Subgroups — #25115803

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10621885	C₂	1	1	yes	maximal, characteristic
2	#19137550	C₂	1	1	yes	maximal, characteristic
3	#19135284	C₂	1	2	yes	maximal
4	#19135163	C₂	1	2	yes	maximal
5	#19134936	C₂	1	2	yes	maximal
6	#19134722	C₂	1	1	yes	maximal, characteristic
7	#19134600	C₂	1	1	yes	maximal, characteristic
8	#19134597	C₂	1	1	yes	maximal, characteristic
9	#19134464	C₂	1	1	yes	maximal, characteristic
10	#19134425	C₂	1	2	yes	maximal
11	Q₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10621885	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	C₄×#10621885	C₄	1	8	yes	complemented
15	C₂×#13063258	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13063249	C₂²	1	2	yes	—
18	C₂×#13063249	C₂²	1	1	yes	characteristic
19	C₂×#13063248	C₂²	1	2	yes	—
20	C₂×#13063248	C₂²	1	1	yes	characteristic
21	C₂×#13063236	C₂²	1	2	yes	—
22	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	#14582805	C₂²	1	2	yes	—
24	#14582786	—	2	2	no	—
25	#14582769	C₂²	1	1	yes	characteristic
26	#14582764	—	2	1	no	—
27	C₄⋊C₄×Dic₄₃	—	2	1	no	—
28	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
29	#14582661	C₂²	1	2	yes	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	2	yes	—
32	#14582661	C₂²	1	2	yes	—
33	#14582654	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#389	—	2	2	no	—
37	C₄₃×#389	C₂²	1	2	yes	—
38	C₄₃×#384	—	2	1	no	—
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
43	C₂×#10621885	—	2	2	no	—
44	C₂×#10621885	—	2	2	no	—
45	C₂×#10621885	C₂×C₄	1	4	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
49	C₄×Dic₈₆	—	2	2	no	—
50	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄⋊Dic₄₃	—	2	1	no	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
55	C₂×Dic₄₃⋊C₄	—	2	1	no	—
56	C₂×C₄×Dic₄₃	—	2	1	no	—
57	C₂×C₄×Dic₄₃	—	2	2	no	—
58	#13063258	C₂×C₄	1	4	yes	—
59	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
60	#13063249	—	2	4	no	—
61	#13063249	C₂×C₄	1	4	yes	—
62	#13063248	—	4	2	no	—
63	#13063248	C₂×C₄	1	4	yes	—
64	#13063236	—	4	2	no	—
65	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
70	C₄×Q₈×C₄₃	—	2	2	no	—
71	C₄×Q₈×C₄₃	—	2	4	no	—
72	C₄×Q₈×C₄₃	—	4	2	no	—
73	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	—	2	1	no	—
84	C₂×C₄²×C₄₃	—	2	2	no	—
85	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
87	#95×C₄₃	—	2	2	no	—
88	#95×C₄₃	D₄	1	2	yes	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×Q₈×C₄₃	—	2	1	no	—
91	C₂×Q₈×C₄₃	—	2	1	no	—
92	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
93	C₂×Q₈×C₄₃	#41	1	2	yes	—
94	C₂×Q₈×C₄₃	#41	1	2	yes	—
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₃	—	2	1	no	—
104	C₂²×Dic₄₃	—	2	1	no	—
105	C₂²×Dic₄₃	—	2	2	no	—
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	—	2	1	no	—
108	C₂×Dic₈₆	—	2	1	no	—
109	C₂×Dic₈₆	—	2	1	no	—
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
112	C₄⋊C₄×C₄₃	—	2	4	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₄⋊C₄×C₄₃	—	2	1	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	4	4	no	—
119	C₄⋊C₄×C₄₃	—	4	2	no	—
120	C₄⋊C₄×C₄₃	—	8	1	no	—
121	C₄⋊C₄×C₄₃	—	8	2	no	—
122	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₃	—	2	4	no	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	4	4	no	—
127	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₃	#41	1	2	yes	—
129	#10621885	—	2	8	no	—
130	C₄⋊Dic₄₃	—	2	1	no	—
131	C₄⋊Dic₄₃	—	2	2	no	—
132	C₄⋊Dic₄₃	—	2	2	no	—
133	C₄⋊Dic₄₃	—	4	2	no	—
134	C₄⋊Dic₄₃	—	8	1	no	—
135	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
136	Dic₄₃⋊C₄	—	2	4	no	—
137	C₄×Dic₄₃	—	2	4	no	—
138	C₄×Dic₄₃	—	8	2	no	—
139	C₂×C₄₃⋊C₈	—	2	1	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	2	2	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
148	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₄₃	—	2	2	no	—
150	Q₈×C₄₃	—	2	2	no	—
151	Q₈×C₄₃	—	2	2	no	—
152	Q₈×C₄₃	#117	1	4	yes	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₄₃	#137	1	2	yes	—
173	C₂×C₄×C₄₃	#137	1	2	yes	—
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	C₂×Dic₄₃	—	4	1	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	C₂×Dic₄₃	—	4	2	no	—
188	C₂×Dic₄₃	—	4	2	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	2	2	no	—
191	Dic₈₆	—	4	1	no	—
192	Dic₈₆	—	4	1	no	—
193	C₄₃⋊C₈	—	2	2	no	—
194	C₄₃⋊C₈	—	2	2	no	—
195	C₄₃⋊C₈	—	4	2	no	—
196	#22763	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₃	#546	1	1	yes	characteristic
199	C₂²×C₄₃	#548	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
202	C₂²×C₄₃	#576	1	1	yes	characteristic
203	C₂²×C₄₃	#578	1	1	yes	characteristic
204	C₄×C₄₃	—	2	4	no	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	4	2	no	—
207	C₄×C₄₃	—	4	2	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	#441	1	4	yes	—
211	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
212	C₄×C₄₃	#520	1	1	yes	characteristic
213	C₄×C₄₃	#552	1	1	yes	characteristic
214	C₄×C₄₃	#553	1	1	yes	characteristic
215	Dic₄₃	—	4	2	no	—
216	Dic₄₃	—	4	2	no	—
217	Dic₄₃	—	8	2	no	—
218	C₂×C₄×Q₁₆	—	43	1	no	—
219	#2355	—	43	1	no	—
220	Q₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic
221	#1935	—	43	2	no	—
222	#1918	—	43	2	no	—
223	#1878	—	43	2	no	—
224	#1834	—	43	1	no	—
225	#1803	—	43	1	no	—
226	#1803	—	43	1	no	—
227	#1770	—	43	1	no	—
228	#1763	—	43	2	no	—
229	C₂×C₄₃	#2352	1	1	yes	characteristic
230	C₂×C₄₃	C₂×#441	1	1	yes	characteristic
231	C₂×C₄₃	#2951	1	1	yes	characteristic
232	C₂×C₄₃	#3328	1	1	yes	characteristic
233	C₂×C₄₃	#3333	1	1	yes	characteristic
234	C₂×C₄₃	#3374	1	1	yes	characteristic
235	C₂×C₄₃	#3375	1	1	yes	characteristic
236	C₂²×Q₁₆	—	43	1	no	—
237	C₂×C₄×Q₈	—	43	1	no	—
238	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
239	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
240	C₄×Q₁₆	—	43	8	no	—
241	C₂×#107	—	43	1	no	—
242	C₂×C₄⋊C₈	—	43	1	no	—
243	C₂×#103	—	43	1	no	—
244	C₂×#103	—	43	1	no	—
245	C₂×#103	—	43	2	no	—
246	C₂×#103	—	43	2	no	—
247	C₂×#97	—	43	2	no	—
248	C₂×C₄×C₈	—	43	1	no	—
249	#391	—	43	2	no	—
250	#389	—	2	2	no	—
251	#389	C₂×D₄₃	1	2	yes	—
252	#387	—	86	2	no	—
253	#384	—	2	1	no	—
254	#384	—	43	1	no	—
255	#384	C₂×D₄₃	1	1	yes	characteristic
256	#382	—	86	1	no	—
257	C₄×C₄⋊C₄	—	2	1	no	—
258	C₄×C₄⋊C₄	—	43	2	no	—
259	C₄×C₄⋊C₄	—	86	1	no	—
260	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
261	#340	—	43	2	no	—
262	#340	—	43	2	no	—
263	#340	—	43	2	no	—
264	#340	—	43	2	no	—
265	#336	—	43	2	no	—
266	C₄₃	#22763	1	1	yes	characteristic, complemented, Sylow
267	C₂²×Q₈	—	43	1	no	—
268	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
269	C₂×Q₁₆	—	43	4	no	—
270	C₂×Q₁₆	—	86	2	no	—
271	C₂×Q₁₆	—	86	2	no	—
272	C₂²×C₈	—	43	1	no	—
273	C₂²×C₈	—	43	1	no	—
274	C₂²×C₈	—	43	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	—	4	2	no	—
278	C₄×Q₈	—	43	4	no	—
279	C₄×Q₈	—	86	2	no	—
280	C₄×Q₈	C₄×D₄₃	1	4	yes	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	43	1	no	—
287	C₂×C₄⋊C₄	—	43	2	no	—
288	C₂×C₄⋊C₄	—	86	1	no	—
289	C₂×C₄⋊C₄	—	86	1	no	—
290	C₂×C₄⋊C₄	—	86	1	no	—
291	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	86	1	no	—
298	C₂×C₄²	—	86	2	no	—
299	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
300	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
301	#107	—	43	4	no	—
302	C₄⋊C₈	—	86	2	no	—
303	#103	—	43	4	no	—
304	#103	—	43	4	no	—
305	#103	—	86	4	no	—
306	#103	—	172	2	no	—
307	#97	—	172	2	no	—
308	C₄×C₈	—	43	4	no	—
309	#95	—	2	2	no	—
310	#95	—	86	2	no	—
311	#95	—	86	2	no	—
312	#95	—	86	2	no	—
313	#95	C₂²⋊D₄₃	1	2	yes	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	43	2	no	—
318	C₂×Q₈	—	86	1	no	—
319	C₂×Q₈	—	86	1	no	—
320	C₂×Q₈	—	86	1	no	—
321	C₂×Q₈	—	86	1	no	—
322	C₂×Q₈	—	86	1	no	—
323	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
324	C₂×Q₈	#10621900	1	2	yes	—
325	C₂×Q₈	#10621902	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	86	1	no	—
330	C₂²×C₄	—	86	1	no	—
331	C₂²×C₄	—	86	2	no	—
332	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
333	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
334	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
337	Q₁₆	—	86	8	no	—
338	C₂×C₈	—	43	2	no	—
339	C₂×C₈	—	43	2	no	—
340	C₂×C₈	—	86	1	no	—
341	C₂×C₈	—	86	1	no	—
342	C₂×C₈	—	86	1	no	—
343	C₂×C₈	—	86	1	no	—
344	C₂×C₈	—	86	2	no	—
345	C₂×C₈	—	86	2	no	—
346	C₂×C₈	—	86	2	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	8	1	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	—	43	2	no	—
358	C₄⋊C₄	—	86	4	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₄⋊C₄	—	86	2	no	—
361	C₄⋊C₄	—	86	2	no	—
362	C₄⋊C₄	—	344	1	no	—
363	C₄⋊C₄	—	172	2	no	—
364	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	4	no	—
369	C₄²	—	86	4	no	—
370	C₄²	—	344	2	no	—
371	C₄²	C₂×C₄×D₄₃	1	2	yes	—
372	C₄²	#10621898	1	2	yes	—
373	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	86	2	no	—
378	Q₈	—	86	2	no	—
379	Q₈	—	172	1	no	—
380	Q₈	—	172	1	no	—
381	Q₈	#13063283	1	4	yes	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	86	2	no	—
400	C₂×C₄	—	86	2	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	—	172	2	no	—
403	C₂×C₄	—	172	2	no	—
404	C₂×C₄	—	172	1	no	—
405	C₂×C₄	—	172	1	no	—
406	C₂×C₄	—	172	1	no	—
407	C₂×C₄	—	172	1	no	—
408	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
409	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
410	C₂×C₄	#13063355	1	2	yes	—
411	C₂×C₄	#13063356	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
413	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
414	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
415	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
416	C₂×C₄	#13063370	1	1	yes	characteristic
417	C₂×C₄	#13063373	1	1	yes	characteristic
418	C₈	—	86	2	no	—
419	C₈	—	86	2	no	—
420	C₈	—	172	2	no	—
421	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
422	C₂²	#14583543	1	1	yes	characteristic
423	C₂²	#14583560	1	1	yes	characteristic
424	C₂²	C₂×#13063355	1	1	yes	characteristic
425	C₂²	C₂×#13063356	1	1	yes	characteristic
426	C₂²	#14583702	1	1	yes	characteristic
427	C₂²	#14583714	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	2	4	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	2	no	—
434	C₄	—	344	2	no	—
435	C₄	—	172	2	no	—
436	C₄	—	172	2	no	—
437	C₄	#14583004	1	4	yes	—
438	C₄	C₂×#13063283	1	1	yes	characteristic
439	C₄	#14583380	1	1	yes	characteristic
440	C₄	#14583584	1	1	yes	characteristic
441	C₄	#14583597	1	1	yes	characteristic
442	C₂	#19137520	1	1	yes	characteristic
443	C₂	C₂×#14583004	1	1	yes	characteristic
444	C₂	#19143468	1	1	yes	characteristic
445	C₂	#19146878	1	1	yes	characteristic
446	C₂	#19146933	1	1	yes	characteristic
447	C₂	#19147398	1	1	yes	characteristic
448	C₂	#19147409	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	Q₈×C₄⋊C₄×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	Q₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#22763
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ Q₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
14. C₄×#10621885	C₄	semidirect
266. C₄₃	#22763	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621885	2
#19137550	2
#19135284	2
#19135163	2
#19134936	2
#19134722	2
#19134600	2
#19134597	2
#19134464	2
#19134425	2
Q₈×C₄⋊C₄×C₄₃	2
#22763	43