Finite Group Databasebeta

← #23774270

Subgroups — #23774270

Order 10112.

410 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#19099137C211yesmaximal, characteristic, complemented
2#19099129C211yesmaximal, characteristic
3#19098903C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098888C211yesmaximal, characteristic, complemented
6#19098884C211yesmaximal, characteristic, complemented
7#19098812C211yesmaximal, characteristic, complemented
8#19098806C211yesmaximal, characteristic, complemented
9#19098795C211yesmaximal, characteristic, complemented
10#19098789C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098712C211yesmaximal, characteristic, complemented
13#19098702C211yesmaximal, characteristic, complemented
14#19098528C211yesmaximal, characteristic, complemented
15#448×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929607C2211yescharacteristic, complemented
21C2×C8×D79C2211yescharacteristic, complemented
22#14579159—21no—
23#14579157—21no—
24#14579150—21no—
25#14579147—21no—
26#14579144—21no—
27#14579144—21no—
28#14579137C2211yescharacteristic
29#14579137C2211yescharacteristic
30#14579137C2211yescharacteristic, complemented
31#14579137C2211yescharacteristic, complemented
32#14579136C2211yescharacteristic
33#14579135C2211yescharacteristic
34#14579132C2211yescharacteristic
35#14579131—21no—
36#14579129—21no—
37#14579120C2211yescharacteristic, complemented
38#14579119C2211yescharacteristic
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C22×Q8×C79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—41no—
61#11929624—41no—
62C2×Dic158D411yescharacteristic
63C2×D316—21no—
64C2×D316D411yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79D411yescharacteristic
70C2×C22⋊D79D411yescharacteristic
71D4×D79—41no—
72D4×D79—41no—
73C2×C4×D79C2311yescharacteristic
74C2×C4×D79C2311yescharacteristic
75#11929611—41no—
76#11929611—41no—
77#11929607—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C8×D79—41no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97C4×Dic79—21no—
98C4×Dic79—21no—
99C2×Q8×C79—21no—
100C2×Q8×C79—41no—
101C2×Q8×C79—41no—
102C2×Q8×C79C2311yescharacteristic
103C2×Q8×C79C2311yescharacteristic
104C2×D4×C79—21no—
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79—21no—
107C22×C4×C79C2311yescharacteristic
108SD16×C79—41no—
109SD16×C79—41no—
110C2×C8×C79C2311yescharacteristic
111C2×C8×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79C2×D411yescharacteristic
116C22×D79—21no—
117C22×D79—42no—
118C22×D79—81no—
119C22×D79—81no—
120C22×D79C2×D411yescharacteristic
121C22×D79C2×D411yescharacteristic
122Q8×C79—21no—
123Q8×C79—21no—
124Q8×C79—21no—
125Q8×C79—21no—
126Q8×C79—42no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—81no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—42no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2411yescharacteristic
138C22⋊D79—41no—
139C22⋊D79—41no—
140C22⋊D79—42no—
141C22⋊D79—81no—
142C22⋊D79—81no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148D316—21no—
149D316—21no—
150D316—41no—
151D316—81no—
152C4×D79—21no—
153C4×D79—21no—
154C4×D79—21no—
155C4×D79—21no—
156Dic158—41no—
157C8×C79—21no—
158C8×C79—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79C22×D411yescharacteristic
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—21no—
171C2×D79—21no—
172C2×D79—21no—
173C2×D79—21no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—84no—
178C4×C79—21no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79—41no—
182C4×C79H(5,𝔽2)11yescharacteristic
183C4×C79H(5,𝔽2)11yescharacteristic
184Dic79—21no—
185Dic79—21no—
186Dic79—41no—
187Dic79—41no—
188Dic79—41no—
189C2×C79—41no—
190C2×C79—81no—
191C2×C79#53411yescharacteristic
192C2×C79#57711yescharacteristic
193C2×C79#57711yescharacteristic
194D79—41no—
195D79—41no—
196D79—81no—
197#3200—791nomaximal, Sylow
198C79#320011yescharacteristic, complemented, Sylow
199#536—791no—
200#535—791no—
201#485—791no—
202#485—791no—
203#482—791no—
204#482—791no—
205#468—791no—
206#468—791no—
207#465—791no—
208#465—791no—
209#450—791no—
210#450—791no—
211#448—791no—
212#448D7911yescharacteristic, complemented
213#408—791no—
214C2×#41—791no—
215C22×Q8C2×D7911yescharacteristic, complemented
216C22×D4—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16C2×D7911yescharacteristic
220C2×SD16C2×D7911yescharacteristic
221C2×M16—791no—
222C22×C8—791no—
223C4⋊Q8—1581no—
224#127—1581no—
225#124—1581no—
226#124—1581no—
227#123—1581no—
228#123—1581no—
229C22⋊Q8—791no—
230C22⋊Q8—791no—
231C22⋊Q8—791no—
232C22⋊Q8—791no—
233#121—791no—
234#121—791no—
235#121—791no—
236#121C2×D7911yescharacteristic
237#120—1581no—
238#120—1581no—
239#117—791no—
240#117—791no—
241#107—791no—
242#107—791no—
243#106—791no—
244#106—791no—
245#103—791no—
246#103—791no—
247#103C2×D7911yescharacteristic, complemented
248#103C2×D7911yescharacteristic, complemented
249#102—791no—
250#102—791no—
251#102—791no—
252#102—791no—
253C22⋊C8—791no—
254C22⋊C8—791no—
255C22⋊C8—791no—
256C22⋊C8C2×D7911yescharacteristic, complemented
257C24—1581no—
258#41—3161no—
259#41—3161no—
260C2×Q8—21no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—791no—
264C2×Q8C22×D7911yescharacteristic
265C2×Q8C22×D7911yescharacteristic
266C2×D4—21no—
267C2×D4—3161no—
268C2×D4—3161no—
269C2×D4—791no—
270C2×D4—791no—
271C2×D4—791no—
272C2×D4—791no—
273C2×D4—1581no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4C22×D7911yescharacteristic
278C22×C4—21no—
279C22×C4—791no—
280C22×C4—791no—
281C22×C4C22×D7911yescharacteristic
282SD16—41no—
283SD16—41no—
284SD16—3161no—
285SD16—3161no—
286M16—3161no—
287C2×C8—3161no—
288C2×C8—791no—
289C2×C8—791no—
290C2×C8C22×D7911yescharacteristic
291C2×C8C22×D7911yescharacteristic
292C4⋊C4—791no—
293C4⋊C4—791no—
294C4⋊C4—791no—
295C4⋊C4—1581no—
296C4⋊C4—1581no—
297C4⋊C4—1581no—
298C4⋊C4—1581no—
299C4⋊C4C22×D7911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C42—1581no—
311C42—1581no—
312C23—21no—
313C23—3162no—
314C23—791no—
315C23—791no—
316C23—6321no—
317C23—6321no—
318C23—1581no—
319C23D4×D7911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—3161no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—3161no—
330D4—3161no—
331D4—3161no—
332D4—3162no—
333D4—6321no—
334D4—6321no—
335D4—6321no—
336D4—1581no—
337D4—1581no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—791no—
345C2×C4—791no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4D4×D7911yescharacteristic
354C2×C4C23×D7911yescharacteristic
355C8—21no—
356C8—21no—
357C8—1581no—
358C8—1581no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22—6324no—
369C22—1581no—
370C22—1581no—
371C22—1581no—
372C22—1581no—
373C22—1581no—
374C22—1581no—
375C22C2×D4×D7911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3161no—
381C4—3161no—
382C4—3161no—
383C4—1581no—
384C4—1581no—
385C4#1457920611yescharacteristic
386C4#1457920611yescharacteristic
387C2—41no—
388C2—81no—
389C2—3161no—
390C2—3161no—
391C2—6321no—
392C2#1909912311yescharacteristic
393C2#1909936911yescharacteristic
394C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#448×C79C2
socleC22×C79C22×D4
prime radical#19099129C2
hypercenter#448D79
hypocenterC79#3200
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #19099137C2semidirect
3. #19098903C2semidirect
4. #19098902C2semidirect
5. #19098888C2semidirect
6. #19098884C2semidirect
7. #19098812C2semidirect
8. #19098806C2semidirect
9. #19098795C2semidirect
10. #19098789C2semidirect
11. #19098712C2semidirect
12. #19098712C2semidirect
13. #19098702C2semidirect
14. #19098528C2semidirect
15. #448×C79C2semidirect
20. C2×#11929607C22semidirect
21. C2×C8×D79C22semidirect
30. #14579137C22semidirect
31. #14579137C22semidirect
37. #14579120C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579093C22semidirect
42. #14579092C22semidirect
43. #14579085C22semidirect
44. #14579085C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
52. C22×Q8×C79C22semidirect
56. #103×C79C22semidirect
57. #103×C79C22semidirect
58. C22⋊C8×C79C22semidirect
198. C79#3200semidirect
212. #448D79semidirect
215. C22×Q8C2×D79semidirect
247. #103C2×D79semidirect
248. #103C2×D79semidirect
256. C22⋊C8C2×D79semidirect