Subgroups — #24989309

Order 11008.

548 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137056	C₂	1	1	yes	maximal, characteristic
2	#19134711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582628	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
6	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063282	—	2	1	no	—
10	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₃⋊C₈	—	2	1	no	—
12	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	#14582800	C₄	1	1	yes	characteristic
14	#14582800	C₄	1	1	yes	characteristic
15	#14582795	C₄	1	1	yes	characteristic
16	#14582795	C₄	1	1	yes	characteristic
17	#14582788	—	2	1	no	—
18	#14582788	—	2	1	no	—
19	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
20	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
21	#14582653	—	2	1	no	—
22	#14582653	—	2	1	no	—
23	#14582653	—	2	1	no	—
24	#14582628	—	2	2	no	—
25	#14582626	—	2	2	no	—
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×D₁₇₂	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₃	—	2	1	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₄×D₁₇₂	—	2	1	no	—
34	C₄×D₁₇₂	—	2	1	no	—
35	C₄×D₁₇₂	D₄	1	2	yes	—
36	C₄×D₁₇₂	Q₈	1	2	yes	—
37	#13063282	—	4	2	no	—
38	#13063282	—	4	2	no	—
39	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂×Dic₄₃⋊C₄	—	2	1	no	—
41	C₂×Dic₄₃⋊C₄	—	2	1	no	—
42	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
43	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
44	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
47	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
53	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
55	Dic₄₃⋊C₈	—	2	4	no	—
56	C₄×C₄₃⋊C₈	—	2	1	no	—
57	C₄×C₄₃⋊C₈	—	2	1	no	—
58	C₄₃⋊#95	—	2	1	no	—
59	C₄₃⋊#95	—	2	1	no	—
60	C₂²×C₈×C₄₃	—	2	1	no	—
61	C₂²×C₈×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
68	C₄×C₈×C₄₃	—	2	1	no	—
69	C₄×C₈×C₄₃	—	2	1	no	—
70	#95×C₄₃	—	2	1	no	—
71	C₂³×D₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	—	2	1	no	—
73	C₂²×C₄×C₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₄₃	—	2	1	no	—
78	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×D₁₇₂	—	2	1	no	—
83	C₂×D₁₇₂	—	2	1	no	—
84	C₂×D₁₇₂	—	2	1	no	—
85	C₂×D₁₇₂	—	2	1	no	—
86	C₂×D₁₇₂	—	2	1	no	—
87	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
88	C₂×C₄×D₄₃	—	2	2	no	—
89	C₂×C₄×D₄₃	—	2	2	no	—
90	C₂×C₄×D₄₃	—	4	1	no	—
91	C₂×C₄×D₄₃	—	4	1	no	—
92	C₂×C₄×D₄₃	—	4	1	no	—
93	C₂×C₄×D₄₃	—	4	1	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	C₂×C₈×C₄₃	—	4	1	no	—
100	C₄⋊C₄×C₄₃	—	2	1	no	—
101	C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₄²×C₄₃	—	4	1	no	—
105	C₄²×C₄₃	—	4	1	no	—
106	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
108	C₄²×C₄₃	#41	1	1	yes	characteristic
109	C₄²×C₄₃	#41	1	1	yes	characteristic
110	(C₂×D₄₃)⋊C₄	—	2	2	no	—
111	(C₂×D₄₃)⋊C₄	—	2	2	no	—
112	(C₂×D₄₃)⋊C₄	—	4	2	no	—
113	(C₂×D₄₃)⋊C₄	—	4	2	no	—
114	(C₂×D₄₃)⋊C₄	—	4	2	no	—
115	(C₂×D₄₃)⋊C₄	—	4	2	no	—
116	C₄⋊Dic₄₃	—	2	1	no	—
117	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
118	Dic₄₃⋊C₄	—	4	2	no	—
119	Dic₄₃⋊C₄	—	4	2	no	—
120	C₄×Dic₄₃	—	2	1	no	—
121	C₄×Dic₄₃	—	2	1	no	—
122	C₄×Dic₄₃	—	2	1	no	—
123	C₄×Dic₄₃	—	2	1	no	—
124	C₄×Dic₄₃	—	2	1	no	—
125	C₄×Dic₄₃	—	2	1	no	—
126	C₄×Dic₄₃	—	2	1	no	—
127	C₄×Dic₄₃	—	2	1	no	—
128	C₄×Dic₄₃	—	2	2	no	—
129	C₄×Dic₄₃	—	4	1	no	—
130	C₂×C₄₃⋊C₈	—	2	2	no	—
131	C₂×C₄₃⋊C₈	—	4	1	no	—
132	C₂×C₄₃⋊C₈	—	4	1	no	—
133	C₂×C₄₃⋊C₈	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	—	4	1	no	—
136	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×D₄₃	—	2	2	no	—
138	C₂²×D₄₃	—	4	1	no	—
139	C₂²×D₄₃	—	4	1	no	—
140	C₂²×D₄₃	—	4	1	no	—
141	C₂²×D₄₃	—	4	1	no	—
142	C₂²×D₄₃	—	4	1	no	—
143	C₂²×D₄₃	—	4	1	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	4	1	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
161	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
164	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	—	2	1	no	—
175	C₂×Dic₄₃	—	2	1	no	—
176	C₂×Dic₄₃	—	2	1	no	—
177	C₂×Dic₄₃	—	2	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	#104	1	2	yes	—
181	D₁₇₂	—	2	2	no	—
182	D₁₇₂	—	2	2	no	—
183	D₁₇₂	—	4	1	no	—
184	D₁₇₂	—	4	1	no	—
185	C₄×D₄₃	—	4	2	no	—
186	C₄×D₄₃	—	4	2	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	—	4	2	no	—
189	C₈×C₄₃	—	4	2	no	—
190	C₈×C₄₃	—	8	1	no	—
191	C₄₃⋊C₈	—	4	2	no	—
192	C₄₃⋊C₈	—	8	1	no	—
193	#8569	—	43	1	no	maximal, Sylow
194	C₂²×C₄₃	#380	1	1	yes	characteristic
195	C₂²×C₄₃	#408	1	1	yes	characteristic
196	C₂²×C₄₃	#408	1	1	yes	characteristic
197	C₂²×C₄₃	#416	1	1	yes	characteristic
198	C₂²×C₄₃	#418	1	1	yes	characteristic
199	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
200	C₂²×C₄₃	#421	1	1	yes	characteristic
201	C₂×D₄₃	—	4	2	no	—
202	C₂×D₄₃	—	4	2	no	—
203	C₂×D₄₃	—	4	2	no	—
204	C₂×D₄₃	—	8	1	no	—
205	C₂×D₄₃	—	8	1	no	—
206	C₂×D₄₃	—	8	1	no	—
207	C₂×D₄₃	—	8	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	8	1	no	—
211	C₄×C₄₃	—	8	1	no	—
212	C₄×C₄₃	#424	1	1	yes	characteristic
213	C₄×C₄₃	#424	1	1	yes	characteristic
214	C₄×C₄₃	#433	1	1	yes	characteristic
215	C₄×C₄₃	#433	1	1	yes	characteristic
216	C₄×C₄₃	#463	1	1	yes	characteristic
217	C₄×C₄₃	#463	1	1	yes	characteristic
218	C₄×C₄₃	#478	1	1	yes	characteristic
219	C₄×C₄₃	#478	1	1	yes	characteristic
220	Dic₄₃	—	2	2	no	—
221	Dic₄₃	—	4	2	no	—
222	Dic₄₃	—	4	1	no	—
223	Dic₄₃	—	4	1	no	—
224	Dic₄₃	—	4	1	no	—
225	#2293	—	43	1	no	—
226	#1831	—	43	1	no	—
227	C₄×C₄⋊C₈	—	43	1	no	—
228	C₂×D₄⋊C₈	—	43	1	no	—
229	C₂×D₄⋊C₈	—	43	1	no	—
230	#1279	—	43	1	no	—
231	#1279	D₄₃	1	1	yes	characteristic, complemented
232	C₂×C₄₃	#1482	1	1	yes	characteristic
233	C₂×C₄₃	#1484	1	1	yes	characteristic
234	C₂×C₄₃	#1494	1	1	yes	characteristic
235	C₂×C₄₃	#1496	1	1	yes	characteristic
236	C₂×C₄₃	#1798	1	1	yes	characteristic
237	C₂×C₄₃	#1804	1	1	yes	characteristic
238	C₂×C₄₃	#1806	1	1	yes	characteristic
239	D₄₃	—	8	2	no	—
240	C₂×C₄×D₄	—	43	1	no	—
241	C₂×#117	—	86	1	no	—
242	C₂×C₄⋊C₈	—	43	1	no	—
243	C₂×C₄⋊C₈	—	86	1	no	—
244	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
245	C₂×C₄×C₈	—	43	1	no	—
246	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
247	#390	—	43	1	no	—
248	#390	—	43	1	no	—
249	#389	—	43	1	no	—
250	#389	—	43	1	no	—
251	#388	—	86	1	no	—
252	#388	—	86	1	no	—
253	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	—	86	1	no	—
255	C₄³	—	43	1	no	—
256	#336	—	86	1	no	—
257	#336	—	86	1	no	—
258	#336	—	86	1	no	—
259	D₄⋊C₈	—	86	2	no	—
260	D₄⋊C₈	—	86	2	no	—
261	C₄₃	#8569	1	1	yes	characteristic, complemented, Sylow
262	C₂²×D₄	—	43	1	no	—
263	C₂³×C₄	—	86	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	86	1	no	—
267	C₂²×C₈	—	86	1	no	—
268	C₄×D₄	—	43	2	no	—
269	C₄×D₄	—	43	2	no	—
270	C₄×D₄	—	86	1	no	—
271	C₄×D₄	—	86	1	no	—
272	#117	—	172	2	no	—
273	#117	—	172	2	no	—
274	C₂×C₄⋊C₄	—	43	1	no	—
275	C₂×C₄⋊C₄	—	86	1	no	—
276	C₂×C₄⋊C₄	—	86	1	no	—
277	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	86	1	no	—
280	C₂×C₂²⋊C₄	—	86	1	no	—
281	C₂×C₂²⋊C₄	—	86	1	no	—
282	C₂×C₂²⋊C₄	—	86	1	no	—
283	C₂×C₂²⋊C₄	—	86	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	43	1	no	—
286	C₂×C₄²	—	43	1	no	—
287	C₂×C₄²	—	43	1	no	—
288	C₂×C₄²	—	43	1	no	—
289	C₂×C₄²	—	43	1	no	—
290	C₂×C₄²	—	43	1	no	—
291	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	86	4	no	—
295	C₄⋊C₈	—	86	1	no	—
296	C₄⋊C₈	—	86	1	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	86	1	no	—
300	C₄×C₈	—	86	1	no	—
301	#95	—	2	1	no	—
302	#95	—	86	1	no	—
303	#95	—	86	1	no	—
304	C₂⁴	—	86	1	no	—
305	C₂×D₄	—	43	2	no	—
306	C₂×D₄	—	86	1	no	—
307	C₂×D₄	—	86	1	no	—
308	C₂×D₄	—	86	1	no	—
309	C₂×D₄	—	86	1	no	—
310	C₂×D₄	—	86	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	43	1	no	—
314	C₂²×C₄	—	43	1	no	—
315	C₂²×C₄	—	43	1	no	—
316	C₂²×C₄	—	43	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	—	86	2	no	—
319	C₂²×C₄	—	86	2	no	—
320	C₂²×C₄	—	172	1	no	—
321	C₂²×C₄	—	172	1	no	—
322	C₂²×C₄	—	172	1	no	—
323	C₂²×C₄	—	172	1	no	—
324	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
325	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
326	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	86	2	no	—
334	C₂×C₈	—	172	1	no	—
335	C₂×C₈	—	172	1	no	—
336	C₂×C₈	—	172	1	no	—
337	C₂×C₈	—	172	1	no	—
338	C₂×C₈	—	172	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	43	2	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	172	2	no	—
346	C₄⋊C₄	—	172	2	no	—
347	C₂²⋊C₄	—	86	2	no	—
348	C₂²⋊C₄	—	86	2	no	—
349	C₂²⋊C₄	—	172	2	no	—
350	C₂²⋊C₄	—	172	2	no	—
351	C₂²⋊C₄	—	172	2	no	—
352	C₂²⋊C₄	—	172	2	no	—
353	C₄²	—	4	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	86	2	no	—
356	C₄²	—	86	1	no	—
357	C₄²	—	86	1	no	—
358	C₄²	—	86	1	no	—
359	C₄²	—	86	1	no	—
360	C₄²	—	86	1	no	—
361	C₄²	—	86	1	no	—
362	C₄²	—	86	1	no	—
363	C₄²	—	86	1	no	—
364	C₄²	—	172	1	no	—
365	C₄²	#10621898	1	1	yes	characteristic
366	C₄²	#10621898	1	1	yes	characteristic
367	C₄²	D₄×D₄₃	1	1	yes	characteristic
368	C₄²	Q₈×D₄₃	1	1	yes	characteristic
369	C₂³	—	86	2	no	—
370	C₂³	—	172	1	no	—
371	C₂³	—	172	1	no	—
372	C₂³	—	172	1	no	—
373	C₂³	—	172	1	no	—
374	C₂³	—	172	1	no	—
375	C₂³	—	172	1	no	—
376	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
377	D₄	—	86	2	no	—
378	D₄	—	86	2	no	—
379	D₄	—	172	1	no	—
380	D₄	—	172	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	43	2	no	—
390	C₂×C₄	—	86	1	no	—
391	C₂×C₄	—	86	1	no	—
392	C₂×C₄	—	86	1	no	—
393	C₂×C₄	—	86	1	no	—
394	C₂×C₄	—	86	1	no	—
395	C₂×C₄	—	86	1	no	—
396	C₂×C₄	—	86	1	no	—
397	C₂×C₄	—	86	1	no	—
398	C₂×C₄	—	86	1	no	—
399	C₂×C₄	—	86	1	no	—
400	C₂×C₄	—	86	1	no	—
401	C₂×C₄	—	86	2	no	—
402	C₂×C₄	—	172	1	no	—
403	C₂×C₄	—	172	1	no	—
404	C₂×C₄	—	172	2	no	—
405	C₂×C₄	—	172	2	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
409	C₂×C₄	#13063282	1	1	yes	characteristic
410	C₂×C₄	#13063298	1	1	yes	characteristic
411	C₂×C₄	#13063298	1	1	yes	characteristic
412	C₂×C₄	#13063303	1	1	yes	characteristic
413	C₂×C₄	#13063303	1	1	yes	characteristic
414	C₂×C₄	#13063331	1	1	yes	characteristic
415	C₂×C₄	#13063331	1	1	yes	characteristic
416	C₂×C₄	#13063333	1	1	yes	characteristic
417	C₂×C₄	#13063333	1	1	yes	characteristic
418	C₂×C₄	#13063346	1	1	yes	characteristic
419	C₂×C₄	#13063348	1	1	yes	characteristic
420	C₂×C₄	#13063349	1	1	yes	characteristic
421	C₂×C₄	#13063352	1	1	yes	characteristic
422	C₈	—	4	2	no	—
423	C₈	—	8	1	no	—
424	C₈	—	344	1	no	—
425	C₈	—	172	2	no	—
426	C₂²	—	344	1	no	—
427	C₂²	—	344	1	no	—
428	C₂²	—	344	1	no	—
429	C₂²	—	344	1	no	—
430	C₂²	—	172	2	no	—
431	C₂²	—	172	2	no	—
432	C₂²	—	172	2	no	—
433	C₂²	#14582758	1	1	yes	characteristic
434	C₂²	#14582864	1	1	yes	characteristic
435	C₂²	#14582864	1	1	yes	characteristic
436	C₂²	#14582894	1	1	yes	characteristic
437	C₂²	#14582902	1	1	yes	characteristic
438	C₂²	#104×D₄₃	1	1	yes	characteristic
439	C₂²	#14582914	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	86	2	no	—
445	C₄	—	172	1	no	—
446	C₄	—	172	1	no	—
447	C₄	—	172	1	no	—
448	C₄	—	172	2	no	—
449	C₄	#14582924	1	1	yes	characteristic
450	C₄	#14582924	1	1	yes	characteristic
451	C₄	#14582958	1	1	yes	characteristic
452	C₄	#14582961	1	1	yes	characteristic
453	C₄	#14583113	1	1	yes	characteristic
454	C₄	#14583117	1	1	yes	characteristic
455	C₄	#14583198	1	1	yes	characteristic
456	C₄	#14583202	1	1	yes	characteristic
457	C₂	—	344	2	no	—
458	C₂	#19133002	1	1	yes	characteristic
459	C₂	#19133010	1	1	yes	characteristic
460	C₂	#19133054	1	1	yes	characteristic
461	C₂	#19133062	1	1	yes	characteristic
462	C₂	#19134578	1	1	yes	characteristic
463	C₂	#19134604	1	1	yes	characteristic
464	C₂	#19134614	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#8569
LCS	G ▷ C₂²×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
2. #19134711	C₂	semidirect
3. C₄×Dic₄₃⋊C₈	C₂	semidirect
6. #19132436	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
231. #1279	D₄₃	semidirect
261. C₄₃	#8569	semidirect

Maximal subgroups

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

subgroup	index
#19137056	2
#19134711	2
C₄×Dic₄₃⋊C₈	2
C₂×#14582628	2
C₂×#14582626	2
#19132436	2
C₄₃×#1279	2
#8569	43