Subgroups — #25115389

Order 11008.

896 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×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583023	C₂	1	1	yes	maximal, characteristic
3	C₄×#13063290	C₂	1	1	yes	maximal, characteristic
4	#19135314	C₂	1	1	yes	maximal, characteristic
5	#19135312	C₂	1	2	yes	maximal
6	#19135310	C₂	1	2	yes	maximal
7	#19134746	C₂	1	1	yes	maximal, characteristic
8	#19134746	C₂	1	2	yes	maximal
9	C₄×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
10	#19134443	C₂	1	2	yes	maximal
11	C₄₃×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	C₂×#13063290	C₄	1	1	yes	characteristic
14	C₂×#13063290	C₄	1	1	yes	characteristic
15	C₈×Dic₈₆	—	2	4	no	—
16	#14583023	—	2	4	no	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
19	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
20	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
22	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
23	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
24	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
27	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₃	C₄	1	1	yes	characteristic
29	C₄⋊C₄×Dic₄₃	C₄	1	1	yes	characteristic
30	C₄×Dic₄₃⋊C₄	C₂²	1	2	yes	—
31	#14582750	C₄	1	2	yes	—
32	#14582750	C₄	1	2	yes	—
33	C₄²×Dic₄₃	C₂²	1	2	yes	—
34	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
35	#14582654	C₂²	1	2	yes	—
36	#14582653	C₂²	1	1	yes	characteristic
37	#14582653	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₄×Dic₈₆	D₄	1	4	yes	—
48	C₄×Dic₈₆	Q₈	1	4	yes	—
49	#13063290	—	2	4	no	—
50	#13063290	C₈	1	8	yes	complemented
51	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
65	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
68	Dic₄₃⋊C₈	—	2	4	no	—
69	Dic₄₃⋊C₈	—	2	4	no	—
70	Dic₄₃⋊C₈	—	2	4	no	—
71	Dic₄₃⋊C₈	—	2	2	no	—
72	Dic₄₃⋊C₈	—	4	2	no	—
73	Dic₄₃⋊C₈	Q₈	1	4	yes	complemented
74	C₄×C₄₃⋊C₈	—	2	2	no	—
75	C₈×Dic₄₃	—	2	4	no	—
76	C₈×Dic₄₃	—	2	4	no	—
77	C₄₃⋊#95	C₂×C₄	1	2	yes	—
78	C₄₃⋊#95	C₂×C₄	1	2	yes	—
79	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₃	—	2	2	no	—
87	C₄⋊C₈×C₄₃	—	4	2	no	—
88	C₄×C₈×C₄₃	—	2	2	no	—
89	#95×C₄₃	C₂×C₄	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
100	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×Dic₈₆	C₄⋊C₄	1	4	yes	—
102	C₂×Dic₈₆	C₂×C₈	1	4	yes	—
103	C₂×Dic₈₆	M₁₆	1	4	yes	—
104	C₂×C₈×C₄₃	—	2	1	no	—
105	C₂×C₈×C₄₃	—	2	1	no	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	C₂×C₈	1	4	yes	—
115	C₄²×C₄₃	—	2	2	no	—
116	C₄²×C₄₃	—	2	2	no	—
117	C₄²×C₄₃	C₂×D₄	1	2	yes	—
118	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
119	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
120	Dic₄₃⋊C₄	—	2	4	no	—
121	Dic₄₃⋊C₄	C₄⋊C₄	1	8	yes	—
122	Dic₄₃⋊C₄	C₂×C₈	1	8	yes	—
123	C₄×Dic₄₃	—	2	2	no	—
124	C₄×Dic₄₃	—	2	1	no	—
125	C₄×Dic₄₃	—	2	1	no	—
126	C₄×Dic₄₃	—	2	4	no	—
127	C₄×Dic₄₃	—	2	4	no	—
128	C₄×Dic₄₃	—	2	2	no	—
129	C₄×Dic₄₃	—	4	1	no	—
130	C₄×Dic₄₃	—	4	2	no	—
131	C₄×Dic₄₃	C₂×C₈	1	4	yes	—
132	C₄×Dic₄₃	C₂×C₈	1	8	yes	—
133	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
134	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
135	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
136	C₄×Dic₄₃	#41	1	2	yes	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂×C₄₃⋊C₈	—	2	1	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	2	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
146	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₄₃	C₂²×C₈	1	4	yes	—
157	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
159	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×Dic₄₃	—	2	1	no	—
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	2	1	no	—
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
175	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
177	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
178	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
179	C₂×Dic₄₃	C₂²×C₈	1	4	yes	—
180	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
181	C₂×Dic₄₃	C₂×M₁₆	1	4	yes	—
182	C₂×Dic₄₃	#131	1	2	yes	—
183	Dic₈₆	C₄⋊C₈	1	16	yes	complemented
184	C₈×C₄₃	—	2	2	no	—
185	C₈×C₄₃	—	4	1	no	—
186	C₈×C₄₃	—	4	2	no	—
187	C₄₃⋊C₈	—	2	2	no	—
188	C₄₃⋊C₈	—	4	2	no	—
189	C₄₃⋊C₈	—	4	1	no	—
190	Q₈×C₄⋊C₈	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
193	C₂²×C₄₃	#520	1	1	yes	characteristic
194	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
195	C₂²×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
196	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
197	C₂²×C₄₃	#568	1	1	yes	characteristic
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	2	4	no	—
200	C₄×C₄₃	—	4	2	no	—
201	C₄×C₄₃	C₂×C₄⋊C₈	1	4	yes	—
202	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
203	C₄×C₄₃	#550	1	1	yes	characteristic
204	C₄×C₄₃	#557	1	1	yes	characteristic
205	C₄×C₄₃	Q₈²	1	1	yes	characteristic
206	Dic₄₃	—	2	4	no	—
207	Dic₄₃	—	2	2	no	—
208	Dic₄₃	—	2	2	no	—
209	Dic₄₃	—	4	1	no	—
210	Dic₄₃	C₂×C₄⋊C₈	1	8	yes	—
211	Dic₄₃	C₈×Q₈	1	4	yes	complemented
212	C₂×C₈×Q₈	—	43	1	no	—
213	C₂×C₈×Q₈	—	43	1	no	—
214	C₄²×Q₈	—	43	1	no	—
215	#1939	—	43	2	no	—
216	#1939	—	43	1	no	—
217	#1939	—	43	2	no	—
218	#1939	D₄₃	1	1	yes	characteristic
219	#1842	—	43	2	no	—
220	#1842	—	43	1	no	—
221	C₄×C₄⋊C₈	—	43	1	no	—
222	C₄×C₄⋊C₈	—	43	2	no	—
223	C₂×C₄₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
225	C₂×C₄₃	#2906	1	1	yes	characteristic
226	C₂×C₄₃	C₂×C₈×Q₈	1	1	yes	characteristic
227	C₂×C₄₃	Q₈×M₁₆	1	1	yes	characteristic
228	C₂×C₄₃	#2988	1	1	yes	characteristic
229	C₂×C₄₃	#2991	1	1	yes	characteristic
230	C₂×C₄×Q₈	—	43	1	no	—
231	C₂×C₄×Q₈	—	43	1	no	—
232	C₂×C₄×Q₈	—	43	1	no	—
233	C₈×Q₈	—	86	4	no	—
234	C₈×Q₈	—	86	4	no	—
235	C₂×C₄⋊C₈	—	43	1	no	—
236	C₂×C₄⋊C₈	—	43	1	no	—
237	C₂×C₄⋊C₈	—	43	2	no	—
238	C₂×C₄⋊C₈	—	43	2	no	—
239	C₂×C₄⋊C₈	—	43	2	no	—
240	C₂×C₄⋊C₈	—	43	1	no	—
241	C₂×C₄⋊C₈	—	43	2	no	—
242	C₂×C₄⋊C₈	—	43	2	no	—
243	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
245	C₂×C₄×C₈	—	43	2	no	—
246	C₂×C₄×C₈	—	43	2	no	—
247	C₂×C₄×C₈	—	43	1	no	—
248	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
249	C₄×C₄⋊C₄	—	43	1	no	—
250	C₄×C₄⋊C₄	—	43	1	no	—
251	C₄×C₄⋊C₄	—	43	2	no	—
252	C₄×C₄⋊C₄	—	43	2	no	—
253	C₄×C₄⋊C₄	—	43	2	no	—
254	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
255	C₄³	—	43	2	no	—
256	C₄³	—	43	1	no	—
257	#336	—	43	1	no	—
258	#336	—	43	1	no	—
259	#336	—	43	2	no	—
260	#336	C₂×D₄₃	1	2	yes	—
261	C₄₃	Q₈×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
262	C₂²×Q₈	—	43	1	no	—
263	C₂²×C₈	—	43	1	no	—
264	C₂²×C₈	—	43	1	no	—
265	C₂²×C₈	—	43	2	no	—
266	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
268	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
269	C₄×Q₈	—	43	8	no	—
270	C₄×Q₈	—	43	4	no	—
271	C₄×Q₈	—	43	4	no	—
272	C₄×Q₈	—	86	4	no	—
273	C₂×C₄⋊C₄	—	43	2	no	—
274	C₂×C₄⋊C₄	—	43	2	no	—
275	C₂×C₄⋊C₄	—	43	1	no	—
276	C₂×C₄⋊C₄	—	43	2	no	—
277	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
279	C₂×C₄²	—	43	2	no	—
280	C₂×C₄²	—	43	1	no	—
281	C₂×C₄²	—	43	2	no	—
282	C₂×C₄²	—	43	1	no	—
283	C₂×C₄²	—	43	2	no	—
284	C₂×C₄²	—	43	1	no	—
285	C₂×C₄²	—	43	2	no	—
286	C₂×C₄²	—	43	1	no	—
287	C₂×C₄²	—	43	1	no	—
288	C₂×C₄²	—	43	1	no	—
289	C₂×C₄²	—	43	2	no	—
290	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
291	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	4	2	no	—
294	C₄⋊C₈	—	43	4	no	—
295	C₄⋊C₈	—	86	2	no	—
296	C₄⋊C₈	—	86	4	no	—
297	C₄⋊C₈	—	86	4	no	—
298	C₄⋊C₈	—	86	4	no	—
299	C₄⋊C₈	—	86	2	no	—
300	C₄⋊C₈	—	172	2	no	—
301	C₄⋊C₈	—	172	2	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	—	86	4	no	—
304	C₄×C₈	—	86	4	no	—
305	C₄×C₈	—	86	2	no	—
306	#95	—	43	2	no	—
307	#95	—	43	2	no	—
308	#95	C₄×D₄₃	1	2	yes	—
309	C₂×Q₈	—	43	4	no	—
310	C₂×Q₈	—	43	4	no	—
311	C₂×Q₈	—	43	4	no	—
312	C₂²×C₄	—	43	1	no	—
313	C₂²×C₄	—	43	2	no	—
314	C₂²×C₄	—	43	2	no	—
315	C₂²×C₄	—	43	1	no	—
316	C₂²×C₄	—	43	1	no	—
317	C₂²×C₄	—	43	1	no	—
318	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
319	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
321	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
322	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	43	2	no	—
332	C₂×C₈	—	86	1	no	—
333	C₂×C₈	—	86	1	no	—
334	C₂×C₈	—	86	2	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	86	1	no	—
337	C₂×C₈	—	86	2	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	86	2	no	—
340	C₂×C₈	Q₈×D₄₃	1	2	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	43	8	no	—
343	C₄⋊C₄	—	43	4	no	—
344	C₄⋊C₄	—	43	8	no	—
345	C₄⋊C₄	—	86	4	no	—
346	C₄⋊C₄	C₈×D₄₃	1	4	yes	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	43	8	no	—
350	C₄²	—	43	4	no	—
351	C₄²	—	43	4	no	—
352	C₄²	—	43	2	no	—
353	C₄²	—	43	4	no	—
354	C₄²	—	43	2	no	—
355	C₄²	—	86	4	no	—
356	C₄²	—	86	2	no	—
357	C₄²	—	86	4	no	—
358	C₄²	—	86	2	no	—
359	C₄²	—	86	1	no	—
360	C₄²	—	86	1	no	—
361	C₄²	—	172	2	no	—
362	C₄²	—	172	1	no	—
363	C₄²	D₄×D₄₃	1	2	yes	—
364	C₄²	Q₈×D₄₃	1	2	yes	—
365	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
366	Q₈	—	43	16	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	43	4	no	—
375	C₂×C₄	—	43	2	no	—
376	C₂×C₄	—	43	2	no	—
377	C₂×C₄	—	43	4	no	—
378	C₂×C₄	—	43	4	no	—
379	C₂×C₄	—	43	2	no	—
380	C₂×C₄	—	43	4	no	—
381	C₂×C₄	—	43	2	no	—
382	C₂×C₄	—	43	2	no	—
383	C₂×C₄	—	86	1	no	—
384	C₂×C₄	—	86	1	no	—
385	C₂×C₄	—	86	2	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	86	1	no	—
388	C₂×C₄	—	86	2	no	—
389	C₂×C₄	—	86	1	no	—
390	C₂×C₄	—	86	1	no	—
391	C₂×C₄	—	86	1	no	—
392	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
393	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
394	C₂×C₄	C₂×C₈×D₄₃	1	4	yes	—
395	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
396	C₂×C₄	M₁₆×D₄₃	1	2	yes	—
397	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
400	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
401	C₂×C₄	#13063370	1	1	yes	characteristic
402	C₂×C₄	#13063372	1	1	yes	characteristic
403	C₈	—	2	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	86	2	no	—
407	C₈	—	172	2	no	—
408	C₈	—	172	1	no	—
409	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
410	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
411	C₂²	#14583378	1	1	yes	characteristic
412	C₂²	C₂²×C₈×D₄₃	1	1	yes	characteristic
413	C₂²	C₂×M₁₆×D₄₃	1	1	yes	characteristic
414	C₂²	#131×D₄₃	1	1	yes	characteristic
415	C₂²	#14583664	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	43	4	no	—
420	C₄	—	43	8	no	—
421	C₄	—	86	2	no	—
422	C₄	—	86	2	no	—
423	C₄	—	86	4	no	—
424	C₄	—	172	1	no	—
425	C₄	C₄⋊C₈×D₄₃	1	4	yes	—
426	C₄	#14583562	1	1	yes	characteristic
427	C₄	#14583567	1	1	yes	characteristic
428	C₄	#14583626	1	1	yes	characteristic
429	C₄	#14583629	1	1	yes	characteristic
430	C₂	#19137509	1	1	yes	characteristic
431	C₂	C₂×C₄⋊C₈×D₄₃	1	1	yes	characteristic
432	C₂	#19143162	1	1	yes	characteristic
433	C₂	C₈×Q₈×D₄₃	1	1	yes	characteristic
434	C₂	#19143547	1	1	yes	characteristic
435	C₂	#19143702	1	1	yes	characteristic
436	C₂	#19143723	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂³×C₈
Fitting	C₄₃×#1939	C₂
socle, prime radical	C₂³×C₄₃	C₂³×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1939	D₄₃
hypocenter	C₄₃	Q₈×C₄⋊C₈
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
50. #13063290	C₈	semidirect
73. Dic₄₃⋊C₈	Q₈	semidirect
183. Dic₈₆	C₄⋊C₈	semidirect
211. Dic₄₃	C₈×Q₈	semidirect
261. C₄₃	Q₈×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₈₆	2
C₂×#14583023	2
C₄×#13063290	2
#19135314	2
#19135312	2
#19135310	2
#19134746	2
C₄×Dic₄₃⋊C₈	2
#19134443	2
C₄₃×#1939	2
Q₈×C₄⋊C₈	43