Finite Group Databasebeta

← #19144874

Subgroups — #19144874

Order 5504.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583520C211yesmaximal, characteristic, complemented
2#14583379C211yesmaximal, characteristic, complemented
3#14583230C211yesmaximal, characteristic, complemented
4#14583218C211yesmaximal, characteristic, complemented
5#14583190C211yesmaximal, characteristic, complemented
6#14583185C211yesmaximal, characteristic, complemented
7#14583122C211yesmaximal, characteristic, complemented
8#14583115C211yesmaximal, characteristic, complemented
9#14583063C211yesmaximal, characteristic, complemented
10#14583046C211yesmaximal, characteristic
11#14583012C211yesmaximal, characteristic, complemented
12#14583007C211yesmaximal, characteristic, complemented
13C4×#10621873C211yesmaximal, characteristic, complemented
14C4×#10621873C211yesmaximal, characteristic, complemented
15C43×#433C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×D344C2211yescharacteristic
21#13063325C2211yescharacteristic
22#13063320—21no—
23#13063313C2211yescharacteristic
24#13063311—21no—
25#13063307—21no—
26#13063304C2211yescharacteristic
27#13063303—21no—
28#13063299C2211yescharacteristic
29C4×Dic86C2211yescharacteristic
30C4×Dic86C2211yescharacteristic
31C4×Dic86C2211yescharacteristic
32C4×D172C2211yescharacteristic
33C4×D172C2211yescharacteristic
34C4×D172C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36(C22⋊D43)⋊C4—21no—
37#13063283—21no—
38C2×C4⋊Dic43C2211yescharacteristic
39C4⋊C4×D43—21no—
40#13063257C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063257C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063250C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063250C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063247C2211yescharacteristic
50#13063247C2211yescharacteristic
51#13063247C2211yescharacteristic
52#117×C43C2211yescharacteristic
53C4⋊C8×C43C2211yescharacteristic
54C4⋊C8×C43C2211yescharacteristic
55C22⋊C8×C43C2211yescharacteristic
56C22⋊C8×C43C2211yescharacteristic
57#97×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C2×C22⋊D43—21no—
61C2×C22⋊D43—21no—
62C22×Dic43—21no—
63#10621898—22no—
64#10621898—22no—
65C2×D172C2311yescharacteristic
66C2×D172C2311yescharacteristic
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×Dic86—21no—
72C2×Dic86C2311yescharacteristic
73C2×Dic86C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43D411yescharacteristic
79C4⋊C4×C43D411yescharacteristic
80C22⋊C4×C43D411yescharacteristic
81C22⋊C4×C43D411yescharacteristic
82C42×C43C2311yescharacteristic
83C42×C43C2311yescharacteristic
84C22⋊Dic43—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104Dic172—22no—
105D344—22no—
106#10621873—22no—
107#10621873—22no—
108C23×C43C2×D411yescharacteristic
109C22×D43—21no—
110C22×D43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43C2×D411yescharacteristic
114C2×C4×C43C2×D411yescharacteristic
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2411yescharacteristic
119C22⋊D43—24no—
120C22⋊D43—81no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—81no—
128D172—21no—
129D172—21no—
130D172—21no—
131D172#4112yes—
132C4×D43—24no—
133C4×D43—81no—
134C4×D43—81no—
135C4×D43—81no—
136Dic86—21no—
137Dic86—21no—
138Dic86—21no—
139Dic86—81no—
140Dic86#4112yes—
141C8×C43—21no—
142C8×C43—21no—
143C8×C43—21no—
144C8×C43—21no—
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43C22×D411yescharacteristic
149C2×D43—22no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43C2×#4111yescharacteristic
161C4×C43C2×#4111yescharacteristic
162Dic43—22no—
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168#3125—431nomaximal, Sylow
169C2×C43—41no—
170C2×C43#52511yescharacteristic
171C2×C43#57711yescharacteristic
172C2×C43#57711yescharacteristic
173D43—42no—
174D43—81no—
175#542—431no—
176#520—431no—
177#483—431no—
178#481—431no—
179#476—431no—
180#475—431no—
181#464—431no—
182#463—431no—
183#452—431no—
184#449—431no—
185#442—431no—
186#441—431no—
187C4×SD16—431no—
188C4×SD16—431no—
189#433D4311yescharacteristic, complemented
190C43#312511yescharacteristic, complemented, Sylow
191C2×#41—431no—
192C2×Q16—431no—
193C2×SD16—431no—
194C2×SD16—431no—
195C2×D8—431no—
196C4⋊Q8—431no—
197#126—861no—
198#124—431no—
199#124—861no—
200#123—861no—
201C22⋊Q8—431no—
202C22⋊Q8—861no—
203#121—431no—
204C4×Q8—431no—
205C4×Q8—431no—
206C4×Q8—431no—
207C4×D4—431no—
208C4×D4—431no—
209C4×D4—431no—
210C4×D4—861no—
211C4×D4—861no—
212#117—861no—
213#117C2×D4311yescharacteristic
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216#106—431no—
217#106—431no—
218#106—431no—
219#106—431no—
220C4⋊C8C2×D4311yescharacteristic
221C4⋊C8C2×D4311yescharacteristic
222#103—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#102—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230C22⋊C8C2×D4311yescharacteristic
231C22⋊C8C2×D4311yescharacteristic
232#97C2×D4311yescharacteristic
233C4×C8C2×D4311yescharacteristic
234#41—862no—
235#41—862no—
236C2×Q8—431no—
237C2×Q8—431no—
238C2×Q8—861no—
239C2×D4—431no—
240C2×D4—431no—
241C2×D4—861no—
242C2×D4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246C22×C4—861no—
247C22×C4—861no—
248C22×C4C22×D4311yescharacteristic
249Q16—862no—
250SD16—862no—
251SD16—862no—
252D8—862no—
253C2×C8C22×D4311yescharacteristic
254C2×C8C22×D4311yescharacteristic
255C2×C8C22×D4311yescharacteristic
256C2×C8C22×D4311yescharacteristic
257C4⋊C4—431no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4D17211yescharacteristic
268C4⋊C4D17211yescharacteristic
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4D17211yescharacteristic
277C22⋊C4D17211yescharacteristic
278C42—861no—
279C42—861no—
280C42—861no—
281C42C22×D4311yescharacteristic
282C42C22×D4311yescharacteristic
283C23—861no—
284C23—861no—
285C23C2×D17211yescharacteristic
286Q8—432no—
287Q8—861no—
288Q8—861no—
289Q8—861no—
290Q8—3441no—
291D4—432no—
292D4—864no—
293D4—861no—
294D4—861no—
295D4—861no—
296D4—3441no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—864no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—3441no—
309C2×C4—3441no—
310C2×C4C2×D17211yescharacteristic
311C2×C4C2×D17211yescharacteristic
312C2×C4C2×D17211yescharacteristic
313C2×C4C2×D17211yescharacteristic
314C2×C4C2×D17211yescharacteristic
315C2×C4C23×D4311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—862no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22—1721no—
328C22—1721no—
329C22C22×D17211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—862no—
336C4—1721no—
337C4—1721no—
338C4—1721no—
339C4—1721no—
340C4—1721no—
341C4#41×D4311yescharacteristic
342C4#41×D4311yescharacteristic
343C2—41no—
344C2—3441no—
345C2—1722no—
346C2#1458341111yescharacteristic
347C2#1458371111yescharacteristic
348C2#1458371111yescharacteristic
subgroupG/H
centerC22C22×D172
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#433C2
socleC22×C43C22×D4
hypercenter#433D43
hypocenterC43#3125
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14583520C2semidirect
2. #14583379C2semidirect
3. #14583230C2semidirect
4. #14583218C2semidirect
5. #14583190C2semidirect
6. #14583185C2semidirect
7. #14583122C2semidirect
8. #14583115C2semidirect
9. #14583063C2semidirect
11. #14583012C2semidirect
12. #14583007C2semidirect
13. C4×#10621873C2semidirect
14. C4×#10621873C2semidirect
15. C43×#433C2semidirect
189. #433D43semidirect
190. C43#3125semidirect