Subgroups — #41×#10621884 #25978009

Order 11008.

2116 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×D₁₇₂	C₂	1	1	yes	maximal, characteristic
2	#19147572	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147266	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147233	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146946	C₂	1	3	yes	maximal, complemented
7	#19146460	C₂	1	3	yes	maximal, complemented
8	#19146413	C₂	1	3	yes	maximal, complemented
9	D₄×#10621884	C₂	1	3	yes	maximal, complemented
10	#19145155	C₂	1	3	yes	maximal, complemented
11	#19144626	C₂	1	3	yes	maximal, complemented
12	#19144599	C₂	1	3	yes	maximal, complemented
13	#41×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×#10621884	C₂	1	3	yes	maximal, complemented
15	Q₈×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₄₃	—	2	1	no	—
17	C₂²×#10621884	C₂²	1	3	yes	—
18	#14583571	C₂²	1	1	yes	characteristic
19	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic
20	#14583561	—	2	1	no	—
21	#14583553	C₂²	1	3	yes	—
22	#14583544	—	2	3	no	—
23	D₄×D₁₇₂	C₂²	1	3	yes	—
24	#14583449	C₂²	1	3	yes	—
25	#14583411	—	2	3	no	—
26	C₂×C₄×D₁₇₂	C₂²	1	3	yes	—
27	#14583295	C₂²	1	3	yes	complemented
28	#14583273	C₂²	1	3	yes	complemented
29	#14583249	C₂²	1	3	yes	complemented
30	#14583247	C₂²	1	3	yes	complemented
31	#14583227	C₂²	1	6	yes	complemented
32	#14583217	C₂²	1	6	yes	complemented
33	#14583186	C₂²	1	3	yes	—
34	#14583186	C₂²	1	3	yes	complemented
35	#14583184	C₂²	1	3	yes	complemented
36	#14583184	C₂²	1	3	yes	complemented
37	#14583130	C₂²	1	6	yes	complemented
38	#14583130	C₂²	1	6	yes	complemented
39	#14583101	C₂²	1	3	yes	—
40	#14583101	C₂²	1	3	yes	complemented
41	#14583099	C₂²	1	3	yes	complemented
42	#14583099	C₂²	1	3	yes	complemented
43	#14583049	C₂²	1	6	yes	—
44	#14583038	C₂²	1	6	yes	complemented
45	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₄×#10621884	C₂²	1	3	yes	—
48	C₄×#10621884	C₂²	1	3	yes	—
49	C₄×#10621884	C₂²	1	3	yes	—
50	C₄×#10621884	C₂²	1	1	yes	characteristic
51	C₄×#10621884	C₂²	1	3	yes	complemented
52	C₄×#10621884	C₂²	1	3	yes	complemented
53	C₄×#10621884	C₂²	1	6	yes	complemented
54	C₄×#10621884	C₂²	1	3	yes	complemented
55	C₄×#10621884	C₂²	1	3	yes	complemented
56	D₄×C₄₃⋊C₈	C₂²	1	3	yes	complemented
57	D₄×C₄₃⋊C₈	C₂²	1	3	yes	complemented
58	#14582952	C₂²	1	3	yes	complemented
59	C₂×#13063256	C₂²	1	3	yes	complemented
60	C₂×#13063249	C₂²	1	3	yes	complemented
61	C₂×#13063245	C₂²	1	3	yes	—
62	C₂×C₄×C₄₃⋊C₈	C₂²	1	3	yes	complemented
63	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
64	C₄₃×#557	—	2	1	no	—
65	C₄₃×#557	C₂²	1	1	yes	characteristic, complemented
66	C₄₃×#554	—	2	3	no	—
67	C₄₃×#554	C₂²	1	3	yes	complemented
68	D₄×Q₈×C₄₃	C₂²	1	3	yes	complemented
69	C₄₃×#533	—	2	3	no	—
70	C₄₃×#533	C₂²	1	3	yes	complemented
71	C₄×#41×C₄₃	—	2	1	no	—
72	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
73	C₂×C₄×Q₈×C₄₃	C₂²	1	3	yes	complemented
74	C₂×#10621902	—	2	1	no	—
75	C₂×#10621898	—	2	3	no	—
76	C₂×#10621900	—	2	3	no	—
77	#41×D₄₃	—	4	8	no	—
78	C₂×Q₈×D₄₃	—	2	1	no	—
79	C₂²×D₁₇₂	C₂³	1	3	yes	—
80	C₂×D₄×D₄₃	—	2	3	no	—
81	C₂²×C₄×D₄₃	—	2	3	no	—
82	C₂×#10621884	—	2	12	no	—
83	C₂×#10621884	C₂³	1	3	yes	—
84	C₂×#10621884	C₂³	1	3	yes	—
85	C₂×#10621884	C₂³	1	3	yes	—
86	C₂×#10621884	C₂³	1	6	yes	—
87	C₂×#10621884	C₂³	1	1	yes	characteristic
88	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	—
89	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	—
90	#13063325	C₂³	1	3	yes	—
91	#13063322	C₂³	1	3	yes	—
92	#13063313	—	2	3	no	—
93	#13063309	—	2	6	no	—
94	#13063305	—	2	3	no	—
95	#13063305	—	2	3	no	—
96	#13063300	—	2	3	no	—
97	#13063300	—	2	3	no	—
98	#13063299	—	2	3	no	—
99	#13063299	C₂³	1	6	yes	—
100	#13063295	—	2	6	no	—
101	C₄×D₁₇₂	—	2	3	no	—
102	C₄×D₁₇₂	—	2	3	no	—
103	C₄×D₁₇₂	—	2	3	no	—
104	C₄×D₁₇₂	C₂³	1	3	yes	—
105	C₄×D₁₇₂	C₂³	1	3	yes	—
106	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
107	C₄×D₁₇₂	C₂³	1	3	yes	—
108	C₂×C₄⋊Dic₄₃	C₂³	1	3	yes	—
109	C₂×(C₂×D₄₃)⋊C₄	—	2	3	no	—
110	#13063256	C₂³	1	3	yes	—
111	#13063256	C₂³	1	6	yes	—
112	#13063256	C₂³	1	3	yes	—
113	#13063256	C₂³	1	1	yes	characteristic
114	#13063256	C₂³	1	3	yes	—
115	C₄⋊(C₄₃⋊C₈)	C₂³	1	3	yes	—
116	C₄⋊(C₄₃⋊C₈)	C₂³	1	3	yes	—
117	#13063249	C₂³	1	6	yes	—
118	#13063249	C₂³	1	3	yes	—
119	#13063249	C₂³	1	3	yes	—
120	#13063249	C₂³	1	1	yes	characteristic
121	#13063249	C₂³	1	3	yes	—
122	#13063245	C₂³	1	3	yes	—
123	#13063245	C₂³	1	6	yes	—
124	#13063245	C₂³	1	3	yes	—
125	#13063245	C₂³	1	3	yes	—
126	#13063245	C₂³	1	1	yes	characteristic
127	C₂²⋊(C₄₃⋊C₈)	C₂³	1	6	yes	—
128	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
129	C₄×C₄₃⋊C₈	C₂³	1	3	yes	—
130	C₄×C₄₃⋊C₈	C₂³	1	3	yes	—
131	C₄×C₄₃⋊C₈	C₂³	1	3	yes	—
132	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
133	C₂²×Q₈×C₄₃	C₂³	1	3	yes	—
134	C₄⋊Q₈×C₄₃	—	2	3	no	—
135	C₄⋊Q₈×C₄₃	—	2	3	no	—
136	C₄⋊Q₈×C₄₃	C₂³	1	3	yes	—
137	C₄⋊Q₈×C₄₃	C₂³	1	3	yes	—
138	#125×C₄₃	—	2	3	no	—
139	#125×C₄₃	—	2	3	no	—
140	#125×C₄₃	—	2	3	no	—
141	C₂²⋊Q₈×C₄₃	—	2	3	no	—
142	C₂²⋊Q₈×C₄₃	—	2	6	no	—
143	C₂²⋊Q₈×C₄₃	—	2	6	no	—
144	C₂²⋊Q₈×C₄₃	C₂³	1	6	yes	—
145	C₄×Q₈×C₄₃	—	2	1	no	—
146	C₄×Q₈×C₄₃	—	2	1	no	—
147	C₄×Q₈×C₄₃	—	2	3	no	—
148	C₄×Q₈×C₄₃	—	2	3	no	—
149	C₄×Q₈×C₄₃	—	2	3	no	—
150	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
151	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
152	C₄×Q₈×C₄₃	C₂³	1	3	yes	—
153	C₄×Q₈×C₄₃	C₂³	1	3	yes	—
154	C₄×Q₈×C₄₃	C₂³	1	3	yes	—
155	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
156	C₄×D₄×C₄₃	—	2	3	no	—
157	C₄×D₄×C₄₃	—	2	3	no	—
158	C₄×D₄×C₄₃	D₄	1	3	yes	—
159	C₄×D₄×C₄₃	C₂³	1	3	yes	—
160	#117×C₄₃	—	2	3	no	—
161	#117×C₄₃	D₄	1	3	yes	—
162	C₂×C₄⋊C₄×C₄₃	—	2	3	no	—
163	C₂×C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
164	C₂×C₄²×C₄₃	—	2	3	no	—
165	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
166	C₂³×D₄₃	—	2	3	no	—
167	#41×C₄₃	SD₁₆	1	8	yes	complemented
168	C₂×Q₈×C₄₃	—	2	3	no	—
169	C₂×Q₈×C₄₃	—	2	3	no	—
170	C₂×Q₈×C₄₃	—	2	6	no	—
171	C₂×Q₈×C₄₃	—	4	3	no	—
172	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
173	C₂×Q₈×C₄₃	C₂⁴	1	3	yes	—
174	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
175	C₂×D₄×C₄₃	C₂×D₄	1	3	yes	—
176	C₂²×C₄×C₄₃	—	2	3	no	—
177	C₂²×C₄×C₄₃	—	2	3	no	—
178	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
179	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
180	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
181	C₂×C₂²⋊D₄₃	—	2	6	no	—
182	C₂²×Dic₄₃	—	2	3	no	—
183	#10621902	—	4	4	no	—
184	Q₈×D₄₃	—	4	4	no	—
185	#10621900	—	4	12	no	—
186	D₄×D₄₃	—	4	12	no	—
187	#10621898	—	4	12	no	—
188	C₂×D₁₇₂	—	2	3	no	—
189	C₂×D₁₇₂	—	2	3	no	—
190	C₂×D₁₇₂	—	2	3	no	—
191	C₂×D₁₇₂	—	2	6	no	—
192	C₂×D₁₇₂	—	4	3	no	—
193	C₂×D₁₇₂	C₂⁴	1	3	yes	—
194	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
195	C₂×C₄×D₄₃	—	2	1	no	—
196	C₂×C₄×D₄₃	—	2	3	no	—
197	C₂×C₄×D₄₃	—	2	3	no	—
198	C₂×C₄×D₄₃	—	2	3	no	—
199	C₂×C₄×D₄₃	—	4	12	no	—
200	C₂×Dic₈₆	—	2	3	no	—
201	C₄⋊C₄×C₄₃	—	2	1	no	—
202	C₄⋊C₄×C₄₃	—	2	3	no	—
203	C₄⋊C₄×C₄₃	—	2	3	no	—
204	C₄⋊C₄×C₄₃	—	2	3	no	—
205	C₄⋊C₄×C₄₃	—	2	3	no	—
206	C₄⋊C₄×C₄₃	—	2	3	no	—
207	C₄⋊C₄×C₄₃	—	2	3	no	—
208	C₄⋊C₄×C₄₃	—	2	3	no	—
209	C₄⋊C₄×C₄₃	—	2	6	no	—
210	C₄⋊C₄×C₄₃	C₂×D₄	1	3	yes	—
211	C₄⋊C₄×C₄₃	C₂×D₄	1	3	yes	—
212	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
213	C₄⋊C₄×C₄₃	C₂⁴	1	3	yes	—
214	C₂²⋊C₄×C₄₃	—	2	6	no	—
215	C₂²⋊C₄×C₄₃	C₂×D₄	1	6	yes	—
216	C₄²×C₄₃	—	2	1	no	—
217	C₄²×C₄₃	—	2	3	no	—
218	C₄²×C₄₃	—	2	3	no	—
219	C₄²×C₄₃	—	2	3	no	—
220	C₄²×C₄₃	C₂×D₄	1	3	yes	—
221	C₄²×C₄₃	C₂×D₄	1	3	yes	—
222	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
223	C₄²×C₄₃	C₂⁴	1	3	yes	—
224	#10621884	—	2	6	no	—
225	#10621884	—	2	6	no	—
226	#10621884	—	2	6	no	—
227	#10621884	—	4	6	no	—
228	#10621884	#41	1	4	yes	direct product factor
229	(C₂×D₄₃)⋊C₄	—	2	1	no	—
230	(C₂×D₄₃)⋊C₄	—	2	3	no	—
231	(C₂×D₄₃)⋊C₄	—	2	3	no	—
232	(C₂×D₄₃)⋊C₄	—	2	3	no	—
233	(C₂×D₄₃)⋊C₄	—	2	6	no	—
234	C₄⋊Dic₄₃	—	2	3	no	—
235	C₄⋊Dic₄₃	—	2	3	no	—
236	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
237	C₄⋊Dic₄₃	C₂⁴	1	3	yes	—
238	C₂×C₄₃⋊C₈	—	2	6	no	—
239	C₂×C₄₃⋊C₈	—	4	3	no	—
240	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
241	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
242	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
243	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
244	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
245	C₂²×D₄₃	—	2	1	no	—
246	C₂²×D₄₃	—	2	3	no	—
247	C₂²×D₄₃	—	4	6	no	—
248	C₂²×D₄₃	—	4	6	no	—
249	C₂²×D₄₃	—	8	3	no	—
250	Q₈×C₄₃	—	2	1	no	—
251	Q₈×C₄₃	—	2	3	no	—
252	Q₈×C₄₃	—	2	3	no	—
253	Q₈×C₄₃	—	4	6	no	—
254	Q₈×C₄₃	—	8	3	no	—
255	Q₈×C₄₃	C₂×SD₁₆	1	4	yes	complemented
256	Q₈×C₄₃	C₂×#41	1	2	yes	complemented
257	D₄×C₄₃	C₂×SD₁₆	1	12	yes	complemented
258	C₂×C₄×C₄₃	—	2	1	no	—
259	C₂×C₄×C₄₃	—	2	3	no	—
260	C₂×C₄×C₄₃	—	2	3	no	—
261	C₂×C₄×C₄₃	—	2	1	no	—
262	C₂×C₄×C₄₃	—	2	3	no	—
263	C₂×C₄×C₄₃	—	2	3	no	—
264	C₂×C₄×C₄₃	—	4	3	no	—
265	C₂×C₄×C₄₃	—	4	6	no	—
266	C₂×C₄×C₄₃	—	8	3	no	—
267	C₂×C₄×C₄₃	C₂×SD₁₆	1	12	yes	complemented
268	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
269	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
270	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
272	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
274	C₂²⋊D₄₃	—	4	12	no	—
275	C₂×Dic₄₃	—	2	3	no	—
276	C₂×Dic₄₃	—	2	1	no	—
277	C₂×Dic₄₃	—	4	6	no	—
278	D₁₇₂	—	2	3	no	—
279	D₁₇₂	—	2	1	no	—
280	D₁₇₂	—	2	3	no	—
281	D₁₇₂	—	4	6	no	—
282	D₁₇₂	—	4	6	no	—
283	D₁₇₂	—	8	3	no	—
284	D₁₇₂	C₂×#41	1	2	yes	—
285	C₄×D₄₃	—	4	2	no	—
286	C₄×D₄₃	—	4	6	no	—
287	C₄×D₄₃	—	4	6	no	—
288	C₄×D₄₃	—	4	6	no	—
289	Dic₈₆	—	4	6	no	—
290	C₄₃⋊C₈	—	2	3	no	—
291	C₄₃⋊C₈	—	2	1	no	—
292	C₄₃⋊C₈	—	2	3	no	—
293	C₄₃⋊C₈	C₂×#41	1	2	yes	complemented
294	SD₁₆×#41	—	43	1	no	maximal, Sylow
295	C₂²×C₄₃	—	2	3	no	—
296	C₂²×C₄₃	—	2	3	no	—
297	C₂²×C₄₃	C₂²×SD₁₆	1	6	yes	—
298	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
299	C₂×D₄₃	—	2	2	no	—
300	C₂×D₄₃	—	4	1	no	—
301	C₂×D₄₃	—	4	1	no	—
302	C₂×D₄₃	—	4	3	no	—
303	C₂×D₄₃	—	4	3	no	—
304	C₂×D₄₃	—	4	3	no	—
305	C₂×D₄₃	—	8	12	no	—
306	C₄×C₄₃	—	2	3	no	—
307	C₄×C₄₃	—	2	1	no	—
308	C₄×C₄₃	—	2	3	no	—
309	C₄×C₄₃	—	2	2	no	—
310	C₄×C₄₃	—	4	1	no	—
311	C₄×C₄₃	—	4	3	no	—
312	C₄×C₄₃	—	4	3	no	—
313	C₄×C₄₃	C₂²×SD₁₆	1	6	yes	—
314	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
315	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
316	C₄×C₄₃	#585	1	1	yes	characteristic
317	Dic₄₃	—	4	3	no	—
318	Dic₄₃	—	4	1	no	—
319	Q₈×#41	D₄₃	1	1	yes	characteristic, complemented
320	D₄×#41	—	43	1	no	—
321	#3392	—	43	1	no	—
322	Q₈×SD₁₆	—	43	1	no	—
323	#3362	—	43	1	no	—
324	#3359	—	43	1	no	—
325	#3335	—	43	3	no	—
326	#3298	—	43	3	no	—
327	#3295	—	43	3	no	—
328	D₄×SD₁₆	—	43	3	no	—
329	#3167	—	43	3	no	—
330	#3103	—	43	3	no	—
331	#3101	—	43	3	no	—
332	C₈×#41	—	43	1	no	—
333	C₂×C₄×SD₁₆	—	43	3	no	—
334	C₂×C₄₃	—	2	6	no	—
335	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
336	C₂×C₄₃	C₂³×SD₁₆	1	1	yes	characteristic
337	C₂×C₄₃	#3584	1	1	yes	characteristic
338	D₄₃	—	4	2	no	—
339	D₄₃	—	8	3	no	—
340	C₂²×#41	—	86	1	no	—
341	C₂²×SD₁₆	—	43	3	no	—
342	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
343	#557	—	2	1	no	—
344	#557	C₂×D₄₃	1	1	yes	characteristic, complemented
345	#554	—	2	3	no	—
346	#554	C₂×D₄₃	1	3	yes	complemented
347	#550	—	43	1	no	—
348	D₄×Q₈	—	43	1	no	—
349	D₄×Q₈	C₂×D₄₃	1	3	yes	complemented
350	#548	—	86	1	no	—
351	#547	—	43	3	no	—
352	#546	—	86	3	no	—
353	D₄²	—	43	3	no	—
354	#533	—	2	3	no	—
355	#533	C₂×D₄₃	1	3	yes	complemented
356	#532	—	43	3	no	—
357	#525	—	86	3	no	—
358	C₄×#41	—	2	1	no	—
359	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂×D₄₃	1	3	yes	complemented
361	C₂×C₄×D₄	—	43	3	no	—
362	#498	—	43	3	no	—
363	#492	—	43	3	no	—
364	#487	—	43	3	no	—
365	#486	—	43	3	no	—
366	#483	—	43	6	no	—
367	#481	—	43	6	no	—
368	#476	—	43	3	no	—
369	#476	—	43	3	no	—
370	#475	—	43	3	no	—
371	#475	—	43	3	no	—
372	#465	—	43	6	no	—
373	#465	—	43	6	no	—
374	#461	—	43	3	no	—
375	#461	—	43	3	no	—
376	#460	—	43	3	no	—
377	#460	—	43	3	no	—
378	#450	—	43	6	no	—
379	#448	—	43	6	no	—
380	C₈×Q₈	—	43	1	no	—
381	C₈×Q₈	—	43	1	no	—
382	C₄×SD₁₆	—	43	3	no	—
383	C₄×SD₁₆	—	43	3	no	—
384	C₄×SD₁₆	—	43	6	no	—
385	C₄×SD₁₆	—	43	3	no	—
386	C₄×SD₁₆	—	43	3	no	—
387	C₄×SD₁₆	—	43	3	no	—
388	C₄×SD₁₆	—	43	3	no	—
389	C₄×SD₁₆	—	43	3	no	—
390	C₄×SD₁₆	—	43	1	no	—
391	C₈×D₄	—	43	3	no	—
392	C₈×D₄	—	43	3	no	—
393	#431	—	43	3	no	—
394	C₂×#106	—	43	3	no	—
395	C₂×#103	—	43	3	no	—
396	C₂×#102	—	43	3	no	—
397	C₂×C₄×C₈	—	43	3	no	—
398	C₄₃	SD₁₆×#41	1	1	yes	characteristic, complemented, Sylow
399	C₂×#41	—	86	1	no	—
400	C₂×#41	—	86	3	no	—
401	C₂×#41	—	86	3	no	—
402	C₂×#41	—	172	8	no	—
403	C₂×#41	C₂²⋊D₄₃	1	1	yes	characteristic
404	C₂²×Q₈	—	86	1	no	—
405	C₂²×Q₈	C₂²×D₄₃	1	3	yes	—
406	C₂²×D₄	—	43	3	no	—
407	C₂²×D₄	—	86	3	no	—
408	C₂³×C₄	—	86	3	no	—
409	C₂×SD₁₆	—	43	1	no	—
410	C₂×SD₁₆	—	43	3	no	—
411	C₂×SD₁₆	—	43	3	no	—
412	C₂×SD₁₆	—	43	3	no	—
413	C₂×SD₁₆	—	43	6	no	—
414	C₂×SD₁₆	—	86	12	no	—
415	C₂²×C₈	—	43	3	no	—
416	C₂²×C₈	—	43	3	no	—
417	C₄⋊Q₈	—	2	3	no	—
418	C₄⋊Q₈	—	2	3	no	—
419	C₄⋊Q₈	—	43	3	no	—
420	C₄⋊Q₈	C₂²×D₄₃	1	3	yes	—
421	C₄⋊Q₈	C₂²×D₄₃	1	3	yes	—
422	#127	—	43	3	no	—
423	#125	—	2	3	no	—
424	#125	—	2	3	no	—
425	#125	—	2	3	no	—
426	#124	—	86	3	no	—
427	#123	—	86	6	no	—
428	C₂²⋊Q₈	—	2	3	no	—
429	C₂²⋊Q₈	—	2	6	no	—
430	C₂²⋊Q₈	—	2	6	no	—
431	C₂²⋊Q₈	—	86	3	no	—
432	C₂²⋊Q₈	—	86	3	no	—
433	C₂²⋊Q₈	C₂²×D₄₃	1	6	yes	—
434	#121	—	43	6	no	—
435	#121	—	86	3	no	—
436	#121	—	86	3	no	—
437	#121	—	86	3	no	—
438	#120	—	86	6	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×Q₈	—	2	1	no	—
441	C₄×Q₈	—	2	3	no	—
442	C₄×Q₈	—	2	3	no	—
443	C₄×Q₈	—	2	3	no	—
444	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
445	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
446	C₄×Q₈	C₂²×D₄₃	1	3	yes	—
447	C₄×Q₈	C₂²×D₄₃	1	3	yes	—
448	C₄×Q₈	C₂²×D₄₃	1	3	yes	—
449	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
450	C₄×D₄	—	2	3	no	—
451	C₄×D₄	—	2	3	no	—
452	C₄×D₄	—	43	1	no	—
453	C₄×D₄	—	43	3	no	—
454	C₄×D₄	—	43	3	no	—
455	C₄×D₄	—	43	3	no	—
456	C₄×D₄	—	86	3	no	—
457	C₄×D₄	—	86	3	no	—
458	C₄×D₄	—	86	3	no	—
459	C₄×D₄	C₂²⋊D₄₃	1	3	yes	—
460	C₄×D₄	C₂²×D₄₃	1	3	yes	—
461	#117	—	2	3	no	—
462	#117	C₂²⋊D₄₃	1	3	yes	—
463	C₂×C₄⋊C₄	—	2	3	no	—
464	C₂×C₄⋊C₄	—	43	3	no	—
465	C₂×C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
466	C₂×C₂²⋊C₄	—	86	3	no	—
467	C₂×C₄²	—	2	3	no	—
468	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
469	#106	—	43	1	no	—
470	#106	—	43	3	no	—
471	#106	—	43	3	no	—
472	#106	—	43	3	no	—
473	#106	—	43	6	no	—
474	C₄⋊C₈	—	43	3	no	—
475	C₄⋊C₈	—	43	3	no	—
476	#103	—	43	1	no	—
477	#103	—	43	3	no	—
478	#103	—	43	3	no	—
479	#103	—	43	3	no	—
480	#103	—	43	6	no	—
481	#102	—	43	1	no	—
482	#102	—	43	3	no	—
483	#102	—	43	3	no	—
484	#102	—	43	3	no	—
485	#102	—	43	6	no	—
486	C₂²⋊C₈	—	43	6	no	—
487	C₄×C₈	—	43	1	no	—
488	C₄×C₈	—	43	3	no	—
489	C₄×C₈	—	43	3	no	—
490	C₄×C₈	—	43	3	no	—
491	C₂⁴	—	86	3	no	—
492	#41	—	172	4	no	—
493	#41	—	172	12	no	—
494	#41	—	172	12	no	—
495	#41	#10621884	1	8	yes	direct product factor
496	C₂×Q₈	—	2	3	no	—
497	C₂×Q₈	—	2	3	no	—
498	C₂×Q₈	—	2	6	no	—
499	C₂×Q₈	—	4	3	no	—
500	C₂×Q₈	—	86	3	no	—
501	C₂×Q₈	—	172	4	no	—
502	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
503	C₂×Q₈	C₂³×D₄₃	1	3	yes	—
504	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
505	C₂×D₄	—	43	1	no	—
506	C₂×D₄	—	43	3	no	—
507	C₂×D₄	—	86	6	no	—
508	C₂×D₄	—	86	6	no	—
509	C₂×D₄	—	86	3	no	—
510	C₂×D₄	—	86	3	no	—
511	C₂×D₄	—	86	3	no	—
512	C₂×D₄	—	172	3	no	—
513	C₂×D₄	—	172	12	no	—
514	C₂×D₄	C₂×C₂²⋊D₄₃	1	3	yes	—
515	C₂²×C₄	—	2	3	no	—
516	C₂²×C₄	—	2	3	no	—
517	C₂²×C₄	—	86	3	no	—
518	C₂²×C₄	—	86	3	no	—
519	C₂²×C₄	—	86	3	no	—
520	C₂²×C₄	—	86	1	no	—
521	C₂²×C₄	—	86	3	no	—
522	C₂²×C₄	—	172	12	no	—
523	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
524	C₂²×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
525	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
526	SD₁₆	—	43	4	no	—
527	SD₁₆	—	86	6	no	—
528	SD₁₆	—	86	6	no	—
529	SD₁₆	—	86	6	no	—
530	SD₁₆	—	172	6	no	—
531	C₂×C₈	—	43	1	no	—
532	C₂×C₈	—	43	1	no	—
533	C₂×C₈	—	43	3	no	—
534	C₂×C₈	—	43	3	no	—
535	C₂×C₈	—	86	6	no	—
536	C₂×C₈	—	172	3	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	3	no	—
539	C₄⋊C₄	—	2	3	no	—
540	C₄⋊C₄	—	2	3	no	—
541	C₄⋊C₄	—	2	3	no	—
542	C₄⋊C₄	—	2	3	no	—
543	C₄⋊C₄	—	2	3	no	—
544	C₄⋊C₄	—	2	3	no	—
545	C₄⋊C₄	—	2	6	no	—
546	C₄⋊C₄	—	43	1	no	—
547	C₄⋊C₄	—	43	3	no	—
548	C₄⋊C₄	—	86	3	no	—
549	C₄⋊C₄	—	86	3	no	—
550	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
551	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
552	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
553	C₄⋊C₄	C₂³×D₄₃	1	3	yes	—
554	C₂²⋊C₄	—	2	6	no	—
555	C₂²⋊C₄	—	86	1	no	—
556	C₂²⋊C₄	—	86	3	no	—
557	C₂²⋊C₄	—	86	3	no	—
558	C₂²⋊C₄	—	86	3	no	—
559	C₂²⋊C₄	—	86	6	no	—
560	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	6	yes	—
561	C₄²	—	2	3	no	—
562	C₄²	—	2	3	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	3	no	—
565	C₄²	C₂×C₂²⋊D₄₃	1	3	yes	—
566	C₄²	C₂×C₂²⋊D₄₃	1	3	yes	—
567	C₄²	C₂³×D₄₃	1	3	yes	—
568	C₄²	C₂³×D₄₃	1	1	yes	characteristic
569	C₂³	—	86	1	no	—
570	C₂³	—	86	3	no	—
571	C₂³	—	344	3	no	—
572	C₂³	—	172	6	no	—
573	C₂³	—	172	6	no	—
574	C₂³	C₂²×C₂²⋊D₄₃	1	3	yes	—
575	Q₈	—	2	1	no	—
576	Q₈	—	2	3	no	—
577	Q₈	—	2	3	no	—
578	Q₈	—	4	6	no	—
579	Q₈	—	8	3	no	—
580	Q₈	—	172	6	no	—
581	Q₈	C₂×#10621884	1	4	yes	complemented
582	Q₈	#41×D₄₃	1	2	yes	complemented
583	D₄	—	43	2	no	—
584	D₄	—	86	3	no	—
585	D₄	—	86	1	no	—
586	D₄	—	86	3	no	—
587	D₄	—	344	3	no	—
588	D₄	—	172	6	no	—
589	D₄	—	172	12	no	—
590	D₄	—	172	6	no	—
591	D₄	C₂×#10621884	1	12	yes	complemented
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	3	no	—
594	C₂×C₄	—	2	3	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	3	no	—
597	C₂×C₄	—	2	3	no	—
598	C₂×C₄	—	4	3	no	—
599	C₂×C₄	—	4	6	no	—
600	C₂×C₄	—	8	3	no	—
601	C₂×C₄	—	86	1	no	—
602	C₂×C₄	—	86	3	no	—
603	C₂×C₄	—	172	6	no	—
604	C₂×C₄	—	172	2	no	—
605	C₂×C₄	—	172	6	no	—
606	C₂×C₄	—	172	6	no	—
607	C₂×C₄	—	172	6	no	—
608	C₂×C₄	C₂×#10621884	1	12	yes	complemented
609	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
610	C₂×C₄	C₂²×C₂²⋊D₄₃	1	3	yes	—
611	C₂×C₄	C₂²×C₂²⋊D₄₃	1	3	yes	—
612	C₂×C₄	C₂²×C₂²⋊D₄₃	1	3	yes	—
613	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
615	C₈	—	43	2	no	—
616	C₈	—	86	3	no	—
617	C₈	—	86	1	no	—
618	C₈	—	86	3	no	—
619	C₂²	—	2	3	no	—
620	C₂²	—	2	3	no	—
621	C₂²	—	86	2	no	—
622	C₂²	—	344	12	no	—
623	C₂²	—	172	3	no	—
624	C₂²	—	172	3	no	—
625	C₂²	—	172	3	no	—
626	C₂²	—	172	1	no	—
627	C₂²	—	172	1	no	—
628	C₂²	C₂²×#10621884	1	6	yes	—
629	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
630	C₄	—	2	3	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	3	no	—
634	C₄	—	4	3	no	—
635	C₄	—	4	1	no	—
636	C₄	—	4	3	no	—
637	C₄	—	172	1	no	—
638	C₄	—	172	3	no	—
639	C₄	C₂²×#10621884	1	2	yes	—
640	C₄	C₂²×#10621884	1	6	yes	—
641	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
642	C₄	#14583735	1	1	yes	characteristic
643	C₂	—	2	6	no	—
644	C₂	—	344	3	no	—
645	C₂	—	172	2	no	—
646	C₂	#41×C₂²⋊D₄₃	1	1	yes	characteristic
647	C₂	C₂³×#10621884	1	1	yes	characteristic
648	C₂	#19149366	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	Q₈×#41×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#41×D₁₇₂	C₂
hypercenter	Q₈×#41	D₄₃
hypocenter	C₄₃	SD₁₆×#41
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
2. #19147572	C₂	semidirect
3. Q₈×#10621884	C₂	semidirect
4. #19147266	C₂	semidirect
5. #19147233	C₂	semidirect
6. #19146946	C₂	semidirect
7. #19146460	C₂	semidirect
8. #19146413	C₂	semidirect
9. D₄×#10621884	C₂	semidirect
10. #19145155	C₂	semidirect
11. #19144626	C₂	semidirect
12. #19144599	C₂	semidirect
13. #41×C₄₃⋊C₈	C₂	semidirect
14. C₂×C₄×#10621884	C₂	semidirect
15. Q₈×#41×C₄₃	C₂	semidirect
27. #14583295	C₂²	semidirect
28. #14583273	C₂²	semidirect
29. #14583249	C₂²	semidirect
30. #14583247	C₂²	semidirect
31. #14583227	C₂²	semidirect
32. #14583217	C₂²	semidirect
34. #14583186	C₂²	semidirect
35. #14583184	C₂²	semidirect
36. #14583184	C₂²	semidirect
37. #14583130	C₂²	semidirect
38. #14583130	C₂²	semidirect
40. #14583101	C₂²	semidirect
41. #14583099	C₂²	semidirect
42. #14583099	C₂²	semidirect
44. #14583038	C₂²	semidirect
45. Q₈×C₄₃⋊C₈	C₂²	semidirect
46. Q₈×C₄₃⋊C₈	C₂²	semidirect
51. C₄×#10621884	C₂²	semidirect
52. C₄×#10621884	C₂²	semidirect
53. C₄×#10621884	C₂²	semidirect
54. C₄×#10621884	C₂²	semidirect
55. C₄×#10621884	C₂²	semidirect
56. D₄×C₄₃⋊C₈	C₂²	semidirect
57. D₄×C₄₃⋊C₈	C₂²	semidirect
58. #14582952	C₂²	semidirect
59. C₂×#13063256	C₂²	semidirect
60. C₂×#13063249	C₂²	semidirect
62. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
63. Q₈²×C₄₃	C₂²	semidirect
65. C₄₃×#557	C₂²	semidirect
67. C₄₃×#554	C₂²	semidirect
68. D₄×Q₈×C₄₃	C₂²	semidirect
70. C₄₃×#533	C₂²	semidirect
73. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
167. #41×C₄₃	SD₁₆	semidirect
228. #10621884	#41	direct (N × H)
255. Q₈×C₄₃	C₂×SD₁₆	semidirect
256. Q₈×C₄₃	C₂×#41	semidirect
257. D₄×C₄₃	C₂×SD₁₆	semidirect
267. C₂×C₄×C₄₃	C₂×SD₁₆	semidirect
293. C₄₃⋊C₈	C₂×#41	semidirect
319. Q₈×#41	D₄₃	semidirect
342. Q₈²	C₂×D₄₃	semidirect
344. #557	C₂×D₄₃	semidirect
346. #554	C₂×D₄₃	semidirect
349. D₄×Q₈	C₂×D₄₃	semidirect
355. #533	C₂×D₄₃	semidirect
360. C₂×C₄×Q₈	C₂×D₄₃	semidirect
398. C₄₃	SD₁₆×#41	semidirect
495. #41	#10621884	direct (N × H)
581. Q₈	C₂×#10621884	semidirect
582. Q₈	#41×D₄₃	semidirect
591. D₄	C₂×#10621884	semidirect
608. C₂×C₄	C₂×#10621884	semidirect

Maximal subgroups

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

subgroup	index
#41×D₁₇₂	2
#19147572	2
Q₈×#10621884	2
#19147266	2
#19147233	2
#19146946	2
#19146460	2
#19146413	2
D₄×#10621884	2
#19145155	2
#19144626	2
#19144599	2
#41×C₄₃⋊C₈	2
C₂×C₄×#10621884	2
Q₈×#41×C₄₃	2
SD₁₆×#41	43