Subgroups — #24986151

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582921	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19136999	C₂	1	1	yes	maximal, characteristic
4	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621872	—	2	1	no	—
9	C₂²×C₈×D₄₃	—	2	1	no	—
10	C₂×#13063282	—	2	1	no	—
11	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
12	#14582921	—	2	2	no	—
13	#14582921	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₃⋊C₈	—	2	1	no	—
16	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₄₃	—	2	1	no	—
18	C₄×C₈×D₄₃	—	2	2	no	—
19	C₄×C₈×D₄₃	C₄	1	4	yes	complemented
20	#14582768	C₄	1	2	yes	—
21	#14582763	—	2	1	no	—
22	#14582758	—	2	1	no	—
23	#14582756	C₄	1	2	yes	—
24	C₄×Dic₄₃⋊C₄	—	2	1	no	—
25	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
32	C₂×#10621872	—	2	4	no	—
33	C₂×#10621872	—	4	2	no	—
34	C₂×#10621872	—	4	2	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	C₂×C₈×D₄₃	—	2	8	no	—
38	C₂×C₈×D₄₃	—	2	4	no	—
39	#13063282	—	4	2	no	—
40	#13063282	—	4	2	no	—
41	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
42	C₂×Dic₄₃⋊C₄	—	2	2	no	—
43	C₂×Dic₄₃⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
45	C₂×C₄×Dic₄₃	—	2	1	no	—
46	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
49	C₄²×D₄₃	C₂×C₄	1	2	yes	—
50	C₄²×D₄₃	C₂×C₄	1	2	yes	—
51	C₄²×D₄₃	D₄	1	2	yes	—
52	C₄²×D₄₃	Q₈	1	2	yes	—
53	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
55	Dic₄₃⋊C₈	—	2	4	no	—
56	C₄×C₄₃⋊C₈	—	2	1	no	—
57	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
58	C₈×Dic₄₃	—	2	4	no	—
59	C₄₃⋊#95	—	2	1	no	—
60	C₄₃⋊#95	—	2	2	no	—
61	C₂²×C₈×C₄₃	—	2	1	no	—
62	C₂²×C₈×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₄₃	—	2	1	no	—
65	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₄₃	—	2	1	no	—
67	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₄₃	—	2	1	no	—
69	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
70	#95×C₄₃	—	2	1	no	—
71	C₂³×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×Dic₄₃	—	2	2	no	—
77	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₄₃	—	2	2	no	—
81	C₂×C₄×D₄₃	—	2	2	no	—
82	C₂×C₄×D₄₃	—	2	4	no	—
83	C₂×C₄×D₄₃	C₄²	1	2	yes	—
84	C₂×C₄×D₄₃	C₂²⋊C₄	1	2	yes	—
85	C₂×C₄×D₄₃	C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
87	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₃	D₈	1	2	yes	—
90	C₂×C₄×D₄₃	SD₁₆	1	2	yes	—
91	C₂×C₄×D₄₃	SD₁₆	1	2	yes	—
92	C₂×C₄×D₄₃	Q₁₆	1	2	yes	—
93	C₂×C₈×C₄₃	—	2	4	no	—
94	C₂×C₈×C₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₂×C₈×C₄₃	—	4	1	no	—
98	C₄⋊C₄×C₄₃	—	2	2	no	—
99	C₄⋊C₄×C₄₃	—	2	2	no	—
100	C₄²×C₄₃	—	4	1	no	—
101	C₄²×C₄₃	—	4	1	no	—
102	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
106	(C₂×D₄₃)⋊C₄	—	4	4	no	—
107	C₄⋊Dic₄₃	—	2	2	no	—
108	C₄⋊Dic₄₃	—	2	2	no	—
109	Dic₄₃⋊C₄	—	4	4	no	—
110	Dic₄₃⋊C₄	—	4	4	no	—
111	C₄×Dic₄₃	—	4	1	no	—
112	C₄×Dic₄₃	—	4	1	no	—
113	C₄×Dic₄₃	C₄²	1	2	yes	—
114	C₄×Dic₄₃	C₂²⋊C₄	1	2	yes	—
115	C₄×Dic₄₃	C₂²⋊C₄	1	2	yes	—
116	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
117	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
118	C₄×Dic₄₃	C₄⋊C₄	1	2	yes	—
119	C₂×C₄₃⋊C₈	—	2	4	no	—
120	C₂×C₄₃⋊C₈	—	2	2	no	—
121	C₂×C₄₃⋊C₈	—	2	2	no	—
122	C₂×C₄₃⋊C₈	—	4	1	no	—
123	C₂×C₄₃⋊C₈	—	4	1	no	—
124	#10621872	—	4	8	no	—
125	C₈×D₄₃	—	2	16	no	—
126	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×D₄₃	—	2	2	no	—
128	C₂²×D₄₃	—	2	2	no	—
129	C₂²×D₄₃	#95	1	2	yes	—
130	C₂²×D₄₃	#102	1	2	yes	—
131	C₂²×D₄₃	#103	1	2	yes	—
132	C₂×C₄×C₄₃	—	2	2	no	—
133	C₂×C₄×C₄₃	—	4	2	no	—
134	C₂×C₄×C₄₃	—	4	2	no	—
135	C₂×C₄×C₄₃	—	4	2	no	—
136	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	#131	1	2	yes	—
143	C₂×C₄×C₄₃	#131	1	2	yes	—
144	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
148	C₂×Dic₄₃	—	2	2	no	—
149	C₂×Dic₄₃	—	4	2	no	—
150	C₂×Dic₄₃	—	4	2	no	—
151	C₂×Dic₄₃	—	4	2	no	—
152	C₂×Dic₄₃	#95	1	2	yes	—
153	C₂×Dic₄₃	#95	1	2	yes	—
154	C₂×Dic₄₃	#95	1	2	yes	—
155	C₂×Dic₄₃	#102	1	2	yes	—
156	C₂×Dic₄₃	#103	1	2	yes	—
157	C₂×Dic₄₃	#104	1	4	yes	—
158	C₄×D₄₃	—	2	2	no	—
159	C₄×D₄₃	—	2	2	no	—
160	C₄×D₄₃	—	2	4	no	—
161	C₄×D₄₃	—	2	4	no	—
162	C₄×D₄₃	—	2	4	no	—
163	C₄×D₄₃	#102	1	4	yes	—
164	C₄×D₄₃	#103	1	4	yes	—
165	C₄×D₄₃	#106	1	4	yes	—
166	C₄×D₄₃	#107	1	4	yes	—
167	C₈×C₄₃	—	2	4	no	—
168	C₈×C₄₃	—	4	2	no	—
169	C₄₃⋊C₈	—	2	4	no	—
170	C₄₃⋊C₈	—	4	2	no	—
171	#7897	—	43	1	no	maximal, Sylow
172	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
173	C₂²×C₄₃	#408	1	2	yes	—
174	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
175	C₂²×C₄₃	C₂×#103	1	1	yes	characteristic
176	C₂²×C₄₃	C₂×#104	1	2	yes	—
177	C₂×D₄₃	—	2	2	no	—
178	C₂×D₄₃	—	2	2	no	—
179	C₂×D₄₃	—	2	4	no	—
180	C₂×D₄₃	—	2	4	no	—
181	C₂×D₄₃	#340	1	4	yes	—
182	C₄×C₄₃	—	2	1	no	—
183	C₄×C₄₃	—	2	1	no	—
184	C₄×C₄₃	—	8	2	no	—
185	C₄×C₄₃	#405	1	1	yes	characteristic
186	C₄×C₄₃	#405	1	1	yes	characteristic
187	C₄×C₄₃	C₂×#102	1	1	yes	characteristic
188	C₄×C₄₃	C₂×#103	1	1	yes	characteristic
189	C₄×C₄₃	#424	1	2	yes	—
190	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
191	C₄×C₄₃	C₂×#107	1	1	yes	characteristic
192	Dic₄₃	—	2	2	no	—
193	Dic₄₃	—	8	2	no	—
194	Dic₄₃	#339	1	4	yes	—
195	Dic₄₃	#340	1	4	yes	—
196	C₂×#423	—	43	1	no	—
197	C₂²×C₄×C₈	—	43	1	no	—
198	#2285	—	43	1	no	—
199	#1279	—	43	1	no	—
200	#1279	—	43	1	no	—
201	#1279	—	43	1	no	—
202	#1279	D₄₃	1	1	yes	characteristic, complemented
203	C₂×C₄₃	#1492	1	2	yes	—
204	C₂×C₄₃	#1493	1	2	yes	—
205	C₂×C₄₃	#1729	1	1	yes	characteristic
206	C₂×C₄₃	C₂×#339	1	1	yes	characteristic
207	C₂×C₄₃	C₂×#340	1	1	yes	characteristic
208	D₄₃	—	2	4	no	—
209	C₂²×M₁₆	—	86	1	no	—
210	C₂³×C₈	—	86	1	no	—
211	C₂×#117	—	86	1	no	—
212	C₂²×C₄²	—	43	1	no	—
213	#423	—	43	4	no	—
214	#423	—	86	2	no	—
215	C₂×C₄⋊C₈	—	43	1	no	—
216	C₂×C₄⋊C₈	—	86	1	no	—
217	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
218	C₂×C₄×C₈	—	43	1	no	—
219	C₂×C₄×C₈	—	43	4	no	—
220	C₂×C₄×C₈	—	86	2	no	—
221	C₂×C₄×C₈	—	86	1	no	—
222	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
223	#384	—	43	2	no	—
224	#382	—	86	1	no	—
225	#380	—	43	2	no	—
226	#380	—	86	1	no	—
227	C₄×C₄⋊C₄	—	43	1	no	—
228	C₄×C₄⋊C₄	—	86	1	no	—
229	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
230	C₄₃	#7897	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₄	—	43	1	no	—
232	C₂³×C₄	—	43	1	no	—
233	C₂³×C₄	—	43	1	no	—
234	C₂×M₁₆	—	86	4	no	—
235	C₂×M₁₆	—	172	2	no	—
236	C₂×M₁₆	—	172	2	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	86	4	no	—
240	C₂²×C₈	—	86	8	no	—
241	C₂²×C₈	—	86	1	no	—
242	C₂²×C₈	—	86	1	no	—
243	#117	—	172	2	no	—
244	#117	—	172	2	no	—
245	C₂×C₄⋊C₄	—	43	2	no	—
246	C₂×C₄⋊C₄	—	86	2	no	—
247	C₂×C₄⋊C₄	—	86	2	no	—
248	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
249	C₂×C₂²⋊C₄	—	86	2	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	43	1	no	—
252	C₂×C₄²	—	43	1	no	—
253	C₂×C₄²	—	43	1	no	—
254	C₂×C₄²	—	43	2	no	—
255	C₂×C₄²	—	43	2	no	—
256	C₂×C₄²	—	43	2	no	—
257	C₂×C₄²	—	43	2	no	—
258	C₂×C₄²	—	86	1	no	—
259	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	43	2	no	—
262	C₄⋊C₈	—	86	4	no	—
263	C₄⋊C₈	—	86	1	no	—
264	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	43	2	no	—
267	C₄×C₈	—	86	4	no	—
268	C₄×C₈	—	86	1	no	—
269	C₄×C₈	C₄×D₄₃	1	2	yes	—
270	#95	—	2	1	no	—
271	#95	—	86	2	no	—
272	#95	—	86	1	no	—
273	C₂⁴	—	43	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	43	1	no	—
276	C₂²×C₄	—	43	1	no	—
277	C₂²×C₄	—	43	2	no	—
278	C₂²×C₄	—	43	2	no	—
279	C₂²×C₄	—	43	2	no	—
280	C₂²×C₄	—	43	2	no	—
281	C₂²×C₄	—	43	2	no	—
282	C₂²×C₄	—	43	2	no	—
283	C₂²×C₄	—	43	1	no	—
284	C₂²×C₄	—	43	2	no	—
285	C₂²×C₄	—	43	2	no	—
286	C₂²×C₄	—	43	2	no	—
287	C₂²×C₄	—	43	2	no	—
288	C₂²×C₄	—	86	4	no	—
289	C₂²×C₄	—	86	2	no	—
290	C₂²×C₄	—	86	2	no	—
291	C₂²×C₄	—	86	2	no	—
292	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
293	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
294	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
295	M₁₆	—	172	8	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	86	16	no	—
302	C₂×C₈	—	86	4	no	—
303	C₂×C₈	—	86	2	no	—
304	C₂×C₈	—	86	2	no	—
305	C₂×C₈	—	172	1	no	—
306	C₂×C₈	—	172	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	86	2	no	—
310	C₄⋊C₄	—	86	2	no	—
311	C₄⋊C₄	—	172	4	no	—
312	C₄⋊C₄	—	172	4	no	—
313	C₂²⋊C₄	—	172	4	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	4	1	no	—
316	C₄²	—	43	2	no	—
317	C₄²	—	43	2	no	—
318	C₄²	—	43	2	no	—
319	C₄²	—	43	2	no	—
320	C₄²	—	43	2	no	—
321	C₄²	—	43	2	no	—
322	C₄²	—	172	1	no	—
323	C₄²	—	172	1	no	—
324	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
325	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
326	C₄²	D₄×D₄₃	1	1	yes	characteristic
327	C₄²	Q₈×D₄₃	1	1	yes	characteristic
328	C₂³	—	43	2	no	—
329	C₂³	—	43	2	no	—
330	C₂³	—	43	2	no	—
331	C₂³	—	86	2	no	—
332	C₂³	—	86	2	no	—
333	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	43	2	no	—
339	C₂×C₄	—	43	2	no	—
340	C₂×C₄	—	43	4	no	—
341	C₂×C₄	—	43	2	no	—
342	C₂×C₄	—	43	2	no	—
343	C₂×C₄	—	43	4	no	—
344	C₂×C₄	—	43	4	no	—
345	C₂×C₄	—	43	4	no	—
346	C₂×C₄	—	43	4	no	—
347	C₂×C₄	—	43	2	no	—
348	C₂×C₄	—	86	4	no	—
349	C₂×C₄	—	86	4	no	—
350	C₂×C₄	—	86	2	no	—
351	C₂×C₄	—	86	2	no	—
352	C₂×C₄	—	86	2	no	—
353	C₂×C₄	—	86	4	no	—
354	C₂×C₄	—	172	2	no	—
355	C₂×C₄	—	172	2	no	—
356	C₂×C₄	—	172	2	no	—
357	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
358	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
359	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
360	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
361	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
362	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
363	C₂×C₄	#13063331	1	2	yes	—
364	C₂×C₄	#13063333	1	2	yes	—
365	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
366	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
367	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
368	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	4	2	no	—
371	C₈	—	86	4	no	—
372	C₈	—	172	2	no	—
373	C₂²	—	43	4	no	—
374	C₂²	—	86	2	no	—
375	C₂²	—	86	2	no	—
376	C₂²	—	86	4	no	—
377	C₂²	—	86	4	no	—
378	C₂²	#95×D₄₃	1	1	yes	characteristic
379	C₂²	#14582864	1	2	yes	—
380	C₂²	#102×D₄₃	1	1	yes	characteristic
381	C₂²	#103×D₄₃	1	1	yes	characteristic
382	C₂²	#104×D₄₃	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	8	2	no	—
386	C₄	—	43	4	no	—
387	C₄	—	43	4	no	—
388	C₄	—	86	2	no	—
389	C₄	—	344	2	no	—
390	C₄	#14582853	1	1	yes	characteristic
391	C₄	#14582856	1	1	yes	characteristic
392	C₄	#102×D₄₃	1	1	yes	characteristic
393	C₄	#103×D₄₃	1	1	yes	characteristic
394	C₄	#14582924	1	2	yes	—
395	C₄	#106×D₄₃	1	1	yes	characteristic
396	C₄	#107×D₄₃	1	1	yes	characteristic
397	C₂	—	86	4	no	—
398	C₂	#19133044	1	2	yes	—
399	C₂	#19133048	1	2	yes	—
400	C₂	#19134290	1	1	yes	characteristic
401	C₂	#339×D₄₃	1	1	yes	characteristic
402	C₂	#340×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#7897
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #19132436	C₂	semidirect
5. #19132435	C₂	semidirect
6. #19132434	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
13. #14582921	C₄	semidirect
19. C₄×C₈×D₄₃	C₄	semidirect
202. #1279	D₄₃	semidirect
230. C₄₃	#7897	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582921	2
C₂×C₄×C₈×D₄₃	2
#19136999	2
#19132436	2
#19132435	2
#19132434	2
C₄₃×#1279	2
#7897	43