Finite Group Databasebeta

← #23775627

Subgroups — #23775627

Order 10112.

448 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#19099281C211yesmaximal, characteristic, complemented
2D4×C22⋊D79C211yesmaximal, characteristic
3#19098908C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098885C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098809C211yesmaximal, characteristic, complemented
8#19098808C211yesmaximal, characteristic, complemented
9#19098762C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098714C211yesmaximal, characteristic, complemented
12#19098654C211yesmaximal, characteristic, complemented
13#19098639C211yesmaximal, characteristic, complemented
14#19098566C211yesmaximal, characteristic, complemented
15#418×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79—21no—
17C2×D4×D79C2211yescharacteristic
18C2×#11929613C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic
20C2×#11929612C2211yescharacteristic, complemented
21C2×#11929607C2211yescharacteristic, complemented
22#14579160C2211yescharacteristic, complemented
23#14579157C2211yescharacteristic
24#14579155—21no—
25#14579154—21no—
26#14579147—21no—
27#14579141C2211yescharacteristic, complemented
28#14579140C2211yescharacteristic, complemented
29#14579135C2211yescharacteristic
30#14579133—21no—
31#14579132C2211yescharacteristic
32#14579130—21no—
33#14579129—21no—
34C4×Dic158—21no—
35#14579126C2211yescharacteristic, complemented
36D4×Dic79C2211yescharacteristic
37C4×C22⋊D79C2211yescharacteristic
38#14579119C2211yescharacteristic, complemented
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic, complemented
54#117×C79C2211yescharacteristic, complemented
55#102×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—44no—
69C2×C22⋊D79D411yescharacteristic
70D4×D79—22no—
71D4×D79—41no—
72C22×Dic79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929613—41no—
75#11929612—22no—
76#11929612—41no—
77#11929607—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C24×C79—21no—
99C2×D4×C79—22no—
100C2×D4×C79—21no—
101C2×D4×C79—41no—
102C2×D4×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105M16×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C42×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—42no—
115C23×C79—42no—
116C23×C79—81no—
117C23×C79C2×D411yescharacteristic
118C22×D79—21no—
119C22×D79—42no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79C2×D411yescharacteristic
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—42no—
127D4×C79#4112yes—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—22no—
135C22⋊D79—42no—
136C22⋊D79—42no—
137C22⋊D79—42no—
138C22⋊D79—42no—
139C22⋊D79—81no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—42no—
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147D316—21no—
148D316—21no—
149C4×D79—21no—
150C4×D79—21no—
151Dic158—21no—
152Dic158—21no—
153Dic158—42no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—22no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—84no—
168C22×C79C22×D411yescharacteristic
169C2×D79—21no—
170C2×D79—21no—
171C2×D79—21no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—84no—
176C4×C79—21no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79C2×#4111yescharacteristic
180C4×C79H(5,𝔽2)11yescharacteristic
181Dic79—21no—
182Dic79—21no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186Dic79AGL(1,ℤ/8)12yes—
187C2×C79—42no—
188C2×C79—41no—
189C2×C79—81no—
190C2×C79#54611yescharacteristic
191C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C79#57711yescharacteristic
193D79—41no—
194D79—81no—
195#3324—791nomaximal, Sylow
196C79#332411yescharacteristic, complemented, Sylow
197#556—791no—
198D42—791no—
199#486—791no—
200#482—791no—
201#482—791no—
202#474—791no—
203#468—791no—
204#468—791no—
205#460—791no—
206#450—791no—
207#450—791no—
208C4×SD16—791no—
209#436—791no—
210#418—791no—
211#418D7911yescharacteristic, complemented
212C22×D4—791no—
213C22×D4—1581no—
214C22×D4C2×D7911yescharacteristic
215C2×SD16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×M16—791no—
219C2×M16C2×D7911yescharacteristic, complemented
220C4⋊Q8—791no—
221#127—791no—
222#126—1581no—
223#126—1581no—
224#124—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231#120—1581no—
232C4×Q8—791no—
233C4×Q8—1581no—
234C4×D4—791no—
235C4×D4—791no—
236#117—791no—
237#117C2×D7911yescharacteristic, complemented
238#107—791no—
239#107—791no—
240#106—791no—
241C4⋊C8—791no—
242#103—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102C2×D7911yescharacteristic
249#102C2×D7911yescharacteristic
250#102C2×D7911yescharacteristic, complemented
251#102C2×D7911yescharacteristic, complemented
252C22⋊C8—791no—
253C22⋊C8—791no—
254C4×C8—791no—
255C24—21no—
256C24—1581no—
257C2×Q8—791no—
258C2×Q8—1581no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—3164no—
263C2×D4—3161no—
264C2×D4—791no—
265C2×D4—791no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1582no—
272C2×D4C22×D7911yescharacteristic
273C2×D4C22×D7911yescharacteristic
274C22×C4—791no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277SD16—3161no—
278SD16—3161no—
279SD16—1582no—
280M16—41no—
281M16—3161no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C4⋊C4—791no—
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—1581no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4C22×D7911yescharacteristic
294C4⋊C4C22×D7911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—791no—
297C22⋊C4—791no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C42—21no—
305C42—791no—
306C42—1581no—
307C42—1581no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—3162no—
314C23—3162no—
315C23—791no—
316C23—6321no—
317C23—1581no—
318C23D4×D7911yescharacteristic
319Q8—3162no—
320Q8—1581no—
321Q8—1581no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—3162no—
327D4—3162no—
328D4—3162no—
329D4—3162no—
330D4—6321no—
331D4—1582no—
332D4—1581no—
333D4—1581no—
334D4#1192962412yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—3162no—
340C2×C4—791no—
341C2×C4—791no—
342C2×C4—791no—
343C2×C4—1581no—
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—22no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—6324no—
368C22—1581no—
369C22—1581no—
370C22—1581no—
371C22C2×D4×D7911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—3161no—
376C4—3161no—
377C4—3161no—
378C4—792no—
379C4—1581no—
380C4—1581no—
381C4C2×#1192962411yescharacteristic
382C4#1457920611yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—3161no—
387C2—6321no—
388C2#1909920311yescharacteristic
389C2AGL(1,ℤ/8)×D7911yescharacteristic
390C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#418×C79C2
socleC22×C79C22×D4
prime radicalD4×C22⋊D79C2
hypercenter#418D79
hypocenterC79#3324
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #19099281C2semidirect
3. #19098908C2semidirect
4. #19098887C2semidirect
5. #19098885C2semidirect
6. #19098841C2semidirect
7. #19098809C2semidirect
8. #19098808C2semidirect
9. #19098762C2semidirect
10. #19098715C2semidirect
11. #19098714C2semidirect
12. #19098654C2semidirect
13. #19098639C2semidirect
14. #19098566C2semidirect
15. #418×C79C2semidirect
18. C2×#11929613C22semidirect
20. C2×#11929612C22semidirect
21. C2×#11929607C22semidirect
22. #14579160C22semidirect
27. #14579141C22semidirect
28. #14579140C22semidirect
35. #14579126C22semidirect
38. #14579119C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579092C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579083C22semidirect
46. #14579082C22semidirect
47. #14579081C22semidirect
48. #14579081C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
53. C2×M16×C79C22semidirect
54. #117×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
196. C79#3324semidirect
211. #418D79semidirect
219. C2×M16C2×D79semidirect
237. #117C2×D79semidirect
250. #102C2×D79semidirect
251. #102C2×D79semidirect