Subgroups — #24991959

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10621877	C₂	1	1	yes	maximal, characteristic
2	#19134575	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#19132436	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10621877	—	2	1	no	—
7	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
9	C₄×#10621877	—	2	4	no	—
10	C₂×#13063236	—	2	1	no	—
11	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
12	#14582654	—	2	1	no	—
13	Q₈⋊(C₄₃⋊C₈)	—	2	4	no	—
14	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#391	C₄	1	1	yes	characteristic
18	C₄₃×#389	C₄	1	1	yes	characteristic
19	C₄₃×#387	—	2	1	no	—
20	C₄₃×#385	—	2	1	no	—
21	C₄₃×#380	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
25	C₂×#10621877	—	2	4	no	—
26	C₂×#10621877	—	2	4	no	—
27	C₂×#10621877	—	2	4	no	—
28	C₂²×C₄₃⋊C₈	—	2	2	no	—
29	C₂²×C₄₃⋊C₈	—	2	2	no	—
30	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
31	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
32	C₂²⋊(C₄₃⋊C₈)	—	4	2	no	—
33	#13063236	—	2	4	no	—
34	C₄×C₄₃⋊C₈	—	2	2	no	—
35	C₄×C₄₃⋊C₈	D₄	1	4	yes	—
36	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂²⋊Q₈×C₄₃	—	2	2	no	—
41	C₂²⋊Q₈×C₄₃	—	2	2	no	—
42	C₄×Q₈×C₄₃	—	2	2	no	—
43	C₄×Q₈×C₄₃	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
52	C₂×C₄²×C₄₃	—	2	2	no	—
53	C₂×C₄²×C₄₃	—	2	2	no	—
54	C₂×C₄²×C₄₃	—	2	1	no	—
55	C₂×C₄²×C₄₃	—	2	1	no	—
56	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
60	#95×C₄₃	—	2	1	no	—
61	#95×C₄₃	—	2	1	no	—
62	#95×C₄₃	—	2	1	no	—
63	#95×C₄₃	—	2	1	no	—
64	#95×C₄₃	—	2	1	no	—
65	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×Q₈×C₄₃	—	2	1	no	—
67	C₂×Q₈×C₄₃	—	2	2	no	—
68	C₂×Q₈×C₄₃	—	2	2	no	—
69	C₂×Q₈×C₄₃	M₁₆	1	2	yes	complemented
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	—	2	1	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	2	1	no	—
76	C₂²×C₄×C₄₃	—	2	1	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	1	no	—
79	C₂²×C₄×C₄₃	—	2	1	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₄⋊C₄×C₄₃	—	2	4	no	—
93	C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₄⋊C₄×C₄₃	—	2	2	no	—
95	C₄⋊C₄×C₄₃	—	2	2	no	—
96	C₄⋊C₄×C₄₃	—	4	2	no	—
97	C₄⋊C₄×C₄₃	—	4	1	no	—
98	C₄⋊C₄×C₄₃	—	4	1	no	—
99	C₄⋊C₄×C₄₃	M₁₆	1	2	yes	complemented
100	C₂²⋊C₄×C₄₃	—	2	4	no	—
101	C₂²⋊C₄×C₄₃	—	4	2	no	—
102	C₄²×C₄₃	—	2	2	no	—
103	C₄²×C₄₃	—	2	1	no	—
104	C₄²×C₄₃	—	2	2	no	—
105	C₄²×C₄₃	—	2	1	no	—
106	C₄²×C₄₃	—	4	2	no	—
107	C₄²×C₄₃	—	4	1	no	—
108	C₄²×C₄₃	—	4	1	no	—
109	C₄²×C₄₃	C₂×D₄	1	2	yes	—
110	C₄²×C₄₃	#41	1	2	yes	—
111	#10621877	—	2	16	no	—
112	C₂×C₄₃⋊C₈	—	2	4	no	—
113	C₂×C₄₃⋊C₈	—	2	4	no	—
114	C₂×C₄₃⋊C₈	—	2	4	no	—
115	C₂×C₄₃⋊C₈	—	4	2	no	—
116	C₂×C₄₃⋊C₈	—	4	2	no	—
117	C₂×C₄₃⋊C₈	—	4	2	no	—
118	C₂³×C₄₃	—	2	1	no	—
119	C₂³×C₄₃	—	2	1	no	—
120	C₂³×C₄₃	—	2	1	no	—
121	C₂³×C₄₃	—	2	1	no	—
122	C₂³×C₄₃	—	2	1	no	—
123	C₂³×C₄₃	—	2	1	no	—
124	C₂³×C₄₃	#104	1	2	yes	—
125	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	Q₈×C₄₃	—	2	4	no	—
127	Q₈×C₄₃	—	4	2	no	—
128	C₂×C₄×C₄₃	—	2	4	no	—
129	C₂×C₄×C₄₃	—	2	4	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	—	2	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	1	no	—
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	2	no	—
137	C₂×C₄×C₄₃	—	2	2	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	4	1	no	—
143	C₂×C₄×C₄₃	—	4	1	no	—
144	C₂×C₄×C₄₃	—	4	1	no	—
145	C₂×C₄×C₄₃	—	4	1	no	—
146	C₂×C₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	—	4	2	no	—
148	C₂×C₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	1	no	—
154	C₂×C₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	#104	1	2	yes	—
157	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#121	1	2	yes	—
160	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#131	1	2	yes	—
164	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#137	1	2	yes	—
167	C₄₃⋊C₈	—	2	8	no	—
168	C₄₃⋊C₈	—	8	2	no	—
169	#9077	—	43	1	no	maximal, Sylow
170	C₂²×C₄₃	—	2	2	no	—
171	C₂²×C₄₃	—	2	2	no	—
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	4	1	no	—
174	C₂²×C₄₃	—	4	1	no	—
175	C₂²×C₄₃	—	4	1	no	—
176	C₂²×C₄₃	—	4	1	no	—
177	C₂²×C₄₃	#386	1	1	yes	characteristic
178	C₂²×C₄₃	#407	1	1	yes	characteristic
179	C₂²×C₄₃	#408	1	1	yes	characteristic
180	C₂²×C₄₃	#417	1	1	yes	characteristic
181	C₂²×C₄₃	#419	1	1	yes	characteristic
182	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
184	C₄×C₄₃	—	2	1	no	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	4	1	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	4	1	no	—
190	C₄×C₄₃	—	4	2	no	—
191	C₄×C₄₃	—	8	1	no	—
192	C₄×C₄₃	—	8	1	no	—
193	C₄×C₄₃	#435	1	2	yes	—
194	C₄×C₄₃	#436	1	2	yes	—
195	C₄×C₄₃	#468	1	2	yes	—
196	C₄×C₄₃	#470	1	2	yes	—
197	C₂×C₄×M₁₆	—	43	1	no	—
198	C₄×C₂²⋊Q₈	D₄₃	1	1	yes	characteristic
199	#1797	—	43	1	no	—
200	C₂×Q₈⋊C₈	—	43	2	no	—
201	#1279	—	43	2	no	—
202	C₂×C₄₃	—	4	2	no	—
203	C₂×C₄₃	#1483	1	1	yes	characteristic
204	C₂×C₄₃	#1485	1	1	yes	characteristic
205	C₂×C₄₃	#1489	1	1	yes	characteristic
206	C₂×C₄₃	#1491	1	1	yes	characteristic
207	C₂×C₄₃	#1870	1	1	yes	characteristic
208	C₂×C₄₃	#1894	1	1	yes	characteristic
209	C₂×C₄₃	#1896	1	1	yes	characteristic
210	C₂²×M₁₆	—	86	1	no	—
211	C₂×C₂²⋊Q₈	Dic₄₃	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
213	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	43	2	no	—
215	C₂×C₂²⋊C₈	—	86	1	no	—
216	C₄×M₁₆	—	86	4	no	—
217	C₂×#97	—	86	1	no	—
218	C₂×C₄×C₈	—	43	2	no	—
219	#391	Dic₄₃	1	1	yes	characteristic
220	#389	Dic₄₃	1	1	yes	characteristic
221	#387	—	2	1	no	—
222	#385	—	2	1	no	—
223	#380	Dic₄₃	1	1	yes	characteristic
224	C₄×C₄⋊C₄	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
226	C₄×C₂²⋊C₄	—	2	1	no	—
227	#336	—	86	1	no	—
228	Q₈⋊C₈	—	86	4	no	—
229	C₄₃	#9077	1	1	yes	characteristic, complemented, Sylow
230	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
231	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
233	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
234	C₂×M₁₆	—	86	4	no	—
235	C₂×M₁₆	—	86	4	no	—
236	C₂×M₁₆	—	86	4	no	—
237	C₂²×C₈	—	86	2	no	—
238	C₂²×C₈	—	86	2	no	—
239	C₂²⋊Q₈	—	2	2	no	—
240	C₂²⋊Q₈	—	2	2	no	—
241	C₄×Q₈	—	2	2	no	—
242	C₄×Q₈	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
256	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
257	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
258	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
259	C₄⋊C₈	—	86	2	no	—
260	C₄⋊C₈	—	86	2	no	—
261	C₂²⋊C₈	—	172	2	no	—
262	#97	—	86	4	no	—
263	C₄×C₈	—	43	4	no	—
264	C₄×C₈	—	86	2	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	#95	—	2	1	no	—
268	#95	—	2	1	no	—
269	#95	—	2	1	no	—
270	C₂⁴	C₂²⋊Dic₄₃	1	1	yes	characteristic
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	#10621877	1	2	yes	complemented
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
292	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
297	M₁₆	—	86	16	no	—
298	C₂×C₈	—	86	4	no	—
299	C₂×C₈	—	86	4	no	—
300	C₂×C₈	—	86	4	no	—
301	C₂×C₈	—	172	2	no	—
302	C₂×C₈	—	172	2	no	—
303	C₂×C₈	—	172	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	#10621877	1	2	yes	complemented
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	4	2	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	1	no	—
321	C₄²	D₄×D₄₃	1	2	yes	—
322	C₄²	#10621900	1	2	yes	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	1	no	—
329	C₂³	#13063252	1	2	yes	—
330	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
331	Q₈	—	2	4	no	—
332	Q₈	—	4	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	#13063252	1	2	yes	—
362	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
363	C₂×C₄	#13063293	1	1	yes	characteristic
364	C₂×C₄	#13063297	1	2	yes	—
365	C₂×C₄	#13063306	1	1	yes	characteristic
366	C₂×C₄	C₂×#10621877	1	1	yes	characteristic
367	C₂×C₄	C₂×#10621877	1	1	yes	characteristic
368	C₂×C₄	#13063332	1	2	yes	—
369	C₂×C₄	#13063350	1	1	yes	characteristic
370	C₂×C₄	#13063355	1	1	yes	characteristic
371	C₂×C₄	#13063356	1	2	yes	—
372	C₈	—	86	8	no	—
373	C₈	—	344	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	#14582779	1	1	yes	characteristic
382	C₂²	#14582863	1	1	yes	characteristic
383	C₂²	#14582866	1	1	yes	characteristic
384	C₂²	#14582900	1	1	yes	characteristic
385	C₂²	#14582908	1	1	yes	characteristic
386	C₂²	C₂×#13063252	1	1	yes	characteristic
387	C₂²	C₂×#13063252	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	1	no	—
397	C₄	#14582971	1	2	yes	—
398	C₄	#14582977	1	2	yes	—
399	C₄	#14583147	1	2	yes	—
400	C₄	#14583155	1	2	yes	—
401	C₂	—	4	2	no	—
402	C₂	#19133008	1	1	yes	characteristic
403	C₂	#19133016	1	1	yes	characteristic
404	C₂	#19133034	1	1	yes	characteristic
405	C₂	#19133042	1	1	yes	characteristic
406	C₂	#19134893	1	1	yes	characteristic
407	C₂	#19135029	1	1	yes	characteristic
408	C₂	#19135039	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄×C₂²⋊Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₄₃
hypocenter	C₄₃	#9077
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈⋊(C₄₃⋊C₈)	C₂	semidirect
4. #19132436	C₂	semidirect
69. C₂×Q₈×C₄₃	M₁₆	semidirect
99. C₄⋊C₄×C₄₃	M₁₆	semidirect
229. C₄₃	#9077	semidirect
274. C₂×Q₈	#10621877	semidirect
311. C₄⋊C₄	#10621877	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621877	2
#19134575	2
C₂×Q₈⋊(C₄₃⋊C₈)	2
#19132436	2
C₄×C₂²⋊Q₈×C₄₃	2
#9077	43