Subgroups — #25155576

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 418 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	#19136139	C₂	1	2	yes	maximal
3	#19135973	C₂	1	2	yes	maximal
4	#19135358	C₂	1	1	yes	maximal, characteristic
5	#19135356	C₂	1	2	yes	maximal
6	#19135314	C₂	1	1	yes	maximal, characteristic
7	#19135170	C₂	1	2	yes	maximal
8	#19134751	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×#13063256	C₂²	1	2	yes	—
14	C₂×#13063256	C₂²	1	2	yes	—
15	C₂×#13063256	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×#13063248	C₂²	1	1	yes	characteristic
19	C₂×#13063248	C₂²	1	1	yes	characteristic
20	C₂×#13063248	C₂²	1	2	yes	—
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	#14582805	C₂²	1	2	yes	—
23	#14582786	—	2	2	no	—
24	#14582769	C₂²	1	1	yes	characteristic
25	#14582764	—	2	1	no	—
26	C₄⋊C₄×Dic₄₃	—	2	1	no	—
27	C₄×C₄⋊Dic₄₃	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	—	2	1	no	—
34	C₄₃×#398	—	2	2	no	—
35	C₄₃×#389	—	2	1	no	—
36	C₄₃×#389	C₂²	1	2	yes	—
37	C₄₃×#384	C₂²	1	1	yes	characteristic
38	C₄₃×#384	C₂²	1	2	yes	—
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	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
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	#13063256	—	2	4	no	—
55	#13063256	—	4	2	no	—
56	#13063256	—	4	2	no	—
57	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
59	#13063248	—	2	2	no	—
60	#13063248	—	2	2	no	—
61	#13063248	—	4	2	no	—
62	C₄×C₄₃⋊C₈	—	2	2	no	—
63	C₄₃⋊#95	—	2	2	no	—
64	C₄₃⋊#95	—	2	2	no	—
65	C₄₃⋊#95	—	2	2	no	—
66	#125×C₄₃	—	4	4	no	—
67	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₃	—	2	1	no	—
78	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	#95×C₄₃	—	2	1	no	—
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	D₄	1	2	yes	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
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	2	yes	—
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₃	—	2	1	no	—
92	C₂²×Dic₄₃	—	2	1	no	—
93	C₂²×Dic₄₃	—	2	2	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	—	2	1	no	—
99	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	2	1	no	—
107	C₄⋊C₄×C₄₃	—	4	4	no	—
108	C₄⋊C₄×C₄₃	—	4	4	no	—
109	C₄⋊C₄×C₄₃	—	4	2	no	—
110	C₄⋊C₄×C₄₃	—	8	1	no	—
111	C₄⋊C₄×C₄₃	—	8	2	no	—
112	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
113	C₄²×C₄₃	—	2	2	no	—
114	C₄²×C₄₃	—	2	2	no	—
115	C₄²×C₄₃	—	4	2	no	—
116	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
117	C₄²×C₄₃	#41	1	2	yes	—
118	C₄⋊Dic₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	C₄⋊Dic₄₃	—	4	2	no	—
122	C₄⋊Dic₄₃	—	8	1	no	—
123	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
124	Dic₄₃⋊C₄	—	2	4	no	—
125	C₄×Dic₄₃	—	2	4	no	—
126	C₄×Dic₄₃	—	8	2	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	1	no	—
131	C₂×C₄₃⋊C₈	—	2	2	no	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	—	2	2	no	—
134	C₂×C₄₃⋊C₈	#41	1	2	yes	—
135	C₂×C₄₃⋊C₈	#41	1	2	yes	—
136	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	—	2	2	no	—
138	C₂×C₄×C₄₃	—	2	2	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	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	—	4	1	no	—
145	C₂×C₄×C₄₃	—	4	1	no	—
146	C₂×C₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
156	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
157	C₂×C₄×C₄₃	#137	1	2	yes	—
158	C₂×C₄×C₄₃	C₂²×Q₈	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	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	2	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	C₂×Dic₄₃	—	4	2	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	—	4	2	no	—
173	Dic₈₆	—	2	2	no	—
174	Dic₈₆	—	2	2	no	—
175	Dic₈₆	—	4	1	no	—
176	Dic₈₆	—	4	1	no	—
177	C₄₃⋊C₈	—	2	2	no	—
178	C₄₃⋊C₈	—	2	2	no	—
179	C₄₃⋊C₈	—	4	2	no	—
180	#26088	—	43	1	no	maximal, Sylow
181	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²×C₄₃	#547	1	1	yes	characteristic
183	C₂²×C₄₃	#550	1	1	yes	characteristic
184	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
185	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
186	C₂²×C₄₃	#577	1	1	yes	characteristic
187	C₂²×C₄₃	#577	1	1	yes	characteristic
188	C₄×C₄₃	—	2	4	no	—
189	C₄×C₄₃	—	2	2	no	—
190	C₄×C₄₃	—	4	2	no	—
191	C₄×C₄₃	—	8	1	no	—
192	C₄×C₄₃	—	8	1	no	—
193	C₄×C₄₃	—	8	2	no	—
194	C₄×C₄₃	#475	1	4	yes	—
195	C₄×C₄₃	#533	1	1	yes	characteristic
196	C₄×C₄₃	#544	1	1	yes	characteristic
197	C₄×C₄₃	#552	1	1	yes	characteristic
198	C₄×C₄₃	#553	1	1	yes	characteristic
199	Dic₄₃	—	4	2	no	—
200	Dic₄₃	—	4	2	no	—
201	Dic₄₃	—	8	2	no	—
202	#2552	D₄₃	1	1	yes	characteristic
203	#2355	—	43	1	no	—
204	#2096	—	43	2	no	—
205	#2066	—	43	2	no	—
206	#1948	—	43	2	no	—
207	#1948	—	43	1	no	—
208	#1939	—	43	1	no	—
209	#1919	—	43	2	no	—
210	#1844	—	43	1	no	—
211	#1803	—	43	1	no	—
212	C₄×#103	—	43	1	no	—
213	C₂×C₄₃	#2441	1	1	yes	characteristic
214	C₂×C₄₃	C₂×#475	1	1	yes	characteristic
215	C₂×C₄₃	#3084	1	1	yes	characteristic
216	C₂×C₄₃	#3335	1	1	yes	characteristic
217	C₂×C₄₃	#3356	1	1	yes	characteristic
218	C₂×C₄₃	#3392	1	1	yes	characteristic
219	C₂×C₄₃	#3400	1	1	yes	characteristic
220	C₂×#125	—	2	1	no	—
221	C₂×C₄×Q₈	—	43	1	no	—
222	C₂×#106	—	43	2	no	—
223	C₂×#106	—	43	2	no	—
224	C₂×#106	—	43	2	no	—
225	C₂×C₄⋊C₈	—	43	1	no	—
226	C₂×C₄⋊C₈	—	43	2	no	—
227	C₂×#103	—	43	1	no	—
228	C₂×#103	—	43	1	no	—
229	C₂×#103	—	43	2	no	—
230	C₂×C₄×C₈	—	43	1	no	—
231	#398	—	2	2	no	—
232	#391	—	43	2	no	—
233	#389	—	2	1	no	—
234	#389	C₂×D₄₃	1	2	yes	—
235	#387	—	86	2	no	—
236	#384	—	43	1	no	—
237	#384	C₂×D₄₃	1	1	yes	characteristic
238	#384	C₂×D₄₃	1	2	yes	—
239	#382	—	86	1	no	—
240	C₄×C₄⋊C₄	—	43	2	no	—
241	C₄×C₄⋊C₄	—	86	1	no	—
242	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
243	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
244	#340	—	43	2	no	—
245	#340	—	43	2	no	—
246	#340	—	43	1	no	—
247	#340	—	43	1	no	—
248	#336	—	43	2	no	—
249	C₄₃	#26088	1	1	yes	characteristic, complemented, Sylow
250	C₂²×Q₈	—	43	1	no	—
251	C₂²×C₈	—	43	1	no	—
252	C₂²×C₈	—	43	1	no	—
253	C₂²×C₈	—	43	2	no	—
254	#125	—	4	4	no	—
255	C₄×Q₈	—	43	4	no	—
256	C₄×Q₈	—	86	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	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	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
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	#106	—	86	4	no	—
278	#106	—	172	2	no	—
279	#106	—	172	2	no	—
280	C₄⋊C₈	—	86	4	no	—
281	C₄⋊C₈	—	86	2	no	—
282	#103	—	86	2	no	—
283	#103	—	86	2	no	—
284	#103	—	172	2	no	—
285	C₄×C₈	—	86	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	2	no	—
288	#95	—	86	2	no	—
289	#95	—	86	2	no	—
290	#95	—	86	2	no	—
291	#95	C₂²⋊D₄₃	1	2	yes	—
292	C₂×Q₈	—	43	2	no	—
293	C₂×Q₈	—	86	1	no	—
294	C₂×Q₈	—	86	1	no	—
295	C₂×Q₈	—	86	1	no	—
296	C₂×Q₈	—	86	1	no	—
297	C₂×Q₈	—	86	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	86	1	no	—
302	C₂²×C₄	—	86	1	no	—
303	C₂²×C₄	—	86	2	no	—
304	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
305	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
307	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
308	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
309	C₂×C₈	—	43	2	no	—
310	C₂×C₈	—	43	2	no	—
311	C₂×C₈	—	86	1	no	—
312	C₂×C₈	—	86	1	no	—
313	C₂×C₈	—	86	1	no	—
314	C₂×C₈	—	86	1	no	—
315	C₂×C₈	—	86	2	no	—
316	C₂×C₈	—	86	2	no	—
317	C₂×C₈	—	86	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	8	1	no	—
329	C₄⋊C₄	—	8	2	no	—
330	C₄⋊C₄	—	43	2	no	—
331	C₄⋊C₄	—	86	4	no	—
332	C₄⋊C₄	—	86	1	no	—
333	C₄⋊C₄	—	86	2	no	—
334	C₄⋊C₄	—	86	2	no	—
335	C₄⋊C₄	—	344	1	no	—
336	C₄⋊C₄	—	172	2	no	—
337	C₄⋊C₄	#10621883	1	4	yes	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	86	4	no	—
342	C₄²	—	344	2	no	—
343	C₄²	Q₈×D₄₃	1	2	yes	—
344	C₄²	#10621902	1	2	yes	—
345	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
346	Q₈	—	86	2	no	—
347	Q₈	—	86	2	no	—
348	Q₈	—	172	1	no	—
349	Q₈	—	172	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	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	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	86	2	no	—
367	C₂×C₄	—	86	2	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	—	172	2	no	—
371	C₂×C₄	—	172	1	no	—
372	C₂×C₄	—	172	1	no	—
373	C₂×C₄	—	172	1	no	—
374	C₂×C₄	—	172	1	no	—
375	C₂×C₄	#13063301	1	2	yes	—
376	C₂×C₄	#13063301	1	2	yes	—
377	C₂×C₄	C₂×#10621883	1	4	yes	—
378	C₂×C₄	C₂×#10621883	1	2	yes	—
379	C₂×C₄	#13063356	1	2	yes	—
380	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
381	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
382	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
383	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
384	C₂×C₄	#13063371	1	1	yes	characteristic
385	C₂×C₄	#13063372	1	1	yes	characteristic
386	C₈	—	86	2	no	—
387	C₈	—	86	2	no	—
388	C₈	—	172	2	no	—
389	C₂²	C₂×#13063301	1	1	yes	characteristic
390	C₂²	#14583548	1	1	yes	characteristic
391	C₂²	#14583568	1	1	yes	characteristic
392	C₂²	C₂²×#10621883	1	1	yes	characteristic
393	C₂²	C₂×#13063356	1	1	yes	characteristic
394	C₂²	#14583707	1	1	yes	characteristic
395	C₂²	#14583710	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	4	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	1	no	—
402	C₄	—	344	2	no	—
403	C₄	—	172	2	no	—
404	C₄	—	172	2	no	—
405	C₄	#14583181	1	4	yes	—
406	C₄	#14583455	1	1	yes	characteristic
407	C₄	#14583529	1	1	yes	characteristic
408	C₄	#14583587	1	1	yes	characteristic
409	C₄	#14583602	1	1	yes	characteristic
410	C₂	#19138304	1	1	yes	characteristic
411	C₂	C₂×#14583181	1	1	yes	characteristic
412	C₂	#19144453	1	1	yes	characteristic
413	C₂	#19146952	1	1	yes	characteristic
414	C₂	#19147210	1	1	yes	characteristic
415	C₂	#19147576	1	1	yes	characteristic
416	C₂	#19147644	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	#26088
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
249. C₄₃	#26088	semidirect

Maximal subgroups

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

subgroup	index
#19137550	2
#19136139	2
#19135973	2
#19135358	2
#19135356	2
#19135314	2
#19135170	2
#19134751	2
#19134597	2
C₄×#13063248	2
C₄₃×#2552	2
#26088	43