Finite Group Databasebeta

← #23775623

Subgroups — #23775623

Order 10112.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099254C211yesmaximal, characteristic, complemented
2#19099206C211yesmaximal, characteristic
3#19098917C211yesmaximal, characteristic, complemented
4#19098903C211yesmaximal, characteristic, complemented
5#19098880C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098818C211yesmaximal, characteristic, complemented
8#19098806C211yesmaximal, characteristic, complemented
9#19098724C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11C4×#11929611C211yesmaximal, characteristic, complemented
12#19098640C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098563C211yesmaximal, characteristic, complemented
15#464×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929607C2211yescharacteristic
20C2×#11929607C2211yescharacteristic, complemented
21#14579155—21no—
22#14579153C2211yescharacteristic, complemented
23#14579151—21no—
24#14579146—21no—
25#14579143—21no—
26#14579137C2211yescharacteristic
27#14579137C2211yescharacteristic
28#14579137C2211yescharacteristic, complemented
29#14579134—21no—
30#14579132C2211yescharacteristic
31#14579131—21no—
32C4×D316C2211yescharacteristic
33C4×D316C2211yescharacteristic
34#14579119C2211yescharacteristic
35#14579118—21no—
36C4⋊C4×D79C2211yescharacteristic, complemented
37C22⋊C4×D79—21no—
38#14579095C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C4×C79⋊C8C2211yescharacteristic, complemented
52C2×Q16×C79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54#124×C79C2211yescharacteristic
55C4×Q8×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60#11929625—22no—
61#11929625—41no—
62C2×D316—21no—
63C2×D316D411yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67D4×D79—22no—
68D4×D79—41no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73C2×C4×D79C2311yescharacteristic
74#11929611—22no—
75#11929607—41no—
76#11929607—41no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C4⋊Dic79D411yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—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)⋊C4D411yescharacteristic
96(C2×D79)⋊C4D411yescharacteristic
97C4×Dic79—21no—
98C2×Q8×C79C2311yescharacteristic
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101Q16×C79—41no—
102SD16×C79—41no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C22×D79—21no—
113C22×D79—42no—
114C22×D79—42no—
115C22×D79—81no—
116C22×D79C2×D411yescharacteristic
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120Q8×C79—21no—
121Q8×C79—21no—
122D4×C79—21no—
123D4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—42no—
131C22⋊D79—81no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316—41no—
139D316—42no—
140D316#4112yes—
141C4×D79—21no—
142C4×D79—21no—
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—42no—
146C4×D79—42no—
147C4×D79—81no—
148C8×C79—21no—
149C8×C79—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79C22×D411yescharacteristic
156C2×D79—22no—
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—21no—
162C2×D79—21no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—84no—
166C4×C79—21no—
167C4×C79—21no—
168C4×C79—41no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79C2×#4111yescharacteristic
172C4×C79H(5,𝔽2)11yescharacteristic
173Dic79—21no—
174Dic79—21no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178C2×C79—81no—
179C2×C79#54611yescharacteristic
180C2×C79#57511yescharacteristic
181C2×C79#57711yescharacteristic
182D79—41no—
183D79—41no—
184D79—42no—
185#3323—791nomaximal, Sylow
186C79#332311yescharacteristic, complemented, Sylow
187#552—791no—
188#546—791no—
189#488—791no—
190#485—791no—
191#481—791no—
192#478—791no—
193#470—791no—
194#468—791no—
195#464D7911yescharacteristic, complemented
196#452—791no—
197#450—791no—
198C4×SD16—791no—
199#436—791no—
200#418—791no—
201#417—791no—
202C2×#41—791no—
203C22×D4—791no—
204C2×Q16C2×D7911yescharacteristic, complemented
205C2×SD16—791no—
206C2×SD16C2×D7911yescharacteristic
207C2×M16—791no—
208C2×M16—791no—
209#126—1581no—
210#125—791no—
211#125—1581no—
212#124C2×D7911yescharacteristic
213#123—1581no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—791no—
218#121—791no—
219#121—1581no—
220#120—1581no—
221C4×Q8C2×D7911yescharacteristic, complemented
222C4×D4—791no—
223C4×D4—791no—
224#117—791no—
225#117—1581no—
226C2×C4⋊C4—791no—
227C2×C22⋊C4—1581no—
228#107—791no—
229#106—791no—
230#106—791no—
231C4⋊C8C2×D7911yescharacteristic, complemented
232#103—791no—
233#103—791no—
234#103—791no—
235#103C2×D7911yescharacteristic, complemented
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102C2×D7911yescharacteristic
242C22⋊C8—791no—
243C22⋊C8—791no—
244C4×C8—791no—
245C24—1581no—
246#41—3161no—
247#41—1582no—
248C2×Q8C22×D7911yescharacteristic
249C2×Q8C22×D7911yescharacteristic
250C2×D4—3161no—
251C2×D4—791no—
252C2×D4—791no—
253C2×D4—1581no—
254C2×D4—1581no—
255C2×D4—1582no—
256C2×D4—1581no—
257C2×D4C22×D7911yescharacteristic
258C22×C4—791no—
259C22×C4—791no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4—1581no—
263Q16—41no—
264SD16—41no—
265SD16—1582no—
266M16—3161no—
267M16—3161no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8C22×D7911yescharacteristic
271C2×C8C22×D7911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—791no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4C22×D7911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—791no—
287C22⋊C4—791no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C42—21no—
295C42—1581no—
296C42C22×D7911yescharacteristic
297C23—21no—
298C23—3162no—
299C23—3162no—
300C23—791no—
301C23—791no—
302C23—6321no—
303C23—1581no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—3161no—
311D4—3162no—
312D4—3162no—
313D4—792no—
314D4—6321no—
315D4—1581no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—3162no—
320C2×C4—3162no—
321C2×C4—791no—
322C2×C4—791no—
323C2×C4—6321no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4D4×D7911yescharacteristic
332C2×C4D4×D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1581no—
337C8—1581no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—3161no—
342C22—3161no—
343C22—6324no—
344C22—1582no—
345C22—1581no—
346C22—1581no—
347C22—1581no—
348C22—1581no—
349C22—1581no—
350C22—1581no—
351C22C2×D4×D7911yescharacteristic
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—3161no—
358C4—3161no—
359C4—3161no—
360C4—1581no—
361C4—1581no—
362C4#41×D7911yescharacteristic
363C4#1457920611yescharacteristic
364C2—81no—
365C2—3162no—
366C2—3161no—
367C2—3161no—
368C2#1909921011yescharacteristic
369C2#1909936011yescharacteristic
370C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#464×C79C2
socleC22×C79C22×D4
prime radical#19099206C2
hypercenter#464D79
hypocenterC79#3323
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #19099254C2semidirect
3. #19098917C2semidirect
4. #19098903C2semidirect
5. #19098880C2semidirect
6. #19098864C2semidirect
7. #19098818C2semidirect
8. #19098806C2semidirect
9. #19098724C2semidirect
10. #19098712C2semidirect
11. C4×#11929611C2semidirect
12. #19098640C2semidirect
13. #19098566C2semidirect
14. #19098563C2semidirect
15. #464×C79C2semidirect
20. C2×#11929607C22semidirect
22. #14579153C22semidirect
28. #14579137C22semidirect
36. C4⋊C4×D79C22semidirect
38. #14579095C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. #14579085C22semidirect
42. #14579085C22semidirect
43. #14579085C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C4×C79⋊C8C22semidirect
52. C2×Q16×C79C22semidirect
55. C4×Q8×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #103×C79C22semidirect
186. C79#3323semidirect
195. #464D79semidirect
204. C2×Q16C2×D79semidirect
221. C4×Q8C2×D79semidirect
231. C4⋊C8C2×D79semidirect
235. #103C2×D79semidirect