Finite Group Databasebeta

← #23774498

Subgroups — #23774498

Order 10112.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099186C211yesmaximal, characteristic, complemented
2#19099130C211yesmaximal, characteristic, complemented
3#19098949C211yesmaximal, characteristic, complemented
4#19098944C211yesmaximal, characteristic, complemented
5#19098921C211yesmaximal, characteristic, complemented
6#19098908C211yesmaximal, characteristic, complemented
7#19098783C211yesmaximal, characteristic, complemented
8#19098777C211yesmaximal, characteristic, complemented
9#19098761C211yesmaximal, characteristic, complemented
10#19098757C211yesmaximal, characteristic, complemented
11#19098723C211yesmaximal, characteristic, complemented
12#19098710C211yesmaximal, characteristic, complemented
13#19098697C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929614C2211yescharacteristic, complemented
18C2×#11929613C2211yescharacteristic, complemented
19C2×#11929611C2211yescharacteristic, complemented
20C2×D632C2211yescharacteristic, complemented
21C2×#11929609C2211yescharacteristic
22C2×#11929609C2211yescharacteristic
23#14579160C2211yescharacteristic, complemented
24#14579157C2211yescharacteristic
25#14579157C2211yescharacteristic
26#14579156—21no—
27#14579150C2211yescharacteristic, complemented
28#14579148C2211yescharacteristic
29#14579148C2211yescharacteristic
30#14579147—21no—
31#14579143—21no—
32#14579141—21no—
33#14579135C2211yescharacteristic
34#14579132—21no—
35#14579132—21no—
36#14579130—21no—
37#14579130—21no—
38Q8×Dic79C2211yescharacteristic, complemented
39#14579123C2211yescharacteristic, complemented
40#14579120C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929624—41no—
60#11929624—41no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73#11929614—41no—
74#11929613—41no—
75#11929611—41no—
76D632—41no—
77#11929609—41no—
78#11929609—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79—21no—
82C4⋊Dic79D411yescharacteristic
83C4⋊Dic79D411yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C4×Dic79C2311yescharacteristic
99C24×C79—21no—
100C2×Q8×C79C2311yescharacteristic
101C2×D4×C79—21no—
102C2×D4×C79—41no—
103C2×D4×C79—41no—
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79C2311yescharacteristic
107SD16×C79—41no—
108SD16×C79—41no—
109C2×C8×C79C2311yescharacteristic
110C2×C8×C79C2311yescharacteristic
111C4⋊C4×C79—21no—
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—42no—
117C23×C79—81no—
118C23×C79—81no—
119C23×C79C2×D411yescharacteristic
120C22×D79—21no—
121C22×D79—21no—
122Q8×C79—21no—
123Q8×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—42no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—42no—
136C22⋊D79—81no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C22⋊D79—81no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79C2×D411yescharacteristic
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147D316—21no—
148D316—21no—
149D316—21no—
150D316—21no—
151C4×D79—42no—
152C4×D79—81no—
153Dic158—21no—
154Dic158—21no—
155Dic158—81no—
156C8×C79—21no—
157C8×C79—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—84no—
170C22×C79C22×D411yescharacteristic
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C4×C79—21no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79H(5,𝔽2)11yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—21no—
183Dic79—21no—
184Dic79—21no—
185Dic79—21no—
186Dic79—41no—
187Dic79—41no—
188C2×C79—41no—
189C2×C79—81no—
190C2×C79—81no—
191C2×C79#53511yescharacteristic
192C2×C79#57611yescharacteristic
193C2×C79#57711yescharacteristic
194D79—81no—
195D79—81no—
196#3224—791nomaximal, Sylow
197C79#322411yescharacteristic, complemented, Sylow
198#542—791no—
199#535—791no—
200#496—791no—
201#495—791no—
202#489—791no—
203#486—791no—
204#464—791no—
205#463—791no—
206#460—791no—
207#459—791no—
208#452—791no—
209#450D7911yescharacteristic, complemented
210#449—791no—
211#447—791no—
212#433—791no—
213C2×#41—791no—
214C22×D4C2×D7911yescharacteristic
215C2×Q16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×SD16C2×D7911yescharacteristic
219C2×SD16C2×D7911yescharacteristic
220C2×D8—791no—
221C2×D8—791no—
222C2×D8—791no—
223C4⋊Q8—791no—
224#127—791no—
225#127—791no—
226#126—1581no—
227#124—791no—
228#124—791no—
229#124—791no—
230#124—1581no—
231#123—1581no—
232C22⋊Q8—1581no—
233C22⋊Q8C2×D7911yescharacteristic
234#121—791no—
235#121—1581no—
236#121—1581no—
237#120—1581no—
238#120—1581no—
239C4×Q8—791no—
240C4×D4—791no—
241#117—791no—
242C4⋊C8—791no—
243C4⋊C8—791no—
244#103—791no—
245#103—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102C2×D7911yescharacteristic
251#102C2×D7911yescharacteristic
252C22⋊C8—791no—
253C22⋊C8C2×D7911yescharacteristic
254#97—791no—
255C4×C8—791no—
256C24—21no—
257#41—3161no—
258#41—3161no—
259C2×Q8—791no—
260C2×Q8—1581no—
261C2×Q8C22×D7911yescharacteristic
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—791no—
266C2×D4—791no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4—1581no—
273C2×D4C22×D7911yescharacteristic
274C2×D4C22×D7911yescharacteristic
275C22×C4—1581no—
276C22×C4—1581no—
277C22×C4C22×D7911yescharacteristic
278Q16—3161no—
279SD16—41no—
280SD16—41no—
281SD16—3161no—
282SD16—3161no—
283D8—3161no—
284D8—3161no—
285D8—3161no—
286C2×C8—791no—
287C2×C8—791no—
288C2×C8C22×D7911yescharacteristic
289C2×C8C22×D7911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—791no—
292C4⋊C4—791no—
293C4⋊C4—791no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—791no—
299C22⋊C4—791no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C42—791no—
309C42—791no—
310C42—1581no—
311C23—21no—
312C23—21no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—1581no—
317C23—1581no—
318C23D4×D7911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—6321no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—3162no—
330D4—6321no—
331D4—6321no—
332D4—6321no—
333D4—6321no—
334D4—6321no—
335D4—1581no—
336D4—1581no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—3162no—
344C2×C4—791no—
345C2×C4—791no—
346C2×C4—791no—
347C2×C4—791no—
348C2×C4—6321no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4D4×D7911yescharacteristic
352C2×C4C23×D7911yescharacteristic
353C8—21no—
354C8—21no—
355C8—1581no—
356C8—1581no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—3161no—
368C22—3161no—
369C22—3161no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22C2×D4×D7911yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—3161no—
378C4—3161no—
379C4—1581no—
380C4—1581no—
381C4—1581no—
382C4—1581no—
383C4#1457920611yescharacteristic
384C4#1457920611yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—6321no—
389C2—6321no—
390C2#1909912811yescharacteristic
391C2#1909936711yescharacteristic
392C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
hypercenter#450D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #19099186C2semidirect
2. #19099130C2semidirect
3. #19098949C2semidirect
4. #19098944C2semidirect
5. #19098921C2semidirect
6. #19098908C2semidirect
7. #19098783C2semidirect
8. #19098777C2semidirect
9. #19098761C2semidirect
10. #19098757C2semidirect
11. #19098723C2semidirect
12. #19098710C2semidirect
13. #19098697C2semidirect
14. #19098621C2semidirect
15. #450×C79C2semidirect
17. C2×#11929614C22semidirect
18. C2×#11929613C22semidirect
19. C2×#11929611C22semidirect
20. C2×D632C22semidirect
23. #14579160C22semidirect
27. #14579150C22semidirect
38. Q8×Dic79C22semidirect
39. #14579123C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
45. #14579083C22semidirect
48. #14579081C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
197. C79#3224semidirect
209. #450D79semidirect