Finite Group Databasebeta

← #23775619

Subgroups — #23775619

Order 10112.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099248C211yesmaximal, characteristic, complemented
2#19099210C211yesmaximal, characteristic
3#19098916C211yesmaximal, characteristic, complemented
4#19098907C211yesmaximal, characteristic, complemented
5#19098862C211yesmaximal, characteristic, complemented
6#19098822C211yesmaximal, characteristic, complemented
7#19098807C211yesmaximal, characteristic, complemented
8#19098784C211yesmaximal, characteristic, complemented
9#19098727C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098650C211yesmaximal, characteristic, complemented
12#19098638C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098562C211yesmaximal, characteristic, complemented
15#481×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929608C2211yescharacteristic, complemented
22C2×#11929607C2211yescharacteristic
23#14579156—21no—
24#14579152C2211yescharacteristic, complemented
25#14579151—21no—
26#14579148C2211yescharacteristic
27#14579144—21no—
28#14579143—21no—
29#14579141C2211yescharacteristic
30#14579141C2211yescharacteristic
31#14579140C2211yescharacteristic, complemented
32#14579132—21no—
33#14579129—21no—
34#14579126C2211yescharacteristic, complemented
35#14579123C2211yescharacteristic
36C4×C22⋊D79C2211yescharacteristic
37#14579120—21no—
38#14579119C2211yescharacteristic
39C22⋊C4×D79—21no—
40#14579094C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic, complemented
52#121×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic, complemented
54#106×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
63C2×Dic158C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79D411yescharacteristic
68D4×D79—22no—
69D4×D79—41no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73Dic316—41no—
74#11929613—22no—
75#11929612—41no—
76#11929608—41no—
77#11929607—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79—21no—
81C4⋊Dic79—21no—
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4D411yescharacteristic
97C4×Dic79—21no—
98C4×Dic79—21no—
99C4×Dic79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—42no—
115C22×D79—42no—
116C22×D79—81no—
117C22×D79C2×D411yescharacteristic
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—81no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—42no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—41no—
130C22⋊D79—42no—
131C22⋊D79—42no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316#4112yes—
140C4×D79—21no—
141C4×D79—21no—
142C4×D79—42no—
143C4×D79—81no—
144Dic158—21no—
145Dic158—21no—
146Dic158—21no—
147Dic158—21no—
148C8×C79—21no—
149C8×C79—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79C22×D411yescharacteristic
159C2×D79—22no—
160C2×D79—21no—
161C2×D79—21no—
162C2×D79—21no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—84no—
166C4×C79—21no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79—41no—
170C4×C79C2×#4111yescharacteristic
171C4×C79H(5,𝔽2)11yescharacteristic
172Dic79—21no—
173Dic79—21no—
174Dic79—21no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178C2×C79—41no—
179C2×C79—81no—
180C2×C79#54611yescharacteristic
181C2×C79#57511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—41no—
184D79—42no—
185#3323—791nomaximal, Sylow
186C79#332311yescharacteristic, complemented, Sylow
187#552—791no—
188#546—791no—
189#488—791no—
190#485—791no—
191#481D7911yescharacteristic, complemented
192#478—791no—
193#470—791no—
194#468—791no—
195#464—791no—
196#452—791no—
197#450—791no—
198C4×SD16—791no—
199#436—791no—
200#418—791no—
201#417—791no—
202C2×#41—791no—
203C22×D4—791no—
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16—791no—
207C2×M16—791no—
208C2×M16—791no—
209#126—1581no—
210#125—791no—
211#125—1581no—
212#124—791no—
213#123—1581no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—791no—
218#121—1581no—
219#121C2×D7911yescharacteristic
220#120—1581no—
221C4×Q8—791no—
222C4×D4—791no—
223C4×D4—791no—
224#117—791no—
225#117—1581no—
226C2×C4⋊C4C2×D7911yescharacteristic, complemented
227C2×C22⋊C4—1581no—
228#107—791no—
229#106C2×D7911yescharacteristic, complemented
230#106C2×D7911yescharacteristic, complemented
231C4⋊C8—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102C2×D7911yescharacteristic
241#102C2×D7911yescharacteristic
242C22⋊C8—791no—
243C22⋊C8C2×D7911yescharacteristic, complemented
244C4×C8—791no—
245C24—1581no—
246#41—3161no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8—791no—
250C2×D4—21no—
251C2×D4—3161no—
252C2×D4—791no—
253C2×D4—791no—
254C2×D4—1581no—
255C2×D4—1582no—
256C2×D4—1581no—
257C2×D4C22×D7911yescharacteristic
258C22×C4—21no—
259C22×C4—791no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—3161no—
265SD16—1582no—
266M16—3161no—
267M16—3161no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8C22×D7911yescharacteristic
271C2×C8C22×D7911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4C22×D7911yescharacteristic
282C4⋊C4C22×D7911yescharacteristic
283C4⋊C4C22×D7911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—791no—
286C22⋊C4—791no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C42—791no—
295C42—1581no—
296C42—1581no—
297C23—21no—
298C23—3162no—
299C23—3162no—
300C23—791no—
301C23—6321no—
302C23—1581no—
303C23D4×D7911yescharacteristic
304Q8—1581no—
305Q8—1581no—
306Q8—1581no—
307Q8—1581no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—3162no—
312D4—3161no—
313D4—3162no—
314D4—792no—
315D4—1581no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—3162no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—791no—
326C2×C4—6321no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4D4×D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1581no—
337C8—1581no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—3161no—
345C22—3161no—
346C22—6324no—
347C22—1582no—
348C22—1581no—
349C22—1581no—
350C22—1581no—
351C22C2×D4×D7911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—1581no—
360C4—1581no—
361C4—1581no—
362C4#41×D7911yescharacteristic
363C4#1457920711yescharacteristic
364C2—41no—
365C2—81no—
366C2—3162no—
367C2—3161no—
368C2#1909920511yescharacteristic
369C2#1909935911yescharacteristic
370C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#481×C79C2
socleC22×C79C22×D4
prime radical#19099210C2
hypercenter#481D79
hypocenterC79#3323
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #19099248C2semidirect
3. #19098916C2semidirect
4. #19098907C2semidirect
5. #19098862C2semidirect
6. #19098822C2semidirect
7. #19098807C2semidirect
8. #19098784C2semidirect
9. #19098727C2semidirect
10. #19098715C2semidirect
11. #19098650C2semidirect
12. #19098638C2semidirect
13. #19098566C2semidirect
14. #19098562C2semidirect
15. #481×C79C2semidirect
18. C2×Dic316C22semidirect
21. C2×#11929608C22semidirect
24. #14579152C22semidirect
31. #14579140C22semidirect
34. #14579126C22semidirect
40. #14579094C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
44. #14579084C22semidirect
45. #14579084C22semidirect
51. C8×Dic79C22semidirect
53. C2×C4⋊C4×C79C22semidirect
54. #106×C79C22semidirect
55. #106×C79C22semidirect
58. C22⋊C8×C79C22semidirect
186. C79#3323semidirect
191. #481D79semidirect
226. C2×C4⋊C4C2×D79semidirect
229. #106C2×D79semidirect
230. #106C2×D79semidirect
243. C22⋊C8C2×D79semidirect