Subgroups — #25065941

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143727	C₂	1	1	yes	maximal, characteristic
2	#19143562	C₂	1	1	yes	maximal, characteristic
3	#19133386	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133383	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133376	C₂	1	2	yes	maximal, complemented
6	#19133365	C₂	1	2	yes	maximal, complemented
7	#19133363	C₂	1	2	yes	maximal, complemented
8	#19133350	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133345	C₂	1	2	yes	maximal, complemented
10	#19133341	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2990	C₂	1	1	yes	maximal, characteristic
12	#14583030	C₄	1	1	yes	characteristic
13	#14583030	C₄	1	1	yes	characteristic
14	Q₈×C₄₃⋊C₈	—	2	1	no	—
15	#14582977	—	2	1	no	—
16	#14582977	—	2	2	no	—
17	#14582977	C₄	1	1	yes	characteristic
18	#14582977	C₄	1	1	yes	characteristic
19	#14582971	C₄	1	2	yes	—
20	#14582971	C₄	1	2	yes	—
21	#14582952	C₂²	1	1	yes	characteristic
22	#14582952	C₂²	1	2	yes	—
23	#14582952	C₂²	1	2	yes	—
24	#14582952	C₂²	1	1	yes	characteristic
25	#14582923	C₂²	1	1	yes	characteristic
26	#14582923	C₂²	1	2	yes	—
27	C₄×#10621877	C₂²	1	2	yes	—
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14582651	C₂²	1	1	yes	characteristic
30	#14582651	C₂²	1	1	yes	characteristic
31	#14582651	C₂²	1	2	yes	—
32	#14582651	C₂²	1	2	yes	—
33	#14582649	C₂²	1	1	yes	characteristic
34	#14582649	C₂²	1	1	yes	characteristic
35	#14582649	C₂²	1	2	yes	—
36	#14582649	C₂²	1	2	yes	—
37	#14582649	C₂²	1	2	yes	—
38	#14582649	C₂²	1	2	yes	—
39	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#446	—	2	1	no	—
41	C₄₃×#435	—	2	2	no	—
42	C₈×D₄×C₄₃	—	2	1	no	—
43	C₄₃×#432	C₂²	1	2	yes	—
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
47	C₂×#10621877	—	2	2	no	—
48	C₂×#10621877	—	2	1	no	—
49	C₂×#10621877	C₂×C₄	1	2	yes	—
50	C₂×#10621877	C₂×C₄	1	2	yes	—
51	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
55	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
57	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
58	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
59	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
60	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
62	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
63	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
65	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
66	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
67	#13063236	C₂×C₄	1	2	yes	—
68	#13063236	C₂×C₄	1	2	yes	—
69	C₄×C₄₃⋊C₈	—	2	1	no	—
70	C₄×C₄₃⋊C₈	—	2	2	no	—
71	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
76	C₂×#41×C₄₃	Q₈	1	1	yes	characteristic
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂²×C₈×C₄₃	—	2	2	no	—
79	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
80	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
81	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
84	C₄×D₄×C₄₃	D₄	1	2	yes	—
85	#117×C₄₃	Q₈	1	1	yes	characteristic
86	#117×C₄₃	Q₈	1	2	yes	—
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
89	C₄⋊C₈×C₄₃	—	2	2	no	—
90	C₄⋊C₈×C₄₃	—	2	1	no	—
91	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
93	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₄₃	—	2	1	no	—
95	C₂²⋊C₈×C₄₃	—	2	2	no	—
96	#97×C₄₃	—	2	2	no	—
97	C₄×C₈×C₄₃	—	2	1	no	—
98	#41×C₄₃	—	4	2	no	—
99	C₂×Q₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×D₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₄₃	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
108	M₁₆×C₄₃	—	8	1	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	—	8	2	no	—
113	C₄⋊C₄×C₄₃	C₄⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
115	C₄⋊C₄×C₄₃	C₄⋊C₄	1	2	yes	—
116	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	2	yes	—
120	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
122	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₃	C₂×D₄	1	2	yes	—
124	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
125	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
126	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
127	#10621877	—	2	4	no	—
128	#10621877	—	4	2	no	—
129	#10621877	—	8	2	no	—
130	#10621877	—	8	1	no	—
131	C₂×C₄₃⋊C₈	—	2	2	no	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	2	no	—
135	C₂×C₄₃⋊C₈	—	4	1	no	—
136	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
144	Q₈×C₄₃	—	2	2	no	—
145	D₄×C₄₃	—	2	2	no	—
146	D₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	2	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	1	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
166	C₈×C₄₃	—	4	1	no	—
167	C₈×C₄₃	—	4	1	no	—
168	C₈×C₄₃	—	4	2	no	—
169	C₄₃⋊C₈	—	2	1	no	—
170	C₄₃⋊C₈	—	2	2	no	—
171	C₄₃⋊C₈	—	2	1	no	—
172	C₄₃⋊C₈	—	2	1	no	—
173	C₄₃⋊C₈	—	2	2	no	—
174	C₄₃⋊C₈	—	4	1	no	—
175	C₄₃⋊C₈	—	4	1	no	—
176	C₄₃⋊C₈	—	4	2	no	—
177	C₄₃⋊C₈	#131	1	2	yes	—
178	#17841	—	43	1	no	maximal, Sylow
179	C₂²×C₄₃	—	2	1	no	—
180	C₂²×C₄₃	—	2	2	no	—
181	C₂²×C₄₃	—	2	2	no	—
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	—	2	1	no	—
184	C₂²×C₄₃	—	2	2	no	—
185	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	2	2	no	—
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	2	1	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	#430	1	2	yes	—
193	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
194	C₄×C₄₃	#568	1	1	yes	characteristic
195	C₄×C₄₃	#577	1	1	yes	characteristic
196	C₄×C₄₃	#577	1	1	yes	characteristic
197	#2991	—	43	1	no	—
198	#2990	D₄₃	1	1	yes	characteristic
199	#2965	—	43	1	no	—
200	#1574	—	43	1	no	—
201	#1574	—	43	1	no	—
202	#1572	—	43	2	no	—
203	#1570	—	43	2	no	—
204	#1569	—	43	2	no	—
205	#1566	—	43	1	no	—
206	#1565	—	43	2	no	—
207	#1564	—	43	1	no	—
208	C₂×C₄₃	—	4	1	no	—
209	C₂×C₄₃	—	4	2	no	—
210	C₂×C₄₃	#2906	1	1	yes	characteristic
211	C₂×C₄₃	#2912	1	1	yes	characteristic
212	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
213	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
214	#446	—	2	1	no	—
215	#446	—	43	1	no	—
216	#446	—	43	1	no	—
217	C₈×Q₈	—	86	1	no	—
218	#436	—	43	1	no	—
219	#436	—	43	1	no	—
220	#436	—	86	1	no	—
221	#436	—	86	2	no	—
222	#435	—	2	2	no	—
223	#435	—	43	2	no	—
224	#435	—	43	2	no	—
225	C₈×D₄	—	2	1	no	—
226	#432	C₂×D₄₃	1	2	yes	—
227	#431	—	43	2	no	—
228	#431	—	43	1	no	—
229	#431	—	43	1	no	—
230	#431	—	43	2	no	—
231	#431	C₂×D₄₃	1	1	yes	characteristic
232	#423	—	43	1	no	—
233	#423	—	43	2	no	—
234	#423	C₂×D₄₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
236	C₄×M₁₆	—	43	2	no	—
237	C₂×C₄×C₈	—	43	1	no	—
238	#335	—	43	1	no	—
239	#335	—	43	1	no	—
240	#335	—	43	2	no	—
241	#335	—	43	2	no	—
242	#334	—	43	1	no	—
243	#334	—	43	1	no	—
244	#334	—	43	2	no	—
245	#334	—	43	2	no	—
246	#334	—	43	2	no	—
247	#334	—	43	2	no	—
248	C₄₃	#17841	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	Dic₈₆	1	1	yes	characteristic
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	43	2	no	—
252	C₂×M₁₆	—	43	2	no	—
253	C₂×M₁₆	—	86	2	no	—
254	C₂×M₁₆	—	86	1	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	43	1	no	—
257	C₂²×C₈	—	43	1	no	—
258	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
259	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
260	C₄×D₄	C₄×D₄₃	1	2	yes	—
261	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
262	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
263	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
264	#117	Dic₈₆	1	1	yes	characteristic
265	#117	Dic₈₆	1	2	yes	—
266	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	43	2	no	—
271	C₄⋊C₈	—	43	2	no	—
272	C₄⋊C₈	—	43	1	no	—
273	C₄⋊C₈	—	43	1	no	—
274	C₄⋊C₈	—	43	1	no	—
275	C₄⋊C₈	—	43	2	no	—
276	C₄⋊C₈	—	43	1	no	—
277	C₄⋊C₈	—	86	1	no	—
278	C₄⋊C₈	—	86	2	no	—
279	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
280	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
281	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	43	2	no	—
285	C₂²⋊C₈	—	43	2	no	—
286	C₂²⋊C₈	—	43	2	no	—
287	C₂²⋊C₈	—	86	2	no	—
288	C₂²⋊C₈	—	86	1	no	—
289	#97	—	2	2	no	—
290	#97	—	43	2	no	—
291	#97	—	43	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	43	1	no	—
294	C₄×C₈	—	43	1	no	—
295	C₄×C₈	—	43	1	no	—
296	C₄×C₈	—	43	1	no	—
297	C₄×C₈	—	43	2	no	—
298	C₄×C₈	—	86	1	no	—
299	C₄×C₈	—	86	2	no	—
300	#41	—	4	2	no	—
301	C₂×Q₈	Dic₄₃⋊C₄	1	1	yes	characteristic
302	C₂×D₄	Dic₄₃⋊C₄	1	1	yes	characteristic
303	C₂×D₄	Dic₄₃⋊C₄	1	2	yes	—
304	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
305	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
310	M₁₆	—	8	1	no	—
311	M₁₆	—	86	4	no	—
312	M₁₆	—	344	2	no	—
313	M₁₆	—	344	1	no	—
314	M₁₆	—	172	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	8	2	no	—
319	C₂×C₈	—	43	1	no	—
320	C₂×C₈	—	43	1	no	—
321	C₂×C₈	—	43	1	no	—
322	C₂×C₈	—	43	1	no	—
323	C₂×C₈	—	43	2	no	—
324	C₂×C₈	—	43	2	no	—
325	C₂×C₈	—	86	2	no	—
326	C₂×C₈	—	86	1	no	—
327	C₂×C₈	—	86	1	no	—
328	C₂×C₈	—	86	2	no	—
329	C₂×C₈	—	172	1	no	—
330	C₄⋊C₄	Dic₄₃⋊C₄	1	2	yes	—
331	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
332	C₄⋊C₄	Dic₄₃⋊C₄	1	2	yes	—
333	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
334	C₂²⋊C₄	Dic₄₃⋊C₄	1	2	yes	—
335	C₂²⋊C₄	Dic₄₃⋊C₄	1	2	yes	—
336	C₂²⋊C₄	Dic₄₃⋊C₄	1	2	yes	—
337	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
338	C₄²	C₂×Dic₈₆	1	2	yes	—
339	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₄₃	1	2	yes	—
341	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
342	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
343	C₄²	C₂³×D₄₃	1	1	yes	characteristic
344	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
345	C₂³	C₂×Dic₄₃⋊C₄	1	2	yes	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
361	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×Dic₄₃⋊C₄	1	2	yes	—
364	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
367	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	2	no	—
371	C₈	—	43	2	no	—
372	C₈	—	86	1	no	—
373	C₈	—	86	2	no	—
374	C₈	—	86	1	no	—
375	C₈	—	86	1	no	—
376	C₈	—	86	2	no	—
377	C₈	—	172	1	no	—
378	C₈	—	172	2	no	—
379	C₈	—	172	1	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	#14582947	1	2	yes	—
394	C₄	#131×D₄₃	1	1	yes	characteristic
395	C₄	#14583664	1	1	yes	characteristic
396	C₄	#14583707	1	1	yes	characteristic
397	C₄	#14583710	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	#19143161	1	1	yes	characteristic
401	C₂	#19143188	1	1	yes	characteristic
402	C₂	C₂×#14582947	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2990	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₄₃	Q₈
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2990	D₄₃
hypocenter	C₄₃	#17841
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
3. #19133386	C₂	semidirect
4. #19133383	C₂	semidirect
5. #19133376	C₂	semidirect
6. #19133365	C₂	semidirect
7. #19133363	C₂	semidirect
8. #19133350	C₂	semidirect
9. #19133345	C₂	semidirect
10. #19133341	C₂	semidirect
248. C₄₃	#17841	semidirect

Maximal subgroups

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

subgroup	index
#19143727	2
#19143562	2
#19133386	2
#19133383	2
#19133376	2
#19133365	2
#19133363	2
#19133350	2
#19133345	2
#19133341	2
C₄₃×#2990	2
#17841	43