Subgroups — #25147994

Order 11008.

880 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583171	C₂	1	1	yes	maximal, characteristic
2	#19144246	C₂	1	1	yes	maximal, characteristic
3	#19144122	C₂	1	2	yes	maximal
4	#19143463	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135860	C₂	1	2	yes	maximal, complemented
6	#19135631	C₂	1	2	yes	maximal
7	#19135511	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135343	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134989	C₂	1	2	yes	maximal, complemented
10	#19134432	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	C₂²	1	2	yes	—
13	C₂×#13063331	C₂²	1	1	yes	characteristic
14	#14583473	C₂²	1	2	yes	—
15	#14583377	C₂²	1	2	yes	—
16	#14583171	—	2	4	no	—
17	#14583154	—	2	2	no	—
18	#14583137	—	2	2	no	—
19	#14583123	—	2	4	no	—
20	#14583107	—	2	4	no	—
21	#14583006	—	2	2	no	—
22	Q₁₆×Dic₄₃	—	2	2	no	—
23	C₂×#13063261	C₂²	1	1	yes	characteristic
24	#14582937	C₂²	1	1	yes	characteristic
25	#14582925	C₂²	1	2	yes	—
26	C₂×#13063253	C₂²	1	1	yes	characteristic
27	#14582908	C₂²	1	2	yes	—
28	#14582908	C₂²	1	2	yes	—
29	#14582908	C₂²	1	2	yes	—
30	#14582896	C₂²	1	1	yes	characteristic
31	C₂×#13063244	C₂²	1	2	yes	—
32	C₂×#13063244	C₂²	1	2	yes	—
33	#14582854	C₂²	1	1	yes	characteristic
34	#14582664	C₂²	1	1	yes	characteristic
35	#14582659	C₂²	1	1	yes	characteristic
36	#14582659	C₂²	1	2	yes	—
37	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
38	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
39	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
41	C₄₃×#494	—	2	4	no	—
42	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#10621898	C₂³	1	1	yes	characteristic
44	#13063356	—	2	4	no	—
45	#13063356	—	4	2	no	—
46	C₂×#10621885	—	2	2	no	—
47	C₂×#10621884	—	2	2	no	—
48	#13063331	—	2	2	no	—
49	#13063331	—	2	2	no	—
50	C₂×#10621877	C₂³	1	1	yes	characteristic
51	C₂×#10621877	C₂³	1	1	yes	characteristic
52	C₂×#10621877	C₂³	1	2	yes	—
53	C₂×#10621872	—	2	1	no	—
54	C₂×C₈×D₄₃	—	2	1	no	—
55	#13063323	—	2	2	no	—
56	#13063314	—	2	2	no	—
57	#13063308	—	4	2	no	—
58	#13063301	—	2	4	no	—
59	Q₈×Dic₄₃	—	2	4	no	—
60	Q₈×Dic₄₃	—	2	4	no	—
61	#13063284	—	4	2	no	—
62	#13063284	C₂³	1	1	yes	characteristic
63	#13063284	C₂³	1	2	yes	—
64	#13063261	—	2	2	no	—
65	#13063259	D₄	1	2	yes	—
66	#13063257	D₄	1	2	yes	—
67	Dic₄₃⋊C₈	—	2	4	no	—
68	#13063253	—	2	2	no	—
69	#13063250	D₄	1	2	yes	—
70	#13063249	—	2	4	no	—
71	#13063249	—	2	4	no	—
72	#13063249	—	2	4	no	—
73	#13063247	D₄	1	2	yes	—
74	#13063244	—	2	4	no	—
75	#13063244	—	4	2	no	—
76	#13063235	—	2	1	no	—
77	C₈×Dic₄₃	—	2	1	no	—
78	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
79	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₄₃	—	2	4	no	—
81	C₂×Q₁₆×C₄₃	—	2	1	no	—
82	C₂×Q₁₆×C₄₃	—	2	1	no	—
83	C₂×Q₁₆×C₄₃	—	2	4	no	—
84	C₂×Q₁₆×C₄₃	—	2	1	no	—
85	C₂×Q₁₆×C₄₃	—	2	1	no	—
86	C₂×Q₁₆×C₄₃	—	2	2	no	—
87	C₂×Q₁₆×C₄₃	—	2	2	no	—
88	C₂×Q₁₆×C₄₃	—	2	2	no	—
89	C₂×Q₁₆×C₄₃	—	4	2	no	—
90	C₂×Q₁₆×C₄₃	D₄	1	4	yes	—
91	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
93	C₄⋊Q₈×C₄₃	—	2	4	no	—
94	C₄⋊Q₈×C₄₃	—	2	4	no	—
95	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	2	1	no	—
115	#10621898	—	2	1	no	—
116	#10621898	—	2	1	no	—
117	#10621898	—	2	1	no	—
118	#10621898	—	2	1	no	—
119	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₄₃	—	2	1	no	—
121	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
122	Q₁₆×C₄₃	—	2	4	no	—
123	Q₁₆×C₄₃	—	2	4	no	—
124	Q₁₆×C₄₃	—	4	8	no	—
125	Q₁₆×C₄₃	—	4	2	no	—
126	Q₁₆×C₄₃	—	4	2	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₄₃	#41	1	2	yes	—
134	C₄⋊C₄×C₄₃	—	4	8	no	—
135	C₄²×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	#41	1	2	yes	—
137	C₂²⋊Dic₄₃	—	2	1	no	—
138	C₂²⋊Dic₄₃	—	2	2	no	—
139	#10621885	—	4	4	no	—
140	#10621884	—	4	4	no	—
141	(C₂×D₄₃)⋊C₄	—	4	4	no	—
142	C₄⋊Dic₄₃	—	4	4	no	—
143	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
144	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
145	Dic₄₃⋊C₄	—	4	4	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	—	2	2	no	—
148	C₄×Dic₄₃	—	4	4	no	—
149	#10621877	—	2	1	no	—
150	#10621877	—	2	2	no	—
151	#10621877	—	2	1	no	—
152	#10621877	—	2	1	no	—
153	#10621877	—	2	1	no	—
154	#10621877	—	2	2	no	—
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	#10621872	—	4	2	no	—
159	C₈×D₄₃	—	4	2	no	—
160	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₄₃	—	2	1	no	—
162	Q₈×C₄₃	—	2	4	no	—
163	Q₈×C₄₃	—	2	4	no	—
164	Q₈×C₄₃	—	4	2	no	—
165	Q₈×C₄₃	—	4	2	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	Q₈×C₄₃	—	4	2	no	—
168	Q₈×C₄₃	—	4	2	no	—
169	Q₈×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	2	4	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	4	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂²⋊D₄₃	—	4	1	no	—
185	C₂²⋊D₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	4	no	—
188	C₂×Dic₄₃	—	2	1	no	—
189	D₁₇₂	—	2	1	no	—
190	D₁₇₂	—	2	1	no	—
191	C₄×D₄₃	—	4	1	no	—
192	C₄×D₄₃	—	4	1	no	—
193	Dic₈₆	—	2	1	no	—
194	Dic₈₆	—	2	1	no	—
195	C₈×C₄₃	—	2	2	no	—
196	C₈×C₄₃	#121	1	2	yes	—
197	C₈×C₄₃	#121	1	2	yes	—
198	C₄₃⋊C₈	—	4	1	no	—
199	C₄₃⋊C₈	—	4	2	no	—
200	C₄₃⋊C₈	—	4	1	no	—
201	#25435	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	#540	1	1	yes	characteristic
204	C₂²×C₄₃	D₄²	1	1	yes	characteristic
205	C₂²×C₄₃	#546	1	1	yes	characteristic
206	C₂×D₄₃	—	4	1	no	—
207	C₂×D₄₃	—	4	2	no	—
208	C₄×C₄₃	—	2	4	no	—
209	C₄×C₄₃	—	4	4	no	—
210	C₄×C₄₃	—	8	2	no	—
211	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
212	C₄×C₄₃	#532	1	1	yes	characteristic
213	C₄×C₄₃	D₄²	1	1	yes	characteristic
214	C₄×C₄₃	#550	1	1	yes	characteristic
215	Dic₄₃	—	4	1	no	—
216	Dic₄₃	—	4	2	no	—
217	Dic₄₃	—	4	4	no	—
218	C₂×#494	D₄₃	1	1	yes	characteristic, complemented
219	C₂×#473	—	43	1	no	—
220	#3059	—	43	1	no	—
221	#3044	—	43	2	no	—
222	#2950	—	43	1	no	—
223	#2047	—	43	2	no	—
224	#2005	—	43	2	no	—
225	#1979	—	43	1	no	—
226	#1945	—	43	1	no	—
227	#1886	—	43	2	no	—
228	#1764	—	43	1	no	—
229	C₂×C₄₃	—	2	1	no	—
230	C₂×C₄₃	—	2	1	no	—
231	C₂×C₄₃	#2428	1	1	yes	characteristic
232	C₂×C₄₃	#3293	1	2	yes	—
233	D₄₃	—	8	1	no	—
234	C₂×#137	—	43	2	no	—
235	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
236	C₂²×Q₁₆	C₂×D₄₃	1	2	yes	—
237	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
238	C₂×#131	—	43	1	no	—
239	#536	—	43	2	no	—
240	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
241	#519	—	43	2	no	—
242	#494	—	2	4	no	—
243	#473	—	86	4	no	—
244	#470	—	86	2	no	—
245	#467	—	86	2	no	—
246	#464	—	86	4	no	—
247	#462	—	86	4	no	—
248	#441	—	86	2	no	—
249	C₄×Q₁₆	—	86	2	no	—
250	C₂×#108	—	43	1	no	—
251	#427	—	43	1	no	—
252	#424	—	43	2	no	—
253	C₂×#104	—	43	1	no	—
254	#419	—	43	2	no	—
255	#419	—	43	2	no	—
256	#419	—	43	2	no	—
257	#416	—	43	1	no	—
258	C₂×#101	—	43	2	no	—
259	C₂×#101	—	43	2	no	—
260	#405	—	43	1	no	—
261	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
262	#341	—	43	1	no	—
263	#339	—	43	1	no	—
264	#339	—	43	2	no	—
265	C₄₃	#25435	1	1	yes	characteristic, complemented, Sylow
266	C₂×#41	—	43	1	no	—
267	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
268	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
269	#137	—	86	4	no	—
270	#137	—	172	2	no	—
271	C₂×Q₁₆	—	2	4	no	—
272	C₂×Q₁₆	—	2	1	no	—
273	C₂×Q₁₆	—	2	1	no	—
274	C₂×Q₁₆	—	2	4	no	—
275	C₂×Q₁₆	—	2	1	no	—
276	C₂×Q₁₆	—	2	1	no	—
277	C₂×Q₁₆	—	2	2	no	—
278	C₂×Q₁₆	—	2	2	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×Q₁₆	—	4	2	no	—
281	C₂×Q₁₆	—	86	2	no	—
282	C₂×Q₁₆	C₂²⋊D₄₃	1	4	yes	—
283	C₂×SD₁₆	—	86	2	no	—
284	#131	—	86	2	no	—
285	#131	—	86	2	no	—
286	C₂×M₁₆	—	43	1	no	—
287	C₂×M₁₆	—	43	2	no	—
288	C₂×M₁₆	—	43	1	no	—
289	C₂×M₁₆	—	86	1	no	—
290	C₂²×C₈	—	86	1	no	—
291	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
292	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
293	C₄⋊Q₈	—	2	4	no	—
294	C₄⋊Q₈	—	2	4	no	—
295	C₄⋊Q₈	—	86	2	no	—
296	#124	—	86	2	no	—
297	#123	—	172	2	no	—
298	C₂²⋊Q₈	—	86	4	no	—
299	C₄×Q₈	—	86	4	no	—
300	C₄×Q₈	—	86	4	no	—
301	#117	—	43	1	no	—
302	#117	—	43	2	no	—
303	#117	—	172	2	no	—
304	C₂×C₄⋊C₄	—	4	2	no	—
305	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
306	#108	—	86	2	no	—
307	#107	—	43	2	no	—
308	#106	—	43	2	no	—
309	C₄⋊C₈	—	86	4	no	—
310	#104	—	86	2	no	—
311	#103	—	43	2	no	—
312	#103	—	86	4	no	—
313	#103	—	86	4	no	—
314	#103	—	86	4	no	—
315	#102	—	43	2	no	—
316	#101	—	86	4	no	—
317	#101	—	172	2	no	—
318	#97	—	86	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	86	1	no	—
321	#41	—	86	1	no	—
322	#41	—	86	1	no	—
323	#41	—	86	1	no	—
324	#41	—	86	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	43	1	no	—
337	C₂×Q₈	C₂×C₂²⋊D₄₃	1	4	yes	—
338	C₂×D₄	—	43	1	no	—
339	C₂×D₄	—	86	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
345	Q₁₆	—	2	4	no	—
346	Q₁₆	—	2	4	no	—
347	Q₁₆	—	4	8	no	—
348	Q₁₆	—	4	2	no	—
349	Q₁₆	—	4	2	no	—
350	Q₁₆	—	172	4	no	—
351	SD₁₆	—	172	4	no	—
352	M₁₆	—	86	1	no	—
353	M₁₆	—	86	2	no	—
354	M₁₆	—	86	1	no	—
355	M₁₆	—	86	1	no	—
356	M₁₆	—	86	1	no	—
357	M₁₆	—	86	2	no	—
358	M₁₆	—	172	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	86	1	no	—
362	C₂×C₈	—	86	1	no	—
363	C₂×C₈	—	86	2	no	—
364	C₂×C₈	—	172	2	no	—
365	C₂×C₈	D₄×D₄₃	1	2	yes	—
366	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
367	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
368	C₂×C₈	#10621900	1	2	yes	—
369	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
370	C₄⋊C₄	—	4	8	no	—
371	C₄⋊C₄	—	43	2	no	—
372	C₄⋊C₄	—	43	4	no	—
373	C₄⋊C₄	—	172	4	no	—
374	C₄⋊C₄	—	172	4	no	—
375	C₂²⋊C₄	—	86	1	no	—
376	C₂²⋊C₄	—	86	2	no	—
377	C₂²⋊C₄	—	172	4	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	86	1	no	—
380	C₄²	—	86	2	no	—
381	C₄²	—	172	4	no	—
382	C₄²	#10621900	1	2	yes	—
383	C₂³	—	86	1	no	—
384	C₂³	#13063370	1	1	yes	characteristic
385	Q₈	—	2	4	no	—
386	Q₈	—	2	4	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	86	1	no	—
394	Q₈	—	86	1	no	—
395	D₄	—	86	1	no	—
396	D₄	—	86	1	no	—
397	D₄	—	172	1	no	—
398	D₄	—	172	1	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	86	2	no	—
408	C₂×C₄	—	86	4	no	—
409	C₂×C₄	—	86	1	no	—
410	C₂×C₄	—	172	1	no	—
411	C₂×C₄	—	172	1	no	—
412	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
416	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
417	C₂×C₄	#13063370	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	172	1	no	—
420	C₈	—	172	1	no	—
421	C₈	—	172	2	no	—
422	C₈	#13063297	1	2	yes	—
423	C₈	#13063297	1	2	yes	—
424	C₂²	—	2	2	no	—
425	C₂²	—	172	1	no	—
426	C₂²	—	172	2	no	—
427	C₂²	#14583503	1	1	yes	characteristic
428	C₂²	#14583534	1	1	yes	characteristic
429	C₂²	#14583543	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	4	4	no	—
432	C₄	—	8	2	no	—
433	C₄	—	172	1	no	—
434	C₄	—	172	2	no	—
435	C₄	—	172	4	no	—
436	C₄	C₂×#13063297	1	1	yes	characteristic
437	C₄	#14583447	1	1	yes	characteristic
438	C₄	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
439	C₄	#14583569	1	1	yes	characteristic
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	344	1	no	—
443	C₂	#19138186	1	1	yes	characteristic
444	C₂	#19146399	1	2	yes	—

	subgroup	G/H
center	C₂²	#14583534
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#494	C₂
socle	C₂²×C₄₃	D₄²
prime radical	C₂×#10621898	C₂³
hypercenter	C₂×#494	D₄₃
hypocenter	C₄₃	#25435
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#494

Complements

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

N	H ≅ G/N	type
4. #19143463	C₂	semidirect
5. #19135860	C₂	semidirect
7. #19135511	C₂	semidirect
8. #19135343	C₂	semidirect
9. #19134989	C₂	semidirect
11. C₂×C₄₃×#494	C₂	semidirect
218. C₂×#494	D₄₃	semidirect
265. C₄₃	#25435	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583171	2
#19144246	2
#19144122	2
#19143463	2
#19135860	2
#19135631	2
#19135511	2
#19135343	2
#19134989	2
#19134432	2
C₂×C₄₃×#494	2
#25435	43