Subgroups — #26003125

Order 11008.

2038 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149364	C₂	1	2	yes	maximal, complemented
2	#19147745	C₂	1	2	yes	maximal, complemented
3	#19147744	C₂	1	2	yes	maximal, complemented
4	#19147738	C₂	1	4	yes	maximal, complemented
5	#19147737	C₂	1	4	yes	maximal, complemented
6	#19147733	C₂	1	2	yes	maximal, complemented
7	#19147732	C₂	1	2	yes	maximal, complemented
8	#19147729	C₂	1	2	yes	maximal, complemented
9	#19147728	C₂	1	4	yes	maximal, complemented
10	C₂×#14583331	C₂	1	1	yes	maximal, characteristic, complemented
11	#508×D₄₃	C₂	1	4	yes	maximal, complemented
12	C₂×#14583315	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583735	—	2	2	no	—
15	#14583713	C₂²	1	4	yes	complemented
16	#14583712	C₂²	1	4	yes	complemented
17	#14583706	—	2	4	no	—
18	#14583705	—	2	4	no	—
19	#14583701	C₂²	1	4	yes	complemented
20	#14583700	C₂²	1	4	yes	complemented
21	#14583697	—	2	2	no	—
22	#14583696	—	2	4	no	—
23	C₂×#13063347	C₂²	1	2	yes	complemented
24	#135×D₄₃	C₂²	1	8	yes	complemented
25	C₂×#13063331	C₂²	1	1	yes	characteristic
26	#14583341	C₂²	1	8	yes	complemented
27	#14583340	C₂²	1	4	yes	complemented
28	#14583339	C₂²	1	4	yes	complemented
29	#14583338	C₂²	1	8	yes	complemented
30	#14583336	C₂²	1	8	yes	complemented
31	#14583335	C₂²	1	4	yes	complemented
32	#14583334	C₂²	1	4	yes	complemented
33	#14583333	C₂²	1	8	yes	complemented
34	#14583332	C₂²	1	4	yes	complemented
35	#14583331	C₂²	1	2	yes	complemented
36	#14583331	C₂²	1	2	yes	complemented
37	#14583331	C₂²	1	2	yes	complemented
38	#14583331	C₂²	1	2	yes	complemented
39	#14583330	C₂²	1	8	yes	complemented
40	#14583329	C₂²	1	8	yes	complemented
41	#14583328	C₂²	1	4	yes	complemented
42	C₂×Dic₃₄₄	C₂²	1	1	yes	characteristic, complemented
43	Q₃₂×D₄₃	C₂²	1	4	yes	complemented
44	C₂×#13063270	C₂²	1	2	yes	complemented
45	SD₃₂×D₄₃	C₂²	1	8	yes	complemented
46	C₂×D₆₈₈	C₂²	1	1	yes	characteristic, complemented
47	D₁₆×D₄₃	C₂²	1	4	yes	complemented
48	#14583315	C₂²	1	2	yes	complemented
49	#14583315	C₂²	1	2	yes	complemented
50	#14583315	C₂²	1	2	yes	complemented
51	#14583315	C₂²	1	2	yes	complemented
52	C₂×#13063265	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13063264	C₂²	1	2	yes	complemented
54	C₂×C₁₆×D₄₃	C₂²	1	2	yes	complemented
55	C₂×#135×C₄₃	C₂²	1	2	yes	complemented
56	C₄₃×#508	C₂²	1	2	yes	complemented
57	C₄₃×#508	C₂²	1	2	yes	complemented
58	C₄₃×#508	C₂²	1	2	yes	complemented
59	C₄₃×#508	C₂²	1	2	yes	complemented
60	C₂×Q₃₂×C₄₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×SD₃₂×C₄₃	C₂²	1	2	yes	complemented
62	C₂×D₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
64	#13063373	—	2	4	no	—
65	#13063372	—	2	4	no	—
66	#13063372	—	4	2	no	—
67	#13063371	—	2	4	no	—
68	#13063371	—	4	2	no	—
69	#13063370	—	2	4	no	—
70	#13063370	—	4	4	no	—
71	C₂×#10621898	—	2	2	no	—
72	C₂×#10621898	—	4	4	no	—
73	C₂×#10621898	D₄	1	1	yes	characteristic
74	#41×D₄₃	—	2	8	no	—
75	#41×D₄₃	—	4	4	no	—
76	#13063357	—	2	8	no	—
77	#13063356	—	2	4	no	—
78	#13063355	—	2	4	no	—
79	#13063354	—	2	8	no	—
80	#13063352	—	2	8	no	—
81	#13063351	—	2	4	no	—
82	#13063350	—	2	4	no	—
83	#13063349	—	2	8	no	—
84	#13063348	C₂³	1	8	yes	—
85	#13063347	—	2	2	no	—
86	#13063347	—	2	2	no	—
87	#13063347	C₂³	1	4	yes	—
88	#13063347	C₂³	1	4	yes	—
89	#13063346	—	2	8	no	—
90	#13063345	—	2	8	no	—
91	#13063344	C₂³	1	8	yes	—
92	C₂×Dic₁₇₂	C₂³	1	2	yes	—
93	Q₁₆×D₄₃	C₂³	1	8	yes	—
94	C₂×#10621873	—	2	2	no	—
95	SD₁₆×D₄₃	—	2	8	no	—
96	C₂×D₃₄₄	C₂³	1	2	yes	—
97	D₈×D₄₃	C₂³	1	8	yes	—
98	#13063331	D₄	1	2	yes	—
99	#13063331	D₄	1	2	yes	—
100	#13063331	C₂³	1	2	yes	—
101	#13063331	C₂³	1	2	yes	—
102	C₂×#10621877	D₄	1	1	yes	characteristic
103	C₂×#10621872	D₄	1	2	yes	—
104	C₂×C₈×D₄₃	C₂³	1	2	yes	—
105	Dic₃₄₄	C₂³	1	2	yes	—
106	Dic₃₄₄	C₂³	1	2	yes	—
107	#13063271	C₂³	1	8	yes	—
108	#13063270	C₂³	1	4	yes	—
109	#13063270	C₂³	1	4	yes	—
110	#13063269	C₂³	1	8	yes	—
111	#13063268	C₂³	1	8	yes	—
112	D₆₈₈	C₂³	1	2	yes	—
113	D₆₈₈	C₂³	1	2	yes	—
114	#13063266	C₂³	1	8	yes	—
115	#13063265	C₂³	1	2	yes	—
116	#13063265	C₂³	1	2	yes	—
117	#13063264	C₂³	1	4	yes	—
118	#13063264	C₂³	1	4	yes	—
119	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
120	C₁₆×D₄₃	C₂³	1	4	yes	—
121	C₁₆×D₄₃	C₂³	1	4	yes	—
122	C₂×#41×C₄₃	—	2	2	no	—
123	#135×C₄₃	—	2	2	no	—
124	#135×C₄₃	—	2	2	no	—
125	#135×C₄₃	C₂³	1	4	yes	—
126	#135×C₄₃	C₂³	1	4	yes	—
127	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₄₃	—	2	2	no	—
129	C₂×D₈×C₄₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
131	Q₃₂×C₄₃	C₂³	1	2	yes	—
132	Q₃₂×C₄₃	C₂³	1	2	yes	—
133	SD₃₂×C₄₃	C₂³	1	4	yes	—
134	SD₃₂×C₄₃	C₂³	1	4	yes	—
135	D₁₆×C₄₃	C₂³	1	2	yes	—
136	D₁₆×C₄₃	C₂³	1	2	yes	—
137	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
138	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
139	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
140	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
141	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
142	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
143	#41×C₄₃	—	2	4	no	—
144	#41×C₄₃	—	2	4	no	—
145	#41×C₄₃	—	4	2	no	—
146	#41×C₄₃	—	4	2	no	—
147	C₂×Q₈×C₄₃	—	2	2	no	—
148	C₂×D₄×C₄₃	—	2	2	no	—
149	C₂×D₄×C₄₃	—	4	2	no	—
150	C₂²×C₄×C₄₃	—	4	2	no	—
151	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₂²⋊D₄₃	—	4	8	no	—
153	C₂×C₂²⋊D₄₃	—	4	2	no	—
154	C₂×C₂²⋊D₄₃	D₈	1	2	yes	—
155	#10621902	—	2	8	no	—
156	#10621902	—	4	4	no	—
157	Q₈×D₄₃	—	2	8	no	—
158	Q₈×D₄₃	—	4	4	no	—
159	#10621900	—	2	8	no	—
160	#10621900	—	4	8	no	—
161	#10621900	—	4	8	no	—
162	#10621900	—	4	4	no	—
163	D₄×D₄₃	—	2	8	no	—
164	D₄×D₄₃	—	4	8	no	—
165	D₄×D₄₃	—	4	4	no	—
166	D₄×D₄₃	—	4	8	no	—
167	#10621898	—	2	4	no	—
168	#10621898	—	2	4	no	—
169	#10621898	—	4	2	no	—
170	#10621898	—	4	2	no	—
171	#10621898	—	4	8	no	—
172	#10621898	—	4	4	no	—
173	#10621898	—	4	8	no	—
174	#10621898	—	4	4	no	—
175	#10621898	D₈	1	2	yes	—
176	#10621898	D₈	1	2	yes	—
177	#10621898	C₂×D₄	1	2	yes	—
178	#10621898	C₂×D₄	1	2	yes	—
179	C₂×D₁₇₂	—	2	2	no	—
180	C₂×D₁₇₂	—	4	4	no	—
181	C₂×D₁₇₂	D₈	1	1	yes	characteristic
182	C₂×C₄×D₄₃	—	4	2	no	—
183	C₂×C₄×D₄₃	—	4	8	no	—
184	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
185	C₂×Dic₈₆	—	2	2	no	—
186	C₂×Dic₈₆	—	4	4	no	—
187	C₂×Dic₈₆	D₈	1	1	yes	characteristic
188	Q₁₆×C₄₃	—	2	2	no	—
189	Q₁₆×C₄₃	C₂⁴	1	4	yes	—
190	SD₁₆×C₄₃	—	2	4	no	—
191	SD₁₆×C₄₃	—	2	4	no	—
192	D₈×C₄₃	—	2	2	no	—
193	D₈×C₄₃	C₂⁴	1	4	yes	—
194	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
198	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
199	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
200	#10621885	—	2	8	no	—
201	#10621884	—	2	8	no	—
202	#10621883	—	2	8	no	—
203	#10621882	—	2	8	no	—
204	#10621877	C₂×D₄	1	2	yes	—
205	#10621877	C₂×D₄	1	2	yes	—
206	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
207	Dic₁₇₂	—	2	2	no	—
208	Dic₁₇₂	C₂⁴	1	4	yes	—
209	D₃₄₄	—	2	2	no	—
210	D₃₄₄	C₂⁴	1	4	yes	—
211	#10621873	—	2	4	no	—
212	#10621873	—	2	4	no	—
213	#10621872	C₂×D₄	1	4	yes	—
214	#10621872	C₂×D₄	1	4	yes	—
215	C₈×D₄₃	C₂×D₄	1	4	yes	—
216	C₈×D₄₃	C₂⁴	1	4	yes	—
217	C₁₆×C₄₃	C₂⁴	1	1	yes	characteristic
218	C₁₆×C₄₃	C₂⁴	1	1	yes	characteristic
219	C₁₆×C₄₃	C₂⁴	1	1	yes	characteristic
220	C₁₆×C₄₃	C₂⁴	1	1	yes	characteristic
221	C₄₃⋊C₁₆	C₂⁴	1	4	yes	—
222	C₂³×C₄₃	—	4	2	no	—
223	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
224	C₂²×D₄₃	—	4	2	no	—
225	C₂²×D₄₃	—	4	8	no	—
226	C₂²×D₄₃	C₂×D₈	1	2	yes	—
227	Q₈×C₄₃	—	2	4	no	—
228	Q₈×C₄₃	—	4	2	no	—
229	D₄×C₄₃	—	2	4	no	—
230	D₄×C₄₃	—	4	4	no	—
231	D₄×C₄₃	—	4	4	no	—
232	D₄×C₄₃	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	4	no	—
235	C₂×C₄×C₄₃	—	4	4	no	—
236	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂²⋊D₄₃	—	4	4	no	—
243	C₂²⋊D₄₃	—	4	4	no	—
244	C₂²⋊D₄₃	—	4	8	no	—
245	C₂²⋊D₄₃	—	4	8	no	—
246	C₂²⋊D₄₃	C₂×D₈	1	4	yes	—
247	C₂²⋊D₄₃	C₂×D₈	1	4	yes	—
248	C₂×Dic₄₃	—	4	2	no	—
249	C₂×Dic₄₃	—	4	8	no	—
250	C₂×Dic₄₃	C₂×D₈	1	2	yes	—
251	D₁₇₂	—	2	4	no	—
252	D₁₇₂	—	4	8	no	—
253	D₁₇₂	—	4	2	no	—
254	D₁₇₂	C₂×D₈	1	2	yes	—
255	D₁₇₂	C₂×D₈	1	2	yes	—
256	C₄×D₄₃	—	4	8	no	—
257	C₄×D₄₃	—	4	4	no	—
258	C₄×D₄₃	—	4	4	no	—
259	C₄×D₄₃	—	4	8	no	—
260	C₄×D₄₃	C₂×D₈	1	4	yes	—
261	C₄×D₄₃	C₂²×D₄	1	4	yes	—
262	Dic₈₆	—	2	4	no	—
263	Dic₈₆	—	4	2	no	—
264	Dic₈₆	—	4	8	no	—
265	Dic₈₆	C₂×D₈	1	2	yes	—
266	Dic₈₆	C₂×D₈	1	2	yes	—
267	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
268	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
269	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
270	C₈×C₄₃	C₂⁵	1	1	yes	characteristic
271	C₄₃⋊C₈	C₂²×D₄	1	4	yes	—
272	#62635	—	43	1	no	maximal, Sylow
273	C₂²×C₄₃	—	4	1	no	—
274	C₂²×C₄₃	—	4	4	no	—
275	C₂²×C₄₃	—	16	2	no	—
276	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
277	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
278	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
279	C₂×D₄₃	—	4	2	no	—
280	C₂×D₄₃	—	4	4	no	—
281	C₂×D₄₃	—	16	8	no	—
282	C₂×D₄₃	—	16	2	no	—
283	C₂×D₄₃	C₂²×D₈	1	4	yes	—
284	C₄×C₄₃	—	4	4	no	—
285	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
286	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
287	C₄×C₄₃	C₂²×D₈	1	1	yes	characteristic
288	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
289	Dic₄₃	—	4	4	no	—
290	Dic₄₃	C₂²×D₈	1	4	yes	—
291	#3584	—	43	2	no	—
292	#3417	—	43	2	no	—
293	#3417	—	43	2	no	—
294	#3416	—	43	4	no	—
295	#3416	—	43	4	no	—
296	#3415	—	43	2	no	—
297	#3415	—	43	2	no	—
298	#3414	—	43	4	no	—
299	#3414	—	43	2	no	—
300	C₂×#508	—	43	4	no	—
301	C₂×#508	—	43	1	no	—
302	C₂×#508	D₄₃	1	1	yes	characteristic, complemented
303	C₂×#504	—	43	1	no	—
304	C₂×C₄₃	—	2	1	no	—
305	C₂×C₄₃	—	2	1	no	—
306	C₂×C₄₃	—	2	1	no	—
307	C₂×C₄₃	—	8	4	no	—
308	C₂×C₄₃	C₂³×D₈	1	1	yes	characteristic
309	D₄₃	—	2	4	no	—
310	D₄₃	—	8	4	no	—
311	#585	—	86	2	no	—
312	#578	—	43	4	no	—
313	#578	—	43	4	no	—
314	#577	—	86	4	no	—
315	#577	—	86	4	no	—
316	#576	—	43	4	no	—
317	#576	—	43	4	no	—
318	#575	—	86	4	no	—
319	#575	—	86	2	no	—
320	C₂×#135	—	43	8	no	—
321	C₂×#135	—	43	2	no	—
322	C₂×#135	C₂×D₄₃	1	2	yes	complemented
323	C₂×#131	—	43	1	no	—
324	#510	—	43	4	no	—
325	#510	—	43	4	no	—
326	#510	—	43	8	no	—
327	#510	—	43	8	no	—
328	#509	—	43	4	no	—
329	#509	—	43	4	no	—
330	#509	—	43	8	no	—
331	#509	—	43	8	no	—
332	#508	—	43	8	no	—
333	#508	—	43	4	no	—
334	#508	—	43	8	no	—
335	#508	—	43	4	no	—
336	#508	—	43	2	no	—
337	#508	—	43	2	no	—
338	#508	—	43	2	no	—
339	#508	—	43	2	no	—
340	#508	C₂×D₄₃	1	2	yes	complemented
341	#508	C₂×D₄₃	1	2	yes	complemented
342	#508	C₂×D₄₃	1	2	yes	complemented
343	#508	C₂×D₄₃	1	2	yes	complemented
344	C₂×Q₃₂	—	43	4	no	—
345	C₂×Q₃₂	—	43	1	no	—
346	C₂×Q₃₂	C₂×D₄₃	1	1	yes	characteristic, complemented
347	C₂×SD₃₂	—	43	8	no	—
348	C₂×SD₃₂	—	43	2	no	—
349	C₂×SD₃₂	C₂×D₄₃	1	2	yes	complemented
350	C₂×D₁₆	—	43	4	no	—
351	C₂×D₁₆	—	43	1	no	—
352	C₂×D₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
353	#504	—	43	2	no	—
354	#504	—	43	2	no	—
355	#504	—	43	2	no	—
356	#504	—	43	2	no	—
357	C₂×M₃₂	—	43	1	no	—
358	C₂×M₃₂	—	43	2	no	—
359	C₂²×C₁₆	—	43	2	no	—
360	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
361	C₄₃	#62635	1	1	yes	characteristic, complemented, Sylow
362	2₋¹⁺⁴	—	86	4	no	—
363	2₋¹⁺⁴	—	86	4	no	—
364	2₋¹⁺⁴	—	172	2	no	—
365	H(5,𝔽₂)	—	86	4	no	—
366	H(5,𝔽₂)	—	86	4	no	—
367	H(5,𝔽₂)	—	172	4	no	—
368	H(5,𝔽₂)	—	172	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	43	1	no	—
371	C₂×#41	—	86	8	no	—
372	C₂×#41	—	86	2	no	—
373	C₂×#41	—	172	4	no	—
374	C₂×#41	—	172	4	no	—
375	#137	—	86	8	no	—
376	#137	—	86	8	no	—
377	#137	—	86	4	no	—
378	#137	—	86	4	no	—
379	AGL(1,ℤ/8)	—	86	8	no	—
380	AGL(1,ℤ/8)	—	86	8	no	—
381	AGL(1,ℤ/8)	—	86	4	no	—
382	AGL(1,ℤ/8)	—	86	4	no	—
383	#135	—	2	2	no	—
384	#135	—	2	2	no	—
385	#135	—	43	8	no	—
386	#135	—	43	8	no	—
387	#135	—	43	4	no	—
388	#135	—	43	4	no	—
389	#135	—	86	8	no	—
390	#135	—	86	8	no	—
391	#135	—	86	2	no	—
392	#135	—	86	2	no	—
393	#135	C₂²×D₄₃	1	4	yes	—
394	#135	C₂²×D₄₃	1	4	yes	—
395	C₂×Q₁₆	—	43	8	no	—
396	C₂×Q₁₆	—	43	2	no	—
397	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	86	8	no	—
400	C₂×SD₁₆	—	86	2	no	—
401	C₂×D₈	—	43	8	no	—
402	C₂×D₈	—	43	2	no	—
403	C₂×D₈	C₂²×D₄₃	1	2	yes	—
404	#131	—	43	2	no	—
405	#131	—	43	2	no	—
406	#131	—	43	2	no	—
407	#131	—	43	2	no	—
408	C₂×M₁₆	—	43	1	no	—
409	C₂×M₁₆	—	43	2	no	—
410	C₂²×C₈	—	43	2	no	—
411	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
412	Q₃₂	—	43	8	no	—
413	Q₃₂	—	43	2	no	—
414	Q₃₂	—	43	2	no	—
415	Q₃₂	C₂²×D₄₃	1	2	yes	—
416	Q₃₂	C₂²×D₄₃	1	2	yes	—
417	SD₃₂	—	43	8	no	—
418	SD₃₂	—	43	8	no	—
419	SD₃₂	—	43	4	no	—
420	SD₃₂	—	43	4	no	—
421	SD₃₂	C₂²×D₄₃	1	4	yes	—
422	SD₃₂	C₂²×D₄₃	1	4	yes	—
423	D₁₆	—	43	8	no	—
424	D₁₆	—	43	2	no	—
425	D₁₆	—	43	2	no	—
426	D₁₆	C₂²×D₄₃	1	2	yes	—
427	D₁₆	C₂²×D₄₃	1	2	yes	—
428	M₃₂	—	43	2	no	—
429	M₃₂	—	43	2	no	—
430	M₃₂	—	43	4	no	—
431	M₃₂	—	43	4	no	—
432	C₂×C₁₆	—	43	2	no	—
433	C₂×C₁₆	—	43	4	no	—
434	C₂×C₁₆	—	43	4	no	—
435	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
436	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
437	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
438	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
439	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
440	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	4	2	no	—
444	#41	—	4	2	no	—
445	#41	—	43	2	no	—
446	#41	—	43	2	no	—
447	#41	—	43	2	no	—
448	#41	—	43	2	no	—
449	#41	—	86	8	no	—
450	#41	—	86	8	no	—
451	#41	—	86	4	no	—
452	#41	—	86	4	no	—
453	#41	—	172	8	no	—
454	#41	—	172	8	no	—
455	#41	—	172	4	no	—
456	#41	—	172	4	no	—
457	#41	—	172	8	no	—
458	#41	—	172	8	no	—
459	#41	—	172	4	no	—
460	#41	—	172	4	no	—
461	#41	—	172	2	no	—
462	#41	—	172	2	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	43	1	no	—
465	C₂×Q₈	—	86	8	no	—
466	C₂×Q₈	—	86	2	no	—
467	C₂×Q₈	—	172	4	no	—
468	C₂×Q₈	—	172	4	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	43	2	no	—
472	C₂×D₄	—	43	1	no	—
473	C₂×D₄	—	86	8	no	—
474	C₂×D₄	—	86	2	no	—
475	C₂×D₄	—	172	4	no	—
476	C₂×D₄	—	172	8	no	—
477	C₂×D₄	—	172	4	no	—
478	C₂×D₄	—	172	8	no	—
479	C₂×D₄	—	172	8	no	—
480	C₂×D₄	—	172	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	43	2	no	—
483	C₂²×C₄	—	172	8	no	—
484	C₂²×C₄	—	172	2	no	—
485	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
486	Q₁₆	—	2	2	no	—
487	Q₁₆	—	43	4	no	—
488	Q₁₆	—	86	8	no	—
489	Q₁₆	—	86	2	no	—
490	Q₁₆	C₂³×D₄₃	1	4	yes	—
491	SD₁₆	—	2	4	no	—
492	SD₁₆	—	2	4	no	—
493	SD₁₆	—	86	8	no	—
494	SD₁₆	—	86	8	no	—
495	SD₁₆	—	86	4	no	—
496	SD₁₆	—	86	4	no	—
497	D₈	—	2	2	no	—
498	D₈	—	43	4	no	—
499	D₈	—	86	8	no	—
500	D₈	—	86	2	no	—
501	D₈	C₂³×D₄₃	1	4	yes	—
502	M₁₆	—	43	2	no	—
503	M₁₆	—	43	2	no	—
504	M₁₆	—	43	4	no	—
505	M₁₆	—	43	4	no	—
506	C₂×C₈	—	43	2	no	—
507	C₂×C₈	—	43	4	no	—
508	C₂×C₈	—	43	4	no	—
509	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
510	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
511	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
512	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
513	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
514	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
515	C₁₆	—	43	4	no	—
516	C₁₆	C₂³×D₄₃	1	1	yes	characteristic
517	C₁₆	C₂³×D₄₃	1	1	yes	characteristic
518	C₁₆	C₂³×D₄₃	1	1	yes	characteristic
519	C₁₆	C₂³×D₄₃	1	1	yes	characteristic
520	C₂³	—	4	2	no	—
521	C₂³	—	43	2	no	—
522	C₂³	—	172	8	no	—
523	C₂³	—	172	2	no	—
524	C₂³	D₈×D₄₃	1	1	yes	characteristic
525	Q₈	—	2	4	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	43	2	no	—
528	Q₈	—	43	2	no	—
529	Q₈	—	86	4	no	—
530	Q₈	—	172	8	no	—
531	Q₈	—	172	2	no	—
532	D₄	—	2	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	2	no	—
536	D₄	—	43	4	no	—
537	D₄	—	43	4	no	—
538	D₄	—	43	2	no	—
539	D₄	—	43	2	no	—
540	D₄	—	86	4	no	—
541	D₄	—	172	8	no	—
542	D₄	—	172	8	no	—
543	D₄	—	172	8	no	—
544	D₄	—	172	4	no	—
545	D₄	—	172	4	no	—
546	D₄	—	172	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	43	2	no	—
551	C₂×C₄	—	43	4	no	—
552	C₂×C₄	—	43	4	no	—
553	C₂×C₄	—	172	8	no	—
554	C₂×C₄	—	172	8	no	—
555	C₂×C₄	—	172	8	no	—
556	C₂×C₄	—	172	2	no	—
557	C₂×C₄	—	172	4	no	—
558	C₂×C₄	—	172	4	no	—
559	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
560	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
561	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
562	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
563	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
564	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
565	C₈	—	43	4	no	—
566	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
567	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
568	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
569	C₈	C₂⁴×D₄₃	1	1	yes	characteristic
570	C₂²	—	4	1	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	16	2	no	—
573	C₂²	—	43	4	no	—
574	C₂²	—	172	2	no	—
575	C₂²	—	172	4	no	—
576	C₂²	—	688	2	no	—
577	C₂²	—	688	8	no	—
578	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
579	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
580	C₂²	C₂×D₈×D₄₃	1	1	yes	characteristic
581	C₄	—	4	4	no	—
582	C₄	—	43	4	no	—
583	C₄	—	172	4	no	—
584	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
585	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
586	C₄	C₂×D₈×D₄₃	1	1	yes	characteristic
587	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	8	4	no	—
592	C₂	—	86	4	no	—
593	C₂	—	344	4	no	—
594	C₂	C₂²×D₈×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₄₃
commutator, cosocle	C₈×C₄₃	C₂⁵
Frattini	C₈	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#508	C₂
socle	C₂×C₄₃	C₂³×D₈
hypercenter	C₂×#508	D₄₃
hypocenter	C₄₃	#62635
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. #19149364	C₂	semidirect
2. #19147745	C₂	semidirect
3. #19147744	C₂	semidirect
4. #19147738	C₂	semidirect
5. #19147737	C₂	semidirect
6. #19147733	C₂	semidirect
7. #19147732	C₂	semidirect
8. #19147729	C₂	semidirect
9. #19147728	C₂	semidirect
10. C₂×#14583331	C₂	semidirect
11. #508×D₄₃	C₂	semidirect
12. C₂×#14583315	C₂	semidirect
13. C₂×C₄₃×#508	C₂	semidirect
15. #14583713	C₂²	semidirect
16. #14583712	C₂²	semidirect
19. #14583701	C₂²	semidirect
20. #14583700	C₂²	semidirect
23. C₂×#13063347	C₂²	semidirect
24. #135×D₄₃	C₂²	semidirect
26. #14583341	C₂²	semidirect
27. #14583340	C₂²	semidirect
28. #14583339	C₂²	semidirect
29. #14583338	C₂²	semidirect
30. #14583336	C₂²	semidirect
31. #14583335	C₂²	semidirect
32. #14583334	C₂²	semidirect
33. #14583333	C₂²	semidirect
34. #14583332	C₂²	semidirect
35. #14583331	C₂²	semidirect
36. #14583331	C₂²	semidirect
37. #14583331	C₂²	semidirect
38. #14583331	C₂²	semidirect
39. #14583330	C₂²	semidirect
40. #14583329	C₂²	semidirect
41. #14583328	C₂²	semidirect
42. C₂×Dic₃₄₄	C₂²	semidirect
43. Q₃₂×D₄₃	C₂²	semidirect
44. C₂×#13063270	C₂²	semidirect
45. SD₃₂×D₄₃	C₂²	semidirect
46. C₂×D₆₈₈	C₂²	semidirect
47. D₁₆×D₄₃	C₂²	semidirect
48. #14583315	C₂²	semidirect
49. #14583315	C₂²	semidirect
50. #14583315	C₂²	semidirect
51. #14583315	C₂²	semidirect
52. C₂×#13063265	C₂²	semidirect
53. C₂×#13063264	C₂²	semidirect
54. C₂×C₁₆×D₄₃	C₂²	semidirect
55. C₂×#135×C₄₃	C₂²	semidirect
56. C₄₃×#508	C₂²	semidirect
57. C₄₃×#508	C₂²	semidirect
58. C₄₃×#508	C₂²	semidirect
59. C₄₃×#508	C₂²	semidirect
60. C₂×Q₃₂×C₄₃	C₂²	semidirect
61. C₂×SD₃₂×C₄₃	C₂²	semidirect
62. C₂×D₁₆×C₄₃	C₂²	semidirect
63. C₂²×C₁₆×C₄₃	C₂²	semidirect
302. C₂×#508	D₄₃	semidirect
322. C₂×#135	C₂×D₄₃	semidirect
340. #508	C₂×D₄₃	semidirect
341. #508	C₂×D₄₃	semidirect
342. #508	C₂×D₄₃	semidirect
343. #508	C₂×D₄₃	semidirect
346. C₂×Q₃₂	C₂×D₄₃	semidirect
349. C₂×SD₃₂	C₂×D₄₃	semidirect
352. C₂×D₁₆	C₂×D₄₃	semidirect
360. C₂²×C₁₆	C₂×D₄₃	semidirect
361. C₄₃	#62635	semidirect

Maximal subgroups

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

subgroup	index
#19149364	2
#19147745	2
#19147744	2
#19147738	2
#19147737	2
#19147733	2
#19147732	2
#19147729	2
#19147728	2
C₂×#14583331	2
#508×D₄₃	2
C₂×#14583315	2
C₂×C₄₃×#508	2
#62635	43