Finite Group Databasebeta

← #23775604

Subgroups — #23775604

Order 10112.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099261C211yesmaximal, characteristic, complemented
2#19099210C211yesmaximal, characteristic, complemented
3#19098916C211yesmaximal, characteristic, complemented
4#19098906C211yesmaximal, characteristic, complemented
5#19098866C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098810C211yesmaximal, characteristic, complemented
8#19098777C211yesmaximal, characteristic, complemented
9#19098710C211yesmaximal, characteristic, complemented
10#19098698C211yesmaximal, characteristic, complemented
11#19098645C211yesmaximal, characteristic, complemented
12#19098638C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098562C211yesmaximal, characteristic, complemented
15#480×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929613C2211yescharacteristic, complemented
19C2×D632C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic, complemented
22C2×#11929607C2211yescharacteristic
23#14579156—21no—
24#14579152C2211yescharacteristic, complemented
25#14579148C2211yescharacteristic
26#14579146—21no—
27#14579143—21no—
28#14579141C2211yescharacteristic
29#14579136C2211yescharacteristic
30#14579135—21no—
31#14579135C2211yescharacteristic, complemented
32#14579132—21no—
33#14579129—21no—
34#14579123C2211yescharacteristic
35#14579123C2211yescharacteristic, complemented
36C4×C22⋊D79—21no—
37C4×C22⋊D79C2211yescharacteristic
38#14579119C2211yescharacteristic
39C22⋊C4×D79—21no—
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic, complemented
52#121×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic, complemented
54#107×C79C2211yescharacteristic, complemented
55#107×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79D411yescharacteristic
70D4×D79—22no—
71D4×D79—41no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76#11929613—41no—
77D632—22no—
78#11929609—41no—
79#11929608—41no—
80#11929607—41no—
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C4⋊Dic79—21no—
84C4⋊Dic79—21no—
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4D411yescharacteristic
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)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4D411yescharacteristic
98C4×Dic79—21no—
99C4×Dic79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118C22×D79C2×D411yescharacteristic
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—81no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—81no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—41no—
131C22⋊D79—42no—
132C22⋊D79—42no—
133C22⋊D79—42no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139D316—21no—
140D316—21no—
141D316—21no—
142D316—81no—
143D316#4112yes—
144C4×D79—21no—
145C4×D79—21no—
146C4×D79—42no—
147C4×D79—81no—
148C4×D79—81no—
149Dic158—21no—
150Dic158—21no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—22no—
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—84no—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79C2×#4111yescharacteristic
177C4×C79H(5,𝔽2)11yescharacteristic
178Dic79—21no—
179Dic79—21no—
180Dic79—21no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—41no—
184C2×C79—81no—
185C2×C79#54611yescharacteristic
186C2×C79#57511yescharacteristic
187C2×C79#57611yescharacteristic
188D79—41no—
189D79—42no—
190D79—81no—
191#3322—791nomaximal, Sylow
192C79#332211yescharacteristic, complemented, Sylow
193#553—791no—
194#546—791no—
195#488—791no—
196#485—791no—
197#480D7911yescharacteristic, complemented
198#478—791no—
199#469—791no—
200#468—791no—
201#463—791no—
202#449—791no—
203#447—791no—
204C4×D8—791no—
205#436—791no—
206#418—791no—
207#417—791no—
208C2×#41—791no—
209C22×D4—791no—
210C2×SD16—791no—
211C2×D8—791no—
212C2×D8—791no—
213C2×M16—791no—
214C2×M16—791no—
215#126—1581no—
216#125—791no—
217#124—791no—
218#123—1581no—
219#123—1581no—
220C22⋊Q8—791no—
221#121—791no—
222#121—791no—
223#121—1581no—
224#121—1581no—
225#121C2×D7911yescharacteristic
226#120—1581no—
227C4×D4—791no—
228C4×D4—791no—
229C4×D4—791no—
230C4×D4—1581no—
231#117—791no—
232C2×C4⋊C4C2×D7911yescharacteristic, complemented
233C2×C22⋊C4—1581no—
234#107C2×D7911yescharacteristic, complemented
235#107C2×D7911yescharacteristic, complemented
236#106—791no—
237C4⋊C8—791no—
238#103—791no—
239#103—791no—
240#103—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102C2×D7911yescharacteristic
247#102C2×D7911yescharacteristic
248C22⋊C8—791no—
249C22⋊C8C2×D7911yescharacteristic, complemented
250C4×C8—791no—
251C24—1581no—
252#41—3161no—
253#41—1582no—
254C2×Q8—791no—
255C2×D4—21no—
256C2×D4—3161no—
257C2×D4—791no—
258C2×D4—791no—
259C2×D4—791no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1582no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C22×C4—21no—
267C22×C4—791no—
268C22×C4—1581no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4C22×D7911yescharacteristic
272SD16—3161no—
273D8—3161no—
274D8—1582no—
275M16—3161no—
276M16—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4C22×D7911yescharacteristic
288C4⋊C4C22×D7911yescharacteristic
289C4⋊C4C22×D7911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—791no—
292C22⋊C4—791no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C42—791no—
302C42—1581no—
303C23—21no—
304C23—3162no—
305C23—3162no—
306C23—791no—
307C23—6321no—
308C23—1581no—
309C23—1581no—
310C23D4×D7911yescharacteristic
311Q8—1581no—
312Q8—1581no—
313D4—21no—
314D4—21no—
315D4—81no—
316D4—3162no—
317D4—3162no—
318D4—3161no—
319D4—3162no—
320D4—792no—
321D4—6321no—
322D4—1581no—
323D4—1581no—
324D4—1581no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—81no—
331C2×C4—3162no—
332C2×C4—791no—
333C2×C4—791no—
334C2×C4—791no—
335C2×C4—6321no—
336C2×C4—6321no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4D4×D7911yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1581no—
346C8—1581no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3161no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—6324no—
359C22—1582no—
360C22—1581no—
361C22—1581no—
362C22—1581no—
363C22C2×D4×D7911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3161no—
369C4—3161no—
370C4—1581no—
371C4—1581no—
372C4—1581no—
373C4#41×D7911yescharacteristic
374C4#1457920711yescharacteristic
375C2—41no—
376C2—81no—
377C2—3162no—
378C2—3161no—
379C2—6321no—
380C2#1909920511yescharacteristic
381C2#1909936211yescharacteristic
382C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#480×C79C2
socleC22×C79C22×D4
hypercenter#480D79
hypocenterC79#3322
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #19099261C2semidirect
2. #19099210C2semidirect
3. #19098916C2semidirect
4. #19098906C2semidirect
5. #19098866C2semidirect
6. #19098814C2semidirect
7. #19098810C2semidirect
8. #19098777C2semidirect
9. #19098710C2semidirect
10. #19098698C2semidirect
11. #19098645C2semidirect
12. #19098638C2semidirect
13. #19098566C2semidirect
14. #19098562C2semidirect
15. #480×C79C2semidirect
18. C2×#11929613C22semidirect
21. C2×#11929608C22semidirect
24. #14579152C22semidirect
31. #14579135C22semidirect
35. #14579123C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
44. #14579084C22semidirect
49. #14579081C22semidirect
51. C8×Dic79C22semidirect
53. C2×C4⋊C4×C79C22semidirect
54. #107×C79C22semidirect
55. #107×C79C22semidirect
58. C22⋊C8×C79C22semidirect
192. C79#3322semidirect
197. #480D79semidirect
232. C2×C4⋊C4C2×D79semidirect
234. #107C2×D79semidirect
235. #107C2×D79semidirect
249. C22⋊C8C2×D79semidirect