Subgroups — #25080371

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144388	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144055	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134015	C₂	1	2	yes	maximal, complemented
5	#19134001	C₂	1	2	yes	maximal, complemented
6	#19133967	C₂	1	2	yes	maximal, complemented
7	#19133933	C₂	1	2	yes	maximal, complemented
8	#19133351	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133285	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133272	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063350	—	2	1	no	—
13	C₂²×C₈×D₄₃	—	2	1	no	—
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	#14583196	—	2	2	no	—
16	#14583186	C₂²	1	2	yes	—
17	#14583176	C₂²	1	2	yes	—
18	#14583111	—	2	2	no	—
19	#14583101	C₂²	1	2	yes	—
20	#14583091	C₂²	1	2	yes	—
21	C₈×D₁₇₂	—	2	1	no	—
22	C₈×D₁₇₂	—	2	1	no	—
23	C₈×D₁₇₂	C₂²	1	2	yes	—
24	C₈×D₁₇₂	C₂²	1	2	yes	—
25	#14582942	—	2	1	no	—
26	#14582923	C₂²	1	1	yes	characteristic
27	#14582923	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	#14582903	—	2	1	no	—
30	#14582900	—	2	1	no	—
31	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
32	#14582650	C₂²	1	2	yes	complemented
33	#14582650	C₂²	1	2	yes	complemented
34	#14582648	C₂²	1	2	yes	complemented
35	#14582645	C₂²	1	2	yes	complemented
36	#14582645	C₂²	1	2	yes	complemented
37	#14582643	C₂²	1	2	yes	complemented
38	C₄₃×#533	C₂²	1	1	yes	characteristic
39	C₄₃×#532	C₂²	1	1	yes	characteristic
40	C₄₃×#498	C₂²	1	1	yes	characteristic, complemented
41	C₄₃×#492	C₂²	1	1	yes	characteristic, complemented
42	C₄₃×#487	C₂²	1	1	yes	characteristic, complemented
43	C₄₃×#486	C₂²	1	1	yes	characteristic, complemented
44	C₄₃×#465	—	2	1	no	—
45	C₄₃×#465	—	2	1	no	—
46	C₄×SD₁₆×C₄₃	—	2	1	no	—
47	C₄×SD₁₆×C₄₃	—	2	1	no	—
48	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₃	—	2	1	no	—
51	#13063350	—	4	4	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂×#10621882	—	2	2	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	C₂×C₈×D₄₃	—	2	2	no	—
58	C₂×C₈×D₄₃	—	2	2	no	—
59	C₂×C₈×D₄₃	—	4	4	no	—
60	C₄×D₁₇₂	—	2	1	no	—
61	C₄×D₁₇₂	—	2	1	no	—
62	C₄×D₁₇₂	D₄	1	2	yes	—
63	C₄×D₁₇₂	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
65	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
66	#13063258	—	2	2	no	—
67	#13063256	—	2	2	no	—
68	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
72	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	#13063249	—	2	2	no	—
75	#13063246	—	2	2	no	—
76	#13063245	—	2	2	no	—
77	#13063245	—	2	2	no	—
78	(C₂×D₄₃)⋊C₈	—	2	2	no	—
79	(C₂×D₄₃)⋊C₈	—	2	2	no	—
80	C₂×#41×C₄₃	—	2	1	no	—
81	C₂×SD₁₆×C₄₃	—	2	1	no	—
82	C₂×SD₁₆×C₄₃	—	2	1	no	—
83	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
88	#127×C₄₃	C₂³	1	1	yes	characteristic
89	#125×C₄₃	—	2	1	no	—
90	#124×C₄₃	—	2	1	no	—
91	C₂²⋊Q₈×C₄₃	—	2	1	no	—
92	C₂²⋊Q₈×C₄₃	—	2	1	no	—
93	#121×C₄₃	—	2	1	no	—
94	#121×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	C₄×Q₈×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	—	2	1	no	—
99	#117×C₄₃	—	2	1	no	—
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	#106×C₄₃	—	2	1	no	—
102	#106×C₄₃	—	2	1	no	—
103	#103×C₄₃	—	2	1	no	—
104	#103×C₄₃	—	2	1	no	—
105	#102×C₄₃	—	2	1	no	—
106	#102×C₄₃	—	2	1	no	—
107	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
108	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
109	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
111	C₂³×D₄₃	—	2	1	no	—
112	#41×C₄₃	—	4	2	no	—
113	#41×C₄₃	—	4	2	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×Q₈×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	2	1	no	—
118	C₂×D₄×C₄₃	—	2	1	no	—
119	C₂×D₄×C₄₃	—	2	1	no	—
120	C₂×D₄×C₄₃	—	4	1	no	—
121	C₂²×C₄×C₄₃	—	4	1	no	—
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
125	C₂²×Dic₄₃	—	2	1	no	—
126	C₂×D₁₇₂	—	2	1	no	—
127	C₂×D₁₇₂	—	2	2	no	—
128	C₂×D₁₇₂	SD₁₆	1	4	yes	complemented
129	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
130	C₂×C₄×D₄₃	—	2	2	no	—
131	C₂×C₄×D₄₃	—	2	2	no	—
132	C₂×C₄×D₄₃	—	4	2	no	—
133	C₂×C₄×D₄₃	—	4	2	no	—
134	SD₁₆×C₄₃	—	4	2	no	—
135	SD₁₆×C₄₃	—	4	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	4	1	no	—
138	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	—	2	1	no	—
145	C₄⋊C₄×C₄₃	—	2	1	no	—
146	C₄⋊C₄×C₄₃	—	2	1	no	—
147	C₄⋊C₄×C₄₃	—	2	1	no	—
148	C₄⋊C₄×C₄₃	—	4	1	no	—
149	C₄⋊C₄×C₄₃	—	4	1	no	—
150	C₂²⋊C₄×C₄₃	—	4	1	no	—
151	C₂²⋊C₄×C₄₃	—	4	1	no	—
152	C₂²⋊C₄×C₄₃	—	4	1	no	—
153	C₄²×C₄₃	—	4	1	no	—
154	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₄₃	#41	1	1	yes	characteristic
157	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
158	#10621884	—	4	4	no	—
159	#10621882	—	4	4	no	—
160	(C₂×D₄₃)⋊C₄	—	2	2	no	—
161	(C₂×D₄₃)⋊C₄	—	2	2	no	—
162	C₄⋊Dic₄₃	—	2	1	no	—
163	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
164	#10621877	—	4	2	no	—
165	#10621877	—	4	2	no	—
166	C₂×C₄₃⋊C₈	—	2	2	no	—
167	C₂×C₄₃⋊C₈	—	2	2	no	—
168	C₂×C₄₃⋊C₈	—	2	2	no	—
169	C₂×C₄₃⋊C₈	—	4	2	no	—
170	C₈×D₄₃	—	4	4	no	—
171	C₈×D₄₃	—	4	4	no	—
172	C₂³×C₄₃	—	4	1	no	—
173	C₂³×C₄₃	#121	1	1	yes	characteristic
174	C₂²×D₄₃	—	2	2	no	—
175	C₂²×D₄₃	—	2	4	no	—
176	C₂²×D₄₃	—	4	2	no	—
177	C₂²×D₄₃	—	4	2	no	—
178	Q₈×C₄₃	—	4	1	no	—
179	Q₈×C₄₃	—	4	1	no	—
180	Q₈×C₄₃	—	4	1	no	—
181	Q₈×C₄₃	—	4	1	no	—
182	Q₈×C₄₃	—	8	1	no	—
183	D₄×C₄₃	—	4	1	no	—
184	D₄×C₄₃	—	4	1	no	—
185	D₄×C₄₃	—	4	1	no	—
186	D₄×C₄₃	—	4	1	no	—
187	D₄×C₄₃	—	8	1	no	—
188	D₄×C₄₃	—	8	2	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	—	4	1	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	1	no	—
195	C₂×C₄×C₄₃	—	8	2	no	—
196	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
198	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₄₃	#135	1	2	yes	—
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
204	C₂×Dic₄₃	—	2	2	no	—
205	C₂×Dic₄₃	—	4	2	no	—
206	D₁₇₂	—	2	2	no	—
207	D₁₇₂	—	2	4	no	—
208	D₁₇₂	C₂×SD₁₆	1	4	yes	—
209	C₄×D₄₃	—	4	4	no	—
210	C₄×D₄₃	—	4	2	no	—
211	C₄×D₄₃	—	4	2	no	—
212	C₈×C₄₃	—	2	1	no	—
213	C₈×C₄₃	—	2	1	no	—
214	C₈×C₄₃	—	2	1	no	—
215	C₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	complemented
216	C₄₃⋊C₈	—	4	2	no	—
217	C₄₃⋊C₈	—	4	2	no	—
218	C₄₃⋊C₈	—	4	2	no	—
219	#19254	—	43	1	no	maximal, Sylow
220	C₂²×C₄₃	—	2	1	no	—
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	—	8	1	no	—
223	C₂²×C₄₃	—	8	1	no	—
224	C₂²×C₄₃	—	8	1	no	—
225	C₂²×C₄₃	#465	1	2	yes	—
226	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
227	C₂×D₄₃	—	2	4	no	—
228	C₂×D₄₃	—	4	8	no	—
229	C₂×D₄₃	—	4	2	no	—
230	C₂×D₄₃	—	4	2	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	—	8	1	no	—
235	C₄×C₄₃	—	8	1	no	—
236	C₄×C₄₃	—	8	1	no	—
237	C₄×C₄₃	#465	1	2	yes	—
238	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
239	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
240	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₄×C₄₃	#575	1	1	yes	characteristic
242	Dic₄₃	—	4	2	no	—
243	#3167	D₄₃	1	1	yes	characteristic, complemented
244	#3077	—	43	1	no	—
245	#3036	—	43	1	no	—
246	C₂×C₈×D₄	—	43	1	no	—
247	#1679	—	43	2	no	—
248	#1677	—	43	2	no	—
249	#1671	—	43	2	no	—
250	#1665	—	43	2	no	—
251	#1566	—	43	1	no	—
252	#1550	—	43	1	no	—
253	#1547	—	43	1	no	—
254	C₂×C₄₃	—	2	2	no	—
255	C₂×C₄₃	—	16	1	no	—
256	C₂×C₄₃	#3036	1	1	yes	characteristic
257	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
258	C₂×C₄₃	#3067	1	1	yes	characteristic
259	D₄₃	—	4	4	no	—
260	C₂×AGL(1,ℤ/8)	—	86	1	no	—
261	C₂³×C₈	—	86	1	no	—
262	#533	C₂×D₄₃	1	1	yes	characteristic
263	#532	C₂×D₄₃	1	1	yes	characteristic
264	C₂×C₄×D₄	—	43	1	no	—
265	#498	C₂×D₄₃	1	1	yes	characteristic, complemented
266	#492	C₂×D₄₃	1	1	yes	characteristic, complemented
267	#487	C₂×D₄₃	1	1	yes	characteristic, complemented
268	#486	C₂×D₄₃	1	1	yes	characteristic, complemented
269	#478	—	86	2	no	—
270	#476	—	43	2	no	—
271	#474	—	43	2	no	—
272	#465	—	2	1	no	—
273	#465	—	2	1	no	—
274	#463	—	86	2	no	—
275	#461	—	43	2	no	—
276	#459	—	43	2	no	—
277	C₄×SD₁₆	—	2	1	no	—
278	C₄×SD₁₆	—	2	1	no	—
279	C₈×D₄	—	43	2	no	—
280	C₈×D₄	—	43	2	no	—
281	C₈×D₄	—	86	1	no	—
282	C₈×D₄	—	86	1	no	—
283	#428	—	86	1	no	—
284	#423	—	43	1	no	—
285	#423	—	43	1	no	—
286	C₂×C₄⋊C₈	—	43	1	no	—
287	#418	—	86	1	no	—
288	#417	—	86	1	no	—
289	C₂×C₂²⋊C₈	—	86	1	no	—
290	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
291	#334	—	43	2	no	—
292	#334	—	43	2	no	—
293	#333	—	43	2	no	—
294	#332	—	43	2	no	—
295	#332	—	43	2	no	—
296	#331	—	43	2	no	—
297	C₄₃	#19254	1	1	yes	characteristic, complemented, Sylow
298	C₂×#41	—	2	1	no	—
299	C₂²×D₄	—	43	1	no	—
300	C₂³×C₄	—	86	1	no	—
301	AGL(1,ℤ/8)	—	172	4	no	—
302	C₂×SD₁₆	—	2	1	no	—
303	C₂×SD₁₆	—	2	1	no	—
304	C₂×SD₁₆	—	86	2	no	—
305	C₂×D₈	—	86	2	no	—
306	C₂×M₁₆	—	86	1	no	—
307	C₂×M₁₆	—	86	1	no	—
308	C₂²×C₈	—	86	1	no	—
309	C₂²×C₈	—	86	2	no	—
310	C₂²×C₈	—	86	2	no	—
311	C₂²×C₈	—	172	4	no	—
312	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
313	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
314	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
315	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
316	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
317	#127	C₂²×D₄₃	1	1	yes	characteristic
318	#125	—	2	1	no	—
319	#124	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	43	2	no	—
329	C₄×D₄	—	43	2	no	—
330	C₄×D₄	—	86	1	no	—
331	C₄×D₄	—	86	1	no	—
332	#117	—	2	1	no	—
333	C₂×C₄⋊C₄	—	43	1	no	—
334	C₂×C₂²⋊C₄	—	86	1	no	—
335	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
336	#107	—	86	2	no	—
337	#106	—	2	1	no	—
338	#106	—	2	1	no	—
339	#106	—	86	2	no	—
340	C₄⋊C₈	—	43	2	no	—
341	C₄⋊C₈	—	43	2	no	—
342	C₄⋊C₈	—	43	2	no	—
343	C₄⋊C₈	—	86	1	no	—
344	C₄⋊C₈	—	86	1	no	—
345	C₄⋊C₈	—	86	1	no	—
346	#103	—	2	1	no	—
347	#103	—	2	1	no	—
348	#103	—	86	2	no	—
349	#102	—	2	1	no	—
350	#102	—	2	1	no	—
351	#102	—	86	2	no	—
352	#102	—	86	2	no	—
353	#102	—	86	2	no	—
354	C₂²⋊C₈	—	86	2	no	—
355	C₂²⋊C₈	—	86	2	no	—
356	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
357	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
358	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
360	C₂⁴	—	86	1	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	43	4	no	—
371	C₂×D₄	—	43	2	no	—
372	C₂×D₄	—	86	1	no	—
373	C₂×D₄	—	86	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	86	1	no	—
376	C₂²×C₄	—	86	2	no	—
377	C₂²×C₄	—	86	2	no	—
378	C₂²×C₄	—	172	2	no	—
379	C₂²×C₄	—	172	2	no	—
380	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
381	C₂²×C₄	#10621900	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
383	SD₁₆	—	4	2	no	—
384	SD₁₆	—	4	2	no	—
385	SD₁₆	—	172	4	no	—
386	D₈	—	172	4	no	—
387	M₁₆	—	172	2	no	—
388	M₁₆	—	172	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	1	no	—
391	C₂×C₈	—	86	2	no	—
392	C₂×C₈	—	86	2	no	—
393	C₂×C₈	—	86	2	no	—
394	C₂×C₈	—	172	4	no	—
395	C₂×C₈	—	172	2	no	—
396	C₂×C₈	—	172	4	no	—
397	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
398	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
399	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
400	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	43	2	no	—
410	C₄⋊C₄	—	86	1	no	—
411	C₂²⋊C₄	—	4	1	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	86	2	no	—
415	C₂²⋊C₄	—	86	2	no	—
416	C₄²	—	4	1	no	—
417	C₄²	D₄×D₄₃	1	1	yes	characteristic
418	C₄²	#10621900	1	1	yes	characteristic
419	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
420	C₄²	C₂³×D₄₃	1	1	yes	characteristic
421	C₂³	—	4	1	no	—
422	C₂³	—	86	4	no	—
423	C₂³	—	86	2	no	—
424	C₂³	—	172	2	no	—
425	C₂³	—	172	2	no	—
426	C₂³	#13063296	1	1	yes	characteristic
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	1	no	—
431	Q₈	—	8	1	no	—
432	D₄	—	4	1	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	8	1	no	—
437	D₄	—	8	2	no	—
438	D₄	—	43	4	no	—
439	D₄	—	86	4	no	—
440	D₄	—	86	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	86	2	no	—
449	C₂×C₄	—	172	4	no	—
450	C₂×C₄	—	172	2	no	—
451	C₂×C₄	—	172	2	no	—
452	C₂×C₄	—	172	2	no	—
453	C₂×C₄	#13063296	1	1	yes	characteristic
454	C₂×C₄	#13063296	1	1	yes	characteristic
455	C₂×C₄	#13063296	1	1	yes	characteristic
456	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
457	C₂×C₄	#13063346	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	172	2	no	—
465	C₈	—	172	2	no	—
466	C₈	—	172	2	no	—
467	C₈	#13063350	1	2	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	86	4	no	—
474	C₂²	—	172	8	no	—
475	C₂²	—	172	2	no	—
476	C₂²	—	172	2	no	—
477	C₂²	#14583125	1	2	yes	—
478	C₂²	C₂×#13063296	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	172	2	no	—
486	C₄	#14583125	1	2	yes	—
487	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
488	C₄	C₂×#13063346	1	1	yes	characteristic
489	C₄	C₂×#13063350	1	1	yes	characteristic
490	C₄	#14583697	1	1	yes	characteristic
491	C₂	—	2	2	no	—
492	C₂	—	16	1	no	—
493	C₂	—	172	4	no	—
494	C₂	#19144055	1	1	yes	characteristic
495	C₂	C₂×#14583125	1	1	yes	characteristic
496	C₂	#19144311	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3167	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19144055	C₂
hypercenter	#3167	D₄₃
hypocenter	C₄₃	#19254
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #19144388	C₂	semidirect
3. C₂×C₈×D₁₇₂	C₂	semidirect
4. #19134015	C₂	semidirect
5. #19134001	C₂	semidirect
6. #19133967	C₂	semidirect
7. #19133933	C₂	semidirect
8. #19133351	C₂	semidirect
9. #19133285	C₂	semidirect
10. #19133272	C₂	semidirect
11. C₄₃×#3167	C₂	semidirect
32. #14582650	C₂²	semidirect
33. #14582650	C₂²	semidirect
34. #14582648	C₂²	semidirect
35. #14582645	C₂²	semidirect
36. #14582645	C₂²	semidirect
37. #14582643	C₂²	semidirect
40. C₄₃×#498	C₂²	semidirect
41. C₄₃×#492	C₂²	semidirect
42. C₄₃×#487	C₂²	semidirect
43. C₄₃×#486	C₂²	semidirect
128. C₂×D₁₇₂	SD₁₆	semidirect
215. C₈×C₄₃	AGL(1,ℤ/8)	semidirect
243. #3167	D₄₃	semidirect
265. #498	C₂×D₄₃	semidirect
266. #492	C₂×D₄₃	semidirect
267. #487	C₂×D₄₃	semidirect
268. #486	C₂×D₄₃	semidirect
297. C₄₃	#19254	semidirect
467. C₈	#13063350	semidirect

Maximal subgroups

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

subgroup	index
#19144388	2
#19144055	2
C₂×C₈×D₁₇₂	2
#19134015	2
#19134001	2
#19133967	2
#19133933	2
#19133351	2
#19133285	2
#19133272	2
C₄₃×#3167	2
#19254	43