Subgroups — #25104267

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	#19135544	C₂	1	1	yes	maximal, characteristic
4	#19135359	C₂	1	1	yes	maximal, characteristic
5	#19135168	C₂	1	2	yes	maximal
6	#19134865	C₂	1	2	yes	maximal
7	#19134600	C₂	1	1	yes	maximal, characteristic
8	#19134494	C₂	1	2	yes	maximal
9	#19134450	C₂	1	1	yes	maximal, characteristic
10	#19134427	C₂	1	2	yes	maximal
11	C₂×C₄₃×#477	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₃	—	2	1	no	—
13	C₂×Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂×#13063257	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13063249	C₂²	1	2	yes	—
18	C₂×#13063235	C₂²	1	2	yes	—
19	#14582806	—	2	1	no	—
20	#14582798	—	2	1	no	—
21	#14582798	C₂²	1	2	yes	—
22	#14582769	C₂²	1	1	yes	characteristic
23	C₄⋊C₄×Dic₄₃	—	2	1	no	—
24	C₄⋊C₄×Dic₄₃	—	2	1	no	—
25	C₄⋊C₄×Dic₄₃	—	2	1	no	—
26	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₃	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₄₃	—	2	1	no	—
30	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
31	C₄²×Dic₄₃	—	2	1	no	—
32	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582662	C₂²	1	2	yes	—
34	#14582661	C₂²	1	2	yes	—
35	#14582661	C₂²	1	2	yes	—
36	#14582661	C₂²	1	2	yes	—
37	#14582653	C₂²	1	2	yes	—
38	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#477	C₄	1	8	yes	complemented
41	C₂×#107×C₄₃	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×#103×C₄₃	C₂²	1	2	yes	—
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	Q₈×Dic₄₃	—	2	2	no	—
46	Q₈×Dic₄₃	—	2	2	no	—
47	Q₈×Dic₄₃	—	2	2	no	—
48	Q₈×Dic₄₃	—	4	4	no	—
49	Q₈×Dic₄₃	Q₈	1	4	yes	complemented
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄⋊Dic₄₃	—	2	1	no	—
53	C₂×C₄⋊Dic₄₃	—	2	1	no	—
54	C₂×C₄⋊Dic₄₃	—	2	2	no	—
55	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₃	—	2	1	no	—
59	C₂×C₄×Dic₄₃	—	2	1	no	—
60	C₂×C₄×Dic₄₃	—	2	1	no	—
61	C₂×C₄×Dic₄₃	—	2	2	no	—
62	C₂×C₄×Dic₄₃	—	2	1	no	—
63	C₂×C₄×Dic₄₃	—	2	1	no	—
64	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
70	#13063257	—	2	4	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
72	#13063249	—	2	4	no	—
73	#13063235	—	2	4	no	—
74	C₄₃⋊#95	—	2	1	no	—
75	C₄₃⋊#95	—	2	2	no	—
76	C₄₃⋊#95	—	2	2	no	—
77	C₄₃⋊#95	—	2	1	no	—
78	C₄₃⋊#95	—	2	1	no	—
79	C₂²×Q₈×C₄₃	—	2	1	no	—
80	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₄₃	—	2	2	no	—
83	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
84	C₄×Q₈×C₄₃	—	2	2	no	—
85	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	—	2	1	no	—
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	#107×C₄₃	C₂×C₄	1	8	yes	—
93	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
94	#103×C₄₃	C₂×C₄	1	8	yes	—
95	C₂×Q₈×C₄₃	—	2	4	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	4	2	no	—
100	C₂×Q₈×C₄₃	—	4	2	no	—
101	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
102	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
103	C₂×Q₈×C₄₃	#41	1	2	yes	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₃	—	2	1	no	—
111	C₂²×Dic₄₃	—	2	1	no	—
112	C₂²×Dic₄₃	—	2	2	no	—
113	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
120	C₄⋊C₄×C₄₃	—	2	4	no	—
121	C₄⋊C₄×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
125	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₃	—	2	4	no	—
127	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₃	#41	1	2	yes	—
129	C₄⋊Dic₄₃	—	2	4	no	—
130	C₄⋊Dic₄₃	—	2	1	no	—
131	C₄⋊Dic₄₃	—	2	1	no	—
132	C₄⋊Dic₄₃	—	2	4	no	—
133	C₄⋊Dic₄₃	—	2	2	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	4	2	no	—
136	C₄⋊Dic₄₃	—	4	2	no	—
137	C₄⋊Dic₄₃	—	4	4	no	—
138	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
139	C₄⋊Dic₄₃	#41	1	2	yes	—
140	C₄×Dic₄₃	—	2	4	no	—
141	C₄×Dic₄₃	—	2	2	no	—
142	C₄×Dic₄₃	—	2	2	no	—
143	C₄×Dic₄₃	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₄×Dic₄₃	—	2	4	no	—
146	C₄×Dic₄₃	—	2	2	no	—
147	C₄×Dic₄₃	—	4	1	no	—
148	C₄×Dic₄₃	—	4	2	no	—
149	C₄×Dic₄₃	—	4	4	no	—
150	C₄×Dic₄₃	—	4	2	no	—
151	C₄×Dic₄₃	—	4	2	no	—
152	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
153	C₄×Dic₄₃	#41	1	2	yes	—
154	C₂×C₄₃⋊C₈	—	2	2	no	—
155	C₂×C₄₃⋊C₈	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	2	2	no	—
157	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₄₃	—	2	2	no	—
159	Q₈×C₄₃	—	2	2	no	—
160	Q₈×C₄₃	—	2	2	no	—
161	Q₈×C₄₃	—	4	8	no	—
162	Q₈×C₄₃	C₄×Q₈	1	4	yes	complemented
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₄₃	#137	1	2	yes	—
177	C₂×C₄×C₄₃	#137	1	2	yes	—
178	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₄₃	—	2	1	no	—
185	C₂×Dic₄₃	—	2	1	no	—
186	C₂×Dic₄₃	—	2	1	no	—
187	C₂×Dic₄₃	—	2	1	no	—
188	C₂×Dic₄₃	—	2	1	no	—
189	C₂×Dic₄₃	—	2	1	no	—
190	C₂×Dic₄₃	—	2	2	no	—
191	C₂×Dic₄₃	—	2	1	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	—	2	1	no	—
194	C₂×Dic₄₃	—	2	1	no	—
195	C₂×Dic₄₃	—	4	1	no	—
196	C₂×Dic₄₃	—	4	1	no	—
197	C₂×Dic₄₃	—	4	1	no	—
198	C₂×Dic₄₃	—	4	1	no	—
199	C₂×Dic₄₃	—	4	2	no	—
200	C₂×Dic₄₃	—	4	2	no	—
201	C₂×Dic₄₃	—	4	2	no	—
202	C₂×Dic₄₃	C₂²⋊Q₈	1	2	yes	—
203	C₂×Dic₄₃	C₂²⋊Q₈	1	2	yes	—
204	C₂×Dic₄₃	AGL(1,ℤ/8)	1	2	yes	—
205	C₈×C₄₃	—	2	4	no	—
206	C₄₃⋊C₈	—	4	2	no	—
207	#21616	—	43	1	no	maximal, Sylow
208	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₂²×C₄₃	#525	1	1	yes	characteristic
211	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
213	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
214	C₂²×C₄₃	#575	1	1	yes	characteristic
215	C₄×C₄₃	—	2	2	no	—
216	C₄×C₄₃	—	2	4	no	—
217	C₄×C₄₃	—	4	2	no	—
218	C₄×C₄₃	—	4	4	no	—
219	C₄×C₄₃	#441	1	4	yes	—
220	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
221	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
222	C₄×C₄₃	#529	1	1	yes	characteristic
223	C₄×C₄₃	#533	1	1	yes	characteristic
224	Dic₄₃	—	2	2	no	—
225	Dic₄₃	—	2	2	no	—
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	4	2	no	—
228	Dic₄₃	—	4	1	no	—
229	Dic₄₃	—	4	2	no	—
230	Dic₄₃	—	8	2	no	—
231	C₂×#477	D₄₃	1	1	yes	characteristic
232	C₄×C₄⋊Q₈	—	43	1	no	—
233	C₄²×Q₈	—	43	1	no	—
234	#1987	—	43	1	no	—
235	#1948	—	43	1	no	—
236	#1918	—	43	2	no	—
237	#1865	—	43	2	no	—
238	#1803	—	43	1	no	—
239	#1776	—	43	2	no	—
240	#1767	—	43	1	no	—
241	#1763	—	43	2	no	—
242	C₂×C₄₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#441	1	1	yes	characteristic
244	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₄₃	#3078	1	1	yes	characteristic
246	C₂×C₄₃	#3079	1	1	yes	characteristic
247	C₂×C₄₃	#3112	1	1	yes	characteristic
248	C₂×C₄₃	#3116	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
250	C₂×C₄×Q₈	—	43	1	no	—
251	C₂×C₄×Q₈	—	43	1	no	—
252	C₂×C₄×Q₈	—	86	1	no	—
253	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
254	#477	Dic₄₃	1	8	yes	complemented
255	C₂×#107	C₂×D₄₃	1	2	yes	—
256	C₂×#106	—	43	2	no	—
257	C₂×C₄⋊C₈	—	43	1	no	—
258	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
259	C₂×#103	—	43	2	no	—
260	C₂×#103	C₂×D₄₃	1	2	yes	—
261	C₂×#97	—	43	2	no	—
262	#391	—	86	1	no	—
263	#389	—	43	2	no	—
264	#389	—	86	1	no	—
265	#384	—	43	1	no	—
266	C₄×C₄⋊C₄	—	43	2	no	—
267	C₄×C₄⋊C₄	—	43	1	no	—
268	C₄×C₄⋊C₄	—	43	1	no	—
269	C₄×C₄⋊C₄	—	43	1	no	—
270	C₄×C₄⋊C₄	—	86	1	no	—
271	C₄×C₄⋊C₄	—	86	1	no	—
272	C₄×C₄⋊C₄	—	86	1	no	—
273	C₄×C₄⋊C₄	—	86	1	no	—
274	C₄³	—	43	1	no	—
275	C₄³	—	86	1	no	—
276	#340	—	43	2	no	—
277	#340	—	43	2	no	—
278	#340	—	43	2	no	—
279	#340	—	43	2	no	—
280	#336	—	43	2	no	—
281	C₄₃	#21616	1	1	yes	characteristic, complemented, Sylow
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
284	C₂²×C₈	—	43	2	no	—
285	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	C₂×Dic₄₃	1	4	yes	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×Q₈	—	43	4	no	—
290	C₄×Q₈	—	86	2	no	—
291	C₄×Q₈	—	86	2	no	—
292	C₄×Q₈	—	86	2	no	—
293	C₄×Q₈	—	172	4	no	—
294	C₄×Q₈	C₂×Dic₄₃	1	4	yes	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	43	1	no	—
298	C₂×C₄⋊C₄	—	43	1	no	—
299	C₂×C₄⋊C₄	—	43	2	no	—
300	C₂×C₄⋊C₄	—	86	1	no	—
301	C₂×C₄⋊C₄	—	86	1	no	—
302	C₂×C₄⋊C₄	—	86	2	no	—
303	C₂×C₄⋊C₄	—	86	1	no	—
304	C₂×C₄⋊C₄	—	86	1	no	—
305	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	43	1	no	—
309	C₂×C₄²	—	43	1	no	—
310	C₂×C₄²	—	43	1	no	—
311	C₂×C₄²	—	43	1	no	—
312	C₂×C₄²	—	43	1	no	—
313	C₂×C₄²	—	43	1	no	—
314	C₂×C₄²	—	86	1	no	—
315	C₂×C₄²	—	86	1	no	—
316	C₂×C₄²	—	86	2	no	—
317	C₂×C₄²	—	86	1	no	—
318	C₂×C₄²	—	86	1	no	—
319	C₂×C₄²	—	86	1	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#107	C₂×Dic₄₃	1	8	yes	—
322	#106	—	86	4	no	—
323	C₄⋊C₈	—	86	2	no	—
324	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	—
325	#103	—	86	4	no	—
326	#103	C₂×Dic₄₃	1	8	yes	—
327	#97	—	86	4	no	—
328	#95	—	86	1	no	—
329	#95	—	86	1	no	—
330	#95	—	86	2	no	—
331	#95	—	86	2	no	—
332	#95	—	86	1	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	4	2	no	—
338	C₂×Q₈	—	4	2	no	—
339	C₂×Q₈	Q₈×D₄₃	1	2	yes	—
340	C₂×Q₈	#10621902	1	2	yes	—
341	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	43	1	no	—
346	C₂²×C₄	—	43	1	no	—
347	C₂²×C₄	—	43	1	no	—
348	C₂²×C₄	—	43	1	no	—
349	C₂²×C₄	—	86	1	no	—
350	C₂²×C₄	—	86	1	no	—
351	C₂²×C₄	—	86	2	no	—
352	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	86	2	no	—
358	C₂×C₈	—	86	2	no	—
359	C₂×C₈	—	86	2	no	—
360	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	43	2	no	—
366	C₄⋊C₄	—	43	2	no	—
367	C₄⋊C₄	—	86	4	no	—
368	C₄⋊C₄	—	86	4	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	2	no	—
372	C₄⋊C₄	—	86	2	no	—
373	C₄⋊C₄	—	172	2	no	—
374	C₄⋊C₄	—	172	4	no	—
375	C₄⋊C₄	—	172	2	no	—
376	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
377	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
378	C₄²	—	2	4	no	—
379	C₄²	—	43	2	no	—
380	C₄²	—	43	2	no	—
381	C₄²	—	86	2	no	—
382	C₄²	—	86	4	no	—
383	C₄²	—	86	4	no	—
384	C₄²	—	86	2	no	—
385	C₄²	—	86	2	no	—
386	C₄²	—	86	1	no	—
387	C₄²	—	86	1	no	—
388	C₄²	—	172	1	no	—
389	C₄²	—	172	2	no	—
390	C₄²	—	172	4	no	—
391	C₄²	—	172	2	no	—
392	C₄²	—	172	2	no	—
393	C₄²	#10621900	1	2	yes	—
394	C₄²	C₂²×Dic₄₃	1	2	yes	—
395	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
396	Q₈	—	2	2	no	—
397	Q₈	—	2	2	no	—
398	Q₈	—	2	2	no	—
399	Q₈	—	4	8	no	—
400	Q₈	Q₈×Dic₄₃	1	4	yes	complemented
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	43	2	no	—
413	C₂×C₄	—	43	2	no	—
414	C₂×C₄	—	43	2	no	—
415	C₂×C₄	—	86	1	no	—
416	C₂×C₄	—	86	1	no	—
417	C₂×C₄	—	86	1	no	—
418	C₂×C₄	—	86	1	no	—
419	C₂×C₄	—	86	1	no	—
420	C₂×C₄	—	86	1	no	—
421	C₂×C₄	—	86	2	no	—
422	C₂×C₄	—	86	2	no	—
423	C₂×C₄	—	86	1	no	—
424	C₂×C₄	—	86	1	no	—
425	C₂×C₄	—	86	1	no	—
426	C₂×C₄	—	172	2	no	—
427	C₂×C₄	—	172	2	no	—
428	C₂×C₄	—	172	2	no	—
429	C₂×C₄	—	172	1	no	—
430	C₂×C₄	—	172	1	no	—
431	C₂×C₄	—	172	1	no	—
432	C₂×C₄	—	172	1	no	—
433	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
434	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
435	C₂×C₄	#13063357	1	2	yes	—
436	C₂×C₄	#13063357	1	2	yes	—
437	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
439	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
440	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
441	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
442	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
443	C₈	—	2	4	no	—
444	C₈	—	172	2	no	—
445	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
446	C₂²	C₂²⋊Q₈×D₄₃	1	1	yes	characteristic
447	C₂²	#14583412	1	1	yes	characteristic
448	C₂²	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
449	C₂²	C₂×#13063357	1	1	yes	characteristic
450	C₂²	C₂×#13063357	1	1	yes	characteristic
451	C₂²	#14583695	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	86	2	no	—
457	C₄	—	86	2	no	—
458	C₄	—	86	2	no	—
459	C₄	—	344	2	no	—
460	C₄	—	172	1	no	—
461	C₄	—	172	2	no	—
462	C₄	—	172	2	no	—
463	C₄	#14583006	1	4	yes	—
464	C₄	C₂×Q₈×Dic₄₃	1	1	yes	characteristic
465	C₄	#41×Dic₄₃	1	1	yes	characteristic
466	C₄	#14583435	1	1	yes	characteristic
467	C₄	#14583451	1	1	yes	characteristic
468	C₂	C₂²⋊Q₈×Dic₄₃	1	1	yes	characteristic
469	C₂	C₂×#14583006	1	1	yes	characteristic
470	C₂	AGL(1,ℤ/8)×Dic₄₃	1	1	yes	characteristic
471	C₂	#19144401	1	1	yes	characteristic
472	C₂	#19144409	1	1	yes	characteristic
473	C₂	#19144719	1	1	yes	characteristic
474	C₂	#19144760	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#477	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#477	D₄₃
hypocenter	C₄₃	#21616
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#477

Complements

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

N	H ≅ G/N	type
40. C₄₃×#477	C₄	semidirect
49. Q₈×Dic₄₃	Q₈	semidirect
162. Q₈×C₄₃	C₄×Q₈	semidirect
254. #477	Dic₄₃	semidirect
281. C₄₃	#21616	semidirect
400. Q₈	Q₈×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊Q₈×Dic₄₃	2
C₄×Q₈×Dic₄₃	2
#19135544	2
#19135359	2
#19135168	2
#19134865	2
#19134600	2
#19134494	2
#19134450	2
#19134427	2
C₂×C₄₃×#477	2
#21616	43