Subgroups — #24991159

Order 11008.

620 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10621873	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582964	C₂	1	1	yes	maximal, characteristic
3	#19135530	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582629	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
6	C₄₃⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621873	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₄₃	—	2	1	no	—
10	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
12	C₄×#10621873	—	2	2	no	—
13	C₄×#10621873	—	2	2	no	—
14	#14582964	—	2	2	no	—
15	#14582964	—	2	2	no	—
16	C₂×#13063257	C₄	1	1	yes	characteristic
17	C₂×#13063250	C₄	1	1	yes	characteristic
18	C₂×#13063247	C₄	1	1	yes	characteristic
19	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
20	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	#14582653	—	2	1	no	—
23	#14582653	—	2	1	no	—
24	#14582629	—	2	2	no	—
25	#14582626	—	2	2	no	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₃	—	2	1	no	—
32	C₂×#10621873	—	2	2	no	—
33	C₂×#10621873	—	2	2	no	—
34	C₂×#10621873	C₈	1	4	yes	complemented
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
37	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
38	C₂×C₈×D₄₃	—	2	4	no	—
39	C₂×C₈×D₄₃	—	4	2	no	—
40	C₂×C₈×D₄₃	—	4	2	no	—
41	C₄×Dic₈₆	—	2	1	no	—
42	C₄×Dic₈₆	—	2	1	no	—
43	C₄×Dic₈₆	—	2	1	no	—
44	C₄×Dic₈₆	—	2	1	no	—
45	C₄×D₁₇₂	—	2	1	no	—
46	C₄×D₁₇₂	—	2	1	no	—
47	C₄×D₁₇₂	D₄	1	2	yes	—
48	C₄×D₁₇₂	D₄	1	2	yes	—
49	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂×Dic₄₃⋊C₄	—	2	1	no	—
52	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
53	C₂×C₄×Dic₄₃	—	2	1	no	—
54	#13063257	—	2	2	no	—
55	#13063250	—	2	2	no	—
56	#13063247	—	2	2	no	—
57	(C₂×D₄₃)⋊C₈	—	2	4	no	—
58	C₄×C₄₃⋊C₈	—	2	1	no	—
59	C₄×C₄₃⋊C₈	—	2	1	no	—
60	C₄×C₄₃⋊C₈	—	2	1	no	—
61	C₄×C₄₃⋊C₈	—	2	1	no	—
62	C₂²×C₈×C₄₃	—	2	1	no	—
63	C₂²×C₈×C₄₃	—	2	1	no	—
64	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₄₃	—	2	1	no	—
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄⋊C₈×C₄₃	—	2	1	no	—
70	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
71	C₄×C₈×C₄₃	—	2	1	no	—
72	C₄×C₈×C₄₃	—	2	1	no	—
73	C₂³×D₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
77	C₂²×Dic₄₃	—	2	1	no	—
78	C₂²×Dic₄₃	—	2	1	no	—
79	C₂²×Dic₄₃	—	2	1	no	—
80	C₂×D₁₇₂	—	2	1	no	—
81	C₂×D₁₇₂	—	2	1	no	—
82	C₂×D₁₇₂	—	2	1	no	—
83	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
84	C₂×D₁₇₂	C₂×C₈	1	2	yes	—
85	C₂×D₁₇₂	M₁₆	1	2	yes	—
86	C₂×C₄×D₄₃	—	2	2	no	—
87	C₂×C₄×D₄₃	—	2	2	no	—
88	C₂×C₄×D₄₃	—	4	1	no	—
89	C₂×C₄×D₄₃	—	4	1	no	—
90	C₂×C₄×D₄₃	—	4	1	no	—
91	C₂×C₄×D₄₃	—	4	1	no	—
92	C₂×Dic₈₆	—	2	1	no	—
93	C₂×Dic₈₆	—	2	1	no	—
94	C₂×Dic₈₆	—	2	1	no	—
95	C₂×Dic₈₆	—	2	1	no	—
96	C₂×Dic₈₆	—	2	1	no	—
97	C₂×Dic₈₆	C₂×C₈	1	2	yes	complemented
98	C₂×C₈×C₄₃	—	2	1	no	—
99	C₂×C₈×C₄₃	—	2	1	no	—
100	C₂×C₈×C₄₃	—	2	1	no	—
101	C₂×C₈×C₄₃	—	2	2	no	—
102	C₂×C₈×C₄₃	—	2	1	no	—
103	C₂×C₈×C₄₃	—	2	1	no	—
104	C₂×C₈×C₄₃	—	4	1	no	—
105	C₂×C₈×C₄₃	—	4	1	no	—
106	C₂×C₈×C₄₃	—	4	1	no	—
107	C₂×C₈×C₄₃	—	4	1	no	—
108	C₂×C₈×C₄₃	—	4	1	no	—
109	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	complemented
110	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₄₃	#41	1	1	yes	characteristic
114	(C₂×D₄₃)⋊C₄	—	2	2	no	—
115	(C₂×D₄₃)⋊C₄	—	2	2	no	—
116	C₄⋊Dic₄₃	—	2	1	no	—
117	C₄⋊Dic₄₃	—	2	1	no	—
118	C₄⋊Dic₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	C₂²⋊C₄	1	2	yes	—
120	Dic₄₃⋊C₄	—	4	1	no	—
121	Dic₄₃⋊C₄	—	4	1	no	—
122	C₄×Dic₄₃	—	4	1	no	—
123	C₄×Dic₄₃	—	4	1	no	—
124	C₂×C₄₃⋊C₈	—	2	1	no	—
125	C₂×C₄₃⋊C₈	—	2	1	no	—
126	C₂×C₄₃⋊C₈	—	2	2	no	—
127	C₂×C₄₃⋊C₈	—	2	1	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	4	1	no	—
131	C₂×C₄₃⋊C₈	—	4	1	no	—
132	C₂×C₄₃⋊C₈	SD₁₆	1	2	yes	complemented
133	#10621873	—	2	8	no	—
134	C₈×D₄₃	—	4	8	no	—
135	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
136	C₂²×D₄₃	—	2	2	no	—
137	C₂²×D₄₃	—	2	2	no	—
138	C₂²×D₄₃	—	2	2	no	—
139	C₂²×D₄₃	—	4	1	no	—
140	C₂²×D₄₃	—	4	1	no	—
141	C₂²×D₄₃	—	4	1	no	—
142	C₂²×D₄₃	—	4	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
148	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
149	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
150	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
157	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
159	C₂×Dic₄₃	—	2	2	no	—
160	C₂×Dic₄₃	—	2	2	no	—
161	C₂×Dic₄₃	—	4	1	no	—
162	C₂×Dic₄₃	—	4	1	no	—
163	C₂×Dic₄₃	—	4	1	no	—
164	C₂×Dic₄₃	—	4	1	no	—
165	C₂×Dic₄₃	—	4	1	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	D₁₇₂	—	2	2	no	—
169	D₁₇₂	—	2	2	no	—
170	D₁₇₂	—	2	2	no	—
171	D₁₇₂	C₂²⋊C₈	1	4	yes	—
172	C₄×D₄₃	—	4	2	no	—
173	C₄×D₄₃	—	4	2	no	—
174	C₄×D₄₃	—	4	2	no	—
175	C₄×D₄₃	—	4	2	no	—
176	Dic₈₆	—	2	2	no	—
177	Dic₈₆	—	2	2	no	—
178	Dic₈₆	—	4	1	no	—
179	Dic₈₆	—	4	1	no	—
180	C₈×C₄₃	—	2	2	no	—
181	C₈×C₄₃	—	4	1	no	—
182	C₈×C₄₃	—	4	2	no	—
183	C₈×C₄₃	—	8	1	no	—
184	C₄₃⋊C₈	—	2	2	no	—
185	C₄₃⋊C₈	—	4	2	no	—
186	C₄₃⋊C₈	—	4	1	no	—
187	#8945	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	#386	1	1	yes	characteristic
189	C₂²×C₄₃	C₈×D₄	1	1	yes	characteristic
190	C₂²×C₄₃	#435	1	1	yes	characteristic
191	C₂²×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
192	C₂²×C₄₃	#440	1	1	yes	characteristic
193	C₂²×C₄₃	#443	1	1	yes	characteristic
194	C₂²×C₄₃	#444	1	1	yes	characteristic
195	C₂×D₄₃	—	2	4	no	—
196	C₂×D₄₃	—	4	2	no	—
197	C₂×D₄₃	—	4	2	no	—
198	C₂×D₄₃	—	4	2	no	—
199	C₂×D₄₃	—	4	2	no	—
200	C₂×D₄₃	—	4	2	no	—
201	C₂×D₄₃	—	4	2	no	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	—	2	1	no	—
204	C₄×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
205	C₄×C₄₃	#408	1	1	yes	characteristic
206	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
207	C₄×C₄₃	#435	1	1	yes	characteristic
208	C₄×C₄₃	#450	1	1	yes	characteristic
209	C₄×C₄₃	#452	1	1	yes	characteristic
210	C₄×C₄₃	#461	1	1	yes	characteristic
211	C₄×C₄₃	#463	1	1	yes	characteristic
212	Dic₄₃	—	4	2	no	—
213	Dic₄₃	—	4	2	no	—
214	Dic₄₃	—	8	1	no	—
215	C₂×C₄×SD₁₆	—	43	1	no	—
216	C₂×C₈×D₄	—	43	1	no	—
217	#1984	—	43	1	no	—
218	C₂×Q₈⋊C₈	—	43	1	no	—
219	C₂×D₄⋊C₈	—	43	1	no	—
220	#1277	D₄₃	1	1	yes	characteristic, complemented
221	#1273	—	43	1	no	—
222	C₂×C₄₃	C₈×SD₁₆	1	1	yes	characteristic
223	C₂×C₄₃	SD₁₆⋊C₈	1	1	yes	characteristic
224	C₂×C₄₃	#1582	1	1	yes	characteristic
225	C₂×C₄₃	#1585	1	1	yes	characteristic
226	C₂×C₄₃	#1869	1	1	yes	characteristic
227	C₂×C₄₃	#1876	1	1	yes	characteristic
228	C₂×C₄₃	#1877	1	1	yes	characteristic
229	D₄₃	—	4	4	no	—
230	C₂²×SD₁₆	—	43	1	no	—
231	C₂³×C₈	—	86	1	no	—
232	C₂×C₄×Q₈	—	43	1	no	—
233	C₂×C₄×D₄	—	43	1	no	—
234	C₄×SD₁₆	—	86	2	no	—
235	C₄×SD₁₆	—	86	2	no	—
236	C₈×D₄	—	86	2	no	—
237	C₈×D₄	—	86	2	no	—
238	C₂×#106	—	43	1	no	—
239	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
241	C₂×#103	—	43	1	no	—
242	C₂×#102	—	43	1	no	—
243	C₂×C₂²⋊C₈	—	86	1	no	—
244	C₂×C₄×C₈	—	43	1	no	—
245	C₂×C₄×C₈	—	43	1	no	—
246	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
247	#336	—	86	1	no	—
248	#336	—	86	1	no	—
249	Q₈⋊C₈	—	86	2	no	—
250	D₄⋊C₈	—	86	2	no	—
251	C₄₃	#8945	1	1	yes	characteristic, complemented, Sylow
252	C₂²×Q₈	—	43	1	no	—
253	C₂²×D₄	—	43	1	no	—
254	C₂³×C₄	—	86	1	no	—
255	C₂×SD₁₆	—	43	4	no	—
256	C₂×SD₁₆	—	86	2	no	—
257	C₂×SD₁₆	—	86	2	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	43	1	no	—
261	C₂²×C₈	—	43	1	no	—
262	C₂²×C₈	—	86	4	no	—
263	C₂²×C₈	—	86	1	no	—
264	C₂²×C₈	—	172	2	no	—
265	C₂²×C₈	—	172	2	no	—
266	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
267	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
268	C₄×Q₈	—	86	1	no	—
269	C₄×Q₈	—	86	1	no	—
270	C₄×Q₈	—	86	1	no	—
271	C₄×Q₈	—	86	1	no	—
272	C₄×D₄	—	43	2	no	—
273	C₄×D₄	—	43	2	no	—
274	C₄×D₄	—	86	1	no	—
275	C₄×D₄	—	86	1	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	43	1	no	—
278	C₂×C₄⋊C₄	—	86	1	no	—
279	C₂×C₂²⋊C₄	—	86	1	no	—
280	C₂×C₄²	—	86	1	no	—
281	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
282	#106	—	86	2	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	D₁₇₂	1	2	yes	—
287	#103	—	86	2	no	—
288	#102	—	86	2	no	—
289	C₂²⋊C₈	—	86	4	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	86	1	no	—
293	C₄×C₈	—	86	1	no	—
294	C₄×C₈	—	86	1	no	—
295	C₄×C₈	—	86	1	no	—
296	C₂⁴	—	86	1	no	—
297	C₂×Q₈	—	43	2	no	—
298	C₂×Q₈	—	86	1	no	—
299	C₂×Q₈	—	86	1	no	—
300	C₂×Q₈	—	86	1	no	—
301	C₂×Q₈	—	86	1	no	—
302	C₂×Q₈	—	86	1	no	—
303	C₂×D₄	—	43	2	no	—
304	C₂×D₄	—	43	2	no	—
305	C₂×D₄	—	43	2	no	—
306	C₂×D₄	—	86	1	no	—
307	C₂×D₄	—	86	1	no	—
308	C₂×D₄	—	86	1	no	—
309	C₂²×C₄	—	86	1	no	—
310	C₂²×C₄	—	86	1	no	—
311	C₂²×C₄	—	86	2	no	—
312	C₂²×C₄	—	86	2	no	—
313	C₂²×C₄	—	86	1	no	—
314	C₂²×C₄	—	172	1	no	—
315	C₂²×C₄	—	172	1	no	—
316	C₂²×C₄	—	172	1	no	—
317	C₂²×C₄	—	172	1	no	—
318	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	#10621902	1	1	yes	characteristic
321	SD₁₆	—	86	8	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	43	2	no	—
334	C₂×C₈	—	86	1	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	86	2	no	—
337	C₂×C₈	—	86	1	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	—	172	8	no	—
341	C₂×C₈	—	172	1	no	—
342	C₂×C₈	—	172	1	no	—
343	C₂×C₈	C₈×D₄₃	1	2	yes	complemented
344	C₄⋊C₄	—	43	2	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	86	1	no	—
348	C₄⋊C₄	—	172	1	no	—
349	C₄⋊C₄	—	172	1	no	—
350	C₂²⋊C₄	—	86	2	no	—
351	C₂²⋊C₄	—	86	2	no	—
352	C₄²	—	172	1	no	—
353	C₄²	—	172	1	no	—
354	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
355	C₄²	#10621898	1	1	yes	characteristic
356	C₄²	D₄×D₄₃	1	1	yes	characteristic
357	C₄²	D₄×D₄₃	1	1	yes	characteristic
358	C₂³	—	86	2	no	—
359	C₂³	—	86	2	no	—
360	C₂³	—	86	2	no	—
361	C₂³	—	172	1	no	—
362	C₂³	—	172	1	no	—
363	C₂³	—	172	1	no	—
364	C₂³	—	172	1	no	—
365	C₂³	#13063287	1	1	yes	characteristic
366	Q₈	—	86	2	no	—
367	Q₈	—	86	2	no	—
368	Q₈	—	172	1	no	—
369	Q₈	—	172	1	no	—
370	D₄	—	43	4	no	—
371	D₄	—	86	2	no	—
372	D₄	—	86	2	no	—
373	D₄	—	86	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	86	2	no	—
377	C₂×C₄	—	86	2	no	—
378	C₂×C₄	—	172	1	no	—
379	C₂×C₄	—	172	1	no	—
380	C₂×C₄	—	172	1	no	—
381	C₂×C₄	—	172	1	no	—
382	C₂×C₄	—	172	1	no	—
383	C₂×C₄	—	172	1	no	—
384	C₂×C₄	—	172	1	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	—	172	2	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
390	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
391	C₂×C₄	#13063295	1	1	yes	characteristic
392	C₂×C₄	#13063298	1	1	yes	characteristic
393	C₂×C₄	#13063300	1	1	yes	characteristic
394	C₂×C₄	#13063310	1	1	yes	characteristic
395	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
396	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
397	C₂×C₄	#13063331	1	1	yes	characteristic
398	C₂×C₄	#13063333	1	1	yes	characteristic
399	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
400	C₂×C₄	#13063346	1	1	yes	characteristic
401	C₂×C₄	#13063349	1	1	yes	characteristic
402	C₂×C₄	#13063357	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	1	no	—
406	C₈	—	8	1	no	—
407	C₈	—	86	2	no	—
408	C₈	—	172	2	no	—
409	C₈	—	172	1	no	—
410	C₂²	—	86	4	no	—
411	C₂²	—	172	2	no	—
412	C₂²	—	172	2	no	—
413	C₂²	—	172	2	no	—
414	C₂²	—	172	2	no	—
415	C₂²	—	172	2	no	—
416	C₂²	—	172	2	no	—
417	C₂²	#14582777	1	1	yes	characteristic
418	C₂²	#14582964	1	1	yes	characteristic
419	C₂²	#14582969	1	1	yes	characteristic
420	C₂²	#14582986	1	1	yes	characteristic
421	C₂²	#14582998	1	1	yes	characteristic
422	C₂²	#14583015	1	1	yes	characteristic
423	C₂²	#14583020	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	344	1	no	—
427	C₄	—	172	2	no	—
428	C₄	—	172	2	no	—
429	C₄	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
430	C₄	#14582864	1	1	yes	characteristic
431	C₄	C₈×D₁₇₂	1	1	yes	characteristic
432	C₄	#14582972	1	1	yes	characteristic
433	C₄	#14583051	1	1	yes	characteristic
434	C₄	#14583064	1	1	yes	characteristic
435	C₄	#14583103	1	1	yes	characteristic
436	C₄	#14583113	1	1	yes	characteristic
437	C₂	—	172	4	no	—
438	C₂	#19133394	1	1	yes	characteristic
439	C₂	#19133406	1	1	yes	characteristic
440	C₂	#19133430	1	1	yes	characteristic
441	C₂	#19133451	1	1	yes	characteristic
442	C₂	#19134886	1	1	yes	characteristic
443	C₂	#19134923	1	1	yes	characteristic
444	C₂	#19134930	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1277	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1277	D₄₃
hypocenter	C₄₃	#8945
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
3. #19135530	C₂	semidirect
4. C₂×#14582629	C₂	semidirect
6. C₄₃⋊#1273	C₂	semidirect
7. C₄₃×#1277	C₂	semidirect
34. C₂×#10621873	C₈	semidirect
97. C₂×Dic₈₆	C₂×C₈	semidirect
109. C₂×C₈×C₄₃	C₂×C₈	semidirect
132. C₂×C₄₃⋊C₈	SD₁₆	semidirect
220. #1277	D₄₃	semidirect
251. C₄₃	#8945	semidirect
343. C₂×C₈	C₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621873	2
C₂×#14582964	2
#19135530	2
C₂×#14582629	2
C₂×#14582626	2
C₄₃⋊#1273	2
C₄₃×#1277	2
#8945	43