Subgroups — #24990786

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137495	C₂	1	1	yes	maximal, characteristic
2	#19135359	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134751	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134596	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
6	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063287	—	2	1	no	—
10	C₂×C₄⋊C₄×D₄₃	—	2	1	no	—
11	C₂×#13063257	—	2	1	no	—
12	C₂×#13063256	—	2	2	no	—
13	C₂×#13063247	—	2	1	no	—
14	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	#14582795	—	2	1	no	—
16	#14582770	—	2	2	no	—
17	#14582769	C₂²	1	1	yes	characteristic
18	#14582756	—	2	1	no	—
19	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
20	#14582662	—	2	1	no	—
21	#14582662	—	2	1	no	—
22	#14582626	C₄	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#384	C₂²	1	1	yes	characteristic
26	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₄₃	—	2	1	no	—
28	C₂²×C₄×D₄₃	—	2	2	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	#13063287	—	4	2	no	—
35	#13063287	—	4	2	no	—
36	C₂×C₄⋊Dic₄₃	—	2	1	no	—
37	C₂×C₄⋊Dic₄₃	—	2	1	no	—
38	C₂×C₄⋊Dic₄₃	—	2	1	no	—
39	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
42	C₂×Dic₄₃⋊C₄	—	2	2	no	—
43	C₄⋊C₄×D₄₃	—	4	2	no	—
44	C₄⋊C₄×D₄₃	—	4	2	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	#13063257	—	4	2	no	—
49	#13063256	—	4	4	no	—
50	#13063247	—	4	2	no	—
51	C₄×C₄₃⋊C₈	—	2	1	no	—
52	C₄×C₄₃⋊C₈	C₂×C₄	1	2	yes	complemented
53	C₄₃⋊#95	—	2	2	no	—
54	C₄₃⋊#95	—	2	1	no	—
55	C₂²×C₈×C₄₃	—	2	1	no	—
56	C₂²×C₈×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
60	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₄₃	—	2	1	no	—
62	C₄⋊C₈×C₄₃	—	2	1	no	—
63	C₄⋊C₈×C₄₃	—	2	1	no	—
64	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	complemented
65	C₂³×D₄₃	—	2	1	no	—
66	C₂²×C₄×C₄₃	—	2	2	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	1	no	—
72	C₂²×Dic₄₃	—	2	1	no	—
73	C₂²×Dic₄₃	—	4	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×D₁₇₂	SD₁₆	1	2	yes	—
79	C₂×D₁₇₂	SD₁₆	1	2	yes	—
80	C₂×C₄×D₄₃	—	2	2	no	—
81	C₂×C₄×D₄₃	—	2	2	no	—
82	C₂×C₄×D₄₃	—	4	4	no	—
83	C₂×C₄×D₄₃	—	4	1	no	—
84	C₂×C₄×D₄₃	—	4	1	no	—
85	C₂×C₄×D₄₃	—	4	1	no	—
86	C₂×C₄×D₄₃	—	4	1	no	—
87	C₂×C₄×D₄₃	—	4	4	no	—
88	C₂×C₄×D₄₃	—	8	2	no	—
89	C₂×C₈×C₄₃	—	2	2	no	—
90	C₂×C₈×C₄₃	—	4	1	no	—
91	C₂×C₈×C₄₃	—	4	1	no	—
92	C₂×C₈×C₄₃	—	4	1	no	—
93	C₂×C₈×C₄₃	—	4	1	no	—
94	C₂×C₈×C₄₃	—	4	1	no	—
95	C₄⋊C₄×C₄₃	—	4	2	no	—
96	C₄⋊C₄×C₄₃	—	4	1	no	—
97	C₄⋊C₄×C₄₃	—	4	1	no	—
98	C₄⋊C₄×C₄₃	—	4	1	no	—
99	C₄⋊C₄×C₄₃	—	4	1	no	—
100	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
102	C₄²×C₄₃	#41	1	1	yes	characteristic
103	C₄²×C₄₃	#41	1	1	yes	characteristic
104	(C₂×D₄₃)⋊C₄	—	2	2	no	—
105	(C₂×D₄₃)⋊C₄	—	2	2	no	—
106	(C₂×D₄₃)⋊C₄	—	4	4	no	—
107	C₄⋊Dic₄₃	—	2	1	no	—
108	C₄⋊Dic₄₃	—	2	1	no	—
109	C₄⋊Dic₄₃	—	2	1	no	—
110	C₄⋊Dic₄₃	—	2	1	no	—
111	C₄⋊Dic₄₃	—	4	2	no	—
112	C₄⋊Dic₄₃	—	4	1	no	—
113	C₄⋊Dic₄₃	—	4	1	no	—
114	C₄⋊Dic₄₃	—	4	1	no	—
115	C₄⋊Dic₄₃	—	4	1	no	—
116	C₄⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
117	C₄⋊Dic₄₃	SD₁₆	1	2	yes	—
118	Dic₄₃⋊C₄	—	4	4	no	—
119	C₄×Dic₄₃	—	4	1	no	—
120	C₄×Dic₄₃	—	4	1	no	—
121	C₂×C₄₃⋊C₈	—	2	2	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	—	2	2	no	—
124	C₂³×C₄₃	#120	1	1	yes	characteristic
125	C₂²×D₄₃	—	2	2	no	—
126	C₂²×D₄₃	—	2	2	no	—
127	C₂²×D₄₃	—	2	2	no	—
128	C₂²×D₄₃	—	4	1	no	—
129	C₂²×D₄₃	—	4	1	no	—
130	C₂²×D₄₃	—	4	1	no	—
131	C₂²×D₄₃	—	4	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	1	no	—
134	C₂×C₄×C₄₃	—	4	2	no	—
135	C₂×C₄×C₄₃	—	4	2	no	—
136	C₂×C₄×C₄₃	—	4	2	no	—
137	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
143	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
147	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
151	C₂×Dic₄₃	—	2	2	no	—
152	C₂×Dic₄₃	—	2	2	no	—
153	C₂×Dic₄₃	—	4	1	no	—
154	C₂×Dic₄₃	—	4	1	no	—
155	C₂×Dic₄₃	—	4	1	no	—
156	C₂×Dic₄₃	—	4	1	no	—
157	C₂×Dic₄₃	—	4	1	no	—
158	C₂×Dic₄₃	—	4	1	no	—
159	C₂×Dic₄₃	—	4	1	no	—
160	C₂×Dic₄₃	—	8	1	no	—
161	C₂×Dic₄₃	—	8	1	no	—
162	C₂×Dic₄₃	—	8	1	no	—
163	D₁₇₂	—	2	2	no	—
164	D₁₇₂	—	2	2	no	—
165	D₁₇₂	—	2	2	no	—
166	D₁₇₂	#106	1	4	yes	complemented
167	C₄×D₄₃	—	4	2	no	—
168	C₄×D₄₃	—	4	2	no	—
169	C₄×D₄₃	—	4	2	no	—
170	C₄×D₄₃	—	4	2	no	—
171	C₄×D₄₃	—	8	8	no	—
172	C₈×C₄₃	—	4	2	no	—
173	C₈×C₄₃	—	8	1	no	—
174	C₄₃⋊C₈	—	2	4	no	—
175	#8886	—	43	1	no	maximal, Sylow
176	C₂²×C₄₃	#385	1	1	yes	characteristic
177	C₂²×C₄₃	#448	1	1	yes	characteristic
178	C₂²×C₄₃	#449	1	1	yes	characteristic
179	C₂²×C₄₃	#450	1	1	yes	characteristic
180	C₂²×C₄₃	#450	1	1	yes	characteristic
181	C₂²×C₄₃	#453	1	1	yes	characteristic
182	C₂²×C₄₃	#456	1	1	yes	characteristic
183	C₂×D₄₃	—	2	4	no	—
184	C₂×D₄₃	—	4	2	no	—
185	C₂×D₄₃	—	4	2	no	—
186	C₂×D₄₃	—	4	2	no	—
187	C₂×D₄₃	—	4	2	no	—
188	C₂×D₄₃	—	4	2	no	—
189	C₂×D₄₃	—	4	2	no	—
190	C₄×C₄₃	—	2	1	no	—
191	C₄×C₄₃	—	2	1	no	—
192	C₄×C₄₃	—	8	2	no	—
193	C₄×C₄₃	C₂×#106	1	1	yes	characteristic
194	C₄×C₄₃	#428	1	1	yes	characteristic
195	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
196	C₄×C₄₃	#442	1	1	yes	characteristic
197	C₄×C₄₃	#476	1	1	yes	characteristic
198	C₄×C₄₃	#478	1	1	yes	characteristic
199	C₄×C₄₃	#481	1	1	yes	characteristic
200	C₄×C₄₃	#483	1	1	yes	characteristic
201	Dic₄₃	—	4	2	no	—
202	Dic₄₃	—	4	2	no	—
203	Dic₄₃	—	8	1	no	—
204	Dic₄₃	—	16	1	no	—
205	D₄×C₄⋊C₄	—	43	1	no	—
206	#1948	—	43	1	no	—
207	#1844	—	43	1	no	—
208	#1802	—	43	1	no	—
209	C₂×D₄⋊C₈	—	43	1	no	—
210	#1296	D₄₃	1	1	yes	characteristic, complemented
211	#1279	—	43	1	no	—
212	C₂×C₄₃	#1622	1	1	yes	characteristic
213	C₂×C₄₃	#1629	1	1	yes	characteristic
214	C₂×C₄₃	#1651	1	1	yes	characteristic
215	C₂×C₄₃	#1654	1	1	yes	characteristic
216	C₂×C₄₃	#1853	1	1	yes	characteristic
217	C₂×C₄₃	#1859	1	1	yes	characteristic
218	C₂×C₄₃	#1864	1	1	yes	characteristic
219	D₄₃	—	4	4	no	—
220	C₂×C₄×D₄	—	43	1	no	—
221	C₂×C₄×D₄	—	86	1	no	—
222	C₂²×C₄⋊C₄	—	86	1	no	—
223	C₂×#106	—	86	1	no	—
224	C₂×#106	—	86	2	no	—
225	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
227	C₂×#102	—	86	1	no	—
228	C₂×C₄×C₈	—	43	1	no	—
229	#389	—	86	1	no	—
230	#385	—	86	2	no	—
231	#384	—	43	1	no	—
232	#384	C₂×D₄₃	1	1	yes	characteristic
233	#380	—	86	1	no	—
234	C₄×C₄⋊C₄	—	43	1	no	—
235	#340	—	86	1	no	—
236	#340	—	86	1	no	—
237	D₄⋊C₈	—	43	4	no	—
238	C₄₃	#8886	1	1	yes	characteristic, complemented, Sylow
239	C₂²×D₄	—	43	1	no	—
240	C₂³×C₄	—	86	2	no	—
241	C₂³×C₄	—	86	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	86	1	no	—
245	C₄×D₄	—	43	2	no	—
246	C₄×D₄	—	43	2	no	—
247	C₄×D₄	—	86	1	no	—
248	C₄×D₄	—	86	1	no	—
249	C₄×D₄	—	172	2	no	—
250	C₄×D₄	—	172	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	43	1	no	—
254	C₂×C₄⋊C₄	—	43	1	no	—
255	C₂×C₄⋊C₄	—	43	1	no	—
256	C₂×C₄⋊C₄	—	86	2	no	—
257	C₂×C₄⋊C₄	—	86	1	no	—
258	C₂×C₄⋊C₄	—	86	1	no	—
259	C₂×C₄⋊C₄	—	86	1	no	—
260	C₂×C₄⋊C₄	—	172	2	no	—
261	C₂×C₄⋊C₄	—	172	2	no	—
262	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
263	C₂×C₂²⋊C₄	—	86	1	no	—
264	C₂×C₂²⋊C₄	—	86	2	no	—
265	C₂×C₄²	—	86	1	no	—
266	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
267	#106	—	172	4	no	—
268	#106	—	172	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	C₄×D₄₃	1	2	yes	complemented
273	#102	—	172	2	no	—
274	C₄×C₈	—	43	2	no	—
275	C₄×C₈	—	86	1	no	—
276	#95	—	86	2	no	—
277	#95	—	86	1	no	—
278	C₂⁴	—	86	1	no	—
279	C₂×D₄	—	43	2	no	—
280	C₂×D₄	—	43	2	no	—
281	C₂×D₄	—	43	2	no	—
282	C₂×D₄	—	86	1	no	—
283	C₂×D₄	—	86	1	no	—
284	C₂×D₄	—	86	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	86	1	no	—
287	C₂²×C₄	—	86	1	no	—
288	C₂²×C₄	—	86	2	no	—
289	C₂²×C₄	—	86	2	no	—
290	C₂²×C₄	—	86	1	no	—
291	C₂²×C₄	—	344	2	no	—
292	C₂²×C₄	—	172	4	no	—
293	C₂²×C₄	—	172	4	no	—
294	C₂²×C₄	—	172	1	no	—
295	C₂²×C₄	—	172	1	no	—
296	C₂²×C₄	—	172	1	no	—
297	C₂²×C₄	—	172	1	no	—
298	C₂²×C₄	—	172	1	no	—
299	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
301	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	86	2	no	—
309	C₂×C₈	—	86	2	no	—
310	C₂×C₈	—	86	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	43	2	no	—
317	C₄⋊C₄	—	43	2	no	—
318	C₄⋊C₄	—	86	1	no	—
319	C₄⋊C₄	—	86	1	no	—
320	C₄⋊C₄	—	86	1	no	—
321	C₄⋊C₄	—	86	1	no	—
322	C₄⋊C₄	—	172	2	no	—
323	C₄⋊C₄	—	172	4	no	—
324	C₄⋊C₄	—	172	1	no	—
325	C₄⋊C₄	—	172	1	no	—
326	C₄⋊C₄	—	172	1	no	—
327	C₄⋊C₄	—	172	1	no	—
328	C₂²⋊C₄	—	86	2	no	—
329	C₂²⋊C₄	—	86	2	no	—
330	C₂²⋊C₄	—	172	4	no	—
331	C₄²	—	172	1	no	—
332	C₄²	—	172	1	no	—
333	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
334	C₄²	#10621898	1	1	yes	characteristic
335	C₄²	#10621900	1	1	yes	characteristic
336	C₄²	Q₈×D₄₃	1	1	yes	characteristic
337	C₂³	—	86	2	no	—
338	C₂³	—	86	2	no	—
339	C₂³	—	86	2	no	—
340	C₂³	—	172	1	no	—
341	C₂³	—	172	1	no	—
342	C₂³	—	172	1	no	—
343	C₂³	—	172	1	no	—
344	C₂³	#13063295	1	1	yes	characteristic
345	D₄	—	43	4	no	—
346	D₄	—	86	2	no	—
347	D₄	—	86	2	no	—
348	D₄	—	86	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	86	2	no	—
355	C₂×C₄	—	86	2	no	—
356	C₂×C₄	—	344	8	no	—
357	C₂×C₄	—	344	1	no	—
358	C₂×C₄	—	344	1	no	—
359	C₂×C₄	—	344	1	no	—
360	C₂×C₄	—	172	1	no	—
361	C₂×C₄	—	172	1	no	—
362	C₂×C₄	—	172	1	no	—
363	C₂×C₄	—	172	1	no	—
364	C₂×C₄	—	172	1	no	—
365	C₂×C₄	—	172	1	no	—
366	C₂×C₄	—	172	1	no	—
367	C₂×C₄	—	172	2	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	—	172	2	no	—
371	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
372	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
374	C₂×C₄	#13063303	1	1	yes	characteristic
375	C₂×C₄	#13063305	1	1	yes	characteristic
376	C₂×C₄	#13063307	1	1	yes	characteristic
377	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
378	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
379	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
380	C₂×C₄	#13063348	1	1	yes	characteristic
381	C₂×C₄	#13063349	1	1	yes	characteristic
382	C₂×C₄	#13063349	1	1	yes	characteristic
383	C₂×C₄	#13063352	1	1	yes	characteristic
384	C₂×C₄	#13063357	1	1	yes	characteristic
385	C₈	—	4	2	no	—
386	C₈	—	8	1	no	—
387	C₈	—	86	4	no	—
388	C₂²	—	86	4	no	—
389	C₂²	—	172	2	no	—
390	C₂²	—	172	2	no	—
391	C₂²	—	172	2	no	—
392	C₂²	—	172	2	no	—
393	C₂²	—	172	2	no	—
394	C₂²	—	172	2	no	—
395	C₂²	#14582773	1	1	yes	characteristic
396	C₂²	#14583039	1	1	yes	characteristic
397	C₂²	#14583047	1	1	yes	characteristic
398	C₂²	#14583051	1	1	yes	characteristic
399	C₂²	#14583051	1	1	yes	characteristic
400	C₂²	#14583069	1	1	yes	characteristic
401	C₂²	#14583084	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	344	1	no	—
406	C₄	—	172	2	no	—
407	C₄	—	172	2	no	—
408	C₄	—	688	1	no	—
409	C₄	#106×D₄₃	1	1	yes	characteristic
410	C₄	#14582940	1	1	yes	characteristic
411	C₄	#14582984	1	1	yes	characteristic
412	C₄	#14583008	1	1	yes	characteristic
413	C₄	#14583188	1	1	yes	characteristic
414	C₄	#14583202	1	1	yes	characteristic
415	C₄	#14583216	1	1	yes	characteristic
416	C₄	#14583228	1	1	yes	characteristic
417	C₂	—	172	4	no	—
418	C₂	#19133668	1	1	yes	characteristic
419	C₂	#19133712	1	1	yes	characteristic
420	C₂	#19133859	1	1	yes	characteristic
421	C₂	#19133880	1	1	yes	characteristic
422	C₂	#19134789	1	1	yes	characteristic
423	C₂	#19134824	1	1	yes	characteristic
424	C₂	#19134857	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1296	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1296	D₄₃
hypocenter	C₄₃	#8886
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #19135359	C₂	semidirect
3. #19134751	C₂	semidirect
6. #19132434	C₂	semidirect
7. C₄₃×#1296	C₂	semidirect
22. #14582626	C₄	semidirect
52. C₄×C₄₃⋊C₈	C₂×C₄	semidirect
64. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
166. D₁₇₂	#106	semidirect
210. #1296	D₄₃	semidirect
238. C₄₃	#8886	semidirect
272. C₄⋊C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19137495	2
#19135359	2
#19134751	2
#19134596	2
C₂×#14582626	2
#19132434	2
C₄₃×#1296	2
#8886	43