Subgroups — #25114705

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582937	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063257	C₂	1	1	yes	maximal, characteristic, complemented
3	#19137524	C₂	1	2	yes	maximal
4	#19135365	C₂	1	2	yes	maximal, complemented
5	#19134796	C₂	1	2	yes	maximal, complemented
6	#19134785	C₂	1	2	yes	maximal, complemented
7	#19134759	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134620	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134620	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13063257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063284	C₂²	1	2	yes	—
13	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	—
14	#14582937	—	2	4	no	—
15	C₂×#13063259	C₂²	1	2	yes	—
16	C₂×#13063259	C₂²	1	2	yes	—
17	C₂×#13063257	—	2	4	no	—
18	C₂×#13063257	C₂²	1	1	yes	characteristic
19	C₂×#13063257	C₂²	1	1	yes	characteristic
20	C₂×#13063257	C₂²	1	1	yes	characteristic
21	C₂×#13063257	C₂²	1	2	yes	—
22	C₂×#13063257	C₂²	1	1	yes	characteristic
23	#14582792	—	2	2	no	—
24	#14582785	—	2	2	no	—
25	#14582779	—	2	2	no	—
26	#14582765	C₂²	1	2	yes	—
27	#14582759	C₂²	1	2	yes	—
28	#14582759	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
30	C₂²⋊C₄×Dic₄₃	—	2	2	no	—
31	#14582662	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	2	yes	—
34	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
37	C₈×D₄×C₄₃	C₄	1	8	yes	complemented
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₃	—	2	2	no	—
43	#13063284	—	2	4	no	—
44	#13063284	—	4	2	no	—
45	C₂×C₄⋊Dic₄₃	—	2	4	no	—
46	C₂×C₄⋊Dic₄₃	—	2	2	no	—
47	C₂×C₄⋊Dic₄₃	—	4	2	no	—
48	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
52	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
54	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
55	C₂×C₄×Dic₄₃	—	2	2	no	—
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	#13063259	—	2	4	no	—
58	#13063259	—	4	2	no	—
59	#13063257	—	2	2	no	—
60	#13063257	—	2	2	no	—
61	#13063257	—	2	2	no	—
62	#13063257	—	2	4	no	—
63	#13063257	D₄	1	4	yes	complemented
64	C₄₃⋊#95	—	2	2	no	—
65	C₄₃⋊#95	—	2	2	no	—
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₃	—	2	2	no	—
73	C₂²×C₈×C₄₃	—	2	2	no	—
74	C₂²×C₈×C₄₃	—	2	2	no	—
75	C₂²×C₈×C₄₃	—	2	2	no	—
76	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
83	C₄×D₄×C₄₃	Q₈	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	complemented
89	C₂²⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
90	C₂²⋊C₈×C₄₃	C₂×C₄	1	4	yes	complemented
91	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₄₃	—	2	4	no	—
95	C₂×D₄×C₄₃	C₄⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂²×Dic₄₃	—	2	2	no	—
115	C₂²×Dic₄₃	—	2	2	no	—
116	C₂²×Dic₄₃	—	2	2	no	—
117	C₂²×Dic₄₃	—	4	4	no	—
118	C₂²×Dic₄₃	—	4	4	no	—
119	C₂²×Dic₄₃	—	8	2	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	2	8	no	—
127	C₂×C₈×C₄₃	—	2	8	no	—
128	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₄₃	#41	1	2	yes	—
134	C₄⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
135	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
136	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	4	yes	—
137	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
138	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
139	C₂²⋊Dic₄₃	—	4	4	no	—
140	C₂²⋊Dic₄₃	—	4	4	no	—
141	C₂²⋊Dic₄₃	—	8	2	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄⋊Dic₄₃	—	2	2	no	—
144	C₄⋊Dic₄₃	—	2	2	no	—
145	C₄⋊Dic₄₃	—	2	2	no	—
146	C₄⋊Dic₄₃	—	2	2	no	—
147	C₄⋊Dic₄₃	—	2	2	no	—
148	C₄⋊Dic₄₃	—	2	2	no	—
149	C₄⋊Dic₄₃	—	4	4	no	—
150	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
151	C₄×Dic₄₃	—	4	4	no	—
152	C₄×Dic₄₃	—	8	2	no	—
153	C₂³×C₄₃	—	2	1	no	—
154	C₂³×C₄₃	—	2	1	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂³×C₄₃	#135	1	4	yes	—
163	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	D₄×C₄₃	—	2	8	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
181	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
182	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
183	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×Dic₄₃	—	2	4	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	C₂×Dic₄₃	—	4	2	no	—
194	C₂×Dic₄₃	—	4	2	no	—
195	C₂×Dic₄₃	—	4	2	no	—
196	C₂×Dic₄₃	—	4	2	no	—
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	4	2	no	—
200	C₂×Dic₄₃	—	4	2	no	—
201	C₂×Dic₄₃	—	8	8	no	—
202	C₈×C₄₃	—	2	2	no	—
203	C₈×C₄₃	—	2	2	no	—
204	C₈×C₄₃	—	2	2	no	—
205	C₈×C₄₃	C₄×D₄	1	4	yes	—
206	#22654	—	43	1	no	maximal, Sylow
207	C₂²×C₄₃	—	2	4	no	—
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	—	2	4	no	—
211	C₂²×C₄₃	—	2	2	no	—
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	4	2	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	#427	1	4	yes	complemented
217	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
218	C₂²×C₄₃	D₄²	1	1	yes	characteristic
219	C₂²×C₄₃	#547	1	1	yes	characteristic
220	C₂²×C₄₃	C₂×#135	1	2	yes	—
221	C₂²×C₄₃	#577	1	2	yes	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	2	2	no	—
224	C₄×C₄₃	—	2	2	no	—
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₄₃	#520	1	1	yes	characteristic
228	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
229	C₄×C₄₃	#554	1	1	yes	characteristic
230	Dic₄₃	—	4	4	no	—
231	Dic₄₃	—	8	2	no	—
232	Dic₄₃	—	8	2	no	—
233	Dic₄₃	—	8	2	no	—
234	C₂×C₈×D₄	D₄₃	1	1	yes	characteristic
235	C₂×#427	—	43	1	no	—
236	C₂²×#106	—	43	1	no	—
237	#2352	—	43	2	no	—
238	#1949	—	43	2	no	—
239	#1854	—	43	2	no	—
240	#1852	—	43	2	no	—
241	#1846	—	43	1	no	—
242	#1807	—	43	1	no	—
243	#1807	—	43	1	no	—
244	C₄×#106	—	43	1	no	—
245	C₂×C₄₃	—	2	4	no	—
246	C₂×C₄₃	—	4	2	no	—
247	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₄₃	C₂×#427	1	1	yes	characteristic
249	C₂×C₄₃	#2912	1	1	yes	characteristic
250	C₂×C₄₃	#3282	1	2	yes	—
251	C₂×C₄₃	#3337	1	2	yes	—
252	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
253	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
255	C₂×#117	—	43	2	no	—
256	C₂²×C₄⋊C₄	—	43	2	no	—
257	C₈×D₄	Dic₄₃	1	8	yes	complemented
258	#427	—	86	4	no	—
259	C₂×#107	—	43	2	no	—
260	C₂×#107	—	43	2	no	—
261	C₂×#106	—	43	1	no	—
262	C₂×#106	—	43	1	no	—
263	C₂×#106	—	43	1	no	—
264	C₂×#106	—	43	1	no	—
265	C₂×#106	—	43	2	no	—
266	C₂×#106	—	86	4	no	—
267	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
270	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
271	#388	—	86	2	no	—
272	#387	—	86	2	no	—
273	#386	—	86	2	no	—
274	#382	—	43	2	no	—
275	#380	—	43	2	no	—
276	#380	—	43	2	no	—
277	C₄×C₄⋊C₄	—	43	2	no	—
278	C₄×C₂²⋊C₄	—	86	2	no	—
279	#340	—	43	2	no	—
280	#340	—	43	2	no	—
281	#340	—	43	2	no	—
282	C₄₃	#22654	1	1	yes	characteristic, complemented, Sylow
283	C₂²×D₄	D₁₇₂	1	1	yes	characteristic
284	C₂³×C₄	—	86	2	no	—
285	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
286	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
292	C₂²×C₈	C₂×Dic₄₃	1	4	yes	complemented
293	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
294	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
295	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
296	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
297	C₄×D₄	Dic₈₆	1	4	yes	—
298	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
299	#117	—	86	4	no	—
300	#117	—	172	2	no	—
301	C₂×C₄⋊C₄	—	43	2	no	—
302	C₂×C₄⋊C₄	—	43	2	no	—
303	C₂×C₄⋊C₄	—	43	2	no	—
304	C₂×C₄⋊C₄	—	43	2	no	—
305	C₂×C₄⋊C₄	—	86	4	no	—
306	C₂×C₄⋊C₄	—	86	2	no	—
307	C₂×C₄⋊C₄	—	172	2	no	—
308	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	86	2	no	—
310	C₂×C₂²⋊C₄	—	86	2	no	—
311	C₂×C₂²⋊C₄	—	86	2	no	—
312	C₂×C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
314	C₂×C₄²	—	86	2	no	—
315	C₂×C₄²	—	86	2	no	—
316	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
317	#107	—	86	4	no	—
318	#107	—	172	2	no	—
319	#106	—	43	4	no	—
320	#106	—	86	4	no	—
321	#106	—	86	2	no	—
322	#106	—	86	2	no	—
323	#106	—	86	2	no	—
324	C₄⋊C₈	C₂×Dic₄₃	1	4	yes	complemented
325	C₂²⋊C₈	C₂×Dic₄₃	1	4	yes	—
326	C₂²⋊C₈	C₂×Dic₄₃	1	4	yes	complemented
327	C₄×C₈	C₂×Dic₄₃	1	4	yes	complemented
328	#95	—	86	2	no	—
329	#95	—	86	2	no	—
330	#95	—	86	2	no	—
331	#95	—	86	2	no	—
332	#95	—	86	2	no	—
333	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
334	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	C₄⋊Dic₄₃	1	4	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	86	2	no	—
346	C₂²×C₄	—	86	2	no	—
347	C₂²×C₄	—	86	2	no	—
348	C₂²×C₄	—	86	2	no	—
349	C₂²×C₄	—	344	2	no	—
350	C₂²×C₄	—	172	4	no	—
351	C₂²×C₄	—	172	4	no	—
352	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
353	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
354	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
358	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
359	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
360	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	—	2	8	no	—
369	C₂×C₈	D₄×D₄₃	1	2	yes	—
370	C₂×C₈	#10621900	1	2	yes	—
371	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
372	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
373	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
374	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
375	C₄⋊C₄	—	43	4	no	—
376	C₄⋊C₄	—	86	2	no	—
377	C₄⋊C₄	—	86	2	no	—
378	C₄⋊C₄	—	86	2	no	—
379	C₄⋊C₄	—	86	2	no	—
380	C₄⋊C₄	—	86	2	no	—
381	C₄⋊C₄	—	86	2	no	—
382	C₄⋊C₄	—	86	2	no	—
383	C₄⋊C₄	—	172	4	no	—
384	C₄⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
385	C₂²⋊C₄	—	344	2	no	—
386	C₂²⋊C₄	—	172	4	no	—
387	C₂²⋊C₄	—	172	4	no	—
388	C₂²⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
389	C₂²⋊C₄	C₄⋊Dic₄₃	1	4	yes	—
390	C₄²	—	344	2	no	—
391	C₄²	—	172	4	no	—
392	C₄²	C₂×Dic₈₆	1	2	yes	—
393	C₄²	C₂²×Dic₄₃	1	2	yes	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
402	C₂³	C₂×C₄⋊Dic₄₃	1	2	yes	—
403	C₂³	#13063347	1	4	yes	—
404	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
405	D₄	—	2	8	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	86	4	no	—
421	C₂×C₄	—	344	8	no	—
422	C₂×C₄	—	172	2	no	—
423	C₂×C₄	—	172	2	no	—
424	C₂×C₄	—	172	2	no	—
425	C₂×C₄	—	172	2	no	—
426	C₂×C₄	—	172	2	no	—
427	C₂×C₄	—	172	2	no	—
428	C₂×C₄	—	172	2	no	—
429	C₂×C₄	—	172	2	no	—
430	C₂×C₄	—	172	2	no	—
431	C₂×C₄	—	172	2	no	—
432	C₂×C₄	—	172	2	no	—
433	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
434	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
435	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
436	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
437	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
438	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
440	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
441	C₂×C₄	#13063371	1	1	yes	characteristic
442	C₂×C₄	#13063372	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	D₄×Dic₄₃	1	4	yes	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	#14582937	1	4	yes	complemented
457	C₂²	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
458	C₂²	D₄×D₁₇₂	1	1	yes	characteristic
459	C₂²	#14583553	1	1	yes	characteristic
460	C₂²	C₂×#13063347	1	2	yes	—
461	C₂²	#14583711	1	2	yes	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	344	2	no	—
467	C₄	—	344	2	no	—
468	C₄	—	344	2	no	—
469	C₄	—	172	4	no	—
470	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
471	C₄	#14583382	1	1	yes	characteristic
472	C₄	D₄×Dic₈₆	1	1	yes	characteristic
473	C₄	#14583606	1	1	yes	characteristic
474	C₂	—	2	4	no	—
475	C₂	—	4	2	no	—
476	C₂	D₄×C₄⋊Dic₄₃	1	1	yes	characteristic
477	C₂	C₂×#14582937	1	1	yes	characteristic
478	C₂	#19143190	1	1	yes	characteristic
479	C₂	#19146307	1	2	yes	—
480	C₂	#19146976	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₈×D₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₃
hypocenter	C₄₃	#22654
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#14582937	C₂	semidirect
2. C₂²×#13063257	C₂	semidirect
4. #19135365	C₂	semidirect
5. #19134796	C₂	semidirect
6. #19134785	C₂	semidirect
7. #19134759	C₂	semidirect
8. #19134620	C₂	semidirect
9. #19134620	C₂	semidirect
10. C₄×#13063257	C₂	semidirect
37. C₈×D₄×C₄₃	C₄	semidirect
63. #13063257	D₄	semidirect
77. C₂²×C₈×C₄₃	C₂×C₄	semidirect
88. C₄⋊C₈×C₄₃	C₂×C₄	semidirect
90. C₂²⋊C₈×C₄₃	C₂×C₄	semidirect
91. C₄×C₈×C₄₃	C₂×C₄	semidirect
216. C₂²×C₄₃	#427	semidirect
257. C₈×D₄	Dic₄₃	semidirect
282. C₄₃	#22654	semidirect
292. C₂²×C₈	C₂×Dic₄₃	semidirect
324. C₄⋊C₈	C₂×Dic₄₃	semidirect
326. C₂²⋊C₈	C₂×Dic₄₃	semidirect
327. C₄×C₈	C₂×Dic₄₃	semidirect
456. C₂²	#14582937	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582937	2
C₂²×#13063257	2
#19137524	2
#19135365	2
#19134796	2
#19134785	2
#19134759	2
#19134620	2
C₄×#13063257	2
C₂×C₈×D₄×C₄₃	2
#22654	43