Finite Group Databasebeta

← #19147325

Subgroups — #19147325

Order 5504.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583625C211yesmaximal, characteristic, complemented
2#14583570C211yesmaximal, characteristic
3#14583264C211yesmaximal, characteristic, complemented
4#14583262C211yesmaximal, characteristic, complemented
5#14583244C211yesmaximal, characteristic, complemented
6#14583202C211yesmaximal, characteristic, complemented
7#14583199C211yesmaximal, characteristic, complemented
8#14583178C211yesmaximal, characteristic, complemented
9#14583099C211yesmaximal, characteristic, complemented
10#14583097C211yesmaximal, characteristic, complemented
11#14583097C211yesmaximal, characteristic, complemented
12#14583027C211yesmaximal, characteristic, complemented
13#14583002C211yesmaximal, characteristic, complemented
14#14582984C211yesmaximal, characteristic, complemented
15C43×#440C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621884C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19#13063324—21no—
20#13063324C2211yescharacteristic
21#13063322C2211yescharacteristic
22#13063321C2211yescharacteristic
23#13063321C2211yescharacteristic
24#13063317—21no—
25#13063317C2211yescharacteristic
26#13063316—21no—
27#13063316C2211yescharacteristic
28#13063299—21no—
29#13063298—21no—
30#13063298—21no—
31Q8×Dic43C2211yescharacteristic
32Q8×Dic43C2211yescharacteristic
33C4×Dic86—21no—
34C4×Dic86C2211yescharacteristic
35#13063287C2211yescharacteristic
36#13063287C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063256C2211yescharacteristic
39C4⋊(C43⋊C8)C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063247C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66#10621898—44no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×Dic86—21no—
74C2×Dic86D411yescharacteristic
75SD16×C43—22no—
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C22⋊C4×C43—21no—
82C42×C43—21no—
83C42×C43C2311yescharacteristic
84#10621884—22no—
85#10621884—22no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43D411yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4D411yescharacteristic
99Dic43⋊C4D411yescharacteristic
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43C2311yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C23×C43—21no—
107C22×D43—21no—
108C22×D43—21no—
109Q8×C43—21no—
110Q8×C43#4112yescomplemented
111D4×C43—21no—
112D4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—42no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2411yescharacteristic
120C22⋊D43—42no—
121C22⋊D43—42no—
122C22⋊D43—81no—
123C22⋊D43—81no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130D172—21no—
131D172—21no—
132D172—21no—
133D172—21no—
134D172—42no—
135D172—81no—
136C4×D43—42no—
137C4×D43—42no—
138Dic86—22no—
139Dic86—42no—
140C8×C43—21no—
141C8×C43—21no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43C22×D411yescharacteristic
148C2×D43—41no—
149C2×D43—41no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C4×C43—22no—
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C432−1+411yescharacteristic
161Dic43—21no—
162Dic43—21no—
163Dic43—21no—
164Dic43—41no—
165Dic43—41no—
166Dic43AGL(1,ℤ/8)12yes—
167#3368—431nomaximal, Sylow
168C2×C43—81no—
169C2×C43#54811yescharacteristic
170C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C43#57711yescharacteristic
172D43—81no—
173D43—81no—
174#557—431no—
175#550—431no—
176#490—431no—
177#490—431no—
178#486—431no—
179#478—431no—
180#478—431no—
181#474—431no—
182#460—431no—
183#460—431no—
184#460—431no—
185#446—431no—
186#440—431no—
187#440D4311yescharacteristic, complemented
188C4×SD16—431no—
189C43#336811yescharacteristic, complemented, Sylow
190C2×#41—861no—
191C2×SD16—431no—
192C2×SD16—431no—
193C2×SD16C2×D4311yescharacteristic
194C4⋊Q8—431no—
195C4⋊Q8—861no—
196#127—431no—
197#127—431no—
198#127—431no—
199#125—431no—
200#125—431no—
201#125—861no—
202#125—861no—
203#121—861no—
204#121—861no—
205#121—861no—
206C4×Q8—431no—
207C4×Q8—431no—
208C4×Q8—431no—
209C4×Q8—861no—
210C4×Q8C2×D4311yescharacteristic
211C4×D4—431no—
212C4×D4—431no—
213C4×D4C2×D4311yescharacteristic
214#107—431no—
215#107C2×D4311yescharacteristic
216#106—431no—
217C4⋊C8—431no—
218C4⋊C8—431no—
219C4⋊C8—431no—
220#103C2×D4311yescharacteristic
221#102—431no—
222#102—431no—
223#102—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228#102—431no—
229#102C2×D4311yescharacteristic
230#97—431no—
231#97C2×D4311yescharacteristic
232C4×C8—431no—
233#41—1724no—
234C2×Q8—431no—
235C2×Q8—861no—
236C2×Q8C22×D4311yescharacteristic
237C2×D4—431no—
238C2×D4—431no—
239C2×D4—861no—
240C2×D4—861no—
241C2×D4—861no—
242C2×D4—861no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4C22×D4311yescharacteristic
246C22×C4—21no—
247C22×C4—861no—
248C22×C4—861no—
249SD16—22no—
250SD16—862no—
251SD16—862no—
252C2×C8—431no—
253C2×C8—431no—
254C2×C8C22×D4311yescharacteristic
255C2×C8C22×D4311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—431no—
258C4⋊C4—431no—
259C4⋊C4—431no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22×D4311yescharacteristic
270C4⋊C4C22×D4311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C42—21no—
275C42—431no—
276C42—431no—
277C42—861no—
278C42—861no—
279C42C22×D4311yescharacteristic
280C23—21no—
281C23—861no—
282C23—861no—
283Q8—21no—
284Q8—862no—
285Q8—1722no—
286Q8#1062189812yescomplemented
287D4—21no—
288D4—21no—
289D4—861no—
290D4—861no—
291D4—861no—
292D4—861no—
293D4—3441no—
294D4—3441no—
295D4—3441no—
296D4—1722no—
297D4—1722no—
298D4—1722no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—431no—
304C2×C4—431no—
305C2×C4—431no—
306C2×C4—431no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4D4×D4311yescharacteristic
312C2×C4D4×D4311yescharacteristic
313C2×C4C23×D4311yescharacteristic
314C8—21no—
315C8—21no—
316C8—861no—
317C8—861no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—1721no—
322C22—1721no—
323C22—1721no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22C2×D4×D4311yescharacteristic
328C4—22no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—432no—
334C4—861no—
335C4—861no—
336C4—861no—
337C4—1721no—
338C4—1721no—
339C4C2×#1062189811yescharacteristic
340C4#1306337211yescharacteristic
341C2—81no—
342C2—3441no—
343C2—3441no—
344C2#1458355811yescharacteristic
345C2AGL(1,ℤ/8)×D4311yescharacteristic
346C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#440C2
socleC22×C43C22×D4
hypercenter#440D43
hypocenterC43#3368
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #14583625C2semidirect
3. #14583264C2semidirect
4. #14583262C2semidirect
5. #14583244C2semidirect
6. #14583202C2semidirect
7. #14583199C2semidirect
8. #14583178C2semidirect
9. #14583099C2semidirect
10. #14583097C2semidirect
11. #14583097C2semidirect
12. #14583027C2semidirect
13. #14583002C2semidirect
14. #14582984C2semidirect
15. C43×#440C2semidirect
110. Q8×C43#41semidirect
187. #440D43semidirect
189. C43#3368semidirect
286. Q8#10621898semidirect