Finite Group Databasebeta

← #23775474

Subgroups — #23775474

Order 10112.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099271C211yesmaximal, characteristic, complemented
2#19099201C211yesmaximal, characteristic
3#19098924C211yesmaximal, characteristic, complemented
4#19098897C211yesmaximal, characteristic, complemented
5#19098877C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098801C211yesmaximal, characteristic, complemented
9#19098787C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12#19098637C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#452×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18C2×#11929608C2211yescharacteristic, complemented
19C2×C8×D79C2211yescharacteristic
20#14579160C2211yescharacteristic, complemented
21#14579151—21no—
22#14579150C2211yescharacteristic
23#14579144—21no—
24#14579141—21no—
25#14579138—21no—
26#14579137C2211yescharacteristic
27#14579137C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579133—21no—
30#14579129—21no—
31Q8×Dic79C2211yescharacteristic, complemented
32D4×Dic79C2211yescharacteristic
33C4×C22⋊D79C2211yescharacteristic
34(C22⋊D79)⋊C4—21no—
35C2×C4⋊Dic79C2211yescharacteristic, complemented
36C4⋊C4×D79C2211yescharacteristic
37C2×(C2×D79)⋊C4—21no—
38#14579095C2211yescharacteristic, complemented
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C2×C22⋊D79D411yescharacteristic
65D4×D79—22no—
66D4×D79—41no—
67C22×Dic79—21no—
68C22×Dic79—21no—
69C2×C4×D79—21no—
70C2×C4×D79C2311yescharacteristic
71#11929611—41no—
72#11929608—41no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C8×D79—41no—
76C4⋊Dic79—21no—
77C4⋊Dic79—21no—
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4D411yescharacteristic
86C22⋊Dic79—21no—
87C22⋊Dic79D411yescharacteristic
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4D411yescharacteristic
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96#41×C79—22no—
97#41×C79—41no—
98C2×Q8×C79C2311yescharacteristic
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104Q16×C79—41no—
105SD16×C79—22no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—42no—
115C22×D79—42no—
116C22×D79—81no—
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120Q8×C79—21no—
121Q8×C79—21no—
122D4×C79—21no—
123D4×C79—42no—
124D4×C79#4112yes—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—42no—
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2411yescharacteristic
133C22⋊D79—22no—
134C22⋊D79—42no—
135C22⋊D79—81no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—81no—
140C2×Dic79—81no—
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143C2×Dic79C2×D411yescharacteristic
144D316—21no—
145D316—21no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—81no—
149Dic158—81no—
150C8×C79—21no—
151C8×C79—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C22×C79—22no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79C22×D411yescharacteristic
161C2×D79—21no—
162C2×D79—21no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—84no—
167C2×D79#13712yes—
168C4×C79—21no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79C2×#4111yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—21no—
175Dic79—21no—
176Dic79—21no—
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—42no—
181C2×C79—41no—
182C2×C79#54611yescharacteristic
183C2×C79C2×#13711yescharacteristic
184C2×C79#57611yescharacteristic
185D79—22no—
186D79—81no—
187#3314—791nomaximal, Sylow
188C79#331411yescharacteristic, complemented, Sylow
189#554—791no—
190#546—791no—
191#489—791no—
192#484—791no—
193#480—791no—
194#474—791no—
195#468—791no—
196#467—791no—
197#464—791no—
198#452D7911yescharacteristic, complemented
199#450—791no—
200#440—791no—
201#435—791no—
202#417—791no—
203C2×#102—791no—
204C2×#41C2×D7911yescharacteristic
205C22×D4—791no—
206C2×Q16C2×D7911yescharacteristic, complemented
207C2×SD16—791no—
208C2×SD16C2×D7911yescharacteristic
209C2×M16—791no—
210C22×C8—791no—
211C4⋊Q8—791no—
212#125—1581no—
213#124—791no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—1581no—
218C22⋊Q8—1581no—
219C22⋊Q8C2×D7911yescharacteristic, complemented
220#121—791no—
221#121—1581no—
222#120—1581no—
223C4×Q8—791no—
224C4×D4—791no—
225C4×D4—791no—
226C4×D4—1581no—
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C22⋊C4—1581no—
230#107—791no—
231#107—791no—
232#107—791no—
233C4⋊C8—791no—
234#103—791no—
235#103—791no—
236#103—791no—
237#103C2×D7911yescharacteristic, complemented
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102C2×D7911yescharacteristic
244C22⋊C8—791no—
245C22⋊C8C2×D7911yescharacteristic, complemented
246#97—791no—
247C24—1581no—
248#41—22no—
249#41—41no—
250C2×Q8—1581no—
251C2×Q8C22×D7911yescharacteristic
252C2×Q8C22×D7911yescharacteristic
253C2×D4—21no—
254C2×D4—3161no—
255C2×D4—791no—
256C2×D4—791no—
257C2×D4—1581no—
258C2×D4—1582no—
259C2×D4—1581no—
260C2×D4C22×D7911yescharacteristic
261C22×C4—21no—
262C22×C4—791no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4C22×D7911yescharacteristic
267Q16—41no—
268SD16—22no—
269SD16—3161no—
270M16—3161no—
271C2×C8—3161no—
272C2×C8—791no—
273C2×C8—791no—
274C2×C8C22×D7911yescharacteristic
275C2×C8C22×D7911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4—791no—
280C4⋊C4—791no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—791no—
290C22⋊C4—791no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C42—791no—
298C42—1581no—
299C23—21no—
300C23—3162no—
301C23—3162no—
302C23—791no—
303C23—6321no—
304C23—1581no—
305C23D4×D7911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—6321no—
311D4—21no—
312D4—42no—
313D4—3162no—
314D4—6321no—
315D4—1582no—
316D4—1581no—
317D4—1581no—
318D4#1192962312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—791no—
326C2×C4—791no—
327C2×C4—791no—
328C2×C4—6321no—
329C2×C4—6321no—
330C2×C4—6321no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4D4×D7911yescharacteristic
337C2×C4C23×D7911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1581no—
341C8—1581no—
342C22—21no—
343C22—22no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—3161no—
349C22—3161no—
350C22—3161no—
351C22—792no—
352C22—6324no—
353C22—1581no—
354C22—1581no—
355C22C2×D4×D7911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3161no—
361C4—3161no—
362C4—3161no—
363C4—1581no—
364C4—1581no—
365C4—1581no—
366C4C2×#1192962311yescharacteristic
367C4#1457920611yescharacteristic
368C2—41no—
369C2—42no—
370C2—6321no—
371C2—1582no—
372C2#1909920011yescharacteristic
373C2#137×D7911yescharacteristic
374C2#1909936511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#452×C79C2
socleC22×C79C22×D4
prime radical#19099201C2
hypercenter#452D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #19099271C2semidirect
3. #19098924C2semidirect
4. #19098897C2semidirect
5. #19098877C2semidirect
6. #19098841C2semidirect
7. #19098811C2semidirect
8. #19098801C2semidirect
9. #19098787C2semidirect
10. #19098712C2semidirect
11. #19098664C2semidirect
12. #19098637C2semidirect
13. #19098564C2semidirect
14. #102×D79C2semidirect
15. #452×C79C2semidirect
18. C2×#11929608C22semidirect
20. #14579160C22semidirect
31. Q8×Dic79C22semidirect
35. C2×C4⋊Dic79C22semidirect
38. #14579095C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579085C22semidirect
43. #14579085C22semidirect
44. #14579085C22semidirect
51. #14579071C22semidirect
53. C2×Q16×C79C22semidirect
55. C22⋊Q8×C79C22semidirect
56. #103×C79C22semidirect
58. C22⋊C8×C79C22semidirect
188. C79#3314semidirect
198. #452D79semidirect
206. C2×Q16C2×D79semidirect
219. C22⋊Q8C2×D79semidirect
237. #103C2×D79semidirect
245. C22⋊C8C2×D79semidirect