Subgroups — C₄₃×#17076 #24937093

Order 11008.

1130 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#400	C₂	1	2	yes	maximal
2	C₄₃×#1444	C₂	1	4	yes	maximal
3	C₄₃×#1442	C₂	1	4	yes	maximal
4	C₄₃×#1441	C₂	1	2	yes	maximal
5	C₄₃×C₄⋊#95	C₂	1	2	yes	maximal
6	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#400	—	2	8	no	—
15	C₂×#95×C₄₃	C₂²	1	4	yes	—
16	C₂×#95×C₄₃	C₂²	1	2	yes	—
17	C₂×#95×C₄₃	C₂²	1	4	yes	—
18	C₂×#95×C₄₃	C₂²	1	4	yes	—
19	C₂×#95×C₄₃	C₂²	1	4	yes	—
20	C₂×#95×C₄₃	C₂²	1	2	yes	—
21	C₂×#95×C₄₃	C₂²	1	4	yes	—
22	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
23	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
24	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
25	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
26	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
28	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
29	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
30	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
31	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
32	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
33	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
34	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
35	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
36	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
37	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
38	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
39	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
40	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
41	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
42	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
43	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₄₃	Q₈	1	4	yes	—
45	C₂×C₄²×C₄₃	—	4	1	no	—
46	C₂×C₄²×C₄₃	—	4	1	no	—
47	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
48	#95×C₄₃	—	2	4	no	—
49	#95×C₄₃	—	2	8	no	—
50	#95×C₄₃	—	2	8	no	—
51	#95×C₄₃	—	2	8	no	—
52	#95×C₄₃	—	2	8	no	—
53	#95×C₄₃	—	4	2	no	—
54	#95×C₄₃	—	4	4	no	—
55	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
56	C₂²×C₄×C₄₃	—	2	4	no	—
57	C₂²×C₄×C₄₃	—	2	4	no	—
58	C₂²×C₄×C₄₃	—	2	4	no	—
59	C₂²×C₄×C₄₃	—	2	4	no	—
60	C₂²×C₄×C₄₃	—	2	4	no	—
61	C₂²×C₄×C₄₃	—	2	4	no	—
62	C₂²×C₄×C₄₃	—	2	4	no	—
63	C₂²×C₄×C₄₃	—	2	4	no	—
64	C₂²×C₄×C₄₃	—	2	1	no	—
65	C₂²×C₄×C₄₃	—	2	2	no	—
66	C₂²×C₄×C₄₃	—	2	1	no	—
67	C₂²×C₄×C₄₃	—	2	2	no	—
68	C₂²×C₄×C₄₃	—	2	1	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	4	no	—
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	2	4	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	—	2	4	no	—
78	C₂²×C₄×C₄₃	—	2	4	no	—
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	1	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	4	no	—
84	C₂²×C₄×C₄₃	—	2	4	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
90	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₄₃	#41	1	4	yes	—
93	C₂²×C₄×C₄₃	#41	1	4	yes	—
94	C₄⋊C₄×C₄₃	—	4	4	no	—
95	C₄⋊C₄×C₄₃	—	4	4	no	—
96	C₄⋊C₄×C₄₃	—	4	8	no	—
97	C₄⋊C₄×C₄₃	—	4	8	no	—
98	C₄⋊C₄×C₄₃	—	4	8	no	—
99	C₄⋊C₄×C₄₃	—	4	8	no	—
100	C₄²×C₄₃	—	4	4	no	—
101	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
102	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
103	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
104	C₂³×C₄₃	C₂×#41	1	2	yes	—
105	C₂³×C₄₃	C₂×#41	1	2	yes	—
106	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
107	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
108	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
109	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
110	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
111	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
112	C₂×C₄×C₄₃	—	2	2	no	—
113	C₂×C₄×C₄₃	—	2	2	no	—
114	C₂×C₄×C₄₃	—	2	4	no	—
115	C₂×C₄×C₄₃	—	2	4	no	—
116	C₂×C₄×C₄₃	—	2	4	no	—
117	C₂×C₄×C₄₃	—	2	4	no	—
118	C₂×C₄×C₄₃	—	2	4	no	—
119	C₂×C₄×C₄₃	—	2	2	no	—
120	C₂×C₄×C₄₃	—	2	2	no	—
121	C₂×C₄×C₄₃	—	2	4	no	—
122	C₂×C₄×C₄₃	—	2	2	no	—
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	4	no	—
125	C₂×C₄×C₄₃	—	2	4	no	—
126	C₂×C₄×C₄₃	—	2	8	no	—
127	C₂×C₄×C₄₃	—	2	8	no	—
128	C₂×C₄×C₄₃	—	4	4	no	—
129	C₂×C₄×C₄₃	—	4	4	no	—
130	C₂×C₄×C₄₃	—	4	2	no	—
131	C₂×C₄×C₄₃	—	4	2	no	—
132	C₂×C₄×C₄₃	—	4	2	no	—
133	C₂×C₄×C₄₃	—	4	2	no	—
134	C₂×C₄×C₄₃	—	4	4	no	—
135	C₂×C₄×C₄₃	—	4	4	no	—
136	C₂×C₄×C₄₃	—	4	4	no	—
137	C₂×C₄×C₄₃	—	4	4	no	—
138	C₂×C₄×C₄₃	—	4	4	no	—
139	C₂×C₄×C₄₃	—	4	4	no	—
140	C₂×C₄×C₄₃	—	4	4	no	—
141	C₂×C₄×C₄₃	—	4	4	no	—
142	C₂×C₄×C₄₃	—	4	4	no	—
143	C₂×C₄×C₄₃	—	4	4	no	—
144	C₂×C₄×C₄₃	—	4	4	no	—
145	C₂×C₄×C₄₃	—	4	4	no	—
146	C₂×C₄×C₄₃	—	4	4	no	—
147	C₂×C₄×C₄₃	—	4	4	no	—
148	C₂×C₄×C₄₃	#125	1	8	yes	—
149	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
150	#17076	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂²×C₄₃	C₂×#125	1	2	yes	—
152	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
153	C₂²×C₄₃	#534	1	1	yes	characteristic
154	C₂²×C₄₃	#537	1	1	yes	characteristic
155	C₂²×C₄₃	#538	1	2	yes	—
156	C₂²×C₄₃	#538	1	2	yes	—
157	C₂²×C₄₃	#539	1	2	yes	—
158	C₂²×C₄₃	#539	1	2	yes	—
159	C₂²×C₄₃	#543	1	1	yes	characteristic
160	C₂²×C₄₃	#543	1	1	yes	characteristic
161	C₂²×C₄₃	#544	1	1	yes	characteristic
162	C₂²×C₄₃	#544	1	2	yes	—
163	C₂²×C₄₃	#544	1	1	yes	characteristic
164	C₂²×C₄₃	#547	1	2	yes	—
165	C₂²×C₄₃	#550	1	2	yes	—
166	C₂²×C₄₃	#554	1	2	yes	—
167	C₂²×C₄₃	#555	1	1	yes	characteristic
168	C₂²×C₄₃	#556	1	2	yes	—
169	C₂²×C₄₃	#557	1	2	yes	—
170	C₂²×C₄₃	#559	1	1	yes	characteristic
171	C₂²×C₄₃	H(3,𝔽₄)	1	1	yes	characteristic
172	C₂²×C₄₃	#563	1	1	yes	characteristic
173	C₂²×C₄₃	#563	1	2	yes	—
174	C₄×C₄₃	—	2	8	no	—
175	C₄×C₄₃	—	2	4	no	—
176	C₄×C₄₃	—	4	4	no	—
177	C₄×C₄₃	—	4	4	no	—
178	C₄×C₄₃	—	8	4	no	—
179	C₄×C₄₃	—	8	4	no	—
180	C₂×#400	C₂×C₄₃	1	2	yes	—
181	#1444	C₂×C₄₃	1	4	yes	—
182	#1442	C₂×C₄₃	1	4	yes	—
183	#1441	C₂×C₄₃	1	2	yes	—
184	C₄⋊#95	C₂×C₄₃	1	2	yes	—
185	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
186	C₂×C₄₃	#2552	1	2	yes	—
187	C₂×C₄₃	#2571	1	1	yes	characteristic
188	C₂×C₄₃	#2646	1	2	yes	—
189	C₂×C₄₃	#2659	1	1	yes	characteristic
190	C₂×C₄₃	#2724	1	1	yes	characteristic
191	C₂×C₄₃	#2727	1	2	yes	—
192	C₂×C₄₃	#2733	1	1	yes	characteristic
193	C₂×C₄₃	#2804	1	1	yes	characteristic
194	C₂×C₄₃	#2805	1	2	yes	—
195	C₂×C₄₃	#2809	1	1	yes	characteristic
196	C₂×C₄₃	#2844	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
198	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
199	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
200	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
201	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
202	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
203	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
204	#400	—	2	8	no	—
205	C₂×#95	C₂²×C₄₃	1	4	yes	—
206	C₂×#95	C₂²×C₄₃	1	2	yes	—
207	C₂×#95	C₂²×C₄₃	1	4	yes	—
208	C₂×#95	C₂²×C₄₃	1	4	yes	—
209	C₂×#95	C₂²×C₄₃	1	4	yes	—
210	C₂×#95	C₂²×C₄₃	1	2	yes	—
211	C₂×#95	C₂²×C₄₃	1	4	yes	—
212	C₄₃	#17076	1	1	yes	characteristic, direct product factor, Sylow
213	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
214	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
215	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
216	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
217	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	4	1	no	—
223	C₂×C₄⋊C₄	—	4	1	no	—
224	C₂×C₄⋊C₄	—	4	1	no	—
225	C₂×C₄⋊C₄	—	4	1	no	—
226	C₂×C₄⋊C₄	—	4	2	no	—
227	C₂×C₄⋊C₄	—	4	2	no	—
228	C₂×C₄⋊C₄	—	4	2	no	—
229	C₂×C₄⋊C₄	—	4	2	no	—
230	C₂×C₄⋊C₄	—	4	2	no	—
231	C₂×C₄⋊C₄	—	4	2	no	—
232	C₂×C₄⋊C₄	—	4	4	no	—
233	C₂×C₄⋊C₄	—	4	2	no	—
234	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
235	C₂×C₄⋊C₄	Q₈×C₄₃	1	4	yes	—
236	C₂×C₄²	—	4	1	no	—
237	C₂×C₄²	—	4	1	no	—
238	C₂×C₄²	Q₈×C₄₃	1	4	yes	—
239	#95	—	2	4	no	—
240	#95	—	2	8	no	—
241	#95	—	2	8	no	—
242	#95	—	2	8	no	—
243	#95	—	2	8	no	—
244	#95	—	4	2	no	—
245	#95	—	4	4	no	—
246	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
278	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
279	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
280	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
281	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
282	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
283	C₂²×C₄	#41×C₄₃	1	4	yes	—
284	C₂²×C₄	#41×C₄₃	1	4	yes	—
285	C₄⋊C₄	—	4	4	no	—
286	C₄⋊C₄	—	4	4	no	—
287	C₄⋊C₄	—	4	8	no	—
288	C₄⋊C₄	—	4	8	no	—
289	C₄⋊C₄	—	4	8	no	—
290	C₄⋊C₄	—	4	8	no	—
291	C₄²	—	4	4	no	—
292	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
293	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
294	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
295	C₂³	C₂×#41×C₄₃	1	2	yes	—
296	C₂³	C₂×#41×C₄₃	1	2	yes	—
297	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
298	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
299	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
300	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
301	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
302	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	#125×C₄₃	1	8	yes	—
340	C₂×C₄	C₄⋊Q₈×C₄₃	1	4	yes	—
341	C₂²	C₂×#125×C₄₃	1	2	yes	—
342	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
343	C₂²	C₄₃×#534	1	1	yes	characteristic
344	C₂²	C₄₃×#537	1	1	yes	characteristic
345	C₂²	C₄₃×#538	1	2	yes	—
346	C₂²	C₄₃×#538	1	2	yes	—
347	C₂²	C₄₃×#539	1	2	yes	—
348	C₂²	C₄₃×#539	1	2	yes	—
349	C₂²	C₄₃×#543	1	1	yes	characteristic
350	C₂²	C₄₃×#543	1	1	yes	characteristic
351	C₂²	C₄₃×#544	1	2	yes	—
352	C₂²	C₄₃×#544	1	1	yes	characteristic
353	C₂²	C₄₃×#544	1	1	yes	characteristic
354	C₂²	C₄₃×#547	1	2	yes	—
355	C₂²	C₄₃×#550	1	2	yes	—
356	C₂²	C₄₃×#554	1	2	yes	—
357	C₂²	C₄₃×#555	1	1	yes	characteristic
358	C₂²	C₄₃×#556	1	2	yes	—
359	C₂²	C₄₃×#557	1	2	yes	—
360	C₂²	C₄₃×#559	1	1	yes	characteristic
361	C₂²	C₄₃×H(3,𝔽₄)	1	1	yes	characteristic
362	C₂²	C₄₃×#563	1	1	yes	characteristic
363	C₂²	C₄₃×#563	1	2	yes	—
364	C₄	—	2	8	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	—	8	4	no	—
369	C₄	—	8	4	no	—
370	C₂	C₄₃×#2552	1	2	yes	—
371	C₂	C₄₃×#2571	1	1	yes	characteristic
372	C₂	C₄₃×#2646	1	2	yes	—
373	C₂	C₄₃×#2659	1	1	yes	characteristic
374	C₂	C₄₃×#2724	1	1	yes	characteristic
375	C₂	C₄₃×#2727	1	2	yes	—
376	C₂	C₄₃×#2733	1	1	yes	characteristic
377	C₂	C₄₃×#2804	1	1	yes	characteristic
378	C₂	C₄₃×#2805	1	2	yes	—
379	C₂	C₄₃×#2809	1	1	yes	characteristic
380	C₂	C₄₃×#2844	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
150. #17076	C₄₃	direct (N × H)
212. C₄₃	#17076	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#400	2
C₄₃×#1444	2
C₄₃×#1442	2
C₄₃×#1441	2
C₄₃×C₄⋊#95	2
#17076	43

Subgroups — C43×#17076 #24937093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17076 #24937093