Finite Group Databasebeta

← #19146479

Subgroups — #19146479

Order 5504.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583587C211yesmaximal, characteristic, complemented
2#14583561C211yesmaximal, characteristic
3#14583256C211yesmaximal, characteristic, complemented
4#14583243C211yesmaximal, characteristic, complemented
5#14583214C211yesmaximal, characteristic, complemented
6#14583141C211yesmaximal, characteristic, complemented
7#14583129C211yesmaximal, characteristic, complemented
8#14583122C211yesmaximal, characteristic, complemented
9#14583064C211yesmaximal, characteristic, complemented
10#14583056C211yesmaximal, characteristic, complemented
11C4×#10621885C211yesmaximal, characteristic, complemented
12#14582964C211yesmaximal, characteristic, complemented
13#14582894C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#479C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621873C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063320—21no—
24#13063316—21no—
25#13063313—21no—
26#13063313C2211yescharacteristic
27#13063310—21no—
28#13063305—21no—
29#13063305C2211yescharacteristic
30#13063305C2211yescharacteristic
31#13063305C2211yescharacteristic
32#13063300—21no—
33#13063300C2211yescharacteristic
34C4×Dic86C2211yescharacteristic
35C4×D172—21no—
36C4×D172C2211yescharacteristic
37#13063283—21no—
38#13063283C2211yescharacteristic
39C4⋊C4×D43C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C4×C43⋊C8C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#103×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60#10621902—22no—
61#10621902—41no—
62Q8×D43—22no—
63Q8×D43—41no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172D411yescharacteristic
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×C4×D43C2311yescharacteristic
73C2×Dic86—21no—
74C2×Dic86C2311yescharacteristic
75C2×Dic86C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C42×C43—21no—
85C42×C43C2311yescharacteristic
86#10621885—22no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95(C2×D43)⋊C4D411yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43D411yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107Dic172—41no—
108#10621873—41no—
109C8×D43—41no—
110C8×D43—41no—
111C22×D43—21no—
112C22×D43C2×D411yescharacteristic
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43#4112yes—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2411yescharacteristic
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—22no—
129D172—21no—
130D172—21no—
131D172—42no—
132D172—42no—
133C4×D43—21no—
134C4×D43—21no—
135C4×D43—21no—
136C4×D43—21no—
137C4×D43—42no—
138C4×D43—42no—
139C4×D43—42no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—42no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43C22×D411yescharacteristic
150C2×D43—21no—
151C2×D43—21no—
152C2×D43—21no—
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43#13512yes—
159C4×C43—22no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43C2×#4111yescharacteristic
166C4×C43H(5,𝔽2)11yescharacteristic
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172#3300—431nomaximal, Sylow
173C2×C43#54611yescharacteristic
174C2×C43C2×#13511yescharacteristic
175C2×C43#57811yescharacteristic
176D43—22no—
177D43—41no—
178D43—81no—
179#552—431no—
180#548—431no—
181#488—431no—
182#485—431no—
183#480—431no—
184#479D4311yescharacteristic, complemented
185#467—431no—
186#465—431no—
187#464—431no—
188#452—431no—
189#451—431no—
190C4×Q16—431no—
191C8×D4—431no—
192#416—431no—
193C2×#103—431no—
194C43#330011yescharacteristic, complemented, Sylow
195C2×#41—431no—
196C22×Q8—431no—
197C2×Q16—431no—
198C2×Q16—431no—
199C2×SD16—431no—
200C22×C8—431no—
201C22×C8—431no—
202#126—861no—
203#125—861no—
204#125C2×D4311yescharacteristic
205#124—431no—
206#124—861no—
207#123—861no—
208C22⋊Q8—431no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212#121—431no—
213#121—861no—
214C4×Q8—431no—
215C4×Q8C2×D4311yescharacteristic
216C4×D4—431no—
217C4×D4—861no—
218#117—431no—
219#117—861no—
220C2×C4⋊C4—431no—
221#107—431no—
222#107C2×D4311yescharacteristic
223#106C2×D4311yescharacteristic
224C4⋊C8C2×D4311yescharacteristic
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103C2×D4311yescharacteristic
231#103C2×D4311yescharacteristic
232#102—431no—
233#102—431no—
234#102—431no—
235C22⋊C8—431no—
236C22⋊C8—431no—
237C4×C8—431no—
238#41—862no—
239#41—1721no—
240C2×Q8—431no—
241C2×Q8—431no—
242C2×Q8—861no—
243C2×Q8—862no—
244C2×Q8—1721no—
245C2×Q8C22×D4311yescharacteristic
246C2×D4—431no—
247C2×D4—431no—
248C2×D4—861no—
249C2×D4—861no—
250C22×C4—431no—
251C22×C4—431no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255Q16—862no—
256Q16—1721no—
257SD16—1721no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8—1721no—
261C2×C8—1721no—
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4C22×D4311yescharacteristic
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—431no—
278C22⋊C4—431no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—21no—
287C42—861no—
288C42—861no—
289C42C22×D4311yescharacteristic
290C23—431no—
291C23—431no—
292C23—861no—
293Q8—21no—
294Q8—861no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—1722no—
299Q8#1062190212yes—
300D4—862no—
301D4—861no—
302D4—861no—
303D4—1722no—
304D4—1722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4—1722no—
321C2×C4D4×D4311yescharacteristic
322C2×C4D4×D4311yescharacteristic
323C2×C4C23×D4311yescharacteristic
324C8—21no—
325C8—21no—
326C8—861no—
327C8—861no—
328C22—432no—
329C22—861no—
330C22—861no—
331C22—861no—
332C22—861no—
333C22—861no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—861no—
345C4—861no—
346C4—1721no—
347C4—1721no—
348C4—1721no—
349C4C2×#1062190211yescharacteristic
350C4#1306337111yescharacteristic
351C2—862no—
352C2—3441no—
353C2—1721no—
354C2#1458354011yescharacteristic
355C2#135×D4311yescharacteristic
356C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#479C2
socleC22×C43C22×D4
hypercenter#479D43
hypocenterC43#3300
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #14583587C2semidirect
3. #14583256C2semidirect
4. #14583243C2semidirect
5. #14583214C2semidirect
6. #14583141C2semidirect
7. #14583129C2semidirect
8. #14583122C2semidirect
9. #14583064C2semidirect
10. #14583056C2semidirect
11. C4×#10621885C2semidirect
12. #14582964C2semidirect
13. #14582894C2semidirect
14. #103×D43C2semidirect
15. C43×#479C2semidirect
184. #479D43semidirect
194. C43#3300semidirect