Subgroups — #44535086

Order 31347.

788 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782809	C₃	1	3	yes	maximal, complemented
2	#23782807	C₃	1	3	yes	maximal, complemented
3	#23782807	C₃	1	3	yes	maximal, complemented
4	#23782805	C₃	1	1	yes	maximal, characteristic, complemented
5	#23782805	C₃	1	1	yes	maximal, characteristic, complemented
6	#23782804	C₃	1	1	yes	maximal, characteristic, complemented
7	#23782804	C₃	1	3	yes	maximal, complemented
8	#23782803	C₃	1	1	yes	maximal, characteristic, complemented
9	#23782801	C₃	1	3	yes	maximal, complemented
10	#23782801	C₃	1	3	yes	maximal, complemented
11	#23782800	C₃	1	1	yes	maximal, characteristic, complemented
12	#23782799	C₃	1	3	yes	maximal, complemented
13	#23782799	C₃	1	3	yes	maximal, complemented
14	#23782796	C₃	1	1	yes	maximal, characteristic, complemented
15	(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
16	H(3,𝔽₃)×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
17	C₉×C₃²⋊(C₄₃⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
18	#23782783	C₃	1	1	yes	maximal, characteristic, complemented
19	#23782783	C₃	1	3	yes	maximal, complemented
20	C₃×(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
21	C₃²⋊C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
22	C₄₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
23	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
24	C₃×#11923958	C₃²	1	3	yes	complemented
25	C₃×#11923957	C₃²	1	3	yes	complemented
26	C₃×#11923957	C₃²	1	3	yes	complemented
27	C₃×#11923956	C₃²	1	3	yes	—
28	C₃×#11923956	C₃²	1	3	yes	complemented
29	C₃×#11923956	C₃²	1	3	yes	complemented
30	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
31	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
32	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
33	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
34	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
35	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
36	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
37	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	complemented
38	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	—
39	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	complemented
40	C₃×C₉×C₄₃⋊C₃	C₃²	1	3	yes	complemented
41	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
42	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
43	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
44	C₃²⋊(C₄₃⋊C₉)	C₃²	1	1	yes	characteristic
45	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	complemented
46	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	complemented
47	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	complemented
48	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	complemented
49	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	—
50	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	—
51	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
52	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
53	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
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	3	yes	—
61	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	—
62	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
63	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
64	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
65	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	3	yes	complemented
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	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	complemented
75	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	1	yes	characteristic
76	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
77	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
78	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
79	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	complemented
80	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	complemented
81	C₃²×C₄₃⋊C₃	—	3	3	no	—
82	C₃²×C₄₃⋊C₃	—	3	3	no	—
83	C₃²×C₄₃⋊C₃	—	9	1	no	—
84	C₃²×C₄₃⋊C₃	—	9	1	no	—
85	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
86	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
87	C₃²×C₄₃⋊C₃	C₃³	1	3	yes	—
88	C₃²×C₄₃⋊C₃	C₃³	1	3	yes	—
89	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
90	#11923958	—	9	3	no	—
91	#11923957	—	9	3	no	—
92	#11923957	—	9	3	no	—
93	#11923956	—	9	3	no	—
94	#11923956	—	9	3	no	—
95	#11923956	—	9	3	no	—
96	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
97	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
98	C₃²⋊(C₄₃⋊C₃)	—	3	9	no	—
99	C₃²⋊(C₄₃⋊C₃)	—	9	3	no	—
100	C₃²⋊(C₄₃⋊C₃)	—	9	3	no	—
101	C₃×C₄₃⋊C₉	—	9	1	no	—
102	C₃×C₄₃⋊C₉	—	9	1	no	—
103	C₃×C₄₃⋊C₉	—	9	3	no	—
104	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
105	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
106	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
107	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
108	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
109	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
110	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
111	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
112	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
113	C₃×C₄₃⋊C₉	C₃³	1	3	yes	—
114	C₉×C₄₃⋊C₃	—	9	3	no	—
115	C₉×C₄₃⋊C₃	—	9	3	no	—
116	C₉×C₄₃⋊C₃	—	9	3	no	—
117	C₃³×C₄₃	C₃³	1	3	yes	—
118	C₃³×C₄₃	C₃³	1	1	yes	characteristic
119	3₋¹⁺²×C₄₃	—	9	3	no	—
120	H(3,𝔽₃)×C₄₃	—	3	3	no	—
121	C₃×C₉×C₄₃	—	9	1	no	—
122	C₃×C₉×C₄₃	C₃³	1	3	yes	—
123	C₃×C₉×C₄₃	C₃³	1	3	yes	—
124	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
125	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
126	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
127	#10624905	—	43	1	no	maximal, Sylow
128	C₃²×C₄₃	—	3	1	no	—
129	C₃²×C₄₃	—	3	1	no	—
130	C₃²×C₄₃	—	3	1	no	—
131	C₃²×C₄₃	—	3	3	no	—
132	C₃²×C₄₃	—	3	3	no	—
133	C₃²×C₄₃	—	3	3	no	—
134	C₃²×C₄₃	—	3	3	no	—
135	C₃²×C₄₃	#737	1	3	yes	—
136	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
137	C₃×C₄₃⋊C₃	—	3	1	no	—
138	C₃×C₄₃⋊C₃	—	3	1	no	—
139	C₃×C₄₃⋊C₃	—	3	1	no	—
140	C₃×C₄₃⋊C₃	—	3	3	no	—
141	C₃×C₄₃⋊C₃	—	3	3	no	—
142	C₃×C₄₃⋊C₃	—	3	3	no	—
143	C₃×C₄₃⋊C₃	—	3	3	no	—
144	C₃×C₄₃⋊C₃	—	3	1	no	—
145	C₃×C₄₃⋊C₃	—	3	1	no	—
146	C₃×C₄₃⋊C₃	—	3	1	no	—
147	C₃×C₄₃⋊C₃	—	3	1	no	—
148	C₃×C₄₃⋊C₃	—	3	3	no	—
149	C₃×C₄₃⋊C₃	—	3	3	no	—
150	C₃×C₄₃⋊C₃	—	3	1	no	—
151	C₃×C₄₃⋊C₃	—	3	1	no	—
152	C₃×C₄₃⋊C₃	—	3	1	no	—
153	C₃×C₄₃⋊C₃	—	3	3	no	—
154	C₃×C₄₃⋊C₃	—	3	3	no	—
155	C₃×C₄₃⋊C₃	—	3	1	no	—
156	C₃×C₄₃⋊C₃	—	9	9	no	—
157	C₃×C₄₃⋊C₃	#737	1	3	yes	—
158	C₉×C₄₃	—	3	1	no	—
159	C₉×C₄₃	—	3	1	no	—
160	C₉×C₄₃	—	3	1	no	—
161	C₉×C₄₃	—	3	3	no	—
162	C₉×C₄₃	—	3	3	no	—
163	C₄₃⋊C₉	—	3	3	no	—
164	C₄₃⋊C₉	—	3	1	no	—
165	C₄₃⋊C₉	—	3	3	no	—
166	C₄₃⋊C₉	—	3	3	no	—
167	C₄₃⋊C₉	—	3	1	no	—
168	C₄₃⋊C₉	—	3	1	no	—
169	C₄₃⋊C₉	—	3	3	no	—
170	C₄₃⋊C₉	—	3	1	no	—
171	C₄₃⋊C₉	—	3	1	no	—
172	C₄₃⋊C₉	—	3	1	no	—
173	#6893	—	43	3	no	—
174	#6893	—	43	3	no	—
175	#6893	—	43	3	no	—
176	C₉⋊H(3,𝔽₃)	—	43	3	no	—
177	C₉⋊H(3,𝔽₃)	—	43	3	no	—
178	C₉⋊H(3,𝔽₃)	—	43	1	no	—
179	C₉⋊H(3,𝔽₃)	—	43	1	no	—
180	C₉⋊H(3,𝔽₃)	—	43	1	no	—
181	C₉⋊H(3,𝔽₃)	—	43	1	no	—
182	C₉⋊H(3,𝔽₃)	—	43	1	no	—
183	C₉⋊H(3,𝔽₃)	—	43	3	no	—
184	C₉⋊H(3,𝔽₃)	—	43	3	no	—
185	C₉⋊H(3,𝔽₃)	—	43	3	no	—
186	C₉⋊H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic, complemented
187	#6891	—	43	1	no	—
188	C₃²⋊H(3,𝔽₃)	—	43	1	no	—
189	C₉×H(3,𝔽₃)	—	43	1	no	—
190	C₉×H(3,𝔽₃)	—	43	1	no	—
191	C₉×H(3,𝔽₃)	—	43	1	no	—
192	C₉×H(3,𝔽₃)	—	43	3	no	—
193	C₃×C₃²⋊C₉	—	43	1	no	—
194	C₃×C₃²⋊C₉	—	43	1	no	—
195	C₃×C₄₃	—	3	3	no	—
196	C₃×C₄₃	—	9	3	no	—
197	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
198	C₃×C₄₃	C₃×#737	1	1	yes	characteristic
199	C₃×C₄₃	H(5,𝔽₃)	1	1	yes	characteristic
200	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
201	C₄₃⋊C₃	—	3	3	no	—
202	C₄₃⋊C₃	—	9	3	no	—
203	C₄₃⋊C₃	—	9	3	no	—
204	C₄₃⋊C₃	—	9	1	no	—
205	C₄₃⋊C₃	—	9	1	no	—
206	C₃⁴	—	43	1	no	—
207	C₃×3₋¹⁺²	—	43	3	no	—
208	C₃×3₋¹⁺²	—	43	3	no	—
209	C₃×3₋¹⁺²	—	43	3	no	—
210	C₃×3₋¹⁺²	—	43	3	no	—
211	C₃×3₋¹⁺²	—	43	3	no	—
212	C₃×3₋¹⁺²	—	43	3	no	—
213	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	complemented
214	C₃×H(3,𝔽₃)	—	43	3	no	—
215	C₃×H(3,𝔽₃)	—	43	1	no	—
216	C₃×H(3,𝔽₃)	—	43	1	no	—
217	C₃×H(3,𝔽₃)	—	43	3	no	—
218	C₃×H(3,𝔽₃)	—	43	3	no	—
219	C₃×H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	1	yes	characteristic
220	C₃²×C₉	—	43	1	no	—
221	C₃²×C₉	—	43	1	no	—
222	C₃²×C₉	—	43	3	no	—
223	C₃²×C₉	—	43	3	no	—
224	C₃²×C₉	—	43	3	no	—
225	C₃²×C₉	—	43	3	no	—
226	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
227	C₃²⋊C₉	—	43	1	no	—
228	C₃²⋊C₉	—	43	1	no	—
229	C₃²⋊C₉	—	43	1	no	—
230	C₃²⋊C₉	—	43	1	no	—
231	C₃²⋊C₉	—	43	3	no	—
232	C₃²⋊C₉	—	43	3	no	—
233	C₃²⋊C₉	—	43	3	no	—
234	C₃²⋊C₉	—	43	3	no	—
235	C₃²⋊C₉	—	43	1	no	—
236	C₃²⋊C₉	—	43	1	no	—
237	C₃²⋊C₉	—	43	3	no	—
238	C₃²⋊C₉	—	43	1	no	—
239	C₃²⋊C₉	—	43	1	no	—
240	C₃²⋊C₉	—	43	1	no	—
241	C₃²⋊C₉	—	43	1	no	—
242	C₃²⋊C₉	—	43	1	no	—
243	C₃²⋊C₉	—	43	3	no	—
244	C₃²⋊C₉	—	43	1	no	—
245	C₃²⋊C₉	—	43	1	no	—
246	C₃²⋊C₉	—	43	3	no	—
247	C₃²⋊C₉	—	43	3	no	—
248	C₃²⋊C₉	—	43	3	no	—
249	C₃²⋊C₉	—	43	3	no	—
250	C₃²⋊C₉	—	43	3	no	—
251	C₃²⋊C₉	—	43	3	no	—
252	C₃²⋊C₉	—	43	3	no	—
253	C₃²⋊C₉	—	43	3	no	—
254	C₃²⋊C₉	—	43	3	no	—
255	C₃²⋊C₉	—	43	3	no	—
256	C₃²⋊C₉	—	43	3	no	—
257	C₃²⋊C₉	—	43	3	no	—
258	C₃²⋊C₉	—	43	3	no	—
259	C₃²⋊C₉	—	43	3	no	—
260	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
261	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
262	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	complemented
263	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	complemented
264	C₄₃	#10624905	1	1	yes	characteristic, complemented, Sylow
265	C₃³	—	43	1	no	—
266	C₃³	—	43	1	no	—
267	C₃³	—	43	3	no	—
268	C₃³	—	43	3	no	—
269	C₃³	—	43	1	no	—
270	C₃³	—	129	3	no	—
271	C₃³	—	129	3	no	—
272	C₃³	—	387	1	no	—
273	C₃³	—	387	1	no	—
274	C₃³	C₃²×C₄₃⋊C₃	1	3	yes	—
275	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
276	3₋¹⁺²	—	9	3	no	—
277	3₋¹⁺²	—	387	3	no	—
278	3₋¹⁺²	—	387	3	no	—
279	3₋¹⁺²	—	387	3	no	—
280	3₋¹⁺²	—	387	3	no	—
281	3₋¹⁺²	—	387	3	no	—
282	3₋¹⁺²	—	387	3	no	—
283	H(3,𝔽₃)	—	3	3	no	—
284	H(3,𝔽₃)	—	129	9	no	—
285	H(3,𝔽₃)	—	129	3	no	—
286	H(3,𝔽₃)	—	129	3	no	—
287	H(3,𝔽₃)	—	387	3	no	—
288	H(3,𝔽₃)	—	387	3	no	—
289	C₃×C₉	—	9	1	no	—
290	C₃×C₉	—	43	3	no	—
291	C₃×C₉	—	43	1	no	—
292	C₃×C₉	—	43	1	no	—
293	C₃×C₉	—	43	3	no	—
294	C₃×C₉	—	43	3	no	—
295	C₃×C₉	—	43	3	no	—
296	C₃×C₉	—	43	1	no	—
297	C₃×C₉	—	43	1	no	—
298	C₃×C₉	—	43	1	no	—
299	C₃×C₉	—	43	1	no	—
300	C₃×C₉	—	387	3	no	—
301	C₃×C₉	—	387	3	no	—
302	C₃×C₉	—	387	3	no	—
303	C₃×C₉	—	387	3	no	—
304	C₃×C₉	—	387	1	no	—
305	C₃×C₉	—	387	1	no	—
306	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
307	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
308	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
309	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
310	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
311	C₃²	—	3	1	no	—
312	C₃²	—	3	1	no	—
313	C₃²	—	3	1	no	—
314	C₃²	—	3	3	no	—
315	C₃²	—	3	3	no	—
316	C₃²	—	3	3	no	—
317	C₃²	—	3	3	no	—
318	C₃²	—	43	3	no	—
319	C₃²	—	129	1	no	—
320	C₃²	—	129	1	no	—
321	C₃²	—	129	1	no	—
322	C₃²	—	129	3	no	—
323	C₃²	—	129	3	no	—
324	C₃²	—	129	1	no	—
325	C₃²	—	129	1	no	—
326	C₃²	—	129	3	no	—
327	C₃²	—	129	3	no	—
328	C₃²	—	129	1	no	—
329	C₃²	—	129	1	no	—
330	C₃²	—	129	3	no	—
331	C₃²	—	129	3	no	—
332	C₃²	—	129	1	no	—
333	C₃²	—	129	1	no	—
334	C₃²	—	129	1	no	—
335	C₃²	—	129	3	no	—
336	C₃²	—	129	3	no	—
337	C₃²	—	129	1	no	—
338	C₃²	—	387	9	no	—
339	C₃²	#16812526	1	3	yes	—
340	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
341	C₉	—	3	1	no	—
342	C₉	—	3	1	no	—
343	C₉	—	3	1	no	—
344	C₉	—	3	3	no	—
345	C₉	—	3	3	no	—
346	C₉	—	129	3	no	—
347	C₉	—	129	1	no	—
348	C₉	—	129	1	no	—
349	C₉	—	129	3	no	—
350	C₉	—	129	3	no	—
351	C₉	—	129	1	no	—
352	C₉	—	129	3	no	—
353	C₉	—	129	1	no	—
354	C₉	—	129	1	no	—
355	C₉	—	129	1	no	—
356	C₃	—	3	3	no	—
357	C₃	—	9	3	no	—
358	C₃	—	129	3	no	—
359	C₃	—	387	3	no	—
360	C₃	—	387	3	no	—
361	C₃	—	387	1	no	—
362	C₃	—	387	1	no	—
363	C₃	#737×C₄₃⋊C₃	1	1	yes	characteristic
364	C₃	C₃×#16812526	1	1	yes	characteristic
365	C₃	C₄₃⋊H(5,𝔽₃)	1	1	yes	characteristic
366	C₃	#23782921	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×C₉⋊H(3,𝔽₃)	C₃
prime radical	(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	C₃
hypercenter	C₉⋊H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	#10624905
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₉⋊H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. #23782809	C₃	semidirect
2. #23782807	C₃	semidirect
3. #23782807	C₃	semidirect
4. #23782805	C₃	semidirect
5. #23782805	C₃	semidirect
6. #23782804	C₃	semidirect
7. #23782804	C₃	semidirect
8. #23782803	C₃	semidirect
9. #23782801	C₃	semidirect
10. #23782801	C₃	semidirect
11. #23782800	C₃	semidirect
12. #23782799	C₃	semidirect
13. #23782799	C₃	semidirect
14. #23782796	C₃	semidirect
16. H(3,𝔽₃)×C₄₃⋊C₉	C₃	semidirect
17. C₉×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
18. #23782783	C₃	semidirect
19. #23782783	C₃	semidirect
20. C₃×(C₃×C₄₃⋊C₃)⋊C₉	C₃	semidirect
21. C₃²⋊C₉×C₄₃⋊C₃	C₃	semidirect
22. C₄₃×C₉⋊H(3,𝔽₃)	C₃	semidirect
24. C₃×#11923958	C₃²	semidirect
25. C₃×#11923957	C₃²	semidirect
26. C₃×#11923957	C₃²	semidirect
28. C₃×#11923956	C₃²	semidirect
29. C₃×#11923956	C₃²	semidirect
37. C₃²×C₄₃⋊C₉	C₃²	semidirect
39. C₃×C₉×C₄₃⋊C₃	C₃²	semidirect
40. C₃×C₉×C₄₃⋊C₃	C₃²	semidirect
45. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
46. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
47. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
48. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
62. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
63. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
64. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
65. (C₃×C₄₃⋊C₃)⋊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. C₃×3₋¹⁺²×C₄₃	C₃²	semidirect
79. C₄₃×C₃²⋊C₉	C₃²	semidirect
80. C₄₃×C₃²⋊C₉	C₃²	semidirect
186. C₉⋊H(3,𝔽₃)	C₄₃⋊C₃	semidirect
213. C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	semidirect
262. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
263. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
264. C₄₃	#10624905	semidirect

Maximal subgroups

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

subgroup	index
#23782809	3
#23782807	3
#23782805	3
#23782804	3
#23782803	3
#23782801	3
#23782800	3
#23782799	3
#23782796	3
(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	3
H(3,𝔽₃)×C₄₃⋊C₉	3
C₉×C₃²⋊(C₄₃⋊C₃)	3
#23782783	3
C₃×(C₃×C₄₃⋊C₃)⋊C₉	3
C₃²⋊C₉×C₄₃⋊C₃	3
C₄₃×C₉⋊H(3,𝔽₃)	3
#10624905	43