Subgroups — #25097178

Order 11008.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137204	C₂	1	2	yes	maximal
2	#19134763	C₂	1	2	yes	maximal, complemented
3	#19134726	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134723	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134628	C₂	1	2	yes	maximal
6	#19134624	C₂	1	1	yes	maximal, characteristic
7	#19134620	C₂	1	1	yes	maximal, characteristic
8	#19134492	C₂	1	2	yes	maximal, complemented
9	C₄×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063259	C₂²	1	2	yes	—
13	C₂×#13063259	C₂²	1	2	yes	—
14	C₂×#13063257	C₂²	1	2	yes	—
15	C₂×#13063257	C₂²	1	2	yes	—
16	#14582792	—	2	2	no	—
17	#14582792	—	2	2	no	—
18	#14582785	—	2	2	no	—
19	#14582785	—	2	2	no	—
20	#14582769	C₂²	1	2	yes	—
21	#14582765	C₂²	1	2	yes	—
22	#14582759	C₂²	1	2	yes	—
23	#14582759	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
25	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
26	#14582662	C₂²	1	1	yes	characteristic
27	#14582662	C₂²	1	1	yes	characteristic
28	#14582662	C₂²	1	2	yes	—
29	#14582662	C₂²	1	1	yes	characteristic
30	#14582662	C₂²	1	1	yes	characteristic
31	#14582662	C₂²	1	2	yes	—
32	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
35	C₄₃×#405	C₄	1	8	yes	complemented
36	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Dic₄₃	—	2	2	no	—
41	C₂×C₄⋊Dic₄₃	—	2	2	no	—
42	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
43	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
44	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
45	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
46	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
47	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
48	C₂×C₄×Dic₄₃	—	2	2	no	—
49	C₂×C₄×Dic₄₃	—	2	2	no	—
50	#13063259	—	2	4	no	—
51	#13063259	—	2	4	no	—
52	#13063257	—	2	4	no	—
53	#13063257	—	2	4	no	—
54	C₄₃⋊#95	—	2	2	no	—
55	C₄₃⋊#95	—	2	2	no	—
56	C₄₃⋊#95	—	2	2	no	—
57	C₄₃⋊#95	—	2	2	no	—
58	C₄₃⋊#95	—	2	2	no	—
59	C₄₃⋊#95	—	2	2	no	—
60	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₄₃	—	2	4	no	—
62	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
63	C₂²×C₈×C₄₃	—	2	4	no	—
64	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
65	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
69	#117×C₄₃	C₂×C₄	1	4	yes	—
70	#117×C₄₃	Q₈	1	4	yes	—
71	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	#97×C₄₃	C₂×C₄	1	4	yes	—
78	#97×C₄₃	C₂×C₄	1	4	yes	—
79	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
80	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
81	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₄₃	—	2	2	no	—
93	C₂²×Dic₄₃	—	2	2	no	—
94	C₂²×Dic₄₃	—	2	2	no	—
95	C₂²×Dic₄₃	—	2	2	no	—
96	M₁₆×C₄₃	—	2	8	no	—
97	C₂×C₈×C₄₃	—	2	2	no	—
98	C₂×C₈×C₄₃	—	2	2	no	—
99	C₂×C₈×C₄₃	—	2	8	no	—
100	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₃	#41	1	4	yes	—
105	C₂×C₈×C₄₃	#41	1	4	yes	—
106	C₄⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
107	C₄⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
108	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
109	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
110	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
111	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
112	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
113	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
114	C₂²⋊Dic₄₃	—	8	2	no	—
115	C₂²⋊Dic₄₃	—	8	2	no	—
116	C₄⋊Dic₄₃	—	2	2	no	—
117	C₄⋊Dic₄₃	—	2	2	no	—
118	C₄⋊Dic₄₃	—	2	2	no	—
119	C₄⋊Dic₄₃	—	2	2	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	C₄⋊Dic₄₃	—	2	2	no	—
122	C₄⋊Dic₄₃	—	2	2	no	—
123	C₄⋊Dic₄₃	—	2	2	no	—
124	C₄⋊Dic₄₃	—	8	2	no	—
125	C₄⋊Dic₄₃	—	8	2	no	—
126	C₄×Dic₄₃	—	8	2	no	—
127	C₄×Dic₄₃	—	8	2	no	—
128	C₂³×C₄₃	—	2	2	no	—
129	C₂³×C₄₃	—	2	1	no	—
130	C₂³×C₄₃	—	2	2	no	—
131	C₂³×C₄₃	—	2	1	no	—
132	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
133	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₃	—	2	2	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
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	4	no	—
144	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₃	C₂×C₄⋊C₄	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	C₂×#41	1	2	yes	—
152	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
153	C₂×Dic₄₃	—	4	2	no	—
154	C₂×Dic₄₃	—	4	2	no	—
155	C₂×Dic₄₃	—	4	2	no	—
156	C₂×Dic₄₃	—	4	2	no	—
157	C₂×Dic₄₃	—	4	2	no	—
158	C₂×Dic₄₃	—	4	2	no	—
159	C₂×Dic₄₃	—	4	2	no	—
160	C₂×Dic₄₃	—	4	2	no	—
161	C₂×Dic₄₃	—	4	2	no	—
162	C₂×Dic₄₃	—	4	2	no	—
163	C₂×Dic₄₃	—	4	2	no	—
164	C₂×Dic₄₃	—	4	2	no	—
165	C₈×C₄₃	—	2	2	no	—
166	C₈×C₄₃	—	2	2	no	—
167	C₈×C₄₃	#117	1	4	yes	—
168	C₈×C₄₃	#117	1	4	yes	—
169	#20822	—	43	1	no	maximal, Sylow
170	C₂²×C₄₃	—	2	2	no	—
171	C₂²×C₄₃	—	2	2	no	—
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	4	2	no	—
174	C₂²×C₄₃	—	4	2	no	—
175	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₃	#532	1	2	yes	—
177	C₂²×C₄₃	#576	1	1	yes	characteristic
178	C₂²×C₄₃	#577	1	2	yes	—
179	C₂²×C₄₃	#578	1	1	yes	characteristic
180	C₄×C₄₃	—	2	2	no	—
181	C₄×C₄₃	—	2	2	no	—
182	C₄×C₄₃	—	2	2	no	—
183	C₄×C₄₃	—	2	2	no	—
184	C₄×C₄₃	—	2	2	no	—
185	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
186	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
187	C₄×C₄₃	#533	1	2	yes	—
188	Dic₄₃	—	8	2	no	—
189	Dic₄₃	—	8	2	no	—
190	Dic₄₃	—	8	2	no	—
191	Dic₄₃	—	8	2	no	—
192	C₂×#405	D₄₃	1	1	yes	characteristic
193	#2314	—	43	2	no	—
194	#1847	—	43	2	no	—
195	#1835	—	43	1	no	—
196	#1834	—	43	1	no	—
197	#1809	—	43	2	no	—
198	#1808	—	43	1	no	—
199	#1807	—	43	1	no	—
200	#1776	—	43	2	no	—
201	C₄×#107	—	43	1	no	—
202	C₄×#106	—	43	1	no	—
203	C₂×C₄₃	—	4	2	no	—
204	C₂×C₄₃	#2285	1	1	yes	characteristic
205	C₂×C₄₃	#2912	1	1	yes	characteristic
206	C₂×C₄₃	#2913	1	1	yes	characteristic
207	C₂×C₄₃	#3178	1	2	yes	—
208	C₂×C₄₃	#3179	1	2	yes	—
209	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
210	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
211	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
212	C₂×#107	—	43	2	no	—
213	C₂×#107	—	43	2	no	—
214	C₂×#106	—	43	2	no	—
215	C₂×#106	—	43	2	no	—
216	#405	Dic₄₃	1	8	yes	complemented
217	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
218	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
221	#388	—	86	2	no	—
222	#388	—	86	2	no	—
223	#387	—	86	2	no	—
224	#387	—	86	2	no	—
225	#384	—	43	2	no	—
226	#382	—	43	2	no	—
227	#380	—	43	2	no	—
228	#380	—	43	2	no	—
229	C₄×C₄⋊C₄	—	43	2	no	—
230	C₄×C₄⋊C₄	—	43	2	no	—
231	#340	—	43	1	no	—
232	#340	—	43	1	no	—
233	#340	—	43	1	no	—
234	#340	—	43	1	no	—
235	#340	—	43	2	no	—
236	#340	—	43	2	no	—
237	C₄₃	#20822	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
239	C₂×M₁₆	—	2	4	no	—
240	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
243	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
244	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
245	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
246	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
247	#117	Dic₈₆	1	4	yes	—
248	#117	C₂×Dic₄₃	1	4	yes	—
249	C₂×C₄⋊C₄	—	43	2	no	—
250	C₂×C₄⋊C₄	—	43	2	no	—
251	C₂×C₄⋊C₄	—	43	2	no	—
252	C₂×C₄⋊C₄	—	43	2	no	—
253	C₂×C₄⋊C₄	—	86	2	no	—
254	C₂×C₄⋊C₄	—	86	2	no	—
255	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
256	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	86	2	no	—
258	C₂×C₂²⋊C₄	—	86	2	no	—
259	C₂×C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
261	C₂×C₄²	—	86	2	no	—
262	C₂×C₄²	—	86	2	no	—
263	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
265	#107	—	86	4	no	—
266	#107	—	86	4	no	—
267	#106	—	86	4	no	—
268	#106	—	86	4	no	—
269	#97	C₂×Dic₄₃	1	4	yes	—
270	#97	C₂×Dic₄₃	1	4	yes	—
271	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
272	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
273	#95	—	86	2	no	—
274	#95	—	86	2	no	—
275	#95	—	86	2	no	—
276	#95	—	86	2	no	—
277	#95	—	86	2	no	—
278	#95	—	86	2	no	—
279	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	86	2	no	—
283	C₂²×C₄	—	86	2	no	—
284	C₂²×C₄	—	86	2	no	—
285	C₂²×C₄	—	86	2	no	—
286	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
287	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
292	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
293	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
294	M₁₆	—	2	8	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	8	no	—
298	C₂×C₈	#10621898	1	4	yes	—
299	C₂×C₈	#10621898	1	4	yes	—
300	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
301	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
302	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
303	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
304	C₄⋊C₄	—	86	2	no	—
305	C₄⋊C₄	—	86	2	no	—
306	C₄⋊C₄	—	86	2	no	—
307	C₄⋊C₄	—	86	2	no	—
308	C₄⋊C₄	—	86	2	no	—
309	C₄⋊C₄	—	86	2	no	—
310	C₄⋊C₄	—	86	2	no	—
311	C₄⋊C₄	—	86	2	no	—
312	C₄⋊C₄	—	344	2	no	—
313	C₄⋊C₄	—	344	2	no	—
314	C₄⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
315	C₄⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
316	C₂²⋊C₄	—	344	2	no	—
317	C₂²⋊C₄	—	344	2	no	—
318	C₂²⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
319	C₂²⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
320	C₄²	—	344	2	no	—
321	C₄²	—	344	2	no	—
322	C₄²	C₂×Dic₈₆	1	2	yes	—
323	C₄²	C₂×Dic₈₆	1	2	yes	—
324	C₄²	C₂²×Dic₄₃	1	2	yes	—
325	C₄²	C₂²×Dic₄₃	1	2	yes	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
331	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	172	2	no	—
343	C₂×C₄	—	172	2	no	—
344	C₂×C₄	—	172	2	no	—
345	C₂×C₄	—	172	2	no	—
346	C₂×C₄	—	172	2	no	—
347	C₂×C₄	—	172	2	no	—
348	C₂×C₄	—	172	2	no	—
349	C₂×C₄	—	172	2	no	—
350	C₂×C₄	—	172	2	no	—
351	C₂×C₄	—	172	2	no	—
352	C₂×C₄	—	172	2	no	—
353	C₂×C₄	—	172	2	no	—
354	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
355	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
356	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
357	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
358	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
359	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
361	C₂×C₄	C₂×#10621898	1	2	yes	—
362	C₂×C₄	C₂×#10621898	1	2	yes	—
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	#13063284	1	4	yes	—
366	C₈	#13063284	1	4	yes	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
373	C₂²	#14583449	1	2	yes	—
374	C₂²	#14583704	1	1	yes	characteristic
375	C₂²	#14583711	1	2	yes	—
376	C₂²	#14583716	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	344	2	no	—
383	C₄	—	344	2	no	—
384	C₄	—	344	2	no	—
385	C₄	—	344	2	no	—
386	C₄	C₂×#13063284	1	1	yes	characteristic
387	C₄	C₂×#13063284	1	1	yes	characteristic
388	C₄	#14583456	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	#19137002	1	1	yes	characteristic
391	C₂	#19143190	1	1	yes	characteristic
392	C₂	#19143195	1	1	yes	characteristic
393	C₂	#19145263	1	2	yes	—
394	C₂	#19145278	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#20822
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #19134763	C₂	semidirect
3. #19134726	C₂	semidirect
4. #19134723	C₂	semidirect
8. #19134492	C₂	semidirect
9. C₄×#13063259	C₂	semidirect
10. C₄×#13063257	C₂	semidirect
35. C₄₃×#405	C₄	semidirect
216. #405	Dic₄₃	semidirect
237. C₄₃	#20822	semidirect

Maximal subgroups

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

subgroup	index
#19137204	2
#19134763	2
#19134726	2
#19134723	2
#19134628	2
#19134624	2
#19134620	2
#19134492	2
C₄×#13063259	2
C₄×#13063257	2
C₂×C₄₃×#405	2
#20822	43