Subgroups — #24991037

Order 11008.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137659	C₂	1	1	yes	maximal, characteristic
2	#19135401	C₂	1	1	yes	maximal, characteristic
3	#19135359	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135358	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582642	C₂	1	1	yes	maximal, characteristic
6	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13063322	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₇₂	—	2	1	no	—
10	C₂×#13063287	—	2	1	no	—
11	C₂×#13063257	—	2	1	no	—
12	C₂×#13063256	—	2	1	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063247	—	2	2	no	—
15	#14582801	—	2	1	no	—
16	#14582800	—	2	1	no	—
17	#14582777	—	2	2	no	—
18	#14582769	C₂²	1	1	yes	characteristic
19	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	#14582662	—	2	1	no	—
21	#14582661	—	2	1	no	—
22	#14582642	C₄	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×D₁₇₂	—	2	1	no	—
27	C₂²×D₁₇₂	—	2	1	no	—
28	C₂²×D₁₇₂	D₄	1	2	yes	—
29	C₂²×C₄×D₄₃	—	2	2	no	—
30	C₂²×C₄₃⋊C₈	—	2	1	no	—
31	#13063322	—	2	1	no	—
32	#13063322	—	2	1	no	—
33	#13063322	C₂×C₄	1	2	yes	—
34	#13063322	Q₈	1	2	yes	—
35	C₄×D₁₇₂	—	4	2	no	—
36	C₄×D₁₇₂	—	4	2	no	—
37	#13063287	—	4	2	no	—
38	#13063287	—	4	2	no	—
39	C₂×C₄⋊Dic₄₃	—	2	1	no	—
40	C₂×C₄⋊Dic₄₃	—	2	1	no	—
41	C₂×C₄⋊Dic₄₃	—	2	1	no	—
42	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
44	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	#13063257	—	4	2	no	—
49	#13063256	—	4	2	no	—
50	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	complemented
52	#13063247	—	4	4	no	—
53	C₄₃⋊#95	—	2	1	no	—
54	C₂²×C₈×C₄₃	—	2	1	no	—
55	C₂²×C₈×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	—	2	1	no	—
59	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
60	C₄⋊C₈×C₄₃	—	2	1	no	—
61	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	complemented
62	C₄×C₈×C₄₃	—	2	1	no	—
63	C₄×C₈×C₄₃	—	2	1	no	—
64	#95×C₄₃	—	2	1	no	—
65	C₂³×D₄₃	—	2	2	no	—
66	C₂²×C₄×C₄₃	—	2	1	no	—
67	C₂²×C₄×C₄₃	—	2	1	no	—
68	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
71	C₂²×Dic₄₃	—	2	1	no	—
72	C₂²×Dic₄₃	—	2	1	no	—
73	C₂²×Dic₄₃	—	4	1	no	—
74	C₂×D₁₇₂	—	2	2	no	—
75	C₂×D₁₇₂	—	2	2	no	—
76	C₂×D₁₇₂	—	2	2	no	—
77	C₂×D₁₇₂	—	2	2	no	—
78	C₂×D₁₇₂	—	2	2	no	—
79	C₂×D₁₇₂	—	4	1	no	—
80	C₂×D₁₇₂	—	4	1	no	—
81	C₂×D₁₇₂	—	4	1	no	—
82	C₂×D₁₇₂	—	4	1	no	—
83	C₂×D₁₇₂	—	4	1	no	—
84	C₂×D₁₇₂	—	4	1	no	—
85	C₂×D₁₇₂	—	4	1	no	—
86	C₂×D₁₇₂	—	4	1	no	—
87	C₂×D₁₇₂	—	4	2	no	—
88	C₂×D₁₇₂	—	4	2	no	—
89	C₂×D₁₇₂	C₄⋊C₄	1	4	yes	—
90	C₂×C₄×D₄₃	—	4	4	no	—
91	C₂×C₄×D₄₃	—	4	4	no	—
92	C₂×C₄×D₄₃	—	8	2	no	—
93	C₂×C₈×C₄₃	—	2	2	no	—
94	C₂×C₈×C₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	—	4	1	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₂×C₈×C₄₃	—	4	1	no	—
98	C₂×C₈×C₄₃	—	4	1	no	—
99	C₄⋊C₄×C₄₃	—	2	1	no	—
100	C₄⋊C₄×C₄₃	—	2	1	no	—
101	C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₄⋊C₄×C₄₃	SD₁₆	1	2	yes	—
103	C₄²×C₄₃	—	4	1	no	—
104	C₄²×C₄₃	—	4	1	no	—
105	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
107	C₄²×C₄₃	#41	1	1	yes	characteristic
108	C₄²×C₄₃	#41	1	1	yes	characteristic
109	(C₂×D₄₃)⋊C₄	—	4	4	no	—
110	(C₂×D₄₃)⋊C₄	—	4	4	no	—
111	(C₂×D₄₃)⋊C₄	—	8	2	no	—
112	C₄⋊Dic₄₃	—	2	1	no	—
113	C₄⋊Dic₄₃	—	2	1	no	—
114	C₄⋊Dic₄₃	—	2	1	no	—
115	C₄⋊Dic₄₃	—	4	2	no	—
116	C₄⋊Dic₄₃	—	4	1	no	—
117	C₄⋊Dic₄₃	—	4	1	no	—
118	C₄⋊Dic₄₃	—	4	1	no	—
119	C₄⋊Dic₄₃	—	4	1	no	—
120	C₄⋊Dic₄₃	SD₁₆	1	2	yes	—
121	C₄×Dic₄₃	—	4	1	no	—
122	C₄×Dic₄₃	—	4	1	no	—
123	C₂×C₄₃⋊C₈	—	2	2	no	—
124	C₂×C₄₃⋊C₈	—	4	1	no	—
125	C₂×C₄₃⋊C₈	—	4	1	no	—
126	C₂³×C₄₃	#120	1	1	yes	characteristic
127	C₂²×D₄₃	—	2	4	no	—
128	C₂²×D₄₃	—	4	2	no	—
129	C₂²×D₄₃	—	4	2	no	—
130	C₂²×D₄₃	—	4	2	no	—
131	C₂²×D₄₃	—	4	2	no	—
132	C₂²×D₄₃	—	4	2	no	—
133	C₂²×D₄₃	—	4	2	no	—
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	2	no	—
137	C₂×C₄×C₄₃	—	4	1	no	—
138	C₂×C₄×C₄₃	—	4	1	no	—
139	C₂×C₄×C₄₃	—	4	1	no	—
140	C₂×C₄×C₄₃	—	4	1	no	—
141	C₂×C₄×C₄₃	—	4	1	no	—
142	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
152	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×Dic₄₃	—	2	2	no	—
157	C₂×Dic₄₃	—	4	1	no	—
158	C₂×Dic₄₃	—	4	1	no	—
159	C₂×Dic₄₃	—	4	1	no	—
160	C₂×Dic₄₃	—	4	1	no	—
161	C₂×Dic₄₃	—	4	1	no	—
162	C₂×Dic₄₃	—	8	1	no	—
163	C₂×Dic₄₃	—	8	1	no	—
164	C₂×Dic₄₃	—	8	1	no	—
165	D₁₇₂	—	4	4	no	—
166	D₁₇₂	—	4	2	no	—
167	D₁₇₂	—	4	2	no	—
168	D₁₇₂	—	4	2	no	—
169	D₁₇₂	—	4	2	no	—
170	D₁₇₂	—	4	2	no	—
171	D₁₇₂	—	4	2	no	—
172	D₁₇₂	—	4	2	no	—
173	D₁₇₂	—	4	2	no	—
174	D₁₇₂	—	8	2	no	—
175	C₄×D₄₃	—	8	8	no	—
176	C₈×C₄₃	—	4	2	no	—
177	C₈×C₄₃	—	4	2	no	—
178	C₄₃⋊C₈	—	4	2	no	—
179	#8924	—	43	1	no	maximal, Sylow
180	C₂²×C₄₃	#385	1	1	yes	characteristic
181	C₂²×C₄₃	#449	1	1	yes	characteristic
182	C₂²×C₄₃	#449	1	1	yes	characteristic
183	C₂²×C₄₃	#450	1	1	yes	characteristic
184	C₂²×C₄₃	#450	1	1	yes	characteristic
185	C₂²×C₄₃	#453	1	1	yes	characteristic
186	C₂²×C₄₃	#455	1	1	yes	characteristic
187	C₂×D₄₃	—	4	4	no	—
188	C₂×D₄₃	—	4	4	no	—
189	C₂×D₄₃	—	4	4	no	—
190	C₂×D₄₃	—	8	2	no	—
191	C₂×D₄₃	—	8	2	no	—
192	C₂×D₄₃	—	8	2	no	—
193	C₂×D₄₃	—	8	2	no	—
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	2	1	no	—
196	C₄×C₄₃	—	4	2	no	—
197	C₄×C₄₃	—	8	1	no	—
198	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
199	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
200	C₄×C₄₃	#442	1	1	yes	characteristic
201	C₄×C₄₃	#442	1	1	yes	characteristic
202	C₄×C₄₃	#476	1	1	yes	characteristic
203	C₄×C₄₃	#476	1	1	yes	characteristic
204	C₄×C₄₃	#478	1	1	yes	characteristic
205	C₄×C₄₃	#478	1	1	yes	characteristic
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	8	1	no	—
208	Dic₄₃	—	16	1	no	—
209	#2366	—	43	1	no	—
210	#1957	—	43	1	no	—
211	#1948	—	43	1	no	—
212	#1948	—	43	1	no	—
213	C₂×#331	—	43	1	no	—
214	#1279	—	43	1	no	—
215	#1279	D₄₃	1	1	yes	characteristic, complemented
216	C₂×C₄₃	#1620	1	1	yes	characteristic
217	C₂×C₄₃	#1629	1	1	yes	characteristic
218	C₂×C₄₃	#1642	1	1	yes	characteristic
219	C₂×C₄₃	#1642	1	1	yes	characteristic
220	C₂×C₄₃	#1856	1	1	yes	characteristic
221	C₂×C₄₃	#1864	1	1	yes	characteristic
222	C₂×C₄₃	#1864	1	1	yes	characteristic
223	D₄₃	—	8	4	no	—
224	C₂×#127	—	43	1	no	—
225	C₂×C₄×D₄	—	86	1	no	—
226	C₂×C₄×D₄	—	86	1	no	—
227	C₂×#106	—	86	1	no	—
228	C₂×#106	—	86	1	no	—
229	C₂×C₄⋊C₈	—	43	1	no	—
230	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
231	C₂×#102	—	86	2	no	—
232	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
233	#390	—	86	1	no	—
234	#390	—	86	1	no	—
235	#386	—	86	2	no	—
236	#384	—	43	1	no	—
237	C₄×C₄⋊C₄	—	43	1	no	—
238	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
239	#340	—	86	1	no	—
240	#340	—	86	1	no	—
241	#331	—	43	4	no	—
242	C₄₃	#8924	1	1	yes	characteristic, complemented, Sylow
243	C₂²×D₄	—	43	2	no	—
244	C₂²×D₄	—	86	1	no	—
245	C₂²×D₄	—	86	1	no	—
246	C₂³×C₄	—	86	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	86	1	no	—
250	#127	—	43	2	no	—
251	#127	—	43	2	no	—
252	#127	—	86	1	no	—
253	#127	—	86	1	no	—
254	C₄×D₄	—	172	2	no	—
255	C₄×D₄	—	172	2	no	—
256	C₄×D₄	—	172	2	no	—
257	C₄×D₄	—	172	2	no	—
258	C₂×C₄⋊C₄	—	43	1	no	—
259	C₂×C₄⋊C₄	—	43	1	no	—
260	C₂×C₄⋊C₄	—	86	1	no	—
261	C₂×C₄⋊C₄	—	86	1	no	—
262	C₂×C₄⋊C₄	—	86	1	no	—
263	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	86	2	no	—
266	C₂×C₂²⋊C₄	—	86	2	no	—
267	C₂×C₂²⋊C₄	—	86	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	86	1	no	—
270	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
271	#106	—	172	2	no	—
272	#106	—	172	2	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	43	2	no	—
275	C₄⋊C₈	—	86	1	no	—
276	C₄⋊C₈	C₄×D₄₃	1	2	yes	complemented
277	#102	—	172	4	no	—
278	C₄×C₈	—	2	1	no	—
279	C₄×C₈	—	2	1	no	—
280	#95	—	2	1	no	—
281	#95	—	86	1	no	—
282	C₂⁴	—	86	2	no	—
283	C₂×D₄	—	43	4	no	—
284	C₂×D₄	—	86	2	no	—
285	C₂×D₄	—	86	2	no	—
286	C₂×D₄	—	86	2	no	—
287	C₂×D₄	—	86	2	no	—
288	C₂×D₄	—	86	2	no	—
289	C₂×D₄	—	172	2	no	—
290	C₂×D₄	—	172	2	no	—
291	C₂×D₄	—	172	1	no	—
292	C₂×D₄	—	172	1	no	—
293	C₂×D₄	—	172	1	no	—
294	C₂×D₄	—	172	1	no	—
295	C₂×D₄	—	172	1	no	—
296	C₂×D₄	—	172	1	no	—
297	C₂×D₄	—	172	1	no	—
298	C₂×D₄	—	172	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	86	1	no	—
302	C₂²×C₄	—	86	1	no	—
303	C₂²×C₄	—	344	2	no	—
304	C₂²×C₄	—	172	4	no	—
305	C₂²×C₄	—	172	4	no	—
306	C₂²×C₄	—	172	1	no	—
307	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	86	2	no	—
317	C₂×C₈	—	172	1	no	—
318	C₂×C₈	—	172	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	43	2	no	—
323	C₄⋊C₄	—	86	1	no	—
324	C₄⋊C₄	—	86	1	no	—
325	C₄⋊C₄	—	86	1	no	—
326	C₄⋊C₄	—	172	2	no	—
327	C₄⋊C₄	—	172	1	no	—
328	C₄⋊C₄	—	172	1	no	—
329	C₄⋊C₄	—	172	1	no	—
330	C₄⋊C₄	—	172	1	no	—
331	C₄⋊C₄	#10621873	1	2	yes	—
332	C₂²⋊C₄	—	344	2	no	—
333	C₂²⋊C₄	—	172	4	no	—
334	C₂²⋊C₄	—	172	4	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	172	1	no	—
338	C₄²	—	172	1	no	—
339	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
340	C₄²	#10621898	1	1	yes	characteristic
341	C₄²	#10621900	1	1	yes	characteristic
342	C₄²	Q₈×D₄₃	1	1	yes	characteristic
343	C₂³	—	86	4	no	—
344	C₂³	—	172	2	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	#13063295	1	1	yes	characteristic
351	D₄	—	344	2	no	—
352	D₄	—	172	4	no	—
353	D₄	—	172	2	no	—
354	D₄	—	172	2	no	—
355	D₄	—	172	2	no	—
356	D₄	—	172	2	no	—
357	D₄	—	172	2	no	—
358	D₄	—	172	2	no	—
359	D₄	—	172	2	no	—
360	D₄	—	172	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	86	2	no	—
370	C₂×C₄	—	344	8	no	—
371	C₂×C₄	—	344	1	no	—
372	C₂×C₄	—	344	1	no	—
373	C₂×C₄	—	344	1	no	—
374	C₂×C₄	—	172	1	no	—
375	C₂×C₄	—	172	1	no	—
376	C₂×C₄	—	172	1	no	—
377	C₂×C₄	—	172	1	no	—
378	C₂×C₄	—	172	1	no	—
379	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
380	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
382	C₂×C₄	#13063303	1	1	yes	characteristic
383	C₂×C₄	#13063305	1	1	yes	characteristic
384	C₂×C₄	#13063307	1	1	yes	characteristic
385	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
386	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
387	C₂×C₄	#13063347	1	1	yes	characteristic
388	C₂×C₄	#13063348	1	1	yes	characteristic
389	C₂×C₄	#13063349	1	1	yes	characteristic
390	C₂×C₄	#13063352	1	1	yes	characteristic
391	C₂×C₄	#13063353	1	1	yes	characteristic
392	C₂×C₄	#13063353	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₈	—	172	2	no	—
396	C₂²	—	344	2	no	—
397	C₂²	—	344	2	no	—
398	C₂²	—	344	2	no	—
399	C₂²	—	344	2	no	—
400	C₂²	—	172	4	no	—
401	C₂²	—	172	4	no	—
402	C₂²	—	172	4	no	—
403	C₂²	#14582773	1	1	yes	characteristic
404	C₂²	#14583046	1	1	yes	characteristic
405	C₂²	#14583047	1	1	yes	characteristic
406	C₂²	#14583051	1	1	yes	characteristic
407	C₂²	#14583052	1	1	yes	characteristic
408	C₂²	#14583068	1	1	yes	characteristic
409	C₂²	#14583078	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	344	1	no	—
415	C₄	—	172	2	no	—
416	C₄	—	688	1	no	—
417	C₄	#14582984	1	1	yes	characteristic
418	C₄	C₄×#10621873	1	1	yes	characteristic
419	C₄	#14583008	1	1	yes	characteristic
420	C₄	#14583012	1	1	yes	characteristic
421	C₄	#14583188	1	1	yes	characteristic
422	C₄	#14583190	1	1	yes	characteristic
423	C₄	#14583200	1	1	yes	characteristic
424	C₄	#14583202	1	1	yes	characteristic
425	C₂	—	344	4	no	—
426	C₂	#19133656	1	1	yes	characteristic
427	C₂	#19133713	1	1	yes	characteristic
428	C₂	#19133797	1	1	yes	characteristic
429	C₂	#19133798	1	1	yes	characteristic
430	C₂	#19134806	1	1	yes	characteristic
431	C₂	#19134857	1	1	yes	characteristic
432	C₂	#19134859	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂×#13063322	C₂²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#8924
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
3. #19135359	C₂	semidirect
4. #19135358	C₂	semidirect
6. #19132435	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
22. #14582642	C₄	semidirect
51. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
61. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
215. #1279	D₄₃	semidirect
242. C₄₃	#8924	semidirect
276. C₄⋊C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19137659	2
#19135401	2
#19135359	2
#19135358	2
C₂×#14582642	2
#19132435	2
C₄₃×#1279	2
#8924	43