	—
223	C₃×C₄⋊C₄	—	3	2	no	—
224	C₃×C₄⋊C₄	—	3	1	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	2	no	—
229	C₃×C₄⋊C₄	—	9	2	no	—
230	C₃×C₄⋊C₄	—	9	2	no	—
231	C₃×C₄⋊C₄	—	9	1	no	—
232	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
233	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
234	C₃×C₂²⋊C₄	—	9	2	no	—
235	C₃×C₂²⋊C₄	—	9	2	no	—
236	C₃×C₄²	—	3	1	no	—
237	C₃×C₄²	—	3	2	no	—
238	C₃×C₄²	—	9	1	no	—
239	C₃×C₄²	—	9	1	no	—
240	C₃×C₄²	—	9	1	no	—
241	C₃×C₄²	—	9	2	no	—
242	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
243	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
244	(C₂×D₃)⋊C₄	—	3	2	no	—
245	(C₂×D₃)⋊C₄	—	3	2	no	—
246	C₄⋊Dic₃	—	3	1	no	—
247	C₄⋊Dic₃	—	3	2	no	—
248	Dic₃⋊C₄	—	3	2	no	—
249	Dic₃⋊C₄	—	3	2	no	—
250	Dic₃⋊C₄	—	3	2	no	—
251	Dic₃⋊C₄	—	3	2	no	—
252	Dic₃⋊C₄	—	3	2	no	—
253	C₄×Dic₃	—	3	1	no	—
254	C₄×Dic₃	—	3	2	no	—
255	C₄×Dic₃	—	3	1	no	—
256	C₄×Dic₃	—	3	1	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	C₃²×C₄	—	2	2	no	—
262	C₃²×C₄	—	2	2	no	—
263	C₃²×C₄	—	2	1	no	—
264	C₃²×C₄	#235	1	2	yes	—
265	C₃²×C₄	D₃×Q₈	1	2	yes	—
266	C₃×Dic₃	—	3	2	no	—
267	C₃×Dic₃	—	3	2	no	—
268	C₃×Dic₃	—	6	2	no	—
269	C₃×Dic₃	—	6	1	no	—
270	C₃×Dic₃	—	6	2	no	—
271	C₂²×C₉	—	2	1	no	—
272	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
273	C₂×D₉	—	2	1	no	—
274	C₂×D₉	—	2	1	no	—
275	C₂×D₉	C₂×C₃×Q₈	1	2	yes	—
276	C₄×C₉	—	2	4	no	—
277	C₄×C₉	—	2	2	no	—
278	C₄×C₉	—	2	1	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	2	no	—
281	C₄×C₉	—	2	2	no	—
282	C₄×C₉	—	4	2	no	—
283	C₄×C₉	—	4	1	no	—
284	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
285	C₄×C₉	C₃×#41	1	2	yes	—
286	Dic₉	—	2	2	no	—
287	Dic₉	—	2	2	no	—
288	Dic₉	—	2	1	no	—
289	Dic₉	C₂×C₃×Q₈	1	2	yes	—
290	Dic₉	C₃×#41	1	2	yes	—
291	C₄⋊Q₈	—	9	1	no	—
292	C₄⋊Q₈	—	9	1	no	—
293	#125	—	9	2	no	—
294	C₂²⋊Q₈	—	9	1	no	—
295	C₂²⋊Q₈	—	9	2	no	—
296	C₂²⋊Q₈	—	9	1	no	—
297	C₄×Q₈	—	9	2	no	—
298	C₄×Q₈	—	9	1	no	—
299	C₄×Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
300	#117	—	9	2	no	—
301	C₂×C₄²	—	9	1	no	—
302	3₋¹⁺²	#533	1	1	yes	characteristic, complemented, Sylow
303	C₂³×C₃	—	9	1	no	—
304	C₂²×D₃	—	3	1	no	—
305	C₃×Q₈	—	2	2	no	—
306	C₃×Q₈	—	6	2	no	—
307	C₃×Q₈	—	18	2	no	—
308	C₃×Q₈	—	18	4	no	—
309	C₂×C₃×C₄	—	3	1	no	—
310	C₂×C₃×C₄	—	3	1	no	—
311	C₂×C₃×C₄	—	3	2	no	—
312	C₂×C₃×C₄	—	3	2	no	—
313	C₂×C₃×C₄	—	3	1	no	—
314	C₂×C₃×C₄	—	9	4	no	—
315	C₂×C₃×C₄	—	9	1	no	—
316	C₂×C₃×C₄	—	9	1	no	—
317	C₂×C₃×C₄	—	9	1	no	—
318	C₂×C₃×C₄	—	9	2	no	—
319	C₂×C₃×C₄	—	9	2	no	—
320	C₂×C₃×C₄	—	18	2	no	—
321	C₂×C₃×C₄	—	18	2	no	—
322	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
323	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
324	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
325	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂×Dic₃	—	3	1	no	—
328	C₂×Dic₃	—	3	1	no	—
329	C₂×Dic₃	—	3	1	no	—
330	C₂×Dic₃	—	3	2	no	—
331	C₂×Dic₃	—	3	2	no	—
332	C₄×D₃	—	3	4	no	—
333	C₄×D₃	—	6	2	no	—
334	C₄×D₃	—	6	2	no	—
335	Dic₆	—	6	4	no	—
336	Dic₆	—	6	2	no	—
337	C₂×C₃²	C₂×#235	1	1	yes	characteristic
338	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
339	C₂×C₃²	D₃×#41	1	1	yes	characteristic
340	C₃×D₃	—	6	2	no	—
341	C₂×C₉	—	2	1	no	—
342	C₂×C₉	—	2	1	no	—
343	C₂×C₉	—	2	1	no	—
344	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
345	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
346	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
347	D₉	—	2	2	no	—
348	C₂×Q₈	—	9	2	no	—
349	C₂×Q₈	—	9	1	no	—
350	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
351	C₂²×C₄	—	9	1	no	—
352	C₂²×C₄	—	9	1	no	—
353	C₂²×C₄	—	9	1	no	—
354	C₄⋊C₄	—	9	2	no	—
355	C₄⋊C₄	—	9	2	no	—
356	C₄⋊C₄	—	9	2	no	—
357	C₄⋊C₄	—	9	2	no	—
358	C₄⋊C₄	—	9	2	no	—
359	C₄⋊C₄	—	9	2	no	—
360	C₄⋊C₄	—	9	1	no	—
361	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
362	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
363	C₂²⋊C₄	—	9	2	no	—
364	C₂²⋊C₄	—	9	2	no	—
365	C₄²	—	9	1	no	—
366	C₄²	—	9	1	no	—
367	C₄²	—	9	1	no	—
368	C₄²	—	9	2	no	—
369	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
370	C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
371	C₂²×C₃	—	3	1	no	—
372	C₂²×C₃	—	9	2	no	—
373	C₂²×C₃	—	18	1	no	—
374	C₂²×C₃	—	18	1	no	—
375	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
376	C₂×D₃	—	3	2	no	—
377	C₂×D₃	—	6	1	no	—
378	C₂×D₃	—	6	1	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	3	2	no	—
383	C₃×C₄	—	3	2	no	—
384	C₃×C₄	—	6	1	no	—
385	C₃×C₄	—	6	2	no	—
386	C₃×C₄	—	6	2	no	—
387	C₃×C₄	—	9	2	no	—
388	C₃×C₄	—	9	2	no	—
389	C₃×C₄	—	18	1	no	—
390	C₃×C₄	—	18	2	no	—
391	C₃×C₄	—	18	2	no	—
392	C₃×C₄	C₃×#235	1	2	yes	—
393	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
394	Dic₃	—	3	2	no	—
395	Dic₃	—	3	2	no	—
396	Dic₃	—	6	2	no	—
397	Dic₃	—	6	1	no	—
398	Dic₃	—	6	2	no	—
399	C₃²	#5578	1	1	yes	characteristic
400	C₉	—	2	1	no	—
401	C₉	C₃×#533	1	1	yes	characteristic, complemented
402	C₂³	—	9	1	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	18	4	no	—
405	Q₈	—	18	2	no	—
406	C₂×C₄	—	9	1	no	—
407	C₂×C₄	—	9	1	no	—
408	C₂×C₄	—	9	4	no	—
409	C₂×C₄	—	9	1	no	—
410	C₂×C₄	—	9	2	no	—
411	C₂×C₄	—	9	2	no	—
412	C₂×C₄	—	18	2	no	—
413	C₂×C₄	—	18	2	no	—
414	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
415	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
416	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
417	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
418	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
419	C₂×C₃	—	3	1	no	—
420	C₂×C₃	—	3	1	no	—
421	C₂×C₃	—	3	1	no	—
422	C₂×C₃	—	18	2	no	—
423	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
424	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
425	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
426	D₃	—	6	2	no	—
427	C₂²	—	9	2	no	—
428	C₂²	—	18	1	no	—
429	C₂²	—	18	1	no	—
430	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	2	no	—
434	C₄	—	9	2	no	—
435	C₄	—	9	2	no	—
436	C₄	—	18	1	no	—
437	C₄	—	18	2	no	—
438	C₄	—	18	2	no	—
439	C₄	#3697⋊C₃	1	2	yes	—
440	C₄	Q₈×AGL(1,ℤ/9)	1	2	yes	—
441	C₃	—	3	1	no	—
442	C₃	C₃×#5578	1	1	yes	characteristic
443	C₂	—	18	2	no	—
444	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
445	C₂	C₂×Q₈×AGL(1,ℤ/9)	1	1	yes	characteristic
446	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	C₂²×AGL(1,ℤ/9)	C₂³
hypercenter	C₄×Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#533
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
3. #63506⋊C₃	C₂	semidirect
6. #63451⋊C₃	C₂	semidirect
7. #63450⋊C₃	C₂	semidirect
10. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
11. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
13. #10589680	C₃	semidirect
49. C₄×Q₈×C₉	C₂×C₃	semidirect
51. #63506	C₂×C₃	semidirect
54. #63451	C₂×C₃	semidirect
55. #63450	C₂×C₃	semidirect
58. C₄×Dic₁₈	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
74. C₄×AGL(1,ℤ/9)	Q₈	semidirect
203. C₄×D₉	C₃×Q₈	semidirect
299. C₄×Q₈	AGL(1,ℤ/9)	semidirect
302. 3₋¹⁺²	#533	semidirect
401. C₉	C₃×#533	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
#63459⋊C₃	2
#63458⋊C₃	2
#63451⋊C₃	2
#63450⋊C₃	2
#63434⋊C₃	2
C₄²×AGL(1,ℤ/9)	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5578	3
#10589680	3

Subgroups — #10589680⋊C3 #13152739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589680⋊C₃ #13152739