Subgroups — #25065668

Order 11008.

668 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143225	C₂	1	1	yes	maximal, characteristic
2	#431×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#431×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#19133376	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133375	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133373	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133368	C₂	1	2	yes	maximal, complemented
8	#19133364	C₂	1	2	yes	maximal, complemented
9	#19133342	C₂	1	2	yes	maximal, complemented
10	#19133340	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
13	#14582956	C₂²	1	1	yes	characteristic
14	#14582954	—	2	1	no	—
15	#14582952	C₂²	1	1	yes	characteristic
16	#14582952	C₂²	1	1	yes	characteristic
17	#14582951	C₄	1	2	yes	—
18	#14582951	C₂²	1	2	yes	—
19	#14582951	C₂²	1	2	yes	—
20	#14582950	—	2	1	no	—
21	#14582950	C₂²	1	1	yes	characteristic
22	#14582950	C₂²	1	1	yes	characteristic
23	#14582949	—	2	1	no	—
24	#14582949	—	2	1	no	—
25	#14582949	C₄	1	2	yes	—
26	#14582921	C₂²	1	2	yes	—
27	C₄⋊C₈×D₄₃	C₄	1	2	yes	—
28	C₄⋊C₈×D₄₃	C₂²	1	2	yes	—
29	#14582861	—	2	1	no	—
30	C₂²⋊C₈×D₄₃	—	2	1	no	—
31	C₂²⋊C₈×D₄₃	C₄	1	2	yes	—
32	#14582851	—	2	1	no	—
33	C₄×C₈×D₄₃	—	2	1	no	—
34	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
36	#14582652	C₂²	1	2	yes	complemented
37	#14582651	C₂²	1	2	yes	complemented
38	#14582651	C₂²	1	2	yes	complemented
39	#14582650	C₂²	1	2	yes	complemented
40	#14582649	C₂²	1	2	yes	complemented
41	#14582649	C₂²	1	2	yes	complemented
42	C₄₃×#432	C₂²	1	1	yes	characteristic
43	C₄₃×#431	C₂²	1	1	yes	characteristic
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	2	yes	complemented
46	C₄₃×#334	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₄₃	Q₈	1	1	yes	characteristic
50	C₂×#10621872	—	2	2	no	—
51	C₂×C₈×D₄₃	—	2	2	no	—
52	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₃	Q₈	1	1	yes	characteristic
57	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₄₃	D₄	1	1	yes	characteristic
60	C₄²×D₄₃	D₄	1	1	yes	characteristic
61	C₄²×D₄₃	Q₈	1	1	yes	characteristic
62	C₄²×D₄₃	Q₈	1	1	yes	characteristic
63	C₄²×D₄₃	C₂³	1	1	yes	characteristic
64	C₄²×D₄₃	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
68	Dic₄₃⋊C₈	—	2	2	no	—
69	Dic₄₃⋊C₈	—	2	2	no	—
70	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
71	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
75	(C₂×D₄₃)⋊C₈	—	2	2	no	—
76	(C₂×D₄₃)⋊C₈	—	2	2	no	—
77	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
78	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
79	#13063236	—	2	1	no	—
80	C₄×C₄₃⋊C₈	—	2	1	no	—
81	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₈×Dic₄₃	—	2	2	no	—
84	C₈×Dic₄₃	—	2	2	no	—
85	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
86	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
89	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
90	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
91	C₂²⋊C₈×C₄₃	—	2	1	no	—
92	C₂²⋊C₈×C₄₃	—	2	1	no	—
93	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
94	#97×C₄₃	—	2	1	no	—
95	C₄×C₈×C₄₃	—	2	1	no	—
96	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₂³×D₄₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
102	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₄₃	—	2	4	no	—
106	C₂×C₄×D₄₃	—	2	4	no	—
107	C₂×C₄×D₄₃	—	4	2	no	—
108	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
128	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
139	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
140	C₂×C₄₃⋊C₈	—	2	2	no	—
141	C₂×C₄₃⋊C₈	—	2	2	no	—
142	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
144	#10621872	—	4	4	no	—
145	C₈×D₄₃	—	2	4	no	—
146	C₈×D₄₃	—	2	4	no	—
147	C₈×D₄₃	—	4	4	no	—
148	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂²×D₄₃	—	2	2	no	—
150	C₂²×D₄₃	—	2	2	no	—
151	C₂²×D₄₃	—	4	1	no	—
152	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
163	C₂×Dic₄₃	—	2	2	no	—
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	2	no	—
166	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₄×D₄₃	—	2	2	no	—
173	C₄×D₄₃	—	2	2	no	—
174	C₄×D₄₃	—	2	2	no	—
175	C₄×D₄₃	—	2	2	no	—
176	C₄×D₄₃	—	2	2	no	—
177	C₄×D₄₃	—	2	2	no	—
178	C₄×D₄₃	—	2	2	no	—
179	C₄×D₄₃	—	2	2	no	—
180	C₄×D₄₃	—	4	1	no	—
181	C₄×D₄₃	—	4	1	no	—
182	C₄×D₄₃	#131	1	4	yes	—
183	C₄×D₄₃	#135	1	4	yes	—
184	C₈×C₄₃	—	2	2	no	—
185	C₈×C₄₃	—	2	2	no	—
186	C₈×C₄₃	—	4	2	no	—
187	C₈×C₄₃	—	4	2	no	—
188	C₄₃⋊C₈	—	2	2	no	—
189	C₄₃⋊C₈	—	2	2	no	—
190	C₄₃⋊C₈	—	4	2	no	—
191	C₄₃⋊C₈	—	4	2	no	—
192	#17803	—	43	1	no	maximal, Sylow
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
197	C₂×D₄₃	—	2	1	no	—
198	C₂×D₄₃	—	2	1	no	—
199	C₂×D₄₃	—	2	1	no	—
200	C₂×D₄₃	—	2	1	no	—
201	C₂×D₄₃	—	4	4	no	—
202	C₂×D₄₃	#424	1	2	yes	—
203	C₂×D₄₃	#427	1	2	yes	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	C₂×#131	1	2	yes	—
209	C₄×C₄₃	C₂×#135	1	2	yes	—
210	Dic₄₃	—	2	1	no	—
211	Dic₄₃	—	2	1	no	—
212	Dic₄₃	—	2	1	no	—
213	Dic₄₃	#424	1	2	yes	—
214	Dic₄₃	#427	1	2	yes	—
215	Dic₄₃	#430	1	2	yes	—
216	#2920	—	43	1	no	—
217	C₂×#431	—	43	1	no	—
218	C₂×#431	—	43	1	no	—
219	#1572	—	43	1	no	—
220	#1572	—	43	1	no	—
221	#1572	—	43	1	no	—
222	#1572	D₄₃	1	1	yes	characteristic, complemented
223	#1571	—	43	2	no	—
224	#1570	—	43	2	no	—
225	#1564	—	43	2	no	—
226	#1564	—	43	2	no	—
227	C₂×C₄₃	—	4	1	no	—
228	C₂×C₄₃	C₂×#424	1	1	yes	characteristic
229	C₂×C₄₃	C₂×#427	1	1	yes	characteristic
230	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
231	D₄₃	—	2	2	no	—
232	D₄₃	—	2	2	no	—
233	C₂²×C₄²	—	43	1	no	—
234	#432	—	43	1	no	—
235	#432	—	86	1	no	—
236	#432	C₂×D₄₃	1	1	yes	characteristic
237	#431	—	43	1	no	—
238	#431	—	43	2	no	—
239	#431	—	43	2	no	—
240	#431	—	43	1	no	—
241	#431	—	43	1	no	—
242	#431	—	43	1	no	—
243	#431	—	43	2	no	—
244	#431	—	43	2	no	—
245	#431	—	86	1	no	—
246	#431	—	86	1	no	—
247	#431	—	86	1	no	—
248	#431	C₂×D₄₃	1	1	yes	characteristic
249	#431	C₂×D₄₃	1	1	yes	characteristic
250	#423	—	43	2	no	—
251	C₂×C₄⋊C₈	—	43	2	no	—
252	C₂×C₄⋊C₈	—	43	2	no	—
253	#407	—	86	1	no	—
254	C₂×C₂²⋊C₈	—	43	2	no	—
255	C₂×C₂²⋊C₈	—	86	1	no	—
256	C₄×M₁₆	—	86	1	no	—
257	C₂×C₄×C₈	—	43	1	no	—
258	C₂×C₄×C₈	—	43	1	no	—
259	C₂×C₄×C₈	—	86	1	no	—
260	#335	—	43	2	no	—
261	#335	—	43	2	no	—
262	#335	—	43	2	no	—
263	#335	C₂×D₄₃	1	2	yes	complemented
264	#334	—	43	2	no	—
265	#334	—	43	2	no	—
266	#334	—	43	2	no	—
267	#334	C₂×D₄₃	1	2	yes	complemented
268	C₄₃	#17803	1	1	yes	characteristic, complemented, Sylow
269	C₂³×C₄	—	43	1	no	—
270	C₂³×C₄	—	43	1	no	—
271	C₂³×C₄	—	43	1	no	—
272	C₂×M₁₆	—	86	2	no	—
273	C₂²×C₈	—	43	2	no	—
274	C₂²×C₈	—	43	2	no	—
275	C₂²×C₈	—	86	2	no	—
276	C₂×C₄²	—	43	1	no	—
277	C₂×C₄²	—	43	1	no	—
278	C₂×C₄²	—	43	1	no	—
279	C₂×C₄²	—	43	1	no	—
280	C₂×C₄²	—	43	1	no	—
281	C₂×C₄²	—	43	1	no	—
282	C₂×C₄²	—	43	1	no	—
283	C₂×C₄²	—	43	1	no	—
284	C₂×C₄²	—	43	1	no	—
285	C₂×C₄²	—	43	1	no	—
286	C₂×C₄²	—	43	1	no	—
287	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
288	C₄⋊C₈	—	43	2	no	—
289	C₄⋊C₈	—	43	2	no	—
290	C₄⋊C₈	—	43	2	no	—
291	C₄⋊C₈	—	43	2	no	—
292	C₄⋊C₈	—	43	2	no	—
293	C₄⋊C₈	—	86	2	no	—
294	C₄⋊C₈	—	86	2	no	—
295	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
296	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
297	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	43	2	no	—
301	C₂²⋊C₈	—	43	2	no	—
302	C₂²⋊C₈	—	43	2	no	—
303	C₂²⋊C₈	—	86	2	no	—
304	C₂²⋊C₈	—	86	2	no	—
305	C₂²⋊C₈	—	86	1	no	—
306	C₂²⋊C₈	—	86	1	no	—
307	C₂²⋊C₈	C₄×D₄₃	1	2	yes	—
308	#97	—	2	1	no	—
309	#97	—	86	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	43	2	no	—
312	C₄×C₈	—	43	2	no	—
313	C₄×C₈	—	43	1	no	—
314	C₄×C₈	—	43	1	no	—
315	C₄×C₈	—	86	2	no	—
316	C₄×C₈	—	86	2	no	—
317	C₄×C₈	—	86	1	no	—
318	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₂⁴	—	43	1	no	—
321	C₂²×C₄	—	43	1	no	—
322	C₂²×C₄	—	43	1	no	—
323	C₂²×C₄	—	43	1	no	—
324	C₂²×C₄	—	43	1	no	—
325	C₂²×C₄	—	43	1	no	—
326	C₂²×C₄	—	43	1	no	—
327	C₂²×C₄	—	43	1	no	—
328	C₂²×C₄	—	43	1	no	—
329	C₂²×C₄	—	43	1	no	—
330	C₂²×C₄	—	43	1	no	—
331	C₂²×C₄	—	43	1	no	—
332	C₂²×C₄	—	43	1	no	—
333	C₂²×C₄	—	43	1	no	—
334	C₂²×C₄	—	43	1	no	—
335	C₂²×C₄	—	43	1	no	—
336	C₂²×C₄	—	86	4	no	—
337	C₂²×C₄	—	86	4	no	—
338	C₂²×C₄	—	172	2	no	—
339	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
341	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
342	M₁₆	—	172	4	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	43	2	no	—
346	C₂×C₈	—	43	2	no	—
347	C₂×C₈	—	86	4	no	—
348	C₂×C₈	—	86	4	no	—
349	C₂×C₈	—	86	2	no	—
350	C₂×C₈	—	86	2	no	—
351	C₂×C₈	—	172	4	no	—
352	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
353	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
354	C₄²	—	43	1	no	—
355	C₄²	—	43	1	no	—
356	C₄²	—	43	1	no	—
357	C₄²	—	43	1	no	—
358	C₄²	—	43	1	no	—
359	C₄²	—	43	1	no	—
360	C₄²	—	43	1	no	—
361	C₄²	—	43	1	no	—
362	C₄²	—	43	1	no	—
363	C₄²	—	43	1	no	—
364	C₄²	—	43	1	no	—
365	C₄²	—	43	1	no	—
366	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
367	C₄²	D₄×D₄₃	1	1	yes	characteristic
368	C₄²	Q₈×D₄₃	1	1	yes	characteristic
369	C₄²	C₂³×D₄₃	1	1	yes	characteristic
370	C₂³	—	43	1	no	—
371	C₂³	—	43	1	no	—
372	C₂³	—	86	2	no	—
373	C₂³	—	86	2	no	—
374	C₂³	—	172	1	no	—
375	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	43	1	no	—
380	C₂×C₄	—	43	1	no	—
381	C₂×C₄	—	43	1	no	—
382	C₂×C₄	—	43	4	no	—
383	C₂×C₄	—	43	4	no	—
384	C₂×C₄	—	43	1	no	—
385	C₂×C₄	—	43	1	no	—
386	C₂×C₄	—	43	1	no	—
387	C₂×C₄	—	86	2	no	—
388	C₂×C₄	—	86	2	no	—
389	C₂×C₄	—	86	2	no	—
390	C₂×C₄	—	86	2	no	—
391	C₂×C₄	—	86	2	no	—
392	C₂×C₄	—	86	2	no	—
393	C₂×C₄	—	86	2	no	—
394	C₂×C₄	—	86	2	no	—
395	C₂×C₄	—	86	2	no	—
396	C₂×C₄	—	86	2	no	—
397	C₂×C₄	—	86	2	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	86	2	no	—
411	C₈	—	86	2	no	—
412	C₈	—	172	2	no	—
413	C₈	—	172	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	43	2	no	—
418	C₂²	—	43	2	no	—
419	C₂²	—	86	1	no	—
420	C₂²	—	86	1	no	—
421	C₂²	—	86	1	no	—
422	C₂²	—	86	1	no	—
423	C₂²	—	172	4	no	—
424	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	43	2	no	—
430	C₄	—	43	2	no	—
431	C₄	—	43	2	no	—
432	C₄	—	86	1	no	—
433	C₄	—	86	1	no	—
434	C₄	—	86	1	no	—
435	C₄	#131×D₄₃	1	2	yes	—
436	C₄	#135×D₄₃	1	2	yes	—
437	C₂	—	4	1	no	—
438	C₂	—	86	2	no	—
439	C₂	—	86	2	no	—
440	C₂	#424×D₄₃	1	1	yes	characteristic
441	C₂	#427×D₄₃	1	1	yes	characteristic
442	C₂	#430×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1572	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₃	C₄⋊C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1572	D₄₃
hypocenter	C₄₃	#17803
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
4. #19133376	C₂	semidirect
5. #19133375	C₂	semidirect
6. #19133373	C₂	semidirect
7. #19133368	C₂	semidirect
8. #19133364	C₂	semidirect
9. #19133342	C₂	semidirect
10. #19133340	C₂	semidirect
11. C₄₃×#1572	C₂	semidirect
36. #14582652	C₂²	semidirect
37. #14582651	C₂²	semidirect
38. #14582651	C₂²	semidirect
39. #14582650	C₂²	semidirect
40. #14582649	C₂²	semidirect
41. #14582649	C₂²	semidirect
45. C₄₃×#335	C₂²	semidirect
46. C₄₃×#334	C₂²	semidirect
222. #1572	D₄₃	semidirect
263. #335	C₂×D₄₃	semidirect
267. #334	C₂×D₄₃	semidirect
268. C₄₃	#17803	semidirect

Maximal subgroups

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

subgroup	index
#19143225	2
#431×D₄₃	2
#19133376	2
#19133375	2
#19133373	2
#19133368	2
#19133364	2
#19133342	2
#19133340	2
C₄₃×#1572	2
#17803	43