Finite Group Databasebeta

← #23774366

Subgroups — #23774366

Order 10112.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099098C211yesmaximal, characteristic, complemented
2#124×D79C211yesmaximal, characteristic, complemented
3#19098947C211yesmaximal, characteristic, complemented
4#19098945C211yesmaximal, characteristic, complemented
5#19098920C211yesmaximal, characteristic, complemented
6#19098788C211yesmaximal, characteristic, complemented
7#19098784C211yesmaximal, characteristic, complemented
8#19098781C211yesmaximal, characteristic, complemented
9#19098777C211yesmaximal, characteristic, complemented
10#19098720C211yesmaximal, characteristic, complemented
11#19098715C211yesmaximal, characteristic, complemented
12#19098703C211yesmaximal, characteristic, complemented
13#19098698C211yesmaximal, characteristic
14#19098614C211yesmaximal, characteristic, complemented
15#488×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929614C2211yescharacteristic, complemented
20C2×#11929613C2211yescharacteristic
21C2×#11929613C2211yescharacteristic, complemented
22C2×#11929612C2211yescharacteristic
23C2×#11929611C2211yescharacteristic, complemented
24C2×D632C2211yescharacteristic
25C2×#11929609C2211yescharacteristic
26#14579156—21no—
27#14579150C2211yescharacteristic
28#14579149C2211yescharacteristic
29#14579149C2211yescharacteristic, complemented
30#14579148C2211yescharacteristic
31#14579147—21no—
32#14579147—21no—
33#14579146—21no—
34#14579141C2211yescharacteristic
35#14579136C2211yescharacteristic
36#14579126C2211yescharacteristic, complemented
37#14579123—21no—
38#14579123C2211yescharacteristic, complemented
39#14579119—21no—
40C22⋊C4×D79—21no—
41C22⋊C4×D79—21no—
42C42×D79C2211yescharacteristic
43Dic79⋊C8C2211yescharacteristic, complemented
44Dic79⋊C8C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579084C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C4×C79⋊C8C2211yescharacteristic, complemented
52#125×C79C2211yescharacteristic, complemented
53#124×C79C2211yescharacteristic
54#103×C79C2211yescharacteristic, complemented
55#103×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×Dic158C2311yescharacteristic
63Q8×D79—41no—
64Q8×D79—41no—
65C2×D316—21no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69D4×D79—41no—
70D4×D79—41no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79D411yescharacteristic
74C2×C4×D79D411yescharacteristic
75C2×C4×D79C2311yescharacteristic
76Dic316—41no—
77#11929614—41no—
78#11929613—41no—
79#11929613—41no—
80#11929612—41no—
81#11929611—41no—
82D632—41no—
83#11929609—41no—
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C4⋊Dic79—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—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99C4×Dic79—21no—
100C4×Dic79D411yescharacteristic
101C4×Dic79D411yescharacteristic
102C4×Dic79C2311yescharacteristic
103C2×Q8×C79C2311yescharacteristic
104C2×D4×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79C2×D411yescharacteristic
121Q8×C79—21no—
122Q8×C79—21no—
123D4×C79—21no—
124D4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—42no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316—21no—
139D316—21no—
140D316—21no—
141D316—42no—
142C4×D79—22no—
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—41no—
146C4×D79—42no—
147C4×D79—42no—
148Dic158—21no—
149Dic158—21no—
150Dic158—21no—
151Dic158—21no—
152Dic158—42no—
153C8×C79—21no—
154C8×C79—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C22×C79—41no—
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—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—84no—
170C2×D79#13512yes—
171C4×C79—21no—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79H(5,𝔽2)11yescharacteristic
177C4×C79H(5,𝔽2)11yescharacteristic
178Dic79—21no—
179Dic79—21no—
180Dic79—21no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—81no—
184C2×C79#53511yescharacteristic
185C2×C79C2×#13511yescharacteristic
186C2×C79#57511yescharacteristic
187D79—22no—
188D79—81no—
189D79—81no—
190#3211—791nomaximal, Sylow
191C79#321111yescharacteristic, complemented, Sylow
192#529—791no—
193C2×#124—791no—
194#495—791no—
195#495—791no—
196#488—791no—
197#488D7911yescharacteristic, complemented
198#464—791no—
199#464—791no—
200#463—791no—
201#463—791no—
202#451—791no—
203#450—791no—
204#448—791no—
205#447—791no—
206#431—791no—
207C22×Q8—791no—
208C22×D4—791no—
209C2×Q16—791no—
210C2×Q16—791no—
211C2×SD16—791no—
212C2×SD16—791no—
213C2×SD16—791no—
214C2×SD16—791no—
215C2×D8—791no—
216C2×D8—791no—
217#126—1581no—
218#125C2×D7911yescharacteristic, complemented
219#124—791no—
220#124—791no—
221#124—791no—
222#124—791no—
223#124—1581no—
224#124—1581no—
225#124C2×D7911yescharacteristic
226#123—1581no—
227C22⋊Q8—791no—
228#121—791no—
229C4×Q8—791no—
230C4×D4—791no—
231C4×D4—1581no—
232#117—1581no—
233C2×C22⋊C4—1581no—
234C2×C22⋊C4—1581no—
235C2×C42—791no—
236C4⋊C8—791no—
237C4⋊C8—791no—
238#103—791no—
239#103—791no—
240#103C2×D7911yescharacteristic, complemented
241#103C2×D7911yescharacteristic, complemented
242#102—791no—
243#102—791no—
244#102C2×D7911yescharacteristic
245#102C2×D7911yescharacteristic
246C22⋊C8—791no—
247C22⋊C8—791no—
248C4×C8—791no—
249C4×C8C2×D7911yescharacteristic, complemented
250C24—1581no—
251C2×Q8—3161no—
252C2×Q8—3161no—
253C2×Q8—791no—
254C2×Q8—791no—
255C2×Q8—1581no—
256C2×Q8C22×D7911yescharacteristic
257C2×D4—3161no—
258C2×D4—3161no—
259C2×D4—791no—
260C2×D4—791no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4C22×D7911yescharacteristic
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—1581no—
268C22×C4—1581no—
269Q16—3161no—
270Q16—3161no—
271SD16—3161no—
272SD16—3161no—
273SD16—3161no—
274SD16—3161no—
275D8—3161no—
276D8—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4C22×D7911yescharacteristic
286C4⋊C4C22×D7911yescharacteristic
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C42—791no—
301C42—791no—
302C42—791no—
303C42—1581no—
304C42C22×D7911yescharacteristic
305C23—21no—
306C23—3162no—
307C23—3162no—
308C23—3162no—
309C23—791no—
310C23—1581no—
311C23—1581no—
312Q8—21no—
313Q8—21no—
314Q8—3162no—
315Q8—1581no—
316Q8—1581no—
317Q8—1581no—
318Q8—1581no—
319D4—21no—
320D4—21no—
321D4—3162no—
322D4—3162no—
323D4—1581no—
324D4—1581no—
325D4—1581no—
326D4—1581no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3161no—
331C2×C4—3162no—
332C2×C4—3162no—
333C2×C4—791no—
334C2×C4—791no—
335C2×C4—791no—
336C2×C4—1582no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4D4×D7911yescharacteristic
342C2×C4D4×D7911yescharacteristic
343C2×C4C23×D7911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1581no—
347C8—1581no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—3161no—
352C22—3161no—
353C22—3161no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—792no—
358C22—6324no—
359C22—1581no—
360C22—1581no—
361C22C2×D4×D7911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—3161no—
368C4—3161no—
369C4—1581no—
370C4—1581no—
371C4—1581no—
372C4#1457920711yescharacteristic
373C4#1457920711yescharacteristic
374C2—81no—
375C2—6321no—
376C2—6321no—
377C2—1582no—
378C2#1909913111yescharacteristic
379C2#135×D7911yescharacteristic
380C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#488×C79C2
socleC22×C79C22×D4
prime radical#19098698C2
hypercenter#488D79
hypocenterC79#3211
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #19099098C2semidirect
2. #124×D79C2semidirect
3. #19098947C2semidirect
4. #19098945C2semidirect
5. #19098920C2semidirect
6. #19098788C2semidirect
7. #19098784C2semidirect
8. #19098781C2semidirect
9. #19098777C2semidirect
10. #19098720C2semidirect
11. #19098715C2semidirect
12. #19098703C2semidirect
14. #19098614C2semidirect
15. #488×C79C2semidirect
18. C2×Dic316C22semidirect
19. C2×#11929614C22semidirect
21. C2×#11929613C22semidirect
23. C2×#11929611C22semidirect
29. #14579149C22semidirect
36. #14579126C22semidirect
38. #14579123C22semidirect
43. Dic79⋊C8C22semidirect
44. Dic79⋊C8C22semidirect
45. #14579084C22semidirect
46. #14579084C22semidirect
51. C4×C79⋊C8C22semidirect
52. #125×C79C22semidirect
54. #103×C79C22semidirect
55. #103×C79C22semidirect
58. C4×C8×C79C22semidirect
191. C79#3211semidirect
197. #488D79semidirect
218. #125C2×D79semidirect
240. #103C2×D79semidirect
241. #103C2×D79semidirect
249. C4×C8C2×D79semidirect