Subgroups — #25127542

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063325	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063317	C₂	1	1	yes	maximal, characteristic
3	#19136078	C₂	1	2	yes	maximal
4	#19136073	C₂	1	1	yes	maximal, characteristic
5	#19136068	C₂	1	1	yes	maximal, characteristic
6	#19135934	C₂	1	2	yes	maximal
7	#19135929	C₂	1	1	yes	maximal, characteristic
8	#19135924	C₂	1	1	yes	maximal, characteristic
9	#19134492	C₂	1	2	yes	maximal
10	#19134492	C₂	1	2	yes	maximal
11	C₄₃×#1745	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	C₂×#13063317	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₈₆	—	2	1	no	—
15	C₂×#13063259	C₂²	1	2	yes	—
16	C₂×#13063259	C₂²	1	2	yes	—
17	C₂×#13063257	C₂²	1	2	yes	—
18	C₂×#13063257	C₂²	1	2	yes	—
19	#14582805	—	2	1	no	—
20	#14582797	—	2	1	no	—
21	#14582797	C₂²	1	1	yes	characteristic
22	#14582797	C₂²	1	1	yes	characteristic
23	#14582797	C₂²	1	2	yes	—
24	#14582783	—	2	1	no	—
25	#14582783	—	2	1	no	—
26	#14582769	C₂²	1	1	yes	characteristic
27	#14582765	C₂²	1	1	yes	characteristic
28	C₄×Dic₄₃⋊C₄	—	2	1	no	—
29	C₄×Dic₄₃⋊C₄	—	2	1	no	—
30	C₄×C₄⋊Dic₄₃	—	2	1	no	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
34	#14582662	C₂²	1	2	yes	—
35	#14582662	C₂²	1	2	yes	—
36	#14582662	C₂²	1	2	yes	—
37	#14582662	C₂²	1	2	yes	—
38	C₂×#97×C₄₃	C₂²	1	2	yes	—
39	C₄³×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#336	C₂²	1	1	yes	characteristic
41	C₄₃×#336	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Dic₈₆	—	2	1	no	—
44	#13063325	—	2	4	no	—
45	#13063317	—	2	2	no	—
46	#13063317	—	2	2	no	—
47	C₄×Dic₈₆	—	4	4	no	—
48	C₂×C₄⋊Dic₄₃	—	2	1	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
57	C₂×Dic₄₃⋊C₄	—	2	1	no	—
58	C₂×Dic₄₃⋊C₄	—	2	1	no	—
59	C₂×Dic₄₃⋊C₄	—	2	2	no	—
60	C₂×Dic₄₃⋊C₄	—	2	1	no	—
61	C₂×Dic₄₃⋊C₄	—	2	1	no	—
62	C₂×C₄×Dic₄₃	—	2	2	no	—
63	C₂×C₄×Dic₄₃	—	2	1	no	—
64	C₂×C₄×Dic₄₃	—	2	1	no	—
65	#13063259	—	2	4	no	—
66	#13063259	—	2	4	no	—
67	#13063257	—	2	4	no	—
68	#13063257	—	2	4	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	1	no	—
72	C₄₃⋊#95	—	2	1	no	—
73	C₄₃⋊#95	—	2	1	no	—
74	C₄₃⋊#95	—	2	1	no	—
75	C₄₃⋊#95	—	2	1	no	—
76	C₄₃⋊#95	—	2	1	no	—
77	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	#97×C₄₃	Q₈	1	8	yes	complemented
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₃	—	2	1	no	—
95	C₂²×Dic₄₃	—	2	1	no	—
96	C₂²×Dic₄₃	—	2	2	no	—
97	C₂²×Dic₄₃	—	2	1	no	—
98	C₂²×Dic₄₃	—	2	1	no	—
99	C₂²×Dic₄₃	—	2	2	no	—
100	C₂×Dic₈₆	—	2	4	no	—
101	C₂×Dic₈₆	—	4	2	no	—
102	C₂×Dic₈₆	—	4	2	no	—
103	C₂×C₈×C₄₃	—	2	2	no	—
104	C₂×C₈×C₄₃	—	2	2	no	—
105	C₂×C₈×C₄₃	—	2	2	no	—
106	C₂×C₈×C₄₃	—	2	2	no	—
107	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
108	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
109	C₄²×C₄₃	—	2	2	no	—
110	C₄²×C₄₃	—	2	2	no	—
111	C₄²×C₄₃	—	2	1	no	—
112	C₄²×C₄₃	—	2	1	no	—
113	C₄²×C₄₃	—	2	2	no	—
114	C₄²×C₄₃	—	4	1	no	—
115	C₄²×C₄₃	—	4	1	no	—
116	C₄²×C₄₃	C₂×Q₈	1	4	yes	—
117	C₄⋊Dic₄₃	—	2	4	no	—
118	C₄⋊Dic₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	—	2	1	no	—
120	C₄⋊Dic₄₃	—	2	2	no	—
121	C₄⋊Dic₄₃	—	2	2	no	—
122	C₄⋊Dic₄₃	—	2	2	no	—
123	C₄⋊Dic₄₃	—	2	2	no	—
124	C₄⋊Dic₄₃	—	2	2	no	—
125	C₄⋊Dic₄₃	—	4	2	no	—
126	C₄⋊Dic₄₃	—	4	2	no	—
127	C₄⋊Dic₄₃	#41	1	2	yes	—
128	C₄⋊Dic₄₃	#41	1	4	yes	—
129	C₄⋊Dic₄₃	#41	1	2	yes	—
130	Dic₄₃⋊C₄	—	2	4	no	—
131	Dic₄₃⋊C₄	—	2	4	no	—
132	Dic₄₃⋊C₄	—	4	4	no	—
133	Dic₄₃⋊C₄	—	4	2	no	—
134	Dic₄₃⋊C₄	—	4	2	no	—
135	C₄×Dic₄₃	—	4	2	no	—
136	C₄×Dic₄₃	—	4	2	no	—
137	C₄×Dic₄₃	—	4	4	no	—
138	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	1	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
154	C₂×C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₄₃	#137	1	2	yes	—
157	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
159	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₃	—	2	2	no	—
162	C₂×Dic₄₃	—	2	2	no	—
163	C₂×Dic₄₃	—	2	4	no	—
164	C₂×Dic₄₃	—	4	2	no	—
165	C₂×Dic₄₃	—	4	1	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	—	4	1	no	—
175	C₂×Dic₄₃	—	4	1	no	—
176	C₂×Dic₄₃	—	4	1	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	Dic₈₆	—	4	8	no	—
180	C₈×C₄₃	—	2	4	no	—
181	C₈×C₄₃	—	2	4	no	—
182	#23841	—	43	1	no	maximal, Sylow
183	C₂²×C₄₃	#525	1	1	yes	characteristic
184	C₂²×C₄₃	#525	1	1	yes	characteristic
185	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
186	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
188	C₂²×C₄₃	#575	1	1	yes	characteristic
189	C₂²×C₄₃	#575	1	1	yes	characteristic
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	2	no	—
194	C₄×C₄₃	—	4	1	no	—
195	C₄×C₄₃	—	4	1	no	—
196	C₄×C₄₃	#533	1	2	yes	—
197	C₄×C₄₃	#533	1	2	yes	—
198	Dic₄₃	—	4	4	no	—
199	Dic₄₃	—	4	2	no	—
200	Dic₄₃	—	4	2	no	—
201	Dic₄₃	—	8	1	no	—
202	Dic₄₃	—	8	2	no	—
203	Dic₄₃	—	8	1	no	—
204	C₄×C₄⋊Q₈	—	43	1	no	—
205	C₄×#125	—	43	1	no	—
206	#2085	—	43	2	no	—
207	#2084	—	43	1	no	—
208	#2083	—	43	1	no	—
209	#2059	—	43	2	no	—
210	#2058	—	43	1	no	—
211	#2057	—	43	1	no	—
212	#1776	—	43	2	no	—
213	#1776	—	43	2	no	—
214	#1745	D₄₃	1	1	yes	characteristic
215	C₂×C₄₃	#2399	1	1	yes	characteristic
216	C₂×C₄₃	#3114	1	1	yes	characteristic
217	C₂×C₄₃	#3115	1	1	yes	characteristic
218	C₂×C₄₃	#3116	1	1	yes	characteristic
219	C₂×C₄₃	#3117	1	1	yes	characteristic
220	C₂×C₄₃	#3165	1	1	yes	characteristic
221	C₂×C₄₃	#3166	1	1	yes	characteristic
222	C₂×C₄⋊Q₈	—	43	1	no	—
223	C₂×#125	—	43	1	no	—
224	C₂×C₄×Q₈	—	86	1	no	—
225	C₂×#107	—	43	2	no	—
226	C₂×#107	—	43	2	no	—
227	C₂×#106	—	43	2	no	—
228	C₂×#106	—	43	2	no	—
229	C₂×#97	C₂×D₄₃	1	2	yes	—
230	#391	—	86	1	no	—
231	#389	—	43	1	no	—
232	#389	—	43	1	no	—
233	#389	—	43	2	no	—
234	#389	—	86	1	no	—
235	#387	—	86	1	no	—
236	#387	—	86	1	no	—
237	#384	—	43	1	no	—
238	#382	—	43	1	no	—
239	C₄×C₄⋊C₄	—	43	1	no	—
240	C₄×C₄⋊C₄	—	43	1	no	—
241	C₄×C₄⋊C₄	—	43	2	no	—
242	C₄×C₄⋊C₄	—	86	1	no	—
243	C₄×C₄⋊C₄	—	86	1	no	—
244	C₄×C₄⋊C₄	—	86	1	no	—
245	C₄³	C₂×D₄₃	1	1	yes	characteristic
246	#340	—	43	2	no	—
247	#340	—	43	2	no	—
248	#340	—	43	2	no	—
249	#340	—	43	2	no	—
250	#336	C₂×D₄₃	1	1	yes	characteristic
251	#336	C₂×D₄₃	1	1	yes	characteristic
252	#336	C₂×D₄₃	1	2	yes	—
253	C₄₃	#23841	1	1	yes	characteristic, complemented, Sylow
254	C₂²×Q₈	—	86	1	no	—
255	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
256	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
257	C₄⋊Q₈	—	86	4	no	—
258	#125	—	86	2	no	—
259	#125	—	86	2	no	—
260	C₄×Q₈	—	172	4	no	—
261	C₂×C₄⋊C₄	—	43	1	no	—
262	C₂×C₄⋊C₄	—	43	1	no	—
263	C₂×C₄⋊C₄	—	43	2	no	—
264	C₂×C₄⋊C₄	—	43	1	no	—
265	C₂×C₄⋊C₄	—	43	1	no	—
266	C₂×C₄⋊C₄	—	43	2	no	—
267	C₂×C₄⋊C₄	—	86	1	no	—
268	C₂×C₄⋊C₄	—	86	1	no	—
269	C₂×C₄⋊C₄	—	86	1	no	—
270	C₂×C₄⋊C₄	—	86	2	no	—
271	C₂×C₄⋊C₄	—	86	1	no	—
272	C₂×C₄⋊C₄	—	86	1	no	—
273	C₂×C₄⋊C₄	—	86	1	no	—
274	C₂×C₄⋊C₄	—	86	1	no	—
275	C₂×C₄²	—	86	2	no	—
276	C₂×C₄²	—	86	1	no	—
277	C₂×C₄²	—	86	1	no	—
278	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
279	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
280	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
281	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
282	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
283	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
284	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
285	#107	—	86	4	no	—
286	#107	—	86	4	no	—
287	#106	—	86	4	no	—
288	#106	—	86	4	no	—
289	#97	Dic₈₆	1	8	yes	complemented
290	#95	—	86	1	no	—
291	#95	—	86	1	no	—
292	#95	—	86	2	no	—
293	#95	—	86	1	no	—
294	#95	—	86	1	no	—
295	#95	—	86	1	no	—
296	#95	—	86	1	no	—
297	#95	—	86	2	no	—
298	C₂×Q₈	—	86	4	no	—
299	C₂×Q₈	—	172	2	no	—
300	C₂×Q₈	—	172	2	no	—
301	C₂²×C₄	—	86	1	no	—
302	C₂²×C₄	—	86	1	no	—
303	C₂²×C₄	—	86	2	no	—
304	C₂²×C₄	—	86	1	no	—
305	C₂²×C₄	—	86	1	no	—
306	C₂²×C₄	—	86	2	no	—
307	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
313	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
319	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
320	C₄⋊C₄	—	43	2	no	—
321	C₄⋊C₄	—	43	4	no	—
322	C₄⋊C₄	—	43	2	no	—
323	C₄⋊C₄	—	86	4	no	—
324	C₄⋊C₄	—	86	4	no	—
325	C₄⋊C₄	—	86	4	no	—
326	C₄⋊C₄	—	86	1	no	—
327	C₄⋊C₄	—	86	1	no	—
328	C₄⋊C₄	—	86	2	no	—
329	C₄⋊C₄	—	86	2	no	—
330	C₄⋊C₄	—	86	2	no	—
331	C₄⋊C₄	—	86	2	no	—
332	C₄⋊C₄	—	86	2	no	—
333	C₄⋊C₄	—	172	4	no	—
334	C₄⋊C₄	—	172	2	no	—
335	C₄⋊C₄	—	172	2	no	—
336	C₄⋊C₄	—	172	2	no	—
337	C₄⋊C₄	—	172	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	—	172	4	no	—
346	C₄²	—	172	2	no	—
347	C₄²	—	172	2	no	—
348	C₄²	C₂×Dic₈₆	1	4	yes	—
349	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
350	Q₈	—	172	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	86	2	no	—
366	C₂×C₄	—	86	2	no	—
367	C₂×C₄	—	86	4	no	—
368	C₂×C₄	—	172	1	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	—	172	2	no	—
372	C₂×C₄	—	172	1	no	—
373	C₂×C₄	—	172	1	no	—
374	C₂×C₄	—	172	1	no	—
375	C₂×C₄	—	172	1	no	—
376	C₂×C₄	—	172	2	no	—
377	C₂×C₄	—	172	2	no	—
378	C₂×C₄	—	172	1	no	—
379	C₂×C₄	—	172	1	no	—
380	C₂×C₄	—	172	1	no	—
381	C₂×C₄	—	172	1	no	—
382	C₂×C₄	—	172	2	no	—
383	C₂×C₄	#13063325	1	2	yes	—
384	C₂×C₄	#13063325	1	2	yes	—
385	C₂×C₄	#13063353	1	2	yes	—
386	C₂×C₄	#13063358	1	2	yes	—
387	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
388	C₂×C₄	#41×D₄₃	1	2	yes	—
389	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
390	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	2	4	no	—
393	C₂²	#14583411	1	1	yes	characteristic
394	C₂²	#14583411	1	1	yes	characteristic
395	C₂²	C₂×#13063325	1	1	yes	characteristic
396	C₂²	C₂×#13063353	1	1	yes	characteristic
397	C₂²	C₂×#13063358	1	1	yes	characteristic
398	C₂²	#14583699	1	1	yes	characteristic
399	C₂²	#14583699	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	344	1	no	—
407	C₄	—	344	2	no	—
408	C₄	—	344	1	no	—
409	C₄	—	172	4	no	—
410	C₄	—	172	2	no	—
411	C₄	—	172	2	no	—
412	C₄	#14583452	1	2	yes	—
413	C₄	#14583452	1	2	yes	—
414	C₂	#19137888	1	1	yes	characteristic
415	C₂	#19144735	1	1	yes	characteristic
416	C₂	#19144747	1	1	yes	characteristic
417	C₂	#19144758	1	1	yes	characteristic
418	C₂	#19144768	1	1	yes	characteristic
419	C₂	#19145141	1	1	yes	characteristic
420	C₂	#19145147	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1745	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#1745	D₄₃
hypocenter	C₄₃	#23841
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1745

Complements

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

N	H ≅ G/N	type
86. #97×C₄₃	Q₈	semidirect
253. C₄₃	#23841	semidirect
289. #97	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063325	2
C₄×#13063317	2
#19136078	2
#19136073	2
#19136068	2
#19135934	2
#19135929	2
#19135924	2
#19134492	2
C₄₃×#1745	2
#23841	43