Finite Group Databasebeta

← #23774274

Subgroups — #23774274

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#19099139C211yesmaximal, characteristic, complemented
2#19099129C211yesmaximal, characteristic
3#19098907C211yesmaximal, characteristic, complemented
4#19098906C211yesmaximal, characteristic, complemented
5#19098887C211yesmaximal, characteristic, complemented
6#19098810C211yesmaximal, characteristic, complemented
7#19098808C211yesmaximal, characteristic, complemented
8#19098793C211yesmaximal, characteristic, complemented
9#19098791C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098715C211yesmaximal, characteristic, complemented
12#19098704C211yesmaximal, characteristic, complemented
13#19098701C211yesmaximal, characteristic, complemented
14#19098528C211yesmaximal, characteristic, complemented
15#482×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic, complemented
18C2×D4×D79C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21C2×#11929612C2211yescharacteristic
22C2×#11929612C2211yescharacteristic
23C2×#11929607C2211yescharacteristic, complemented
24C2×C8×D79C2211yescharacteristic, complemented
25#14579161—21no—
26#14579157—21no—
27#14579149—21no—
28#14579147—21no—
29#14579145—21no—
30#14579145—21no—
31#14579141C2211yescharacteristic
32#14579141C2211yescharacteristic
33#14579141C2211yescharacteristic, complemented
34#14579141C2211yescharacteristic, complemented
35#14579136C2211yescharacteristic
36#14579135C2211yescharacteristic
37#14579132C2211yescharacteristic
38#14579131—21no—
39#14579129—21no—
40#14579119C2211yescharacteristic
41#14579094C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579084C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52#121×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic, complemented
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—41no—
61#11929624—41no—
62C2×Dic158—21no—
63C2×Dic158—41no—
64C2×Dic158—41no—
65C2×Dic158D411yescharacteristic
66C2×Dic158C2311yescharacteristic
67C2×Dic158C2311yescharacteristic
68C2×D316—21no—
69C2×D316D411yescharacteristic
70C2×D316C2311yescharacteristic
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79D411yescharacteristic
75C2×C22⋊D79D411yescharacteristic
76D4×D79—41no—
77D4×D79—41no—
78C22×Dic79—21no—
79C2×C4×D79C2311yescharacteristic
80C2×C4×D79C2311yescharacteristic
81#11929613—41no—
82#11929613—41no—
83#11929612—41no—
84#11929612—41no—
85#11929607—41no—
86C2×C79⋊C8C2311yescharacteristic
87C2×C79⋊C8C2311yescharacteristic
88C8×D79—41no—
89C4⋊Dic79—21no—
90C4⋊Dic79—21no—
91C4⋊Dic79—21no—
92C4⋊Dic79—21no—
93C4⋊Dic79C2311yescharacteristic
94C22⋊Dic79—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4—21no—
102C4×Dic79—21no—
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×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
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—81no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—41no—
133C22⋊D79—41no—
134C22⋊D79—42no—
135C22⋊D79—81no—
136C22⋊D79—81no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—42no—
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143D316—21no—
144D316—21no—
145D316—41no—
146D316—81no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—21no—
150C4×D79—21no—
151Dic158—21no—
152Dic158—21no—
153Dic158—21no—
154Dic158—21no—
155Dic158—41no—
156Dic158—42no—
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#482D7911yescharacteristic, complemented
205#468—791no—
206#468—791no—
207#465—791no—
208#465—791no—
209#450—791no—
210#450—791no—
211#448—791no—
212#448—791no—
213#408—791no—
214C2×#41—791no—
215C22×Q8—791no—
216C22×D4—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C2×SD16—791no—
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#117C2×D7911yescharacteristic, complemented
241#107—791no—
242#107C2×D7911yescharacteristic, complemented
243#106—791no—
244#106C2×D7911yescharacteristic, complemented
245#103—791no—
246#103—791no—
247#103—791no—
248#103—791no—
249#102—791no—
250#102—791no—
251#102C2×D7911yescharacteristic
252#102C2×D7911yescharacteristic
253C22⋊C8—791no—
254C22⋊C8—791no—
255C22⋊C8—791no—
256C22⋊C8C2×D7911yescharacteristic, complemented
257C24—1581no—
258#41—3161no—
259#41—3161no—
260C2×Q8—3161no—
261C2×Q8—3161no—
262C2×Q8—791no—
263C2×Q8—791no—
264C2×Q8—791no—
265C2×Q8—1581no—
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—791no—
279C22×C4—791no—
280C22×C4—1581no—
281C22×C4C22×D7911yescharacteristic
282SD16—3161no—
283SD16—3161no—
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—1581no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4—1581no—
297C4⋊C4C22×D7911yescharacteristic
298C4⋊C4C22×D7911yescharacteristic
299C4⋊C4C22×D7911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—21no—
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—21no—
311C42—1581no—
312C23—21no—
313C23—3162no—
314C23—791no—
315C23—791no—
316C23—6321no—
317C23—6321no—
318C23—1581no—
319C23D4×D7911yescharacteristic
320Q8—3162no—
321Q8—3161no—
322Q8—1581no—
323Q8—1581no—
324Q8—1581no—
325Q8—1581no—
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—3162no—
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#1457920711yescharacteristic
386C4#1457920711yescharacteristic
387C2—41no—
388C2—81no—
389C2—3161no—
390C2—3161no—
391C2—6321no—
392C2#1909912411yescharacteristic
393C2#1909937011yescharacteristic
394C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#482×C79C2
socleC22×C79C22×D4
prime radical#19099129C2
hypercenter#482D79
hypocenterC79#3200
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #19099139C2semidirect
3. #19098907C2semidirect
4. #19098906C2semidirect
5. #19098887C2semidirect
6. #19098810C2semidirect
7. #19098808C2semidirect
8. #19098793C2semidirect
9. #19098791C2semidirect
10. #19098715C2semidirect
11. #19098715C2semidirect
12. #19098704C2semidirect
13. #19098701C2semidirect
14. #19098528C2semidirect
15. #482×C79C2semidirect
17. C22×Dic158C22semidirect
23. C2×#11929607C22semidirect
24. C2×C8×D79C22semidirect
33. #14579141C22semidirect
34. #14579141C22semidirect
41. #14579094C22semidirect
42. #14579092C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579084C22semidirect
46. #14579084C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
53. #117×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
58. C22⋊C8×C79C22semidirect
198. C79#3200semidirect
204. #482D79semidirect
240. #117C2×D79semidirect
242. #107C2×D79semidirect
244. #106C2×D79semidirect
256. C22⋊C8C2×D79semidirect