Subgroups — #19103249

Order 5103.

758 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#10588061	C₃	1	1	yes	maximal, characteristic
2	#13133597	C₃	1	1	yes	maximal, characteristic, complemented
3	#13133596	C₃	1	1	yes	maximal, characteristic, complemented
4	#13133593	C₃	1	1	yes	maximal, characteristic, complemented
5	#13133590	C₃	1	2	yes	maximal, complemented
6	#13133589	C₃	1	2	yes	maximal, complemented
7	#13133585	C₃	1	2	yes	maximal, complemented
8	#13133576	C₃	1	1	yes	maximal, characteristic, complemented
9	#13133575	C₃	1	1	yes	maximal, characteristic, complemented
10	#13133574	C₃	1	2	yes	maximal, complemented
11	#13133574	C₃	1	2	yes	maximal, complemented
12	#13133572	C₃	1	1	yes	maximal, characteristic, complemented
13	#13133571	C₃	1	2	yes	maximal, complemented
14	#13133562	C₃	1	2	yes	maximal, complemented
15	#13133561	C₃	1	2	yes	maximal, complemented
16	#13133559	C₃	1	1	yes	maximal, characteristic, complemented
17	#13133558	C₃	1	1	yes	maximal, characteristic, complemented
18	#13133549	C₃	1	2	yes	maximal
19	#13133547	C₃	1	1	yes	maximal, characteristic
20	C₉×#4428	C₃	1	2	yes	maximal, complemented
21	C₉×#4428	C₃	1	1	yes	maximal, characteristic, complemented
22	C₉×#4427	C₃	1	2	yes	maximal, complemented
23	C₉×#4427	C₃	1	1	yes	maximal, characteristic, complemented
24	C₉×#4430	C₃	1	2	yes	maximal, complemented
25	#13133528	C₃	1	2	yes	maximal, complemented
26	C₉²×ΓL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic, complemented
27	C₇×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
28	#10624879	—	7	1	no	maximal, Sylow
29	C₃×C₇×3₋¹⁺²	C₃²	1	1	yes	characteristic
30	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
31	C₃×C₇⋊H(3,𝔽₃)	C₃²	1	1	yes	characteristic
32	C₃×#4430	C₃²	1	1	yes	characteristic
33	C₃×#4430	C₃²	1	2	yes	—
34	C₃×#4430	C₃²	1	1	yes	characteristic
35	#10588061	—	3	9	no	—
36	C₃×#4428	C₃²	1	1	yes	characteristic
37	C₃×#4428	C₃²	1	2	yes	—
38	C₃×#4428	C₃²	1	1	yes	characteristic
39	C₃×#4428	C₃²	1	1	yes	characteristic
40	C₃×#4428	C₃²	1	1	yes	characteristic
41	C₃×#4427	C₃²	1	1	yes	characteristic
42	C₃×#4427	C₃²	1	2	yes	—
43	C₃×#4427	C₃²	1	1	yes	characteristic
44	C₃×#4427	C₃²	1	1	yes	characteristic
45	C₃×#4427	C₃²	1	1	yes	characteristic
46	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
47	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
48	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
49	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	2	yes	—
50	C₃×C₉×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
51	C₇×C₉⋊C₉	C₃²	1	2	yes	—
52	C₇×C₉⋊C₉	C₃²	1	2	yes	—
53	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
54	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
55	C₇×C₃²⋊C₉	C₃²	1	2	yes	—
56	C₇×C₉²	C₃²	1	1	yes	characteristic
57	C₇×C₉²	C₃²	1	2	yes	—
58	C₃²⋊(C₇⋊C₉)	C₃²	1	2	yes	—
59	C₃²⋊(C₇⋊C₉)	C₃²	1	2	yes	—
60	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
61	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
62	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
63	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
64	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
65	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
66	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
67	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
68	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃²	1	2	yes	—
69	#10588036	C₃²	1	2	yes	—
70	#10588036	C₃²	1	1	yes	characteristic
71	#10588036	C₃²	1	2	yes	—
72	#10588036	C₃²	1	1	yes	characteristic
73	#10588035	C₃²	1	2	yes	—
74	#10588035	C₃²	1	1	yes	characteristic
75	#10588035	C₃²	1	2	yes	—
76	#10588035	C₃²	1	1	yes	characteristic
77	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
78	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
79	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
80	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
81	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
82	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
83	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
84	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
85	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
86	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
87	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
88	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
89	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
90	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
91	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
92	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
93	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
94	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
95	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
96	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
97	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
98	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
99	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
100	(C₇⋊C₉)⋊C₉	C₃²	1	2	yes	—
101	C₉×C₇⋊C₉	C₃²	1	2	yes	—
102	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
103	C₉×C₇⋊C₉	C₃²	1	2	yes	—
104	C₉×C₇⋊C₉	C₃²	1	1	yes	characteristic
105	C₉×C₇⋊C₉	C₃²	1	2	yes	—
106	C₉×C₇⋊C₉	C₃²	1	2	yes	—
107	C₉×C₇⋊C₉	C₃²	1	2	yes	—
108	C₃×#737	—	7	1	no	—
109	#6900	—	7	1	no	—
110	#6900	—	7	1	no	—
111	#6900	—	7	1	no	—
112	#6899	—	7	2	no	—
113	#6899	—	7	2	no	—
114	#6899	—	7	2	no	—
115	#6896	—	7	1	no	—
116	#6896	—	7	2	no	—
117	#6896	—	7	2	no	—
118	#6896	—	7	1	no	—
119	#6896	—	7	1	no	—
120	#6896	—	7	2	no	—
121	#6894	—	7	1	no	—
122	#6894	—	7	1	no	—
123	#6894	—	7	2	no	—
124	#6894	—	7	2	no	—
125	C₉⋊H(3,𝔽₃)	—	7	1	no	—
126	C₉⋊H(3,𝔽₃)	—	7	2	no	—
127	C₉×3₋¹⁺²	—	7	2	no	—
128	C₉×3₋¹⁺²	—	7	2	no	—
129	C₉×3₋¹⁺²	—	7	1	no	—
130	C₉×3₋¹⁺²	—	7	2	no	—
131	C₉×3₋¹⁺²	—	7	1	no	—
132	C₉×3₋¹⁺²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
133	#6887	—	7	2	no	—
134	C₃×C₉²	—	7	1	no	—
135	C₃³×C₇	C₃³	1	1	yes	characteristic
136	C₃²×ΓL(1,𝔽₈)	C₃³	1	1	yes	characteristic
137	C₃²×ΓL(1,𝔽₈)	C₃³	1	1	yes	characteristic
138	C₃²×ΓL(1,𝔽₈)	C₃³	1	1	yes	characteristic
139	C₇×3₋¹⁺²	—	3	3	no	—
140	C₃×C₇×C₉	—	3	3	no	—
141	C₃×C₇×C₉	C₃³	1	2	yes	—
142	C₃×C₇×C₉	C₃³	1	2	yes	—
143	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
144	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
145	C₃×C₇×C₉	C₃³	1	2	yes	—
146	C₃×C₇×C₉	C₃³	1	2	yes	—
147	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
148	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
149	C₇⋊H(3,𝔽₃)	—	3	3	no	—
150	#4430	—	3	3	no	—
151	#4430	—	3	3	no	—
152	#4430	—	3	6	no	—
153	C₃×C₇⋊C₉	C₃³	1	2	yes	—
154	C₃×C₇⋊C₉	C₃³	1	2	yes	—
155	C₃×C₇⋊C₉	C₃³	1	2	yes	—
156	C₃×C₇⋊C₉	C₃³	1	2	yes	—
157	C₃×C₇⋊C₉	C₃³	1	2	yes	—
158	C₃×C₇⋊C₉	C₃³	1	2	yes	—
159	C₃×C₇⋊C₉	C₃³	1	2	yes	—
160	C₃×C₇⋊C₉	C₃³	1	2	yes	—
161	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
162	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
163	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
164	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
165	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
166	C₃×C₇⋊C₉	C₃³	1	1	yes	characteristic
167	C₃×C₇⋊C₉	C₃³	1	2	yes	—
168	#4428	—	3	3	no	—
169	#4428	—	3	3	no	—
170	#4428	—	3	3	no	—
171	#4428	—	3	3	no	—
172	#4428	—	3	6	no	—
173	#4427	—	3	3	no	—
174	#4427	—	3	3	no	—
175	#4427	—	3	3	no	—
176	#4427	—	3	3	no	—
177	#4427	—	3	6	no	—
178	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
179	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
180	C₉×ΓL(1,𝔽₈)	—	3	3	no	—
181	C₉×ΓL(1,𝔽₈)	—	3	6	no	—
182	C₉×ΓL(1,𝔽₈)	3₋¹⁺²	1	9	yes	complemented
183	#737	—	21	9	no	—
184	C₃×3₋¹⁺²	—	7	1	no	—
185	C₃×3₋¹⁺²	—	7	1	no	—
186	C₃×3₋¹⁺²	—	7	2	no	—
187	C₃×3₋¹⁺²	—	7	1	no	—
188	C₃×3₋¹⁺²	—	7	1	no	—
189	C₃×3₋¹⁺²	—	7	1	no	—
190	C₃×3₋¹⁺²	—	7	1	no	—
191	C₃×3₋¹⁺²	—	7	1	no	—
192	C₃×3₋¹⁺²	—	7	1	no	—
193	C₃×3₋¹⁺²	—	7	2	no	—
194	C₃×3₋¹⁺²	—	7	1	no	—
195	C₃×3₋¹⁺²	—	7	2	no	—
196	C₃×3₋¹⁺²	—	7	1	no	—
197	C₃×3₋¹⁺²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
198	C₃×H(3,𝔽₃)	—	7	1	no	—
199	C₃²×C₉	—	7	1	no	—
200	C₃²×C₉	—	7	2	no	—
201	C₃²×C₉	—	7	1	no	—
202	C₃²×C₉	—	7	1	no	—
203	C₃²×C₉	—	7	1	no	—
204	C₃²×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
205	C₉⋊C₉	—	7	2	no	—
206	C₉⋊C₉	—	7	2	no	—
207	C₉⋊C₉	—	7	2	no	—
208	C₉⋊C₉	—	7	2	no	—
209	C₉⋊C₉	—	7	2	no	—
210	C₉⋊C₉	—	7	2	no	—
211	C₉⋊C₉	—	7	2	no	—
212	C₉⋊C₉	—	7	2	no	—
213	C₉⋊C₉	—	7	2	no	—
214	C₉⋊C₉	—	7	2	no	—
215	C₉⋊C₉	—	7	2	no	—
216	C₉⋊C₉	—	7	2	no	—
217	C₉⋊C₉	—	7	2	no	—
218	C₉⋊C₉	—	7	2	no	—
219	C₉⋊C₉	—	7	2	no	—
220	C₉⋊C₉	—	7	2	no	—
221	C₉⋊C₉	—	7	2	no	—
222	C₉⋊C₉	—	7	2	no	—
223	C₉⋊C₉	—	7	2	no	—
224	C₉⋊C₉	—	7	2	no	—
225	C₉⋊C₉	—	7	2	no	—
226	C₉⋊C₉	—	7	2	no	—
227	C₉⋊C₉	—	7	2	no	—
228	C₉⋊C₉	—	7	2	no	—
229	C₉⋊C₉	—	7	2	no	—
230	C₉⋊C₉	—	7	2	no	—
231	C₉⋊C₉	—	7	1	no	—
232	C₉⋊C₉	—	7	1	no	—
233	C₉⋊C₉	—	7	2	no	—
234	C₉⋊C₉	—	7	2	no	—
235	C₉⋊C₉	—	7	1	no	—
236	C₉⋊C₉	—	7	1	no	—
237	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	2	yes	—
238	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	2	yes	—
239	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
240	C₉⋊C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
241	C₃²⋊C₉	—	7	2	no	—
242	C₃²⋊C₉	—	7	2	no	—
243	C₃²⋊C₉	—	7	2	no	—
244	C₃²⋊C₉	—	7	2	no	—
245	C₃²⋊C₉	—	7	2	no	—
246	C₃²⋊C₉	—	7	2	no	—
247	C₃²⋊C₉	—	7	2	no	—
248	C₃²⋊C₉	—	7	2	no	—
249	C₃²⋊C₉	—	7	2	no	—
250	C₃²⋊C₉	—	7	2	no	—
251	C₃²⋊C₉	—	7	2	no	—
252	C₃²⋊C₉	C₃×ΓL(1,𝔽₈)	1	2	yes	—
253	C₉²	—	7	2	no	—
254	C₉²	—	7	1	no	—
255	C₉²	—	7	2	no	—
256	C₉²	—	7	1	no	—
257	C₉²	—	7	2	no	—
258	C₉²	—	7	2	no	—
259	C₉²	—	7	2	no	—
260	C₉²	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
261	C₉²	C₃×ΓL(1,𝔽₈)	1	2	yes	—
262	C₃²×C₇	—	3	1	no	—
263	C₃²×C₇	—	3	2	no	—
264	C₃²×C₇	—	3	1	no	—
265	C₃²×C₇	C₃⁴	1	1	yes	characteristic
266	C₃×ΓL(1,𝔽₈)	—	3	2	no	—
267	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
268	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
269	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
270	C₃×ΓL(1,𝔽₈)	—	3	2	no	—
271	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
272	C₃×ΓL(1,𝔽₈)	—	3	2	no	—
273	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
274	C₃×ΓL(1,𝔽₈)	C₃×3₋¹⁺²	1	3	yes	—
275	C₇×C₉	—	3	1	no	—
276	C₇×C₉	—	3	1	no	—
277	C₇×C₉	—	3	2	no	—
278	C₇×C₉	—	3	2	no	—
279	C₇×C₉	—	3	2	no	—
280	C₇×C₉	—	3	2	no	—
281	C₇×C₉	C₃×3₋¹⁺²	1	3	yes	—
282	C₇×C₉	#737	1	3	yes	complemented
283	C₇⋊C₉	—	3	1	no	—
284	C₇⋊C₉	—	3	1	no	—
285	C₇⋊C₉	—	3	1	no	—
286	C₇⋊C₉	—	3	1	no	—
287	C₇⋊C₉	—	3	2	no	—
288	C₇⋊C₉	—	3	2	no	—
289	C₇⋊C₉	—	3	2	no	—
290	C₇⋊C₉	—	3	2	no	—
291	C₇⋊C₉	—	3	2	no	—
292	C₇⋊C₉	—	3	2	no	—
293	C₇⋊C₉	—	3	2	no	—
294	C₇⋊C₉	—	3	2	no	—
295	C₇⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
296	C₇⋊C₉	C₃×3₋¹⁺²	1	3	yes	—
297	C₇⋊C₉	#737	1	6	yes	complemented
298	C₃³	—	7	1	no	—
299	C₃³	—	7	1	no	—
300	C₃³	—	7	1	no	—
301	C₃³	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
302	3₋¹⁺²	—	3	3	no	—
303	3₋¹⁺²	—	21	6	no	—
304	3₋¹⁺²	—	21	3	no	—
305	3₋¹⁺²	—	21	3	no	—
306	3₋¹⁺²	—	21	6	no	—
307	3₋¹⁺²	—	21	3	no	—
308	3₋¹⁺²	—	21	3	no	—
309	3₋¹⁺²	—	21	3	no	—
310	3₋¹⁺²	—	21	3	no	—
311	3₋¹⁺²	—	21	6	no	—
312	3₋¹⁺²	—	21	3	no	—
313	3₋¹⁺²	—	21	3	no	—
314	3₋¹⁺²	—	21	3	no	—
315	3₋¹⁺²	—	21	3	no	—
316	H(3,𝔽₃)	—	21	3	no	—
317	C₃×C₉	—	3	3	no	—
318	C₃×C₉	—	7	1	no	—
319	C₃×C₉	—	7	1	no	—
320	C₃×C₉	—	7	2	no	—
321	C₃×C₉	—	7	9	no	—
322	C₃×C₉	—	7	2	no	—
323	C₃×C₉	—	7	2	no	—
324	C₃×C₉	—	7	2	no	—
325	C₃×C₉	—	7	2	no	—
326	C₃×C₉	—	7	2	no	—
327	C₃×C₉	—	7	2	no	—
328	C₃×C₉	—	7	2	no	—
329	C₃×C₉	—	7	2	no	—
330	C₃×C₉	—	7	1	no	—
331	C₃×C₉	—	7	1	no	—
332	C₃×C₉	—	7	1	no	—
333	C₃×C₉	—	7	1	no	—
334	C₃×C₉	—	21	6	no	—
335	C₃×C₉	—	21	3	no	—
336	C₃×C₉	—	21	3	no	—
337	C₃×C₉	—	21	3	no	—
338	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	2	yes	—
339	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	2	yes	—
340	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	2	yes	—
341	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	2	yes	—
342	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
343	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
344	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
345	C₃×C₉	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
346	C₃×C₇	—	9	1	no	—
347	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
348	C₃×C₇	C₃×#737	1	2	yes	—
349	C₃×C₇	C₃×#737	1	1	yes	characteristic
350	ΓL(1,𝔽₈)	—	3	3	no	—
351	ΓL(1,𝔽₈)	—	9	1	no	—
352	ΓL(1,𝔽₈)	—	9	1	no	—
353	C₃²	—	3	1	no	—
354	C₃²	—	3	2	no	—
355	C₃²	—	3	1	no	—
356	C₃²	—	7	3	no	—
357	C₃²	—	21	2	no	—
358	C₃²	—	21	1	no	—
359	C₃²	—	21	1	no	—
360	C₃²	—	21	1	no	—
361	C₃²	—	21	2	no	—
362	C₃²	—	21	2	no	—
363	C₃²	—	21	1	no	—
364	C₃²	—	21	1	no	—
365	C₃²	C₃³×ΓL(1,𝔽₈)	1	1	yes	characteristic
366	C₉	—	3	1	no	—
367	C₉	—	3	1	no	—
368	C₉	—	3	2	no	—
369	C₉	—	3	2	no	—
370	C₉	—	3	2	no	—
371	C₉	—	3	2	no	—
372	C₉	—	7	3	no	—
373	C₉	—	7	3	no	—
374	C₉	—	7	6	no	—
375	C₉	—	21	1	no	—
376	C₉	—	21	1	no	—
377	C₉	—	21	1	no	—
378	C₉	—	21	1	no	—
379	C₉	—	21	2	no	—
380	C₉	—	21	2	no	—
381	C₉	—	21	2	no	—
382	C₉	—	21	2	no	—
383	C₉	—	21	2	no	—
384	C₉	—	21	2	no	—
385	C₉	—	21	2	no	—
386	C₉	—	21	2	no	—
387	C₉	#10588061	1	3	yes	complemented
388	C₉	ΓL(1,𝔽₈)×3₋¹⁺²	1	3	yes	—
389	C₇	#10624879	1	1	yes	characteristic, complemented, Sylow
390	C₃	—	9	1	no	—
391	C₃	—	21	3	no	—
392	C₃	—	63	1	no	—
393	C₃	—	63	1	no	—
394	C₃	C₃×ΓL(1,𝔽₈)×3₋¹⁺²	1	1	yes	characteristic
395	C₃	ΓL(1,𝔽₈)×#737	1	2	yes	—
396	C₃	C₃×#10588061	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	#10624879
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
2. #13133597	C₃	semidirect
3. #13133596	C₃	semidirect
4. #13133593	C₃	semidirect
5. #13133590	C₃	semidirect
6. #13133589	C₃	semidirect
7. #13133585	C₃	semidirect
8. #13133576	C₃	semidirect
9. #13133575	C₃	semidirect
10. #13133574	C₃	semidirect
11. #13133574	C₃	semidirect
12. #13133572	C₃	semidirect
13. #13133571	C₃	semidirect
14. #13133562	C₃	semidirect
15. #13133561	C₃	semidirect
16. #13133559	C₃	semidirect
17. #13133558	C₃	semidirect
20. C₉×#4428	C₃	semidirect
21. C₉×#4428	C₃	semidirect
22. C₉×#4427	C₃	semidirect
23. C₉×#4427	C₃	semidirect
24. C₉×#4430	C₃	semidirect
25. #13133528	C₃	semidirect
26. C₉²×ΓL(1,𝔽₈)	C₃	semidirect
27. C₇×C₉×3₋¹⁺²	C₃	semidirect
132. C₉×3₋¹⁺²	ΓL(1,𝔽₈)	semidirect
182. C₉×ΓL(1,𝔽₈)	3₋¹⁺²	semidirect
282. C₇×C₉	#737	semidirect
297. C₇⋊C₉	#737	semidirect
387. C₉	#10588061	semidirect
389. C₇	#10624879	semidirect