Subgroups — #25115429

Order 11008.

750 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583023	C₂	1	1	yes	maximal, characteristic
2	#19137554	C₂	1	1	yes	maximal, characteristic
3	#19137550	C₂	1	1	yes	maximal, characteristic
4	#19135366	C₂	1	2	yes	maximal
5	#19135360	C₂	1	2	yes	maximal
6	#19135354	C₂	1	1	yes	maximal, characteristic
7	#19134758	C₂	1	2	yes	maximal
8	#19134751	C₂	1	1	yes	maximal, characteristic
9	C₄×#13063256	C₂	1	1	yes	maximal, characteristic
10	#19134483	C₂	1	2	yes	maximal
11	C₄₃×#1947	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	#14583023	C₄	1	8	yes	complemented
14	C₂×#13063259	C₂²	1	2	yes	—
15	C₂×#13063256	C₂²	1	2	yes	—
16	C₂×#13063256	C₂²	1	1	yes	characteristic
17	C₂×#13063256	C₂²	1	2	yes	—
18	C₂×#13063256	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
22	#14582805	—	2	1	no	—
23	#14582804	—	2	1	no	—
24	#14582786	—	2	2	no	—
25	#14582780	—	2	2	no	—
26	#14582769	C₂²	1	1	yes	characteristic
27	#14582764	C₂²	1	2	yes	—
28	#14582764	C₂²	1	2	yes	—
29	C₄⋊C₄×Dic₄₃	—	2	1	no	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
32	C₄×C₄⋊Dic₄₃	—	2	1	no	—
33	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
34	#14582662	C₂²	1	2	yes	—
35	#14582661	C₂²	1	1	yes	characteristic
36	#14582661	C₂²	1	1	yes	characteristic
37	C₂×#107×C₄₃	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
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	D₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
53	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
54	C₂×C₄×Dic₄₃	—	2	1	no	—
55	C₂×C₄×Dic₄₃	—	2	2	no	—
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
58	#13063259	—	4	2	no	—
59	#13063256	—	2	4	no	—
60	#13063256	—	2	2	no	—
61	#13063256	—	4	2	no	—
62	#13063256	Q₈	1	4	yes	complemented
63	Dic₄₃⋊C₈	C₂×C₄	1	8	yes	—
64	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
65	C₈×Dic₄₃	C₂×C₄	1	8	yes	—
66	C₄₃⋊#95	—	2	1	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	4	2	no	—
82	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
83	#95×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
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	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
94	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
95	C₂×Dic₈₆	—	2	2	no	—
96	C₂×Dic₈₆	—	2	2	no	—
97	C₂×Dic₈₆	C₄⋊C₄	1	4	yes	—
98	C₂×C₈×C₄₃	—	2	2	no	—
99	C₂×C₈×C₄₃	—	2	2	no	—
100	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
101	C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₄⋊C₄×C₄₃	—	2	2	no	—
103	C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₄⋊C₄×C₄₃	—	2	2	no	—
106	C₄⋊C₄×C₄₃	—	4	2	no	—
107	C₄⋊C₄×C₄₃	—	8	1	no	—
108	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
109	C₄²×C₄₃	—	4	2	no	—
110	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
111	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
112	C₄⋊Dic₄₃	—	2	1	no	—
113	C₄⋊Dic₄₃	—	2	1	no	—
114	C₄⋊Dic₄₃	—	2	2	no	—
115	C₄⋊Dic₄₃	—	2	2	no	—
116	C₄⋊Dic₄₃	—	2	1	no	—
117	C₄⋊Dic₄₃	—	4	2	no	—
118	C₄⋊Dic₄₃	—	8	1	no	—
119	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
120	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
121	Dic₄₃⋊C₄	C₄⋊C₄	1	8	yes	—
122	C₄×Dic₄₃	—	4	2	no	—
123	C₄×Dic₄₃	—	8	2	no	—
124	C₄×Dic₄₃	—	8	2	no	—
125	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
126	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
127	C₂×C₄₃⋊C₈	—	2	1	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
132	C₂×C₄₃⋊C₈	#41	1	2	yes	—
133	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
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	2	no	—
141	C₂×C₄×C₄₃	—	4	1	no	—
142	C₂×C₄×C₄₃	—	4	2	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	1	no	—
145	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₃	#135	1	2	yes	—
148	C₂×C₄×C₄₃	#135	1	2	yes	—
149	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₄₃	—	2	2	no	—
156	C₂×Dic₄₃	—	2	2	no	—
157	C₂×Dic₄₃	—	2	2	no	—
158	C₂×Dic₄₃	—	2	2	no	—
159	C₂×Dic₄₃	—	2	2	no	—
160	C₂×Dic₄₃	—	4	1	no	—
161	C₂×Dic₄₃	—	4	1	no	—
162	C₂×Dic₄₃	—	4	2	no	—
163	C₂×Dic₄₃	—	4	1	no	—
164	C₂×Dic₄₃	—	4	1	no	—
165	C₂×Dic₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	4	2	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
169	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
170	Dic₈₆	—	2	8	no	—
171	C₈×C₄₃	—	2	4	no	—
172	C₄₃⋊C₈	—	2	2	no	—
173	C₄₃⋊C₈	C₄×Q₈	1	4	yes	—
174	#22725	—	43	1	no	maximal, Sylow
175	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
177	C₂²×C₄₃	#550	1	1	yes	characteristic
178	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
179	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
180	C₂²×C₄₃	#577	1	1	yes	characteristic
181	C₂²×C₄₃	#577	1	1	yes	characteristic
182	C₄×C₄₃	—	2	2	no	—
183	C₄×C₄₃	—	4	2	no	—
184	C₄×C₄₃	—	8	1	no	—
185	C₄×C₄₃	—	8	2	no	—
186	C₄×C₄₃	#427	1	4	yes	—
187	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
188	C₄×C₄₃	#520	1	1	yes	characteristic
189	C₄×C₄₃	#557	1	1	yes	characteristic
190	C₄×C₄₃	Q₈²	1	1	yes	characteristic
191	Dic₄₃	—	2	4	no	—
192	Dic₄₃	—	2	4	no	—
193	Dic₄₃	—	4	2	no	—
194	Dic₄₃	—	8	1	no	—
195	Dic₄₃	—	8	2	no	—
196	C₂×C₈×Q₈	—	43	1	no	—
197	#2355	—	43	1	no	—
198	#2355	—	43	1	no	—
199	#1949	—	43	2	no	—
200	#1949	—	43	2	no	—
201	#1947	—	43	1	no	—
202	#1947	D₄₃	1	1	yes	characteristic
203	#1846	—	43	2	no	—
204	#1844	—	43	1	no	—
205	C₄×#106	—	43	1	no	—
206	C₄×#106	—	43	2	no	—
207	C₂×C₄₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄₃	C₂×#427	1	1	yes	characteristic
209	C₂×C₄₃	#2912	1	1	yes	characteristic
210	C₂×C₄₃	#3381	1	1	yes	characteristic
211	C₂×C₄₃	#3381	1	1	yes	characteristic
212	C₂×C₄₃	#3394	1	1	yes	characteristic
213	C₂×C₄₃	#3394	1	1	yes	characteristic
214	C₂×C₄×Q₈	—	43	1	no	—
215	C₈×Q₈	—	43	8	no	—
216	C₂×#107	—	43	2	no	—
217	C₂×#107	C₂×D₄₃	1	2	yes	—
218	C₂×#106	—	43	1	no	—
219	C₂×#106	—	43	2	no	—
220	C₂×#106	—	43	1	no	—
221	C₂×#106	—	43	2	no	—
222	C₂×C₄⋊C₈	—	43	2	no	—
223	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
224	C₂×C₄×C₈	—	43	2	no	—
225	C₂×C₄×C₈	—	43	1	no	—
226	#391	—	86	1	no	—
227	#391	—	86	1	no	—
228	#387	—	86	2	no	—
229	#387	—	86	2	no	—
230	#384	—	43	1	no	—
231	#384	C₂×D₄₃	1	1	yes	characteristic
232	#382	—	43	2	no	—
233	#382	—	43	2	no	—
234	C₄×C₄⋊C₄	—	43	2	no	—
235	C₄×C₄⋊C₄	—	43	2	no	—
236	C₄×C₄⋊C₄	—	43	1	no	—
237	C₄×C₄⋊C₄	—	86	1	no	—
238	C₄×C₄⋊C₄	—	86	1	no	—
239	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
240	#340	—	43	2	no	—
241	#340	—	43	1	no	—
242	#340	—	43	1	no	—
243	#340	C₂×D₄₃	1	2	yes	—
244	C₄₃	#22725	1	1	yes	characteristic, complemented, Sylow
245	C₂²×Q₈	—	43	1	no	—
246	C₂²×C₈	—	43	1	no	—
247	C₂²×C₈	—	43	1	no	—
248	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
249	C₄×Q₈	—	43	4	no	—
250	C₄×Q₈	—	43	4	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	43	2	no	—
254	C₂×C₄⋊C₄	—	43	1	no	—
255	C₂×C₄⋊C₄	—	43	1	no	—
256	C₂×C₄⋊C₄	—	43	1	no	—
257	C₂×C₄⋊C₄	—	43	2	no	—
258	C₂×C₄⋊C₄	—	86	1	no	—
259	C₂×C₄⋊C₄	—	86	1	no	—
260	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	—	43	2	no	—
265	C₂×C₄²	—	86	2	no	—
266	C₂×C₄²	—	86	2	no	—
267	C₂×C₄²	—	86	1	no	—
268	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
269	#107	—	4	2	no	—
270	#107	—	172	2	no	—
271	#106	—	43	4	no	—
272	#106	—	86	4	no	—
273	#106	—	86	2	no	—
274	#106	—	172	2	no	—
275	C₄⋊C₈	—	43	8	no	—
276	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
277	C₄×C₈	—	43	8	no	—
278	C₄×C₈	—	43	4	no	—
279	#95	—	2	1	no	—
280	#95	—	86	2	no	—
281	#95	—	86	2	no	—
282	#95	—	86	2	no	—
283	#95	—	86	2	no	—
284	#95	—	86	2	no	—
285	#95	—	86	2	no	—
286	#95	—	86	1	no	—
287	C₂×Q₈	—	43	4	no	—
288	C₂×Q₈	—	86	2	no	—
289	C₂×Q₈	—	86	2	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	43	2	no	—
294	C₂²×C₄	—	43	2	no	—
295	C₂²×C₄	—	86	1	no	—
296	C₂²×C₄	—	86	1	no	—
297	C₂²×C₄	—	86	2	no	—
298	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
299	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
300	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	43	2	no	—
304	C₂×C₈	—	43	2	no	—
305	C₂×C₈	—	43	2	no	—
306	C₂×C₈	—	43	2	no	—
307	C₂×C₈	—	86	1	no	—
308	C₂×C₈	—	86	1	no	—
309	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	8	1	no	—
317	C₄⋊C₄	—	43	8	no	—
318	C₄⋊C₄	—	43	4	no	—
319	C₄⋊C₄	—	43	2	no	—
320	C₄⋊C₄	—	86	1	no	—
321	C₄⋊C₄	—	86	1	no	—
322	C₄⋊C₄	—	86	2	no	—
323	C₄⋊C₄	—	86	2	no	—
324	C₄⋊C₄	—	86	1	no	—
325	C₄⋊C₄	—	344	1	no	—
326	C₄⋊C₄	—	172	2	no	—
327	C₄⋊C₄	Q₈×D₄₃	1	2	yes	—
328	C₄²	—	4	2	no	—
329	C₄²	—	43	4	no	—
330	C₄²	—	43	4	no	—
331	C₄²	—	344	2	no	—
332	C₄²	—	344	2	no	—
333	C₄²	—	172	2	no	—
334	C₄²	C₂×C₄×D₄₃	1	2	yes	—
335	C₄²	Q₈×D₄₃	1	2	yes	—
336	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
337	Q₈	—	86	8	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	43	4	no	—
350	C₂×C₄	—	43	4	no	—
351	C₂×C₄	—	86	2	no	—
352	C₂×C₄	—	86	2	no	—
353	C₂×C₄	—	86	2	no	—
354	C₂×C₄	—	86	2	no	—
355	C₂×C₄	—	86	2	no	—
356	C₂×C₄	—	172	2	no	—
357	C₂×C₄	—	172	1	no	—
358	C₂×C₄	—	172	1	no	—
359	C₂×C₄	—	172	2	no	—
360	C₂×C₄	—	172	2	no	—
361	C₂×C₄	—	172	1	no	—
362	C₂×C₄	—	172	1	no	—
363	C₂×C₄	—	172	1	no	—
364	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
365	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
366	C₂×C₄	#13063344	1	2	yes	—
367	C₂×C₄	#13063348	1	2	yes	—
368	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
370	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
371	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
372	C₂×C₄	#13063370	1	1	yes	characteristic
373	C₂×C₄	#13063372	1	1	yes	characteristic
374	C₈	—	2	4	no	—
375	C₈	—	43	4	no	—
376	C₈	—	86	2	no	—
377	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
378	C₂²	#14583562	1	1	yes	characteristic
379	C₂²	#14583567	1	1	yes	characteristic
380	C₂²	C₂×#13063344	1	1	yes	characteristic
381	C₂²	C₂×#13063348	1	1	yes	characteristic
382	C₂²	#14583708	1	1	yes	characteristic
383	C₂²	#14583709	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	2	no	—
388	C₄	—	86	4	no	—
389	C₄	—	86	4	no	—
390	C₄	—	344	1	no	—
391	C₄	—	344	2	no	—
392	C₄	—	172	2	no	—
393	C₄	#14582936	1	4	yes	—
394	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
395	C₄	#14583378	1	1	yes	characteristic
396	C₄	#14583626	1	1	yes	characteristic
397	C₄	#14583629	1	1	yes	characteristic
398	C₂	#19137509	1	1	yes	characteristic
399	C₂	C₂×#14582936	1	1	yes	characteristic
400	C₂	#19143189	1	1	yes	characteristic
401	C₂	#19147469	1	1	yes	characteristic
402	C₂	#19147474	1	1	yes	characteristic
403	C₂	#19147590	1	1	yes	characteristic
404	C₂	#19147595	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1947	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1947	D₄₃
hypocenter	C₄₃	#22725
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1947

Complements

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

N	H ≅ G/N	type
13. #14583023	C₄	semidirect
62. #13063256	Q₈	semidirect
244. C₄₃	#22725	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583023	2
#19137554	2
#19137550	2
#19135366	2
#19135360	2
#19135354	2
#19134758	2
#19134751	2
C₄×#13063256	2
#19134483	2
C₄₃×#1947	2
#22725	43