Subgroups — #10589749⋊C₃ #13152994

Order 1728.

697 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₂²⋊Q₈	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	#63492⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63491⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63459⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63457⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#63445⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5647	—	3	1	no	maximal
17	#10589749	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
21	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
22	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
26	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
27	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
28	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
29	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
31	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
32	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
33	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
34	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
35	#3676⋊C₃	C₂²	1	1	yes	characteristic
36	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
41	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
42	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
44	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
45	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
46	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
47	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
48	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
49	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
50	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
51	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
53	C₃²×C₂²⋊Q₈	D₃	1	1	yes	characteristic
54	C₃×#947	—	3	1	no	—
55	C₃×#946	—	3	1	no	—
56	C₃×#930	—	3	1	no	—
57	C₃×#929	—	3	1	no	—
58	C₃×#897	—	3	1	no	—
59	C₃×#896	—	3	1	no	—
60	C₃×#895	—	3	1	no	—
61	C₃×#894	—	3	1	no	—
62	C₃×#894	—	3	1	no	—
63	C₃×#889	—	3	1	no	—
64	C₃×#885	—	3	1	no	—
65	C₃×#884	—	3	1	no	—
66	C₃×#884	—	3	1	no	—
67	C₃×#883	—	3	1	no	—
68	C₉×C₂²⋊Q₈	—	2	1	no	—
69	C₉×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
70	#63509	C₂×C₃	1	1	yes	characteristic, complemented
71	#63508	C₂×C₃	1	1	yes	characteristic, complemented
72	#63492	C₂×C₃	1	1	yes	characteristic, complemented
73	#63491	C₂×C₃	1	1	yes	characteristic, complemented
74	#63459	C₂×C₃	1	1	yes	characteristic, complemented
75	#63458	C₂×C₃	1	1	yes	characteristic, complemented
76	#63457	C₂×C₃	1	1	yes	characteristic, complemented
77	#63456	C₂×C₃	1	1	yes	characteristic, complemented
78	#63456	C₂×C₃	1	1	yes	characteristic, complemented
79	#63451	C₂×C₃	1	1	yes	characteristic, complemented
80	#63447	C₂×C₃	1	1	yes	characteristic, complemented
81	#63446	C₂×C₃	1	1	yes	characteristic, complemented
82	#63446	C₂×C₃	1	1	yes	characteristic, complemented
83	#63445	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
85	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
86	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
87	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
88	Q₈×3₋¹⁺²	—	4	1	no	—
89	C₂×C₄×3₋¹⁺²	—	4	1	no	—
90	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
91	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
92	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
93	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
94	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
95	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
96	#611⋊C₃	—	4	1	no	—
97	#611⋊C₃	—	4	1	no	—
98	#611⋊C₃	—	4	1	no	—
99	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
104	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
105	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
106	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
107	C₄×AGL(1,ℤ/9)	—	4	1	no	—
108	C₄×AGL(1,ℤ/9)	—	4	1	no	—
109	C₄×AGL(1,ℤ/9)	—	4	1	no	—
110	3₋¹⁺²⋊Q₈	—	4	1	no	—
111	C₃×#562	—	9	1	no	—
112	#5647	—	3	1	no	—
113	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
115	C₂×C₃×#67	—	3	1	no	—
116	C₂×C₃×#67	—	3	1	no	—
117	C₂×C₃×#67	—	3	1	no	—
118	C₂×C₃×D₁₂	—	3	1	no	—
119	C₂×C₃×D₁₂	—	3	1	no	—
120	C₂×C₃×D₁₂	—	3	1	no	—
121	C₂×C₃×C₄×D₃	—	3	1	no	—
122	C₂×C₃×C₄×D₃	—	3	1	no	—
123	C₂×C₃×C₄×D₃	—	3	1	no	—
124	C₂×C₃×Dic₆	—	3	1	no	—
125	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
127	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
128	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
129	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
130	C₃×#217	—	3	1	no	—
131	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
132	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
133	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
134	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
135	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
136	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
137	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
138	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
139	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
140	C₃×C₄⋊Dic₃	—	3	1	no	—
141	C₃×C₄⋊Dic₃	—	3	1	no	—
142	C₃×Dic₃⋊C₄	—	3	1	no	—
143	C₃×Dic₃⋊C₄	—	3	1	no	—
144	C₃×Dic₃⋊C₄	—	3	1	no	—
145	C₃×Dic₃⋊C₄	—	3	1	no	—
146	C₃×Dic₃⋊C₄	—	3	1	no	—
147	C₃×C₄×Dic₃	—	3	1	no	—
148	C₂×Q₈×C₉	—	2	1	no	—
149	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
150	C₂²×C₄×C₉	—	2	1	no	—
151	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
152	C₂×#611	C₂²×C₃	1	1	yes	characteristic
153	C₂×#611	C₂²×C₃	1	1	yes	characteristic
154	C₂×#611	C₂²×C₃	1	1	yes	characteristic
155	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
156	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
157	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
161	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
162	C₉×C₄⋊C₄	—	2	1	no	—
163	C₉×C₄⋊C₄	—	2	1	no	—
164	C₉×C₄⋊C₄	—	2	1	no	—
165	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₉×C₂²⋊C₄	—	2	1	no	—
169	C₉×C₂²⋊C₄	—	2	1	no	—
170	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	#3676	C₂²×C₃	1	1	yes	characteristic
173	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
183	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
184	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
185	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
187	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
188	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
189	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
190	C₂²×3₋¹⁺²	—	2	1	no	—
191	C₂²×3₋¹⁺²	—	2	1	no	—
192	C₂²×3₋¹⁺²	—	2	1	no	—
193	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
194	C₂×AGL(1,ℤ/9)	—	2	1	no	—
195	C₂×AGL(1,ℤ/9)	—	2	1	no	—
196	C₂×AGL(1,ℤ/9)	—	2	1	no	—
197	C₂×AGL(1,ℤ/9)	—	2	1	no	—
198	C₂×AGL(1,ℤ/9)	—	2	1	no	—
199	C₂×AGL(1,ℤ/9)	—	2	1	no	—
200	C₂×AGL(1,ℤ/9)	—	2	1	no	—
201	C₂×AGL(1,ℤ/9)	—	2	1	no	—
202	C₂×AGL(1,ℤ/9)	—	2	1	no	—
203	C₄×3₋¹⁺²	—	2	1	no	—
204	C₄×3₋¹⁺²	—	2	1	no	—
205	C₄×3₋¹⁺²	—	2	1	no	—
206	C₄×3₋¹⁺²	—	2	1	no	—
207	C₄×3₋¹⁺²	—	2	1	no	—
208	C₄×3₋¹⁺²	—	2	1	no	—
209	3₋¹⁺²⋊C₄	—	2	1	no	—
210	3₋¹⁺²⋊C₄	—	2	1	no	—
211	3₋¹⁺²⋊C₄	—	2	1	no	—
212	3₋¹⁺²⋊C₄	—	2	1	no	—
213	3₋¹⁺²⋊C₄	—	2	1	no	—
214	C₃×#125	—	9	1	no	—
215	C₃×#124	—	9	1	no	—
216	C₃×#124	—	9	1	no	—
217	C₃×#123	—	9	1	no	—
218	C₃×#123	—	9	1	no	—
219	C₃×#123	—	9	1	no	—
220	C₃×#123	—	9	1	no	—
221	C₃×C₂²⋊Q₈	—	3	1	no	—
222	C₃×C₂²⋊Q₈	—	9	1	no	—
223	C₃×C₂²⋊Q₈	—	9	1	no	—
224	C₃×C₂²⋊Q₈	—	9	1	no	—
225	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
226	C₃×#121	—	9	1	no	—
227	C₃×#121	—	9	1	no	—
228	C₃×#121	—	9	1	no	—
229	C₃×#121	—	9	1	no	—
230	#947	—	3	1	no	—
231	#946	—	3	1	no	—
232	#930	—	3	1	no	—
233	#929	—	3	1	no	—
234	#897	—	3	1	no	—
235	#896	—	3	1	no	—
236	#895	—	3	1	no	—
237	#894	—	3	1	no	—
238	#894	—	3	1	no	—
239	#889	—	3	1	no	—
240	#885	—	3	1	no	—
241	#884	—	3	1	no	—
242	#884	—	3	1	no	—
243	#883	—	3	1	no	—
244	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
245	C₂²×C₃×D₃	—	3	1	no	—
246	C₂²×C₃×D₃	—	3	1	no	—
247	C₂²×C₃×D₃	—	3	1	no	—
248	C₃²×Q₈	—	4	1	no	—
249	C₂×C₃²×C₄	—	4	1	no	—
250	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
251	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
252	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
253	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
254	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
255	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₃×#67	—	12	1	no	—
257	C₃×#67	—	12	1	no	—
258	C₃×#67	—	12	1	no	—
259	C₂×C₃×Dic₃	—	3	1	no	—
260	C₂×C₃×Dic₃	—	3	1	no	—
261	C₂×C₃×Dic₃	—	3	1	no	—
262	C₂×C₃×Dic₃	—	3	1	no	—
263	C₂×C₃×Dic₃	—	3	1	no	—
264	C₃×D₁₂	—	12	1	no	—
265	C₃×D₁₂	—	12	1	no	—
266	C₃×D₁₂	—	12	1	no	—
267	C₃×C₄×D₃	—	12	1	no	—
268	C₃×C₄×D₃	—	12	1	no	—
269	C₃×C₄×D₃	—	12	1	no	—
270	C₃×Dic₆	—	12	1	no	—
271	C₂³×C₉	—	2	1	no	—
272	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
273	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
274	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
275	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
276	Q₈×C₉	—	4	1	no	—
277	Q₈×C₉	—	4	2	no	—
278	C₂×C₄×C₉	—	2	1	no	—
279	C₂×C₄×C₉	—	2	1	no	—
280	C₂×C₄×C₉	—	2	1	no	—
281	C₂×C₄×C₉	—	2	1	no	—
282	C₂×C₄×C₉	—	2	1	no	—
283	C₂×C₄×C₉	—	2	1	no	—
284	C₂×C₄×C₉	—	4	1	no	—
285	C₂×C₄×C₉	—	4	2	no	—
286	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
292	#611	—	4	1	no	—
293	#611	—	4	1	no	—
294	#611	—	4	1	no	—
295	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
296	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
297	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
298	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
299	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
300	D₃₆	—	4	1	no	—
301	D₃₆	—	4	1	no	—
302	D₃₆	—	4	1	no	—
303	C₄×D₉	—	4	1	no	—
304	C₄×D₉	—	4	1	no	—
305	C₄×D₉	—	4	1	no	—
306	Dic₁₈	—	4	1	no	—
307	#562	—	9	1	no	Sylow
308	C₂×3₋¹⁺²	—	4	1	no	—
309	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
310	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
311	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
312	AGL(1,ℤ/9)	—	4	1	no	—
313	AGL(1,ℤ/9)	—	4	1	no	—
314	AGL(1,ℤ/9)	—	4	1	no	—
315	C₂×C₃×Q₈	—	3	1	no	—
316	C₂×C₃×Q₈	—	9	1	no	—
317	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
318	C₂×C₃×D₄	—	9	1	no	—
319	C₂×C₃×D₄	—	9	1	no	—
320	C₂×C₃×D₄	—	9	1	no	—
321	C₂×C₃×D₄	—	9	1	no	—
322	C₂×C₃×D₄	—	9	1	no	—
323	C₂×C₃×D₄	—	9	1	no	—
324	C₂²×C₃×C₄	—	3	1	no	—
325	C₂²×C₃×C₄	—	9	1	no	—
326	C₂²×C₃×C₄	—	9	1	no	—
327	C₂²×C₃×C₄	—	9	1	no	—
328	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
329	C₂×#67	—	3	1	no	—
330	C₂×#67	—	3	1	no	—
331	C₂×#67	—	3	1	no	—
332	C₂×D₁₂	—	3	1	no	—
333	C₂×D₁₂	—	3	1	no	—
334	C₂×D₁₂	—	3	1	no	—
335	C₂×C₄×D₃	—	3	1	no	—
336	C₂×C₄×D₃	—	3	1	no	—
337	C₂×C₄×D₃	—	3	1	no	—
338	C₂×Dic₆	—	3	1	no	—
339	C₃×C₄⋊C₄	—	3	1	no	—
340	C₃×C₄⋊C₄	—	3	1	no	—
341	C₃×C₄⋊C₄	—	3	1	no	—
342	C₃×C₄⋊C₄	—	9	1	no	—
343	C₃×C₄⋊C₄	—	9	1	no	—
344	C₃×C₄⋊C₄	—	9	1	no	—
345	C₃×C₄⋊C₄	—	9	1	no	—
346	C₃×C₄⋊C₄	—	9	1	no	—
347	C₃×C₄⋊C₄	—	9	1	no	—
348	C₃×C₄⋊C₄	—	9	1	no	—
349	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
350	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
351	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
352	C₃×C₂²⋊C₄	—	3	1	no	—
353	C₃×C₂²⋊C₄	—	3	1	no	—
354	C₃×C₂²⋊C₄	—	9	1	no	—
355	C₃×C₂²⋊C₄	—	9	1	no	—
356	C₃×C₂²⋊C₄	—	9	1	no	—
357	C₃×C₂²⋊C₄	—	9	1	no	—
358	C₃×C₂²⋊C₄	—	9	1	no	—
359	C₃×C₂²⋊C₄	—	9	1	no	—
360	C₃×C₂²⋊C₄	—	9	1	no	—
361	C₃×C₂²⋊C₄	—	9	1	no	—
362	C₃×C₂²⋊C₄	—	9	1	no	—
363	C₃×C₂²⋊C₄	—	9	1	no	—
364	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
365	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
366	C₃×C₄²	—	9	1	no	—
367	#217	—	3	1	no	—
368	(C₂×D₃)⋊C₄	—	3	1	no	—
369	(C₂×D₃)⋊C₄	—	3	1	no	—
370	(C₂×D₃)⋊C₄	—	3	1	no	—
371	(C₂×D₃)⋊C₄	—	3	1	no	—
372	(C₂×D₃)⋊C₄	—	3	1	no	—
373	(C₂×D₃)⋊C₄	—	3	1	no	—
374	(C₂×D₃)⋊C₄	—	3	1	no	—
375	(C₂×D₃)⋊C₄	—	3	1	no	—
376	(C₂×D₃)⋊C₄	—	3	1	no	—
377	C₄⋊Dic₃	—	3	1	no	—
378	C₄⋊Dic₃	—	3	1	no	—
379	Dic₃⋊C₄	—	3	1	no	—
380	Dic₃⋊C₄	—	3	1	no	—
381	Dic₃⋊C₄	—	3	1	no	—
382	Dic₃⋊C₄	—	3	1	no	—
383	Dic₃⋊C₄	—	3	1	no	—
384	C₄×Dic₃	—	3	1	no	—
385	C₂²×C₃²	—	2	1	no	—
386	C₂²×C₃²	—	2	1	no	—
387	C₂²×C₃²	—	2	1	no	—
388	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
389	C₂×C₃×D₃	—	6	1	no	—
390	C₂×C₃×D₃	—	6	1	no	—
391	C₂×C₃×D₃	—	6	1	no	—
392	C₂×C₃×D₃	—	6	1	no	—
393	C₂×C₃×D₃	—	6	1	no	—
394	C₂×C₃×D₃	—	6	1	no	—
395	C₂×C₃×D₃	—	6	1	no	—
396	C₂×C₃×D₃	—	6	1	no	—
397	C₂×C₃×D₃	—	6	1	no	—
398	C₃²×C₄	—	2	1	no	—
399	C₃²×C₄	—	2	1	no	—
400	C₃²×C₄	—	2	1	no	—
401	C₃²×C₄	—	2	1	no	—
402	C₃²×C₄	—	2	1	no	—
403	C₃²×C₄	—	2	1	no	—
404	C₃×Dic₃	—	6	1	no	—
405	C₃×Dic₃	—	6	1	no	—
406	C₃×Dic₃	—	6	1	no	—
407	C₃×Dic₃	—	6	1	no	—
408	C₃×Dic₃	—	6	1	no	—
409	C₂²×C₉	—	2	2	no	—
410	C₂²×C₉	—	2	1	no	—
411	C₂²×C₉	—	2	1	no	—
412	C₂²×C₉	—	2	1	no	—
413	C₂²×C₉	—	2	1	no	—
414	C₂²×C₉	—	4	1	no	—
415	C₂²×C₉	—	4	1	no	—
416	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
417	C₂×D₉	—	2	1	no	—
418	C₂×D₉	—	2	1	no	—
419	C₂×D₉	—	2	1	no	—
420	C₂×D₉	—	2	1	no	—
421	C₂×D₉	—	2	1	no	—
422	C₂×D₉	—	2	1	no	—
423	C₂×D₉	—	2	1	no	—
424	C₂×D₉	—	2	1	no	—
425	C₂×D₉	—	2	1	no	—
426	C₄×C₉	—	2	2	no	—
427	C₄×C₉	—	2	1	no	—
428	C₄×C₉	—	2	1	no	—
429	C₄×C₉	—	2	1	no	—
430	C₄×C₉	—	2	1	no	—
431	C₄×C₉	—	2	1	no	—
432	C₄×C₉	—	2	1	no	—
433	C₄×C₉	—	4	1	no	—
434	C₄×C₉	—	4	1	no	—
435	C₄×C₉	—	4	1	no	—
436	C₄×C₉	—	4	1	no	—
437	C₄×C₉	—	4	1	no	—
438	Dic₉	—	2	1	no	—
439	Dic₉	—	2	1	no	—
440	Dic₉	—	2	1	no	—
441	Dic₉	—	2	1	no	—
442	Dic₉	—	2	1	no	—
443	#125	—	9	1	no	—
444	#124	—	9	1	no	—
445	#124	—	9	1	no	—
446	#123	—	9	1	no	—
447	#123	—	9	1	no	—
448	#123	—	9	1	no	—
449	#123	—	9	1	no	—
450	C₂²⋊Q₈	—	9	1	no	—
451	C₂²⋊Q₈	—	9	1	no	—
452	C₂²⋊Q₈	—	9	1	no	—
453	C₂²⋊Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
454	#121	—	9	1	no	—
455	#121	—	9	1	no	—
456	#121	—	9	1	no	—
457	#121	—	9	1	no	—
458	3₋¹⁺²	#562	1	1	yes	characteristic, complemented, Sylow
459	C₂³×C₃	—	3	1	no	—
460	C₂³×C₃	—	9	1	no	—
461	C₂³×C₃	—	9	1	no	—
462	C₂³×C₃	—	9	1	no	—
463	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
464	C₂²×D₃	—	3	1	no	—
465	C₂²×D₃	—	3	1	no	—
466	C₂²×D₃	—	3	1	no	—
467	C₃×Q₈	—	4	1	no	—
468	C₃×Q₈	—	12	1	no	—
469	C₃×Q₈	—	36	1	no	—
470	C₃×D₄	—	36	1	no	—
471	C₃×D₄	—	36	1	no	—
472	C₃×D₄	—	36	1	no	—
473	C₃×D₄	—	36	1	no	—
474	C₃×D₄	—	36	1	no	—
475	C₃×D₄	—	36	1	no	—
476	C₂×C₃×C₄	—	3	1	no	—
477	C₂×C₃×C₄	—	3	1	no	—
478	C₂×C₃×C₄	—	3	1	no	—
479	C₂×C₃×C₄	—	3	1	no	—
480	C₂×C₃×C₄	—	3	1	no	—
481	C₂×C₃×C₄	—	3	1	no	—
482	C₂×C₃×C₄	—	4	1	no	—
483	C₂×C₃×C₄	—	9	1	no	—
484	C₂×C₃×C₄	—	9	1	no	—
485	C₂×C₃×C₄	—	9	1	no	—
486	C₂×C₃×C₄	—	9	1	no	—
487	C₂×C₃×C₄	—	9	1	no	—
488	C₂×C₃×C₄	—	12	1	no	—
489	C₂×C₃×C₄	—	36	1	no	—
490	C₂×C₃×C₄	—	36	1	no	—
491	C₂×C₃×C₄	—	36	1	no	—
492	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
493	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
497	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
498	#67	—	12	1	no	—
499	#67	—	12	1	no	—
500	#67	—	12	1	no	—
501	C₂×Dic₃	—	3	1	no	—
502	C₂×Dic₃	—	3	1	no	—
503	C₂×Dic₃	—	3	1	no	—
504	C₂×Dic₃	—	3	1	no	—
505	C₂×Dic₃	—	3	1	no	—
506	D₁₂	—	12	1	no	—
507	D₁₂	—	12	1	no	—
508	D₁₂	—	12	1	no	—
509	C₄×D₃	—	12	1	no	—
510	C₄×D₃	—	12	1	no	—
511	C₄×D₃	—	12	1	no	—
512	Dic₆	—	12	1	no	—
513	C₂×C₃²	—	4	1	no	—
514	C₂×C₃²	#1004	1	1	yes	characteristic
515	C₂×C₃²	#1007	1	1	yes	characteristic
516	C₂×C₃²	#1009	1	1	yes	characteristic
517	C₃×D₃	—	12	1	no	—
518	C₃×D₃	—	12	1	no	—
519	C₃×D₃	—	12	1	no	—
520	C₂×C₉	—	2	1	no	—
521	C₂×C₉	—	2	1	no	—
522	C₂×C₉	—	2	1	no	—
523	C₂×C₉	—	4	2	no	—
524	C₂×C₉	—	4	1	no	—
525	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
526	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
528	D₉	—	4	1	no	—
529	D₉	—	4	1	no	—
530	D₉	—	4	1	no	—
531	C₂×Q₈	—	9	1	no	—
532	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
533	C₂×D₄	—	9	1	no	—
534	C₂×D₄	—	9	1	no	—
535	C₂×D₄	—	9	1	no	—
536	C₂×D₄	—	9	1	no	—
537	C₂×D₄	—	9	1	no	—
538	C₂×D₄	—	9	1	no	—
539	C₂²×C₄	—	9	1	no	—
540	C₂²×C₄	—	9	1	no	—
541	C₂²×C₄	—	9	1	no	—
542	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
543	C₄⋊C₄	—	9	1	no	—
544	C₄⋊C₄	—	9	1	no	—
545	C₄⋊C₄	—	9	1	no	—
546	C₄⋊C₄	—	9	1	no	—
547	C₄⋊C₄	—	9	1	no	—
548	C₄⋊C₄	—	9	1	no	—
549	C₄⋊C₄	—	9	1	no	—
550	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
551	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
552	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
553	C₂²⋊C₄	—	9	1	no	—
554	C₂²⋊C₄	—	9	1	no	—
555	C₂²⋊C₄	—	9	1	no	—
556	C₂²⋊C₄	—	9	1	no	—
557	C₂²⋊C₄	—	9	1	no	—
558	C₂²⋊C₄	—	9	1	no	—
559	C₂²⋊C₄	—	9	1	no	—
560	C₂²⋊C₄	—	9	1	no	—
561	C₂²⋊C₄	—	9	1	no	—
562	C₂²⋊C₄	—	9	1	no	—
563	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
564	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
565	C₄²	—	9	1	no	—
566	C₂²×C₃	—	2	1	no	—
567	C₂²×C₃	—	2	1	no	—
568	C₂²×C₃	—	2	1	no	—
569	C₂²×C₃	—	3	1	no	—
570	C₂²×C₃	—	6	1	no	—
571	C₂²×C₃	—	6	1	no	—
572	C₂²×C₃	—	6	1	no	—
573	C₂²×C₃	—	18	1	no	—
574	C₂²×C₃	—	18	1	no	—
575	C₂²×C₃	—	18	1	no	—
576	C₂²×C₃	—	18	1	no	—
577	C₂²×C₃	—	18	1	no	—
578	C₂²×C₃	—	18	1	no	—
579	C₂²×C₃	—	18	1	no	—
580	C₂²×C₃	—	18	1	no	—
581	C₂²×C₃	—	18	1	no	—
582	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
583	C₂×D₃	—	6	1	no	—
584	C₂×D₃	—	6	1	no	—
585	C₂×D₃	—	6	1	no	—
586	C₂×D₃	—	6	1	no	—
587	C₂×D₃	—	6	1	no	—
588	C₂×D₃	—	6	1	no	—
589	C₂×D₃	—	6	1	no	—
590	C₂×D₃	—	6	1	no	—
591	C₂×D₃	—	6	1	no	—
592	C₃×C₄	—	2	1	no	—
593	C₃×C₄	—	2	1	no	—
594	C₃×C₄	—	2	1	no	—
595	C₃×C₄	—	2	1	no	—
596	C₃×C₄	—	2	1	no	—
597	C₃×C₄	—	2	1	no	—
598	C₃×C₄	—	6	1	no	—
599	C₃×C₄	—	6	1	no	—
600	C₃×C₄	—	6	1	no	—
601	C₃×C₄	—	6	1	no	—
602	C₃×C₄	—	6	1	no	—
603	C₃×C₄	—	6	1	no	—
604	C₃×C₄	—	18	1	no	—
605	C₃×C₄	—	18	1	no	—
606	C₃×C₄	—	18	1	no	—
607	C₃×C₄	—	18	1	no	—
608	C₃×C₄	—	18	1	no	—
609	Dic₃	—	6	1	no	—
610	Dic₃	—	6	1	no	—
611	Dic₃	—	6	1	no	—
612	Dic₃	—	6	1	no	—
613	Dic₃	—	6	1	no	—
614	C₃²	#5647	1	1	yes	characteristic
615	C₉	—	2	1	no	—
616	C₉	C₃×#562	1	1	yes	characteristic, complemented
617	C₂³	—	9	1	no	—
618	C₂³	—	9	1	no	—
619	C₂³	—	9	1	no	—
620	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
621	Q₈	—	4	1	no	—
622	Q₈	—	36	1	no	—
623	D₄	—	36	1	no	—
624	D₄	—	36	1	no	—
625	D₄	—	36	1	no	—
626	D₄	—	36	1	no	—
627	D₄	—	36	1	no	—
628	D₄	—	36	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	9	1	no	—
631	C₂×C₄	—	9	1	no	—
632	C₂×C₄	—	9	1	no	—
633	C₂×C₄	—	9	1	no	—
634	C₂×C₄	—	9	1	no	—
635	C₂×C₄	—	36	1	no	—
636	C₂×C₄	—	36	1	no	—
637	C₂×C₄	—	36	1	no	—
638	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
639	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
640	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
641	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
642	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
643	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
644	C₂×C₃	—	3	1	no	—
645	C₂×C₃	—	3	1	no	—
646	C₂×C₃	—	3	1	no	—
647	C₂×C₃	—	4	1	no	—
648	C₂×C₃	—	12	1	no	—
649	C₂×C₃	—	36	1	no	—
650	C₂×C₃	—	36	1	no	—
651	C₂×C₃	—	36	1	no	—
652	C₂×C₃	C₃×#1004	1	1	yes	characteristic
653	C₂×C₃	C₃×#1007	1	1	yes	characteristic
654	C₂×C₃	C₃×#1009	1	1	yes	characteristic
655	D₃	—	12	1	no	—
656	D₃	—	12	1	no	—
657	D₃	—	12	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	18	1	no	—
662	C₂²	—	18	1	no	—
663	C₂²	—	18	1	no	—
664	C₂²	—	18	1	no	—
665	C₂²	—	18	1	no	—
666	C₂²	—	18	1	no	—
667	C₂²	—	18	1	no	—
668	C₂²	—	18	1	no	—
669	C₂²	—	18	1	no	—
670	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	18	1	no	—
678	C₄	—	18	1	no	—
679	C₄	—	18	1	no	—
680	C₄	—	18	1	no	—
681	C₄	—	18	1	no	—
682	C₃	—	3	1	no	—
683	C₃	C₃×#5647	1	1	yes	characteristic
684	C₂	—	4	1	no	—
685	C₂	—	36	1	no	—
686	C₂	—	36	1	no	—
687	C₂	—	36	1	no	—
688	C₂	#63710⋊C₃	1	1	yes	characteristic
689	C₂	#11722630	1	1	yes	characteristic
690	C₂	#11722641	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	3₋¹⁺²×C₂²⋊Q₈	C₂
hypercenter	C₂²⋊Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#562
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×C₂²⋊Q₈	C₂	semidirect
2. #63509⋊C₃	C₂	semidirect
3. #63508⋊C₃	C₂	semidirect
4. #63492⋊C₃	C₂	semidirect
5. #63491⋊C₃	C₂	semidirect
6. #63459⋊C₃	C₂	semidirect
7. #63458⋊C₃	C₂	semidirect
8. #63457⋊C₃	C₂	semidirect
9. #63456⋊C₃	C₂	semidirect
10. #63456⋊C₃	C₂	semidirect
11. #63451⋊C₃	C₂	semidirect
12. #63447⋊C₃	C₂	semidirect
13. #63446⋊C₃	C₂	semidirect
14. #63446⋊C₃	C₂	semidirect
15. #63445⋊C₃	C₂	semidirect
17. #10589749	C₃	semidirect
69. C₉×C₂²⋊Q₈	C₂×C₃	semidirect
70. #63509	C₂×C₃	semidirect
71. #63508	C₂×C₃	semidirect
72. #63492	C₂×C₃	semidirect
73. #63491	C₂×C₃	semidirect
74. #63459	C₂×C₃	semidirect
75. #63458	C₂×C₃	semidirect
76. #63457	C₂×C₃	semidirect
77. #63456	C₂×C₃	semidirect
78. #63456	C₂×C₃	semidirect
79. #63451	C₂×C₃	semidirect
80. #63447	C₂×C₃	semidirect
81. #63446	C₂×C₃	semidirect
82. #63446	C₂×C₃	semidirect
83. #63445	C₂×C₃	semidirect
453. C₂²⋊Q₈	AGL(1,ℤ/9)	semidirect
458. 3₋¹⁺²	#562	semidirect
616. C₉	C₃×#562	semidirect

Maximal subgroups

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

subgroup	index
3₋¹⁺²×C₂²⋊Q₈	2
#63509⋊C₃	2
#63508⋊C₃	2
#63492⋊C₃	2
#63491⋊C₃	2
#63459⋊C₃	2
#63458⋊C₃	2
#63457⋊C₃	2
#63456⋊C₃	2
#63451⋊C₃	2
#63447⋊C₃	2
#63446⋊C₃	2
#63445⋊C₃	2
C₃×#5647	3
#10589749	3

Subgroups — #10589749⋊C3 #13152994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589749⋊C₃ #13152994