Subgroups — #44535194

Order 31347.

740 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782809	C₃	1	2	yes	maximal, complemented
2	#23782808	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782807	C₃	1	2	yes	maximal, complemented
4	#23782807	C₃	1	2	yes	maximal, complemented
5	#23782807	C₃	1	2	yes	maximal, complemented
6	#23782805	C₃	1	2	yes	maximal, complemented
7	#23782805	C₃	1	2	yes	maximal, complemented
8	#23782802	C₃	1	1	yes	maximal, characteristic, complemented
9	#23782802	C₃	1	1	yes	maximal, characteristic, complemented
10	#23782801	C₃	1	2	yes	maximal, complemented
11	#23782801	C₃	1	2	yes	maximal, complemented
12	#23782801	C₃	1	2	yes	maximal, complemented
13	#23782801	C₃	1	2	yes	maximal, complemented
14	#23782801	C₃	1	2	yes	maximal, complemented
15	#23782801	C₃	1	2	yes	maximal, complemented
16	#23782800	C₃	1	2	yes	maximal, complemented
17	#23782799	C₃	1	2	yes	maximal, complemented
18	#23782799	C₃	1	2	yes	maximal, complemented
19	#23782799	C₃	1	2	yes	maximal, complemented
20	#23782797	C₃	1	1	yes	maximal, characteristic, complemented
21	#23782797	C₃	1	1	yes	maximal, characteristic, complemented
22	#23782795	C₃	1	1	yes	maximal, characteristic, complemented
23	(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
24	C₄₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
26	C₃×#11923958	C₃²	1	2	yes	—
27	C₃×#11923958	C₃²	1	2	yes	complemented
28	C₃×#11923958	C₃²	1	2	yes	complemented
29	C₃×#11923957	C₃²	1	2	yes	—
30	C₃×#11923957	C₃²	1	2	yes	—
31	C₃×#11923957	C₃²	1	1	yes	characteristic
32	C₃×#11923957	C₃²	1	1	yes	characteristic
33	C₃×#11923957	C₃²	1	2	yes	complemented
34	C₃×#11923957	C₃²	1	2	yes	complemented
35	C₃×#11923957	C₃²	1	2	yes	complemented
36	C₃×#11923956	C₃²	1	2	yes	complemented
37	C₃×#11923956	C₃²	1	2	yes	complemented
38	C₃×#11923956	C₃²	1	2	yes	complemented
39	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	2	yes	—
40	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	2	yes	—
41	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	2	yes	—
42	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
43	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
44	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
45	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	2	yes	—
46	C₃²×C₄₃⋊C₉	C₃²	1	2	yes	complemented
47	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	complemented
48	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	complemented
49	C₃×C₉×C₄₃⋊C₃	C₃²	1	2	yes	complemented
50	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
51	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	—
52	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	complemented
53	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	complemented
54	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	complemented
55	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	complemented
56	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	complemented
57	C₃²⋊(C₄₃⋊C₉)	C₃²	1	2	yes	complemented
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	2	yes	—
61	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
62	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
63	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
64	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
65	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
66	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
67	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
68	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
69	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	1	yes	characteristic
70	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
71	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	—
72	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
73	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
74	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
75	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
76	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
77	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
78	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
79	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
80	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
81	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
82	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
83	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
84	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
85	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
86	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
87	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
88	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
89	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	2	yes	complemented
90	C₃×3₋¹⁺²×C₄₃	C₃²	1	1	yes	characteristic
91	C₃×3₋¹⁺²×C₄₃	C₃²	1	2	yes	complemented
92	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	1	yes	characteristic
93	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic, complemented
94	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
95	C₄₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
96	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	complemented
97	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	complemented
98	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	complemented
99	C₃²×C₄₃⋊C₃	—	9	1	no	—
100	C₃²×C₄₃⋊C₃	—	9	1	no	—
101	C₃²×C₄₃⋊C₃	—	9	1	no	—
102	C₃²×C₄₃⋊C₃	—	9	1	no	—
103	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
104	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
105	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
106	C₃²×C₄₃⋊C₃	C₃³	1	2	yes	—
107	C₃²×C₄₃⋊C₃	C₃³	1	2	yes	—
108	C₃²×C₄₃⋊C₃	C₃³	1	2	yes	—
109	#11923958	—	9	2	no	—
110	#11923958	—	9	2	no	—
111	#11923958	—	9	2	no	—
112	#11923957	—	9	1	no	—
113	#11923957	—	9	1	no	—
114	#11923957	—	9	2	no	—
115	#11923957	—	9	2	no	—
116	#11923957	—	9	2	no	—
117	#11923957	—	9	2	no	—
118	#11923957	—	9	2	no	—
119	#11923956	—	9	2	no	—
120	#11923956	—	9	2	no	—
121	#11923956	—	9	2	no	—
122	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
123	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
124	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
125	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
126	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
127	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
128	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
129	C₃×C₄₃⋊C₉	—	9	2	no	—
130	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
131	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
132	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
133	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
134	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
135	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
136	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
137	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
138	C₃×C₄₃⋊C₉	C₃³	1	2	yes	—
139	C₉×C₄₃⋊C₃	—	9	2	no	—
140	C₉×C₄₃⋊C₃	—	9	2	no	—
141	C₉×C₄₃⋊C₃	—	9	2	no	—
142	C₃³×C₄₃	C₃³	1	1	yes	characteristic
143	C₃³×C₄₃	C₃³	1	1	yes	characteristic
144	C₃³×C₄₃	C₃³	1	2	yes	—
145	3₋¹⁺²×C₄₃	—	9	1	no	—
146	3₋¹⁺²×C₄₃	—	9	2	no	—
147	H(3,𝔽₃)×C₄₃	—	9	1	no	—
148	C₃×C₉×C₄₃	—	9	1	no	—
149	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
150	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
151	C₃×C₉×C₄₃	C₃³	1	2	yes	—
152	C₃×C₉×C₄₃	C₃³	1	2	yes	—
153	C₃×C₉×C₄₃	C₃³	1	2	yes	—
154	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
155	#10624910	—	43	1	no	maximal, Sylow
156	C₃²×C₄₃	—	3	1	no	—
157	C₃²×C₄₃	—	3	2	no	—
158	C₃²×C₄₃	—	3	1	no	—
159	C₃²×C₄₃	—	3	1	no	—
160	C₃²×C₄₃	—	3	2	no	—
161	C₃²×C₄₃	—	3	1	no	—
162	C₃²×C₄₃	—	3	1	no	—
163	C₃²×C₄₃	—	3	1	no	—
164	C₃²×C₄₃	—	3	2	no	—
165	C₃²×C₄₃	—	3	2	no	—
166	C₃²×C₄₃	—	3	1	no	—
167	C₃²×C₄₃	—	3	1	no	—
168	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
169	C₃×C₄₃⋊C₃	—	3	2	no	—
170	C₃×C₄₃⋊C₃	—	3	2	no	—
171	C₃×C₄₃⋊C₃	—	3	2	no	—
172	C₃×C₄₃⋊C₃	—	3	1	no	—
173	C₃×C₄₃⋊C₃	—	3	1	no	—
174	C₃×C₄₃⋊C₃	—	3	1	no	—
175	C₃×C₄₃⋊C₃	—	3	1	no	—
176	C₃×C₄₃⋊C₃	—	3	1	no	—
177	C₃×C₄₃⋊C₃	—	3	2	no	—
178	C₃×C₄₃⋊C₃	—	3	2	no	—
179	C₃×C₄₃⋊C₃	—	3	2	no	—
180	C₃×C₄₃⋊C₃	—	3	2	no	—
181	C₃×C₄₃⋊C₃	—	3	2	no	—
182	C₃×C₄₃⋊C₃	—	3	2	no	—
183	C₃×C₄₃⋊C₃	—	3	2	no	—
184	C₃×C₄₃⋊C₃	—	3	2	no	—
185	C₃×C₄₃⋊C₃	—	3	2	no	—
186	C₃×C₄₃⋊C₃	—	3	1	no	—
187	C₃×C₄₃⋊C₃	—	3	1	no	—
188	C₃×C₄₃⋊C₃	—	3	1	no	—
189	C₃×C₄₃⋊C₃	—	3	1	no	—
190	C₃×C₄₃⋊C₃	—	3	1	no	—
191	C₃×C₄₃⋊C₃	—	3	1	no	—
192	C₃×C₄₃⋊C₃	—	3	1	no	—
193	C₃×C₄₃⋊C₃	—	9	9	no	—
194	C₉×C₄₃	—	3	1	no	—
195	C₉×C₄₃	—	3	1	no	—
196	C₉×C₄₃	—	3	1	no	—
197	C₉×C₄₃	—	3	2	no	—
198	C₉×C₄₃	—	3	2	no	—
199	C₉×C₄₃	—	3	2	no	—
200	C₄₃⋊C₉	—	3	2	no	—
201	C₄₃⋊C₉	—	3	2	no	—
202	C₄₃⋊C₉	—	3	2	no	—
203	C₄₃⋊C₉	—	3	2	no	—
204	C₄₃⋊C₉	—	3	2	no	—
205	C₄₃⋊C₉	—	3	2	no	—
206	C₄₃⋊C₉	—	3	2	no	—
207	C₄₃⋊C₉	—	3	2	no	—
208	C₄₃⋊C₉	—	3	2	no	—
209	#6893	—	43	2	no	—
210	#6893	—	43	1	no	—
211	#6893	—	43	2	no	—
212	#6893	—	43	2	no	—
213	#6893	—	43	2	no	—
214	C₉⋊H(3,𝔽₃)	—	43	2	no	—
215	C₉⋊H(3,𝔽₃)	—	43	2	no	—
216	C₉⋊H(3,𝔽₃)	—	43	2	no	—
217	C₉⋊H(3,𝔽₃)	—	43	2	no	—
218	C₉⋊H(3,𝔽₃)	—	43	1	no	—
219	C₉⋊H(3,𝔽₃)	—	43	1	no	—
220	C₉⋊H(3,𝔽₃)	—	43	2	no	—
221	C₉⋊H(3,𝔽₃)	—	43	2	no	—
222	C₉⋊H(3,𝔽₃)	—	43	2	no	—
223	C₉⋊H(3,𝔽₃)	—	43	2	no	—
224	C₉⋊H(3,𝔽₃)	—	43	2	no	—
225	C₉⋊H(3,𝔽₃)	—	43	2	no	—
226	C₉⋊H(3,𝔽₃)	—	43	2	no	—
227	C₉⋊H(3,𝔽₃)	—	43	2	no	—
228	C₉⋊H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic, complemented
229	#6891	—	43	1	no	—
230	#6891	—	43	1	no	—
231	#6891	—	43	1	no	—
232	C₃²⋊H(3,𝔽₃)	—	43	1	no	—
233	C₃×C₄₃	—	9	1	no	—
234	C₃×C₄₃	—	9	1	no	—
235	C₃×C₄₃	—	9	2	no	—
236	C₃×C₄₃	H(5,𝔽₃)	1	1	yes	characteristic
237	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
238	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
239	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
240	C₄₃⋊C₃	—	9	2	no	—
241	C₄₃⋊C₃	—	9	2	no	—
242	C₄₃⋊C₃	—	9	2	no	—
243	C₄₃⋊C₃	—	9	1	no	—
244	C₄₃⋊C₃	—	9	1	no	—
245	C₄₃⋊C₃	—	9	1	no	—
246	C₃⁴	—	43	1	no	—
247	C₃×3₋¹⁺²	—	43	2	no	—
248	C₃×3₋¹⁺²	—	43	2	no	—
249	C₃×3₋¹⁺²	—	43	2	no	—
250	C₃×3₋¹⁺²	—	43	2	no	—
251	C₃×3₋¹⁺²	—	43	2	no	—
252	C₃×3₋¹⁺²	—	43	2	no	—
253	C₃×3₋¹⁺²	—	43	2	no	—
254	C₃×3₋¹⁺²	—	43	2	no	—
255	C₃×3₋¹⁺²	—	43	1	no	—
256	C₃×3₋¹⁺²	—	43	1	no	—
257	C₃×3₋¹⁺²	—	43	2	no	—
258	C₃×3₋¹⁺²	—	43	2	no	—
259	C₃×3₋¹⁺²	—	43	2	no	—
260	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
261	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	2	yes	complemented
262	C₃×H(3,𝔽₃)	—	43	2	no	—
263	C₃×H(3,𝔽₃)	—	43	2	no	—
264	C₃×H(3,𝔽₃)	—	43	2	no	—
265	C₃×H(3,𝔽₃)	—	43	1	no	—
266	C₃×H(3,𝔽₃)	—	43	1	no	—
267	C₃×H(3,𝔽₃)	—	43	2	no	—
268	C₃×H(3,𝔽₃)	—	43	1	no	—
269	C₃×H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	1	yes	characteristic
270	C₃²×C₉	—	43	2	no	—
271	C₃²×C₉	—	43	2	no	—
272	C₃²×C₉	—	43	2	no	—
273	C₃²×C₉	—	43	2	no	—
274	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented
275	C₃²⋊C₉	—	43	2	no	—
276	C₃²⋊C₉	—	43	2	no	—
277	C₃²⋊C₉	—	43	2	no	—
278	C₃²⋊C₉	—	43	2	no	—
279	C₃²⋊C₉	—	43	2	no	—
280	C₃²⋊C₉	—	43	2	no	—
281	C₃²⋊C₉	—	43	2	no	—
282	C₃²⋊C₉	—	43	2	no	—
283	C₃²⋊C₉	—	43	1	no	—
284	C₃²⋊C₉	—	43	1	no	—
285	C₃²⋊C₉	—	43	2	no	—
286	C₃²⋊C₉	—	43	2	no	—
287	C₃²⋊C₉	—	43	1	no	—
288	C₃²⋊C₉	—	43	1	no	—
289	C₃²⋊C₉	—	43	2	no	—
290	C₃²⋊C₉	—	43	2	no	—
291	C₃²⋊C₉	—	43	1	no	—
292	C₃²⋊C₉	—	43	2	no	—
293	C₃²⋊C₉	—	43	2	no	—
294	C₃²⋊C₉	—	43	1	no	—
295	C₃²⋊C₉	—	43	1	no	—
296	C₃²⋊C₉	—	43	2	no	—
297	C₃²⋊C₉	—	43	2	no	—
298	C₃²⋊C₉	—	43	2	no	—
299	C₃²⋊C₉	—	43	2	no	—
300	C₃²⋊C₉	—	43	2	no	—
301	C₃²⋊C₉	—	43	2	no	—
302	C₃²⋊C₉	—	43	2	no	—
303	C₃²⋊C₉	—	43	2	no	—
304	C₃²⋊C₉	—	43	2	no	—
305	C₃²⋊C₉	—	43	2	no	—
306	C₃²⋊C₉	—	43	2	no	—
307	C₃²⋊C₉	—	43	2	no	—
308	C₃²⋊C₉	—	43	2	no	—
309	C₃²⋊C₉	—	43	2	no	—
310	C₃²⋊C₉	—	43	2	no	—
311	C₃²⋊C₉	—	43	2	no	—
312	C₃²⋊C₉	—	43	2	no	—
313	C₃²⋊C₉	—	43	2	no	—
314	C₃²⋊C₉	—	43	2	no	—
315	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
316	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
317	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	complemented
318	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	complemented
319	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	complemented
320	C₄₃	#10624910	1	1	yes	characteristic, complemented, Sylow
321	C₃³	—	43	1	no	—
322	C₃³	—	43	2	no	—
323	C₃³	—	43	2	no	—
324	C₃³	—	43	2	no	—
325	C₃³	—	43	1	no	—
326	C₃³	—	43	1	no	—
327	C₃³	—	387	1	no	—
328	C₃³	—	387	1	no	—
329	C₃³	—	387	1	no	—
330	C₃³	—	387	1	no	—
331	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
332	C₃³	C₃²×C₄₃⋊C₃	1	2	yes	—
333	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
334	3₋¹⁺²	—	9	1	no	—
335	3₋¹⁺²	—	9	2	no	—
336	3₋¹⁺²	—	387	2	no	—
337	3₋¹⁺²	—	387	2	no	—
338	3₋¹⁺²	—	387	2	no	—
339	3₋¹⁺²	—	387	2	no	—
340	3₋¹⁺²	—	387	2	no	—
341	3₋¹⁺²	—	387	1	no	—
342	3₋¹⁺²	—	387	1	no	—
343	3₋¹⁺²	—	387	2	no	—
344	3₋¹⁺²	—	387	2	no	—
345	3₋¹⁺²	—	387	2	no	—
346	3₋¹⁺²	—	387	2	no	—
347	3₋¹⁺²	—	387	2	no	—
348	3₋¹⁺²	—	387	2	no	—
349	H(3,𝔽₃)	—	9	1	no	—
350	H(3,𝔽₃)	—	387	1	no	—
351	H(3,𝔽₃)	—	387	2	no	—
352	H(3,𝔽₃)	—	387	2	no	—
353	H(3,𝔽₃)	—	387	2	no	—
354	H(3,𝔽₃)	—	387	1	no	—
355	H(3,𝔽₃)	—	387	1	no	—
356	H(3,𝔽₃)	—	387	2	no	—
357	C₃×C₉	—	9	1	no	—
358	C₃×C₉	—	43	2	no	—
359	C₃×C₉	—	43	2	no	—
360	C₃×C₉	—	43	2	no	—
361	C₃×C₉	—	43	2	no	—
362	C₃×C₉	—	43	2	no	—
363	C₃×C₉	—	43	2	no	—
364	C₃×C₉	—	43	2	no	—
365	C₃×C₉	—	43	2	no	—
366	C₃×C₉	—	43	2	no	—
367	C₃×C₉	—	387	2	no	—
368	C₃×C₉	—	387	2	no	—
369	C₃×C₉	—	387	2	no	—
370	C₃×C₉	—	387	2	no	—
371	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
372	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
373	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
374	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
375	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
376	C₃×C₉	C₃²×C₄₃⋊C₃	1	2	yes	—
377	C₃²	—	3	1	no	—
378	C₃²	—	3	2	no	—
379	C₃²	—	3	1	no	—
380	C₃²	—	3	2	no	—
381	C₃²	—	3	2	no	—
382	C₃²	—	3	1	no	—
383	C₃²	—	3	1	no	—
384	C₃²	—	3	1	no	—
385	C₃²	—	3	1	no	—
386	C₃²	—	3	1	no	—
387	C₃²	—	3	2	no	—
388	C₃²	—	3	1	no	—
389	C₃²	—	129	2	no	—
390	C₃²	—	129	2	no	—
391	C₃²	—	129	2	no	—
392	C₃²	—	129	1	no	—
393	C₃²	—	129	1	no	—
394	C₃²	—	129	1	no	—
395	C₃²	—	129	1	no	—
396	C₃²	—	129	1	no	—
397	C₃²	—	129	2	no	—
398	C₃²	—	129	2	no	—
399	C₃²	—	129	2	no	—
400	C₃²	—	129	2	no	—
401	C₃²	—	129	2	no	—
402	C₃²	—	129	2	no	—
403	C₃²	—	129	1	no	—
404	C₃²	—	129	1	no	—
405	C₃²	—	129	1	no	—
406	C₃²	—	129	1	no	—
407	C₃²	—	129	2	no	—
408	C₃²	—	129	2	no	—
409	C₃²	—	129	2	no	—
410	C₃²	—	129	1	no	—
411	C₃²	—	129	1	no	—
412	C₃²	—	129	1	no	—
413	C₃²	—	387	9	no	—
414	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
415	C₉	—	3	1	no	—
416	C₉	—	3	1	no	—
417	C₉	—	3	1	no	—
418	C₉	—	3	2	no	—
419	C₉	—	3	2	no	—
420	C₉	—	3	2	no	—
421	C₉	—	129	2	no	—
422	C₉	—	129	2	no	—
423	C₉	—	129	2	no	—
424	C₉	—	129	2	no	—
425	C₉	—	129	2	no	—
426	C₉	—	129	2	no	—
427	C₉	—	129	2	no	—
428	C₉	—	129	2	no	—
429	C₉	—	129	2	no	—
430	C₃	—	9	1	no	—
431	C₃	—	9	2	no	—
432	C₃	—	9	1	no	—
433	C₃	—	387	2	no	—
434	C₃	—	387	2	no	—
435	C₃	—	387	2	no	—
436	C₃	—	387	1	no	—
437	C₃	—	387	1	no	—
438	C₃	—	387	1	no	—
439	C₃	C₄₃⋊H(5,𝔽₃)	1	1	yes	characteristic
440	C₃	#23782922	1	1	yes	characteristic
441	C₃	#23782922	1	1	yes	characteristic
442	C₃	#23782923	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	#10624910
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. #23782808	C₃	semidirect
3. #23782807	C₃	semidirect
4. #23782807	C₃	semidirect
5. #23782807	C₃	semidirect
6. #23782805	C₃	semidirect
7. #23782805	C₃	semidirect
8. #23782802	C₃	semidirect
9. #23782802	C₃	semidirect
10. #23782801	C₃	semidirect
11. #23782801	C₃	semidirect
12. #23782801	C₃	semidirect
13. #23782801	C₃	semidirect
14. #23782801	C₃	semidirect
15. #23782801	C₃	semidirect
16. #23782800	C₃	semidirect
17. #23782799	C₃	semidirect
18. #23782799	C₃	semidirect
19. #23782799	C₃	semidirect
20. #23782797	C₃	semidirect
21. #23782797	C₃	semidirect
22. #23782795	C₃	semidirect
24. C₄₃×C₉⋊H(3,𝔽₃)	C₃	semidirect
27. C₃×#11923958	C₃²	semidirect
28. C₃×#11923958	C₃²	semidirect
33. C₃×#11923957	C₃²	semidirect
34. C₃×#11923957	C₃²	semidirect
35. C₃×#11923957	C₃²	semidirect
36. C₃×#11923956	C₃²	semidirect
37. C₃×#11923956	C₃²	semidirect
38. C₃×#11923956	C₃²	semidirect
46. C₃²×C₄₃⋊C₉	C₃²	semidirect
47. C₃×C₉×C₄₃⋊C₃	C₃²	semidirect
48. C₃×C₉×C₄₃⋊C₃	C₃²	semidirect
49. C₃×C₉×C₄₃⋊C₃	C₃²	semidirect
52. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
53. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
54. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
55. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
56. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
57. C₃²⋊(C₄₃⋊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
78. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
79. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
80. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
81. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
82. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
83. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
84. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
85. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
86. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
87. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
88. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
89. (C₃×C₄₃⋊C₃)⋊C₉	C₃²	semidirect
91. C₃×3₋¹⁺²×C₄₃	C₃²	semidirect
93. C₃²×C₉×C₄₃	C₃²	semidirect
96. C₄₃×C₃²⋊C₉	C₃²	semidirect
97. C₄₃×C₃²⋊C₉	C₃²	semidirect
98. C₄₃×C₃²⋊C₉	C₃²	semidirect
228. C₉⋊H(3,𝔽₃)	C₄₃⋊C₃	semidirect
261. C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	semidirect
274. C₃²×C₉	C₃×C₄₃⋊C₃	semidirect
317. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
318. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
319. C₃²⋊C₉	C₃×C₄₃⋊C₃	semidirect
320. C₄₃	#10624910	semidirect

Maximal subgroups

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

subgroup	index
#23782809	3
#23782808	3
#23782807	3
#23782805	3
#23782802	3
#23782801	3
#23782800	3
#23782799	3
#23782797	3
#23782795	3
(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	3
C₄₃×C₉⋊H(3,𝔽₃)	3
#10624910	43