Subgroups — #24991389

Order 11008.

664 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583176	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#19135557	C₂	1	1	yes	maximal, characteristic, complemented
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×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	—	2	1	no	—
9	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×D₄₃	—	2	1	no	—
11	#14583176	—	2	2	no	—
12	#14583176	C₄	1	4	yes	complemented
13	C₂×#13063258	—	2	1	no	—
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#13063245	—	2	1	no	—
16	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	#14582797	—	2	1	no	—
18	#14582773	—	2	2	no	—
19	#14582769	C₂²	1	1	yes	characteristic
20	#14582756	—	2	1	no	—
21	#14582661	—	2	2	no	—
22	#14582626	—	2	2	no	—
23	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₃	—	2	1	no	—
26	C₂×#103×C₄₃	—	2	1	no	—
27	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
28	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₄₃	—	2	1	no	—
30	C₂²×C₄×D₄₃	—	2	2	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₄×D₁₇₂	—	2	1	no	—
34	C₄×D₁₇₂	—	2	1	no	—
35	C₄×D₁₇₂	—	4	2	no	—
36	C₄×D₁₇₂	—	4	2	no	—
37	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
38	C₄×D₁₇₂	D₄	1	2	yes	—
39	C₂×C₄⋊Dic₄₃	—	2	1	no	—
40	C₂×C₄⋊Dic₄₃	—	2	1	no	—
41	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
42	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
43	C₂×Dic₄₃⋊C₄	—	2	2	no	—
44	C₄⋊C₄×D₄₃	—	4	2	no	—
45	C₄⋊C₄×D₄₃	—	4	2	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
47	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
48	#13063258	—	2	4	no	—
49	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	complemented
51	#13063245	—	2	4	no	—
52	C₄×C₄₃⋊C₈	—	2	1	no	—
53	C₄×C₄₃⋊C₈	—	2	1	no	—
54	C₄₃⋊#95	—	2	2	no	—
55	C₂²×Q₈×C₄₃	—	2	1	no	—
56	C₂²×C₈×C₄₃	—	2	1	no	—
57	C₄⋊Q₈×C₄₃	—	2	1	no	—
58	C₄⋊Q₈×C₄₃	—	2	1	no	—
59	C₄⋊Q₈×C₄₃	—	2	1	no	—
60	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	complemented
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	—	2	1	no	—
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₄₃	—	2	1	no	—
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	#103×C₄₃	—	4	2	no	—
70	#103×C₄₃	—	4	2	no	—
71	#95×C₄₃	—	2	1	no	—
72	C₂³×D₄₃	—	2	1	no	—
73	C₂×Q₈×C₄₃	—	2	2	no	—
74	C₂×Q₈×C₄₃	—	4	1	no	—
75	C₂×Q₈×C₄₃	—	4	1	no	—
76	C₂×Q₈×C₄₃	—	4	1	no	—
77	C₂×Q₈×C₄₃	—	4	1	no	—
78	C₂×Q₈×C₄₃	—	4	1	no	—
79	C₂²×C₄×C₄₃	—	2	1	no	—
80	C₂²×C₄×C₄₃	—	2	1	no	—
81	C₂²×C₄×C₄₃	—	4	1	no	—
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₄₃	—	2	1	no	—
86	C₂²×Dic₄₃	—	2	2	no	—
87	C₂×D₁₇₂	—	2	1	no	—
88	C₂×D₁₇₂	—	2	1	no	—
89	C₂×D₁₇₂	—	2	1	no	—
90	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
91	C₂×D₁₇₂	SD₁₆	1	2	yes	—
92	C₂×D₁₇₂	Q₁₆	1	2	yes	—
93	C₂×C₄×D₄₃	—	2	2	no	—
94	C₂×C₄×D₄₃	—	2	2	no	—
95	C₂×C₄×D₄₃	—	4	4	no	—
96	C₂×C₄×D₄₃	—	4	1	no	—
97	C₂×C₄×D₄₃	—	4	1	no	—
98	C₂×C₄×D₄₃	—	4	1	no	—
99	C₂×C₄×D₄₃	—	4	1	no	—
100	C₂×C₄×D₄₃	—	4	4	no	—
101	C₂×C₄×D₄₃	—	8	2	no	—
102	C₂×C₈×C₄₃	—	4	1	no	—
103	C₂×C₈×C₄₃	—	4	1	no	—
104	C₂×C₈×C₄₃	—	4	1	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₄⋊C₄×C₄₃	—	2	1	no	—
109	C₄⋊C₄×C₄₃	—	2	1	no	—
110	C₄⋊C₄×C₄₃	—	4	1	no	—
111	C₄⋊C₄×C₄₃	—	4	1	no	—
112	C₄⋊C₄×C₄₃	D₈	1	2	yes	—
113	C₄²×C₄₃	—	4	1	no	—
114	C₄²×C₄₃	—	4	1	no	—
115	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₃	#41	1	1	yes	characteristic
118	C₄²×C₄₃	#41	1	1	yes	characteristic
119	(C₂×D₄₃)⋊C₄	—	2	2	no	—
120	(C₂×D₄₃)⋊C₄	—	2	2	no	—
121	(C₂×D₄₃)⋊C₄	—	4	4	no	—
122	C₄⋊Dic₄₃	—	2	1	no	—
123	C₄⋊Dic₄₃	—	4	1	no	—
124	C₄⋊Dic₄₃	—	4	1	no	—
125	C₄⋊Dic₄₃	—	4	1	no	—
126	C₄⋊Dic₄₃	—	4	1	no	—
127	C₄⋊Dic₄₃	—	4	2	no	—
128	C₄⋊Dic₄₃	C₂²⋊C₄	1	2	yes	—
129	Dic₄₃⋊C₄	—	4	4	no	—
130	C₂×C₄₃⋊C₈	—	2	2	no	—
131	C₂×C₄₃⋊C₈	—	2	2	no	—
132	C₂×C₄₃⋊C₈	—	4	1	no	—
133	C₂×C₄₃⋊C₈	—	4	1	no	—
134	C₂×C₄₃⋊C₈	—	4	1	no	—
135	C₂×C₄₃⋊C₈	—	4	1	no	—
136	C₂³×C₄₃	#120	1	1	yes	characteristic
137	C₂²×D₄₃	—	2	2	no	—
138	C₂²×D₄₃	—	2	2	no	—
139	C₂²×D₄₃	—	2	2	no	—
140	C₂²×D₄₃	—	4	1	no	—
141	C₂²×D₄₃	—	4	1	no	—
142	C₂²×D₄₃	—	4	1	no	—
143	C₂²×D₄₃	—	4	1	no	—
144	Q₈×C₄₃	—	4	2	no	—
145	Q₈×C₄₃	—	4	2	no	—
146	Q₈×C₄₃	—	8	1	no	—
147	Q₈×C₄₃	—	8	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	—	8	1	no	—
158	C₂×C₄×C₄₃	—	8	1	no	—
159	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
168	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
169	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
173	C₂×Dic₄₃	—	2	2	no	—
174	C₂×Dic₄₃	—	4	1	no	—
175	C₂×Dic₄₃	—	4	1	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	—	4	2	no	—
179	D₁₇₂	—	2	2	no	—
180	D₁₇₂	—	2	2	no	—
181	D₁₇₂	—	2	2	no	—
182	D₁₇₂	#103	1	4	yes	complemented
183	C₄×D₄₃	—	4	2	no	—
184	C₄×D₄₃	—	4	2	no	—
185	C₄×D₄₃	—	4	2	no	—
186	C₄×D₄₃	—	4	2	no	—
187	C₄×D₄₃	—	8	8	no	—
188	C₈×C₄₃	—	8	1	no	—
189	C₄₃⋊C₈	—	4	2	no	—
190	C₄₃⋊C₈	—	4	2	no	—
191	#8981	—	43	1	no	maximal, Sylow
192	C₂²×C₄₃	#386	1	1	yes	characteristic
193	C₂²×C₄₃	#447	1	1	yes	characteristic
194	C₂²×C₄₃	#449	1	1	yes	characteristic
195	C₂²×C₄₃	#450	1	1	yes	characteristic
196	C₂²×C₄₃	#451	1	1	yes	characteristic
197	C₂²×C₄₃	#455	1	1	yes	characteristic
198	C₂²×C₄₃	#456	1	1	yes	characteristic
199	C₂×D₄₃	—	2	4	no	—
200	C₂×D₄₃	—	4	2	no	—
201	C₂×D₄₃	—	4	2	no	—
202	C₂×D₄₃	—	4	2	no	—
203	C₂×D₄₃	—	4	2	no	—
204	C₂×D₄₃	—	4	2	no	—
205	C₂×D₄₃	—	4	2	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	—	8	1	no	—
211	C₄×C₄₃	C₂×#103	1	1	yes	characteristic
212	C₄×C₄₃	#417	1	1	yes	characteristic
213	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
214	C₄×C₄₃	#442	1	1	yes	characteristic
215	C₄×C₄₃	#459	1	1	yes	characteristic
216	C₄×C₄₃	#463	1	1	yes	characteristic
217	C₄×C₄₃	#483	1	1	yes	characteristic
218	C₄×C₄₃	#484	1	1	yes	characteristic
219	Dic₄₃	—	4	2	no	—
220	Dic₄₃	—	8	2	no	—
221	C₂×#474	—	43	1	no	—
222	D₄×C₄⋊C₄	—	43	1	no	—
223	#1990	—	43	1	no	—
224	#1981	D₄₃	1	1	yes	characteristic, complemented
225	C₂×D₄⋊C₈	—	43	1	no	—
226	#1296	—	43	1	no	—
227	#1279	—	43	1	no	—
228	C₂×C₄₃	#1639	1	1	yes	characteristic
229	C₂×C₄₃	#1644	1	1	yes	characteristic
230	C₂×C₄₃	#1649	1	1	yes	characteristic
231	C₂×C₄₃	#1654	1	1	yes	characteristic
232	C₂×C₄₃	#1872	1	1	yes	characteristic
233	C₂×C₄₃	#1879	1	1	yes	characteristic
234	C₂×C₄₃	#1882	1	1	yes	characteristic
235	D₄₃	—	4	4	no	—
236	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
237	C₂×C₄×D₄	—	43	1	no	—
238	C₂×C₄×D₄	—	86	1	no	—
239	C₂²×C₄⋊C₄	—	86	1	no	—
240	#474	—	43	4	no	—
241	#474	—	86	2	no	—
242	C₂×#107	—	86	1	no	—
243	C₂×C₄⋊C₈	—	43	1	no	—
244	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
245	C₂×#103	—	2	1	no	—
246	C₂×#103	—	2	1	no	—
247	C₂×#102	—	86	1	no	—
248	C₂×C₄×C₈	—	43	1	no	—
249	#389	—	86	1	no	—
250	#385	—	86	2	no	—
251	#384	—	43	1	no	—
252	#380	—	86	1	no	—
253	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
254	#340	—	86	2	no	—
255	D₄⋊C₈	—	86	2	no	—
256	C₄₃	#8981	1	1	yes	characteristic, complemented, Sylow
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×D₄	—	43	1	no	—
259	C₂³×C₄	—	86	2	no	—
260	C₂³×C₄	—	86	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	86	1	no	—
263	C₂²×C₈	—	86	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	C₄×D₄₃	1	2	yes	complemented
268	C₄×D₄	—	43	2	no	—
269	C₄×D₄	—	43	2	no	—
270	C₄×D₄	—	86	1	no	—
271	C₄×D₄	—	86	1	no	—
272	C₄×D₄	—	172	2	no	—
273	C₄×D₄	—	172	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	43	2	no	—
278	C₂×C₄⋊C₄	—	86	2	no	—
279	C₂×C₄⋊C₄	—	86	1	no	—
280	C₂×C₄⋊C₄	—	86	1	no	—
281	C₂×C₄⋊C₄	—	172	2	no	—
282	C₂×C₄⋊C₄	—	172	2	no	—
283	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	86	1	no	—
286	C₂×C₂²⋊C₄	—	86	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
289	#107	—	86	4	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	43	2	no	—
293	C₄⋊C₈	—	86	1	no	—
294	#103	—	4	2	no	—
295	#103	—	4	2	no	—
296	#102	—	86	4	no	—
297	C₄×C₈	—	86	1	no	—
298	C₄×C₈	—	86	1	no	—
299	#95	—	2	1	no	—
300	#95	—	86	2	no	—
301	C₂⁴	—	86	1	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×D₄	—	43	2	no	—
309	C₂×D₄	—	43	2	no	—
310	C₂×D₄	—	43	2	no	—
311	C₂×D₄	—	86	1	no	—
312	C₂×D₄	—	86	1	no	—
313	C₂×D₄	—	86	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	—	86	2	no	—
319	C₂²×C₄	—	86	2	no	—
320	C₂²×C₄	—	86	2	no	—
321	C₂²×C₄	—	344	2	no	—
322	C₂²×C₄	—	172	4	no	—
323	C₂²×C₄	—	172	4	no	—
324	C₂²×C₄	—	172	1	no	—
325	C₂²×C₄	—	172	1	no	—
326	C₂²×C₄	—	172	1	no	—
327	C₂²×C₄	—	172	1	no	—
328	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	86	2	no	—
335	C₂×C₈	—	86	2	no	—
336	C₂×C₈	—	172	1	no	—
337	C₂×C₈	—	172	1	no	—
338	C₂×C₈	—	172	1	no	—
339	C₂×C₈	—	172	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	43	2	no	—
348	C₄⋊C₄	—	86	1	no	—
349	C₄⋊C₄	—	172	2	no	—
350	C₄⋊C₄	—	172	4	no	—
351	C₄⋊C₄	—	172	1	no	—
352	C₄⋊C₄	—	172	1	no	—
353	C₄⋊C₄	—	172	1	no	—
354	C₄⋊C₄	—	172	1	no	—
355	C₄⋊C₄	#10621882	1	2	yes	—
356	C₂²⋊C₄	—	86	2	no	—
357	C₂²⋊C₄	—	86	2	no	—
358	C₂²⋊C₄	—	172	4	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
362	C₄²	#10621898	1	1	yes	characteristic
363	C₄²	D₄×D₄₃	1	1	yes	characteristic
364	C₄²	#10621900	1	1	yes	characteristic
365	C₂³	—	86	2	no	—
366	C₂³	—	86	2	no	—
367	C₂³	—	86	2	no	—
368	C₂³	—	172	1	no	—
369	C₂³	—	172	1	no	—
370	C₂³	—	172	1	no	—
371	C₂³	—	172	1	no	—
372	C₂³	#13063293	1	1	yes	characteristic
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	8	1	no	—
376	Q₈	—	8	1	no	—
377	D₄	—	43	4	no	—
378	D₄	—	86	2	no	—
379	D₄	—	86	2	no	—
380	D₄	—	86	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	1	no	—
391	C₂×C₄	—	8	1	no	—
392	C₂×C₄	—	86	2	no	—
393	C₂×C₄	—	344	8	no	—
394	C₂×C₄	—	172	2	no	—
395	C₂×C₄	—	172	2	no	—
396	C₂×C₄	—	172	2	no	—
397	C₂×C₄	—	172	1	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	2	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	—	172	2	no	—
403	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
404	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂×C₄	#13063296	1	1	yes	characteristic
407	C₂×C₄	#13063298	1	1	yes	characteristic
408	C₂×C₄	#13063307	1	1	yes	characteristic
409	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
411	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
412	C₂×C₄	#13063345	1	1	yes	characteristic
413	C₂×C₄	#13063350	1	1	yes	characteristic
414	C₂×C₄	#13063351	1	1	yes	characteristic
415	C₂×C₄	#13063352	1	1	yes	characteristic
416	C₂×C₄	#13063357	1	1	yes	characteristic
417	C₈	—	8	1	no	—
418	C₈	—	172	2	no	—
419	C₈	—	172	2	no	—
420	C₂²	—	86	4	no	—
421	C₂²	—	172	2	no	—
422	C₂²	—	172	2	no	—
423	C₂²	—	172	2	no	—
424	C₂²	—	172	2	no	—
425	C₂²	—	172	2	no	—
426	C₂²	—	172	2	no	—
427	C₂²	#14582775	1	1	yes	characteristic
428	C₂²	#14583032	1	1	yes	characteristic
429	C₂²	#14583042	1	1	yes	characteristic
430	C₂²	#14583048	1	1	yes	characteristic
431	C₂²	#14583053	1	1	yes	characteristic
432	C₂²	#14583075	1	1	yes	characteristic
433	C₂²	#14583080	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	344	2	no	—
440	C₄	—	172	2	no	—
441	C₄	#103×D₄₃	1	1	yes	characteristic
442	C₄	#14582899	1	1	yes	characteristic
443	C₄	C₄×#10621882	1	1	yes	characteristic
444	C₄	#14583009	1	1	yes	characteristic
445	C₄	#14583091	1	1	yes	characteristic
446	C₄	#14583111	1	1	yes	characteristic
447	C₄	#14583228	1	1	yes	characteristic
448	C₄	#14583233	1	1	yes	characteristic
449	C₂	—	172	4	no	—
450	C₂	#19133772	1	1	yes	characteristic
451	C₂	#19133807	1	1	yes	characteristic
452	C₂	#19133842	1	1	yes	characteristic
453	C₂	#19133877	1	1	yes	characteristic
454	C₂	#19134899	1	1	yes	characteristic
455	C₂	#19134946	1	1	yes	characteristic
456	C₂	#19134961	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063293
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1981	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1981	D₄₃
hypocenter	C₄₃	#8981
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1981

Complements

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

N	H ≅ G/N	type
3. #19135557	C₂	semidirect
5. #19132479	C₂	semidirect
6. #19132436	C₂	semidirect
7. C₄₃×#1981	C₂	semidirect
12. #14583176	C₄	semidirect
50. C₄⋊(C₄₃⋊C₈)	C₂×C₄	semidirect
60. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
182. D₁₇₂	#103	semidirect
224. #1981	D₄₃	semidirect
256. C₄₃	#8981	semidirect
267. C₄⋊Q₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583176	2
C₄⋊C₄×D₁₇₂	2
#19135557	2
C₂×#14582626	2
#19132479	2
#19132436	2
C₄₃×#1981	2
#8981	43