Finite Group Databasebeta

← #23775416

Subgroups — #23775416

Order 10112.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099247C211yesmaximal, characteristic, complemented
2#19099197C211yesmaximal, characteristic
3#19098926C211yesmaximal, characteristic, complemented
4#19098884C211yesmaximal, characteristic, complemented
5#19098878C211yesmaximal, characteristic, complemented
6#19098866C211yesmaximal, characteristic, complemented
7#19098795C211yesmaximal, characteristic, complemented
8#19098761C211yesmaximal, characteristic, complemented
9#19098713C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11#19098666C211yesmaximal, characteristic, complemented
12#19098632C211yesmaximal, characteristic, complemented
13#19098569C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic, complemented
21C2×C8×D79C2211yescharacteristic, complemented
22#14579157C2211yescharacteristic
23#14579154—21no—
24#14579152C2211yescharacteristic, complemented
25#14579151—21no—
26#14579143—21no—
27#14579137C2211yescharacteristic, complemented
28#14579136C2211yescharacteristic
29#14579134—21no—
30#14579131—21no—
31#14579129—21no—
32Q8×Dic79C2211yescharacteristic, complemented
33#14579123C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35#14579120C2211yescharacteristic, complemented
36#14579119—21no—
37C4⋊C4×D79C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579092C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579083C2211yescharacteristic
42#14579083C2211yescharacteristic
43#14579083C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic, complemented
53C2×M16×C79C2211yescharacteristic, complemented
54C22⋊Q8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×D316—21no—
62C2×D316—22no—
63C2×D316—21no—
64C2×D316—41no—
65C2×D316C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79D411yescharacteristic
71D4×D79—22no—
72D4×D79—44no—
73D4×D79—41no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79C2311yescharacteristic
77#11929611—22no—
78#11929611—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C8×D79—41no—
82C4⋊Dic79—21no—
83C4⋊Dic79—21no—
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4D411yescharacteristic
90C22⋊Dic79—21no—
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96C4×Dic79—21no—
97C4×Dic79—21no—
98C4×Dic79C2311yescharacteristic
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79C2311yescharacteristic
103SD16×C79—41no—
104M16×C79—41no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79—81no—
121C22×D79—81no—
122C22×D79C2×D411yescharacteristic
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—42no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—22no—
136C22⋊D79—42no—
137C22⋊D79—42no—
138C22⋊D79—81no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143C2×Dic79C2×D411yescharacteristic
144D316—21no—
145D316—21no—
146D316—21no—
147D316—42no—
148D316—42no—
149D316#4112yes—
150C4×D79—21no—
151C4×D79—21no—
152C4×D79—42no—
153C4×D79—42no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—22no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—84no—
174C2×D79—84no—
175C2×D79AGL(1,ℤ/8)12yes—
176C4×C79—21no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79C2×#4111yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—21no—
183Dic79—21no—
184Dic79—21no—
185Dic79—41no—
186Dic79—41no—
187C2×C79—41no—
188C2×C79—81no—
189C2×C79#54611yescharacteristic
190C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C79#57711yescharacteristic
192D79—22no—
193D79—42no—
194D79—81no—
195#3310—791nomaximal, Sylow
196C79#331011yescharacteristic, complemented, Sylow
197#552—791no—
198D42—791no—
199#490—791no—
200#482—791no—
201#480—791no—
202#478—791no—
203#468D7911yescharacteristic, complemented
204#465—791no—
205#460—791no—
206#450—791no—
207#450—791no—
208#440—791no—
209#435—791no—
210#418—791no—
211C2×#102—791no—
212C22×D4—791no—
213C22×D4—791no—
214C22×D4—1581no—
215C2×SD16—791no—
216C2×SD16—791no—
217C2×SD16C2×D7911yescharacteristic, complemented
218C2×M16C2×D7911yescharacteristic, complemented
219C22×C8—791no—
220#127—791no—
221#126—1581no—
222#125—791no—
223#125—1581no—
224#123—1581no—
225C22⋊Q8—791no—
226C22⋊Q8C2×D7911yescharacteristic, complemented
227#121—791no—
228#121—1581no—
229#121C2×D7911yescharacteristic
230#120—1581no—
231#120—1581no—
232C4×Q8—791no—
233C4×D4—791no—
234C4×D4—791no—
235#117—791no—
236#117—1581no—
237C2×C4⋊C4—791no—
238#107—791no—
239#107C2×D7911yescharacteristic, complemented
240#106—791no—
241C4⋊C8—791no—
242#103C2×D7911yescharacteristic, complemented
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102C2×D7911yescharacteristic, complemented
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97—791no—
255C24—1581no—
256C24—1581no—
257C2×Q8C22×D7911yescharacteristic
258C2×D4—21no—
259C2×D4—3161no—
260C2×D4—3164no—
261C2×D4—3161no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—791no—
265C2×D4—1581no—
266C2×D4—1582no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1582no—
271C2×D4—1581no—
272C2×D4C22×D7911yescharacteristic
273C22×C4—791no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277SD16—41no—
278SD16—3161no—
279SD16—1582no—
280M16—41no—
281C2×C8—3161no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4C22×D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—791no—
300C22⋊C4—791no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C42—791no—
306C42—1581no—
307C42—1581no—
308C23—21no—
309C23—3162no—
310C23—3162no—
311C23—3162no—
312C23—3162no—
313C23—791no—
314C23—6321no—
315C23—6321no—
316C23—1581no—
317C23—1581no—
318C23D4×D7911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—3162no—
325D4—3162no—
326D4—3162no—
327D4—3162no—
328D4—792no—
329D4—6321no—
330D4—1582no—
331D4—1581no—
332D4—1581no—
333D4—1581no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—3162no—
340C2×C4—3162no—
341C2×C4—791no—
342C2×C4—791no—
343C2×C4—791no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4D4×D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1581no—
353C8—1581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—792no—
366C22—6324no—
367C22—6324no—
368C22—1582no—
369C22—1581no—
370C22—1581no—
371C22C2×D4×D7911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—3161no—
377C4—3161no—
378C4—1581no—
379C4—1581no—
380C4—1581no—
381C4#41×D7911yescharacteristic
382C4#1457920611yescharacteristic
383C2—41no—
384C2—81no—
385C2—3162no—
386C2—6321no—
387C2—1582no—
388C2#1909920211yescharacteristic
389C2AGL(1,ℤ/8)×D7911yescharacteristic
390C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
prime radical#19099197C2
hypercenter#468D79
hypocenterC79#3310
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #19099247C2semidirect
3. #19098926C2semidirect
4. #19098884C2semidirect
5. #19098878C2semidirect
6. #19098866C2semidirect
7. #19098795C2semidirect
8. #19098761C2semidirect
9. #19098713C2semidirect
10. #19098712C2semidirect
11. #19098666C2semidirect
12. #19098632C2semidirect
13. #19098569C2semidirect
14. #102×D79C2semidirect
15. #468×C79C2semidirect
20. C2×#11929611C22semidirect
21. C2×C8×D79C22semidirect
24. #14579152C22semidirect
27. #14579137C22semidirect
32. Q8×Dic79C22semidirect
35. #14579120C22semidirect
37. C4⋊C4×D79C22semidirect
38. #14579094C22semidirect
39. #14579092C22semidirect
40. Dic79⋊C8C22semidirect
43. #14579083C22semidirect
44. #14579083C22semidirect
45. #14579082C22semidirect
46. #14579082C22semidirect
48. #14579081C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579071C22semidirect
52. C2×SD16×C79C22semidirect
53. C2×M16×C79C22semidirect
54. C22⋊Q8×C79C22semidirect
56. #107×C79C22semidirect
57. #103×C79C22semidirect
58. #102×C79C22semidirect
196. C79#3310semidirect
203. #468D79semidirect
217. C2×SD16C2×D79semidirect
218. C2×M16C2×D79semidirect
226. C22⋊Q8C2×D79semidirect
239. #107C2×D79semidirect
242. #103C2×D79semidirect
251. #102C2×D79semidirect