Subgroups — #25115063

Order 11008.

870 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583017	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583015	C₂	1	1	yes	maximal, characteristic
3	#19143366	C₂	1	1	yes	maximal, characteristic
4	#19143162	C₂	1	2	yes	maximal, complemented
5	#19135344	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134871	C₂	1	2	yes	maximal, complemented
7	#19134869	C₂	1	2	yes	maximal, complemented
8	#19134765	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134614	C₂	1	2	yes	maximal, complemented
10	C₈×Dic₄₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₂×#13063333	C₂²	1	2	yes	—
14	C₂×#13063331	C₂²	1	2	yes	—
15	#14583367	C₂²	1	2	yes	—
16	#14583017	—	2	4	no	—
17	#14583015	—	2	4	no	—
18	#14582993	C₄	1	1	yes	characteristic, complemented
19	#14582993	C₄	1	1	yes	characteristic, complemented
20	#14582986	C₄	1	2	yes	complemented
21	#14582986	C₄	1	2	yes	complemented
22	#14582981	C₄	1	1	yes	characteristic, complemented
23	#14582981	C₄	1	1	yes	characteristic, complemented
24	C₂×#13063261	C₂²	1	1	yes	characteristic
25	C₂×#13063260	C₂²	1	2	yes	—
26	#14582926	C₂²	1	2	yes	—
27	#14582924	—	2	2	no	—
28	#14582924	—	2	2	no	—
29	#14582922	C₂²	1	2	yes	—
30	#14582921	—	2	2	no	—
31	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₄₃	—	2	2	no	—
33	C₂×#13063253	C₂²	1	2	yes	—
34	C₂×#13063251	C₂²	1	2	yes	—
35	#14582893	C₂²	1	2	yes	—
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
39	#14582658	C₂²	1	2	yes	—
40	#14582654	C₂²	1	1	yes	characteristic
41	#14582653	C₂²	1	1	yes	characteristic
42	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#427	C₂²	1	1	yes	characteristic
44	C₄₃×#424	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
46	C₄₃×#339	C₂²	1	2	yes	—
47	C₂×#10621898	C₂³	1	2	yes	—
48	#13063347	D₄	1	4	yes	—
49	#13063347	Q₈	1	4	yes	—
50	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
51	C₂×#10621873	C₂×C₄	1	2	yes	—
52	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
53	#13063333	—	2	4	no	—
54	#13063333	—	4	2	no	—
55	#13063331	—	2	4	no	—
56	#13063331	—	4	2	no	—
57	C₂×#10621877	C₂³	1	2	yes	—
58	C₂×#10621872	—	2	2	no	—
59	C₂×#10621872	—	2	2	no	—
60	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₄₃	—	2	2	no	—
63	C₂×C₈×D₄₃	—	2	2	no	—
64	#13063290	C₂×C₄	1	2	yes	—
65	#13063290	C₂×C₄	1	2	yes	—
66	#13063287	C₂×C₄	1	2	yes	—
67	#13063287	C₂×C₄	1	2	yes	—
68	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
69	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
70	#13063282	—	2	2	no	—
71	C₂×Dic₄₃⋊C₄	—	2	1	no	—
72	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
74	C₄²×D₄₃	—	2	2	no	—
75	#13063261	—	2	2	no	—
76	#13063260	—	4	2	no	—
77	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
78	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
79	Dic₄₃⋊C₈	—	2	2	no	—
80	Dic₄₃⋊C₈	—	2	2	no	—
81	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
82	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
83	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
84	Dic₄₃⋊C₈	D₄	1	1	yes	characteristic
85	#13063253	—	2	4	no	—
86	#13063251	—	2	4	no	—
87	#13063248	C₂×C₄	1	2	yes	—
88	#13063248	C₂×C₄	1	2	yes	—
89	#13063245	C₂×C₄	1	2	yes	—
90	#13063245	C₂×C₄	1	2	yes	—
91	C₈×Dic₄₃	—	2	2	no	—
92	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
96	C₄₃⋊#95	—	2	1	no	—
97	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
98	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
100	#117×C₄₃	C₂³	1	2	yes	—
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	#108×C₄₃	—	2	2	no	—
103	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
104	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
105	#106×C₄₃	C₂×C₄	1	2	yes	—
106	C₄⋊C₈×C₄₃	—	2	2	no	—
107	C₄⋊C₈×C₄₃	—	2	2	no	—
108	C₄×C₈×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₃	—	2	2	no	—
112	C₂²×Dic₄₃	—	2	1	no	—
113	C₂²×Dic₄₃	#41	1	1	yes	characteristic
114	C₂²×Dic₄₃	#41	1	1	yes	characteristic
115	#10621898	—	2	2	no	—
116	#10621898	—	2	2	no	—
117	#10621898	C₂×D₄	1	4	yes	—
118	#10621898	C₂×Q₈	1	4	yes	—
119	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₄₃	—	2	2	no	—
121	C₂×C₄×D₄₃	—	2	2	no	—
122	C₂×C₄×D₄₃	—	2	2	no	—
123	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
124	M₁₆×C₄₃	—	2	2	no	—
125	M₁₆×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
135	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
137	C₂²⋊C₄×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	—	2	2	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	—	2	1	no	—
141	(C₂×D₄₃)⋊C₄	—	2	2	no	—
142	(C₂×D₄₃)⋊C₄	—	2	2	no	—
143	Dic₄₃⋊C₄	—	2	4	no	—
144	Dic₄₃⋊C₄	—	2	2	no	—
145	Dic₄₃⋊C₄	—	2	2	no	—
146	C₄×Dic₄₃	—	2	2	no	—
147	C₄×Dic₄₃	—	2	2	no	—
148	C₄×Dic₄₃	—	2	1	no	—
149	C₄×Dic₄₃	—	2	1	no	—
150	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
154	#10621877	—	2	2	no	—
155	#10621877	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	1	no	—
158	C₂×C₄₃⋊C₈	—	2	1	no	—
159	C₂×C₄₃⋊C₈	—	2	1	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	Dic₁₇₂	C₄⋊C₄	1	4	yes	complemented
166	D₃₄₄	C₄⋊C₄	1	4	yes	complemented
167	#10621873	C₄⋊C₄	1	8	yes	complemented
168	#10621872	—	4	4	no	—
169	#10621872	—	4	4	no	—
170	C₈×D₄₃	—	4	4	no	—
171	C₈×D₄₃	—	4	4	no	—
172	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₂²×D₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂²⋊D₄₃	—	2	4	no	—
186	C₂²⋊D₄₃	—	2	4	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	4	1	no	—
191	C₂×Dic₄₃	—	4	1	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
194	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
195	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
196	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
197	D₁₇₂	—	2	2	no	—
198	D₁₇₂	C₂×C₄⋊C₄	1	4	yes	—
199	C₄×D₄₃	—	2	4	no	—
200	C₄×D₄₃	—	2	4	no	—
201	C₄×D₄₃	—	4	4	no	—
202	C₄×D₄₃	—	8	2	no	—
203	Dic₈₆	—	2	2	no	—
204	Dic₈₆	C₂×C₄⋊C₄	1	4	yes	—
205	C₈×C₄₃	—	2	1	no	—
206	C₈×C₄₃	—	2	1	no	—
207	C₈×C₄₃	—	4	2	no	—
208	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
209	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
210	C₄₃⋊C₈	—	2	1	no	—
211	C₄₃⋊C₈	—	2	1	no	—
212	C₄₃⋊C₈	—	2	1	no	—
213	C₄₃⋊C₈	—	2	1	no	—
214	C₄₃⋊C₈	—	4	2	no	—
215	#22688	—	43	1	no	maximal, Sylow
216	C₂²×C₄₃	—	2	1	no	—
217	C₂²×C₄₃	—	2	1	no	—
218	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₄₃	#547	1	1	yes	characteristic
220	C₂²×C₄₃	#554	1	1	yes	characteristic
221	C₂×D₄₃	—	2	4	no	—
222	C₂×D₄₃	—	4	2	no	—
223	C₂×D₄₃	—	4	2	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₄₃	#520	1	1	yes	characteristic
229	C₄×C₄₃	D₄²	1	1	yes	characteristic
230	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
231	Dic₄₃	—	2	4	no	—
232	Dic₄₃	—	2	1	no	—
233	Dic₄₃	—	2	1	no	—
234	Dic₄₃	—	2	1	no	—
235	Dic₄₃	—	4	2	no	—
236	Dic₄₃	#443	1	2	yes	complemented
237	C₂×#443	—	43	1	no	—
238	C₂×#443	—	43	1	no	—
239	C₄×#135	—	43	1	no	—
240	#2906	—	43	2	no	—
241	#1945	—	43	1	no	—
242	#1945	D₄₃	1	1	yes	characteristic, complemented
243	#1866	—	43	2	no	—
244	#1866	—	43	2	no	—
245	#1848	—	43	1	no	—
246	#1806	—	43	2	no	—
247	C₈×C₄⋊C₄	—	43	1	no	—
248	C₂×C₄₃	—	2	1	no	—
249	C₂×C₄₃	—	2	1	no	—
250	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
251	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
252	C₂×C₄₃	#2957	1	1	yes	characteristic
253	D₄₃	—	4	4	no	—
254	C₂×#135	—	43	1	no	—
255	C₂×#131	—	43	2	no	—
256	C₂×#131	—	43	2	no	—
257	C₄×#41	—	43	2	no	—
258	#443	—	86	4	no	—
259	#443	—	86	4	no	—
260	C₄×Q₁₆	—	43	1	no	—
261	C₄×Q₁₆	—	43	1	no	—
262	C₄×SD₁₆	—	43	2	no	—
263	C₄×SD₁₆	—	43	2	no	—
264	C₄×D₈	—	43	1	no	—
265	C₄×D₈	—	43	1	no	—
266	C₂×#108	—	43	1	no	—
267	C₂×#108	—	43	2	no	—
268	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
269	#427	C₂×D₄₃	1	1	yes	characteristic
270	#424	—	43	2	no	—
271	#424	—	86	2	no	—
272	#424	—	86	2	no	—
273	#424	C₂×D₄₃	1	2	yes	—
274	#423	—	43	2	no	—
275	#423	—	86	2	no	—
276	C₂×C₄⋊C₈	—	43	1	no	—
277	C₂×C₄⋊C₈	—	86	2	no	—
278	C₂×#104	—	43	2	no	—
279	C₂×#104	—	43	2	no	—
280	#416	—	43	2	no	—
281	C₂×C₄×C₈	—	43	1	no	—
282	C₂×C₄×C₈	—	43	1	no	—
283	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
284	C₄×C₄⋊C₄	—	43	1	no	—
285	#339	—	43	2	no	—
286	#339	C₂×D₄₃	1	2	yes	—
287	#336	—	43	1	no	—
288	#336	—	43	1	no	—
289	C₄₃	#22688	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	43	2	no	—
291	#135	—	43	4	no	—
292	#135	—	43	4	no	—
293	C₂×Q₁₆	—	43	1	no	—
294	C₂×SD₁₆	—	43	2	no	—
295	C₂×D₈	—	43	1	no	—
296	#131	—	86	4	no	—
297	#131	—	86	4	no	—
298	#131	—	172	2	no	—
299	#131	—	172	2	no	—
300	C₂×M₁₆	—	43	2	no	—
301	C₂×M₁₆	—	86	2	no	—
302	C₂×M₁₆	—	86	2	no	—
303	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
304	C₂²×C₈	—	43	1	no	—
305	C₂²×C₈	—	43	1	no	—
306	C₂²×C₈	—	86	2	no	—
307	C₂²×C₈	—	86	2	no	—
308	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
310	C₄×Q₈	—	43	2	no	—
311	C₄×Q₈	—	43	2	no	—
312	C₄×D₄	—	43	2	no	—
313	C₄×D₄	—	43	2	no	—
314	C₄×D₄	—	86	2	no	—
315	C₄×D₄	—	86	2	no	—
316	#117	—	86	2	no	—
317	#117	C₂²×D₄₃	1	2	yes	—
318	C₂×C₄⋊C₄	—	86	1	no	—
319	C₂×C₄²	—	43	1	no	—
320	C₂×C₄²	—	43	1	no	—
321	C₂×C₄²	—	86	2	no	—
322	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
323	#108	—	2	2	no	—
324	#108	—	86	2	no	—
325	#108	—	172	2	no	—
326	#107	C₄×D₄₃	1	1	yes	characteristic
327	#107	C₄×D₄₃	1	1	yes	characteristic
328	#106	C₄×D₄₃	1	2	yes	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	43	1	no	—
332	C₄⋊C₈	—	43	1	no	—
333	C₄⋊C₈	—	43	1	no	—
334	C₄⋊C₈	—	43	1	no	—
335	C₄⋊C₈	—	86	2	no	—
336	C₄⋊C₈	—	86	2	no	—
337	C₄⋊C₈	—	86	2	no	—
338	C₄⋊C₈	—	86	2	no	—
339	#104	—	86	4	no	—
340	#104	—	86	4	no	—
341	#103	—	43	2	no	—
342	#103	—	43	2	no	—
343	#102	—	43	2	no	—
344	#102	—	43	2	no	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	—	43	1	no	—
347	C₄×C₈	—	43	1	no	—
348	C₄×C₈	—	43	1	no	—
349	C₄×C₈	—	43	1	no	—
350	C₄×C₈	—	86	2	no	—
351	#95	—	86	1	no	—
352	#41	—	43	4	no	—
353	#41	—	43	4	no	—
354	#41	—	86	2	no	—
355	#41	—	86	2	no	—
356	C₂×Q₈	—	43	2	no	—
357	C₂×D₄	—	43	2	no	—
358	C₂×D₄	—	86	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	43	1	no	—
361	C₂²×C₄	—	43	1	no	—
362	C₂²×C₄	—	86	2	no	—
363	C₂²×C₄	—	86	2	no	—
364	C₂²×C₄	—	86	2	no	—
365	C₂²×C₄	—	86	1	no	—
366	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
367	Q₁₆	—	43	4	no	—
368	SD₁₆	—	43	8	no	—
369	D₈	—	43	4	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	86	2	no	—
373	M₁₆	—	86	2	no	—
374	M₁₆	—	172	4	no	—
375	M₁₆	—	172	4	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	43	1	no	—
380	C₂×C₈	—	43	1	no	—
381	C₂×C₈	—	43	1	no	—
382	C₂×C₈	—	43	1	no	—
383	C₂×C₈	—	86	1	no	—
384	C₂×C₈	—	86	1	no	—
385	C₂×C₈	—	86	1	no	—
386	C₂×C₈	—	86	1	no	—
387	C₂×C₈	—	86	2	no	—
388	C₂×C₈	—	172	4	no	—
389	C₂×C₈	—	172	4	no	—
390	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
392	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
393	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
394	C₂×C₈	D₄×D₄₃	1	2	yes	—
395	C₂×C₈	Q₈×D₄₃	1	2	yes	—
396	C₄⋊C₄	—	86	2	no	—
397	C₄⋊C₄	—	86	2	no	—
398	C₄⋊C₄	—	86	4	no	—
399	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
400	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	86	2	no	—
403	C₂²⋊C₄	—	86	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	43	1	no	—
408	C₄²	—	43	1	no	—
409	C₄²	—	43	1	no	—
410	C₄²	—	43	1	no	—
411	C₄²	—	86	2	no	—
412	C₄²	—	86	2	no	—
413	C₄²	—	86	1	no	—
414	C₄²	—	86	1	no	—
415	C₂³	—	86	2	no	—
416	C₂³	#41×D₄₃	1	1	yes	characteristic
417	Q₈	—	43	4	no	—
418	Q₈	—	86	2	no	—
419	D₄	—	43	4	no	—
420	D₄	—	86	4	no	—
421	D₄	—	86	4	no	—
422	D₄	—	86	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	43	1	no	—
429	C₂×C₄	—	43	1	no	—
430	C₂×C₄	—	43	1	no	—
431	C₂×C₄	—	43	1	no	—
432	C₂×C₄	—	86	2	no	—
433	C₂×C₄	—	86	2	no	—
434	C₂×C₄	—	86	4	no	—
435	C₂×C₄	—	86	4	no	—
436	C₂×C₄	—	86	2	no	—
437	C₂×C₄	—	344	2	no	—
438	C₂×C₄	—	172	4	no	—
439	C₂×C₄	—	172	1	no	—
440	C₂×C₄	—	172	1	no	—
441	C₂×C₄	—	172	1	no	—
442	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
446	C₂×C₄	#13063371	1	1	yes	characteristic
447	C₂×C₄	#13063373	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	86	1	no	—
452	C₈	—	86	1	no	—
453	C₈	—	86	1	no	—
454	C₈	—	86	1	no	—
455	C₈	—	172	2	no	—
456	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
457	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	86	4	no	—
461	C₂²	—	172	2	no	—
462	C₂²	—	172	2	no	—
463	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
464	C₂²	#14583551	1	1	yes	characteristic
465	C₂²	#14583605	1	1	yes	characteristic
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	43	2	no	—
470	C₄	—	86	1	no	—
471	C₄	—	86	1	no	—
472	C₄	—	86	1	no	—
473	C₄	—	86	4	no	—
474	C₄	—	172	2	no	—
475	C₄	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
476	C₄	#14583381	1	1	yes	characteristic
477	C₄	#14583533	1	1	yes	characteristic
478	C₄	#14583564	1	1	yes	characteristic
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	172	4	no	—
482	C₂	#19137496	1	1	yes	characteristic
483	C₂	#443×D₄₃	1	1	yes	characteristic
484	C₂	#19143507	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1945	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063347	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1945	D₄₃
hypocenter	C₄₃	#22688
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1945

Complements

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

N	H ≅ G/N	type
4. #19143162	C₂	semidirect
5. #19135344	C₂	semidirect
6. #19134871	C₂	semidirect
7. #19134869	C₂	semidirect
8. #19134765	C₂	semidirect
9. #19134614	C₂	semidirect
10. C₈×Dic₄₃⋊C₄	C₂	semidirect
11. C₄₃×#1945	C₂	semidirect
18. #14582993	C₄	semidirect
19. #14582993	C₄	semidirect
20. #14582986	C₄	semidirect
21. #14582986	C₄	semidirect
22. #14582981	C₄	semidirect
23. #14582981	C₄	semidirect
165. Dic₁₇₂	C₄⋊C₄	semidirect
166. D₃₄₄	C₄⋊C₄	semidirect
167. #10621873	C₄⋊C₄	semidirect
236. Dic₄₃	#443	semidirect
242. #1945	D₄₃	semidirect
289. C₄₃	#22688	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583017	2
C₂×#14583015	2
#19143366	2
#19143162	2
#19135344	2
#19134871	2
#19134869	2
#19134765	2
#19134614	2
C₈×Dic₄₃⋊C₄	2
C₄₃×#1945	2
#22688	43