Subgroups — #25972563

Order 11008.

2834 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583700	C₂	1	2	yes	maximal, complemented
2	#19148359	C₂	1	2	yes	maximal, complemented
3	#19146316	C₂	1	2	yes	maximal, complemented
4	#19146281	C₂	1	4	yes	maximal, complemented
5	D₈×D₁₇₂	C₂	1	2	yes	maximal, complemented
6	#19146205	C₂	1	4	yes	maximal, complemented
7	#19146196	C₂	1	4	yes	maximal, complemented
8	#19145023	C₂	1	1	yes	maximal, characteristic, complemented
9	#19144267	C₂	1	2	yes	maximal, complemented
10	#19144059	C₂	1	2	yes	maximal, complemented
11	#19143904	C₂	1	4	yes	maximal, complemented
12	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13063370	C₂²	1	4	yes	complemented
15	#14583700	—	2	16	no	—
16	C₂×#13063351	C₂²	1	4	yes	complemented
17	C₂×#13063349	C₂²	1	8	yes	complemented
18	C₂×#13063347	C₂²	1	2	yes	complemented
19	C₂×#13063347	C₂²	1	2	yes	complemented
20	C₂×#13063344	C₂²	1	4	yes	complemented
21	C₂×D₈×D₄₃	C₂²	1	4	yes	complemented
22	C₂×#13063331	C₂²	1	2	yes	complemented
23	#14583553	—	2	2	no	—
24	#14583553	C₂²	1	4	yes	complemented
25	#14583544	—	2	4	no	—
26	#14583544	C₂²	1	8	yes	complemented
27	D₄×D₁₇₂	—	2	2	no	—
28	D₄×D₁₇₂	C₂²	1	4	yes	complemented
29	#14583480	C₂²	1	4	yes	complemented
30	#14583461	—	2	4	no	—
31	#14583449	C₂²	1	1	yes	characteristic
32	#14583449	C₂²	1	2	yes	complemented
33	C₂×#13063299	—	2	4	no	—
34	#14583283	C₂²	1	2	yes	complemented
35	#14583283	C₂²	1	2	yes	complemented
36	#14583279	C₂²	1	1	yes	characteristic, complemented
37	#14583276	C₂²	1	1	yes	characteristic, complemented
38	#14583272	C₂²	1	2	yes	complemented
39	#14583146	C₂²	1	8	yes	complemented
40	#14583141	C₂²	1	4	yes	complemented
41	#14583136	C₂²	1	4	yes	complemented
42	#14583114	C₂²	1	8	yes	complemented
43	#14583104	C₂²	1	4	yes	complemented
44	#14583094	C₂²	1	4	yes	complemented
45	#14583062	C₂²	1	8	yes	complemented
46	#14583051	C₂²	1	8	yes	complemented
47	#14583045	C₂²	1	8	yes	complemented
48	#14583034	C₂²	1	8	yes	complemented
49	#14582978	C₂²	1	2	yes	complemented
50	#14582978	C₂²	1	2	yes	complemented
51	C₈×D₁₇₂	C₂²	1	2	yes	complemented
52	C₈×D₁₇₂	C₂²	1	2	yes	complemented
53	#14582923	C₂²	1	1	yes	characteristic, complemented
54	#14582898	C₂²	1	4	yes	complemented
55	#14582865	C₂²	1	2	yes	complemented
56	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
58	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
59	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
60	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
61	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
62	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
64	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
65	#13063370	—	2	16	no	—
66	#13063370	—	4	8	no	—
67	C₂×#10621898	C₂³	1	2	yes	—
68	C₂×#10621898	C₂³	1	4	yes	—
69	C₂×#10621900	—	2	4	no	—
70	C₂×#10621900	C₂³	1	8	yes	—
71	C₂²×D₁₇₂	—	2	4	no	—
72	C₂²×C₂²⋊D₄₃	—	2	8	no	—
73	C₂×D₄×D₄₃	—	2	4	no	—
74	C₂×D₄×D₄₃	C₂³	1	8	yes	—
75	#13063351	—	2	16	no	—
76	#13063349	—	2	32	no	—
77	#13063347	—	2	8	no	—
78	#13063347	—	4	4	no	—
79	#13063344	—	2	16	no	—
80	C₂×Dic₁₇₂	C₂³	1	2	yes	—
81	C₂×Dic₁₇₂	C₂³	1	2	yes	—
82	C₂×#10621873	C₂³	1	4	yes	—
83	C₂×#10621873	C₂³	1	4	yes	—
84	C₂×#10621883	C₂³	1	8	yes	—
85	C₂×D₃₄₄	C₂³	1	2	yes	—
86	C₂×D₃₄₄	C₂³	1	2	yes	—
87	C₂×#10621882	C₂³	1	8	yes	—
88	D₈×D₄₃	—	2	16	no	—
89	#13063331	—	2	8	no	—
90	C₂×#10621877	C₂³	1	2	yes	—
91	C₂×#10621872	C₂³	1	4	yes	—
92	C₂×C₈×D₄₃	C₂³	1	4	yes	—
93	#13063325	D₄	1	1	yes	characteristic
94	#13063325	C₂³	1	2	yes	—
95	#13063322	D₄	1	1	yes	characteristic
96	#13063322	C₂³	1	2	yes	—
97	#13063313	D₄	1	2	yes	—
98	#13063313	C₂³	1	4	yes	—
99	#13063309	—	2	8	no	—
100	#13063309	—	2	8	no	—
101	#13063305	—	2	4	no	—
102	#13063305	C₂³	1	8	yes	—
103	#13063300	—	2	4	no	—
104	#13063300	C₂³	1	8	yes	—
105	#13063299	—	2	2	no	—
106	#13063299	—	2	2	no	—
107	#13063299	—	2	8	no	—
108	#13063299	—	2	4	no	—
109	#13063299	—	2	8	no	—
110	#13063299	—	2	4	no	—
111	#13063299	D₄	1	2	yes	—
112	#13063299	D₄	1	2	yes	—
113	#13063295	—	2	8	no	—
114	#13063295	—	2	8	no	—
115	C₄×D₁₇₂	—	2	2	no	—
116	C₄×D₁₇₂	—	2	2	no	—
117	C₄×D₁₇₂	C₂³	1	2	yes	—
118	C₄×D₁₇₂	C₂³	1	2	yes	—
119	C₂×C₄⋊Dic₄₃	—	2	4	no	—
120	C₂×(C₂×D₄₃)⋊C₄	—	2	8	no	—
121	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
122	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
123	#13063248	C₂³	1	8	yes	—
124	#13063245	C₂³	1	8	yes	—
125	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
126	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
127	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₄₃	—	2	2	no	—
129	C₂×D₈×C₄₃	D₄	1	8	yes	complemented
130	C₂×D₈×C₄₃	C₂³	1	2	yes	—
131	C₂×D₈×C₄₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₄₃	—	2	2	no	—
135	C₄×D₄×C₄₃	—	2	2	no	—
136	C₄×D₄×C₄₃	C₂³	1	4	yes	—
137	C₄×D₄×C₄₃	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
140	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
141	#107×C₄₃	C₂³	1	2	yes	—
142	#107×C₄₃	C₂³	1	2	yes	—
143	#102×C₄₃	C₂³	1	4	yes	—
144	#102×C₄₃	C₂³	1	4	yes	—
145	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
149	C₂⁴×C₄₃	—	2	2	no	—
150	C₂³×D₄₃	—	2	8	no	—
151	C₂×D₄×C₄₃	—	2	2	no	—
152	C₂×D₄×C₄₃	—	2	4	no	—
153	C₂×D₄×C₄₃	C₂×D₄	1	8	yes	complemented
154	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₄₃	—	2	4	no	—
156	C₂²×C₄×C₄₃	—	2	4	no	—
157	C₂²×C₄×C₄₃	—	2	2	no	—
158	C₂²×C₄×C₄₃	—	8	4	no	—
159	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₂²⋊D₄₃	—	2	8	no	—
163	C₂×C₂²⋊D₄₃	—	2	4	no	—
164	C₂×C₂²⋊D₄₃	—	2	8	no	—
165	C₂×C₂²⋊D₄₃	—	4	32	no	—
166	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
167	C₂²×Dic₄₃	—	2	8	no	—
168	#10621900	—	2	16	no	—
169	#10621900	—	4	8	no	—
170	#10621900	—	4	16	no	—
171	D₄×D₄₃	—	2	16	no	—
172	D₄×D₄₃	—	4	8	no	—
173	D₄×D₄₃	—	4	16	no	—
174	#10621898	—	2	4	no	—
175	#10621898	—	2	4	no	—
176	#10621898	—	2	8	no	—
177	#10621898	—	2	8	no	—
178	C₂×D₁₇₂	—	2	2	no	—
179	C₂×D₁₇₂	—	2	2	no	—
180	C₂×D₁₇₂	—	2	8	no	—
181	C₂×D₁₇₂	—	8	8	no	—
182	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
183	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
184	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
185	C₂×D₁₇₂	C₂⁴	1	4	yes	—
186	C₂×C₄×D₄₃	—	2	4	no	—
187	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
188	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
189	C₂×Dic₈₆	C₂⁴	1	4	yes	—
190	D₈×C₄₃	C₂×D₄	1	8	yes	complemented
191	D₈×C₄₃	C₂×D₄	1	8	yes	complemented
192	C₂×C₈×C₄₃	—	2	2	no	—
193	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	complemented
194	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
196	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
197	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
198	C₄⋊C₄×C₄₃	—	2	2	no	—
199	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
200	C₂²⋊C₄×C₄₃	—	2	4	no	—
201	C₂²⋊C₄×C₄₃	—	2	4	no	—
202	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
205	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
206	#10621883	—	2	16	no	—
207	#10621882	—	2	16	no	—
208	(C₂×D₄₃)⋊C₄	—	2	4	no	—
209	(C₂×D₄₃)⋊C₄	—	2	4	no	—
210	(C₂×D₄₃)⋊C₄	—	2	8	no	—
211	(C₂×D₄₃)⋊C₄	—	2	8	no	—
212	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
213	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
214	C₄⋊Dic₄₃	—	2	2	no	—
215	C₄⋊Dic₄₃	—	2	2	no	—
216	C₄⋊Dic₄₃	—	2	8	no	—
217	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
218	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
219	#10621877	—	2	4	no	—
220	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
221	Dic₁₇₂	—	2	4	no	—
222	Dic₁₇₂	—	4	2	no	—
223	D₃₄₄	—	2	4	no	—
224	D₃₄₄	—	4	2	no	—
225	#10621873	—	2	8	no	—
226	#10621873	—	4	4	no	—
227	#10621872	—	2	8	no	—
228	C₈×D₄₃	—	2	8	no	—
229	C₂³×C₄₃	—	2	4	no	—
230	C₂³×C₄₃	—	2	8	no	—
231	C₂³×C₄₃	—	8	2	no	—
232	C₂³×C₄₃	—	8	2	no	—
233	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
234	C₂²×D₄₃	—	2	4	no	—
235	C₂²×D₄₃	—	4	16	no	—
236	C₂²×D₄₃	—	8	8	no	—
237	C₂²×D₄₃	—	8	8	no	—
238	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
239	D₄×C₄₃	—	2	8	no	—
240	D₄×C₄₃	—	2	4	no	—
241	D₄×C₄₃	C₂²×D₄	1	8	yes	—
242	C₂×C₄×C₄₃	—	2	2	no	—
243	C₂×C₄×C₄₃	—	2	4	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	8	no	—
246	C₂×C₄×C₄₃	—	8	4	no	—
247	C₂×C₄×C₄₃	—	8	2	no	—
248	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
255	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
256	C₂²⋊D₄₃	—	2	8	no	—
257	C₂²⋊D₄₃	—	4	16	no	—
258	C₂²⋊D₄₃	—	4	16	no	—
259	C₂²⋊D₄₃	—	4	8	no	—
260	C₂×Dic₄₃	—	2	4	no	—
261	C₂×Dic₄₃	—	4	16	no	—
262	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
263	D₁₇₂	—	2	4	no	—
264	D₁₇₂	—	2	4	no	—
265	D₁₇₂	—	2	4	no	—
266	D₁₇₂	—	2	4	no	—
267	D₁₇₂	—	4	2	no	—
268	D₁₇₂	—	4	4	no	—
269	D₁₇₂	—	8	2	no	—
270	D₁₇₂	—	8	8	no	—
271	C₄×D₄₃	—	2	4	no	—
272	C₄×D₄₃	—	2	4	no	—
273	C₄×D₄₃	—	4	8	no	—
274	Dic₈₆	—	2	4	no	—
275	Dic₈₆	—	2	4	no	—
276	Dic₈₆	—	2	4	no	—
277	C₈×C₄₃	—	2	1	no	—
278	C₈×C₄₃	—	2	1	no	—
279	C₈×C₄₃	C₂²×D₄	1	2	yes	—
280	C₈×C₄₃	C₂²×D₄	1	2	yes	—
281	C₄₃⋊C₈	—	2	4	no	—
282	#61084	—	43	1	no	maximal, Sylow
283	C₂²×C₄₃	—	2	1	no	—
284	C₂²×C₄₃	—	2	1	no	—
285	C₂²×C₄₃	—	2	8	no	—
286	C₂²×C₄₃	—	4	4	no	—
287	C₂²×C₄₃	—	4	4	no	—
288	C₂²×C₄₃	—	8	8	no	—
289	C₂²×C₄₃	D₄²	1	2	yes	—
290	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
291	C₂×D₄₃	—	2	4	no	—
292	C₂×D₄₃	—	2	4	no	—
293	C₂×D₄₃	—	2	4	no	—
294	C₂×D₄₃	—	4	4	no	—
295	C₂×D₄₃	—	4	4	no	—
296	C₂×D₄₃	—	4	4	no	—
297	C₂×D₄₃	—	16	16	no	—
298	C₄×C₄₃	—	2	1	no	—
299	C₄×C₄₃	—	2	1	no	—
300	C₄×C₄₃	—	2	1	no	—
301	C₄×C₄₃	—	4	4	no	—
302	C₄×C₄₃	D₄²	1	2	yes	—
303	C₄×C₄₃	#576	1	2	yes	complemented
304	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
305	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
306	Dic₄₃	—	2	4	no	—
307	Dic₄₃	—	4	4	no	—
308	C₂×#576	—	43	2	no	—
309	#3496	—	43	2	no	—
310	#3283	—	43	2	no	—
311	#3280	—	43	4	no	—
312	D₄×D₈	—	43	2	no	—
313	#3273	—	43	4	no	—
314	#3272	—	43	4	no	—
315	#3147	—	43	1	no	—
316	#3061	—	43	2	no	—
317	#3036	—	43	2	no	—
318	#3012	—	43	4	no	—
319	C₂×C₄×D₈	D₄₃	1	1	yes	characteristic, complemented
320	#2931	—	43	1	no	—
321	C₂×C₄₃	—	2	2	no	—
322	C₂×C₄₃	—	4	8	no	—
323	C₂×C₄₃	C₂×D₄²	1	1	yes	characteristic
324	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
325	C₂×C₄₃	#3584	1	1	yes	characteristic
326	D₄₃	—	4	4	no	—
327	D₄₃	—	8	4	no	—
328	C₂×H(5,𝔽₂)	—	43	4	no	—
329	#576	—	86	16	no	—
330	C₂×AGL(1,ℤ/8)	—	43	4	no	—
331	C₂×AGL(1,ℤ/8)	—	43	8	no	—
332	C₂×#135	—	43	4	no	—
333	C₂×#135	—	43	2	no	—
334	C₂×#135	—	43	2	no	—
335	C₂²×D₈	—	43	4	no	—
336	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
337	C₂×#131	—	43	2	no	—
338	#547	—	43	4	no	—
339	#547	—	86	2	no	—
340	#546	—	43	8	no	—
341	#546	—	86	4	no	—
342	D₄²	—	43	4	no	—
343	D₄²	—	86	2	no	—
344	#537	—	43	4	no	—
345	#534	—	86	4	no	—
346	#532	—	43	1	no	—
347	#532	—	43	2	no	—
348	C₂×#121	—	86	4	no	—
349	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
350	#495	—	43	2	no	—
351	#495	—	43	2	no	—
352	#494	—	43	1	no	—
353	#493	—	43	1	no	—
354	#492	—	43	2	no	—
355	#468	—	43	8	no	—
356	#467	—	43	4	no	—
357	#466	—	43	4	no	—
358	#463	—	43	8	no	—
359	#461	—	43	4	no	—
360	#459	—	43	4	no	—
361	#452	—	43	8	no	—
362	#450	—	43	8	no	—
363	#449	—	43	8	no	—
364	#447	—	43	8	no	—
365	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
366	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
367	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
368	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
369	#436	—	43	2	no	—
370	#436	—	43	2	no	—
371	C₈×D₄	—	43	2	no	—
372	C₈×D₄	—	43	2	no	—
373	C₂×#107	C₂×D₄₃	1	1	yes	characteristic, complemented
374	#423	—	43	1	no	—
375	#417	—	43	4	no	—
376	C₂×#102	C₂×D₄₃	1	2	yes	complemented
377	#408	—	43	2	no	—
378	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
379	C₄₃	#61084	1	1	yes	characteristic, complemented, Sylow
380	H(5,𝔽₂)	—	86	16	no	—
381	H(5,𝔽₂)	—	172	8	no	—
382	C₂×#41	—	43	2	no	—
383	C₂×#41	—	43	8	no	—
384	C₂×#41	—	43	4	no	—
385	C₂×#41	—	86	4	no	—
386	C₂²×D₄	—	43	8	no	—
387	C₂²×D₄	—	86	4	no	—
388	C₂²×D₄	—	86	4	no	—
389	C₂²×D₄	—	86	8	no	—
390	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
391	C₂³×C₄	—	2	2	no	—
392	AGL(1,ℤ/8)	—	86	16	no	—
393	AGL(1,ℤ/8)	—	86	32	no	—
394	#135	—	86	16	no	—
395	#135	—	86	8	no	—
396	#135	—	172	4	no	—
397	C₂×Q₁₆	—	43	2	no	—
398	C₂×Q₁₆	—	43	2	no	—
399	C₂×SD₁₆	—	43	8	no	—
400	C₂×SD₁₆	—	43	4	no	—
401	C₂×SD₁₆	—	43	4	no	—
402	C₂×D₈	—	43	8	no	—
403	C₂×D₈	—	43	2	no	—
404	C₂×D₈	—	43	2	no	—
405	C₂×D₈	—	86	16	no	—
406	C₂×D₈	D₁₇₂	1	8	yes	complemented
407	C₂×D₈	C₂²×D₄₃	1	2	yes	—
408	C₂×D₈	C₂²×D₄₃	1	2	yes	—
409	#131	—	86	8	no	—
410	C₂×M₁₆	—	43	2	no	—
411	C₂×M₁₆	—	43	4	no	—
412	C₂²×C₈	—	43	4	no	—
413	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
414	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
415	C₄⋊Q₈	—	43	1	no	—
416	C₄⋊Q₈	—	43	2	no	—
417	#127	—	43	1	no	—
418	#127	—	43	2	no	—
419	#124	—	43	2	no	—
420	#124	—	43	4	no	—
421	#123	—	86	8	no	—
422	#123	—	86	8	no	—
423	C₂²⋊Q₈	—	43	8	no	—
424	C₂²⋊Q₈	—	86	4	no	—
425	#121	—	43	2	no	—
426	#121	—	43	2	no	—
427	#121	—	43	8	no	—
428	#121	—	86	8	no	—
429	#121	—	86	4	no	—
430	#121	—	86	4	no	—
431	#121	—	86	8	no	—
432	#121	—	86	4	no	—
433	#121	—	86	2	no	—
434	#121	—	86	2	no	—
435	#120	—	86	8	no	—
436	#120	—	86	8	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	43	2	no	—
440	C₄×D₄	—	43	2	no	—
441	C₄×D₄	—	86	2	no	—
442	C₄×D₄	—	86	2	no	—
443	C₄×D₄	C₂²×D₄₃	1	4	yes	—
444	C₄×D₄	C₂²×D₄₃	1	4	yes	—
445	C₂×C₄⋊C₄	—	86	4	no	—
446	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
447	C₂×C₂²⋊C₄	—	2	2	no	—
448	C₂×C₂²⋊C₄	—	86	8	no	—
449	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
450	#107	C₂²×D₄₃	1	2	yes	—
451	#107	C₂²×D₄₃	1	2	yes	—
452	C₄⋊C₈	—	43	2	no	—
453	C₄⋊C₈	—	43	2	no	—
454	#103	—	43	8	no	—
455	#102	—	43	8	no	—
456	#102	C₂²×D₄₃	1	4	yes	—
457	#102	C₂²×D₄₃	1	4	yes	—
458	C₂²⋊C₈	—	43	4	no	—
459	C₂²⋊C₈	—	43	4	no	—
460	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
461	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
462	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
463	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
464	C₂⁴	—	2	2	no	—
465	C₂⁴	—	86	8	no	—
466	#41	—	86	4	no	—
467	#41	—	86	4	no	—
468	#41	—	86	16	no	—
469	#41	—	86	8	no	—
470	#41	—	86	8	no	—
471	#41	—	172	8	no	—
472	#41	—	172	16	no	—
473	C₂×Q₈	—	43	2	no	—
474	C₂×Q₈	—	43	4	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	43	4	no	—
478	C₂×D₄	—	43	2	no	—
479	C₂×D₄	—	43	2	no	—
480	C₂×D₄	—	43	2	no	—
481	C₂×D₄	—	43	4	no	—
482	C₂×D₄	—	86	8	no	—
483	C₂×D₄	—	86	8	no	—
484	C₂×D₄	—	86	16	no	—
485	C₂×D₄	—	86	8	no	—
486	C₂×D₄	—	86	4	no	—
487	C₂×D₄	—	86	2	no	—
488	C₂×D₄	—	86	2	no	—
489	C₂×D₄	—	344	8	no	—
490	C₂×D₄	—	172	8	no	—
491	C₂×D₄	—	172	16	no	—
492	C₂×D₄	—	172	32	no	—
493	C₂×D₄	C₂×D₁₇₂	1	8	yes	complemented
494	C₂×D₄	C₂³×D₄₃	1	4	yes	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	8	4	no	—
499	C₂²×C₄	—	43	4	no	—
500	C₂²×C₄	—	86	8	no	—
501	C₂²×C₄	—	86	4	no	—
502	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
503	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
504	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
505	Q₁₆	—	86	4	no	—
506	Q₁₆	—	172	2	no	—
507	SD₁₆	—	86	16	no	—
508	SD₁₆	—	86	8	no	—
509	SD₁₆	—	172	4	no	—
510	D₈	—	86	16	no	—
511	D₈	—	86	4	no	—
512	D₈	—	172	2	no	—
513	D₈	C₂×D₁₇₂	1	8	yes	complemented
514	D₈	C₂×D₁₇₂	1	8	yes	complemented
515	M₁₆	—	86	4	no	—
516	M₁₆	—	86	8	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	43	4	no	—
519	C₂×C₈	—	86	8	no	—
520	C₂×C₈	C₂×D₁₇₂	1	4	yes	complemented
521	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
522	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
523	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
524	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	43	2	no	—
527	C₄⋊C₄	—	43	2	no	—
528	C₄⋊C₄	—	86	8	no	—
529	C₄⋊C₄	—	86	2	no	—
530	C₄⋊C₄	—	86	2	no	—
531	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	43	4	no	—
535	C₂²⋊C₄	—	43	4	no	—
536	C₂²⋊C₄	—	86	8	no	—
537	C₂²⋊C₄	—	86	8	no	—
538	C₂²⋊C₄	—	86	4	no	—
539	C₂²⋊C₄	—	86	4	no	—
540	C₄²	D₄×D₄₃	1	1	yes	characteristic
541	C₄²	D₄×D₄₃	1	1	yes	characteristic
542	C₄²	C₂³×D₄₃	1	1	yes	characteristic
543	C₄²	C₂³×D₄₃	1	1	yes	characteristic
544	C₂³	—	2	4	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	8	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	—	43	4	no	—
549	C₂³	—	86	4	no	—
550	C₂³	—	344	8	no	—
551	C₂³	—	344	8	no	—
552	C₂³	—	172	16	no	—
553	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
554	Q₈	—	86	4	no	—
555	Q₈	—	86	4	no	—
556	Q₈	—	86	4	no	—
557	D₄	—	2	4	no	—
558	D₄	—	2	8	no	—
559	D₄	—	86	8	no	—
560	D₄	—	86	4	no	—
561	D₄	—	86	4	no	—
562	D₄	—	86	4	no	—
563	D₄	—	86	4	no	—
564	D₄	—	344	2	no	—
565	D₄	—	344	8	no	—
566	D₄	—	172	2	no	—
567	D₄	—	172	16	no	—
568	D₄	—	172	16	no	—
569	D₄	—	172	8	no	—
570	D₄	—	172	4	no	—
571	D₄	C₂²×D₁₇₂	1	8	yes	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	8	no	—
576	C₂×C₄	—	8	4	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	43	4	no	—
579	C₂×C₄	—	86	4	no	—
580	C₂×C₄	—	86	4	no	—
581	C₂×C₄	—	86	4	no	—
582	C₂×C₄	—	172	16	no	—
583	C₂×C₄	—	172	8	no	—
584	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
585	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
586	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
587	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
588	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
589	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
590	C₂×C₄	#13063371	1	2	yes	—
591	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
592	C₈	—	2	1	no	—
593	C₈	—	2	1	no	—
594	C₈	—	86	4	no	—
595	C₈	C₂²×D₁₇₂	1	2	yes	—
596	C₈	C₂²×D₁₇₂	1	2	yes	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	8	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	8	8	no	—
603	C₂²	—	86	4	no	—
604	C₂²	—	86	4	no	—
605	C₂²	—	86	4	no	—
606	C₂²	—	172	4	no	—
607	C₂²	—	172	4	no	—
608	C₂²	—	172	4	no	—
609	C₂²	—	688	16	no	—
610	C₂²	D₄×D₁₇₂	1	2	yes	—
611	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	4	4	no	—
616	C₄	—	86	4	no	—
617	C₄	—	172	4	no	—
618	C₄	D₄×D₁₇₂	1	2	yes	—
619	C₄	#14583700	1	2	yes	complemented
620	C₄	C₂³×D₁₇₂	1	1	yes	characteristic
621	C₄	C₂×#13063371	1	1	yes	characteristic
622	C₂	—	2	2	no	—
623	C₂	—	4	8	no	—
624	C₂	—	344	4	no	—
625	C₂	—	172	4	no	—
626	C₂	C₂×D₄×D₁₇₂	1	1	yes	characteristic
627	C₂	C₂×#14583700	1	1	yes	characteristic
628	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×C₄×D₈	D₄₃
hypocenter	C₄₃	#61084
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#14583700	C₂	semidirect
2. #19148359	C₂	semidirect
3. #19146316	C₂	semidirect
4. #19146281	C₂	semidirect
5. D₈×D₁₇₂	C₂	semidirect
6. #19146205	C₂	semidirect
7. #19146196	C₂	semidirect
8. #19145023	C₂	semidirect
9. #19144267	C₂	semidirect
10. #19144059	C₂	semidirect
11. #19143904	C₂	semidirect
12. #19143308	C₂	semidirect
13. C₂×C₄×D₈×C₄₃	C₂	semidirect
14. C₂×#13063370	C₂²	semidirect
16. C₂×#13063351	C₂²	semidirect
17. C₂×#13063349	C₂²	semidirect
18. C₂×#13063347	C₂²	semidirect
19. C₂×#13063347	C₂²	semidirect
20. C₂×#13063344	C₂²	semidirect
21. C₂×D₈×D₄₃	C₂²	semidirect
22. C₂×#13063331	C₂²	semidirect
24. #14583553	C₂²	semidirect
26. #14583544	C₂²	semidirect
28. D₄×D₁₇₂	C₂²	semidirect
29. #14583480	C₂²	semidirect
32. #14583449	C₂²	semidirect
34. #14583283	C₂²	semidirect
35. #14583283	C₂²	semidirect
36. #14583279	C₂²	semidirect
37. #14583276	C₂²	semidirect
38. #14583272	C₂²	semidirect
39. #14583146	C₂²	semidirect
40. #14583141	C₂²	semidirect
41. #14583136	C₂²	semidirect
42. #14583114	C₂²	semidirect
43. #14583104	C₂²	semidirect
44. #14583094	C₂²	semidirect
45. #14583062	C₂²	semidirect
46. #14583051	C₂²	semidirect
47. #14583045	C₂²	semidirect
48. #14583034	C₂²	semidirect
49. #14582978	C₂²	semidirect
50. #14582978	C₂²	semidirect
51. C₈×D₁₇₂	C₂²	semidirect
52. C₈×D₁₇₂	C₂²	semidirect
53. #14582923	C₂²	semidirect
54. #14582898	C₂²	semidirect
55. #14582865	C₂²	semidirect
57. C₂×C₄×D₄×C₄₃	C₂²	semidirect
58. C₄×D₈×C₄₃	C₂²	semidirect
59. C₄×D₈×C₄₃	C₂²	semidirect
60. C₄×D₈×C₄₃	C₂²	semidirect
61. C₄×D₈×C₄₃	C₂²	semidirect
62. C₂×#107×C₄₃	C₂²	semidirect
63. C₂×#102×C₄₃	C₂²	semidirect
64. C₂×C₄×C₈×C₄₃	C₂²	semidirect
129. C₂×D₈×C₄₃	D₄	semidirect
153. C₂×D₄×C₄₃	C₂×D₄	semidirect
190. D₈×C₄₃	C₂×D₄	semidirect
191. D₈×C₄₃	C₂×D₄	semidirect
193. C₂×C₈×C₄₃	C₂×D₄	semidirect
303. C₄×C₄₃	#576	semidirect
319. C₂×C₄×D₈	D₄₃	semidirect
349. C₂×C₄×D₄	C₂×D₄₃	semidirect
365. C₄×D₈	C₂×D₄₃	semidirect
366. C₄×D₈	C₂×D₄₃	semidirect
367. C₄×D₈	C₂×D₄₃	semidirect
368. C₄×D₈	C₂×D₄₃	semidirect
373. C₂×#107	C₂×D₄₃	semidirect
376. C₂×#102	C₂×D₄₃	semidirect
378. C₂×C₄×C₈	C₂×D₄₃	semidirect
379. C₄₃	#61084	semidirect
406. C₂×D₈	D₁₇₂	semidirect
493. C₂×D₄	C₂×D₁₇₂	semidirect
513. D₈	C₂×D₁₇₂	semidirect
514. D₈	C₂×D₁₇₂	semidirect
520. C₂×C₈	C₂×D₁₇₂	semidirect
619. C₄	#14583700	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583700	2
#19148359	2
#19146316	2
#19146281	2
D₈×D₁₇₂	2
#19146205	2
#19146196	2
#19145023	2
#19144267	2
#19144059	2
#19143904	2
#19143308	2
C₂×C₄×D₈×C₄₃	2
#61084	43