Subgroups — #24989383

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063322	C₂	1	1	yes	maximal, characteristic
2	#19134747	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582642	C₂	1	2	yes	maximal
4	#19132479	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#13063322	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₁₇₂	—	2	1	no	—
8	C₂×C₄×D₁₇₂	—	2	1	no	—
9	C₂×C₄×D₁₇₂	C₄	1	2	yes	—
10	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
13	#14582801	—	2	1	no	—
14	#14582801	—	2	1	no	—
15	#14582801	C₄	1	2	yes	—
16	#14582769	C₂²	1	1	yes	characteristic
17	#14582642	—	2	4	no	—
18	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
19	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₄³×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×D₁₇₂	—	2	1	no	—
23	C₂²×D₁₇₂	—	2	1	no	—
24	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
25	C₂²×C₄×D₄₃	—	2	2	no	—
26	C₂²×C₄₃⋊C₈	—	2	2	no	—
27	#13063322	—	2	1	no	—
28	#13063322	—	2	1	no	—
29	#13063322	D₄	1	2	yes	—
30	#13063322	Q₈	1	2	yes	—
31	C₄×D₁₇₂	—	4	4	no	—
32	C₄×D₁₇₂	—	4	2	no	—
33	C₄×D₁₇₂	—	4	2	no	—
34	C₄×D₁₇₂	—	4	2	no	—
35	C₄×D₁₇₂	—	4	2	no	—
36	C₂×C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
39	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
40	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
41	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
42	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
43	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
44	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
45	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
46	C₂²×C₈×C₄₃	—	2	2	no	—
47	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₄₃	—	2	2	no	—
55	C₄⋊C₈×C₄₃	—	2	2	no	—
56	C₄⋊C₈×C₄₃	—	4	2	no	—
57	C₄⋊C₈×C₄₃	—	4	2	no	—
58	C₂³×D₄₃	—	2	2	no	—
59	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×Dic₄₃	—	2	2	no	—
67	C₂×D₁₇₂	—	2	2	no	—
68	C₂×D₁₇₂	—	2	2	no	—
69	C₂×D₁₇₂	—	2	2	no	—
70	C₂×D₁₇₂	—	2	2	no	—
71	C₂×D₁₇₂	—	2	2	no	—
72	C₂×D₁₇₂	—	4	1	no	—
73	C₂×D₁₇₂	—	4	1	no	—
74	C₂×D₁₇₂	—	4	1	no	—
75	C₂×D₁₇₂	—	4	1	no	—
76	C₂×D₁₇₂	—	4	1	no	—
77	C₂×D₁₇₂	—	4	1	no	—
78	C₂×D₁₇₂	—	4	1	no	—
79	C₂×D₁₇₂	—	4	1	no	—
80	C₂×D₁₇₂	—	4	2	no	—
81	C₂×D₁₇₂	—	4	2	no	—
82	C₂×D₁₇₂	C₄⋊C₄	1	4	yes	—
83	C₂×C₄×D₄₃	—	4	4	no	—
84	C₂×C₄×D₄₃	—	4	4	no	—
85	C₂×C₄×D₄₃	—	4	4	no	—
86	C₂×C₈×C₄₃	—	4	2	no	—
87	C₂×C₈×C₄₃	—	4	2	no	—
88	C₂×C₈×C₄₃	—	4	2	no	—
89	C₄²×C₄₃	—	2	2	no	—
90	C₄²×C₄₃	—	2	1	no	—
91	C₄²×C₄₃	—	2	1	no	—
92	C₄²×C₄₃	—	2	1	no	—
93	C₄²×C₄₃	—	2	1	no	—
94	C₄²×C₄₃	—	4	1	no	—
95	C₄²×C₄₃	D₈	1	2	yes	—
96	C₄²×C₄₃	D₈	1	2	yes	—
97	C₄²×C₄₃	SD₁₆	1	2	yes	—
98	C₄²×C₄₃	SD₁₆	1	2	yes	—
99	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
101	C₄²×C₄₃	#41	1	1	yes	characteristic
102	C₄²×C₄₃	#41	1	1	yes	characteristic
103	(C₂×D₄₃)⋊C₄	—	4	4	no	—
104	(C₂×D₄₃)⋊C₄	—	4	4	no	—
105	(C₂×D₄₃)⋊C₄	—	4	4	no	—
106	C₄⋊Dic₄₃	—	4	1	no	—
107	C₄⋊Dic₄₃	—	4	1	no	—
108	C₄⋊Dic₄₃	—	4	1	no	—
109	C₄⋊Dic₄₃	—	4	1	no	—
110	C₄⋊Dic₄₃	—	4	2	no	—
111	C₂×C₄₃⋊C₈	—	4	2	no	—
112	C₂×C₄₃⋊C₈	—	4	2	no	—
113	C₂×C₄₃⋊C₈	—	4	2	no	—
114	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×D₄₃	—	2	4	no	—
116	C₂²×D₄₃	—	4	2	no	—
117	C₂²×D₄₃	—	4	2	no	—
118	C₂²×D₄₃	—	4	2	no	—
119	C₂²×D₄₃	—	4	2	no	—
120	C₂²×D₄₃	—	4	2	no	—
121	C₂²×D₄₃	—	4	2	no	—
122	C₂×C₄×C₄₃	—	2	1	no	—
123	C₂×C₄×C₄₃	—	2	1	no	—
124	C₂×C₄×C₄₃	—	2	1	no	—
125	C₂×C₄×C₄₃	—	2	1	no	—
126	C₂×C₄×C₄₃	—	2	1	no	—
127	C₂×C₄×C₄₃	—	2	1	no	—
128	C₂×C₄×C₄₃	—	2	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	#100	1	2	yes	—
132	C₂×C₄×C₄₃	#102	1	2	yes	—
133	C₂×C₄×C₄₃	#102	1	2	yes	—
134	C₂×C₄×C₄₃	#102	1	2	yes	—
135	C₂×C₄×C₄₃	#102	1	2	yes	—
136	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
138	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
139	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
149	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
150	C₂×Dic₄₃	—	4	2	no	—
151	C₂×Dic₄₃	—	4	2	no	—
152	C₂×Dic₄₃	—	4	2	no	—
153	D₁₇₂	—	4	4	no	—
154	D₁₇₂	—	4	4	no	—
155	D₁₇₂	—	4	2	no	—
156	D₁₇₂	—	4	2	no	—
157	D₁₇₂	—	4	2	no	—
158	D₁₇₂	—	4	2	no	—
159	D₁₇₂	—	4	2	no	—
160	D₁₇₂	—	4	2	no	—
161	D₁₇₂	—	4	2	no	—
162	D₁₇₂	—	4	2	no	—
163	C₄×D₄₃	—	8	8	no	—
164	C₈×C₄₃	—	8	2	no	—
165	C₄₃⋊C₈	—	8	2	no	—
166	#8585	—	43	1	no	maximal, Sylow
167	C₂²×C₄₃	#380	1	1	yes	characteristic
168	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
169	C₂²×C₄₃	#413	1	1	yes	characteristic
170	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
171	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
172	C₂²×C₄₃	#417	1	1	yes	characteristic
173	C₂²×C₄₃	#417	1	1	yes	characteristic
174	C₂×D₄₃	—	4	4	no	—
175	C₂×D₄₃	—	4	4	no	—
176	C₂×D₄₃	—	4	4	no	—
177	C₂×D₄₃	—	8	2	no	—
178	C₂×D₄₃	—	8	2	no	—
179	C₂×D₄₃	—	8	2	no	—
180	C₂×D₄₃	—	8	2	no	—
181	C₄×C₄₃	—	2	1	no	—
182	C₄×C₄₃	—	2	1	no	—
183	C₄×C₄₃	—	2	2	no	—
184	C₄×C₄₃	—	2	2	no	—
185	C₄×C₄₃	—	4	1	no	—
186	C₄×C₄₃	#331	1	4	yes	complemented
187	C₄×C₄₃	#459	1	1	yes	characteristic
188	C₄×C₄₃	#459	1	1	yes	characteristic
189	C₄×C₄₃	#461	1	1	yes	characteristic
190	C₄×C₄₃	#461	1	1	yes	characteristic
191	C₄×C₄₃	#474	1	1	yes	characteristic
192	C₄×C₄₃	#474	1	1	yes	characteristic
193	C₄×C₄₃	#476	1	1	yes	characteristic
194	C₄×C₄₃	#476	1	1	yes	characteristic
195	Dic₄₃	—	8	2	no	—
196	C₄×#127	—	43	1	no	—
197	#1842	—	43	1	no	—
198	#1842	D₄₃	1	1	yes	characteristic, complemented
199	C₂×#331	—	43	2	no	—
200	#1296	—	43	2	no	—
201	C₂×C₄₃	C₂×#331	1	1	yes	characteristic
202	C₂×C₄₃	#1547	1	1	yes	characteristic
203	C₂×C₄₃	#1547	1	1	yes	characteristic
204	C₂×C₄₃	#1560	1	1	yes	characteristic
205	C₂×C₄₃	#1800	1	1	yes	characteristic
206	C₂×C₄₃	#1802	1	1	yes	characteristic
207	C₂×C₄₃	#1802	1	1	yes	characteristic
208	D₄₃	—	8	4	no	—
209	C₂×#127	—	43	1	no	—
210	C₂×C₄×D₄	—	43	2	no	—
211	C₂×C₄×D₄	—	86	1	no	—
212	C₂×C₄×D₄	—	86	1	no	—
213	C₂×C₄⋊C₈	—	2	1	no	—
214	C₂×C₄⋊C₈	—	2	1	no	—
215	C₂×C₄⋊C₈	—	43	2	no	—
216	C₂×C₄⋊C₈	—	86	1	no	—
217	C₂×C₄⋊C₈	—	86	1	no	—
218	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
219	#390	—	43	2	no	—
220	#390	—	86	1	no	—
221	#390	—	86	1	no	—
222	#384	—	43	1	no	—
223	C₄³	C₂×D₄₃	1	1	yes	characteristic
224	#331	—	86	4	no	—
225	C₄₃	#8585	1	1	yes	characteristic, complemented, Sylow
226	C₂²×D₄	—	43	2	no	—
227	C₂²×D₄	—	86	1	no	—
228	C₂²×D₄	—	86	1	no	—
229	C₂³×C₄	—	86	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	86	2	no	—
232	#127	—	43	2	no	—
233	#127	—	43	2	no	—
234	#127	—	86	1	no	—
235	#127	—	86	1	no	—
236	C₄×D₄	—	172	4	no	—
237	C₄×D₄	—	172	2	no	—
238	C₄×D₄	—	172	2	no	—
239	C₄×D₄	—	172	2	no	—
240	C₄×D₄	—	172	2	no	—
241	C₂×C₄⋊C₄	—	43	2	no	—
242	C₂×C₄⋊C₄	—	86	1	no	—
243	C₂×C₄⋊C₄	—	86	1	no	—
244	C₂×C₂²⋊C₄	—	86	2	no	—
245	C₂×C₂²⋊C₄	—	86	2	no	—
246	C₂×C₂²⋊C₄	—	86	2	no	—
247	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
249	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
250	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
253	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	4	2	no	—
257	C₄⋊C₈	—	4	2	no	—
258	C₄⋊C₈	—	86	2	no	—
259	C₄⋊C₈	—	86	2	no	—
260	C₄⋊C₈	—	172	2	no	—
261	C₄⋊C₈	—	172	2	no	—
262	C₂⁴	—	86	2	no	—
263	C₂×D₄	—	43	4	no	—
264	C₂×D₄	—	86	2	no	—
265	C₂×D₄	—	86	2	no	—
266	C₂×D₄	—	86	2	no	—
267	C₂×D₄	—	86	2	no	—
268	C₂×D₄	—	86	2	no	—
269	C₂×D₄	—	172	2	no	—
270	C₂×D₄	—	172	2	no	—
271	C₂×D₄	—	172	1	no	—
272	C₂×D₄	—	172	1	no	—
273	C₂×D₄	—	172	1	no	—
274	C₂×D₄	—	172	1	no	—
275	C₂×D₄	—	172	1	no	—
276	C₂×D₄	—	172	1	no	—
277	C₂×D₄	—	172	1	no	—
278	C₂×D₄	—	172	1	no	—
279	C₂²×C₄	—	86	2	no	—
280	C₂²×C₄	—	172	4	no	—
281	C₂²×C₄	—	172	4	no	—
282	C₂²×C₄	—	172	4	no	—
283	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
284	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
286	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	172	2	no	—
294	C₂×C₈	—	172	2	no	—
295	C₂×C₈	—	172	2	no	—
296	C₄⋊C₄	—	172	2	no	—
297	C₄⋊C₄	—	172	1	no	—
298	C₄⋊C₄	—	172	1	no	—
299	C₄⋊C₄	—	172	1	no	—
300	C₄⋊C₄	—	172	1	no	—
301	C₂²⋊C₄	—	172	4	no	—
302	C₂²⋊C₄	—	172	4	no	—
303	C₂²⋊C₄	—	172	4	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	4	1	no	—
310	C₄²	#10621873	1	2	yes	—
311	C₄²	D₃₄₄	1	2	yes	—
312	C₄²	#10621882	1	2	yes	—
313	C₄²	#10621884	1	2	yes	—
314	C₄²	D₄×D₄₃	1	1	yes	characteristic
315	C₄²	#10621900	1	1	yes	characteristic
316	C₄²	Q₈×D₄₃	1	1	yes	characteristic
317	C₄²	#10621902	1	1	yes	characteristic
318	C₂³	—	86	4	no	—
319	C₂³	—	172	2	no	—
320	C₂³	—	172	2	no	—
321	C₂³	—	172	2	no	—
322	C₂³	—	172	2	no	—
323	C₂³	—	172	2	no	—
324	C₂³	—	172	2	no	—
325	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
326	D₄	—	172	4	no	—
327	D₄	—	172	4	no	—
328	D₄	—	172	2	no	—
329	D₄	—	172	2	no	—
330	D₄	—	172	2	no	—
331	D₄	—	172	2	no	—
332	D₄	—	172	2	no	—
333	D₄	—	172	2	no	—
334	D₄	—	172	2	no	—
335	D₄	—	172	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	344	8	no	—
346	C₂×C₄	—	172	2	no	—
347	C₂×C₄	—	172	2	no	—
348	C₂×C₄	—	172	2	no	—
349	C₂×C₄	#13063241	1	2	yes	—
350	C₂×C₄	#13063245	1	2	yes	—
351	C₂×C₄	#13063245	1	2	yes	—
352	C₂×C₄	#13063247	1	2	yes	—
353	C₂×C₄	#13063247	1	2	yes	—
354	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
355	C₂×C₄	#13063283	1	1	yes	characteristic
356	C₂×C₄	#13063296	1	1	yes	characteristic
357	C₂×C₄	#13063300	1	1	yes	characteristic
358	C₂×C₄	#13063301	1	1	yes	characteristic
359	C₂×C₄	#13063305	1	1	yes	characteristic
360	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
361	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
362	C₂×C₄	C₂×#10621884	1	1	yes	characteristic
363	C₂×C₄	C₂×#10621873	1	1	yes	characteristic
364	C₂×C₄	#13063351	1	1	yes	characteristic
365	C₂×C₄	#13063353	1	1	yes	characteristic
366	C₂×C₄	#13063356	1	1	yes	characteristic
367	C₂×C₄	#13063358	1	1	yes	characteristic
368	C₈	—	8	2	no	—
369	C₈	—	344	2	no	—
370	C₂²	—	344	2	no	—
371	C₂²	—	344	2	no	—
372	C₂²	—	344	2	no	—
373	C₂²	—	344	2	no	—
374	C₂²	—	172	4	no	—
375	C₂²	—	172	4	no	—
376	C₂²	—	172	4	no	—
377	C₂²	#14582756	1	1	yes	characteristic
378	C₂²	C₂×#13063241	1	1	yes	characteristic
379	C₂²	#14582881	1	1	yes	characteristic
380	C₂²	C₂×#13063245	1	1	yes	characteristic
381	C₂²	C₂×#13063247	1	1	yes	characteristic
382	C₂²	#14582898	1	1	yes	characteristic
383	C₂²	#14582901	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	344	2	no	—
390	C₄	#14582642	1	4	yes	complemented
391	C₄	#14583091	1	1	yes	characteristic
392	C₄	#14583095	1	1	yes	characteristic
393	C₄	#14583101	1	1	yes	characteristic
394	C₄	#14583105	1	1	yes	characteristic
395	C₄	#14583176	1	1	yes	characteristic
396	C₄	#14583180	1	1	yes	characteristic
397	C₄	#14583186	1	1	yes	characteristic
398	C₄	#14583190	1	1	yes	characteristic
399	C₂	—	344	4	no	—
400	C₂	C₂×#14582642	1	1	yes	characteristic
401	C₂	#19133270	1	1	yes	characteristic
402	C₂	#19133273	1	1	yes	characteristic
403	C₂	#19133328	1	1	yes	characteristic
404	C₂	#19134584	1	1	yes	characteristic
405	C₂	#19134592	1	1	yes	characteristic
406	C₂	#19134596	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1842	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂×#13063322	C₂²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1842	D₄₃
hypocenter	C₄₃	#8585
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
2. #19134747	C₂	semidirect
4. #19132479	C₂	semidirect
5. C₄₃×#1842	C₂	semidirect
186. C₄×C₄₃	#331	semidirect
198. #1842	D₄₃	semidirect
225. C₄₃	#8585	semidirect
390. C₄	#14582642	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063322	2
#19134747	2
C₂×#14582642	2
#19132479	2
C₄₃×#1842	2
#8585	43