Subgroups — #25100914

Order 11008.

950 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583012	C₂	1	1	yes	maximal, characteristic
2	#19137059	C₂	1	2	yes	maximal, complemented
3	#19135471	C₂	1	1	yes	maximal, characteristic
4	#19135461	C₂	1	1	yes	maximal, characteristic
5	#19135338	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135323	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135292	C₂	1	2	yes	maximal, complemented
8	#19135278	C₂	1	2	yes	maximal, complemented
9	#19134492	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134421	C₂	1	2	yes	maximal, complemented
11	C₄×#97×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
14	C₂×#13063282	—	2	2	no	—
15	#14583012	C₄	1	8	yes	complemented
16	C₂×#13063259	C₂²	1	1	yes	characteristic
17	C₂×#13063257	C₂²	1	1	yes	characteristic
18	C₂×#13063257	C₂²	1	1	yes	characteristic
19	C₂×#13063247	C₂²	1	2	yes	—
20	C₂×#13063247	C₂²	1	2	yes	—
21	C₂×#13063247	C₂²	1	2	yes	—
22	#14582801	C₂²	1	2	yes	—
23	#14582801	C₂²	1	2	yes	—
24	#14582797	C₂²	1	2	yes	—
25	#14582797	C₂²	1	2	yes	—
26	#14582790	—	2	2	no	—
27	#14582790	—	2	2	no	—
28	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
29	C₄×(C₂×D₄₃)⋊C₄	—	2	2	no	—
30	#14582662	C₂²	1	2	yes	—
31	#14582662	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄³×C₄₃	C₂²	1	1	yes	characteristic
40	C₂²×D₁₇₂	C₂³	1	2	yes	—
41	C₂²×C₄×D₄₃	—	2	2	no	—
42	C₂×D₃₄₄	—	2	2	no	—
43	C₂×D₃₄₄	—	2	2	no	—
44	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
45	C₄×D₁₇₂	—	2	4	no	—
46	C₄×D₁₇₂	C₂×C₄	1	8	yes	—
47	#13063282	—	4	8	no	—
48	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
51	C₂×Dic₄₃⋊C₄	—	2	2	no	—
52	C₂×Dic₄₃⋊C₄	—	2	2	no	—
53	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
54	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
58	C₂×C₄×Dic₄₃	—	2	2	no	—
59	#13063259	—	2	2	no	—
60	#13063257	—	2	2	no	—
61	#13063257	C₂×C₄	1	4	yes	—
62	#13063247	—	2	4	no	—
63	#13063247	—	2	4	no	—
64	#13063247	C₂×C₄	1	8	yes	—
65	C₄₃⋊#95	—	2	2	no	—
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	D₄	1	2	yes	—
73	C₂×C₄²×C₄₃	D₄	1	2	yes	—
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#97×C₄₃	—	2	2	no	—
78	#97×C₄₃	—	2	2	no	—
79	#97×C₄₃	—	2	2	no	—
80	#97×C₄₃	C₂×C₄	1	4	yes	—
81	C₄×C₈×C₄₃	—	2	2	no	—
82	C₄×C₈×C₄₃	—	2	2	no	—
83	C₂³×D₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
89	C₂²×Dic₄₃	—	2	2	no	—
90	C₂²×Dic₄₃	—	2	2	no	—
91	C₂²×Dic₄₃	—	2	2	no	—
92	C₂×D₁₇₂	—	2	2	no	—
93	C₂×D₁₇₂	—	2	2	no	—
94	C₂×D₁₇₂	—	2	2	no	—
95	C₂×D₁₇₂	—	2	2	no	—
96	C₂×D₁₇₂	—	2	2	no	—
97	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
98	C₂×C₄×D₄₃	—	2	8	no	—
99	C₂×C₄×D₄₃	—	4	4	no	—
100	C₂×C₄×D₄₃	—	4	4	no	—
101	C₂×C₈×C₄₃	—	2	1	no	—
102	C₂×C₈×C₄₃	—	2	1	no	—
103	C₂×C₈×C₄₃	—	2	1	no	—
104	C₂×C₈×C₄₃	—	2	1	no	—
105	C₂×C₈×C₄₃	—	2	1	no	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₃	#41	1	2	yes	—
110	C₂×C₈×C₄₃	#41	1	2	yes	—
111	C₂×C₈×C₄₃	#41	1	2	yes	—
112	C₂×C₈×C₄₃	#41	1	2	yes	—
113	C₄²×C₄₃	—	2	4	no	—
114	C₄²×C₄₃	—	2	1	no	—
115	C₄²×C₄₃	—	2	1	no	—
116	C₄²×C₄₃	—	2	1	no	—
117	C₄²×C₄₃	—	2	1	no	—
118	C₄²×C₄₃	—	4	2	no	—
119	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₃	#41	1	2	yes	—
121	(C₂×D₄₃)⋊C₄	—	2	8	no	—
122	(C₂×D₄₃)⋊C₄	—	4	4	no	—
123	(C₂×D₄₃)⋊C₄	—	4	4	no	—
124	(C₂×D₄₃)⋊C₄	—	4	4	no	—
125	(C₂×D₄₃)⋊C₄	—	4	4	no	—
126	C₄⋊Dic₄₃	—	2	2	no	—
127	C₄⋊Dic₄₃	—	2	2	no	—
128	C₄⋊Dic₄₃	—	2	2	no	—
129	C₄⋊Dic₄₃	—	2	2	no	—
130	C₄⋊Dic₄₃	—	2	2	no	—
131	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
132	Dic₄₃⋊C₄	—	4	4	no	—
133	Dic₄₃⋊C₄	—	4	4	no	—
134	C₄×Dic₄₃	—	4	4	no	—
135	D₃₄₄	—	2	8	no	—
136	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
137	C₂²×D₄₃	—	2	4	no	—
138	C₂²×D₄₃	—	4	2	no	—
139	C₂²×D₄₃	—	4	2	no	—
140	C₂²×D₄₃	—	4	2	no	—
141	C₂²×D₄₃	—	4	2	no	—
142	C₂²×D₄₃	—	4	2	no	—
143	C₂²×D₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	2	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
153	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
154	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₄₃	—	2	4	no	—
161	C₂×Dic₄₃	—	4	2	no	—
162	C₂×Dic₄₃	—	4	2	no	—
163	C₂×Dic₄₃	—	4	2	no	—
164	C₂×Dic₄₃	—	4	2	no	—
165	C₂×Dic₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	4	2	no	—
167	C₂×Dic₄₃	—	4	2	no	—
168	C₂×Dic₄₃	—	4	2	no	—
169	D₁₇₂	—	2	4	no	—
170	D₁₇₂	—	2	4	no	—
171	D₁₇₂	—	4	2	no	—
172	D₁₇₂	—	4	2	no	—
173	C₄×D₄₃	—	4	16	no	—
174	C₈×C₄₃	—	2	2	no	—
175	C₈×C₄₃	—	2	2	no	—
176	C₈×C₄₃	—	2	2	no	—
177	C₈×C₄₃	#117	1	4	yes	complemented
178	#21286	—	43	1	no	maximal, Sylow
179	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂²×C₄₃	#532	1	1	yes	characteristic
181	C₂²×C₄₃	#532	1	1	yes	characteristic
182	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
183	C₂²×C₄₃	#575	1	2	yes	—
184	C₂×D₄₃	—	4	4	no	—
185	C₂×D₄₃	—	4	4	no	—
186	C₂×D₄₃	—	4	4	no	—
187	C₂×D₄₃	—	8	2	no	—
188	C₂×D₄₃	—	8	2	no	—
189	C₂×D₄₃	—	8	2	no	—
190	C₂×D₄₃	—	8	2	no	—
191	C₄×C₄₃	—	2	4	no	—
192	C₄×C₄₃	—	2	4	no	—
193	C₄×C₄₃	—	4	1	no	—
194	C₄×C₄₃	—	4	1	no	—
195	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
196	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
197	C₄×C₄₃	#529	1	1	yes	characteristic
198	C₄×C₄₃	#529	1	1	yes	characteristic
199	Dic₄₃	—	4	4	no	—
200	Dic₄₃	—	8	2	no	—
201	Dic₄₃	—	8	2	no	—
202	C₂×#442	—	43	1	no	—
203	#2293	—	43	2	no	—
204	#1972	—	43	1	no	—
205	#1970	—	43	1	no	—
206	#1944	—	43	1	no	—
207	#1941	—	43	1	no	—
208	#1936	—	43	2	no	—
209	#1934	—	43	2	no	—
210	#1776	—	43	1	no	—
211	#1762	—	43	2	no	—
212	C₄×#97	D₄₃	1	1	yes	characteristic, complemented
213	C₂×C₄₃	#2293	1	1	yes	characteristic
214	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	2	yes	—
215	C₂×C₄₃	#3180	1	2	yes	—
216	C₂×C₄₃	#3183	1	1	yes	characteristic
217	C₂×C₄₃	#3184	1	1	yes	characteristic
218	D₄₃	—	8	4	no	—
219	C₂²×D₈	—	43	1	no	—
220	C₂×C₄×D₄	—	43	2	no	—
221	C₂×#117	—	86	2	no	—
222	#442	—	43	8	no	—
223	C₂×#107	—	43	1	no	—
224	C₂×#106	—	43	1	no	—
225	C₂×#106	—	43	1	no	—
226	C₂×#102	—	43	2	no	—
227	C₂×#102	—	43	2	no	—
228	C₂×#102	—	43	2	no	—
229	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
230	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
231	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
232	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
235	#390	—	43	2	no	—
236	#390	—	43	2	no	—
237	#389	—	43	2	no	—
238	#389	—	43	2	no	—
239	#388	—	86	2	no	—
240	#388	—	86	2	no	—
241	C₄×C₄⋊C₄	—	43	2	no	—
242	C₄×C₂²⋊C₄	—	86	2	no	—
243	C₄³	C₂×D₄₃	1	1	yes	characteristic
244	#340	—	43	2	no	—
245	#340	—	43	2	no	—
246	#340	—	43	2	no	—
247	C₄₃	#21286	1	1	yes	characteristic, complemented, Sylow
248	C₂²×D₄	—	43	2	no	—
249	C₂³×C₄	—	86	2	no	—
250	C₂×D₈	—	43	4	no	—
251	C₂×D₈	—	86	2	no	—
252	C₂×D₈	—	86	2	no	—
253	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
254	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
255	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
257	C₄×D₄	—	43	8	no	—
258	C₄×D₄	—	86	4	no	—
259	#117	—	172	8	no	—
260	C₂×C₄⋊C₄	—	43	2	no	—
261	C₂×C₄⋊C₄	—	43	2	no	—
262	C₂×C₄⋊C₄	—	43	2	no	—
263	C₂×C₄⋊C₄	—	86	2	no	—
264	C₂×C₄⋊C₄	—	86	2	no	—
265	C₂×C₂²⋊C₄	—	86	2	no	—
266	C₂×C₂²⋊C₄	—	86	2	no	—
267	C₂×C₂²⋊C₄	—	86	2	no	—
268	C₂×C₂²⋊C₄	—	86	2	no	—
269	C₂×C₂²⋊C₄	—	86	2	no	—
270	C₂×C₄²	—	86	2	no	—
271	C₂×C₄²	D₁₇₂	1	2	yes	—
272	C₂×C₄²	D₁₇₂	1	2	yes	—
273	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
274	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
276	#107	—	86	2	no	—
277	#106	—	43	4	no	—
278	#106	—	86	2	no	—
279	#102	—	43	8	no	—
280	#102	—	86	4	no	—
281	#102	—	86	4	no	—
282	#97	—	2	2	no	—
283	#97	—	2	2	no	—
284	#97	—	2	2	no	—
285	#97	C₄×D₄₃	1	4	yes	—
286	C₄×C₈	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	#95	—	86	2	no	—
289	#95	—	86	2	no	—
290	#95	—	86	2	no	—
291	C₂⁴	—	86	2	no	—
292	C₂×D₄	—	43	4	no	—
293	C₂×D₄	—	86	2	no	—
294	C₂×D₄	—	86	2	no	—
295	C₂×D₄	—	86	2	no	—
296	C₂×D₄	—	86	2	no	—
297	C₂×D₄	—	86	2	no	—
298	C₂²×C₄	—	86	2	no	—
299	C₂²×C₄	—	86	8	no	—
300	C₂²×C₄	—	86	2	no	—
301	C₂²×C₄	—	86	2	no	—
302	C₂²×C₄	—	172	4	no	—
303	C₂²×C₄	—	172	4	no	—
304	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
307	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
308	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
309	D₈	—	86	8	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
317	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
318	C₂×C₈	#10621898	1	2	yes	—
319	C₂×C₈	#10621898	1	2	yes	—
320	C₂×C₈	#10621898	1	2	yes	—
321	C₂×C₈	#10621898	1	2	yes	—
322	C₄⋊C₄	—	43	4	no	—
323	C₄⋊C₄	—	86	2	no	—
324	C₄⋊C₄	—	86	2	no	—
325	C₄⋊C₄	—	86	2	no	—
326	C₄⋊C₄	—	86	2	no	—
327	C₄⋊C₄	—	86	2	no	—
328	C₄⋊C₄	—	172	4	no	—
329	C₄⋊C₄	—	172	4	no	—
330	C₂²⋊C₄	—	86	8	no	—
331	C₂²⋊C₄	—	172	4	no	—
332	C₂²⋊C₄	—	172	4	no	—
333	C₂²⋊C₄	—	172	4	no	—
334	C₂²⋊C₄	—	172	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	172	4	no	—
342	C₄²	C₂×C₄×D₄₃	1	2	yes	—
343	C₄²	#10621898	1	2	yes	—
344	C₂³	—	86	4	no	—
345	C₂³	—	172	2	no	—
346	C₂³	—	172	2	no	—
347	C₂³	—	172	2	no	—
348	C₂³	—	172	2	no	—
349	C₂³	—	172	2	no	—
350	C₂³	—	172	2	no	—
351	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
352	D₄	—	86	4	no	—
353	D₄	—	86	4	no	—
354	D₄	—	172	2	no	—
355	D₄	—	172	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	86	4	no	—
365	C₂×C₄	—	172	16	no	—
366	C₂×C₄	—	172	2	no	—
367	C₂×C₄	—	172	2	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	—	172	2	no	—
371	C₂×C₄	—	172	2	no	—
372	C₂×C₄	—	172	2	no	—
373	C₂×C₄	—	172	2	no	—
374	C₂×C₄	C₄×D₁₇₂	1	4	yes	—
375	C₂×C₄	#13063353	1	4	yes	—
376	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
377	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
378	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
379	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
380	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
381	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	2	2	no	—
385	C₈	#13063282	1	4	yes	complemented
386	C₂²	—	344	2	no	—
387	C₂²	—	344	2	no	—
388	C₂²	—	344	2	no	—
389	C₂²	—	344	2	no	—
390	C₂²	—	172	4	no	—
391	C₂²	—	172	4	no	—
392	C₂²	—	172	4	no	—
393	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
394	C₂²	#14583449	1	1	yes	characteristic
395	C₂²	#14583449	1	1	yes	characteristic
396	C₂²	C₂×#13063353	1	2	yes	—
397	C₂²	#14583699	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	344	2	no	—
403	C₄	—	344	2	no	—
404	C₄	—	172	4	no	—
405	C₄	C₂×#13063282	1	1	yes	characteristic
406	C₄	C₄×#10621898	1	1	yes	characteristic
407	C₄	#14583433	1	1	yes	characteristic
408	C₄	#14583433	1	1	yes	characteristic
409	C₂	—	344	4	no	—
410	C₂	#19137059	1	1	yes	characteristic
411	C₂	C₄×#13063353	1	2	yes	—
412	C₂	#19145293	1	2	yes	—
413	C₂	#19145324	1	1	yes	characteristic
414	C₂	#19145333	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#97×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₃₄₄	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#97	D₄₃
hypocenter	C₄₃	#21286
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
2. #19137059	C₂	semidirect
5. #19135338	C₂	semidirect
6. #19135323	C₂	semidirect
7. #19135292	C₂	semidirect
8. #19135278	C₂	semidirect
9. #19134492	C₂	semidirect
10. #19134421	C₂	semidirect
11. C₄×#97×C₄₃	C₂	semidirect
15. #14583012	C₄	semidirect
177. C₈×C₄₃	#117	semidirect
212. C₄×#97	D₄₃	semidirect
247. C₄₃	#21286	semidirect
385. C₈	#13063282	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583012	2
#19137059	2
#19135471	2
#19135461	2
#19135338	2
#19135323	2
#19135292	2
#19135278	2
#19134492	2
#19134421	2
C₄×#97×C₄₃	2
#21286	43