Subgroups — #25110531

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145076	C₂	1	1	yes	maximal, characteristic
2	#19143511	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143447	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135493	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135125	C₂	1	2	yes	maximal, complemented
6	#19135119	C₂	1	2	yes	maximal, complemented
7	#19135080	C₂	1	2	yes	maximal, complemented
8	#19135078	C₂	1	2	yes	maximal, complemented
9	#19134720	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134350	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063351	C₂²	1	2	yes	—
13	C₂×#13063347	C₂²	1	1	yes	characteristic
14	#14583665	C₂²	1	2	yes	—
15	#14583466	C₂²	1	2	yes	—
16	#14583374	C₂²	1	2	yes	—
17	#14583287	C₄	1	4	yes	complemented
18	#14583282	C₄	1	2	yes	complemented
19	#14583274	C₄	1	2	yes	complemented
20	#14583020	—	2	2	no	—
21	#14583015	—	2	2	no	—
22	#14583011	—	2	2	no	—
23	D₈×Dic₄₃	—	2	2	no	—
24	#14582937	C₂²	1	1	yes	characteristic
25	#14582915	C₂²	1	2	yes	—
26	#14582915	C₂²	1	2	yes	—
27	#14582904	C₂²	1	2	yes	—
28	#14582872	C₂²	1	2	yes	—
29	#14582854	C₂²	1	1	yes	characteristic
30	#14582854	C₂²	1	1	yes	characteristic
31	#14582671	C₂²	1	2	yes	—
32	C₄₃⋊#338	C₂²	1	1	yes	characteristic
33	#14582656	C₂²	1	2	yes	—
34	#14582656	C₂²	1	1	yes	characteristic
35	#14582655	C₂²	1	1	yes	characteristic
36	#14582655	C₂²	1	1	yes	characteristic
37	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#418	C₂²	1	2	yes	—
40	C₂×#100×C₄₃	C₂²	1	2	yes	—
41	C₄₃×#405	C₂²	1	1	yes	characteristic
42	C₂×#10621898	C₂³	1	2	yes	—
43	#13063351	—	4	2	no	—
44	#13063351	—	4	2	no	—
45	#13063347	—	2	1	no	—
46	#13063347	—	2	1	no	—
47	#13063347	—	2	1	no	—
48	#13063347	—	2	1	no	—
49	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#10621873	C₂×C₄	1	2	yes	complemented
51	C₂×#10621883	C₂×C₄	1	4	yes	complemented
52	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂×#10621882	C₂×C₄	1	4	yes	complemented
54	#13063333	—	2	4	no	—
55	#13063331	—	4	2	no	—
56	C₂×#10621877	C₂³	1	1	yes	characteristic
57	C₂×#10621877	C₂³	1	1	yes	characteristic
58	M₁₆×D₄₃	—	4	2	no	—
59	#13063321	C₂×C₄	1	4	yes	complemented
60	#13063312	C₂×C₄	1	4	yes	complemented
61	#13063296	—	4	2	no	—
62	#13063294	—	4	2	no	—
63	D₄×Dic₄₃	—	2	4	no	—
64	D₄×Dic₄₃	—	4	2	no	—
65	#13063284	C₂³	1	2	yes	—
66	#13063284	C₂³	1	1	yes	characteristic
67	#13063284	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊Dic₄₃	—	4	2	no	—
69	#13063259	—	2	1	no	—
70	#13063257	—	2	1	no	—
71	#13063251	—	2	4	no	—
72	#13063251	—	4	2	no	—
73	#13063246	—	2	4	no	—
74	#13063239	—	4	2	no	—
75	#13063235	C₂×C₄	1	2	yes	complemented
76	#13063235	D₄	1	2	yes	complemented
77	C₈×Dic₄₃	C₂×C₄	1	2	yes	complemented
78	C₈×Dic₄₃	D₄	1	2	yes	complemented
79	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
80	C₂×D₈×C₄₃	—	2	1	no	—
81	C₂×D₈×C₄₃	—	2	1	no	—
82	C₂×D₈×C₄₃	—	2	1	no	—
83	C₂×D₈×C₄₃	—	2	1	no	—
84	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×D₈×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
87	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	#117×C₄₃	C₂³	1	1	yes	characteristic
90	#108×C₄₃	—	2	1	no	—
91	#108×C₄₃	—	2	1	no	—
92	#102×C₄₃	—	4	2	no	—
93	#100×C₄₃	—	4	2	no	—
94	#97×C₄₃	—	2	1	no	—
95	C₄×C₈×C₄₃	—	2	1	no	—
96	C₂⁴×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₃	—	2	2	no	—
105	C₂×C₂²⋊D₄₃	—	4	4	no	—
106	C₂²×Dic₄₃	—	4	4	no	—
107	#10621898	—	2	2	no	—
108	#10621898	—	2	2	no	—
109	#10621898	—	2	2	no	—
110	#10621898	—	2	2	no	—
111	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₄₃	—	2	2	no	—
113	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
114	D₈×C₄₃	—	2	2	no	—
115	D₈×C₄₃	—	2	2	no	—
116	D₈×C₄₃	—	2	2	no	—
117	D₈×C₄₃	—	2	2	no	—
118	M₁₆×C₄₃	—	2	2	no	—
119	M₁₆×C₄₃	—	2	1	no	—
120	M₁₆×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
129	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₂²⋊C₄×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₂²⋊Dic₄₃	—	2	1	no	—
134	C₂²⋊Dic₄₃	—	2	1	no	—
135	C₂²⋊Dic₄₃	—	2	2	no	—
136	C₂²⋊Dic₄₃	—	4	4	no	—
137	C₂²⋊Dic₄₃	—	4	4	no	—
138	#10621883	—	4	4	no	—
139	#10621882	—	4	4	no	—
140	C₄⋊Dic₄₃	—	2	1	no	—
141	C₄⋊Dic₄₃	—	2	1	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄×Dic₄₃	—	2	2	no	—
144	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
145	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
146	#10621877	—	2	1	no	—
147	#10621877	—	2	1	no	—
148	#10621877	—	2	1	no	—
149	#10621877	—	2	1	no	—
150	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
152	Dic₁₇₂	—	2	1	no	—
153	Dic₁₇₂	—	2	1	no	—
154	D₃₄₄	—	2	1	no	—
155	D₃₄₄	—	2	1	no	—
156	#10621873	—	2	2	no	—
157	#10621873	—	2	2	no	—
158	#10621872	—	4	4	no	—
159	C₈×D₄₃	—	4	4	no	—
160	C₂³×C₄₃	—	2	4	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	16	2	no	—
164	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂²×D₄₃	—	2	2	no	—
166	D₄×C₄₃	—	2	4	no	—
167	D₄×C₄₃	—	2	4	no	—
168	D₄×C₄₃	—	4	2	no	—
169	D₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²⋊D₄₃	—	4	2	no	—
178	C₂²⋊D₄₃	—	4	2	no	—
179	C₂²⋊D₄₃	—	16	4	no	—
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	4	2	no	—
184	C₂×Dic₄₃	—	16	4	no	—
185	D₁₇₂	—	2	2	no	—
186	D₁₇₂	—	2	2	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	—	4	2	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	2	2	no	—
191	C₈×C₄₃	—	4	2	no	—
192	C₈×C₄₃	—	4	1	no	—
193	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
194	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
196	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
197	C₄₃⋊C₈	—	2	2	no	—
198	C₄₃⋊C₈	—	2	2	no	—
199	#22286	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	—	4	1	no	—
201	C₂²×C₄₃	—	4	4	no	—
202	C₂²×C₄₃	—	8	4	no	—
203	C₂²×C₄₃	—	8	4	no	—
204	C₂²×C₄₃	—	16	2	no	—
205	C₂²×C₄₃	#518	1	1	yes	characteristic
206	C₂²×C₄₃	#535	1	1	yes	characteristic
207	C₂²×C₄₃	#540	1	1	yes	characteristic
208	C₂×D₄₃	—	4	2	no	—
209	C₂×D₄₃	—	8	2	no	—
210	C₄×C₄₃	—	8	1	no	—
211	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₄₃	#518	1	1	yes	characteristic
213	C₄×C₄₃	#535	1	1	yes	characteristic
214	C₄×C₄₃	#540	1	1	yes	characteristic
215	Dic₄₃	—	4	2	no	—
216	Dic₄₃	—	4	2	no	—
217	Dic₄₃	—	4	2	no	—
218	Dic₄₃	—	8	2	no	—
219	#3155	—	43	1	no	—
220	#2957	—	43	1	no	—
221	#2948	—	43	1	no	—
222	#1978	D₄₃	1	1	yes	characteristic, complemented
223	#1976	—	43	1	no	—
224	#1911	—	43	2	no	—
225	#1910	—	43	2	no	—
226	#1904	—	43	2	no	—
227	#1903	—	43	2	no	—
228	#1833	—	43	1	no	—
229	#1747	—	43	1	no	—
230	C₂×C₄₃	—	2	1	no	—
231	C₂×C₄₃	—	2	1	no	—
232	C₂×C₄₃	—	2	1	no	—
233	C₂×C₄₃	—	8	4	no	—
234	C₂×C₄₃	#2328	1	1	yes	characteristic
235	D₄₃	—	8	2	no	—
236	C₂×AGL(1,ℤ/8)	—	43	2	no	—
237	C₂×#135	—	43	1	no	—
238	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
239	#568	—	43	2	no	—
240	#535	—	43	2	no	—
241	#518	—	43	2	no	—
242	#496	—	43	4	no	—
243	#495	—	43	2	no	—
244	#493	—	43	2	no	—
245	#444	—	86	2	no	—
246	#443	—	86	2	no	—
247	#442	—	86	2	no	—
248	C₄×D₈	—	86	2	no	—
249	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
250	#427	—	43	1	no	—
251	#421	—	43	2	no	—
252	#421	—	43	2	no	—
253	#418	—	43	2	no	—
254	#418	C₂×D₄₃	1	2	yes	—
255	C₂×#100	C₂×D₄₃	1	2	yes	—
256	#410	—	43	2	no	—
257	#405	—	43	1	no	—
258	#405	—	43	1	no	—
259	#405	C₂×D₄₃	1	1	yes	characteristic
260	#344	—	43	2	no	—
261	#338	—	43	1	no	—
262	H(3,ℤ/4)	—	43	2	no	—
263	H(3,ℤ/4)	—	43	1	no	—
264	H(3,ℤ/4)	—	43	1	no	—
265	H(3,ℤ/4)	—	43	1	no	—
266	C₄₃	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	43	2	no	—
268	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
269	AGL(1,ℤ/8)	—	172	2	no	—
270	AGL(1,ℤ/8)	—	172	2	no	—
271	#135	—	86	1	no	—
272	#135	—	86	1	no	—
273	#135	—	86	1	no	—
274	#135	—	86	1	no	—
275	C₂×Q₁₆	—	43	1	no	—
276	C₂×SD₁₆	—	43	4	no	—
277	C₂×SD₁₆	—	43	2	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	43	4	no	—
283	C₂×D₈	—	43	1	no	—
284	C₂×D₈	C₄×D₄₃	1	2	yes	—
285	C₂×D₈	C₄×D₄₃	1	2	yes	—
286	#131	—	86	4	no	—
287	#131	—	172	2	no	—
288	C₂×M₁₆	—	43	1	no	—
289	C₂×M₁₆	—	43	1	no	—
290	C₂×M₁₆	—	172	2	no	—
291	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
292	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
294	#127	—	43	4	no	—
295	#124	—	43	4	no	—
296	#121	—	172	2	no	—
297	#120	—	172	2	no	—
298	C₄×D₄	—	86	4	no	—
299	C₄×D₄	—	172	2	no	—
300	#117	—	43	1	no	—
301	#117	—	43	1	no	—
302	#117	—	43	2	no	—
303	#117	C₂²×D₄₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	172	2	no	—
305	#108	—	2	1	no	—
306	#108	—	2	1	no	—
307	#107	—	86	1	no	—
308	#106	—	86	1	no	—
309	#104	—	86	4	no	—
310	#104	—	172	2	no	—
311	#102	—	4	2	no	—
312	#102	—	86	4	no	—
313	#100	—	4	2	no	—
314	#99	—	172	2	no	—
315	#97	—	2	1	no	—
316	#97	—	43	2	no	—
317	#97	—	43	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	43	2	no	—
320	C₄×C₈	—	43	2	no	—
321	C₂⁴	—	2	2	no	—
322	#41	—	86	2	no	—
323	#41	—	86	2	no	—
324	#41	—	86	2	no	—
325	#41	—	86	2	no	—
326	C₂×Q₈	—	43	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	43	2	no	—
333	C₂×D₄	—	86	2	no	—
334	C₂×D₄	—	172	4	no	—
335	C₂×D₄	C₂×C₄×D₄₃	1	4	yes	—
336	C₂²×C₄	—	86	2	no	—
337	C₂²×C₄	—	172	4	no	—
338	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
339	Q₁₆	—	86	1	no	—
340	Q₁₆	—	86	1	no	—
341	SD₁₆	—	86	2	no	—
342	SD₁₆	—	86	2	no	—
343	SD₁₆	—	172	4	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	86	1	no	—
349	D₈	—	86	1	no	—
350	D₈	—	172	4	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	86	1	no	—
356	M₁₆	—	86	1	no	—
357	M₁₆	—	86	1	no	—
358	M₁₆	—	86	1	no	—
359	M₁₆	—	172	4	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	43	2	no	—
363	C₂×C₈	—	43	2	no	—
364	C₂×C₈	—	172	4	no	—
365	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
367	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
368	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
369	C₂×C₈	#10621900	1	1	yes	characteristic
370	C₂×C₈	#10621900	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	86	1	no	—
373	C₄⋊C₄	—	86	1	no	—
374	C₄⋊C₄	—	86	2	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	86	1	no	—
377	C₂²⋊C₄	—	86	1	no	—
378	C₂²⋊C₄	—	86	2	no	—
379	C₂²⋊C₄	—	172	4	no	—
380	C₂²⋊C₄	—	172	4	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	43	2	no	—
383	C₄²	—	43	2	no	—
384	C₄²	—	86	2	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	16	2	no	—
389	C₂³	—	86	2	no	—
390	C₂³	#13063371	1	1	yes	characteristic
391	Q₈	—	86	2	no	—
392	Q₈	—	86	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	86	2	no	—
398	D₄	—	86	2	no	—
399	D₄	—	172	2	no	—
400	D₄	—	172	2	no	—
401	D₄	—	688	4	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	86	2	no	—
404	C₂×C₄	—	86	2	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	688	4	no	—
410	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
413	C₂×C₄	#13063370	1	1	yes	characteristic
414	C₂×C₄	#13063370	1	1	yes	characteristic
415	C₂×C₄	#13063371	1	1	yes	characteristic
416	C₈	—	4	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	86	2	no	—
419	C₈	—	86	2	no	—
420	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
421	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
422	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
423	C₈	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	16	2	no	—
429	C₂²	—	344	2	no	—
430	C₂²	—	172	2	no	—
431	C₂²	#14583371	1	1	yes	characteristic
432	C₂²	#14583467	1	1	yes	characteristic
433	C₂²	#14583502	1	1	yes	characteristic
434	C₄	—	8	1	no	—
435	C₄	—	344	2	no	—
436	C₄	—	172	2	no	—
437	C₄	—	172	2	no	—
438	C₄	—	172	2	no	—
439	C₄	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
440	C₄	#14583371	1	1	yes	characteristic
441	C₄	#14583462	1	1	yes	characteristic
442	C₄	#14583502	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	344	2	no	—
448	C₂	#19137319	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19137319
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1978	C₂
socle	C₂×C₄₃	#2328
prime radical	#19145076	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1978	D₄₃
hypocenter	C₄₃	#22286
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1978

Complements

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

N	H ≅ G/N	type
2. #19143511	C₂	semidirect
3. #19143447	C₂	semidirect
4. #19135493	C₂	semidirect
5. #19135125	C₂	semidirect
6. #19135119	C₂	semidirect
7. #19135080	C₂	semidirect
8. #19135078	C₂	semidirect
9. #19134720	C₂	semidirect
10. #19134350	C₂	semidirect
11. C₄₃×#1978	C₂	semidirect
17. #14583287	C₄	semidirect
18. #14583282	C₄	semidirect
19. #14583274	C₄	semidirect
49. C₂×Dic₁₇₂	C₂×C₄	semidirect
50. C₂×#10621873	C₂×C₄	semidirect
51. C₂×#10621883	C₂×C₄	semidirect
52. C₂×D₃₄₄	C₂×C₄	semidirect
53. C₂×#10621882	C₂×C₄	semidirect
59. #13063321	C₂×C₄	semidirect
60. #13063312	C₂×C₄	semidirect
75. #13063235	C₂×C₄	semidirect
76. #13063235	D₄	semidirect
77. C₈×Dic₄₃	C₂×C₄	semidirect
78. C₈×Dic₄₃	D₄	semidirect
222. #1978	D₄₃	semidirect
266. C₄₃	#22286	semidirect

Maximal subgroups

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

subgroup	index
#19145076	2
#19143511	2
#19143447	2
#19135493	2
#19135125	2
#19135119	2
#19135080	2
#19135078	2
#19134720	2
#19134350	2
C₄₃×#1978	2
#22286	43