Subgroups — #25066031

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143618	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13063350	C₂	1	1	yes	maximal, characteristic
3	#19133417	C₂	1	2	yes	maximal, complemented
4	#19133405	C₂	1	2	yes	maximal, complemented
5	C₈×#10621884	C₂	1	2	yes	maximal, complemented
6	C₈×#10621882	C₂	1	2	yes	maximal, complemented
7	#19133345	C₂	1	1	yes	maximal, characteristic, complemented
8	#19132977	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14582626	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2988	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063350	C₄	1	1	yes	characteristic
13	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
14	#14583009	C₄	1	2	yes	—
15	#14582997	C₄	1	2	yes	—
16	C₄×#10621884	C₂²	1	2	yes	—
17	C₄×#10621882	C₂²	1	2	yes	—
18	C₈×D₁₇₂	C₂²	1	2	yes	—
19	C₈×D₁₇₂	C₂²	1	2	yes	—
20	#14582964	—	2	1	no	—
21	#14582964	—	2	1	no	—
22	#14582952	C₂²	1	1	yes	characteristic
23	#14582942	C₄	1	1	yes	characteristic
24	#14582903	C₄	1	1	yes	characteristic
25	#14582900	C₄	1	1	yes	characteristic
26	C₂²⋊C₈×D₄₃	—	2	2	no	—
27	C₄×#10621877	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14582651	C₂²	1	2	yes	complemented
30	#14582649	C₂²	1	2	yes	complemented
31	Q₈⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
32	Q₈⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
33	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
34	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
35	#14582626	C₂²	1	2	yes	—
36	#14582626	C₂²	1	2	yes	—
37	#14582621	C₂²	1	2	yes	complemented
38	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
39	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₄₃	C₂²	1	2	yes	complemented
41	C₈×D₄×C₄₃	—	2	2	no	—
42	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
43	C₄₃×#431	—	2	1	no	—
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₃	—	2	1	no	—
49	#13063350	C₈	1	8	yes	complemented
50	C₂×#10621884	C₂×C₄	1	2	yes	—
51	C₂×#10621882	C₂×C₄	1	2	yes	—
52	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂×C₈×D₄₃	—	2	2	no	—
56	C₂×C₈×D₄₃	—	2	2	no	—
57	C₄×D₁₇₂	—	2	1	no	—
58	C₄×D₁₇₂	—	2	1	no	—
59	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
60	C₄×D₁₇₂	C₂³	1	2	yes	—
61	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
63	#13063258	C₂×C₄	1	2	yes	—
64	#13063256	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
67	#13063249	C₂×C₄	1	2	yes	—
68	#13063246	C₂×C₄	1	2	yes	—
69	#13063245	C₂×C₄	1	2	yes	—
70	#13063245	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
72	(C₂×D₄₃)⋊C₈	—	2	2	no	—
73	(C₂×D₄₃)⋊C₈	—	2	2	no	—
74	#13063236	C₂×C₄	1	2	yes	—
75	C₄×C₄₃⋊C₈	—	2	1	no	—
76	C₄×C₄₃⋊C₈	—	2	1	no	—
77	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
80	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	—	2	1	no	—
82	C₂²×C₈×C₄₃	—	2	2	no	—
83	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₄×D₄×C₄₃	—	2	1	no	—
86	C₄×D₄×C₄₃	—	2	1	no	—
87	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
89	#117×C₄₃	—	2	1	no	—
90	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	—	2	2	no	—
94	C₄⋊C₈×C₄₃	—	2	1	no	—
95	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
98	C₂²⋊C₈×C₄₃	—	2	2	no	—
99	C₂²⋊C₈×C₄₃	D₄	1	2	yes	—
100	C₄×C₈×C₄₃	—	2	2	no	—
101	C₄×C₈×C₄₃	C₂³	1	2	yes	—
102	C₂³×D₄₃	—	2	1	no	—
103	#41×C₄₃	—	2	2	no	—
104	#41×C₄₃	C₂×C₈	1	4	yes	complemented
105	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂²×Dic₄₃	—	2	1	no	—
115	C₂×D₁₇₂	—	2	1	no	—
116	C₂×D₁₇₂	—	2	2	no	—
117	C₂×D₁₇₂	C₂×C₈	1	4	yes	complemented
118	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₄₃	—	2	2	no	—
120	C₂×C₄×D₄₃	—	2	2	no	—
121	C₂×C₄×D₄₃	—	8	1	no	—
122	C₂×C₄×D₄₃	—	8	1	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	8	2	no	—
125	C₂×C₈×C₄₃	—	8	1	no	—
126	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₄₃	—	2	1	no	—
133	C₂²⋊C₄×C₄₃	—	2	1	no	—
134	C₂²⋊C₄×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	—	2	1	no	—
137	C₄²×C₄₃	—	2	1	no	—
138	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	#41	1	1	yes	characteristic
141	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
142	#10621884	C₂×C₈	1	8	yes	complemented
143	#10621882	C₂×C₈	1	8	yes	complemented
144	(C₂×D₄₃)⋊C₄	—	2	2	no	—
145	(C₂×D₄₃)⋊C₄	—	2	2	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
148	#10621877	—	2	2	no	—
149	#10621877	C₂×C₈	1	4	yes	complemented
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	2	1	no	—
153	C₂×C₄₃⋊C₈	—	2	1	no	—
154	C₂×C₄₃⋊C₈	—	4	2	no	—
155	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
157	C₈×D₄₃	—	8	2	no	—
158	C₈×D₄₃	—	8	2	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₄₃	—	2	2	no	—
162	C₂²×D₄₃	—	2	4	no	—
163	C₂²×D₄₃	—	8	1	no	—
164	C₂²×D₄₃	—	8	1	no	—
165	Q₈×C₄₃	—	2	1	no	—
166	Q₈×C₄₃	C₂²×C₈	1	2	yes	—
167	D₄×C₄₃	—	2	4	no	—
168	D₄×C₄₃	—	2	1	no	—
169	D₄×C₄₃	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	8	1	no	—
180	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
184	C₂×C₄×C₄₃	#131	1	2	yes	—
185	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	8	1	no	—
190	D₁₇₂	—	2	2	no	—
191	D₁₇₂	—	2	4	no	—
192	D₁₇₂	C₂²×C₈	1	4	yes	—
193	C₄×D₄₃	—	4	2	no	—
194	C₄×D₄₃	—	4	2	no	—
195	C₄×D₄₃	—	8	2	no	—
196	C₈×C₄₃	—	2	2	no	—
197	C₈×C₄₃	—	2	2	no	—
198	C₈×C₄₃	—	4	2	no	—
199	C₄₃⋊C₈	—	2	2	no	—
200	C₄₃⋊C₈	—	2	2	no	—
201	C₄₃⋊C₈	—	4	1	no	—
202	C₄₃⋊C₈	—	4	1	no	—
203	C₄₃⋊C₈	—	4	1	no	—
204	C₄₃⋊C₈	C₂²×C₈	1	4	yes	—
205	#17852	—	43	1	no	maximal, Sylow
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	4	1	no	—
210	C₂²×C₄₃	—	4	1	no	—
211	C₂²×C₄₃	C₈×D₄	1	2	yes	—
212	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
213	C₂×D₄₃	—	2	4	no	—
214	C₂×D₄₃	—	4	2	no	—
215	C₂×D₄₃	—	4	2	no	—
216	C₂×D₄₃	—	8	4	no	—
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	4	1	no	—
222	C₄×C₄₃	—	4	1	no	—
223	C₄×C₄₃	C₈×D₄	1	2	yes	—
224	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
225	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
226	C₄×C₄₃	#576	1	1	yes	characteristic
227	C₄×C₄₃	#577	1	1	yes	characteristic
228	Dic₄₃	—	4	2	no	—
229	#2988	D₄₃	1	1	yes	characteristic, complemented
230	#2972	—	43	1	no	—
231	C₄×AGL(1,ℤ/8)	—	43	1	no	—
232	#1580	—	43	2	no	—
233	SD₁₆⋊C₈	—	43	2	no	—
234	C₈×SD₁₆	—	43	2	no	—
235	C₈×D₈	—	43	2	no	—
236	#1565	—	43	1	no	—
237	#1476	—	43	1	no	—
238	C₂×D₄⋊C₈	—	43	1	no	—
239	C₈×M₁₆	—	43	1	no	—
240	C₂×C₄₃	—	2	2	no	—
241	C₂×C₄₃	—	4	2	no	—
242	C₂×C₄₃	C₂×C₈×D₄	1	1	yes	characteristic
243	C₂×C₄₃	#2946	1	1	yes	characteristic
244	C₂×C₄₃	#2956	1	1	yes	characteristic
245	D₄₃	—	4	4	no	—
246	C₂×AGL(1,ℤ/8)	—	43	1	no	—
247	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
248	C₂×C₄×D₄	—	43	1	no	—
249	C₈×Q₈	C₂×D₄₃	1	2	yes	complemented
250	#442	—	43	2	no	—
251	#440	—	43	2	no	—
252	C₄×SD₁₆	—	43	2	no	—
253	C₄×D₈	—	43	2	no	—
254	C₈×D₄	—	2	2	no	—
255	C₈×D₄	—	43	2	no	—
256	C₈×D₄	—	43	2	no	—
257	C₈×D₄	—	86	1	no	—
258	C₈×D₄	—	86	1	no	—
259	C₈×D₄	C₂×D₄₃	1	2	yes	complemented
260	#431	—	2	1	no	—
261	#431	—	43	1	no	—
262	#431	C₂×D₄₃	1	1	yes	characteristic
263	#428	—	43	1	no	—
264	C₂×C₄⋊C₈	—	2	1	no	—
265	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
266	#418	—	43	1	no	—
267	#417	—	43	1	no	—
268	C₂×C₂²⋊C₈	—	86	2	no	—
269	C₄×M₁₆	—	43	1	no	—
270	C₂×C₄×C₈	—	43	1	no	—
271	#335	—	43	2	no	—
272	#334	—	43	2	no	—
273	Q₈⋊C₈	—	43	1	no	—
274	Q₈⋊C₈	—	43	1	no	—
275	D₄⋊C₈	—	43	1	no	—
276	D₄⋊C₈	—	43	1	no	—
277	D₄⋊C₈	—	43	2	no	—
278	D₄⋊C₈	—	43	2	no	—
279	#322	—	43	2	no	—
280	C₈²	—	43	2	no	—
281	C₄₃	#17852	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
283	C₂²×D₄	—	43	1	no	—
284	C₂³×C₄	—	86	1	no	—
285	AGL(1,ℤ/8)	—	43	8	no	—
286	C₂×SD₁₆	—	43	2	no	—
287	C₂×D₈	—	43	2	no	—
288	C₂×M₁₆	—	43	1	no	—
289	C₂×M₁₆	—	43	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	86	1	no	—
293	C₂²×C₈	—	86	2	no	—
294	C₂²×C₈	—	86	2	no	—
295	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
296	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	43	2	no	—
300	C₄×D₄	—	43	2	no	—
301	C₄×D₄	—	86	1	no	—
302	C₄×D₄	—	86	1	no	—
303	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
304	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	C₄×D₄₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	—	43	1	no	—
308	C₂×C₂²⋊C₄	—	86	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
311	#107	—	43	2	no	—
312	#106	—	43	2	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	43	1	no	—
316	C₄⋊C₈	—	43	1	no	—
317	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
318	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
320	#103	—	43	2	no	—
321	#102	—	43	2	no	—
322	#102	—	43	2	no	—
323	#102	—	43	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	86	1	no	—
326	C₂²⋊C₈	—	86	2	no	—
327	C₂²⋊C₈	—	86	2	no	—
328	C₂²⋊C₈	C₂²⋊D₄₃	1	2	yes	—
329	#97	—	43	2	no	—
330	C₄×C₈	—	2	2	no	—
331	C₄×C₈	—	43	2	no	—
332	C₄×C₈	—	43	1	no	—
333	C₄×C₈	—	43	1	no	—
334	C₄×C₈	—	86	1	no	—
335	C₄×C₈	—	86	1	no	—
336	C₄×C₈	C₂²×D₄₃	1	2	yes	—
337	C₂⁴	—	86	1	no	—
338	#41	—	2	2	no	—
339	#41	C₈×D₄₃	1	4	yes	complemented
340	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	43	4	no	—
343	C₂×D₄	—	43	2	no	—
344	C₂×D₄	—	86	1	no	—
345	C₂×D₄	—	86	2	no	—
346	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	86	1	no	—
351	C₂²×C₄	—	86	2	no	—
352	C₂²×C₄	—	86	2	no	—
353	C₂²×C₄	—	344	1	no	—
354	C₂²×C₄	—	344	1	no	—
355	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
356	C₂²×C₄	#10621898	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
358	SD₁₆	—	43	8	no	—
359	D₈	—	43	8	no	—
360	M₁₆	—	43	4	no	—
361	M₁₆	—	86	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	8	2	no	—
364	C₂×C₈	—	8	1	no	—
365	C₂×C₈	—	43	2	no	—
366	C₂×C₈	—	43	2	no	—
367	C₂×C₈	—	86	1	no	—
368	C₂×C₈	—	86	1	no	—
369	C₂×C₈	—	86	1	no	—
370	C₂×C₈	—	86	1	no	—
371	C₂×C₈	—	344	2	no	—
372	C₂×C₈	—	344	2	no	—
373	C₂×C₈	—	172	2	no	—
374	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
375	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	43	2	no	—
379	C₄⋊C₄	—	86	1	no	—
380	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
381	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	86	2	no	—
386	C₂²⋊C₄	—	86	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
391	C₄²	#10621898	1	1	yes	characteristic
392	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
393	C₄²	C₂³×D₄₃	1	1	yes	characteristic
394	C₂³	—	2	1	no	—
395	C₂³	—	86	4	no	—
396	C₂³	—	86	2	no	—
397	C₂³	—	344	1	no	—
398	C₂³	—	344	1	no	—
399	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	C₂×C₈×D₄₃	1	2	yes	—
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	43	4	no	—
405	D₄	—	86	2	no	—
406	D₄	—	86	4	no	—
407	D₄	C₂×C₈×D₄₃	1	2	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	8	1	no	—
418	C₂×C₄	—	86	2	no	—
419	C₂×C₄	—	344	2	no	—
420	C₂×C₄	—	344	1	no	—
421	C₂×C₄	—	172	2	no	—
422	C₂×C₄	—	172	2	no	—
423	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
425	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
427	C₂×C₄	#13063331	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
430	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	43	4	no	—
435	C₈	—	86	2	no	—
436	C₈	—	86	2	no	—
437	C₈	—	172	1	no	—
438	C₈	—	172	1	no	—
439	C₈	—	172	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	86	4	no	—
446	C₂²	—	344	4	no	—
447	C₂²	—	172	2	no	—
448	C₂²	—	172	2	no	—
449	C₂²	C₈×C₂²⋊D₄₃	1	2	yes	—
450	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	172	2	no	—
458	C₄	C₈×C₂²⋊D₄₃	1	2	yes	—
459	C₄	C₂²×C₈×D₄₃	1	1	yes	characteristic
460	C₄	C₂×#13063331	1	1	yes	characteristic
461	C₄	#14583702	1	1	yes	characteristic
462	C₄	#14583707	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	4	2	no	—
465	C₂	—	172	4	no	—
466	C₂	C₂×C₈×C₂²⋊D₄₃	1	1	yes	characteristic
467	C₂	#19143423	1	1	yes	characteristic
468	C₂	#19143502	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂³×C₈
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2988	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063350	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2988	D₄₃
hypocenter	C₄₃	#17852
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2988

Complements

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

N	H ≅ G/N	type
1. #19143618	C₂	semidirect
3. #19133417	C₂	semidirect
4. #19133405	C₂	semidirect
5. C₈×#10621884	C₂	semidirect
6. C₈×#10621882	C₂	semidirect
7. #19133345	C₂	semidirect
8. #19132977	C₂	semidirect
9. C₂×#14582626	C₂	semidirect
10. #19132876	C₂	semidirect
11. C₄₃×#2988	C₂	semidirect
29. #14582651	C₂²	semidirect
30. #14582649	C₂²	semidirect
31. Q₈⋊(C₄₃⋊C₈)	C₂²	semidirect
32. Q₈⋊(C₄₃⋊C₈)	C₂²	semidirect
33. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
34. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
37. #14582621	C₂²	semidirect
38. C₈×C₄₃⋊C₈	C₂²	semidirect
40. C₈×Q₈×C₄₃	C₂²	semidirect
42. C₈×D₄×C₄₃	C₂²	semidirect
49. #13063350	C₈	semidirect
104. #41×C₄₃	C₂×C₈	semidirect
117. C₂×D₁₇₂	C₂×C₈	semidirect
142. #10621884	C₂×C₈	semidirect
143. #10621882	C₂×C₈	semidirect
149. #10621877	C₂×C₈	semidirect
229. #2988	D₄₃	semidirect
249. C₈×Q₈	C₂×D₄₃	semidirect
259. C₈×D₄	C₂×D₄₃	semidirect
281. C₄₃	#17852	semidirect
339. #41	C₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19143618	2
C₄×#13063350	2
#19133417	2
#19133405	2
C₈×#10621884	2
C₈×#10621882	2
#19133345	2
#19132977	2
C₂×#14582626	2
#19132876	2
C₄₃×#2988	2
#17852	43