Subgroups — #25098701

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582926	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582855	C₂	1	1	yes	maximal, characteristic
3	#19135161	C₂	1	4	yes	maximal, complemented
4	#19135154	C₂	1	4	yes	maximal, complemented
5	#19134292	C₂	1	1	yes	maximal, characteristic
6	#19134292	C₂	1	1	yes	maximal, characteristic
7	#19134289	C₂	1	1	yes	maximal, characteristic
8	C₂×#14582654	C₂	1	1	yes	maximal, characteristic
9	C₄₃×#2285	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582926	—	2	4	no	—
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
17	#14582855	—	2	4	no	—
18	C₂×#13063236	C₂²	1	2	yes	—
19	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
20	#14582654	C₂²	1	2	yes	—
21	#14582654	C₂²	1	2	yes	—
22	#14582654	C₂²	1	4	yes	—
23	#14582654	C₂²	1	4	yes	—
24	#14582654	C₂²	1	4	yes	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#384	C₄	1	1	yes	characteristic
29	C₄₃×#384	C₄	1	1	yes	characteristic
30	C₄₃×#382	C₄	1	1	yes	characteristic
31	C₄₃×#382	C₄	1	1	yes	characteristic
32	C₄₃×#380	C₄	1	4	yes	—
33	C₄×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
34	C₂×#10621877	—	2	2	no	—
35	C₂×#10621877	—	2	2	no	—
36	C₂×#10621877	—	2	2	no	—
37	C₂×#10621877	—	2	2	no	—
38	C₂×#10621877	—	2	2	no	—
39	C₂×#10621877	Q₈	1	4	yes	—
40	C₂²×C₄₃⋊C₈	—	2	2	no	—
41	C₂²×C₄₃⋊C₈	—	2	2	no	—
42	C₂²×C₄₃⋊C₈	—	2	2	no	—
43	C₂²×C₄₃⋊C₈	—	2	2	no	—
44	C₂²×C₄₃⋊C₈	—	2	2	no	—
45	C₂²×C₄₃⋊C₈	D₄	1	4	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
51	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
52	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
53	#13063236	—	2	4	no	—
54	C₄×C₄₃⋊C₈	—	2	4	no	—
55	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
56	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	#117×C₄₃	—	2	2	no	—
58	#117×C₄₃	—	2	2	no	—
59	#117×C₄₃	—	2	2	no	—
60	#117×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
67	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₄₃	—	2	2	no	—
70	C₂×C₄²×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
76	#95×C₄₃	C₂×C₄	1	4	yes	—
77	#95×C₄₃	C₂×C₄	1	4	yes	—
78	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	4	2	no	—
82	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₃	#41	1	2	yes	—
92	C₂²×C₄×C₄₃	#41	1	2	yes	—
93	C₂²×C₄×C₄₃	#41	1	2	yes	—
94	C₂²×C₄×C₄₃	#41	1	2	yes	—
95	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₄⋊C₄×C₄₃	—	2	2	no	—
97	C₄⋊C₄×C₄₃	—	2	2	no	—
98	C₄⋊C₄×C₄₃	—	2	2	no	—
99	C₄⋊C₄×C₄₃	—	2	2	no	—
100	C₄⋊C₄×C₄₃	—	2	8	no	—
101	C₄⋊C₄×C₄₃	—	4	4	no	—
102	C₂²⋊C₄×C₄₃	—	2	4	no	—
103	C₂²⋊C₄×C₄₃	—	2	4	no	—
104	C₄²×C₄₃	—	2	2	no	—
105	C₄²×C₄₃	—	2	2	no	—
106	C₄²×C₄₃	—	2	2	no	—
107	C₄²×C₄₃	—	2	2	no	—
108	C₄²×C₄₃	—	2	2	no	—
109	C₄²×C₄₃	—	2	2	no	—
110	C₄²×C₄₃	—	2	2	no	—
111	C₄²×C₄₃	—	2	2	no	—
112	#10621877	—	2	8	no	—
113	#10621877	—	4	4	no	—
114	C₂×C₄₃⋊C₈	—	2	8	no	—
115	C₂×C₄₃⋊C₈	—	2	2	no	—
116	C₂×C₄₃⋊C₈	—	2	1	no	—
117	C₂×C₄₃⋊C₈	—	2	1	no	—
118	C₂×C₄₃⋊C₈	—	2	1	no	—
119	C₂×C₄₃⋊C₈	—	2	1	no	—
120	C₂×C₄₃⋊C₈	—	2	2	no	—
121	C₂×C₄₃⋊C₈	—	2	2	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	—	2	2	no	—
124	C₂×C₄₃⋊C₈	—	2	2	no	—
125	C₂×C₄₃⋊C₈	—	2	2	no	—
126	C₂×C₄₃⋊C₈	—	2	2	no	—
127	C₂×C₄₃⋊C₈	—	4	4	no	—
128	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
129	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
130	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
131	C₂³×C₄₃	—	2	2	no	—
132	C₂³×C₄₃	—	2	2	no	—
133	C₂³×C₄₃	#117	1	2	yes	—
134	C₂³×C₄₃	C₄×D₄	1	2	yes	—
135	C₂³×C₄₃	C₄×Q₈	1	2	yes	—
136	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	—	2	2	no	—
138	C₂×C₄×C₄₃	—	2	2	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	2	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	—	2	4	no	—
145	C₂×C₄×C₄₃	—	2	4	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	4	no	—
148	C₂×C₄×C₄₃	—	2	4	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	4	8	no	—
151	C₂×C₄×C₄₃	#117	1	2	yes	—
152	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
154	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₄₃	#123	1	4	yes	—
156	C₂×C₄×C₄₃	#125	1	4	yes	—
157	C₂×C₄×C₄₃	#126	1	4	yes	—
158	C₂×C₄×C₄₃	#131	1	4	yes	—
159	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₄₃⋊C₈	—	2	4	no	—
166	C₄₃⋊C₈	—	2	2	no	—
167	C₄₃⋊C₈	—	2	2	no	—
168	C₄₃⋊C₈	—	4	2	no	—
169	C₄₃⋊C₈	—	4	2	no	—
170	#21025	—	43	1	no	maximal, Sylow
171	C₂²×C₄₃	—	2	4	no	—
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	2	2	no	—
174	C₂²×C₄₃	—	2	4	no	—
175	C₂²×C₄₃	#387	1	4	yes	—
176	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
177	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
179	C₂²×C₄₃	C₂×#131	1	2	yes	—
180	C₂²×C₄₃	#568	1	2	yes	—
181	C₄×C₄₃	—	2	4	no	—
182	C₄×C₄₃	—	4	2	no	—
183	C₄×C₄₃	—	4	2	no	—
184	C₄×C₄₃	—	4	2	no	—
185	C₄×C₄₃	—	4	2	no	—
186	C₄×C₄₃	—	4	2	no	—
187	C₄×C₄₃	#387	1	4	yes	—
188	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
190	C₄×C₄₃	C₂×#125	1	1	yes	characteristic
191	C₄×C₄₃	C₂×#126	1	1	yes	characteristic
192	C₂×#424	—	43	1	no	—
193	C₂×#405	—	43	1	no	—
194	#2285	D₄₃	1	1	yes	characteristic
195	#1917	—	43	4	no	—
196	#1916	—	43	4	no	—
197	#1729	—	43	1	no	—
198	#1729	—	43	1	no	—
199	#1728	—	43	1	no	—
200	C₂×#336	—	43	1	no	—
201	C₂×C₄₃	—	2	4	no	—
202	C₂×C₄₃	C₂×#387	1	1	yes	characteristic
203	C₂×C₄₃	#2924	1	2	yes	—
204	C₂×C₄₃	#2931	1	1	yes	characteristic
205	C₂×C₄₃	#2932	1	1	yes	characteristic
206	C₂×C₄₃	#2962	1	2	yes	—
207	C₂²×M₁₆	—	43	1	no	—
208	C₂²×M₁₆	—	43	1	no	—
209	C₂³×C₈	—	43	1	no	—
210	C₂³×C₈	—	43	1	no	—
211	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
212	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
213	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
214	#424	—	86	4	no	—
215	C₂×C₄⋊C₈	—	43	2	no	—
216	C₂×C₄⋊C₈	—	43	2	no	—
217	#405	—	86	4	no	—
218	C₂×#97	—	43	2	no	—
219	C₂×C₄×C₈	—	43	2	no	—
220	#384	Dic₄₃	1	1	yes	characteristic
221	#384	Dic₄₃	1	1	yes	characteristic
222	#382	Dic₄₃	1	1	yes	characteristic
223	#382	Dic₄₃	1	1	yes	characteristic
224	#380	Dic₄₃	1	4	yes	—
225	C₄×C₄⋊C₄	C₂×D₄₃	1	4	yes	—
226	#336	—	43	2	no	—
227	#336	—	43	4	no	—
228	#336	—	43	4	no	—
229	#336	—	43	4	no	—
230	#336	—	43	2	no	—
231	C₄₃	#21025	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
233	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
234	C₂×M₁₆	—	43	4	no	—
235	C₂×M₁₆	—	86	2	no	—
236	C₂×M₁₆	—	86	2	no	—
237	C₂×M₁₆	—	86	2	no	—
238	C₂×M₁₆	—	86	2	no	—
239	C₂×M₁₆	—	86	2	no	—
240	C₂²×C₈	—	43	4	no	—
241	C₂²×C₈	—	43	1	no	—
242	C₂²×C₈	—	43	1	no	—
243	C₂²×C₈	—	43	2	no	—
244	C₂²×C₈	—	43	2	no	—
245	C₂²×C₈	—	43	2	no	—
246	C₂²×C₈	—	86	2	no	—
247	C₂²×C₈	—	86	2	no	—
248	C₂²×C₈	—	86	2	no	—
249	C₂²×C₈	—	86	2	no	—
250	C₂²×C₈	—	86	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×Dic₄₃	1	4	yes	—
261	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
266	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
268	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
269	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
270	C₄⋊C₈	—	86	4	no	—
271	C₄⋊C₈	—	86	4	no	—
272	#97	—	86	4	no	—
273	C₄×C₈	—	86	4	no	—
274	#95	C₂×Dic₄₃	1	4	yes	—
275	#95	C₂×Dic₄₃	1	4	yes	—
276	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	#10621898	1	2	yes	—
281	C₂²×C₄	#10621898	1	2	yes	—
282	C₂²×C₄	D₄×D₄₃	1	2	yes	—
283	C₂²×C₄	#10621900	1	2	yes	—
284	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
285	C₂²×C₄	#10621902	1	2	yes	—
286	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
287	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
288	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
289	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
290	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
291	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
292	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
293	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
294	M₁₆	—	86	8	no	—
295	M₁₆	—	172	4	no	—
296	C₂×C₈	—	43	2	no	—
297	C₂×C₈	—	43	2	no	—
298	C₂×C₈	—	43	4	no	—
299	C₂×C₈	—	86	8	no	—
300	C₂×C₈	—	86	2	no	—
301	C₂×C₈	—	86	1	no	—
302	C₂×C₈	—	86	1	no	—
303	C₂×C₈	—	86	2	no	—
304	C₂×C₈	—	86	1	no	—
305	C₂×C₈	—	86	1	no	—
306	C₂×C₈	—	86	2	no	—
307	C₂×C₈	—	86	2	no	—
308	C₂×C₈	—	86	2	no	—
309	C₂×C₈	—	86	2	no	—
310	C₂×C₈	—	86	2	no	—
311	C₂×C₈	—	86	2	no	—
312	C₂×C₈	—	172	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	#13063284	1	2	yes	—
332	C₂³	D₄×Dic₄₃	1	2	yes	—
333	C₂³	Q₈×Dic₄₃	1	2	yes	—
334	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	#13063284	1	2	yes	—
350	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
351	C₂×C₄	Q₈×Dic₄₃	1	2	yes	—
352	C₂×C₄	#13063303	1	4	yes	—
353	C₂×C₄	#13063310	1	4	yes	—
354	C₂×C₄	#13063315	1	4	yes	—
355	C₂×C₄	#13063320	1	4	yes	—
356	C₂×C₄	#13063332	1	4	yes	—
357	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
358	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
359	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
360	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
361	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
362	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
363	C₈	—	86	4	no	—
364	C₈	—	86	2	no	—
365	C₈	—	86	2	no	—
366	C₈	—	172	2	no	—
367	C₈	—	172	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	#14582785	1	4	yes	—
373	C₂²	C₂×#13063284	1	1	yes	characteristic
374	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
375	C₂²	C₂×Q₈×Dic₄₃	1	1	yes	characteristic
376	C₂²	C₂×#13063332	1	2	yes	—
377	C₂²	#14583666	1	2	yes	—
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	#14582785	1	4	yes	—
385	C₄	C₂×#13063303	1	1	yes	characteristic
386	C₄	C₂×#13063310	1	1	yes	characteristic
387	C₄	C₂×#13063315	1	1	yes	characteristic
388	C₄	C₂×#13063320	1	1	yes	characteristic
389	C₂	—	2	4	no	—
390	C₂	C₂×#14582785	1	1	yes	characteristic
391	C₂	#19143253	1	2	yes	—
392	C₂	#19143307	1	1	yes	characteristic
393	C₂	#19143313	1	1	yes	characteristic
394	C₂	#19143544	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#2285	C₂
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2285	D₄₃
hypocenter	C₄₃	#21025
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2285

Complements

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

N	H ≅ G/N	type
3. #19135161	C₂	semidirect
4. #19135154	C₂	semidirect
231. C₄₃	#21025	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582926	2
C₂×#14582855	2
#19135161	2
#19135154	2
#19134292	2
#19134289	2
C₂×#14582654	2
C₄₃×#2285	2
#21025	43