Subgroups — #19103233

Order 5103.

662 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13133592	C₃	1	1	yes	maximal, characteristic, complemented
2	#13133591	C₃	1	1	yes	maximal, characteristic, complemented
3	#13133590	C₃	1	1	yes	maximal, characteristic, complemented
4	#13133589	C₃	1	1	yes	maximal, characteristic, complemented
5	#13133586	C₃	1	1	yes	maximal, characteristic, complemented
6	#13133585	C₃	1	1	yes	maximal, characteristic, complemented
7	#13133584	C₃	1	1	yes	maximal, characteristic, complemented
8	#13133584	C₃	1	1	yes	maximal, characteristic, complemented
9	#13133582	C₃	1	1	yes	maximal, characteristic, complemented
10	#13133581	C₃	1	1	yes	maximal, characteristic, complemented
11	#13133581	C₃	1	1	yes	maximal, characteristic, complemented
12	#13133580	C₃	1	1	yes	maximal, characteristic, complemented
13	#13133580	C₃	1	1	yes	maximal, characteristic, complemented
14	#13133577	C₃	1	1	yes	maximal, characteristic, complemented
15	#13133577	C₃	1	1	yes	maximal, characteristic, complemented
16	#13133576	C₃	1	1	yes	maximal, characteristic, complemented
17	#13133575	C₃	1	1	yes	maximal, characteristic, complemented
18	#13133572	C₃	1	1	yes	maximal, characteristic, complemented
19	#13133569	C₃	1	1	yes	maximal, characteristic, complemented
20	#13133569	C₃	1	1	yes	maximal, characteristic, complemented
21	#13133562	C₃	1	1	yes	maximal, characteristic, complemented
22	#13133561	C₃	1	1	yes	maximal, characteristic, complemented
23	#13133559	C₃	1	1	yes	maximal, characteristic, complemented
24	#13133558	C₃	1	1	yes	maximal, characteristic, complemented
25	#13133555	C₃	1	1	yes	maximal, characteristic
26	#13133549	C₃	1	1	yes	maximal, characteristic
27	#13133547	C₃	1	1	yes	maximal, characteristic
28	C₉×#4428	C₃	1	1	yes	maximal, characteristic, complemented
29	C₉×#4428	C₃	1	1	yes	maximal, characteristic, complemented
30	C₉×#4428	C₃	1	1	yes	maximal, characteristic, complemented
31	C₉×#4427	C₃	1	1	yes	maximal, characteristic, complemented
32	C₉×#4427	C₃	1	1	yes	maximal, characteristic, complemented
33	C₉×#4427	C₃	1	1	yes	maximal, characteristic, complemented
34	C₉×#4430	C₃	1	1	yes	maximal, characteristic, complemented
35	C₉×C₇⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
36	#13133530	C₃	1	1	yes	maximal, characteristic, complemented
37	#13133528	C₃	1	1	yes	maximal, characteristic, complemented
38	#13133528	C₃	1	1	yes	maximal, characteristic, complemented
39	C₉²×ΓL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic, complemented
40	C₇×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
41	#10624877	—	7	1	no	maximal, Sylow
42	C₃×C₇×3₋¹⁺²	C₃²	1	1	yes	characteristic
43	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
44	C₃×C₇⋊H(3,𝔽₃)	C₃²	1	1	yes	characteristic
45	C₃×#4430	C₃²	1	1	yes	characteristic
46	C₃×#4428	C₃²	1	1	yes	characteristic
47	C₃×#4428	C₃²	1	1	yes	characteristic
48	C₃×#4428	C₃²	1	1	yes	characteristic
49	C₃×#4427	C₃²	1	1	yes	characteristic
50	C₃×#4427	C₃²	1	1	yes	characteristic
51	C₃×#4427	C₃²	1	1	yes	characteristic
52	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
53	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
54	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
55	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
56	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
57	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
58	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
59	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
60	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
61	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
62	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
63	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
64	C₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
65	C₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
66	C₇×C₉²	C₃²	1	1	yes	characteristic
67	C₇×C₉²	C₃²	1	1	yes	characteristic
68	C₇×C₉²	C₃²	1	1	yes	characteristic
69	C₃²⋊(C₇⋊C₉)	C₃²	1	1	yes	characteristic
70	C₃²⋊(C₇⋊C₉)	C₃²	1	1	yes	characteristic
71	C₃²⋊(C₇⋊C₉)	C₃²	1	1	yes	characteristic
72	C₃²⋊(C₇⋊C₉)	C₃²	1	1	yes	characteristic
73	C₃²⋊(C₇⋊C₉)	C₃²	1	1	yes	characteristic
74	C₃²⋊(C₇⋊C₉)	C₃²	1	1	yes	characteristic
75	C₃²⋊(C₇⋊C₉)	C₃²	1	1	yes	characteristic
76	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
77	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
78	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
79	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
80	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
81	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
82	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
83	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
84	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
85	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
86	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
87	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
88	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
89	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
90	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
91	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
92	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
93	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
94	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
95	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
96	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
97	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
98	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
99	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	1	yes	characteristic
100	#10588036	C₃²	1	1	yes	characteristic
101	#10588036	C₃²	1	1	yes	characteristic
102	#10588036	C₃²	1	1	yes	characteristic
103	#10588036	C₃²	1	1	yes	characteristic
104	#10588036	C₃²	1	1	yes	characteristic
105	#10588036	C₃²	1	1	yes	characteristic
106	#10588036	C₃²	1	1	yes	characteristic
107	#10588036	C₃²	1	1	yes	characteristic
108	#10588036	C₃²	1	1	yes	characteristic
109	#10588035	C₃²	1	1	yes	characteristic
110	#10588035	C₃²	1	1	yes	characteristic
111	#10588035	C₃²	1	1	yes	characteristic
112	#10588035	C₃²	1	1	yes	characteristic
113	#10588035	C₃²	1	1	yes	characteristic
114	#10588035	C₃²	1	1	yes	characteristic
115	#10588035	C₃²	1	1	yes	characteristic
116	#10588035	C₃²	1	1	yes	characteristic
117	#10588035	C₃²	1	1	yes	characteristic
118	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
119	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
120	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
121	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
122	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
123	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
124	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
125	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
126	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
127	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
128	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
129	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
130	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
131	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
132	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
133	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
134	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
135	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
136	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
137	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
138	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
139	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
140	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
141	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
142	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
143	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
144	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
145	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
146	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
147	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
148	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
149	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
150	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
151	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
152	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
153	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
154	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
155	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
156	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
157	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
158	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
159	(C₇⋊C₉)⋊C₉	C₃²	1	1	yes	characteristic
160	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
161	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
162	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
163	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
164	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
165	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
166	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
167	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
168	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
169	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
170	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
171	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
172	#6899	—	7	1	no	—
173	#6899	—	7	1	no	—
174	#6899	—	7	1	no	—
175	#6899	—	7	1	no	—
176	#6899	—	7	1	no	—
177	#6899	—	7	1	no	—
178	#6898	—	7	1	no	—
179	#6898	—	7	1	no	—
180	#6898	—	7	1	no	—
181	#6897	—	7	1	no	—
182	#6897	—	7	1	no	—
183	#6897	—	7	1	no	—
184	#6897	—	7	1	no	—
185	#6897	—	7	1	no	—
186	#6897	—	7	1	no	—
187	#6896	—	7	1	no	—
188	#6896	—	7	1	no	—
189	#6896	—	7	1	no	—
190	#6895	—	7	1	no	—
191	#6895	—	7	1	no	—
192	#6894	—	7	1	no	—
193	#6894	—	7	1	no	—
194	#6894	—	7	1	no	—
195	#6894	—	7	1	no	—
196	#6893	—	7	1	no	—
197	C₉⋊H(3,𝔽₃)	—	7	1	no	—
198	C₉⋊H(3,𝔽₃)	—	7	1	no	—
199	C₉×3₋¹⁺²	—	7	1	no	—
200	C₉×3₋¹⁺²	—	7	1	no	—
201	C₉×3₋¹⁺²	—	7	1	no	—
202	C₉×3₋¹⁺²	—	7	1	no	—
203	C₉×3₋¹⁺²	—	7	1	no	—
204	C₉×3₋¹⁺²	—	7	1	no	—
205	C₉×3₋¹⁺²	—	7	1	no	—
206	C₉×3₋¹⁺²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
207	C₉×H(3,𝔽₃)	—	7	1	no	—
208	#6887	—	7	1	no	—
209	#6887	—	7	1	no	—
210	#6887	—	7	1	no	—
211	C₃×C₉²	—	7	1	no	—
212	C₃³×C₇	C₃³	1	1	yes	characteristic
213	C₃²×ΓL(1,𝔽₈)	C₃³	1	1	yes	characteristic
214	C₃²×ΓL(1,𝔽₈)	C₃³	1	1	yes	characteristic
215	C₃²×ΓL(1,𝔽₈)	C₃³	1	1	yes	characteristic
216	C₇×3₋¹⁺²	—	3	3	no	—
217	C₃×C₇×C₉	—	3	3	no	—
218	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
219	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
220	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
221	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
222	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
223	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
224	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
225	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
226	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
227	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
228	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
229	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
230	C₇⋊H(3,𝔽₃)	—	3	3	no	—
231	#4430	—	3	3	no	—
232	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
233	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
234	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
235	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
236	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
237	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
238	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
239	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
240	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
241	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
242	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
243	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
244	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
245	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
246	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
247	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
248	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
249	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
250	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
251	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
252	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
253	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
254	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
255	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
256	#4428	—	3	3	no	—
257	#4428	—	3	3	no	—
258	#4428	—	3	3	no	—
259	#4427	—	3	3	no	—
260	#4427	—	3	3	no	—
261	#4427	—	3	3	no	—
262	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
263	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
264	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
265	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
266	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
267	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
268	C₃×3₋¹⁺²	—	7	1	no	—
269	C₃×3₋¹⁺²	—	7	1	no	—
270	C₃×3₋¹⁺²	—	7	1	no	—
271	C₃×3₋¹⁺²	—	7	1	no	—
272	C₃×3₋¹⁺²	—	7	1	no	—
273	C₃×3₋¹⁺²	—	7	1	no	—
274	C₃×3₋¹⁺²	—	7	1	no	—
275	C₃×3₋¹⁺²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
276	C₃×H(3,𝔽₃)	—	7	1	no	—
277	C₃²×C₉	—	7	1	no	—
278	C₃²×C₉	—	7	1	no	—
279	C₃²×C₉	—	7	1	no	—
280	C₃²×C₉	—	7	1	no	—
281	C₃²×C₉	—	7	1	no	—
282	C₃²×C₉	—	7	1	no	—
283	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
284	C₉⋊C₉	—	7	1	no	—
285	C₉⋊C₉	—	7	1	no	—
286	C₉⋊C₉	—	7	1	no	—
287	C₉⋊C₉	—	7	1	no	—
288	C₉⋊C₉	—	7	1	no	—
289	C₉⋊C₉	—	7	1	no	—
290	C₉⋊C₉	—	7	1	no	—
291	C₉⋊C₉	—	7	1	no	—
292	C₉⋊C₉	—	7	1	no	—
293	C₉⋊C₉	—	7	1	no	—
294	C₉⋊C₉	—	7	1	no	—
295	C₉⋊C₉	—	7	1	no	—
296	C₉⋊C₉	—	7	1	no	—
297	C₉⋊C₉	—	7	1	no	—
298	C₉⋊C₉	—	7	1	no	—
299	C₉⋊C₉	—	7	1	no	—
300	C₉⋊C₉	—	7	1	no	—
301	C₉⋊C₉	—	7	1	no	—
302	C₉⋊C₉	—	7	1	no	—
303	C₉⋊C₉	—	7	1	no	—
304	C₉⋊C₉	—	7	1	no	—
305	C₉⋊C₉	—	7	1	no	—
306	C₉⋊C₉	—	7	1	no	—
307	C₉⋊C₉	—	7	1	no	—
308	C₉⋊C₉	—	7	1	no	—
309	C₉⋊C₉	—	7	1	no	—
310	C₉⋊C₉	—	7	1	no	—
311	C₉⋊C₉	—	7	1	no	—
312	C₉⋊C₉	—	7	1	no	—
313	C₉⋊C₉	—	7	1	no	—
314	C₉⋊C₉	—	7	1	no	—
315	C₉⋊C₉	—	7	1	no	—
316	C₉⋊C₉	—	7	1	no	—
317	C₉⋊C₉	—	7	1	no	—
318	C₉⋊C₉	—	7	1	no	—
319	C₉⋊C₉	—	7	1	no	—
320	C₉⋊C₉	—	7	1	no	—
321	C₉⋊C₉	—	7	1	no	—
322	C₉⋊C₉	—	7	1	no	—
323	C₉⋊C₉	—	7	1	no	—
324	C₉⋊C₉	—	7	1	no	—
325	C₉⋊C₉	—	7	1	no	—
326	C₉⋊C₉	—	7	1	no	—
327	C₉⋊C₉	—	7	1	no	—
328	C₉⋊C₉	—	7	1	no	—
329	C₉⋊C₉	—	7	1	no	—
330	C₉⋊C₉	—	7	1	no	—
331	C₉⋊C₉	—	7	1	no	—
332	C₉⋊C₉	—	7	1	no	—
333	C₉⋊C₉	—	7	1	no	—
334	C₉⋊C₉	—	7	1	no	—
335	C₉⋊C₉	—	7	1	no	—
336	C₉⋊C₉	—	7	1	no	—
337	C₉⋊C₉	—	7	1	no	—
338	C₉⋊C₉	—	7	1	no	—
339	C₉⋊C₉	—	7	1	no	—
340	C₉⋊C₉	—	7	1	no	—
341	C₉⋊C₉	—	7	1	no	—
342	C₉⋊C₉	—	7	1	no	—
343	C₉⋊C₉	—	7	1	no	—
344	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
345	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
346	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
347	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
348	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
349	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
350	C₃²⋊C₉	—	7	1	no	—
351	C₃²⋊C₉	—	7	1	no	—
352	C₃²⋊C₉	—	7	1	no	—
353	C₃²⋊C₉	—	7	1	no	—
354	C₃²⋊C₉	—	7	1	no	—
355	C₃²⋊C₉	—	7	1	no	—
356	C₃²⋊C₉	—	7	1	no	—
357	C₃²⋊C₉	—	7	1	no	—
358	C₃²⋊C₉	—	7	1	no	—
359	C₃²⋊C₉	—	7	1	no	—
360	C₃²⋊C₉	—	7	1	no	—
361	C₃²⋊C₉	—	7	1	no	—
362	C₃²⋊C₉	—	7	1	no	—
363	C₃²⋊C₉	—	7	1	no	—
364	C₃²⋊C₉	—	7	1	no	—
365	C₃²⋊C₉	—	7	1	no	—
366	C₃²⋊C₉	—	7	1	no	—
367	C₃²⋊C₉	—	7	1	no	—
368	C₃²⋊C₉	—	7	1	no	—
369	C₃²⋊C₉	—	7	1	no	—
370	C₃²⋊C₉	—	7	1	no	—
371	C₃²⋊C₉	—	7	1	no	—
372	C₃²⋊C₉	—	7	1	no	—
373	C₃²⋊C₉	—	7	1	no	—
374	C₃²⋊C₉	—	7	1	no	—
375	C₃²⋊C₉	—	7	1	no	—
376	C₃²⋊C₉	—	7	1	no	—
377	C₃²⋊C₉	—	7	1	no	—
378	C₃²⋊C₉	—	7	1	no	—
379	C₃²⋊C₉	—	7	1	no	—
380	C₃²⋊C₉	—	7	1	no	—
381	C₃²⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
382	C₃²⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
383	C₉²	—	7	1	no	—
384	C₉²	—	7	1	no	—
385	C₉²	—	7	1	no	—
386	C₉²	—	7	1	no	—
387	C₉²	—	7	1	no	—
388	C₉²	—	7	1	no	—
389	C₉²	—	7	1	no	—
390	C₉²	—	7	1	no	—
391	C₉²	—	7	1	no	—
392	C₉²	—	7	1	no	—
393	C₉²	—	7	1	no	—
394	C₉²	—	7	1	no	—
395	C₉²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
396	C₉²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
397	C₉²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
398	C₃²×C₇	—	3	1	no	—
399	C₃²×C₇	—	3	1	no	—
400	C₃²×C₇	—	3	1	no	—
401	C₃²×C₇	—	3	1	no	—
402	C₃²×C₇	C₃⁴	1	1	yes	characteristic
403	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
404	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
405	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
406	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
407	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
408	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
409	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
410	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
411	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
412	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
413	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
414	C₃×ΓL(1,𝔽₈)	#737	1	3	yes	—
415	C₇×C₉	—	3	1	no	—
416	C₇×C₉	—	3	1	no	—
417	C₇×C₉	—	3	1	no	—
418	C₇×C₉	—	3	1	no	—
419	C₇×C₉	—	3	1	no	—
420	C₇×C₉	—	3	1	no	—
421	C₇×C₉	—	3	1	no	—
422	C₇×C₉	—	3	1	no	—
423	C₇×C₉	—	3	1	no	—
424	C₇×C₉	—	3	1	no	—
425	C₇×C₉	#737	1	3	yes	—
426	C₇×C₉	#737	1	3	yes	—
427	C₇⋊C₉	—	3	1	no	—
428	C₇⋊C₉	—	3	1	no	—
429	C₇⋊C₉	—	3	1	no	—
430	C₇⋊C₉	—	3	1	no	—
431	C₇⋊C₉	—	3	1	no	—
432	C₇⋊C₉	—	3	1	no	—
433	C₇⋊C₉	—	3	1	no	—
434	C₇⋊C₉	—	3	1	no	—
435	C₇⋊C₉	—	3	1	no	—
436	C₇⋊C₉	—	3	1	no	—
437	C₇⋊C₉	—	3	1	no	—
438	C₇⋊C₉	—	3	1	no	—
439	C₇⋊C₉	—	3	1	no	—
440	C₇⋊C₉	—	3	1	no	—
441	C₇⋊C₉	—	3	1	no	—
442	C₇⋊C₉	—	3	1	no	—
443	C₇⋊C₉	—	3	1	no	—
444	C₇⋊C₉	—	3	1	no	—
445	C₇⋊C₉	—	3	1	no	—
446	C₇⋊C₉	—	3	1	no	—
447	C₇⋊C₉	—	3	1	no	—
448	C₇⋊C₉	—	3	1	no	—
449	C₇⋊C₉	—	3	1	no	—
450	C₇⋊C₉	#737	1	3	yes	—
451	C₃³	—	7	1	no	—
452	C₃³	—	7	1	no	—
453	C₃³	—	7	1	no	—
454	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
455	3₋¹⁺²	—	3	3	no	—
456	3₋¹⁺²	—	21	3	no	—
457	3₋¹⁺²	—	21	3	no	—
458	3₋¹⁺²	—	21	3	no	—
459	3₋¹⁺²	—	21	3	no	—
460	3₋¹⁺²	—	21	3	no	—
461	3₋¹⁺²	—	21	3	no	—
462	3₋¹⁺²	—	21	3	no	—
463	H(3,𝔽₃)	—	21	3	no	—
464	C₃×C₉	—	3	3	no	—
465	C₃×C₉	—	7	1	no	—
466	C₃×C₉	—	7	1	no	—
467	C₃×C₉	—	7	1	no	—
468	C₃×C₉	—	7	1	no	—
469	C₃×C₉	—	7	1	no	—
470	C₃×C₉	—	7	1	no	—
471	C₃×C₉	—	7	1	no	—
472	C₃×C₉	—	7	1	no	—
473	C₃×C₉	—	7	1	no	—
474	C₃×C₉	—	7	1	no	—
475	C₃×C₉	—	7	1	no	—
476	C₃×C₉	—	7	1	no	—
477	C₃×C₉	—	7	1	no	—
478	C₃×C₉	—	7	1	no	—
479	C₃×C₉	—	7	1	no	—
480	C₃×C₉	—	7	1	no	—
481	C₃×C₉	—	7	1	no	—
482	C₃×C₉	—	7	1	no	—
483	C₃×C₉	—	7	1	no	—
484	C₃×C₉	—	7	1	no	—
485	C₃×C₉	—	7	1	no	—
486	C₃×C₉	—	7	1	no	—
487	C₃×C₉	—	7	1	no	—
488	C₃×C₉	—	7	1	no	—
489	C₃×C₉	—	21	3	no	—
490	C₃×C₉	—	21	3	no	—
491	C₃×C₉	—	21	3	no	—
492	C₃×C₉	—	21	3	no	—
493	C₃×C₉	—	21	3	no	—
494	C₃×C₉	—	21	3	no	—
495	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
496	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
497	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
498	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
499	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
500	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
501	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
502	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
503	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
504	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
505	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
506	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
507	C₃×C₇	—	9	1	no	—
508	C₃×C₇	C₃×#737	1	1	yes	characteristic
509	C₃×C₇	C₃×#737	1	1	yes	characteristic
510	C₃×C₇	C₃×#737	1	1	yes	characteristic
511	C₃×C₇	C₃×#737	1	1	yes	characteristic
512	ΓL(1,𝔽₈)	—	3	3	no	—
513	ΓL(1,𝔽₈)	—	9	1	no	—
514	ΓL(1,𝔽₈)	—	9	1	no	—
515	C₃²	—	3	1	no	—
516	C₃²	—	3	1	no	—
517	C₃²	—	3	1	no	—
518	C₃²	—	3	1	no	—
519	C₃²	—	7	3	no	—
520	C₃²	—	21	1	no	—
521	C₃²	—	21	1	no	—
522	C₃²	—	21	1	no	—
523	C₃²	—	21	1	no	—
524	C₃²	—	21	1	no	—
525	C₃²	—	21	1	no	—
526	C₃²	—	21	1	no	—
527	C₃²	—	21	1	no	—
528	C₃²	—	21	1	no	—
529	C₃²	—	21	1	no	—
530	C₃²	—	21	1	no	—
531	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
532	C₉	—	3	1	no	—
533	C₉	—	3	1	no	—
534	C₉	—	3	1	no	—
535	C₉	—	3	1	no	—
536	C₉	—	3	1	no	—
537	C₉	—	3	1	no	—
538	C₉	—	3	1	no	—
539	C₉	—	3	1	no	—
540	C₉	—	3	1	no	—
541	C₉	—	3	1	no	—
542	C₉	—	7	3	no	—
543	C₉	—	21	1	no	—
544	C₉	—	21	1	no	—
545	C₉	—	21	1	no	—
546	C₉	—	21	1	no	—
547	C₉	—	21	1	no	—
548	C₉	—	21	1	no	—
549	C₉	—	21	1	no	—
550	C₉	—	21	1	no	—
551	C₉	—	21	1	no	—
552	C₉	—	21	1	no	—
553	C₉	—	21	1	no	—
554	C₉	—	21	1	no	—
555	C₉	—	21	1	no	—
556	C₉	—	21	1	no	—
557	C₉	—	21	1	no	—
558	C₉	—	21	1	no	—
559	C₉	—	21	1	no	—
560	C₉	—	21	1	no	—
561	C₉	—	21	1	no	—
562	C₉	—	21	1	no	—
563	C₉	—	21	1	no	—
564	C₉	—	21	1	no	—
565	C₉	—	21	1	no	—
566	C₉	#10588061	1	3	yes	—
567	C₉	#10588065	1	3	yes	—
568	C₇	#10624877	1	1	yes	characteristic, complemented, Sylow
569	C₃	—	9	1	no	—
570	C₃	—	21	3	no	—
571	C₃	—	63	1	no	—
572	C₃	—	63	1	no	—
573	C₃	ΓL(1,𝔽₈)×#737	1	1	yes	characteristic
574	C₃	ΓL(1,𝔽₈)×#737	1	1	yes	characteristic
575	C₃	C₃×#10588061	1	1	yes	characteristic
576	C₃	C₃×#10588065	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²×ΓL(1,𝔽₈)
commutator, socle	C₃²×C₇	C₃⁴
Frattini	C₃²	C₃³×ΓL(1,𝔽₈)
Fitting	C₇×C₉×3₋¹⁺²	C₃
hypercenter	C₉×3₋¹⁺²	ΓL(1,𝔽₈)
hypocenter	C₇	#10624877
LCS	G ▷ C₃²×C₇ ▷ C₇
UCS	C₁ ◁ C₃×C₉ ◁ C₉×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #13133592	C₃	semidirect
2. #13133591	C₃	semidirect
3. #13133590	C₃	semidirect
4. #13133589	C₃	semidirect
5. #13133586	C₃	semidirect
6. #13133585	C₃	semidirect
7. #13133584	C₃	semidirect
8. #13133584	C₃	semidirect
9. #13133582	C₃	semidirect
10. #13133581	C₃	semidirect
11. #13133581	C₃	semidirect
12. #13133580	C₃	semidirect
13. #13133580	C₃	semidirect
14. #13133577	C₃	semidirect
15. #13133577	C₃	semidirect
16. #13133576	C₃	semidirect
17. #13133575	C₃	semidirect
18. #13133572	C₃	semidirect
19. #13133569	C₃	semidirect
20. #13133569	C₃	semidirect
21. #13133562	C₃	semidirect
22. #13133561	C₃	semidirect
23. #13133559	C₃	semidirect
24. #13133558	C₃	semidirect
28. C₉×#4428	C₃	semidirect
29. C₉×#4428	C₃	semidirect
30. C₉×#4428	C₃	semidirect
31. C₉×#4427	C₃	semidirect
32. C₉×#4427	C₃	semidirect
33. C₉×#4427	C₃	semidirect
34. C₉×#4430	C₃	semidirect
36. #13133530	C₃	semidirect
37. #13133528	C₃	semidirect
38. #13133528	C₃	semidirect
39. C₉²×ΓL(1,𝔽₈)	C₃	semidirect
40. C₇×C₉×3₋¹⁺²	C₃	semidirect
206. C₉×3₋¹⁺²	ΓL(1,𝔽₈)	semidirect
568. C₇	#10624877	semidirect