Finite Group Databasebeta

← #23773497

Subgroups — #23773497

Order 10112.

444 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099117C211yesmaximal, characteristic, complemented
2C4×D4×D79C211yesmaximal, characteristic
3#19098900C211yesmaximal, characteristic, complemented
4#19098897C211yesmaximal, characteristic, complemented
5#19098842C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098767C211yesmaximal, characteristic, complemented
8#19098766C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic
10#19098712C211yesmaximal, characteristic
11#19098665C211yesmaximal, characteristic, complemented
12#19098663C211yesmaximal, characteristic, complemented
13#19098661C211yesmaximal, characteristic, complemented
14#19098618C211yesmaximal, characteristic, complemented
15#440×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C22×C4×D79—21no—
18C2×#11929613C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21#14579160C2211yescharacteristic, complemented
22#14579159C2211yescharacteristic, complemented
23#14579151—21no—
24#14579141C2211yescharacteristic
25#14579139—21no—
26#14579137C2211yescharacteristic
27C4×Dic158—21no—
28C4×Dic158C2211yescharacteristic, complemented
29C4×D316C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31#14579123C2211yescharacteristic
32C4×C22⋊D79—21no—
33(C22⋊D79)⋊C4—21no—
34#14579118—21no—
35C4⋊C4×D79C2211yescharacteristic
36C22⋊C4×D79—21no—
37C42×D79C2211yescharacteristic
38#14579095C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579072C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic
53C4×Q8×C79C2211yescharacteristic, complemented
54C4×D4×C79C2211yescharacteristic
55#107×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64D4×D79—22no—
65D4×D79—22no—
66C22×Dic79—21no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—44no—
71C2×C4×D79D411yescharacteristic
72C2×C4×D79D411yescharacteristic
73C2×C4×D79C2311yescharacteristic
74#11929613—22no—
75#11929612—22no—
76#11929611—22no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93C4×Dic79—21no—
94C4×Dic79D411yescharacteristic
95C4×Dic79D411yescharacteristic
96C4×Dic79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79—21no—
100SD16×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79—21no—
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79—21no—
108C42×C79C2311yescharacteristic
109C23×C79—21no—
110C22×D79—24no—
111C22×D79—21no—
112C22×D79—42no—
113C22×D79—42no—
114C22×D79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79—21no—
117D4×C79—21no—
118D4×C79#4112yes—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—42no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C22⋊D79—24no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—42no—
131C2×Dic79C2×D411yescharacteristic
132C2×Dic79C2×D411yescharacteristic
133C2×Dic79C2×D411yescharacteristic
134D316—21no—
135D316#4112yes—
136C4×D79—22no—
137C4×D79—21no—
138C4×D79—21no—
139C4×D79—22no—
140C4×D79—42no—
141C4×D79—42no—
142C4×D79—42no—
143Dic158—21no—
144Dic158—21no—
145Dic158—42no—
146C8×C79—21no—
147C8×C79—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C22×C79—22no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79C22×D411yescharacteristic
154C2×D79—21no—
155C2×D79—21no—
156C2×D79—22no—
157C2×D79—48no—
158C2×D79—41no—
159C2×D79—41no—
160C2×D79#13712yes—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79C2×#4111yescharacteristic
167C4×C79C2×#4111yescharacteristic
168Dic79—21no—
169Dic79—21no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79AGL(1,ℤ/8)12yes—
174C2×C79—42no—
175C2×C79#52511yescharacteristic
176C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
177C2×C79C2×#13711yescharacteristic
178D79—22no—
179D79—42no—
180#3110—791nomaximal, Sylow
181C79#311011yescharacteristic, complemented, Sylow
182#533—791no—
183C2×C4×D4—791no—
184#484—791no—
185#484—791no—
186#474—791no—
187#474—791no—
188#461—791no—
189#461—791no—
190#450—791no—
191#450—791no—
192#440—791no—
193#440—791no—
194#440—791no—
195#440D7911yescharacteristic, complemented
196#432—791no—
197C22×D4—791no—
198C23×C4—1581no—
199C2×SD16—791no—
200C2×SD16—791no—
201C2×SD16—791no—
202C2×SD16C2×D7911yescharacteristic
203C4⋊Q8—791no—
204C4⋊Q8—791no—
205#125—1581no—
206C22⋊Q8—791no—
207C22⋊Q8—791no—
208C22⋊Q8—1581no—
209C4×Q8—791no—
210C4×Q8—1581no—
211C4×Q8C2×D7911yescharacteristic, complemented
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—1581no—
216C4×D4—1581no—
217C4×D4C2×D7911yescharacteristic
218#117—1581no—
219C2×C4⋊C4—791no—
220C2×C22⋊C4—1581no—
221C2×C42—791no—
222#107—791no—
223#107—791no—
224#107—791no—
225#107C2×D7911yescharacteristic, complemented
226C4⋊C8—791no—
227C4⋊C8—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103C2×D7911yescharacteristic, complemented
232#102—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236C22⋊C8—791no—
237C22⋊C8—791no—
238#97—791no—
239#97C2×D7911yescharacteristic, complemented
240C24—1581no—
241C2×Q8—791no—
242C2×Q8—1581no—
243C2×Q8C22×D7911yescharacteristic
244C2×D4—791no—
245C2×D4—1581no—
246C2×D4—1582no—
247C2×D4—1582no—
248C2×D4C22×D7911yescharacteristic
249C22×C4—21no—
250C22×C4—3164no—
251C22×C4—791no—
252C22×C4—791no—
253C22×C4—791no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4—1581no—
258SD16—22no—
259SD16—1582no—
260SD16—1582no—
261SD16—1582no—
262C2×C8—791no—
263C2×C8—791no—
264C2×C8C22×D7911yescharacteristic
265C2×C8C22×D7911yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4C22×D7911yescharacteristic
277C4⋊C4C22×D7911yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C42—21no—
285C42—791no—
286C42—791no—
287C42—791no—
288C42—1581no—
289C42C22×D7911yescharacteristic
290C23—21no—
291C23—3162no—
292C23—3162no—
293C23—791no—
294C23—1584no—
295C23—1581no—
296Q8—21no—
297Q8—21no—
298Q8—3162no—
299Q8—1581no—
300Q8—1581no—
301D4—21no—
302D4—792no—
303D4—1584no—
304D4—1581no—
305D4#1192962412yes—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—3162no—
311C2×C4—3162no—
312C2×C4—3162no—
313C2×C4—3162no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—791no—
317C2×C4—1582no—
318C2×C4—1582no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4D4×D7911yescharacteristic
325C2×C4D4×D7911yescharacteristic
326C2×C4C23×D7911yescharacteristic
327C8—21no—
328C8—21no—
329C8—1581no—
330C8—1581no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—3168no—
335C22—3161no—
336C22—3161no—
337C22—792no—
338C22—1582no—
339C22—1581no—
340C22—1581no—
341C22C2×D4×D7911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3161no—
348C4—3161no—
349C4—3161no—
350C4—792no—
351C4—1581no—
352C4—1581no—
353C4#41×D7911yescharacteristic
354C4C2×#1192962411yescharacteristic
355C2—42no—
356C2—3162no—
357C2—1582no—
358C2#1909907211yescharacteristic
359C2AGL(1,ℤ/8)×D7911yescharacteristic
360C2#137×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#440×C79C2
socleC22×C79C22×D4
prime radicalC2×D4×D79C22
hypercenter#440D79
hypocenterC79#3110
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #19099117C2semidirect
3. #19098900C2semidirect
4. #19098897C2semidirect
5. #19098842C2semidirect
6. #19098841C2semidirect
7. #19098767C2semidirect
8. #19098766C2semidirect
11. #19098665C2semidirect
12. #19098663C2semidirect
13. #19098661C2semidirect
14. #19098618C2semidirect
15. #440×C79C2semidirect
21. #14579160C22semidirect
22. #14579159C22semidirect
28. C4×Dic158C22semidirect
38. #14579095C22semidirect
39. #14579094C22semidirect
40. #14579094C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579085C22semidirect
45. #14579084C22semidirect
51. #14579072C22semidirect
53. C4×Q8×C79C22semidirect
55. #107×C79C22semidirect
56. #103×C79C22semidirect
58. #97×C79C22semidirect
181. C79#3110semidirect
195. #440D79semidirect
211. C4×Q8C2×D79semidirect
225. #107C2×D79semidirect
231. #103C2×D79semidirect
239. #97C2×D79semidirect