Subgroups — #24990777

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137542	C₂	1	1	yes	maximal, characteristic
2	#19134754	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134592	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
5	#19132479	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063283	—	2	1	no	—
10	C₂×#13063258	—	2	2	no	—
11	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×#13063245	—	2	1	no	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	#14582801	—	2	1	no	—
15	#14582791	—	2	2	no	—
16	#14582769	C₂²	1	1	yes	characteristic
17	#14582756	—	2	1	no	—
18	C₄×C₄⋊Dic₄₃	—	2	1	no	—
19	#14582661	—	2	1	no	—
20	#14582626	C₄	1	4	yes	complemented
21	C₂×#106×C₄₃	—	2	1	no	—
22	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#384	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#340	—	2	1	no	—
26	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₄₃	—	2	1	no	—
28	C₂²×C₄₃⋊C₈	—	2	1	no	—
29	C₂²×C₄₃⋊C₈	—	2	1	no	—
30	C₄×D₁₇₂	—	2	1	no	—
31	C₄×D₁₇₂	—	2	1	no	—
32	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
33	C₄×D₁₇₂	Q₈	1	2	yes	—
34	#13063283	—	4	2	no	—
35	#13063283	—	4	2	no	—
36	C₂×C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
40	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
41	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
42	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
43	C₂×C₄×Dic₄₃	—	2	2	no	—
44	#13063258	—	4	4	no	—
45	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
46	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
47	#13063245	—	4	2	no	—
48	C₄×C₄₃⋊C₈	—	2	1	no	—
49	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
50	C₄₃⋊#95	—	2	2	no	—
51	C₂²×C₈×C₄₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₃	—	2	1	no	—
58	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
59	#106×C₄₃	—	4	2	no	—
60	C₄⋊C₈×C₄₃	—	2	1	no	—
61	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
62	#95×C₄₃	—	2	1	no	—
63	C₂³×D₄₃	—	2	1	no	—
64	C₂²×C₄×C₄₃	—	2	1	no	—
65	C₂²×C₄×C₄₃	—	2	1	no	—
66	C₂²×C₄×C₄₃	—	4	1	no	—
67	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×Dic₄₃	—	2	1	no	—
71	C₂²×Dic₄₃	—	2	2	no	—
72	C₂×D₁₇₂	—	2	1	no	—
73	C₂×D₁₇₂	—	2	1	no	—
74	C₂×D₁₇₂	—	2	1	no	—
75	C₂×D₁₇₂	—	2	1	no	—
76	C₂×D₁₇₂	—	2	1	no	—
77	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
78	C₂×C₄×D₄₃	—	2	2	no	—
79	C₂×C₄×D₄₃	—	2	2	no	—
80	C₂×C₄×D₄₃	—	4	1	no	—
81	C₂×C₄×D₄₃	—	4	1	no	—
82	C₂×C₄×D₄₃	—	4	1	no	—
83	C₂×C₄×D₄₃	—	4	1	no	—
84	C₂×C₈×C₄₃	—	2	2	no	—
85	C₂×C₈×C₄₃	—	4	1	no	—
86	C₂×C₈×C₄₃	—	4	1	no	—
87	C₄⋊C₄×C₄₃	—	2	1	no	—
88	C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₄⋊C₄×C₄₃	—	4	2	no	—
91	C₄⋊C₄×C₄₃	—	4	1	no	—
92	C₄⋊C₄×C₄₃	—	4	1	no	—
93	C₄⋊C₄×C₄₃	—	4	1	no	—
94	C₄⋊C₄×C₄₃	—	4	1	no	—
95	C₄⋊C₄×C₄₃	D₈	1	2	yes	—
96	C₄²×C₄₃	—	4	1	no	—
97	C₄²×C₄₃	—	4	1	no	—
98	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
100	C₄²×C₄₃	#41	1	1	yes	characteristic
101	C₄²×C₄₃	#41	1	1	yes	characteristic
102	(C₂×D₄₃)⋊C₄	—	2	2	no	—
103	(C₂×D₄₃)⋊C₄	—	2	2	no	—
104	(C₂×D₄₃)⋊C₄	—	4	4	no	—
105	(C₂×D₄₃)⋊C₄	—	8	2	no	—
106	C₄⋊Dic₄₃	—	2	1	no	—
107	C₄⋊Dic₄₃	—	4	1	no	—
108	C₄⋊Dic₄₃	—	4	1	no	—
109	C₄⋊Dic₄₃	—	4	1	no	—
110	C₄⋊Dic₄₃	—	4	1	no	—
111	C₄⋊Dic₄₃	—	4	2	no	—
112	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
113	C₄×Dic₄₃	—	4	4	no	—
114	C₂×C₄₃⋊C₈	—	2	2	no	—
115	C₂×C₄₃⋊C₈	—	2	2	no	—
116	C₂×C₄₃⋊C₈	—	2	2	no	—
117	C₂×C₄₃⋊C₈	—	4	1	no	—
118	C₂×C₄₃⋊C₈	—	4	1	no	—
119	C₂×C₄₃⋊C₈	—	4	1	no	—
120	C₂³×C₄₃	#120	1	1	yes	characteristic
121	C₂²×D₄₃	—	2	2	no	—
122	C₂²×D₄₃	—	4	1	no	—
123	C₂²×D₄₃	—	4	1	no	—
124	C₂²×D₄₃	—	4	1	no	—
125	C₂²×D₄₃	—	4	1	no	—
126	C₂²×D₄₃	—	4	1	no	—
127	C₂²×D₄₃	—	4	1	no	—
128	C₂×C₄×C₄₃	—	2	1	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	2	no	—
131	C₂×C₄×C₄₃	—	4	1	no	—
132	C₂×C₄×C₄₃	—	4	1	no	—
133	C₂×C₄×C₄₃	—	4	1	no	—
134	C₂×C₄×C₄₃	—	4	1	no	—
135	C₂×C₄×C₄₃	—	4	1	no	—
136	C₂×C₄×C₄₃	—	8	1	no	—
137	C₂×C₄×C₄₃	—	8	1	no	—
138	C₂×C₄×C₄₃	—	8	1	no	—
139	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
147	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
148	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
149	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
152	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
153	C₂×Dic₄₃	—	2	2	no	—
154	C₂×Dic₄₃	—	4	1	no	—
155	C₂×Dic₄₃	—	4	1	no	—
156	C₂×Dic₄₃	—	4	2	no	—
157	C₂×Dic₄₃	—	4	2	no	—
158	C₂×Dic₄₃	—	4	2	no	—
159	D₁₇₂	—	2	2	no	—
160	D₁₇₂	—	2	2	no	—
161	D₁₇₂	—	4	1	no	—
162	D₁₇₂	—	4	1	no	—
163	C₄×D₄₃	—	4	2	no	—
164	C₄×D₄₃	—	4	2	no	—
165	C₄×D₄₃	—	4	2	no	—
166	C₄×D₄₃	—	4	2	no	—
167	C₈×C₄₃	—	4	2	no	—
168	C₄₃⋊C₈	—	2	4	no	—
169	C₄₃⋊C₈	—	8	1	no	—
170	#8885	—	43	1	no	maximal, Sylow
171	C₂²×C₄₃	#385	1	1	yes	characteristic
172	C₂²×C₄₃	#447	1	1	yes	characteristic
173	C₂²×C₄₃	#449	1	1	yes	characteristic
174	C₂²×C₄₃	#452	1	1	yes	characteristic
175	C₂²×C₄₃	#452	1	1	yes	characteristic
176	C₂²×C₄₃	#453	1	1	yes	characteristic
177	C₂²×C₄₃	#456	1	1	yes	characteristic
178	C₂×D₄₃	—	4	2	no	—
179	C₂×D₄₃	—	4	2	no	—
180	C₂×D₄₃	—	4	2	no	—
181	C₂×D₄₃	—	8	1	no	—
182	C₂×D₄₃	—	8	1	no	—
183	C₂×D₄₃	—	8	1	no	—
184	C₂×D₄₃	—	8	1	no	—
185	C₄×C₄₃	—	2	1	no	—
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	4	2	no	—
188	C₄×C₄₃	—	8	1	no	—
189	C₄×C₄₃	—	16	1	no	—
190	C₄×C₄₃	#427	1	1	yes	characteristic
191	C₄×C₄₃	#428	1	1	yes	characteristic
192	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
193	C₄×C₄₃	#440	1	1	yes	characteristic
194	C₄×C₄₃	#474	1	1	yes	characteristic
195	C₄×C₄₃	#478	1	1	yes	characteristic
196	C₄×C₄₃	#482	1	1	yes	characteristic
197	C₄×C₄₃	#485	1	1	yes	characteristic
198	Dic₄₃	—	4	2	no	—
199	Dic₄₃	—	8	2	no	—
200	#2354	—	43	1	no	—
201	#1948	D₄₃	1	1	yes	characteristic, complemented
202	#1845	—	43	1	no	—
203	#1802	—	43	1	no	—
204	C₂×D₄⋊C₈	—	43	1	no	—
205	#1296	—	43	1	no	—
206	#1279	—	43	1	no	—
207	C₂×C₄₃	#1621	1	1	yes	characteristic
208	C₂×C₄₃	#1634	1	1	yes	characteristic
209	C₂×C₄₃	#1647	1	1	yes	characteristic
210	C₂×C₄₃	#1650	1	1	yes	characteristic
211	C₂×C₄₃	#1854	1	1	yes	characteristic
212	C₂×C₄₃	#1859	1	1	yes	characteristic
213	C₂×C₄₃	#1862	1	1	yes	characteristic
214	D₄₃	—	8	2	no	—
215	C₂×C₄×D₄	—	43	1	no	—
216	C₂×#117	—	86	1	no	—
217	C₂×#107	—	86	2	no	—
218	C₂×#106	—	2	1	no	—
219	C₂×C₄⋊C₈	—	43	1	no	—
220	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
221	C₂×#102	—	86	1	no	—
222	C₂×C₄×C₈	—	43	1	no	—
223	#390	—	86	1	no	—
224	#388	—	86	2	no	—
225	#384	—	43	1	no	—
226	#384	C₂×D₄₃	1	1	yes	characteristic
227	#380	—	86	1	no	—
228	C₄×C₄⋊C₄	—	86	1	no	—
229	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
230	#340	—	2	1	no	—
231	#340	—	86	1	no	—
232	D₄⋊C₈	—	43	4	no	—
233	C₄₃	#8885	1	1	yes	characteristic, complemented, Sylow
234	C₂²×D₄	—	43	1	no	—
235	C₂³×C₄	—	86	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	86	1	no	—
238	C₂²×C₈	—	86	1	no	—
239	C₄×D₄	—	43	2	no	—
240	C₄×D₄	—	43	2	no	—
241	C₄×D₄	—	86	1	no	—
242	C₄×D₄	—	86	1	no	—
243	#117	—	172	2	no	—
244	#117	—	172	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	43	1	no	—
249	C₂×C₄⋊C₄	—	43	2	no	—
250	C₂×C₄⋊C₄	—	86	1	no	—
251	C₂×C₄⋊C₄	—	86	1	no	—
252	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	86	1	no	—
255	C₂×C₂²⋊C₄	—	86	2	no	—
256	C₂×C₂²⋊C₄	—	86	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	86	2	no	—
259	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
260	#107	—	172	4	no	—
261	#106	—	4	2	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	86	1	no	—
264	C₄⋊C₈	—	86	1	no	—
265	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
266	#102	—	172	2	no	—
267	C₄×C₈	—	43	2	no	—
268	C₄×C₈	—	86	1	no	—
269	#95	—	2	1	no	—
270	#95	—	86	2	no	—
271	C₂⁴	—	86	1	no	—
272	C₂×D₄	—	43	2	no	—
273	C₂×D₄	—	86	1	no	—
274	C₂×D₄	—	86	1	no	—
275	C₂×D₄	—	86	1	no	—
276	C₂×D₄	—	86	1	no	—
277	C₂×D₄	—	86	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	86	1	no	—
282	C₂²×C₄	—	86	2	no	—
283	C₂²×C₄	—	86	2	no	—
284	C₂²×C₄	—	86	2	no	—
285	C₂²×C₄	—	172	1	no	—
286	C₂²×C₄	—	172	1	no	—
287	C₂²×C₄	—	172	1	no	—
288	C₂²×C₄	—	172	1	no	—
289	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
290	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	86	2	no	—
296	C₂×C₈	—	86	2	no	—
297	C₂×C₈	—	86	2	no	—
298	C₂×C₈	—	172	1	no	—
299	C₂×C₈	—	172	1	no	—
300	C₂×C₈	—	172	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	43	2	no	—
310	C₄⋊C₄	—	86	1	no	—
311	C₄⋊C₄	—	172	2	no	—
312	C₄⋊C₄	—	172	1	no	—
313	C₄⋊C₄	—	172	1	no	—
314	C₄⋊C₄	—	172	1	no	—
315	C₄⋊C₄	—	172	1	no	—
316	C₄⋊C₄	#10621882	1	2	yes	—
317	C₂²⋊C₄	—	86	2	no	—
318	C₂²⋊C₄	—	86	2	no	—
319	C₂²⋊C₄	—	344	2	no	—
320	C₂²⋊C₄	—	172	4	no	—
321	C₄²	—	4	1	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	172	4	no	—
324	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
325	C₄²	#10621898	1	1	yes	characteristic
326	C₄²	Q₈×D₄₃	1	1	yes	characteristic
327	C₄²	#10621902	1	1	yes	characteristic
328	C₂³	—	86	2	no	—
329	C₂³	—	172	1	no	—
330	C₂³	—	172	1	no	—
331	C₂³	—	172	1	no	—
332	C₂³	—	172	1	no	—
333	C₂³	—	172	1	no	—
334	C₂³	—	172	1	no	—
335	C₂³	#13063293	1	1	yes	characteristic
336	D₄	—	86	2	no	—
337	D₄	—	86	2	no	—
338	D₄	—	172	1	no	—
339	D₄	—	172	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	8	1	no	—
349	C₂×C₄	—	8	1	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	—	86	2	no	—
352	C₂×C₄	—	172	2	no	—
353	C₂×C₄	—	172	2	no	—
354	C₂×C₄	—	172	2	no	—
355	C₂×C₄	—	172	1	no	—
356	C₂×C₄	—	172	1	no	—
357	C₂×C₄	—	172	2	no	—
358	C₂×C₄	—	172	2	no	—
359	C₂×C₄	—	172	2	no	—
360	C₂×C₄	—	172	2	no	—
361	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
362	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
363	C₂×C₄	#13063287	1	1	yes	characteristic
364	C₂×C₄	#13063301	1	1	yes	characteristic
365	C₂×C₄	#13063303	1	1	yes	characteristic
366	C₂×C₄	#13063310	1	1	yes	characteristic
367	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
368	C₂×C₄	#13063345	1	1	yes	characteristic
369	C₂×C₄	#13063346	1	1	yes	characteristic
370	C₂×C₄	#13063346	1	1	yes	characteristic
371	C₂×C₄	#13063350	1	1	yes	characteristic
372	C₂×C₄	#13063352	1	1	yes	characteristic
373	C₂×C₄	#13063354	1	1	yes	characteristic
374	C₂×C₄	#13063356	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	86	4	no	—
377	C₈	—	344	1	no	—
378	C₂²	—	344	1	no	—
379	C₂²	—	344	1	no	—
380	C₂²	—	344	1	no	—
381	C₂²	—	344	1	no	—
382	C₂²	—	172	2	no	—
383	C₂²	—	172	2	no	—
384	C₂²	—	172	2	no	—
385	C₂²	#14582770	1	1	yes	characteristic
386	C₂²	#14583032	1	1	yes	characteristic
387	C₂²	#14583043	1	1	yes	characteristic
388	C₂²	#14583058	1	1	yes	characteristic
389	C₂²	#14583059	1	1	yes	characteristic
390	C₂²	#14583065	1	1	yes	characteristic
391	C₂²	#14583080	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	16	1	no	—
397	C₄	—	344	2	no	—
398	C₄	—	172	2	no	—
399	C₄	#14582934	1	1	yes	characteristic
400	C₄	#14582938	1	1	yes	characteristic
401	C₄	C₄×#10621882	1	1	yes	characteristic
402	C₄	#14582997	1	1	yes	characteristic
403	C₄	#14583176	1	1	yes	characteristic
404	C₄	#14583196	1	1	yes	characteristic
405	C₄	#14583225	1	1	yes	characteristic
406	C₄	#14583243	1	1	yes	characteristic
407	C₂	—	344	2	no	—
408	C₂	#19133658	1	1	yes	characteristic
409	C₂	#19133739	1	1	yes	characteristic
410	C₂	#19133828	1	1	yes	characteristic
411	C₂	#19133850	1	1	yes	characteristic
412	C₂	#19134793	1	1	yes	characteristic
413	C₂	#19134818	1	1	yes	characteristic
414	C₂	#19134841	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063293
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1948	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1948	D₄₃
hypocenter	C₄₃	#8885
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1948

Complements

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

N	H ≅ G/N	type
2. #19134754	C₂	semidirect
5. #19132479	C₂	semidirect
6. #19132436	C₂	semidirect
7. C₄₃×#1948	C₂	semidirect
20. #14582626	C₄	semidirect
201. #1948	D₄₃	semidirect
233. C₄₃	#8885	semidirect

Maximal subgroups

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

subgroup	index
#19137542	2
#19134754	2
#19134592	2
C₂×#14582626	2
#19132479	2
#19132436	2
C₄₃×#1948	2
#8885	43