Finite Group Databasebeta

← #23775637

Subgroups — #23775637

Order 10112.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099277C211yesmaximal, characteristic, complemented
2#19099197C211yesmaximal, characteristic, complemented
3#19098908C211yesmaximal, characteristic, complemented
4#19098889C211yesmaximal, characteristic, complemented
5#19098884C211yesmaximal, characteristic, complemented
6#19098852C211yesmaximal, characteristic, complemented
7#19098815C211yesmaximal, characteristic, complemented
8#19098756C211yesmaximal, characteristic, complemented
9#19098696C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11#19098643C211yesmaximal, characteristic, complemented
12#19098639C211yesmaximal, characteristic, complemented
13#19098569C211yesmaximal, characteristic, complemented
14#19098566C211yesmaximal, characteristic, complemented
15#469×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929609C2211yescharacteristic, complemented
21C2×#11929607C2211yescharacteristic, complemented
22#14579160C2211yescharacteristic, complemented
23#14579157C2211yescharacteristic
24#14579148—21no—
25#14579147—21no—
26#14579136C2211yescharacteristic
27#14579134—21no—
28#14579133—21no—
29#14579132C2211yescharacteristic, complemented
30#14579131—21no—
31#14579129—21no—
32D4×Dic79C2211yescharacteristic, complemented
33#14579123C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35#14579120C2211yescharacteristic, complemented
36#14579119C2211yescharacteristic, complemented
37#14579117—21no—
38#14579094C2211yescharacteristic, complemented
39#14579092C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579083C2211yescharacteristic
42#14579083C2211yescharacteristic
43#14579083C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic, complemented
53C2×M16×C79C2211yescharacteristic, complemented
54#121×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic, complemented
56#106×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×Dic158—21no—
62C2×D316—21no—
63C2×D316—22no—
64C2×D316—21no—
65C2×D316—41no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79D411yescharacteristic
73D4×D79—22no—
74D4×D79—44no—
75D4×D79—41no—
76C22×Dic79—21no—
77C2×C4×D79—21no—
78C2×C4×D79C2311yescharacteristic
79#11929609—22no—
80#11929609—41no—
81#11929607—41no—
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96C4×Dic79—21no—
97C4×Dic79—21no—
98C4×Dic79C2311yescharacteristic
99C2×D4×C79—21no—
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104D8×C79—41no—
105M16×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79C2×D411yescharacteristic
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79—81no—
123C22×D79C2×D411yescharacteristic
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—42no—
129D4×C79—81no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2411yescharacteristic
136C22⋊D79—22no—
137C22⋊D79—42no—
138C22⋊D79—42no—
139C22⋊D79—81no—
140C22⋊D79—81no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—42no—
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147D316—21no—
148D316—21no—
149D316—21no—
150D316—42no—
151D316—42no—
152D316#4112yes—
153C4×D79—21no—
154C4×D79—21no—
155C4×D79—42no—
156Dic158—81no—
157C8×C79—21no—
158C8×C79—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79C22×D411yescharacteristic
171C2×D79—22no—
172C2×D79—21no—
173C2×D79—21no—
174C2×D79—21no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—41no—
180C2×D79—84no—
181C2×D79—84no—
182C4×C79—21no—
183C4×C79—41no—
184C4×C79—41no—
185C4×C79C2×#4111yescharacteristic
186C4×C79H(5,𝔽2)11yescharacteristic
187Dic79—21no—
188Dic79—21no—
189Dic79—41no—
190Dic79—41no—
191Dic79AGL(1,ℤ/8)12yes—
192C2×C79—41no—
193C2×C79—81no—
194C2×C79—81no—
195C2×C79#54611yescharacteristic
196C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C79#57611yescharacteristic
198D79—41no—
199D79—42no—
200D79—81no—
201#3325—791nomaximal, Sylow
202C79#332511yescharacteristic, complemented, Sylow
203#555—791no—
204D42—791no—
205#486—791no—
206#482—791no—
207#482—791no—
208#476—791no—
209#469—791no—
210#469D7911yescharacteristic, complemented
211#459—791no—
212#447—791no—
213#447—791no—
214C4×D8—791no—
215#436—791no—
216#418—791no—
217#418—791no—
218C22×D4—791no—
219C22×D4—791no—
220C22×D4—1581no—
221C2×D8—791no—
222C2×D8—791no—
223C2×D8C2×D7911yescharacteristic, complemented
224C2×M16—791no—
225C2×M16C2×D7911yescharacteristic, complemented
226C4⋊Q8—791no—
227#127—791no—
228#124—1581no—
229#124—1581no—
230#121—791no—
231#121—791no—
232#121—1581no—
233#121—1581no—
234#121C2×D7911yescharacteristic
235#121C2×D7911yescharacteristic, complemented
236#120—1581no—
237#120—1581no—
238C4×D4—791no—
239C4×D4—791no—
240C4×D4—791no—
241#117—791no—
242#117—791no—
243#117—1581no—
244#107—791no—
245#106—791no—
246#106C2×D7911yescharacteristic, complemented
247C4⋊C8—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252#102—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102C2×D7911yescharacteristic, complemented
257#102C2×D7911yescharacteristic, complemented
258C22⋊C8—791no—
259C22⋊C8—791no—
260C4×C8—791no—
261C24—1581no—
262C24—1581no—
263C2×Q8—1581no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—3161no—
267C2×D4—3164no—
268C2×D4—3161no—
269C2×D4—791no—
270C2×D4—791no—
271C2×D4—791no—
272C2×D4—1581no—
273C2×D4—1582no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1582no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4C22×D7911yescharacteristic
281C2×D4C22×D7911yescharacteristic
282C22×C4—791no—
283C22×C4—1581no—
284C22×C4—1581no—
285C22×C4C22×D7911yescharacteristic
286D8—41no—
287D8—3161no—
288D8—1582no—
289M16—41no—
290M16—3161no—
291C2×C8—791no—
292C2×C8—791no—
293C2×C8C22×D7911yescharacteristic
294C2×C8C22×D7911yescharacteristic
295C4⋊C4—791no—
296C4⋊C4—791no—
297C4⋊C4—791no—
298C4⋊C4—1581no—
299C4⋊C4C22×D7911yescharacteristic
300C4⋊C4C22×D7911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—791no—
304C22⋊C4—791no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C42—791no—
312C42—1581no—
313C42—1581no—
314C23—21no—
315C23—21no—
316C23—3162no—
317C23—3162no—
318C23—3162no—
319C23—3162no—
320C23—791no—
321C23—6321no—
322C23—6321no—
323C23—1581no—
324C23—1581no—
325C23D4×D7911yescharacteristic
326Q8—6321no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—42no—
332D4—81no—
333D4—3162no—
334D4—3162no—
335D4—3162no—
336D4—3162no—
337D4—792no—
338D4—6321no—
339D4—6321no—
340D4—1582no—
341D4—1581no—
342D4—1581no—
343D4—1581no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—3162no—
349C2×C4—3162no—
350C2×C4—791no—
351C2×C4—791no—
352C2×C4—791no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4D4×D7911yescharacteristic
358C2×C4C23×D7911yescharacteristic
359C8—21no—
360C8—21no—
361C8—1581no—
362C8—1581no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—3161no—
373C22—3161no—
374C22—3161no—
375C22—3161no—
376C22—3161no—
377C22—6324no—
378C22—6324no—
379C22—1581no—
380C22—1582no—
381C22—1581no—
382C22—1581no—
383C22C2×D4×D7911yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—3161no—
388C4—3161no—
389C4—792no—
390C4—1581no—
391C4—1581no—
392C4#41×D7911yescharacteristic
393C4#1457920611yescharacteristic
394C2—41no—
395C2—81no—
396C2—81no—
397C2—3162no—
398C2—3161no—
399C2—6321no—
400C2#1909920211yescharacteristic
401C2AGL(1,ℤ/8)×D7911yescharacteristic
402C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#469×C79C2
socleC22×C79C22×D4
hypercenter#469D79
hypocenterC79#3325
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #19099277C2semidirect
2. #19099197C2semidirect
3. #19098908C2semidirect
4. #19098889C2semidirect
5. #19098884C2semidirect
6. #19098852C2semidirect
7. #19098815C2semidirect
8. #19098756C2semidirect
9. #19098696C2semidirect
10. #19098695C2semidirect
11. #19098643C2semidirect
12. #19098639C2semidirect
13. #19098569C2semidirect
14. #19098566C2semidirect
15. #469×C79C2semidirect
20. C2×#11929609C22semidirect
21. C2×#11929607C22semidirect
22. #14579160C22semidirect
29. #14579132C22semidirect
32. D4×Dic79C22semidirect
35. #14579120C22semidirect
36. #14579119C22semidirect
38. #14579094C22semidirect
39. #14579092C22semidirect
40. Dic79⋊C8C22semidirect
43. #14579083C22semidirect
44. #14579083C22semidirect
45. #14579082C22semidirect
46. #14579082C22semidirect
48. #14579081C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
52. C2×D8×C79C22semidirect
53. C2×M16×C79C22semidirect
55. #121×C79C22semidirect
56. #106×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
202. C79#3325semidirect
210. #469D79semidirect
223. C2×D8C2×D79semidirect
225. C2×M16C2×D79semidirect
235. #121C2×D79semidirect
246. #106C2×D79semidirect
256. #102C2×D79semidirect
257. #102C2×D79semidirect