Finite Group Databasebeta

← #23775423

Subgroups — #23775423

Order 10112.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099253C211yesmaximal, characteristic, complemented
2D4×D316C211yesmaximal, characteristic
3#19098928C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098877C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098809C211yesmaximal, characteristic, complemented
8#19098792C211yesmaximal, characteristic, complemented
9#19098764C211yesmaximal, characteristic, complemented
10#19098716C211yesmaximal, characteristic, complemented
11#19098716C211yesmaximal, characteristic, complemented
12#19098665C211yesmaximal, characteristic, complemented
13#19098569C211yesmaximal, characteristic, complemented
14C2×#14579083C211yesmaximal, characteristic, complemented
15#435×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×D4×D79—21no—
19C2×#11929613C2211yescharacteristic
20C2×#11929613C2211yescharacteristic, complemented
21C2×#11929613C2211yescharacteristic, complemented
22#14579158C2211yescharacteristic
23#14579154—21no—
24#14579153C2211yescharacteristic, complemented
25#14579151—21no—
26#14579142—21no—
27#14579140C2211yescharacteristic, complemented
28#14579140C2211yescharacteristic, complemented
29#14579136—21no—
30#14579135C2211yescharacteristic
31#14579135C2211yescharacteristic
32#14579131—21no—
33#14579131—21no—
34C4×Dic158C2211yescharacteristic, complemented
35C4×D316C2211yescharacteristic
36#14579120C2211yescharacteristic, complemented
37#14579117—21no—
38C2×C4⋊Dic79C2211yescharacteristic, complemented
39#14579095C2211yescharacteristic, complemented
40#14579095C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic, complemented
47#14579083C2211yescharacteristic, complemented
48#14579083C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic, complemented
50#14579083C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic, complemented
52C2×M16×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic, complemented
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic, complemented
56C22⋊C8×C79C2211yescharacteristic, complemented
57C22⋊C8×C79C2211yescharacteristic, complemented
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316—22no—
63C2×D316—22no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—21no—
68C2×D316—41no—
69C2×D316—41no—
70C2×D316C2311yescharacteristic
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75D4×D79—44no—
76C22×Dic79—21no—
77C2×C4×D79—21no—
78#11929613—22no—
79#11929613—41no—
80#11929613—41no—
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97C4×Dic79—21no—
98C4×Dic79—21no—
99C2×D4×C79D411yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102M16×C79—41no—
103C2×C8×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C42×C79C2311yescharacteristic
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79—81no—
123D4×C79—22no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2411yescharacteristic
133C22⋊D79—42no—
134C22⋊D79—42no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—42no—
141D316—21no—
142D316—21no—
143D316—21no—
144D316—21no—
145D316—21no—
146D316—42no—
147D316—42no—
148D316—42no—
149D316—81no—
150D316#4112yes—
151C4×D79—42no—
152Dic158—21no—
153Dic158—21no—
154C8×C79—21no—
155C8×C79—21no—
156C8×C79—21no—
157C8×C79—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79AGL(1,ℤ/8)12yes—
164C22×C79C22×D411yescharacteristic
165C2×D79—22no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—84no—
175C2×D79—84no—
176C4×C79—21no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79C2×#4111yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—41no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186Dic79—41no—
187C2×C79—22no—
188C2×C79—41no—
189C2×C79#54611yescharacteristic
190C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C79#57711yescharacteristic
192D79—42no—
193D79—81no—
194D79—81no—
195#3310—791nomaximal, Sylow
196C79#331011yescharacteristic, complemented, Sylow
197#552—791no—
198D42—791no—
199#490—791no—
200#482—791no—
201#480—791no—
202#478—791no—
203#468—791no—
204#465—791no—
205#460—791no—
206#450—791no—
207#450—791no—
208#440—791no—
209#435D7911yescharacteristic, complemented
210#418—791no—
211C2×#102—791no—
212C22×D4—791no—
213C22×D4—791no—
214C22×D4—1581no—
215C2×SD16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×M16C2×D7911yescharacteristic, complemented
219C22×C8C2×D7911yescharacteristic, complemented
220#127—791no—
221#126—1581no—
222#125—791no—
223#125—1581no—
224#123—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231#120—1581no—
232C4×Q8—791no—
233C4×D4—791no—
234C4×D4C2×D7911yescharacteristic
235#117—791no—
236#117—1581no—
237C2×C4⋊C4—791no—
238#107—791no—
239#107—791no—
240#106—791no—
241C4⋊C8C2×D7911yescharacteristic, complemented
242#103—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252C22⋊C8C2×D7911yescharacteristic, complemented
253C22⋊C8C2×D7911yescharacteristic, complemented
254#97C2×D7911yescharacteristic, complemented
255C24—1581no—
256C24—1581no—
257C2×Q8—791no—
258C2×D4—3161no—
259C2×D4—3161no—
260C2×D4—3164no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—1582no—
265C2×D4—1582no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4D31611yescharacteristic
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4C22×D7911yescharacteristic
276C22×C4C22×D7911yescharacteristic
277SD16—3161no—
278SD16—3161no—
279SD16—1582no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D7911yescharacteristic
283C2×C8C22×D7911yescharacteristic
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C4⋊C4—791no—
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4D31611yescharacteristic
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4D31611yescharacteristic
304C22⋊C4D31611yescharacteristic
305C42—1581no—
306C42—1581no—
307C42C22×D7911yescharacteristic
308C23—3162no—
309C23—3162no—
310C23—3162no—
311C23—3162no—
312C23—6321no—
313C23—6321no—
314C23—1581no—
315C23—1581no—
316C23—1581no—
317C23C2×D31611yescharacteristic
318C23C2×D31611yescharacteristic
319Q8—1581no—
320Q8—1581no—
321D4—22no—
322D4—3162no—
323D4—3162no—
324D4—3162no—
325D4—3162no—
326D4—3162no—
327D4—792no—
328D4—6321no—
329D4—1581no—
330D4—1581no—
331D4—1581no—
332D4—1581no—
333D4—1581no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—3162no—
339C2×C4—3162no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4C2×D31611yescharacteristic
346C2×C4C2×D31611yescharacteristic
347C2×C4C2×D31611yescharacteristic
348C2×C4C2×D31611yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—3161no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—6324no—
368C22—6324no—
369C22—1582no—
370C22#1457918912yes—
371C22C22×D31611yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—3161no—
377C4—3161no—
378C4—3161no—
379C4—3161no—
380C4—3161no—
381C4#41×D7911yescharacteristic
382C4#1457920611yescharacteristic
383C2—22no—
384C2—41no—
385C2—3162no—
386C2—6321no—
387C2—6321no—
388C2#1909920811yescharacteristic
389C2C2×#1457918911yescharacteristic
390C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#435×C79C2
socleC22×C79C22×D4
prime radicalD4×D316C2
hypercenter#435D79
hypocenterC79#3310
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #19099253C2semidirect
3. #19098928C2semidirect
4. #19098888C2semidirect
5. #19098877C2semidirect
6. #19098864C2semidirect
7. #19098809C2semidirect
8. #19098792C2semidirect
9. #19098764C2semidirect
10. #19098716C2semidirect
11. #19098716C2semidirect
12. #19098665C2semidirect
13. #19098569C2semidirect
14. C2×#14579083C2semidirect
15. #435×C79C2semidirect
20. C2×#11929613C22semidirect
21. C2×#11929613C22semidirect
24. #14579153C22semidirect
27. #14579140C22semidirect
28. #14579140C22semidirect
34. C4×Dic158C22semidirect
36. #14579120C22semidirect
38. C2×C4⋊Dic79C22semidirect
39. #14579095C22semidirect
40. #14579095C22semidirect
41. #14579093C22semidirect
42. #14579086C22semidirect
46. #14579083C22semidirect
47. #14579083C22semidirect
48. #14579083C22semidirect
49. #14579083C22semidirect
50. #14579083C22semidirect
51. #14579083C22semidirect
52. C2×M16×C79C22semidirect
53. C22×C8×C79C22semidirect
55. C4⋊C8×C79C22semidirect
56. C22⋊C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. #97×C79C22semidirect
196. C79#3310semidirect
209. #435D79semidirect
218. C2×M16C2×D79semidirect
219. C22×C8C2×D79semidirect
241. C4⋊C8C2×D79semidirect
252. C22⋊C8C2×D79semidirect
253. C22⋊C8C2×D79semidirect
254. #97C2×D79semidirect