Subgroups — #44534962

Order 31347.

1082 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812526	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#16812525	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#16812524	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×3₋¹⁺²×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	#23782809	C₃	1	1	yes	maximal, characteristic, complemented
6	#23782809	C₃	1	1	yes	maximal, characteristic, complemented
7	#23782809	C₃	1	1	yes	maximal, characteristic, complemented
8	#23782808	C₃	1	1	yes	maximal, characteristic, complemented
9	#23782806	C₃	1	1	yes	maximal, characteristic, complemented
10	#23782805	C₃	1	3	yes	maximal, complemented
11	#23782804	C₃	1	3	yes	maximal, complemented
12	#23782801	C₃	1	3	yes	maximal, complemented
13	#23782801	C₃	1	3	yes	maximal, complemented
14	#23782801	C₃	1	3	yes	maximal, complemented
15	#23782801	C₃	1	3	yes	maximal, complemented
16	#23782801	C₃	1	3	yes	maximal, complemented
17	#23782801	C₃	1	3	yes	maximal, complemented
18	#23782795	C₃	1	1	yes	maximal, characteristic, complemented
19	(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
20	#23782783	C₃	1	3	yes	maximal, complemented
21	C₃×(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
22	C₄₃×#6893	C₃	1	1	yes	maximal, characteristic, complemented
23	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
24	#16812526	—	3	9	no	—
25	#16812525	—	3	9	no	—
26	#16812524	—	3	9	no	—
27	C₃×#11923958	C₃²	1	1	yes	characteristic
28	C₃×#11923958	C₃²	1	1	yes	characteristic
29	C₃×#11923958	C₃²	1	1	yes	characteristic
30	C₃×#11923958	C₃²	1	1	yes	characteristic
31	C₃×#11923958	C₃²	1	3	yes	complemented
32	C₃×#11923958	C₃²	1	3	yes	complemented
33	C₃×#11923957	C₃²	1	3	yes	—
34	C₃×#11923957	C₃²	1	3	yes	complemented
35	C₃×#11923957	C₃²	1	3	yes	complemented
36	C₃×#11923956	C₃²	1	3	yes	—
37	C₃×#11923956	C₃²	1	3	yes	complemented
38	C₃×#11923956	C₃²	1	3	yes	complemented
39	3₋¹⁺²×C₄₃⋊C₃	—	3	9	no	—
40	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
41	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
42	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
43	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
44	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
45	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
46	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
47	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	complemented
48	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	—
49	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	complemented
50	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	complemented
51	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	complemented
52	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	complemented
53	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	complemented
54	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
55	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
56	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
57	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
58	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
59	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
60	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
61	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
62	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
63	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	—
64	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	—
65	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	—
66	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
67	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
68	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
69	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
70	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
71	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
72	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
73	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
74	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
75	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
76	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
77	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
78	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
79	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
80	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	1	yes	characteristic
81	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
82	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	complemented
83	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	complemented
84	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	complemented
85	C₃²×C₄₃⋊C₃	—	3	3	no	—
86	C₃²×C₄₃⋊C₃	—	3	3	no	—
87	C₃²×C₄₃⋊C₃	—	9	1	no	—
88	C₃²×C₄₃⋊C₃	—	9	1	no	—
89	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
90	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
91	C₃²×C₄₃⋊C₃	C₃³	1	3	yes	—
92	C₃²×C₄₃⋊C₃	C₃³	1	3	yes	—
93	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
94	#11923958	—	3	3	no	—
95	#11923958	—	3	3	no	—
96	#11923958	—	3	3	no	—
97	#11923958	—	3	9	no	—
98	#11923958	—	3	9	no	—
99	#11923958	H(3,𝔽₃)	1	9	yes	complemented
100	#11923957	—	3	9	no	—
101	#11923957	—	3	9	no	—
102	#11923957	—	3	9	no	—
103	#11923956	—	3	9	no	—
104	#11923956	—	3	9	no	—
105	#11923956	—	3	9	no	—
106	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
107	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
108	C₃²⋊(C₄₃⋊C₃)	—	3	9	no	—
109	C₃²⋊(C₄₃⋊C₃)	—	9	3	no	—
110	C₃²⋊(C₄₃⋊C₃)	—	9	3	no	—
111	C₃×C₄₃⋊C₉	—	3	3	no	—
112	C₃×C₄₃⋊C₉	—	3	3	no	—
113	C₃×C₄₃⋊C₉	—	3	9	no	—
114	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
115	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
116	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
117	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
118	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
119	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
120	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
121	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
122	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
123	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
124	C₉×C₄₃⋊C₃	—	3	9	no	—
125	C₉×C₄₃⋊C₃	—	3	9	no	—
126	C₉×C₄₃⋊C₃	—	3	9	no	—
127	C₃³×C₄₃	C₃³	1	3	yes	—
128	C₃³×C₄₃	C₃³	1	1	yes	characteristic
129	3₋¹⁺²×C₄₃	—	3	3	no	—
130	3₋¹⁺²×C₄₃	—	3	3	no	—
131	H(3,𝔽₃)×C₄₃	—	3	3	no	—
132	C₃×C₉×C₄₃	—	3	3	no	—
133	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
134	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
135	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
136	C₃×C₉×C₄₃	C₃³	1	3	yes	—
137	C₃×C₉×C₄₃	C₃³	1	3	yes	—
138	#10624896	—	43	1	no	maximal, Sylow
139	C₃²×C₄₃	—	3	1	no	—
140	C₃²×C₄₃	—	3	1	no	—
141	C₃²×C₄₃	—	3	1	no	—
142	C₃²×C₄₃	—	3	3	no	—
143	C₃²×C₄₃	—	3	3	no	—
144	C₃²×C₄₃	—	3	3	no	—
145	C₃²×C₄₃	—	3	3	no	—
146	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	3	yes	—
147	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
148	C₃×C₄₃⋊C₃	—	3	1	no	—
149	C₃×C₄₃⋊C₃	—	3	1	no	—
150	C₃×C₄₃⋊C₃	—	3	1	no	—
151	C₃×C₄₃⋊C₃	—	3	3	no	—
152	C₃×C₄₃⋊C₃	—	3	3	no	—
153	C₃×C₄₃⋊C₃	—	3	1	no	—
154	C₃×C₄₃⋊C₃	—	3	1	no	—
155	C₃×C₄₃⋊C₃	—	3	3	no	—
156	C₃×C₄₃⋊C₃	—	3	3	no	—
157	C₃×C₄₃⋊C₃	—	3	1	no	—
158	C₃×C₄₃⋊C₃	—	3	1	no	—
159	C₃×C₄₃⋊C₃	—	3	1	no	—
160	C₃×C₄₃⋊C₃	—	3	1	no	—
161	C₃×C₄₃⋊C₃	—	3	3	no	—
162	C₃×C₄₃⋊C₃	—	3	3	no	—
163	C₃×C₄₃⋊C₃	—	3	3	no	—
164	C₃×C₄₃⋊C₃	—	3	3	no	—
165	C₃×C₄₃⋊C₃	—	3	1	no	—
166	C₃×C₄₃⋊C₃	—	3	1	no	—
167	C₃×C₄₃⋊C₃	—	9	9	no	—
168	C₃×C₄₃⋊C₃	#737	1	3	yes	complemented
169	C₉×C₄₃	—	3	1	no	—
170	C₉×C₄₃	—	3	1	no	—
171	C₉×C₄₃	—	3	1	no	—
172	C₉×C₄₃	—	3	3	no	—
173	C₉×C₄₃	—	3	3	no	—
174	C₄₃⋊C₉	—	3	1	no	—
175	C₄₃⋊C₉	—	3	3	no	—
176	C₄₃⋊C₉	—	3	3	no	—
177	C₄₃⋊C₉	—	3	1	no	—
178	C₄₃⋊C₉	—	3	1	no	—
179	C₄₃⋊C₉	—	3	1	no	—
180	C₄₃⋊C₉	—	3	1	no	—
181	C₄₃⋊C₉	—	3	1	no	—
182	C₄₃⋊C₉	—	3	3	no	—
183	C₄₃⋊C₉	C₃×H(3,𝔽₃)	1	9	yes	—
184	C₃×#737	—	43	1	no	—
185	C₃×#737	—	43	1	no	—
186	C₃×#737	—	43	1	no	—
187	C₃²×3₋¹⁺²	—	43	1	no	—
188	#6893	—	43	1	no	—
189	#6893	—	43	1	no	—
190	#6893	—	43	1	no	—
191	#6893	—	43	1	no	—
192	#6893	—	43	1	no	—
193	#6893	C₄₃⋊C₃	1	1	yes	characteristic, complemented
194	C₉⋊H(3,𝔽₃)	—	43	3	no	—
195	C₉⋊H(3,𝔽₃)	—	43	3	no	—
196	C₉⋊H(3,𝔽₃)	—	43	3	no	—
197	C₉⋊H(3,𝔽₃)	—	43	3	no	—
198	C₉⋊H(3,𝔽₃)	—	43	3	no	—
199	C₉⋊H(3,𝔽₃)	—	43	3	no	—
200	C₉⋊H(3,𝔽₃)	—	43	3	no	—
201	C₉⋊H(3,𝔽₃)	—	43	3	no	—
202	#6891	—	43	1	no	—
203	C₃²⋊H(3,𝔽₃)	—	43	1	no	—
204	C₉×H(3,𝔽₃)	—	43	3	no	—
205	C₃×C₃²⋊C₉	—	43	1	no	—
206	C₃×C₄₃	—	3	3	no	—
207	C₃×C₄₃	—	9	3	no	—
208	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
209	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
210	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
211	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
212	C₄₃⋊C₃	—	3	3	no	—
213	C₄₃⋊C₃	—	9	3	no	—
214	C₄₃⋊C₃	—	9	3	no	—
215	C₄₃⋊C₃	—	9	1	no	—
216	C₄₃⋊C₃	—	9	1	no	—
217	C₃⁴	—	43	1	no	—
218	#737	—	129	9	no	—
219	#737	—	129	9	no	—
220	#737	—	129	9	no	—
221	C₃×3₋¹⁺²	—	43	1	no	—
222	C₃×3₋¹⁺²	—	43	1	no	—
223	C₃×3₋¹⁺²	—	43	1	no	—
224	C₃×3₋¹⁺²	—	43	1	no	—
225	C₃×3₋¹⁺²	—	43	3	no	—
226	C₃×3₋¹⁺²	—	43	3	no	—
227	C₃×3₋¹⁺²	—	43	3	no	—
228	C₃×3₋¹⁺²	—	43	3	no	—
229	C₃×3₋¹⁺²	—	43	3	no	—
230	C₃×3₋¹⁺²	—	43	3	no	—
231	C₃×3₋¹⁺²	—	43	3	no	—
232	C₃×3₋¹⁺²	—	43	3	no	—
233	C₃×3₋¹⁺²	—	129	9	no	—
234	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
235	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
236	C₃×H(3,𝔽₃)	—	43	1	no	—
237	C₃×H(3,𝔽₃)	—	43	1	no	—
238	C₃×H(3,𝔽₃)	—	43	3	no	—
239	C₃×H(3,𝔽₃)	—	43	3	no	—
240	C₃×H(3,𝔽₃)	—	43	3	no	—
241	C₃×H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	1	yes	characteristic
242	C₃²×C₉	—	43	1	no	—
243	C₃²×C₉	—	43	1	no	—
244	C₃²×C₉	—	43	3	no	—
245	C₃²×C₉	—	43	3	no	—
246	C₃²×C₉	—	43	3	no	—
247	C₃²×C₉	—	43	3	no	—
248	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
249	C₃²⋊C₉	—	43	3	no	—
250	C₃²⋊C₉	—	43	3	no	—
251	C₃²⋊C₉	—	43	3	no	—
252	C₃²⋊C₉	—	43	1	no	—
253	C₃²⋊C₉	—	43	1	no	—
254	C₃²⋊C₉	—	43	1	no	—
255	C₃²⋊C₉	—	43	1	no	—
256	C₃²⋊C₉	—	43	1	no	—
257	C₃²⋊C₉	—	43	1	no	—
258	C₃²⋊C₉	—	43	1	no	—
259	C₃²⋊C₉	—	43	1	no	—
260	C₃²⋊C₉	—	43	1	no	—
261	C₃²⋊C₉	—	43	3	no	—
262	C₃²⋊C₉	—	43	3	no	—
263	C₃²⋊C₉	—	43	3	no	—
264	C₃²⋊C₉	—	43	3	no	—
265	C₃²⋊C₉	—	43	3	no	—
266	C₃²⋊C₉	—	43	3	no	—
267	C₃²⋊C₉	—	43	3	no	—
268	C₃²⋊C₉	—	43	3	no	—
269	C₃²⋊C₉	—	43	3	no	—
270	C₃²⋊C₉	—	43	3	no	—
271	C₃²⋊C₉	—	43	3	no	—
272	C₃²⋊C₉	—	43	3	no	—
273	C₃²⋊C₉	—	43	3	no	—
274	C₃²⋊C₉	—	43	3	no	—
275	C₃²⋊C₉	—	43	3	no	—
276	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	complemented
277	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	complemented
278	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	complemented
279	C₄₃	#10624896	1	1	yes	characteristic, complemented, Sylow
280	C₃³	—	43	1	no	—
281	C₃³	—	43	3	no	—
282	C₃³	—	43	3	no	—
283	C₃³	—	43	1	no	—
284	C₃³	—	43	1	no	—
285	C₃³	—	129	3	no	—
286	C₃³	—	129	3	no	—
287	C₃³	—	387	1	no	—
288	C₃³	—	387	1	no	—
289	C₃³	C₃²×C₄₃⋊C₃	1	3	yes	—
290	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
291	3₋¹⁺²	—	3	3	no	—
292	3₋¹⁺²	—	3	3	no	—
293	3₋¹⁺²	—	43	9	no	—
294	3₋¹⁺²	—	129	9	no	—
295	3₋¹⁺²	—	129	9	no	—
296	3₋¹⁺²	—	129	9	no	—
297	3₋¹⁺²	—	129	9	no	—
298	3₋¹⁺²	—	129	9	no	—
299	3₋¹⁺²	—	129	9	no	—
300	3₋¹⁺²	—	129	9	no	—
301	3₋¹⁺²	—	129	9	no	—
302	3₋¹⁺²	—	129	3	no	—
303	3₋¹⁺²	—	129	3	no	—
304	3₋¹⁺²	—	129	3	no	—
305	H(3,𝔽₃)	—	3	3	no	—
306	H(3,𝔽₃)	—	129	9	no	—
307	H(3,𝔽₃)	—	129	3	no	—
308	H(3,𝔽₃)	—	129	3	no	—
309	H(3,𝔽₃)	—	387	3	no	—
310	H(3,𝔽₃)	—	387	3	no	—
311	C₃×C₉	—	3	3	no	—
312	C₃×C₉	—	43	3	no	—
313	C₃×C₉	—	43	1	no	—
314	C₃×C₉	—	43	1	no	—
315	C₃×C₉	—	43	3	no	—
316	C₃×C₉	—	43	3	no	—
317	C₃×C₉	—	43	1	no	—
318	C₃×C₉	—	43	1	no	—
319	C₃×C₉	—	43	1	no	—
320	C₃×C₉	—	43	1	no	—
321	C₃×C₉	—	43	3	no	—
322	C₃×C₉	—	129	9	no	—
323	C₃×C₉	—	129	9	no	—
324	C₃×C₉	—	129	9	no	—
325	C₃×C₉	—	129	9	no	—
326	C₃×C₉	—	129	3	no	—
327	C₃×C₉	—	129	3	no	—
328	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
329	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
330	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
331	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
332	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
333	C₃²	—	3	1	no	—
334	C₃²	—	3	1	no	—
335	C₃²	—	3	1	no	—
336	C₃²	—	3	3	no	—
337	C₃²	—	3	3	no	—
338	C₃²	—	3	3	no	—
339	C₃²	—	3	3	no	—
340	C₃²	—	43	3	no	—
341	C₃²	—	129	1	no	—
342	C₃²	—	129	1	no	—
343	C₃²	—	129	1	no	—
344	C₃²	—	129	3	no	—
345	C₃²	—	129	3	no	—
346	C₃²	—	129	1	no	—
347	C₃²	—	129	1	no	—
348	C₃²	—	129	1	no	—
349	C₃²	—	129	3	no	—
350	C₃²	—	129	3	no	—
351	C₃²	—	129	1	no	—
352	C₃²	—	129	1	no	—
353	C₃²	—	129	3	no	—
354	C₃²	—	129	3	no	—
355	C₃²	—	129	1	no	—
356	C₃²	—	129	3	no	—
357	C₃²	—	129	3	no	—
358	C₃²	—	129	1	no	—
359	C₃²	—	129	1	no	—
360	C₃²	—	387	9	no	—
361	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	3	yes	—
362	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
363	C₉	—	3	1	no	—
364	C₉	—	3	1	no	—
365	C₉	—	3	1	no	—
366	C₉	—	3	3	no	—
367	C₉	—	3	3	no	—
368	C₉	—	43	9	no	—
369	C₉	—	129	1	no	—
370	C₉	—	129	1	no	—
371	C₉	—	129	3	no	—
372	C₉	—	129	3	no	—
373	C₉	—	129	1	no	—
374	C₉	—	129	1	no	—
375	C₉	—	129	3	no	—
376	C₉	—	129	1	no	—
377	C₉	—	129	1	no	—
378	C₃	—	3	3	no	—
379	C₃	—	9	3	no	—
380	C₃	—	129	3	no	—
381	C₃	—	387	3	no	—
382	C₃	—	387	3	no	—
383	C₃	—	387	1	no	—
384	C₃	—	387	1	no	—
385	C₃	C₃×H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
386	C₃	#737×C₄₃⋊C₃	1	1	yes	characteristic
387	C₃	#23782921	1	1	yes	characteristic
388	C₃	#23782922	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×#6893	C₃
prime radical	(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	C₃
hypercenter	#6893	C₄₃⋊C₃
hypocenter	C₄₃	#10624896
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ #6893

Complements

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

N	H ≅ G/N	type
1. C₃×#16812526	C₃	semidirect
2. C₃×#16812525	C₃	semidirect
3. C₃×#16812524	C₃	semidirect
4. C₃×3₋¹⁺²×C₄₃⋊C₃	C₃	semidirect
5. #23782809	C₃	semidirect
6. #23782809	C₃	semidirect
7. #23782809	C₃	semidirect
8. #23782808	C₃	semidirect
9. #23782806	C₃	semidirect
10. #23782805	C₃	semidirect
11. #23782804	C₃	semidirect
12. #23782801	C₃	semidirect
13. #23782801	C₃	semidirect
14. #23782801	C₃	semidirect
15. #23782801	C₃	semidirect
16. #23782801	C₃	semidirect
17. #23782801	C₃	semidirect
18. #23782795	C₃	semidirect
20. #23782783	C₃	semidirect
21. C₃×(C₃×C₄₃⋊C₃)⋊C₉	C₃	semidirect
22. C₄₃×#6893	C₃	semidirect
31. C₃×#11923958	C₃²	semidirect
32. C₃×#11923958	C₃²	semidirect
34. C₃×#11923957	C₃²	semidirect
35. C₃×#11923957	C₃²	semidirect
37. C₃×#11923956	C₃²	semidirect
38. C₃×#11923956	C₃²	semidirect
47. C₃²×C₄₃⋊C₉	C₃²	semidirect
49. C₃×C₉×C₄₃⋊C₃	C₃²	semidirect
50. C₃×C₉×C₄₃⋊C₃	C₃²	semidirect
51. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
52. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
53. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
66. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
67. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
68. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
69. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
70. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
71. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
72. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
73. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
74. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
75. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
76. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
77. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
82. C₄₃×C₃²⋊C₉	C₃²	semidirect
83. C₄₃×C₃²⋊C₉	C₃²	semidirect
84. C₄₃×C₃²⋊C₉	C₃²	semidirect
99. #11923958	H(3,𝔽₃)	semidirect
168. C₃×C₄₃⋊C₃	#737	semidirect
193. #6893	C₄₃⋊C₃	semidirect
276. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
277. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
278. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
279. C₄₃	#10624896	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812526	3
C₃×#16812525	3
C₃×#16812524	3
C₃×3₋¹⁺²×C₄₃⋊C₃	3
#23782809	3
#23782808	3
#23782806	3
#23782805	3
#23782804	3
#23782801	3
#23782795	3
(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	3
#23782783	3
C₃×(C₃×C₄₃⋊C₃)⋊C₉	3
C₄₃×#6893	3
#10624896	43