Subgroups — #19146084

Order 5504.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583556	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583287	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583145	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583132	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583112	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583097	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583050	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583044	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583036	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583031	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583000	C₂	1	1	yes	maximal, characteristic, complemented
14	#14582968	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₄₃	—	2	1	no	—
18	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
19	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
20	C₂×#10621883	C₂²	1	1	yes	characteristic
21	C₂×#10621883	C₂²	1	1	yes	characteristic, complemented
22	C₂×#10621884	C₂²	1	1	yes	characteristic, complemented
23	SD₁₆×D₄₃	—	2	4	no	—
24	C₂×#10621882	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
26	#13063321	C₂²	1	1	yes	characteristic
27	#13063312	—	2	1	no	—
28	#13063312	C₂²	1	1	yes	characteristic, complemented
29	#13063304	—	2	1	no	—
30	#13063304	C₂²	1	1	yes	characteristic, complemented
31	#13063299	C₂²	1	1	yes	characteristic
32	#13063297	—	2	1	no	—
33	#13063296	—	2	1	no	—
34	#13063296	C₂²	1	1	yes	characteristic
35	#13063296	C₂²	1	1	yes	characteristic, complemented
36	#13063294	—	2	1	no	—
37	#13063293	—	2	1	no	—
38	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₄₃	—	2	1	no	—
41	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
42	#13063259	C₂²	1	1	yes	characteristic, complemented
43	Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#13063250	C₂²	1	1	yes	characteristic, complemented
45	#13063249	C₂²	1	1	yes	characteristic, complemented
46	#13063247	C₂²	1	1	yes	characteristic, complemented
47	#13063246	C₂²	1	1	yes	characteristic
48	#13063246	C₂²	1	1	yes	characteristic, complemented
49	#13063246	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	#13063235	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₄₃	—	2	4	no	—
56	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₄₃	—	2	1	no	—
62	C₂³×D₄₃	—	2	1	no	—
63	#41×C₄₃	—	2	2	no	—
64	#41×C₄₃	—	4	1	no	—
65	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₄₃	—	2	1	no	—
67	C₂×D₄×C₄₃	—	2	1	no	—
68	C₂×D₄×C₄₃	—	2	2	no	—
69	C₂×D₄×C₄₃	—	4	1	no	—
70	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₄₃	—	2	1	no	—
76	C₂×C₂²⋊D₄₃	—	2	1	no	—
77	C₂×C₂²⋊D₄₃	—	2	1	no	—
78	C₂×C₂²⋊D₄₃	—	2	1	no	—
79	C₂×C₂²⋊D₄₃	—	2	1	no	—
80	C₂×C₂²⋊D₄₃	—	2	1	no	—
81	C₂×C₂²⋊D₄₃	—	4	4	no	—
82	C₂×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
83	C₂²×Dic₄₃	—	2	1	no	—
84	Q₈×D₄₃	—	2	2	no	—
85	Q₈×D₄₃	—	4	1	no	—
86	D₄×D₄₃	—	2	2	no	—
87	D₄×D₄₃	—	4	1	no	—
88	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₄₃	—	2	1	no	—
90	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
91	C₂×Dic₈₆	—	2	1	no	—
92	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
93	SD₁₆×C₄₃	—	2	2	no	—
94	SD₁₆×C₄₃	D₄	1	4	yes	complemented
95	D₈×C₄₃	—	2	2	no	—
96	D₈×C₄₃	—	2	2	no	—
97	M₁₆×C₄₃	—	2	2	no	—
98	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²⋊Dic₄₃	—	2	1	no	—
101	C₂²⋊Dic₄₃	—	2	1	no	—
102	C₂²⋊Dic₄₃	—	2	1	no	—
103	C₂²⋊Dic₄₃	—	2	1	no	—
104	C₂²⋊Dic₄₃	—	2	1	no	—
105	C₂²⋊Dic₄₃	—	2	1	no	—
106	C₂²⋊Dic₄₃	D₄	1	1	yes	characteristic
107	#10621884	—	2	2	no	—
108	#10621883	—	2	2	no	—
109	#10621883	—	4	1	no	—
110	#10621882	—	4	1	no	—
111	(C₂×D₄₃)⋊C₄	—	2	1	no	—
112	(C₂×D₄₃)⋊C₄	D₄	1	1	yes	characteristic
113	C₄⋊Dic₄₃	—	2	1	no	—
114	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
116	Dic₄₃⋊C₄	—	2	1	no	—
117	Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
118	C₄×Dic₄₃	—	2	1	no	—
119	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
120	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
122	#10621873	—	2	2	no	—
123	C₈×D₄₃	—	2	2	no	—
124	C₂³×C₄₃	—	2	1	no	—
125	C₂³×C₄₃	—	2	1	no	—
126	C₂³×C₄₃	—	2	1	no	—
127	C₂³×C₄₃	—	4	2	no	—
128	C₂³×C₄₃	—	4	2	no	—
129	C₂³×C₄₃	—	8	1	no	—
130	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₄₃	—	2	1	no	—
132	C₂²×D₄₃	—	4	2	no	—
133	C₂²×D₄₃	—	4	2	no	—
134	C₂²×D₄₃	—	8	1	no	—
135	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₄₃	—	2	1	no	—
137	Q₈×C₄₃	C₂×D₄	1	2	yes	complemented
138	D₄×C₄₃	—	2	1	no	—
139	D₄×C₄₃	—	2	1	no	—
140	D₄×C₄₃	—	2	1	no	—
141	D₄×C₄₃	—	2	1	no	—
142	D₄×C₄₃	—	2	1	no	—
143	D₄×C₄₃	—	4	2	no	—
144	D₄×C₄₃	—	4	2	no	—
145	D₄×C₄₃	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₂²⋊D₄₃	—	2	2	no	—
153	C₂²⋊D₄₃	—	4	2	no	—
154	C₂²⋊D₄₃	—	4	2	no	—
155	C₂²⋊D₄₃	—	4	2	no	—
156	C₂²⋊D₄₃	—	4	2	no	—
157	C₂²⋊D₄₃	—	4	2	no	—
158	C₂²⋊D₄₃	—	8	1	no	—
159	C₂×Dic₄₃	—	2	1	no	—
160	C₂×Dic₄₃	—	2	1	no	—
161	C₂×Dic₄₃	—	2	1	no	—
162	C₂×Dic₄₃	—	4	2	no	—
163	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
166	D₁₇₂	—	2	1	no	—
167	D₁₇₂	—	2	1	no	—
168	C₄×D₄₃	—	2	1	no	—
169	C₄×D₄₃	—	2	1	no	—
170	C₄×D₄₃	—	4	2	no	—
171	Dic₈₆	—	2	1	no	—
172	Dic₈₆	—	2	1	no	—
173	Dic₈₆	—	4	2	no	—
174	C₈×C₄₃	—	2	1	no	—
175	C₈×C₄₃	C₂×D₄	1	2	yes	complemented
176	C₄₃⋊C₈	—	2	1	no	—
177	C₄₃⋊C₈	—	2	1	no	—
178	C₂²×C₄₃	—	2	2	no	—
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	1	no	—
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	—	4	1	no	—
183	C₂²×C₄₃	—	4	1	no	—
184	C₂²×C₄₃	—	4	1	no	—
185	C₂²×C₄₃	—	4	1	no	—
186	C₂²×C₄₃	—	4	1	no	—
187	C₂²×C₄₃	—	4	1	no	—
188	C₂²×C₄₃	—	4	1	no	—
189	C₂²×C₄₃	—	4	1	no	—
190	C₂²×C₄₃	—	8	4	no	—
191	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×D₄₃	—	2	1	no	—
193	C₂×D₄₃	—	2	1	no	—
194	C₂×D₄₃	—	4	1	no	—
195	C₂×D₄₃	—	4	1	no	—
196	C₂×D₄₃	—	4	1	no	—
197	C₂×D₄₃	—	8	4	no	—
198	C₂×D₄₃	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₄×C₄₃	—	2	2	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
203	Dic₄₃	—	2	1	no	—
204	Dic₄₃	—	2	1	no	—
205	Dic₄₃	—	2	1	no	—
206	Dic₄₃	—	4	1	no	—
207	Dic₄₃	—	4	1	no	—
208	Dic₄₃	—	4	1	no	—
209	#3265	—	43	1	no	maximal, Sylow
210	C₂×C₄₃	—	4	2	no	—
211	C₂×C₄₃	—	4	1	no	—
212	C₂×C₄₃	—	8	1	no	—
213	C₂×C₄₃	—	8	1	no	—
214	C₂×C₄₃	D₄²	1	1	yes	characteristic
215	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂×C₄₃	#577	1	1	yes	characteristic
217	D₄₃	—	2	2	no	—
218	D₄₃	—	8	1	no	—
219	C₂×AGL(1,ℤ/8)	D₄₃	1	1	yes	characteristic, complemented
220	C₂²×SD₁₆	—	43	1	no	—
221	#548	—	43	1	no	—
222	D₄²	—	43	1	no	—
223	#496	—	43	1	no	—
224	#468	—	43	1	no	—
225	#466	—	43	1	no	—
226	#463	—	43	1	no	—
227	#460	—	43	1	no	—
228	#450	—	43	1	no	—
229	#449	—	43	1	no	—
230	#448	—	43	1	no	—
231	#447	—	43	1	no	—
232	#440	—	43	1	no	—
233	#435	—	43	1	no	—
234	C₄₃	#3265	1	1	yes	characteristic, complemented, Sylow
235	C₂×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
236	C₂²×Q₈	—	43	1	no	—
237	C₂²×D₄	—	43	1	no	—
238	C₂²×D₄	—	86	1	no	—
239	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	2	4	no	—
241	C₂×SD₁₆	—	43	1	no	—
242	C₂×SD₁₆	—	43	1	no	—
243	C₂×SD₁₆	—	43	1	no	—
244	C₂×SD₁₆	—	43	1	no	—
245	C₂×SD₁₆	—	86	4	no	—
246	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
247	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
248	C₂×D₈	—	43	1	no	—
249	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
250	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
251	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
252	C₂²×C₈	—	43	1	no	—
253	#127	—	43	1	no	—
254	#124	—	43	1	no	—
255	#124	—	86	1	no	—
256	C₂²⋊Q₈	—	43	1	no	—
257	C₂²⋊Q₈	—	86	1	no	—
258	#121	—	43	1	no	—
259	#121	—	43	1	no	—
260	#121	—	43	1	no	—
261	#121	—	86	1	no	—
262	#121	—	86	1	no	—
263	#120	—	86	1	no	—
264	#120	—	86	1	no	—
265	C₄×Q₈	—	43	1	no	—
266	C₄×D₄	—	43	1	no	—
267	C₄×D₄	—	43	1	no	—
268	C₄×D₄	—	86	1	no	—
269	#107	—	43	1	no	—
270	C₄⋊C₈	—	43	1	no	—
271	#103	—	43	1	no	—
272	#103	—	43	1	no	—
273	#102	—	43	1	no	—
274	#102	—	43	1	no	—
275	#102	—	43	1	no	—
276	#102	—	43	1	no	—
277	C₂²⋊C₈	—	43	1	no	—
278	C₂²⋊C₈	—	43	1	no	—
279	#97	—	43	1	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	86	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	C₂×Q₈	—	43	1	no	—
285	C₂×Q₈	—	86	1	no	—
286	C₂×Q₈	—	86	2	no	—
287	C₂×Q₈	—	172	1	no	—
288	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	43	1	no	—
294	C₂×D₄	—	43	1	no	—
295	C₂×D₄	—	86	1	no	—
296	C₂×D₄	—	86	1	no	—
297	C₂×D₄	—	86	1	no	—
298	C₂×D₄	—	86	2	no	—
299	C₂×D₄	—	86	1	no	—
300	C₂×D₄	—	86	1	no	—
301	C₂×D₄	—	86	1	no	—
302	C₂×D₄	—	172	1	no	—
303	C₂×D₄	—	172	4	no	—
304	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
306	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	43	1	no	—
309	C₂²×C₄	—	86	1	no	—
310	C₂²×C₄	—	86	1	no	—
311	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	86	2	no	—
314	SD₁₆	—	86	2	no	—
315	SD₁₆	—	86	2	no	—
316	SD₁₆	—	172	1	no	—
317	SD₁₆	C₂²⋊D₄₃	1	4	yes	complemented
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	172	1	no	—
321	M₁₆	—	2	2	no	—
322	C₂×C₈	—	43	1	no	—
323	C₂×C₈	—	43	1	no	—
324	C₂×C₈	—	86	2	no	—
325	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
327	C₄⋊C₄	—	43	1	no	—
328	C₄⋊C₄	—	43	1	no	—
329	C₄⋊C₄	—	43	1	no	—
330	C₄⋊C₄	—	86	1	no	—
331	C₄⋊C₄	—	86	1	no	—
332	C₂²⋊C₄	—	43	1	no	—
333	C₂²⋊C₄	—	43	1	no	—
334	C₂²⋊C₄	—	86	1	no	—
335	C₂²⋊C₄	—	86	1	no	—
336	C₂²⋊C₄	—	86	1	no	—
337	C₂²⋊C₄	—	86	1	no	—
338	C₂²⋊C₄	—	86	1	no	—
339	C₂²⋊C₄	—	86	1	no	—
340	C₂²⋊C₄	—	86	1	no	—
341	C₄²	—	43	1	no	—
342	C₄²	—	86	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	43	1	no	—
350	C₂³	—	86	1	no	—
351	C₂³	—	344	1	no	—
352	C₂³	—	172	2	no	—
353	C₂³	—	172	2	no	—
354	C₂³	D₄×D₄₃	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	86	1	no	—
357	Q₈	—	86	1	no	—
358	Q₈	—	172	2	no	—
359	Q₈	C₂×C₂²⋊D₄₃	1	2	yes	complemented
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	86	2	no	—
368	D₄	—	86	1	no	—
369	D₄	—	86	1	no	—
370	D₄	—	344	1	no	—
371	D₄	—	172	2	no	—
372	D₄	—	172	2	no	—
373	D₄	—	172	2	no	—
374	D₄	—	172	2	no	—
375	D₄	—	172	2	no	—
376	D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	43	1	no	—
382	C₂×C₄	—	43	1	no	—
383	C₂×C₄	—	43	1	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	86	1	no	—
388	C₂×C₄	—	86	1	no	—
389	C₂×C₄	—	172	2	no	—
390	C₂×C₄	—	172	2	no	—
391	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	86	1	no	—
395	C₈	—	86	1	no	—
396	C₈	C₂×C₂²⋊D₄₃	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	43	2	no	—
411	C₂²	—	86	1	no	—
412	C₂²	—	86	1	no	—
413	C₂²	—	344	4	no	—
414	C₂²	—	172	1	no	—
415	C₂²	—	172	1	no	—
416	C₂²	—	172	1	no	—
417	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	86	1	no	—
421	C₄	—	86	1	no	—
422	C₄	—	86	1	no	—
423	C₄	—	172	1	no	—
424	C₄	—	172	1	no	—
425	C₄	—	172	1	no	—
426	C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
427	C₄	#13063370	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	8	1	no	—
432	C₂	—	86	2	no	—
433	C₂	—	344	1	no	—
434	C₂	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
436	C₂	#14583709	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×AGL(1,ℤ/8)×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₄₃
hypocenter	C₄₃	#3265
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₄₃	C₂	semidirect
2. #14583556	C₂	semidirect
3. D₄×C₂²⋊D₄₃	C₂	semidirect
4. #14583287	C₂	semidirect
5. #14583145	C₂	semidirect
6. #14583132	C₂	semidirect
7. #14583112	C₂	semidirect
8. #14583097	C₂	semidirect
9. #14583050	C₂	semidirect
10. #14583044	C₂	semidirect
11. #14583036	C₂	semidirect
12. #14583031	C₂	semidirect
13. #14583000	C₂	semidirect
14. #14582968	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₄₃	C₂	semidirect
16. C₂×Q₈×D₄₃	C₂²	semidirect
19. C₂×#10621873	C₂²	semidirect
21. C₂×#10621883	C₂²	semidirect
22. C₂×#10621884	C₂²	semidirect
24. C₂×#10621882	C₂²	semidirect
25. C₂×C₈×D₄₃	C₂²	semidirect
28. #13063312	C₂²	semidirect
30. #13063304	C₂²	semidirect
35. #13063296	C₂²	semidirect
38. Q₈×Dic₄₃	C₂²	semidirect
42. #13063259	C₂²	semidirect
43. Dic₄₃⋊C₈	C₂²	semidirect
44. #13063250	C₂²	semidirect
45. #13063249	C₂²	semidirect
46. #13063247	C₂²	semidirect
48. #13063246	C₂²	semidirect
49. #13063246	C₂²	semidirect
50. C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
51. (C₂×D₄₃)⋊C₈	C₂²	semidirect
52. #13063235	C₂²	semidirect
53. C₂×#41×C₄₃	C₂²	semidirect
57. C₂×SD₁₆×C₄₃	C₂²	semidirect
59. C₂×D₈×C₄₃	C₂²	semidirect
60. C₂×M₁₆×C₄₃	C₂²	semidirect
94. SD₁₆×C₄₃	D₄	semidirect
137. Q₈×C₄₃	C₂×D₄	semidirect
175. C₈×C₄₃	C₂×D₄	semidirect
198. C₂×D₄₃	AGL(1,ℤ/8)	semidirect
219. C₂×AGL(1,ℤ/8)	D₄₃	semidirect
234. C₄₃	#3265	semidirect
235. C₂×#41	C₂×D₄₃	semidirect
247. C₂×SD₁₆	C₂×D₄₃	semidirect
250. C₂×D₈	C₂×D₄₃	semidirect
251. C₂×M₁₆	C₂×D₄₃	semidirect
317. SD₁₆	C₂²⋊D₄₃	semidirect
359. Q₈	C₂×C₂²⋊D₄₃	semidirect
396. C₈	C₂×C₂²⋊D₄₃	semidirect