Subgroups — #25154709

Order 11008.

658 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	#19137550	C₂	1	1	yes	maximal, characteristic
2	#19135987	C₂	1	2	yes	maximal
3	#19135743	C₂	1	2	yes	maximal
4	#19135553	C₂	1	2	yes	maximal
5	#19135353	C₂	1	1	yes	maximal, characteristic
6	#19135314	C₂	1	1	yes	maximal, characteristic
7	#19135163	C₂	1	2	yes	maximal
8	#19134722	C₂	1	1	yes	maximal, characteristic
9	#19134597	C₂	1	1	yes	maximal, characteristic
10	C₄×#13063248	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2552	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	C₂×#13063258	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
16	C₂×#13063248	C₂²	1	1	yes	characteristic
17	C₂×#13063248	C₂²	1	1	yes	characteristic
18	C₂×#13063248	C₂²	1	2	yes	—
19	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	#14582805	C₂²	1	2	yes	—
21	#14582786	—	2	2	no	—
22	#14582769	C₂²	1	1	yes	characteristic
23	#14582764	—	2	1	no	—
24	C₄⋊C₄×Dic₄₃	—	2	1	no	—
25	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
26	#14582661	C₂²	1	2	yes	—
27	#14582661	C₂²	1	2	yes	—
28	#14582661	C₂²	1	1	yes	characteristic
29	#14582661	C₂²	1	2	yes	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	1	yes	characteristic
32	#14582654	C₂²	1	2	yes	—
33	C₂×#125×C₄₃	C₂²	1	2	yes	—
34	C₄₃×#398	—	2	2	no	—
35	C₄₃×#389	—	2	1	no	—
36	C₄₃×#389	C₂²	1	2	yes	—
37	C₄₃×#384	—	2	1	no	—
38	C₄₃×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	C₄×Dic₈₆	—	2	2	no	—
46	C₄×Dic₈₆	Q₈	1	4	yes	—
47	C₂×C₄⋊Dic₄₃	—	2	1	no	—
48	C₂×C₄⋊Dic₄₃	—	2	1	no	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
51	C₂×Dic₄₃⋊C₄	—	2	1	no	—
52	C₂×C₄×Dic₄₃	—	2	1	no	—
53	C₂×C₄×Dic₄₃	—	2	2	no	—
54	#13063258	—	2	4	no	—
55	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
57	#13063248	—	2	2	no	—
58	#13063248	—	2	2	no	—
59	#13063248	—	4	2	no	—
60	C₄×C₄₃⋊C₈	—	2	2	no	—
61	C₄₃⋊#95	—	2	2	no	—
62	C₄₃⋊#95	—	2	2	no	—
63	C₄₃⋊#95	—	2	2	no	—
64	#125×C₄₃	—	2	4	no	—
65	#125×C₄₃	—	4	2	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
79	#95×C₄₃	—	2	1	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	D₄	1	2	yes	—
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₃	—	2	1	no	—
91	C₂²×Dic₄₃	—	2	1	no	—
92	C₂²×Dic₄₃	—	2	2	no	—
93	C₂×Dic₈₆	—	2	1	no	—
94	C₂×Dic₈₆	—	2	1	no	—
95	C₂×Dic₈₆	—	2	1	no	—
96	C₂×Dic₈₆	—	2	1	no	—
97	C₂×Dic₈₆	—	2	1	no	—
98	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
99	C₄⋊C₄×C₄₃	—	2	2	no	—
100	C₄⋊C₄×C₄₃	—	2	2	no	—
101	C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₄⋊C₄×C₄₃	—	2	2	no	—
104	C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₄⋊C₄×C₄₃	—	4	4	no	—
106	C₄⋊C₄×C₄₃	—	4	4	no	—
107	C₄⋊C₄×C₄₃	—	4	2	no	—
108	C₄⋊C₄×C₄₃	—	8	1	no	—
109	C₄⋊C₄×C₄₃	—	8	2	no	—
110	C₄⋊C₄×C₄₃	#41	1	2	yes	—
111	C₄⋊C₄×C₄₃	#41	1	2	yes	—
112	C₄²×C₄₃	—	2	2	no	—
113	C₄²×C₄₃	—	2	2	no	—
114	C₄²×C₄₃	—	4	2	no	—
115	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
116	C₄²×C₄₃	#41	1	2	yes	—
117	C₄⋊Dic₄₃	—	2	1	no	—
118	C₄⋊Dic₄₃	—	2	2	no	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	4	2	no	—
121	C₄⋊Dic₄₃	—	8	1	no	—
122	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
123	Dic₄₃⋊C₄	—	2	4	no	—
124	C₄×Dic₄₃	—	2	4	no	—
125	C₄×Dic₄₃	—	8	2	no	—
126	C₂×C₄₃⋊C₈	—	2	1	no	—
127	C₂×C₄₃⋊C₈	—	2	1	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	2	2	no	—
131	C₂×C₄₃⋊C₈	—	2	2	no	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	2	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	2	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	2	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	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₃	#135	1	2	yes	—
156	C₂×C₄×C₄₃	#137	1	2	yes	—
157	C₂×C₄×C₄₃	C₂²×Q₈	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×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×Dic₄₃	—	2	2	no	—
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	4	1	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	Dic₈₆	—	2	2	no	—
173	Dic₈₆	—	2	2	no	—
174	Dic₈₆	—	4	1	no	—
175	Dic₈₆	—	4	1	no	—
176	C₄₃⋊C₈	—	4	1	no	—
177	C₄₃⋊C₈	—	4	2	no	—
178	C₄₃⋊C₈	—	4	1	no	—
179	#26023	—	43	1	no	maximal, Sylow
180	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
181	C₂²×C₄₃	#546	1	1	yes	characteristic
182	C₂²×C₄₃	#548	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
184	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
185	C₂²×C₄₃	#576	1	1	yes	characteristic
186	C₂²×C₄₃	#578	1	1	yes	characteristic
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	4	2	no	—
190	C₄×C₄₃	—	4	2	no	—
191	C₄×C₄₃	—	4	2	no	—
192	C₄×C₄₃	—	8	2	no	—
193	C₄×C₄₃	#479	1	4	yes	—
194	C₄×C₄₃	#533	1	1	yes	characteristic
195	C₄×C₄₃	#544	1	1	yes	characteristic
196	C₄×C₄₃	#555	1	1	yes	characteristic
197	C₄×C₄₃	#556	1	1	yes	characteristic
198	Dic₄₃	—	4	2	no	—
199	Dic₄₃	—	4	2	no	—
200	Dic₄₃	—	8	2	no	—
201	#2552	D₄₃	1	1	yes	characteristic
202	#2355	—	43	1	no	—
203	#2068	—	43	2	no	—
204	#2026	—	43	2	no	—
205	#1989	—	43	2	no	—
206	#1947	—	43	1	no	—
207	#1939	—	43	1	no	—
208	#1918	—	43	2	no	—
209	#1834	—	43	1	no	—
210	#1803	—	43	1	no	—
211	C₄×#103	—	43	1	no	—
212	C₂×C₄₃	#2439	1	1	yes	characteristic
213	C₂×C₄₃	C₂×#479	1	1	yes	characteristic
214	C₂×C₄₃	#3083	1	1	yes	characteristic
215	C₂×C₄₃	#3302	1	1	yes	characteristic
216	C₂×C₄₃	#3333	1	1	yes	characteristic
217	C₂×C₄₃	#3361	1	1	yes	characteristic
218	C₂×C₄₃	#3374	1	1	yes	characteristic
219	C₂×#125	C₂×D₄₃	1	2	yes	—
220	C₂×C₄×Q₈	—	43	1	no	—
221	C₂×#107	—	43	2	no	—
222	C₂×C₄⋊C₈	—	43	1	no	—
223	C₂×C₄⋊C₈	—	43	2	no	—
224	C₂×#103	—	43	1	no	—
225	C₂×#103	—	43	1	no	—
226	C₂×#103	—	43	2	no	—
227	C₂×C₄×C₈	—	43	1	no	—
228	#398	—	2	2	no	—
229	#391	—	43	2	no	—
230	#389	—	2	1	no	—
231	#389	C₂×D₄₃	1	2	yes	—
232	#387	—	86	2	no	—
233	#384	—	2	1	no	—
234	#384	—	43	1	no	—
235	#384	C₂×D₄₃	1	1	yes	characteristic
236	#382	—	86	1	no	—
237	C₄×C₄⋊C₄	—	43	2	no	—
238	C₄×C₄⋊C₄	—	86	1	no	—
239	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
240	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
241	#340	—	43	2	no	—
242	#340	—	43	2	no	—
243	#340	—	43	2	no	—
244	#340	—	43	1	no	—
245	#340	—	43	2	no	—
246	#340	—	43	1	no	—
247	#336	—	43	2	no	—
248	C₄₃	#26023	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	—	43	1	no	—
250	C₂²×C₈	—	43	1	no	—
251	C₂²×C₈	—	43	2	no	—
252	C₂²×C₈	—	43	1	no	—
253	#125	—	2	4	no	—
254	#125	—	4	2	no	—
255	C₄×Q₈	—	43	4	no	—
256	C₄×Q₈	—	86	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	43	1	no	—
263	C₂×C₄⋊C₄	—	43	2	no	—
264	C₂×C₄⋊C₄	—	86	1	no	—
265	C₂×C₄⋊C₄	—	86	1	no	—
266	C₂×C₄⋊C₄	—	86	1	no	—
267	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
270	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	86	1	no	—
274	C₂×C₄²	—	86	2	no	—
275	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
276	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
277	#107	—	86	4	no	—
278	C₄⋊C₈	—	86	2	no	—
279	C₄⋊C₈	—	172	2	no	—
280	#103	—	86	2	no	—
281	#103	—	86	2	no	—
282	#103	—	172	2	no	—
283	C₄×C₈	—	86	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	2	no	—
286	#95	—	86	2	no	—
287	#95	—	86	2	no	—
288	#95	—	86	2	no	—
289	#95	C₂²⋊D₄₃	1	2	yes	—
290	C₂×Q₈	—	43	2	no	—
291	C₂×Q₈	—	86	1	no	—
292	C₂×Q₈	—	86	1	no	—
293	C₂×Q₈	—	86	1	no	—
294	C₂×Q₈	—	86	1	no	—
295	C₂×Q₈	—	86	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	86	1	no	—
300	C₂²×C₄	—	86	1	no	—
301	C₂²×C₄	—	86	2	no	—
302	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
303	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
304	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
306	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
307	C₂×C₈	—	86	1	no	—
308	C₂×C₈	—	86	1	no	—
309	C₂×C₈	—	86	1	no	—
310	C₂×C₈	—	86	1	no	—
311	C₂×C₈	—	86	2	no	—
312	C₂×C₈	—	86	2	no	—
313	C₂×C₈	—	86	2	no	—
314	C₂×C₈	—	86	1	no	—
315	C₂×C₈	—	86	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	4	no	—
323	C₄⋊C₄	—	4	4	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	8	1	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	—	43	2	no	—
328	C₄⋊C₄	—	86	4	no	—
329	C₄⋊C₄	—	86	1	no	—
330	C₄⋊C₄	—	86	2	no	—
331	C₄⋊C₄	—	86	2	no	—
332	C₄⋊C₄	—	344	1	no	—
333	C₄⋊C₄	—	172	2	no	—
334	C₄⋊C₄	#10621900	1	2	yes	—
335	C₄⋊C₄	#10621902	1	2	yes	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	4	2	no	—
339	C₄²	—	86	4	no	—
340	C₄²	—	344	2	no	—
341	C₄²	Q₈×D₄₃	1	2	yes	—
342	C₄²	#10621902	1	2	yes	—
343	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
344	Q₈	—	86	2	no	—
345	Q₈	—	86	2	no	—
346	Q₈	—	172	1	no	—
347	Q₈	—	172	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	86	2	no	—
366	C₂×C₄	—	86	2	no	—
367	C₂×C₄	—	172	2	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	—	172	1	no	—
372	C₂×C₄	—	172	1	no	—
373	C₂×C₄	—	172	1	no	—
374	C₂×C₄	#13063301	1	2	yes	—
375	C₂×C₄	#13063301	1	2	yes	—
376	C₂×C₄	#13063345	1	2	yes	—
377	C₂×C₄	#13063355	1	2	yes	—
378	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
379	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
380	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
381	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
382	C₂×C₄	#13063370	1	1	yes	characteristic
383	C₂×C₄	#13063373	1	1	yes	characteristic
384	C₈	—	172	1	no	—
385	C₈	—	172	2	no	—
386	C₈	—	172	1	no	—
387	C₂²	C₂×#13063301	1	1	yes	characteristic
388	C₂²	#14583543	1	1	yes	characteristic
389	C₂²	#14583560	1	1	yes	characteristic
390	C₂²	C₂×#13063345	1	1	yes	characteristic
391	C₂²	C₂×#13063355	1	1	yes	characteristic
392	C₂²	#14583702	1	1	yes	characteristic
393	C₂²	#14583714	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	344	2	no	—
401	C₄	—	172	2	no	—
402	C₄	—	172	2	no	—
403	C₄	#14583203	1	4	yes	—
404	C₄	#14583454	1	1	yes	characteristic
405	C₄	#14583526	1	1	yes	characteristic
406	C₄	#14583615	1	1	yes	characteristic
407	C₄	#14583623	1	1	yes	characteristic
408	C₂	#19138282	1	1	yes	characteristic
409	C₂	C₂×#14583203	1	1	yes	characteristic
410	C₂	#19144442	1	1	yes	characteristic
411	C₂	#19146512	1	1	yes	characteristic
412	C₂	#19146933	1	1	yes	characteristic
413	C₂	#19147255	1	1	yes	characteristic
414	C₂	#19147398	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2552	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#2552	D₄₃
hypocenter	C₄₃	#26023
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2552

Complements

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

N	H ≅ G/N	type
248. C₄₃	#26023	semidirect

Maximal subgroups

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

subgroup	index
#19137550	2
#19135987	2
#19135743	2
#19135553	2
#19135353	2
#19135314	2
#19135163	2
#19134722	2
#19134597	2
C₄×#13063248	2
C₄₃×#2552	2
#26023	43