Subgroups — #25094617

Order 11008.

1018 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582947	C₂	1	1	yes	maximal, characteristic
2	#19143184	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582854	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582854	C₂	1	1	yes	maximal, characteristic
5	#19134480	C₂	1	4	yes	maximal, complemented
6	#19134475	C₂	1	4	yes	maximal, complemented
7	#19134306	C₂	1	1	yes	maximal, characteristic
8	#19134304	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂×#13063284	C₂²	1	1	yes	characteristic
13	C₂×#13063284	C₂²	1	1	yes	characteristic
14	#14582947	C₄	1	8	yes	complemented
15	C₂×#13063260	C₂²	1	4	yes	—
16	#14582942	C₄	1	4	yes	complemented
17	#14582939	C₄	1	4	yes	complemented
18	#14582935	C₂²	1	4	yes	—
19	#14582854	—	2	1	no	—
20	#14582854	—	2	1	no	—
21	#14582854	C₄	1	8	yes	complemented
22	#14582854	C₂²	1	2	yes	—
23	#14582854	C₂²	1	2	yes	—
24	C₂×#13063235	—	2	1	no	—
25	C₂×#13063235	C₂²	1	2	yes	—
26	C₂×C₈×Dic₄₃	—	2	1	no	—
27	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
28	#14582660	C₂²	1	4	yes	—
29	#14582658	C₂²	1	4	yes	—
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#405	—	2	1	no	—
34	C₄₃×#405	—	2	1	no	—
35	C₄₃×#405	C₂²	1	2	yes	—
36	C₄₃×#405	C₂²	1	2	yes	—
37	C₂×#97×C₄₃	—	2	1	no	—
38	C₂×C₄×C₈×C₄₃	—	2	1	no	—
39	C₂×#10621877	—	2	1	no	—
40	C₂×#10621877	—	2	2	no	—
41	C₂×#10621877	C₂×C₄	1	4	yes	—
42	C₂×#10621877	C₂×C₄	1	4	yes	—
43	C₂×#10621877	C₂×C₄	1	2	yes	—
44	C₂×#10621877	C₂×C₄	1	2	yes	—
45	C₂×#10621877	C₂×C₄	1	4	yes	—
46	C₂×#10621877	C₂³	1	2	yes	—
47	C₂²×C₄₃⋊C₈	—	2	1	no	—
48	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
49	#13063284	—	2	1	no	—
50	#13063284	—	2	1	no	—
51	#13063284	—	2	2	no	—
52	#13063284	C₂×C₄	1	2	yes	—
53	#13063284	C₂×C₄	1	4	yes	—
54	#13063284	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₃	—	2	1	no	—
56	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
58	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
59	C₂×C₄×Dic₄₃	—	2	1	no	—
60	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
61	#13063260	C₂×C₄	1	16	yes	complemented
62	#13063258	C₂×C₄	1	8	yes	—
63	#13063256	C₂×C₄	1	8	yes	—
64	#13063235	—	2	2	no	—
65	#13063235	—	2	2	no	—
66	#13063235	C₂×C₄	1	8	yes	complemented
67	C₈×Dic₄₃	—	2	2	no	—
68	C₈×Dic₄₃	—	2	2	no	—
69	C₈×Dic₄₃	C₂×C₄	1	8	yes	complemented
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₄₃	—	2	1	no	—
72	C₂×M₁₆×C₄₃	—	2	2	no	—
73	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
74	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₃	—	2	1	no	—
76	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	Q₈	1	4	yes	—
82	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	#117×C₄₃	—	2	1	no	—
85	#117×C₄₃	—	2	1	no	—
86	#117×C₄₃	C₂×C₄	1	2	yes	—
87	#117×C₄₃	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	—	2	1	no	—
91	#97×C₄₃	—	2	2	no	—
92	#97×C₄₃	—	2	2	no	—
93	C₄×C₈×C₄₃	—	2	2	no	—
94	C₄×C₈×C₄₃	—	2	2	no	—
95	C₂⁴×C₄₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₃	#41	1	2	yes	—
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
107	C₂²×Dic₄₃	—	2	2	no	—
108	C₂²×Dic₄₃	—	2	2	no	—
109	M₁₆×C₄₃	—	2	4	no	—
110	M₁₆×C₄₃	—	2	2	no	—
111	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₄₃	—	2	4	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
115	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
116	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
117	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
118	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
125	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
128	C₂²⋊C₄×C₄₃	—	2	2	no	—
129	C₂²⋊C₄×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	—	2	2	no	—
132	C₂²⋊Dic₄₃	—	2	4	no	—
133	C₂²⋊Dic₄₃	—	2	2	no	—
134	C₂²⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	4	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	C₄×Dic₄₃	—	2	2	no	—
141	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
142	#10621877	—	2	4	no	—
143	#10621877	—	2	2	no	—
144	#10621877	C₄²	1	8	yes	—
145	#10621877	C₄²	1	8	yes	—
146	#10621877	C₂²×C₄	1	4	yes	—
147	C₂×C₄₃⋊C₈	—	2	4	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
150	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
151	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	#117	1	2	yes	—
154	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
155	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
156	C₂³×C₄₃	C₄×Q₈	1	2	yes	—
157	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
161	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
162	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₃	#117	1	2	yes	—
165	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
170	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₄₃	C₄×Q₈	1	2	yes	—
172	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂×Dic₄₃	—	2	4	no	—
179	C₂×Dic₄₃	—	2	4	no	—
180	C₂×Dic₄₃	—	4	4	no	—
181	C₂×Dic₄₃	—	4	4	no	—
182	C₈×C₄₃	—	2	4	no	—
183	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
184	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
185	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
186	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
187	C₄₃⋊C₈	—	2	4	no	—
188	C₄₃⋊C₈	C₂×C₄²	1	8	yes	—
189	#20444	—	43	1	no	maximal, Sylow
190	C₂²×C₄₃	—	2	2	no	—
191	C₂²×C₄₃	—	2	2	no	—
192	C₂²×C₄₃	—	2	2	no	—
193	C₂²×C₄₃	—	4	2	no	—
194	C₂²×C₄₃	—	4	2	no	—
195	C₂²×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
196	C₂²×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
197	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
198	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
200	C₄×C₄₃	—	4	4	no	—
201	C₄×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
202	C₄×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
203	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
204	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
207	Dic₄₃	—	4	4	no	—
208	Dic₄₃	—	4	4	no	—
209	C₂×#430	—	43	1	no	—
210	#2911	—	43	1	no	—
211	C₂×#405	—	43	1	no	—
212	C₂×#405	—	43	1	no	—
213	C₂×#405	D₄₃	1	1	yes	characteristic
214	#1773	—	43	4	no	—
215	#1772	—	43	4	no	—
216	#1733	—	43	1	no	—
217	#1733	—	43	1	no	—
218	C₂×C₄₃	—	2	1	no	—
219	C₂×C₄₃	—	2	1	no	—
220	C₂×C₄₃	—	2	2	no	—
221	C₂×C₄₃	—	2	2	no	—
222	C₂×C₄₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₄₃	#2955	1	2	yes	—
224	C₂²×M₁₆	—	43	1	no	—
225	C₂²×M₁₆	—	43	1	no	—
226	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
227	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
228	C₂×#117	—	43	1	no	—
229	C₂×#117	—	43	1	no	—
230	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
231	#430	—	43	8	no	—
232	C₂×#108	—	43	4	no	—
233	#428	—	43	4	no	—
234	#428	—	43	4	no	—
235	#427	—	43	4	no	—
236	#405	—	2	1	no	—
237	#405	—	2	1	no	—
238	#405	—	43	8	no	—
239	#405	—	43	2	no	—
240	#405	—	43	2	no	—
241	#405	—	86	1	no	—
242	#405	—	86	1	no	—
243	#405	C₂×D₄₃	1	2	yes	—
244	#405	C₂×D₄₃	1	2	yes	—
245	C₂×#97	—	2	1	no	—
246	C₂×#97	—	43	2	no	—
247	C₂×#97	—	86	1	no	—
248	C₂×C₄×C₈	—	2	1	no	—
249	C₂×C₄×C₈	—	43	2	no	—
250	C₂×C₄×C₈	—	86	1	no	—
251	#339	—	43	4	no	—
252	#339	—	43	4	no	—
253	C₄₃	#20444	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	43	4	no	—
258	C₂×M₁₆	—	43	2	no	—
259	C₂×M₁₆	—	43	2	no	—
260	C₂×M₁₆	—	43	4	no	—
261	C₂×M₁₆	—	43	4	no	—
262	C₂×M₁₆	—	43	2	no	—
263	C₂×M₁₆	—	86	2	no	—
264	C₂×M₁₆	—	86	1	no	—
265	C₂×M₁₆	C₄×D₄₃	1	4	yes	—
266	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	43	2	no	—
269	C₂²×C₈	—	86	1	no	—
270	C₂²×C₈	Dic₈₆	1	4	yes	—
271	C₂²×C₈	C₄×D₄₃	1	4	yes	—
272	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
273	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
274	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
276	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
277	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
280	#117	—	43	4	no	—
281	#117	—	43	2	no	—
282	#117	—	43	2	no	—
283	#117	—	86	1	no	—
284	#117	—	86	2	no	—
285	#117	—	86	1	no	—
286	#117	C₄×D₄₃	1	2	yes	—
287	#117	C₂²×D₄₃	1	2	yes	—
288	C₂×C₄⋊C₄	—	43	2	no	—
289	C₂×C₄⋊C₄	—	86	1	no	—
290	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	86	1	no	—
293	C₂×C₂²⋊C₄	—	86	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	43	2	no	—
296	C₂×C₄²	—	86	1	no	—
297	#108	—	43	16	no	—
298	#107	—	43	8	no	—
299	#106	—	43	8	no	—
300	#97	—	2	2	no	—
301	#97	—	2	2	no	—
302	#97	—	43	8	no	—
303	#97	—	86	2	no	—
304	#97	—	86	2	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	2	2	no	—
307	C₄×C₈	—	43	8	no	—
308	C₄×C₈	—	86	2	no	—
309	C₄×C₈	—	86	2	no	—
310	C₂⁴	#10621898	1	1	yes	characteristic
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	86	2	no	—
313	C₂²×C₄	—	86	2	no	—
314	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
315	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
316	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
317	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	#10621898	1	1	yes	characteristic
320	C₂²×C₄	#10621898	1	2	yes	—
321	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
324	M₁₆	—	2	4	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	43	8	no	—
327	M₁₆	—	43	8	no	—
328	M₁₆	—	43	4	no	—
329	M₁₆	—	86	4	no	—
330	M₁₆	—	86	2	no	—
331	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	43	4	no	—
335	C₂×C₈	—	43	4	no	—
336	C₂×C₈	—	43	4	no	—
337	C₂×C₈	—	86	4	no	—
338	C₂×C₈	—	86	2	no	—
339	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
340	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
341	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
342	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
343	C₂×C₈	C₂×Dic₈₆	1	2	yes	—
344	C₂×C₈	C₂×Dic₈₆	1	2	yes	—
345	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
346	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
347	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
348	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	43	4	no	—
353	C₄⋊C₄	—	86	4	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	86	4	no	—
359	C₂²⋊C₄	—	86	2	no	—
360	C₂²⋊C₄	—	86	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	43	4	no	—
364	C₄²	—	86	2	no	—
365	C₄²	—	86	2	no	—
366	C₄²	—	86	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	#13063282	1	2	yes	—
369	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
370	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
371	C₂³	C₄×Dic₈₆	1	2	yes	—
372	C₂³	C₂×#10621898	1	1	yes	characteristic
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	86	4	no	—
376	C₂×C₄	—	86	4	no	—
377	C₂×C₄	—	172	4	no	—
378	C₂×C₄	—	172	4	no	—
379	C₂×C₄	C₄²×D₄₃	1	2	yes	—
380	C₂×C₄	C₄²×D₄₃	1	2	yes	—
381	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
382	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
383	C₂×C₄	#13063282	1	2	yes	—
384	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
385	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
386	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
388	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
389	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
390	C₂×C₄	C₄×Dic₈₆	1	2	yes	—
391	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
396	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
397	C₈	—	2	4	no	—
398	C₈	—	43	8	no	—
399	C₈	—	86	4	no	—
400	C₈	C₂×Dic₄₃⋊C₄	1	2	yes	—
401	C₈	C₂×Dic₄₃⋊C₄	1	2	yes	—
402	C₈	C₂×Dic₄₃⋊C₄	1	2	yes	—
403	C₈	C₂×Dic₄₃⋊C₄	1	2	yes	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₄×Dic₄₃⋊C₄	1	2	yes	—
410	C₂²	C₄×Dic₄₃⋊C₄	1	2	yes	—
411	C₂²	C₂×#13063282	1	1	yes	characteristic
412	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
413	C₂²	C₂×C₄×Dic₈₆	1	1	yes	characteristic
414	C₄	—	4	4	no	—
415	C₄	—	172	4	no	—
416	C₄	—	172	4	no	—
417	C₄	C₄×Dic₄₃⋊C₄	1	2	yes	—
418	C₄	C₄×Dic₄₃⋊C₄	1	2	yes	—
419	C₄	C₂×C₄²×D₄₃	1	1	yes	characteristic
420	C₄	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
421	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
422	C₄	C₂×C₄×Dic₈₆	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	2	2	no	—
426	C₂	—	2	2	no	—
427	C₂	C₂×C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
428	C₂	#19143496	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂⁴×C₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#20444
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
5. #19134480	C₂	semidirect
6. #19134475	C₂	semidirect
14. #14582947	C₄	semidirect
16. #14582942	C₄	semidirect
17. #14582939	C₄	semidirect
21. #14582854	C₄	semidirect
61. #13063260	C₂×C₄	semidirect
66. #13063235	C₂×C₄	semidirect
69. C₈×Dic₄₃	C₂×C₄	semidirect
253. C₄₃	#20444	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582947	2
#19143184	2
C₂×#14582854	2
#19134480	2
#19134475	2
#19134306	2
#19134304	2
C₂×C₄₃×#405	2
#20444	43