Subgroups — D₈×#10621898 #25978001

Order 11008.

2406 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#10621898	C₂	1	2	yes	maximal, complemented
2	#19147569	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147228	C₂	1	2	yes	maximal, complemented
5	#19146944	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146940	C₂	1	2	yes	maximal, complemented
7	#19146410	C₂	1	2	yes	maximal, complemented
8	#19146404	C₂	1	4	yes	maximal, complemented
9	D₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
11	#19145174	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145171	C₂	1	2	yes	maximal, complemented
13	#19144595	C₂	1	2	yes	maximal, complemented
14	#19144593	C₂	1	4	yes	maximal, complemented
15	C₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×D₈×D₄₃	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#10621898	—	2	2	no	—
19	C₂×D₈×D₄₃	C₂²	1	2	yes	—
20	#14583570	C₂²	1	2	yes	complemented
21	D₄×Dic₈₆	C₂²	1	2	yes	complemented
22	#14583558	—	2	2	no	—
23	#14583554	C₂²	1	2	yes	complemented
24	#14583550	C₂²	1	4	yes	complemented
25	#14583545	—	2	2	no	—
26	#14583539	—	2	4	no	—
27	D₄×D₁₇₂	C₂²	1	2	yes	complemented
28	D₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
29	#14583449	C₂²	1	2	yes	complemented
30	#14583446	C₂²	1	4	yes	complemented
31	#14583410	—	2	2	no	—
32	#14583408	—	2	4	no	—
33	C₄×#10621898	C₂²	1	1	yes	characteristic
34	C₄×D₄×D₄₃	C₂²	1	4	yes	complemented
35	#14583304	C₂²	1	1	yes	characteristic, complemented
36	#14583303	C₂²	1	2	yes	complemented
37	#14583276	C₂²	1	1	yes	characteristic, complemented
38	#14583274	C₂²	1	2	yes	complemented
39	#14583246	C₂²	1	2	yes	complemented
40	#14583244	C₂²	1	4	yes	complemented
41	#14583214	C₂²	1	4	yes	complemented
42	#14583212	C₂²	1	4	yes	complemented
43	#14583211	C₂²	1	4	yes	complemented
44	#14583179	C₂²	1	2	yes	complemented
45	#14583179	C₂²	1	2	yes	complemented
46	#14583178	C₂²	1	4	yes	complemented
47	#14583177	C₂²	1	4	yes	complemented
48	#14583136	C₂²	1	2	yes	complemented
49	#14583135	C₂²	1	2	yes	complemented
50	#14583135	C₂²	1	2	yes	complemented
51	#14583134	C₂²	1	4	yes	complemented
52	#14583132	C₂²	1	2	yes	complemented
53	#14583094	C₂²	1	2	yes	complemented
54	#14583094	C₂²	1	2	yes	complemented
55	#14583093	C₂²	1	4	yes	complemented
56	#14583092	C₂²	1	4	yes	complemented
57	#14583034	C₂²	1	4	yes	complemented
58	#14583033	C₂²	1	4	yes	complemented
59	#14583031	C₂²	1	4	yes	complemented
60	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
61	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
62	C₄×D₃₄₄	C₂²	1	2	yes	complemented
63	C₄×D₃₄₄	C₂²	1	2	yes	complemented
64	D₈×Dic₄₃	C₂²	1	2	yes	—
65	#14582981	C₂²	1	2	yes	complemented
66	C₄×#10621882	C₂²	1	4	yes	complemented
67	C₄×#10621882	C₂²	1	4	yes	complemented
68	#14582979	C₂²	1	4	yes	complemented
69	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
70	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
71	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
72	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
73	#14582952	C₂²	1	1	yes	characteristic, complemented
74	#14582950	C₂²	1	2	yes	complemented
75	#107×D₄₃	C₂²	1	2	yes	complemented
76	#102×D₄₃	C₂²	1	4	yes	complemented
77	C₄×C₈×D₄₃	C₂²	1	2	yes	complemented
78	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
80	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
81	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
82	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
84	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
86	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10621898	—	2	2	no	—
90	C₂×#10621898	—	2	4	no	—
91	C₂×#10621898	—	2	2	no	—
92	C₂×#10621898	—	2	4	no	—
93	C₂×#10621898	—	2	2	no	—
94	C₂×#10621898	—	4	16	no	—
95	C₂×#10621898	D₄	1	1	yes	characteristic
96	C₂²×Dic₈₆	—	2	2	no	—
97	C₂²×D₁₇₂	—	2	2	no	—
98	C₂²×C₂²⋊D₄₃	—	2	4	no	—
99	C₂×D₄×D₄₃	C₂³	1	4	yes	—
100	C₂²×C₄×D₄₃	—	2	4	no	—
101	C₂×D₃₄₄	C₂³	1	2	yes	—
102	C₂×D₃₄₄	C₂³	1	2	yes	—
103	C₂×#10621882	C₂³	1	4	yes	—
104	C₂×#10621882	C₂³	1	4	yes	—
105	D₈×D₄₃	—	2	8	no	—
106	C₂×C₈×D₄₃	C₂³	1	2	yes	—
107	C₂×C₈×D₄₃	C₂³	1	2	yes	—
108	#13063325	C₂³	1	2	yes	—
109	#13063324	C₂³	1	4	yes	—
110	#13063322	C₂³	1	2	yes	—
111	#13063321	C₂³	1	4	yes	—
112	#13063313	—	2	2	no	—
113	#13063311	—	2	4	no	—
114	#13063310	—	2	4	no	—
115	#13063308	—	2	4	no	—
116	#13063307	—	2	4	no	—
117	#13063304	—	2	2	no	—
118	#13063304	—	2	2	no	—
119	#13063303	—	2	4	no	—
120	#13063302	—	2	4	no	—
121	#13063300	C₂³	1	4	yes	—
122	#13063299	—	2	2	no	—
123	#13063299	—	2	2	no	—
124	#13063299	—	2	2	no	—
125	#13063299	C₂³	1	4	yes	—
126	#13063298	—	2	4	no	—
127	#13063298	—	2	4	no	—
128	#13063297	—	2	4	no	—
129	#13063296	C₂³	1	4	yes	—
130	#13063295	—	2	4	no	—
131	#13063294	—	2	4	no	—
132	#13063293	—	2	4	no	—
133	C₄×Dic₈₆	D₄	1	1	yes	characteristic
134	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
135	C₄×D₁₇₂	—	2	2	no	—
136	C₄×D₁₇₂	D₄	1	1	yes	characteristic
137	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
138	C₄×D₁₇₂	C₂³	1	4	yes	—
139	D₄×Dic₄₃	C₂³	1	4	yes	—
140	#13063287	C₂³	1	4	yes	—
141	C₄×C₂²⋊D₄₃	—	2	4	no	—
142	C₄×C₂²⋊D₄₃	—	2	4	no	—
143	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
144	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
145	(C₂²⋊D₄₃)⋊C₄	—	2	4	no	—
146	#13063284	D₄	1	1	yes	characteristic
147	#13063282	D₄	1	2	yes	—
148	C₄⋊C₄×D₄₃	C₂³	1	4	yes	—
149	C₂²⋊C₄×D₄₃	—	2	4	no	—
150	C₄²×D₄₃	C₂³	1	2	yes	—
151	#13063259	C₂³	1	2	yes	—
152	#13063259	C₂³	1	2	yes	—
153	#13063258	C₂³	1	4	yes	—
154	#13063258	C₂³	1	4	yes	—
155	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
156	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
157	Dic₄₃⋊C₈	C₂³	1	2	yes	—
158	Dic₄₃⋊C₈	C₂³	1	2	yes	—
159	#13063247	C₂³	1	4	yes	—
160	#13063247	C₂³	1	4	yes	—
161	#13063246	C₂³	1	4	yes	—
162	#13063246	C₂³	1	4	yes	—
163	#13063245	C₂³	1	4	yes	—
164	#13063245	C₂³	1	4	yes	—
165	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
166	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
167	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
168	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
169	C₈×Dic₄₃	C₂³	1	2	yes	—
170	C₈×Dic₄₃	C₂³	1	2	yes	—
171	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
172	C₂³×C₄×C₄₃	—	2	2	no	—
173	C₂×D₈×C₄₃	—	2	4	no	—
174	C₂×D₈×C₄₃	C₂³	1	2	yes	—
175	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
176	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₄₃	—	2	2	no	—
180	C₄×D₄×C₄₃	—	2	2	no	—
181	C₄×D₄×C₄₃	C₂³	1	2	yes	—
182	C₄×D₄×C₄₃	C₂³	1	2	yes	—
183	C₄×D₄×C₄₃	C₂³	1	2	yes	—
184	C₄×D₄×C₄₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
187	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
188	#107×C₄₃	C₂³	1	1	yes	characteristic
189	#107×C₄₃	C₂³	1	2	yes	—
190	#107×C₄₃	C₂³	1	1	yes	characteristic
191	#102×C₄₃	C₂³	1	2	yes	—
192	#102×C₄₃	C₂³	1	2	yes	—
193	#102×C₄₃	C₂³	1	2	yes	—
194	#102×C₄₃	C₂³	1	2	yes	—
195	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
198	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
199	C₂⁴×C₄₃	—	2	2	no	—
200	C₂³×D₄₃	—	2	4	no	—
201	C₂×D₄×C₄₃	—	2	2	no	—
202	C₂×D₄×C₄₃	—	2	4	no	—
203	C₂×D₄×C₄₃	—	4	2	no	—
204	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
205	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₄₃	—	2	2	no	—
207	C₂²×C₄×C₄₃	—	2	2	no	—
208	C₂²×C₄×C₄₃	—	2	2	no	—
209	C₂²×C₄×C₄₃	—	2	2	no	—
210	C₂²×C₄×C₄₃	—	2	2	no	—
211	C₂²×C₄×C₄₃	—	4	8	no	—
212	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
215	C₂×C₂²⋊D₄₃	—	2	4	no	—
216	C₂×C₂²⋊D₄₃	—	2	4	no	—
217	C₂×C₂²⋊D₄₃	—	2	4	no	—
218	C₂×C₂²⋊D₄₃	—	2	4	no	—
219	C₂×C₂²⋊D₄₃	—	2	4	no	—
220	C₂×C₂²⋊D₄₃	—	4	16	no	—
221	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
222	C₂²×Dic₄₃	—	2	4	no	—
223	D₄×D₄₃	—	2	8	no	—
224	D₄×D₄₃	—	4	4	no	—
225	#10621898	—	4	8	no	—
226	#10621898	—	4	16	no	—
227	#10621898	—	4	8	no	—
228	#10621898	—	4	16	no	—
229	#10621898	—	4	8	no	—
230	#10621898	D₈	1	8	yes	direct product factor
231	C₂×D₁₇₂	—	2	2	no	—
232	C₂×D₁₇₂	—	2	2	no	—
233	C₂×D₁₇₂	—	2	4	no	—
234	C₂×D₁₇₂	—	4	8	no	—
235	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
236	C₂×D₁₇₂	C₂⁴	1	4	yes	—
237	C₂×C₄×D₄₃	—	2	4	no	—
238	C₂×C₄×D₄₃	—	2	4	no	—
239	C₂×C₄×D₄₃	—	2	4	no	—
240	C₂×C₄×D₄₃	—	4	16	no	—
241	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
242	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
243	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
244	C₂×Dic₈₆	—	2	2	no	—
245	C₂×Dic₈₆	—	2	4	no	—
246	C₂×Dic₈₆	—	4	8	no	—
247	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
248	D₈×C₄₃	—	2	4	no	—
249	D₈×C₄₃	—	2	2	no	—
250	D₈×C₄₃	#41	1	4	yes	complemented
251	C₂×C₈×C₄₃	—	2	2	no	—
252	C₂×C₈×C₄₃	—	4	1	no	—
253	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₄₃	—	2	2	no	—
258	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
260	C₂²⋊C₄×C₄₃	—	2	2	no	—
261	C₂²⋊C₄×C₄₃	—	2	2	no	—
262	C₂²⋊C₄×C₄₃	—	2	2	no	—
263	C₂²⋊C₄×C₄₃	—	2	2	no	—
264	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
267	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
268	C₂²⋊Dic₄₃	—	2	4	no	—
269	C₂²⋊Dic₄₃	—	2	4	no	—
270	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
271	#10621882	—	2	8	no	—
272	#10621882	—	4	4	no	—
273	(C₂×D₄₃)⋊C₄	—	2	4	no	—
274	(C₂×D₄₃)⋊C₄	—	2	4	no	—
275	(C₂×D₄₃)⋊C₄	—	2	4	no	—
276	(C₂×D₄₃)⋊C₄	—	2	4	no	—
277	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
278	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
279	C₄⋊Dic₄₃	—	2	2	no	—
280	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
281	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
282	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
283	Dic₄₃⋊C₄	—	2	4	no	—
284	Dic₄₃⋊C₄	—	2	4	no	—
285	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
286	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
287	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
288	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
289	C₄×Dic₄₃	C₂⁴	1	2	yes	—
290	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
291	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
292	D₃₄₄	—	2	4	no	—
293	D₃₄₄	—	4	2	no	—
294	C₈×D₄₃	—	2	4	no	—
295	C₈×D₄₃	—	4	2	no	—
296	C₂³×C₄₃	—	2	2	no	—
297	C₂³×C₄₃	—	2	2	no	—
298	C₂³×C₄₃	—	4	4	no	—
299	C₂³×C₄₃	—	4	4	no	—
300	C₂³×C₄₃	—	8	2	no	—
301	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
302	C₂²×D₄₃	—	2	4	no	—
303	C₂²×D₄₃	—	4	8	no	—
304	C₂²×D₄₃	—	4	8	no	—
305	C₂²×D₄₃	—	8	4	no	—
306	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
307	D₄×C₄₃	—	2	2	no	—
308	D₄×C₄₃	—	2	2	no	—
309	D₄×C₄₃	—	2	2	no	—
310	D₄×C₄₃	—	4	4	no	—
311	D₄×C₄₃	C₂×#41	1	4	yes	complemented
312	C₂×C₄×C₄₃	—	2	1	no	—
313	C₂×C₄×C₄₃	—	2	1	no	—
314	C₂×C₄×C₄₃	—	2	2	no	—
315	C₂×C₄×C₄₃	—	2	2	no	—
316	C₂×C₄×C₄₃	—	4	1	no	—
317	C₂×C₄×C₄₃	—	4	4	no	—
318	C₂×C₄×C₄₃	—	4	4	no	—
319	C₂×C₄×C₄₃	—	4	4	no	—
320	C₂×C₄×C₄₃	—	4	4	no	—
321	C₂×C₄×C₄₃	—	4	4	no	—
322	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	complemented
323	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
329	C₂²⋊D₄₃	—	4	8	no	—
330	C₂²⋊D₄₃	—	4	8	no	—
331	C₂²⋊D₄₃	—	4	8	no	—
332	C₂²⋊D₄₃	—	4	8	no	—
333	C₂²⋊D₄₃	—	8	4	no	—
334	C₂²⋊D₄₃	C₂×D₈	1	8	yes	complemented
335	C₂×Dic₄₃	—	2	4	no	—
336	C₂×Dic₄₃	—	4	8	no	—
337	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
338	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
339	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
340	D₁₇₂	—	2	4	no	—
341	D₁₇₂	—	2	4	no	—
342	D₁₇₂	—	4	8	no	—
343	D₁₇₂	—	4	4	no	—
344	D₁₇₂	—	8	2	no	—
345	D₁₇₂	C₂×D₈	1	4	yes	complemented
346	C₄×D₄₃	—	2	2	no	—
347	C₄×D₄₃	—	2	2	no	—
348	C₄×D₄₃	—	4	2	no	—
349	C₄×D₄₃	—	4	8	no	—
350	C₄×D₄₃	—	4	8	no	—
351	C₄×D₄₃	—	4	8	no	—
352	C₄×D₄₃	C₂×D₈	1	8	yes	complemented
353	Dic₈₆	—	4	4	no	—
354	Dic₈₆	—	4	8	no	—
355	Dic₈₆	C₂×D₈	1	4	yes	complemented
356	C₈×C₄₃	—	2	1	no	—
357	C₈×C₄₃	—	2	1	no	—
358	C₈×C₄₃	—	2	1	no	—
359	C₈×C₄₃	C₂×#41	1	2	yes	complemented
360	C₄₃⋊C₈	—	2	2	no	—
361	C₄₃⋊C₈	—	2	2	no	—
362	D₈×#41	—	43	1	no	maximal, Sylow
363	C₂²×C₄₃	—	2	1	no	—
364	C₂²×C₄₃	—	2	1	no	—
365	C₂²×C₄₃	—	2	4	no	—
366	C₂²×C₄₃	—	4	2	no	—
367	C₂²×C₄₃	—	4	2	no	—
368	C₂²×C₄₃	—	4	2	no	—
369	C₂²×C₄₃	—	4	2	no	—
370	C₂²×C₄₃	—	4	2	no	—
371	C₂²×C₄₃	—	8	8	no	—
372	C₂²×C₄₃	C₂²×D₈	1	2	yes	—
373	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
374	C₂×D₄₃	—	2	2	no	—
375	C₂×D₄₃	—	2	2	no	—
376	C₂×D₄₃	—	4	4	no	—
377	C₂×D₄₃	—	4	4	no	—
378	C₂×D₄₃	—	4	4	no	—
379	C₂×D₄₃	—	8	16	no	—
380	C₂×D₄₃	C₂²×D₈	1	4	yes	—
381	C₄×C₄₃	—	2	1	no	—
382	C₄×C₄₃	—	2	1	no	—
383	C₄×C₄₃	—	2	1	no	—
384	C₄×C₄₃	—	4	2	no	—
385	C₄×C₄₃	—	4	2	no	—
386	C₄×C₄₃	C₂²×D₈	1	2	yes	—
387	C₄×C₄₃	C₂²×D₈	1	2	yes	—
388	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
389	C₄×C₄₃	#585	1	1	yes	characteristic
390	Dic₄₃	—	2	2	no	—
391	Dic₄₃	—	2	2	no	—
392	Dic₄₃	—	4	4	no	—
393	Dic₄₃	C₂²×D₈	1	4	yes	—
394	D₄×#41	—	43	2	no	—
395	#3391	—	43	1	no	—
396	Q₈×D₈	—	43	1	no	—
397	#3358	—	43	2	no	—
398	#3334	—	43	1	no	—
399	#3334	—	43	2	no	—
400	#3294	—	43	2	no	—
401	#3294	—	43	4	no	—
402	D₄×D₈	—	43	1	no	—
403	D₄×D₈	—	43	2	no	—
404	#3169	—	43	2	no	—
405	#3169	—	43	1	no	—
406	#3100	—	43	4	no	—
407	#3100	—	43	2	no	—
408	C₈×#41	—	43	1	no	—
409	C₂×C₄×D₈	—	43	2	no	—
410	C₂×C₄×D₈	D₄₃	1	1	yes	characteristic, complemented
411	C₂×C₄₃	—	2	2	no	—
412	C₂×C₄₃	—	4	4	no	—
413	C₂×C₄₃	—	8	2	no	—
414	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
415	C₂×C₄₃	C₂³×D₈	1	1	yes	characteristic
416	C₂×C₄₃	#3584	1	1	yes	characteristic
417	D₄₃	—	2	4	no	—
418	D₄₃	—	8	4	no	—
419	C₂²×#41	—	86	2	no	—
420	C₂²×D₈	—	43	2	no	—
421	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
422	#550	—	43	2	no	—
423	D₄×Q₈	—	43	2	no	—
424	#548	—	86	2	no	—
425	#547	—	43	2	no	—
426	#547	—	43	4	no	—
427	#546	—	86	4	no	—
428	#546	—	86	2	no	—
429	D₄²	—	43	4	no	—
430	D₄²	—	43	2	no	—
431	#532	—	43	4	no	—
432	#532	—	43	2	no	—
433	#525	—	86	4	no	—
434	#525	—	86	2	no	—
435	C₄×#41	—	43	1	no	—
436	C₂×C₄×D₄	—	43	4	no	—
437	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
438	#500	—	43	2	no	—
439	#500	—	43	1	no	—
440	#493	—	43	2	no	—
441	#493	—	43	1	no	—
442	#486	—	43	4	no	—
443	#486	—	43	2	no	—
444	#480	—	43	4	no	—
445	#480	—	43	4	no	—
446	#480	—	43	4	no	—
447	#474	—	43	2	no	—
448	#474	—	43	2	no	—
449	#474	—	43	4	no	—
450	#474	—	43	4	no	—
451	#466	—	43	2	no	—
452	#466	—	43	2	no	—
453	#466	—	43	2	no	—
454	#466	—	43	2	no	—
455	#466	—	43	4	no	—
456	#459	—	43	4	no	—
457	#459	—	43	2	no	—
458	#459	—	43	2	no	—
459	#459	—	43	4	no	—
460	#447	—	43	4	no	—
461	#447	—	43	4	no	—
462	#447	—	43	4	no	—
463	C₈×Q₈	—	43	1	no	—
464	C₈×Q₈	—	43	1	no	—
465	C₄×D₈	—	43	2	no	—
466	C₄×D₈	—	43	4	no	—
467	C₄×D₈	—	43	4	no	—
468	C₄×D₈	—	43	2	no	—
469	C₄×D₈	—	43	4	no	—
470	C₄×D₈	—	43	2	no	—
471	C₄×D₈	—	43	2	no	—
472	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
473	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
474	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
475	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
476	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
477	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
478	C₈×D₄	—	43	2	no	—
479	C₈×D₄	—	43	2	no	—
480	C₈×D₄	—	43	1	no	—
481	C₈×D₄	—	43	1	no	—
482	#431	—	43	1	no	—
483	#431	—	43	2	no	—
484	C₂×#107	—	43	2	no	—
485	C₂×#107	C₂×D₄₃	1	1	yes	characteristic, complemented
486	C₂×#102	—	43	4	no	—
487	C₂×#102	C₂×D₄₃	1	2	yes	complemented
488	C₂×C₄×C₈	—	43	2	no	—
489	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
490	C₄₃	D₈×#41	1	1	yes	characteristic, complemented, Sylow
491	C₂×#41	—	43	1	no	—
492	C₂×#41	—	86	4	no	—
493	C₂×#41	—	86	4	no	—
494	C₂×#41	—	86	2	no	—
495	C₂×#41	—	86	2	no	—
496	C₂×#41	—	86	2	no	—
497	C₂×#41	—	172	16	no	—
498	C₂²×Q₈	—	86	2	no	—
499	C₂²×D₄	—	43	4	no	—
500	C₂²×D₄	—	86	2	no	—
501	C₂²×D₄	—	86	4	no	—
502	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
503	C₂³×C₄	—	2	2	no	—
504	C₂³×C₄	—	86	4	no	—
505	C₂×D₈	—	2	4	no	—
506	C₂×D₈	—	43	4	no	—
507	C₂×D₈	—	43	4	no	—
508	C₂×D₈	—	43	2	no	—
509	C₂×D₈	—	43	2	no	—
510	C₂×D₈	—	86	8	no	—
511	C₂×D₈	C₂²×D₄₃	1	2	yes	—
512	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
513	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
514	C₂²×C₈	—	43	2	no	—
515	C₂²×C₈	—	43	2	no	—
516	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
517	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
518	C₄⋊Q₈	—	43	4	no	—
519	C₄⋊Q₈	—	43	2	no	—
520	#127	—	43	4	no	—
521	#127	—	43	2	no	—
522	#124	—	86	4	no	—
523	#124	—	86	2	no	—
524	#123	—	86	4	no	—
525	#123	—	86	4	no	—
526	#123	—	86	4	no	—
527	C₂²⋊Q₈	—	86	4	no	—
528	C₂²⋊Q₈	—	86	4	no	—
529	C₂²⋊Q₈	—	86	2	no	—
530	C₂²⋊Q₈	—	86	2	no	—
531	#121	—	43	4	no	—
532	#121	—	43	4	no	—
533	#121	—	43	4	no	—
534	#121	—	86	4	no	—
535	#121	—	86	4	no	—
536	#121	—	86	2	no	—
537	#121	—	86	2	no	—
538	#121	—	86	4	no	—
539	#121	—	86	2	no	—
540	#120	—	86	4	no	—
541	#120	—	86	4	no	—
542	#120	—	86	4	no	—
543	C₄×Q₈	—	43	1	no	—
544	C₄×Q₈	—	43	1	no	—
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	43	2	no	—
548	C₄×D₄	—	43	2	no	—
549	C₄×D₄	—	43	4	no	—
550	C₄×D₄	—	43	4	no	—
551	C₄×D₄	—	43	1	no	—
552	C₄×D₄	—	43	1	no	—
553	C₄×D₄	—	43	4	no	—
554	C₄×D₄	—	86	4	no	—
555	C₄×D₄	—	86	4	no	—
556	C₄×D₄	—	86	4	no	—
557	C₄×D₄	—	86	2	no	—
558	C₄×D₄	C₂²×D₄₃	1	2	yes	—
559	C₄×D₄	C₂²×D₄₃	1	2	yes	—
560	C₄×D₄	C₂²×D₄₃	1	2	yes	—
561	C₄×D₄	C₂²×D₄₃	1	2	yes	—
562	#117	—	43	1	no	—
563	#117	—	43	2	no	—
564	C₂×C₄⋊C₄	—	43	4	no	—
565	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
566	C₂×C₂²⋊C₄	—	2	2	no	—
567	C₂×C₂²⋊C₄	—	86	4	no	—
568	C₂×C₄²	—	43	2	no	—
569	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
570	#107	—	43	2	no	—
571	#107	—	43	2	no	—
572	#107	—	43	4	no	—
573	#107	—	43	4	no	—
574	#107	C₂²×D₄₃	1	1	yes	characteristic
575	#107	C₂²×D₄₃	1	1	yes	characteristic
576	#107	C₂²×D₄₃	1	2	yes	—
577	C₄⋊C₈	—	43	2	no	—
578	C₄⋊C₈	—	43	2	no	—
579	C₄⋊C₈	—	43	1	no	—
580	C₄⋊C₈	—	43	1	no	—
581	#102	—	43	4	no	—
582	#102	—	43	4	no	—
583	#102	—	43	4	no	—
584	#102	—	43	4	no	—
585	#102	—	43	4	no	—
586	#102	—	43	4	no	—
587	#102	C₂²×D₄₃	1	2	yes	—
588	#102	C₂²×D₄₃	1	2	yes	—
589	#102	C₂²×D₄₃	1	2	yes	—
590	#102	C₂²×D₄₃	1	2	yes	—
591	C₂²⋊C₈	—	43	2	no	—
592	C₂²⋊C₈	—	43	2	no	—
593	C₂²⋊C₈	—	43	2	no	—
594	C₄×C₈	—	43	2	no	—
595	C₄×C₈	—	43	2	no	—
596	C₄×C₈	—	43	2	no	—
597	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
598	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
599	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
600	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	86	4	no	—
603	#41	—	43	8	no	—
604	#41	—	172	16	no	—
605	#41	—	172	16	no	—
606	#41	—	172	8	no	—
607	#41	—	172	8	no	—
608	#41	—	172	8	no	—
609	C₂×Q₈	—	43	1	no	—
610	C₂×Q₈	—	86	4	no	—
611	C₂×Q₈	—	86	2	no	—
612	C₂×Q₈	—	172	8	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	4	2	no	—
616	C₂×D₄	—	43	2	no	—
617	C₂×D₄	—	43	1	no	—
618	C₂×D₄	—	43	4	no	—
619	C₂×D₄	—	86	4	no	—
620	C₂×D₄	—	86	4	no	—
621	C₂×D₄	—	86	4	no	—
622	C₂×D₄	—	86	4	no	—
623	C₂×D₄	—	86	8	no	—
624	C₂×D₄	—	86	4	no	—
625	C₂×D₄	—	86	4	no	—
626	C₂×D₄	—	86	2	no	—
627	C₂×D₄	—	86	2	no	—
628	C₂×D₄	—	172	8	no	—
629	C₂×D₄	—	172	4	no	—
630	C₂×D₄	—	172	16	no	—
631	C₂×D₄	C₂³×D₄₃	1	2	yes	—
632	C₂×D₄	C₂³×D₄₃	1	2	yes	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	4	8	no	—
639	C₂²×C₄	—	43	2	no	—
640	C₂²×C₄	—	43	2	no	—
641	C₂²×C₄	—	43	2	no	—
642	C₂²×C₄	—	86	4	no	—
643	C₂²×C₄	—	86	4	no	—
644	C₂²×C₄	—	86	4	no	—
645	C₂²×C₄	—	86	4	no	—
646	C₂²×C₄	—	172	16	no	—
647	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
648	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
649	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
650	D₈	—	2	4	no	—
651	D₈	—	2	2	no	—
652	D₈	—	86	8	no	—
653	D₈	—	86	4	no	—
654	D₈	—	172	2	no	—
655	D₈	—	172	4	no	—
656	D₈	#10621898	1	4	yes	direct product factor
657	C₂×C₈	—	2	2	no	—
658	C₂×C₈	—	4	1	no	—
659	C₂×C₈	—	43	2	no	—
660	C₂×C₈	—	43	2	no	—
661	C₂×C₈	—	86	4	no	—
662	C₂×C₈	—	172	2	no	—
663	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
664	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
665	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
666	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	43	2	no	—
669	C₄⋊C₄	—	43	2	no	—
670	C₄⋊C₄	—	43	1	no	—
671	C₄⋊C₄	—	43	1	no	—
672	C₄⋊C₄	—	43	4	no	—
673	C₄⋊C₄	—	86	4	no	—
674	C₄⋊C₄	—	86	4	no	—
675	C₄⋊C₄	—	86	2	no	—
676	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
677	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
678	C₂²⋊C₄	—	2	2	no	—
679	C₂²⋊C₄	—	2	2	no	—
680	C₂²⋊C₄	—	2	2	no	—
681	C₂²⋊C₄	—	2	2	no	—
682	C₂²⋊C₄	—	43	2	no	—
683	C₂²⋊C₄	—	43	2	no	—
684	C₂²⋊C₄	—	43	2	no	—
685	C₂²⋊C₄	—	86	4	no	—
686	C₂²⋊C₄	—	86	4	no	—
687	C₂²⋊C₄	—	86	4	no	—
688	C₂²⋊C₄	—	86	4	no	—
689	C₂²⋊C₄	—	86	4	no	—
690	C₂²⋊C₄	—	86	4	no	—
691	C₄²	—	43	2	no	—
692	C₄²	—	43	2	no	—
693	C₄²	—	43	2	no	—
694	C₄²	D₄×D₄₃	1	1	yes	characteristic
695	C₄²	D₄×D₄₃	1	1	yes	characteristic
696	C₄²	C₂³×D₄₃	1	1	yes	characteristic
697	C₄²	C₂³×D₄₃	1	1	yes	characteristic
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	4	4	no	—
701	C₂³	—	4	4	no	—
702	C₂³	—	8	2	no	—
703	C₂³	—	43	2	no	—
704	C₂³	—	86	4	no	—
705	C₂³	—	344	4	no	—
706	C₂³	—	172	8	no	—
707	C₂³	—	172	8	no	—
708	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
709	Q₈	—	43	4	no	—
710	Q₈	—	172	8	no	—
711	Q₈	—	172	4	no	—
712	D₄	—	2	2	no	—
713	D₄	—	2	2	no	—
714	D₄	—	2	2	no	—
715	D₄	—	4	4	no	—
716	D₄	—	43	8	no	—
717	D₄	—	43	4	no	—
718	D₄	—	86	4	no	—
719	D₄	—	86	4	no	—
720	D₄	—	344	2	no	—
721	D₄	—	344	4	no	—
722	D₄	—	172	8	no	—
723	D₄	—	172	8	no	—
724	D₄	—	172	8	no	—
725	D₄	—	172	8	no	—
726	D₄	—	172	8	no	—
727	D₄	—	172	4	no	—
728	D₄	C₂×#10621898	1	4	yes	complemented
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	4	no	—
735	C₂×C₄	—	4	4	no	—
736	C₂×C₄	—	4	4	no	—
737	C₂×C₄	—	4	4	no	—
738	C₂×C₄	—	4	4	no	—
739	C₂×C₄	—	43	2	no	—
740	C₂×C₄	—	43	8	no	—
741	C₂×C₄	—	43	2	no	—
742	C₂×C₄	—	43	2	no	—
743	C₂×C₄	—	86	2	no	—
744	C₂×C₄	—	86	2	no	—
745	C₂×C₄	—	86	4	no	—
746	C₂×C₄	—	172	2	no	—
747	C₂×C₄	—	172	8	no	—
748	C₂×C₄	—	172	8	no	—
749	C₂×C₄	—	172	8	no	—
750	C₂×C₄	—	172	8	no	—
751	C₂×C₄	D₈×D₄₃	1	4	yes	complemented
752	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
753	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
754	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
755	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
756	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
757	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
758	C₈	—	2	1	no	—
759	C₈	—	2	1	no	—
760	C₈	—	2	1	no	—
761	C₈	—	86	2	no	—
762	C₈	—	86	2	no	—
763	C₈	C₂×#10621898	1	2	yes	complemented
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	4	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	2	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	8	8	no	—
773	C₂²	—	43	4	no	—
774	C₂²	—	86	2	no	—
775	C₂²	—	86	2	no	—
776	C₂²	—	344	16	no	—
777	C₂²	—	172	4	no	—
778	C₂²	—	172	4	no	—
779	C₂²	—	172	4	no	—
780	C₂²	C₂×D₈×D₄₃	1	2	yes	—
781	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
782	C₄	—	2	1	no	—
783	C₄	—	2	1	no	—
784	C₄	—	2	1	no	—
785	C₄	—	4	2	no	—
786	C₄	—	4	2	no	—
787	C₄	—	43	4	no	—
788	C₄	—	86	2	no	—
789	C₄	—	86	2	no	—
790	C₄	—	172	4	no	—
791	C₄	C₂×D₈×D₄₃	1	2	yes	—
792	C₄	C₂×D₈×D₄₃	1	2	yes	—
793	C₄	C₂²×#10621898	1	1	yes	characteristic
794	C₄	#14583735	1	1	yes	characteristic
795	C₂	—	2	2	no	—
796	C₂	—	4	4	no	—
797	C₂	—	8	2	no	—
798	C₂	—	86	4	no	—
799	C₂	—	344	4	no	—
800	C₂	D₄×#10621898	1	1	yes	characteristic
801	C₂	C₂²×D₈×D₄₃	1	1	yes	characteristic
802	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×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	D₈×#41
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#10621898	C₂	semidirect
2. #19147569	C₂	semidirect
3. D₈×Dic₈₆	C₂	semidirect
4. #19147228	C₂	semidirect
5. #19146944	C₂	semidirect
6. #19146940	C₂	semidirect
7. #19146410	C₂	semidirect
8. #19146404	C₂	semidirect
9. D₈×D₁₇₂	C₂	semidirect
10. D₈×C₂²⋊D₄₃	C₂	semidirect
11. #19145174	C₂	semidirect
12. #19145171	C₂	semidirect
13. #19144595	C₂	semidirect
14. #19144593	C₂	semidirect
15. C₈×#10621898	C₂	semidirect
16. C₄×D₈×D₄₃	C₂	semidirect
17. C₂×C₄×D₈×C₄₃	C₂	semidirect
20. #14583570	C₂²	semidirect
21. D₄×Dic₈₆	C₂²	semidirect
23. #14583554	C₂²	semidirect
24. #14583550	C₂²	semidirect
27. D₄×D₁₇₂	C₂²	semidirect
28. D₄×C₂²⋊D₄₃	C₂²	semidirect
29. #14583449	C₂²	semidirect
30. #14583446	C₂²	semidirect
34. C₄×D₄×D₄₃	C₂²	semidirect
35. #14583304	C₂²	semidirect
36. #14583303	C₂²	semidirect
37. #14583276	C₂²	semidirect
38. #14583274	C₂²	semidirect
39. #14583246	C₂²	semidirect
40. #14583244	C₂²	semidirect
41. #14583214	C₂²	semidirect
42. #14583212	C₂²	semidirect
43. #14583211	C₂²	semidirect
44. #14583179	C₂²	semidirect
45. #14583179	C₂²	semidirect
46. #14583178	C₂²	semidirect
47. #14583177	C₂²	semidirect
48. #14583136	C₂²	semidirect
49. #14583135	C₂²	semidirect
50. #14583135	C₂²	semidirect
51. #14583134	C₂²	semidirect
52. #14583132	C₂²	semidirect
53. #14583094	C₂²	semidirect
54. #14583094	C₂²	semidirect
55. #14583093	C₂²	semidirect
56. #14583092	C₂²	semidirect
57. #14583034	C₂²	semidirect
58. #14583033	C₂²	semidirect
59. #14583031	C₂²	semidirect
60. C₈×Dic₈₆	C₂²	semidirect
61. C₈×Dic₈₆	C₂²	semidirect
62. C₄×D₃₄₄	C₂²	semidirect
63. C₄×D₃₄₄	C₂²	semidirect
65. #14582981	C₂²	semidirect
66. C₄×#10621882	C₂²	semidirect
67. C₄×#10621882	C₂²	semidirect
68. #14582979	C₂²	semidirect
69. C₈×D₁₇₂	C₂²	semidirect
70. C₈×D₁₇₂	C₂²	semidirect
71. C₈×C₂²⋊D₄₃	C₂²	semidirect
72. C₈×C₂²⋊D₄₃	C₂²	semidirect
73. #14582952	C₂²	semidirect
74. #14582950	C₂²	semidirect
75. #107×D₄₃	C₂²	semidirect
76. #102×D₄₃	C₂²	semidirect
77. C₄×C₈×D₄₃	C₂²	semidirect
79. C₂×C₄×D₄×C₄₃	C₂²	semidirect
82. C₄×D₈×C₄₃	C₂²	semidirect
83. C₄×D₈×C₄₃	C₂²	semidirect
84. C₄×D₈×C₄₃	C₂²	semidirect
85. C₄×D₈×C₄₃	C₂²	semidirect
86. C₂×#107×C₄₃	C₂²	semidirect
87. C₂×#102×C₄₃	C₂²	semidirect
88. C₂×C₄×C₈×C₄₃	C₂²	semidirect
230. #10621898	D₈	direct (N × H)
250. D₈×C₄₃	#41	semidirect
311. D₄×C₄₃	C₂×#41	semidirect
322. C₂×C₄×C₄₃	C₂×D₈	semidirect
334. C₂²⋊D₄₃	C₂×D₈	semidirect
345. D₁₇₂	C₂×D₈	semidirect
352. C₄×D₄₃	C₂×D₈	semidirect
355. Dic₈₆	C₂×D₈	semidirect
359. C₈×C₄₃	C₂×#41	semidirect
410. C₂×C₄×D₈	D₄₃	semidirect
437. C₂×C₄×D₄	C₂×D₄₃	semidirect
474. C₄×D₈	C₂×D₄₃	semidirect
475. C₄×D₈	C₂×D₄₃	semidirect
476. C₄×D₈	C₂×D₄₃	semidirect
477. C₄×D₈	C₂×D₄₃	semidirect
485. C₂×#107	C₂×D₄₃	semidirect
487. C₂×#102	C₂×D₄₃	semidirect
489. C₂×C₄×C₈	C₂×D₄₃	semidirect
490. C₄₃	D₈×#41	semidirect
656. D₈	#10621898	direct (N × H)
728. D₄	C₂×#10621898	semidirect
751. C₂×C₄	D₈×D₄₃	semidirect
763. C₈	C₂×#10621898	semidirect

Maximal subgroups

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

subgroup	index
D₄×#10621898	2
#19147569	2
D₈×Dic₈₆	2
#19147228	2
#19146944	2
#19146940	2
#19146410	2
#19146404	2
D₈×D₁₇₂	2
D₈×C₂²⋊D₄₃	2
#19145174	2
#19145171	2
#19144595	2
#19144593	2
C₈×#10621898	2
C₄×D₈×D₄₃	2
C₂×C₄×D₈×C₄₃	2
D₈×#41	43

Subgroups — D8×#10621898 #25978001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#10621898 #25978001