Finite Group Databasebeta

← #23774237

Subgroups — #23774237

Order 10112.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099074C211yesmaximal, characteristic, complemented
2#19098904C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098884C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098814C211yesmaximal, characteristic, complemented
8#19098811C211yesmaximal, characteristic, complemented
9#19098807C211yesmaximal, characteristic, complemented
10#19098725C211yesmaximal, characteristic, complemented
11#19098723C211yesmaximal, characteristic, complemented
12#19098708C211yesmaximal, characteristic, complemented
13#19098706C211yesmaximal, characteristic, complemented
14#19098527C211yesmaximal, characteristic, complemented
15#525×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929614C2211yescharacteristic, complemented
18C2×#11929612C2211yescharacteristic, complemented
19C2×#11929611C2211yescharacteristic, complemented
20C2×#11929609C2211yescharacteristic, complemented
21C2×#11929608C2211yescharacteristic
22C2×#11929608C2211yescharacteristic
23#14579144—21no—
24#14579140C2211yescharacteristic
25#14579140C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579135C2211yescharacteristic
28#14579130—21no—
29C4×C22⋊D79—21no—
30C4×C22⋊D79—21no—
31#14579120C2211yescharacteristic
32#14579094C2211yescharacteristic, complemented
33#14579094C2211yescharacteristic, complemented
34#14579092C2211yescharacteristic, complemented
35#14579092C2211yescharacteristic, complemented
36#14579085C2211yescharacteristic, complemented
37#14579085C2211yescharacteristic, complemented
38#14579084C2211yescharacteristic, complemented
39#14579084C2211yescharacteristic, complemented
40#14579082C2211yescharacteristic, complemented
41#14579082C2211yescharacteristic, complemented
42#14579081C2211yescharacteristic, complemented
43#14579081C2211yescharacteristic, complemented
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C23×C4×C79C2211yescharacteristic
50#123×C79—21no—
51C22⋊Q8×C79C2211yescharacteristic
52C22⋊Q8×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic
55#120×C79—21no—
56C4×D4×C79—21no—
57C4×D4×C79—21no—
58#117×C79C2211yescharacteristic
59#11929624—41no—
60#11929624—41no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C4×D79—21no—
67#11929614—41no—
68#11929612—41no—
69#11929611—41no—
70#11929609—41no—
71#11929608—41no—
72#11929608—41no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86C4×Dic79—21no—
87C24×C79D411yescharacteristic
88#41×C79—41no—
89#41×C79—41no—
90C2×Q8×C79C2311yescharacteristic
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79—21no—
94C2×D4×C79C2311yescharacteristic
95C22×C4×C79—21no—
96C22×C4×C79—41no—
97C22×C4×C79—41no—
98C22×C4×C79D411yescharacteristic
99C22×C4×C79D411yescharacteristic
100C22×C4×C79D411yescharacteristic
101C22×C4×C79C2311yescharacteristic
102C22×C4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C4⋊C4×C79—21no—
105C4⋊C4×C79—21no—
106C4⋊C4×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×C79—21no—
114C23×C79—21no—
115C23×C79—41no—
116C23×C79—41no—
117C23×C79—41no—
118C23×C79C2×D411yescharacteristic
119C23×C79C2×D411yescharacteristic
120C23×C79C2×D411yescharacteristic
121C22×D79—21no—
122Q8×C79—21no—
123Q8×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—42no—
127D4×C79—42no—
128D4×C79—42no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—41no—
139C2×C4×C79—41no—
140C2×C4×C79—41no—
141C2×C4×C79—42no—
142C2×C4×C79C2×D411yescharacteristic
143C2×C4×C79C2×D411yescharacteristic
144C2×C4×C79C2×D411yescharacteristic
145C2×C4×C79C2411yescharacteristic
146C22⋊D79—42no—
147C22⋊D79—42no—
148C22⋊D79—42no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152D316—21no—
153D316—21no—
154C4×D79—42no—
155Dic158—21no—
156Dic158—21no—
157C79⋊C8—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—44no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79C22×D411yescharacteristic
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—21no—
181C4×C79—41no—
182C4×C79—41no—
183C4×C79—41no—
184C4×C79H(5,𝔽2)11yescharacteristic
185C4×C79H(5,𝔽2)11yescharacteristic
186Dic79—41no—
187Dic79—41no—
188Dic79—41no—
189C2×C79—41no—
190C2×C79—41no—
191C2×C79—41no—
192C2×C79—81no—
193C2×C79#53411yescharacteristic
194C2×C79#57511yescharacteristic
195C2×C79#57511yescharacteristic
196D79—81no—
197#3197—791nomaximal, Sylow
198C79#319711yescharacteristic, complemented, Sylow
199#525—791no—
200#525D7911yescharacteristic, complemented
201#485—791no—
202#485—791no—
203#482—791no—
204#482—791no—
205#470—791no—
206#469—791no—
207#468—791no—
208#468—791no—
209#452—791no—
210#452—791no—
211#449—791no—
212#449—791no—
213#407—791no—
214C2×#41—791no—
215C2×#41C2×D7911yescharacteristic
216C23×C4C2×D7911yescharacteristic
217C2×Q16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C2×D8—791no—
221C2×M16—791no—
222C2×M16—791no—
223#123—21no—
224#123—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227C22⋊Q8C2×D7911yescharacteristic
228C22⋊Q8C2×D7911yescharacteristic
229#121—791no—
230#121—791no—
231#121C2×D7911yescharacteristic
232#121C2×D7911yescharacteristic
233#120—21no—
234#120—1581no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—1581no—
238C4×D4—1581no—
239#117—791no—
240#117C2×D7911yescharacteristic
241#107—791no—
242#107—791no—
243#106—791no—
244#106—791no—
245#103—791no—
246#103—791no—
247#103—791no—
248#103—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252#102—791no—
253C22⋊C8—791no—
254C22⋊C8—791no—
255C22⋊C8—791no—
256C22⋊C8—791no—
257C24C22⋊D7911yescharacteristic
258#41—41no—
259#41—41no—
260#41—3161no—
261#41—3161no—
262C2×Q8—791no—
263C2×Q8C22×D7911yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—791no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4C22×D7911yescharacteristic
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—1581no—
276C22×C4C22⋊D7911yescharacteristic
277C22×C4C22⋊D7911yescharacteristic
278C22×C4C22⋊D7911yescharacteristic
279C22×C4C22×D7911yescharacteristic
280C22×C4C22×D7911yescharacteristic
281C22×C4C22×D7911yescharacteristic
282Q16—3161no—
283SD16—3161no—
284SD16—3161no—
285D8—3161no—
286M16—3161no—
287M16—3161no—
288C2×C8—791no—
289C2×C8—791no—
290C2×C8—791no—
291C2×C8—791no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—791no—
295C4⋊C4—791no—
296C4⋊C4—1581no—
297C4⋊C4—1581no—
298C4⋊C4C22×D7911yescharacteristic
299C4⋊C4C22×D7911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C42—21no—
311C42—1581no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—1581no—
317C23C2×C22⋊D7911yescharacteristic
318C23C2×C22⋊D7911yescharacteristic
319C23C2×C22⋊D7911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—3162no—
330D4—3162no—
331D4—3162no—
332D4—1581no—
333D4—1581no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—3162no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4C2×C22⋊D7911yescharacteristic
352C2×C4C2×C22⋊D7911yescharacteristic
353C2×C4C2×C22⋊D7911yescharacteristic
354C2×C4C23×D7911yescharacteristic
355C8—1581no—
356C8—1581no—
357C8—1581no—
358C8—1581no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—3161no—
373C22—3161no—
374C22—3161no—
375C22C22×C22⋊D7911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3161no—
383C4—3161no—
384C4—3161no—
385C4#1457920611yescharacteristic
386C4#1457920611yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—6321no—
392C2#1909912211yescharacteristic
393C2#1909936111yescharacteristic
394C2#1909936111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#525×C79C2
socleC22×C79C22×D4
hypercenter#525D79
hypocenterC79#3197
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #19099074C2semidirect
2. #19098904C2semidirect
3. #19098901C2semidirect
4. #19098887C2semidirect
5. #19098884C2semidirect
6. #19098819C2semidirect
7. #19098814C2semidirect
8. #19098811C2semidirect
9. #19098807C2semidirect
10. #19098725C2semidirect
11. #19098723C2semidirect
12. #19098708C2semidirect
13. #19098706C2semidirect
14. #19098527C2semidirect
15. #525×C79C2semidirect
17. C2×#11929614C22semidirect
18. C2×#11929612C22semidirect
19. C2×#11929611C22semidirect
20. C2×#11929609C22semidirect
32. #14579094C22semidirect
33. #14579094C22semidirect
34. #14579092C22semidirect
35. #14579092C22semidirect
36. #14579085C22semidirect
37. #14579085C22semidirect
38. #14579084C22semidirect
39. #14579084C22semidirect
40. #14579082C22semidirect
41. #14579082C22semidirect
42. #14579081C22semidirect
43. #14579081C22semidirect
198. C79#3197semidirect
200. #525D79semidirect