Subgroups — #25116314

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143397	C₂	1	1	yes	maximal, characteristic
2	#19143263	C₂	1	2	yes	maximal, complemented
3	#19135486	C₂	1	1	yes	maximal, characteristic
4	#19135481	C₂	1	1	yes	maximal, characteristic
5	#19135242	C₂	1	2	yes	maximal, complemented
6	#19135242	C₂	1	2	yes	maximal, complemented
7	#19134612	C₂	1	2	yes	maximal, complemented
8	#19134482	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134477	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134467	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1849	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₄×#10621898	C₂²	1	2	yes	—
14	#14583012	C₄	1	2	yes	complemented
15	#14583007	C₄	1	2	yes	complemented
16	#14583001	C₄	1	2	yes	complemented
17	#14583001	C₄	1	2	yes	complemented
18	#14582959	—	2	2	no	—
19	#14582959	—	2	2	no	—
20	#14582955	—	2	2	no	—
21	#14582951	—	2	2	no	—
22	#14582937	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×#13063251	C₂²	1	2	yes	—
25	C₂×#13063251	C₂²	1	2	yes	—
26	#14582896	C₂²	1	2	yes	—
27	#14582867	C₂²	1	2	yes	—
28	#14582867	C₂²	1	2	yes	—
29	#14582857	C₂²	1	2	yes	—
30	#14582857	C₂²	1	2	yes	—
31	C₂×#13063235	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
34	#14582660	C₂²	1	2	yes	—
35	#14582660	C₂²	1	2	yes	—
36	#14582653	C₂²	1	1	yes	characteristic
37	#14582653	C₂²	1	1	yes	characteristic
38	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#108×C₄₃	C₂²	1	2	yes	—
41	C₄₃×#423	C₂²	1	2	yes	—
42	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#10621898	C₂³	1	2	yes	—
44	#13063347	—	2	2	no	—
45	#13063347	—	2	2	no	—
46	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
47	C₂×#10621873	C₂×C₄	1	2	yes	—
48	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
51	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
52	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
53	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
54	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
55	C₄×C₂²⋊D₄₃	—	2	2	no	—
56	C₄×C₂²⋊D₄₃	—	2	2	no	—
57	#13063284	C₂³	1	2	yes	—
58	#13063282	—	2	2	no	—
59	C₂×C₄⋊Dic₄₃	—	2	1	no	—
60	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
62	C₄²×D₄₃	—	2	2	no	—
63	#13063259	C₂×C₄	1	1	yes	characteristic
64	#13063259	C₂×C₄	1	1	yes	characteristic
65	#13063257	C₂×C₄	1	2	yes	—
66	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
68	#13063251	—	4	2	no	—
69	#13063251	—	4	2	no	—
70	#13063250	C₂×C₄	1	2	yes	—
71	#13063250	C₂×C₄	1	2	yes	—
72	#13063247	C₂×C₄	1	2	yes	—
73	#13063247	C₂×C₄	1	2	yes	—
74	(C₂×D₄₃)⋊C₈	—	2	2	no	—
75	(C₂×D₄₃)⋊C₈	—	2	2	no	—
76	(C₂×D₄₃)⋊C₈	—	2	2	no	—
77	(C₂×D₄₃)⋊C₈	—	2	2	no	—
78	#13063235	—	2	2	no	—
79	#13063235	—	2	2	no	—
80	#13063235	—	2	2	no	—
81	C₈×Dic₄₃	—	2	2	no	—
82	C₈×Dic₄₃	—	2	2	no	—
83	C₈×Dic₄₃	—	2	2	no	—
84	C₄₃⋊#95	—	2	1	no	—
85	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
86	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	#108×C₄₃	—	2	2	no	—
91	#108×C₄₃	—	2	2	no	—
92	#108×C₄₃	—	4	2	no	—
93	C₄⋊C₈×C₄₃	—	2	2	no	—
94	C₄⋊C₈×C₄₃	—	2	2	no	—
95	#97×C₄₃	C₂×C₄	1	2	yes	—
96	#97×C₄₃	C₂×C₄	1	2	yes	—
97	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
100	C₂×C₂²⋊D₄₃	—	2	2	no	—
101	C₂²×Dic₄₃	—	2	1	no	—
102	C₂²×Dic₄₃	—	2	1	no	—
103	#10621898	—	2	2	no	—
104	#10621898	—	2	2	no	—
105	#10621898	—	2	2	no	—
106	#10621898	—	2	2	no	—
107	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₄₃	—	2	2	no	—
109	C₂×C₄×D₄₃	—	2	2	no	—
110	C₂×C₄×D₄₃	—	2	2	no	—
111	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
112	M₁₆×C₄₃	—	2	2	no	—
113	M₁₆×C₄₃	—	2	2	no	—
114	M₁₆×C₄₃	—	2	2	no	—
115	M₁₆×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	1	no	—
117	C₂×C₈×C₄₃	—	2	1	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	#41	1	2	yes	—
124	C₂×C₈×C₄₃	#41	1	2	yes	—
125	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₃	C₂×D₄	1	2	yes	—
127	C₂²⋊Dic₄₃	—	2	2	no	—
128	(C₂×D₄₃)⋊C₄	—	2	2	no	—
129	(C₂×D₄₃)⋊C₄	—	2	2	no	—
130	C₄⋊Dic₄₃	—	4	2	no	—
131	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
132	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
133	Dic₄₃⋊C₄	—	2	2	no	—
134	Dic₄₃⋊C₄	—	2	2	no	—
135	C₄×Dic₄₃	—	2	2	no	—
136	C₄×Dic₄₃	—	2	2	no	—
137	C₄×Dic₄₃	—	2	2	no	—
138	C₄×Dic₄₃	—	2	1	no	—
139	C₄×Dic₄₃	—	2	1	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	1	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
148	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
149	Dic₁₇₂	—	2	2	no	—
150	D₃₄₄	—	2	2	no	—
151	#10621873	—	2	4	no	—
152	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
153	C₂²×D₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂²×D₄	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	C₂²⋊D₄₃	—	4	2	no	—
165	C₂²⋊D₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	1	no	—
174	C₂×Dic₄₃	—	4	1	no	—
175	D₁₇₂	—	2	2	no	—
176	D₁₇₂	—	2	2	no	—
177	C₄×D₄₃	—	4	4	no	—
178	C₄×D₄₃	—	4	2	no	—
179	C₄×D₄₃	—	4	2	no	—
180	C₄×D₄₃	—	8	2	no	—
181	Dic₈₆	—	2	2	no	—
182	Dic₈₆	—	2	2	no	—
183	C₈×C₄₃	—	2	2	no	—
184	C₈×C₄₃	—	4	2	no	—
185	C₈×C₄₃	—	4	2	no	—
186	C₈×C₄₃	#117	1	2	yes	—
187	C₈×C₄₃	#117	1	2	yes	—
188	C₄₃⋊C₈	—	2	1	no	—
189	C₄₃⋊C₈	—	2	1	no	—
190	C₄₃⋊C₈	—	2	2	no	—
191	#22804	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂²×C₄₃	#555	1	1	yes	characteristic
196	C₂²×C₄₃	#556	1	1	yes	characteristic
197	C₂×D₄₃	—	4	2	no	—
198	C₂×D₄₃	—	4	2	no	—
199	C₂×D₄₃	—	4	2	no	—
200	C₄×C₄₃	—	2	2	no	—
201	C₄×C₄₃	—	2	2	no	—
202	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
203	C₄×C₄₃	#520	1	1	yes	characteristic
204	C₄×C₄₃	#547	1	1	yes	characteristic
205	C₄×C₄₃	#550	1	1	yes	characteristic
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	4	2	no	—
208	Dic₄₃	—	4	2	no	—
209	Dic₄₃	—	4	2	no	—
210	Dic₄₃	—	8	1	no	—
211	#2943	—	43	1	no	—
212	#2925	—	43	2	no	—
213	#1975	—	43	1	no	—
214	#1974	—	43	1	no	—
215	#1929	—	43	2	no	—
216	#1929	—	43	2	no	—
217	#1849	D₄₃	1	1	yes	characteristic, complemented
218	#1806	—	43	2	no	—
219	#1773	—	43	1	no	—
220	#1772	—	43	1	no	—
221	#1771	—	43	1	no	—
222	C₂×C₄₃	—	2	1	no	—
223	C₂×C₄₃	—	2	1	no	—
224	C₂×C₄₃	#2354	1	1	yes	characteristic
225	C₂×C₄₃	#2955	1	1	yes	characteristic
226	C₂×C₄₃	#2956	1	1	yes	characteristic
227	D₄₃	—	8	2	no	—
228	C₂×#135	—	43	1	no	—
229	C₄×#41	—	43	2	no	—
230	#442	—	43	2	no	—
231	#441	—	43	2	no	—
232	#440	—	43	2	no	—
233	#440	—	43	2	no	—
234	#433	—	86	2	no	—
235	#433	—	86	2	no	—
236	#432	—	86	2	no	—
237	#431	—	86	2	no	—
238	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
239	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
240	C₂×#108	C₂×D₄₃	1	2	yes	—
241	#427	—	43	1	no	—
242	#423	C₂×D₄₃	1	2	yes	—
243	C₂×C₄⋊C₈	—	43	1	no	—
244	C₂×#104	—	43	2	no	—
245	C₂×#104	—	43	2	no	—
246	#416	—	43	2	no	—
247	#408	—	43	2	no	—
248	#408	—	43	2	no	—
249	#405	—	43	2	no	—
250	#405	—	43	2	no	—
251	C₂×#97	—	43	1	no	—
252	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
253	C₂×C₄×C₈	—	43	1	no	—
254	C₄×C₄⋊C₄	—	43	1	no	—
255	#339	—	43	2	no	—
256	#339	—	43	2	no	—
257	#336	—	43	1	no	—
258	#336	—	43	1	no	—
259	C₄₃	#22804	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	43	2	no	—
261	#135	—	86	2	no	—
262	#135	—	86	2	no	—
263	C₂×Q₁₆	—	43	1	no	—
264	C₂×SD₁₆	—	43	2	no	—
265	C₂×D₈	—	43	1	no	—
266	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
267	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
268	C₂²×C₈	—	43	1	no	—
269	C₂²×C₈	—	43	1	no	—
270	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
272	C₄×Q₈	—	43	2	no	—
273	C₄×Q₈	—	43	2	no	—
274	C₄×D₄	—	43	2	no	—
275	C₄×D₄	—	43	2	no	—
276	C₄×D₄	—	86	2	no	—
277	C₄×D₄	—	86	2	no	—
278	#117	—	43	2	no	—
279	#117	—	86	2	no	—
280	C₂×C₄⋊C₄	—	86	1	no	—
281	C₂×C₄²	—	43	1	no	—
282	C₂×C₄²	—	43	1	no	—
283	C₂×C₄²	—	86	2	no	—
284	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
285	#108	—	2	2	no	—
286	#108	—	2	2	no	—
287	#108	—	4	2	no	—
288	#107	—	43	1	no	—
289	#107	—	43	1	no	—
290	#106	—	43	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	43	2	no	—
294	C₄⋊C₈	—	43	2	no	—
295	#104	—	172	2	no	—
296	#104	—	172	2	no	—
297	#103	—	43	2	no	—
298	#103	—	43	2	no	—
299	#102	—	43	2	no	—
300	#102	—	43	2	no	—
301	C₂²⋊C₈	—	86	2	no	—
302	C₂²⋊C₈	—	86	2	no	—
303	C₂²⋊C₈	—	86	2	no	—
304	C₂²⋊C₈	—	86	2	no	—
305	#97	—	86	2	no	—
306	#97	—	86	2	no	—
307	#97	—	86	2	no	—
308	#97	C₄×D₄₃	1	2	yes	—
309	#97	C₄×D₄₃	1	2	yes	—
310	C₄×C₈	—	86	2	no	—
311	C₄×C₈	—	86	2	no	—
312	C₄×C₈	—	86	2	no	—
313	#95	—	86	1	no	—
314	#41	—	86	2	no	—
315	#41	—	86	2	no	—
316	#41	—	86	2	no	—
317	#41	—	86	2	no	—
318	C₂×Q₈	—	43	2	no	—
319	C₂×D₄	—	43	2	no	—
320	C₂×D₄	—	86	2	no	—
321	C₂²×C₄	—	86	1	no	—
322	C₂²×C₄	—	86	2	no	—
323	C₂²×C₄	—	86	2	no	—
324	C₂²×C₄	—	86	2	no	—
325	C₂²×C₄	—	86	1	no	—
326	C₂²×C₄	#10621902	1	1	yes	characteristic
327	C₂²×C₄	#10621902	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
329	Q₁₆	—	86	2	no	—
330	SD₁₆	—	86	4	no	—
331	D₈	—	86	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	43	1	no	—
341	C₂×C₈	—	43	2	no	—
342	C₂×C₈	—	43	1	no	—
343	C₂×C₈	—	86	1	no	—
344	C₂×C₈	—	86	1	no	—
345	C₂×C₈	—	86	1	no	—
346	C₂×C₈	—	86	1	no	—
347	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
348	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂×C₈	#10621900	1	2	yes	—
351	C₂×C₈	#10621902	1	2	yes	—
352	C₄⋊C₄	—	43	2	no	—
353	C₄⋊C₄	—	43	2	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	—	86	2	no	—
356	C₄⋊C₄	—	172	2	no	—
357	C₂²⋊C₄	—	86	2	no	—
358	C₂²⋊C₄	—	86	2	no	—
359	C₂²⋊C₄	—	86	2	no	—
360	C₄²	—	86	2	no	—
361	C₄²	—	86	2	no	—
362	C₄²	—	86	2	no	—
363	C₄²	—	86	1	no	—
364	C₄²	—	86	1	no	—
365	C₄²	—	86	1	no	—
366	C₄²	—	86	1	no	—
367	C₄²	C₂×C₄×D₄₃	1	2	yes	—
368	C₄²	D₄×D₄₃	1	2	yes	—
369	C₂³	—	86	2	no	—
370	C₂³	C₂×#10621902	1	1	yes	characteristic
371	Q₈	—	86	2	no	—
372	Q₈	—	86	2	no	—
373	D₄	—	86	2	no	—
374	D₄	—	86	2	no	—
375	D₄	—	172	2	no	—
376	D₄	—	172	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	86	2	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	86	2	no	—
383	C₂×C₄	—	344	2	no	—
384	C₂×C₄	—	172	4	no	—
385	C₂×C₄	—	172	1	no	—
386	C₂×C₄	—	172	1	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	—	172	1	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	—	172	2	no	—
391	C₂×C₄	—	172	2	no	—
392	C₂×C₄	#13063287	1	2	yes	—
393	C₂×C₄	#13063287	1	2	yes	—
394	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
397	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
398	C₂×C₄	#13063370	1	1	yes	characteristic
399	C₂×C₄	#13063373	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	86	1	no	—
404	C₈	—	86	2	no	—
405	C₈	—	86	1	no	—
406	C₈	#13063283	1	2	yes	—
407	C₈	#13063283	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	172	2	no	—
411	C₂²	—	172	2	no	—
412	C₂²	—	172	2	no	—
413	C₂²	C₂×#13063287	1	1	yes	characteristic
414	C₂²	#14583615	1	1	yes	characteristic
415	C₂²	#14583623	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	344	1	no	—
419	C₄	—	172	2	no	—
420	C₄	—	172	2	no	—
421	C₄	—	172	2	no	—
422	C₄	—	172	2	no	—
423	C₄	C₂×#13063283	1	1	yes	characteristic
424	C₄	#14583380	1	1	yes	characteristic
425	C₄	#14583552	1	1	yes	characteristic
426	C₄	#14583569	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	344	2	no	—
430	C₂	#19137546	1	1	yes	characteristic
431	C₂	#19143497	1	1	yes	characteristic
432	C₂	#19143504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1849	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063347	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1849	D₄₃
hypocenter	C₄₃	#22804
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1849

Complements

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

N	H ≅ G/N	type
2. #19143263	C₂	semidirect
5. #19135242	C₂	semidirect
6. #19135242	C₂	semidirect
7. #19134612	C₂	semidirect
8. #19134482	C₂	semidirect
9. #19134477	C₂	semidirect
10. #19134467	C₂	semidirect
11. C₄₃×#1849	C₂	semidirect
14. #14583012	C₄	semidirect
15. #14583007	C₄	semidirect
16. #14583001	C₄	semidirect
17. #14583001	C₄	semidirect
217. #1849	D₄₃	semidirect
259. C₄₃	#22804	semidirect

Maximal subgroups

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

subgroup	index
#19143397	2
#19143263	2
#19135486	2
#19135481	2
#19135242	2
#19134612	2
#19134482	2
#19134477	2
#19134467	2
C₄₃×#1849	2
#22804	43