Subgroups — #25960940

Order 11008.

2604 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149366	C₂	1	1	yes	maximal, characteristic
2	#19149306	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143510	C₂	1	6	yes	maximal, complemented
4	#19143502	C₂	1	6	yes	maximal, complemented
5	#19143496	C₂	1	6	yes	maximal, complemented
6	C₂×#14583019	C₂	1	6	yes	maximal, complemented
7	#19143204	C₂	1	1	yes	maximal, characteristic, complemented
8	#19143142	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143140	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143021	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3573	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583735	C₂²	1	1	yes	characteristic
13	#14583714	C₄	1	4	yes	complemented
14	#14583710	C₄	1	4	yes	complemented
15	#14583707	C₄	1	4	yes	complemented
16	#14583702	C₄	1	4	yes	complemented
17	#14583697	C₂²	1	6	yes	—
18	C₂×#13063345	C₂²	1	6	yes	—
19	#14583666	C₂²	1	1	yes	characteristic
20	#14583665	C₂²	1	6	yes	complemented
21	#14583664	—	2	4	no	—
22	C₂×#13063332	C₂²	1	1	yes	characteristic
23	C₂×#13063331	C₂²	1	6	yes	complemented
24	#131×D₄₃	—	2	4	no	—
25	#41×Dic₄₃	C₂²	1	1	yes	characteristic
26	#14583019	C₂²	1	4	yes	complemented
27	#14583019	C₂²	1	12	yes	complemented
28	#14583019	C₂²	1	12	yes	complemented
29	#14583019	C₂²	1	12	yes	complemented
30	#14583014	C₂²	1	24	yes	complemented
31	#14582947	C₂²	1	6	yes	complemented
32	C₂×#13063260	C₂²	1	6	yes	complemented
33	#14582916	C₂²	1	6	yes	complemented
34	#14582915	C₂²	1	6	yes	complemented
35	C₂×#13063252	C₂²	1	6	yes	complemented
36	C₂×#13063251	C₂²	1	6	yes	complemented
37	#14582857	C₂²	1	3	yes	complemented
38	#14582854	C₂²	1	3	yes	complemented
39	M₁₆×Dic₄₃	C₂²	1	3	yes	complemented
40	C₂×#13063235	C₂²	1	3	yes	complemented
41	C₄₃×#585	C₂²	1	1	yes	characteristic
42	C₄₃×#568	—	2	4	no	—
43	C₄₃×#568	C₂²	1	1	yes	characteristic
44	C₄₃×#568	C₂²	1	6	yes	complemented
45	C₂×#131×C₄₃	—	2	4	no	—
46	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#131×C₄₃	C₂²	1	6	yes	complemented
48	#13063373	—	2	1	no	—
49	#13063372	C₂×C₄	1	4	yes	—
50	#13063371	C₂×C₄	1	4	yes	—
51	#13063370	—	2	3	no	—
52	C₂×#10621898	C₂³	1	6	yes	—
53	#41×D₄₃	—	2	4	no	—
54	#13063356	C₂×C₄	1	12	yes	complemented
55	#13063355	C₂×C₄	1	12	yes	complemented
56	#13063351	C₂×C₄	1	12	yes	complemented
57	#13063350	C₂×C₄	1	12	yes	complemented
58	#13063345	C₂×C₄	1	12	yes	complemented
59	#13063345	C₂×C₄	1	12	yes	complemented
60	#13063345	C₂³	1	4	yes	—
61	#13063345	C₂³	1	12	yes	—
62	C₂×#10621885	C₂×C₄	1	6	yes	complemented
63	C₂×#10621883	C₂×C₄	1	6	yes	complemented
64	C₂×#10621884	C₂×C₄	1	6	yes	complemented
65	C₂×#10621882	C₂×C₄	1	6	yes	complemented
66	#13063333	—	2	12	no	—
67	#13063332	—	2	4	no	—
68	#13063332	C₂×C₄	1	4	yes	—
69	#13063332	C₂×C₄	1	4	yes	—
70	#13063331	—	2	6	no	—
71	#13063331	—	2	6	no	—
72	#13063331	C₂³	1	4	yes	—
73	#13063331	C₂³	1	12	yes	—
74	C₂×#10621877	C₂³	1	6	yes	—
75	C₂×#10621877	C₂³	1	3	yes	—
76	C₂×#10621872	—	2	6	no	—
77	M₁₆×D₄₃	—	2	12	no	—
78	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	—
79	C₂×C₈×D₄₃	—	2	6	no	—
80	Q₈×Dic₄₃	—	2	1	no	—
81	D₄×Dic₄₃	—	2	3	no	—
82	#13063284	C₂³	1	3	yes	—
83	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
84	#13063260	C₂³	1	4	yes	—
85	#13063260	C₂³	1	12	yes	—
86	#13063252	C₂³	1	4	yes	—
87	#13063252	C₂³	1	12	yes	—
88	#13063251	C₂³	1	4	yes	—
89	#13063251	C₂³	1	12	yes	—
90	#13063235	C₂³	1	1	yes	characteristic
91	#13063235	C₂³	1	3	yes	—
92	#13063235	C₂³	1	3	yes	—
93	#13063235	C₂³	1	3	yes	—
94	C₈×Dic₄₃	C₂³	1	6	yes	—
95	2₋¹⁺⁴×C₄₃	—	2	1	no	—
96	2₋¹⁺⁴×C₄₃	C₂×C₄	1	4	yes	—
97	H(5,𝔽₂)×C₄₃	—	2	3	no	—
98	H(5,𝔽₂)×C₄₃	C₂×C₄	1	4	yes	—
99	C₂×#41×C₄₃	—	2	4	no	—
100	C₂×#41×C₄₃	C₂³	1	6	yes	—
101	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
102	#131×C₄₃	—	2	4	no	—
103	#131×C₄₃	—	2	12	no	—
104	#131×C₄₃	—	2	6	no	—
105	#131×C₄₃	—	2	6	no	—
106	#131×C₄₃	D₄	1	4	yes	—
107	#131×C₄₃	D₄	1	4	yes	—
108	#131×C₄₃	C₂³	1	4	yes	—
109	#131×C₄₃	C₂³	1	12	yes	—
110	C₂×M₁₆×C₄₃	—	2	12	no	—
111	C₂×M₁₆×C₄₃	—	2	6	no	—
112	C₂×M₁₆×C₄₃	C₂³	1	6	yes	—
113	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
114	C₂²×C₈×C₄₃	—	2	6	no	—
115	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
116	#41×C₄₃	—	2	4	no	—
117	#41×C₄₃	—	2	12	no	—
118	#41×C₄₃	—	2	6	no	—
119	#41×C₄₃	—	2	6	no	—
120	#41×C₄₃	C₂²×C₄	1	12	yes	—
121	#41×C₄₃	C₂²×C₄	1	4	yes	—
122	#41×C₄₃	C₂×D₄	1	4	yes	—
123	#41×C₄₃	C₂⁴	1	4	yes	—
124	C₂×Q₈×C₄₃	—	2	4	no	—
125	C₂×Q₈×C₄₃	C₂²×C₄	1	6	yes	—
126	C₂×Q₈×C₄₃	#41	1	1	yes	characteristic
127	C₂×D₄×C₄₃	—	2	12	no	—
128	C₂×D₄×C₄₃	—	2	6	no	—
129	C₂×D₄×C₄₃	C₂²×C₄	1	6	yes	—
130	C₂×D₄×C₄₃	#41	1	3	yes	—
131	C₂²×C₄×C₄₃	—	2	6	no	—
132	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
133	C₂×C₂²⋊D₄₃	—	2	6	no	—
134	C₂²×Dic₄₃	—	2	3	no	—
135	#10621902	—	2	4	no	—
136	Q₈×D₄₃	—	2	4	no	—
137	#10621900	—	2	12	no	—
138	D₄×D₄₃	—	2	12	no	—
139	#10621898	—	2	6	no	—
140	#10621898	—	2	6	no	—
141	#10621898	C₂²×C₄	1	12	yes	—
142	#10621898	C₂⁴	1	4	yes	—
143	C₂×D₁₇₂	C₂²×C₄	1	6	yes	—
144	C₂×C₄×D₄₃	—	2	6	no	—
145	C₂×Dic₈₆	C₂²×C₄	1	6	yes	—
146	M₁₆×C₄₃	—	2	6	no	—
147	M₁₆×C₄₃	—	2	4	no	—
148	M₁₆×C₄₃	—	2	12	no	—
149	M₁₆×C₄₃	C₂×D₄	1	12	yes	—
150	M₁₆×C₄₃	C₂⁴	1	4	yes	—
151	C₂×C₈×C₄₃	—	2	6	no	—
152	C₂×C₈×C₄₃	—	2	4	no	—
153	C₂×C₈×C₄₃	—	2	12	no	—
154	C₂×C₈×C₄₃	C₂×D₄	1	6	yes	—
155	C₂×C₈×C₄₃	C₂×D₄	1	6	yes	—
156	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
158	C₂²⋊Dic₄₃	—	2	3	no	—
159	#10621885	C₂²×C₄	1	4	yes	—
160	#10621885	C₂²×C₄	1	12	yes	—
161	#10621884	C₂²×C₄	1	4	yes	—
162	#10621884	C₂²×C₄	1	12	yes	—
163	#10621883	C₂²×C₄	1	4	yes	—
164	#10621883	C₂²×C₄	1	12	yes	—
165	#10621882	C₂²×C₄	1	4	yes	—
166	#10621882	C₂²×C₄	1	12	yes	—
167	C₄⋊Dic₄₃	—	2	3	no	—
168	C₄×Dic₄₃	—	2	3	no	—
169	C₄×Dic₄₃	C₂⁴	1	3	yes	—
170	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
171	#10621877	—	2	6	no	—
172	#10621877	C₂²×C₄	1	12	yes	—
173	#10621877	C₂⁴	1	4	yes	—
174	C₂×C₄₃⋊C₈	—	2	6	no	—
175	C₂×C₄₃⋊C₈	C₂²×C₄	1	6	yes	—
176	C₂×C₄₃⋊C₈	C₂²×C₄	1	6	yes	—
177	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
178	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
179	#10621872	—	2	12	no	—
180	#10621872	—	2	4	no	—
181	C₈×D₄₃	—	2	4	no	—
182	C₈×D₄₃	—	2	12	no	—
183	C₂³×C₄₃	—	2	6	no	—
184	C₂³×C₄₃	C₂×#41	1	3	yes	—
185	C₂²×D₄₃	—	2	6	no	—
186	Q₈×C₄₃	—	2	6	no	—
187	Q₈×C₄₃	C₄×D₄	1	4	yes	—
188	Q₈×C₄₃	C₂³×C₄	1	4	yes	—
189	D₄×C₄₃	—	2	12	no	—
190	D₄×C₄₃	—	2	4	no	—
191	D₄×C₄₃	—	2	6	no	—
192	D₄×C₄₃	C₄×D₄	1	12	yes	—
193	D₄×C₄₃	C₂³×C₄	1	4	yes	—
194	C₂×C₄×C₄₃	—	2	6	no	—
195	C₂×C₄×C₄₃	—	2	12	no	—
196	C₂×C₄×C₄₃	—	2	4	no	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
198	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
199	C₂×C₄×C₄₃	C₂×#41	1	3	yes	—
200	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
201	C₂²⋊D₄₃	—	2	12	no	—
202	C₂²⋊D₄₃	—	2	4	no	—
203	C₂×Dic₄₃	—	2	6	no	—
204	C₂×Dic₄₃	—	2	1	no	—
205	C₂×Dic₄₃	—	2	3	no	—
206	C₂×Dic₄₃	—	8	3	no	—
207	D₁₇₂	—	2	6	no	—
208	D₁₇₂	C₂³×C₄	1	4	yes	—
209	C₄×D₄₃	—	2	12	no	—
210	C₄×D₄₃	—	2	4	no	—
211	Dic₈₆	—	2	6	no	—
212	Dic₈₆	C₂³×C₄	1	4	yes	—
213	C₈×C₄₃	—	2	4	no	—
214	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₄₃	C₂²×D₄	1	6	yes	—
216	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
217	C₄₃⋊C₈	—	2	4	no	—
218	C₄₃⋊C₈	C₂³×C₄	1	1	yes	characteristic
219	C₄₃⋊C₈	C₂³×C₄	1	1	yes	characteristic
220	C₄₃⋊C₈	C₂³×C₄	1	6	yes	—
221	#60184	—	43	1	no	maximal, Sylow
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	4	3	no	—
224	C₂²×C₄₃	—	8	6	no	—
225	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
226	C₂²×C₄₃	C₂²×#41	1	1	yes	characteristic
227	C₂×D₄₃	—	2	4	no	—
228	C₂×D₄₃	—	8	6	no	—
229	C₄×C₄₃	—	2	4	no	—
230	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
231	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
232	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
233	Dic₄₃	—	2	4	no	—
234	Dic₄₃	—	4	3	no	—
235	Dic₄₃	—	4	1	no	—
236	#3584	—	43	1	no	—
237	#3573	—	43	1	no	—
238	#3573	D₄₃	1	1	yes	characteristic, complemented
239	#2957	—	43	6	no	—
240	#2956	—	43	6	no	—
241	#2955	—	43	6	no	—
242	C₂×#444	—	43	6	no	—
243	#2916	—	43	1	no	—
244	#2901	—	43	1	no	—
245	#2901	—	43	1	no	—
246	#2875	—	43	1	no	—
247	C₂×C₄₃	—	2	1	no	—
248	C₂×C₄₃	—	2	6	no	—
249	C₂×C₄₃	—	4	4	no	—
250	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
251	D₄₃	—	4	4	no	—
252	#585	—	43	1	no	—
253	#585	C₂×D₄₃	1	1	yes	characteristic
254	#578	—	43	4	no	—
255	#577	—	43	4	no	—
256	#577	—	43	4	no	—
257	#576	—	43	4	no	—
258	#575	—	43	6	no	—
259	C₂×#135	—	43	6	no	—
260	#568	—	2	4	no	—
261	#568	—	43	1	no	—
262	#568	—	43	6	no	—
263	#568	—	86	4	no	—
264	#568	C₂×D₄₃	1	1	yes	characteristic
265	#568	C₂×D₄₃	1	6	yes	complemented
266	C₂×#131	—	2	4	no	—
267	C₂×#131	—	43	1	no	—
268	C₂×#131	—	43	6	no	—
269	C₂×#131	—	86	4	no	—
270	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
271	C₂×#131	C₂×D₄₃	1	6	yes	complemented
272	C₄×#41	—	43	1	no	—
273	#444	—	43	4	no	—
274	#444	—	43	12	no	—
275	#444	—	43	12	no	—
276	#444	—	43	12	no	—
277	#443	—	43	24	no	—
278	#430	—	43	6	no	—
279	C₂×#108	—	43	6	no	—
280	#421	—	43	6	no	—
281	#421	—	43	6	no	—
282	C₂×#104	—	43	6	no	—
283	C₂×#104	—	43	6	no	—
284	#405	—	43	3	no	—
285	#405	—	43	3	no	—
286	C₄×M₁₆	—	43	3	no	—
287	C₂×#97	—	43	3	no	—
288	C₄₃	#60184	1	1	yes	characteristic, complemented, Sylow
289	2₋¹⁺⁴	—	2	1	no	—
290	2₋¹⁺⁴	—	43	4	no	—
291	2₋¹⁺⁴	—	86	1	no	—
292	2₋¹⁺⁴	C₄×D₄₃	1	4	yes	—
293	H(5,𝔽₂)	—	2	3	no	—
294	H(5,𝔽₂)	—	43	4	no	—
295	H(5,𝔽₂)	—	86	3	no	—
296	H(5,𝔽₂)	C₄×D₄₃	1	4	yes	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	—	43	6	no	—
299	C₂×#41	—	86	4	no	—
300	C₂×#41	C₂²×D₄₃	1	6	yes	—
301	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
302	#137	—	43	12	no	—
303	#137	—	43	12	no	—
304	AGL(1,ℤ/8)	—	43	12	no	—
305	AGL(1,ℤ/8)	—	43	12	no	—
306	#135	—	43	12	no	—
307	#135	—	43	12	no	—
308	#135	—	43	4	no	—
309	#135	—	43	12	no	—
310	C₂×Q₁₆	—	43	6	no	—
311	C₂×SD₁₆	—	43	6	no	—
312	C₂×SD₁₆	—	43	6	no	—
313	C₂×D₈	—	43	6	no	—
314	#131	—	2	4	no	—
315	#131	—	2	12	no	—
316	#131	—	2	6	no	—
317	#131	—	2	6	no	—
318	#131	—	43	4	no	—
319	#131	—	43	4	no	—
320	#131	—	43	4	no	—
321	#131	—	43	12	no	—
322	#131	—	86	4	no	—
323	#131	—	86	12	no	—
324	#131	—	86	6	no	—
325	#131	—	86	6	no	—
326	#131	C₂²⋊D₄₃	1	4	yes	—
327	#131	C₂²⋊D₄₃	1	4	yes	—
328	#131	C₂²×D₄₃	1	4	yes	—
329	#131	C₂²×D₄₃	1	12	yes	—
330	C₂×M₁₆	—	2	12	no	—
331	C₂×M₁₆	—	2	6	no	—
332	C₂×M₁₆	—	43	3	no	—
333	C₂×M₁₆	—	43	6	no	—
334	C₂×M₁₆	—	86	12	no	—
335	C₂×M₁₆	—	86	6	no	—
336	C₂×M₁₆	C₂²×D₄₃	1	6	yes	—
337	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
338	C₂²×C₈	—	2	6	no	—
339	C₂²×C₈	—	43	3	no	—
340	C₂²×C₈	—	86	6	no	—
341	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
342	C₄×Q₈	—	86	1	no	—
343	C₄×D₄	—	86	3	no	—
344	#117	—	43	3	no	—
345	C₂×C₄²	—	43	3	no	—
346	#108	—	43	4	no	—
347	#108	—	43	12	no	—
348	#104	—	43	4	no	—
349	#104	—	43	12	no	—
350	#104	—	43	4	no	—
351	#104	—	43	12	no	—
352	#97	—	43	1	no	—
353	#97	—	43	3	no	—
354	#97	—	43	3	no	—
355	#97	—	43	3	no	—
356	C₄×C₈	—	43	6	no	—
357	#41	—	2	4	no	—
358	#41	—	2	12	no	—
359	#41	—	2	6	no	—
360	#41	—	2	6	no	—
361	#41	—	43	12	no	—
362	#41	—	43	4	no	—
363	#41	—	86	4	no	—
364	#41	—	86	12	no	—
365	#41	—	86	6	no	—
366	#41	—	86	6	no	—
367	#41	C₂×C₄×D₄₃	1	12	yes	—
368	#41	C₂×C₄×D₄₃	1	4	yes	—
369	#41	C₂×C₂²⋊D₄₃	1	4	yes	—
370	#41	C₂³×D₄₃	1	4	yes	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	43	6	no	—
373	C₂×Q₈	—	86	4	no	—
374	C₂×Q₈	C₂×C₄×D₄₃	1	6	yes	—
375	C₂×Q₈	#10621898	1	1	yes	characteristic
376	C₂×D₄	—	2	6	no	—
377	C₂×D₄	—	2	12	no	—
378	C₂×D₄	—	43	6	no	—
379	C₂×D₄	—	86	6	no	—
380	C₂×D₄	—	86	12	no	—
381	C₂×D₄	C₂×C₄×D₄₃	1	6	yes	—
382	C₂×D₄	#10621898	1	3	yes	—
383	C₂²×C₄	—	2	6	no	—
384	C₂²×C₄	—	86	6	no	—
385	C₂²×C₄	—	86	3	no	—
386	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
387	Q₁₆	—	43	4	no	—
388	Q₁₆	—	43	12	no	—
389	SD₁₆	—	43	4	no	—
390	SD₁₆	—	43	12	no	—
391	SD₁₆	—	43	4	no	—
392	SD₁₆	—	43	12	no	—
393	D₈	—	43	4	no	—
394	D₈	—	43	12	no	—
395	M₁₆	—	2	6	no	—
396	M₁₆	—	2	12	no	—
397	M₁₆	—	2	4	no	—
398	M₁₆	—	43	12	no	—
399	M₁₆	—	43	4	no	—
400	M₁₆	—	86	6	no	—
401	M₁₆	—	86	4	no	—
402	M₁₆	—	86	12	no	—
403	M₁₆	C₂×C₂²⋊D₄₃	1	12	yes	—
404	M₁₆	C₂³×D₄₃	1	4	yes	—
405	C₂×C₈	—	2	6	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	—	2	12	no	—
408	C₂×C₈	—	43	6	no	—
409	C₂×C₈	—	43	6	no	—
410	C₂×C₈	—	43	3	no	—
411	C₂×C₈	—	43	1	no	—
412	C₂×C₈	—	86	6	no	—
413	C₂×C₈	—	86	4	no	—
414	C₂×C₈	—	86	12	no	—
415	C₂×C₈	C₂×C₂²⋊D₄₃	1	6	yes	—
416	C₂×C₈	C₂×C₂²⋊D₄₃	1	6	yes	—
417	C₂×C₈	C₂³×D₄₃	1	3	yes	—
418	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
419	C₄⋊C₄	—	86	3	no	—
420	C₂²⋊C₄	—	86	3	no	—
421	C₄²	—	43	3	no	—
422	C₄²	—	43	1	no	—
423	C₄²	—	86	3	no	—
424	C₂³	—	2	6	no	—
425	C₂³	—	86	6	no	—
426	C₂³	C₂×#10621898	1	3	yes	—
427	Q₈	—	2	6	no	—
428	Q₈	—	43	4	no	—
429	Q₈	—	86	6	no	—
430	Q₈	C₄×C₂²⋊D₄₃	1	4	yes	—
431	Q₈	C₂²×C₄×D₄₃	1	4	yes	—
432	D₄	—	2	12	no	—
433	D₄	—	2	4	no	—
434	D₄	—	2	6	no	—
435	D₄	—	43	4	no	—
436	D₄	—	86	12	no	—
437	D₄	—	86	4	no	—
438	D₄	—	86	6	no	—
439	D₄	C₄×C₂²⋊D₄₃	1	12	yes	—
440	D₄	C₂²×C₄×D₄₃	1	4	yes	—
441	C₂×C₄	—	2	6	no	—
442	C₂×C₄	—	2	12	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	86	6	no	—
445	C₂×C₄	—	86	12	no	—
446	C₂×C₄	—	86	4	no	—
447	C₂×C₄	—	86	1	no	—
448	C₂×C₄	—	86	3	no	—
449	C₂×C₄	—	344	3	no	—
450	C₂×C₄	C₂²×C₄×D₄₃	1	6	yes	—
451	C₂×C₄	C₂²×C₂²⋊D₄₃	1	6	yes	—
452	C₂×C₄	C₂×#10621898	1	3	yes	—
453	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
454	C₈	—	2	4	no	—
455	C₈	—	43	1	no	—
456	C₈	—	43	1	no	—
457	C₈	—	43	6	no	—
458	C₈	—	86	4	no	—
459	C₈	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₈	C₂²×C₂²⋊D₄₃	1	6	yes	—
461	C₈	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
462	C₂²	—	2	4	no	—
463	C₂²	—	4	3	no	—
464	C₂²	—	8	6	no	—
465	C₂²	—	86	4	no	—
466	C₂²	—	344	6	no	—
467	C₂²	C₂×C₄×C₂²⋊D₄₃	1	6	yes	—
468	C₂²	C₂²×#10621898	1	1	yes	characteristic
469	C₄	—	2	4	no	—
470	C₄	—	86	4	no	—
471	C₄	—	172	1	no	—
472	C₄	—	172	3	no	—
473	C₄	C₂×C₄×C₂²⋊D₄₃	1	6	yes	—
474	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
475	C₄	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
476	C₂	—	2	1	no	—
477	C₂	—	2	6	no	—
478	C₂	—	4	4	no	—
479	C₂	—	172	4	no	—
480	C₂	C₂²×C₄×C₂²⋊D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂³×C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3573	C₂
socle	C₂×C₄₃	C₂²×C₄×D₄
prime radical	#19149366	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#3573	D₄₃
hypocenter	C₄₃	#60184
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×#131 ◁ #3573

Complements

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

N	H ≅ G/N	type
2. #19149306	C₂	semidirect
3. #19143510	C₂	semidirect
4. #19143502	C₂	semidirect
5. #19143496	C₂	semidirect
6. C₂×#14583019	C₂	semidirect
7. #19143204	C₂	semidirect
8. #19143142	C₂	semidirect
9. #19143140	C₂	semidirect
10. #19143021	C₂	semidirect
11. C₄₃×#3573	C₂	semidirect
13. #14583714	C₄	semidirect
14. #14583710	C₄	semidirect
15. #14583707	C₄	semidirect
16. #14583702	C₄	semidirect
20. #14583665	C₂²	semidirect
23. C₂×#13063331	C₂²	semidirect
26. #14583019	C₂²	semidirect
27. #14583019	C₂²	semidirect
28. #14583019	C₂²	semidirect
29. #14583019	C₂²	semidirect
30. #14583014	C₂²	semidirect
31. #14582947	C₂²	semidirect
32. C₂×#13063260	C₂²	semidirect
33. #14582916	C₂²	semidirect
34. #14582915	C₂²	semidirect
35. C₂×#13063252	C₂²	semidirect
36. C₂×#13063251	C₂²	semidirect
37. #14582857	C₂²	semidirect
38. #14582854	C₂²	semidirect
39. M₁₆×Dic₄₃	C₂²	semidirect
40. C₂×#13063235	C₂²	semidirect
44. C₄₃×#568	C₂²	semidirect
47. C₂×#131×C₄₃	C₂²	semidirect
54. #13063356	C₂×C₄	semidirect
55. #13063355	C₂×C₄	semidirect
56. #13063351	C₂×C₄	semidirect
57. #13063350	C₂×C₄	semidirect
58. #13063345	C₂×C₄	semidirect
59. #13063345	C₂×C₄	semidirect
62. C₂×#10621885	C₂×C₄	semidirect
63. C₂×#10621883	C₂×C₄	semidirect
64. C₂×#10621884	C₂×C₄	semidirect
65. C₂×#10621882	C₂×C₄	semidirect
238. #3573	D₄₃	semidirect
265. #568	C₂×D₄₃	semidirect
271. C₂×#131	C₂×D₄₃	semidirect
288. C₄₃	#60184	semidirect

Maximal subgroups

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

subgroup	index
#19149366	2
#19149306	2
#19143510	2
#19143502	2
#19143496	2
C₂×#14583019	2
#19143204	2
#19143142	2
#19143140	2
#19143021	2
C₄₃×#3573	2
#60184	43