Finite Group Databasebeta

← #23775544

Subgroups — #23775544

Order 10112.

462 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#19099257C211yesmaximal, characteristic, complemented
2#19099197C211yesmaximal, characteristic, complemented
3#19098926C211yesmaximal, characteristic, complemented
4#19098883C211yesmaximal, characteristic, complemented
5#19098866C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098800C211yesmaximal, characteristic, complemented
8#19098757C211yesmaximal, characteristic, complemented
9#19098699C211yesmaximal, characteristic, complemented
10#19098698C211yesmaximal, characteristic, complemented
11#19098674C211yesmaximal, characteristic, complemented
12#19098637C211yesmaximal, characteristic, complemented
13#19098567C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#482×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C2×D632C2211yescharacteristic
20C2×D632C2211yescharacteristic, complemented
21C2×#11929609C2211yescharacteristic, complemented
22C2×#11929608C2211yescharacteristic, complemented
23C2×C8×D79C2211yescharacteristic, complemented
24#14579157C2211yescharacteristic
25#14579155—21no—
26#14579152C2211yescharacteristic, complemented
27#14579143—21no—
28#14579136C2211yescharacteristic
29#14579136C2211yescharacteristic, complemented
30#14579135C2211yescharacteristic, complemented
31#14579134—21no—
32#14579134—21no—
33#14579131—21no—
34#14579129—21no—
35C4×D316—21no—
36#14579123C2211yescharacteristic
37#14579123C2211yescharacteristic, complemented
38C4×C22⋊D79C2211yescharacteristic
39C4⋊C4×D79C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579083C2211yescharacteristic
43#14579083C2211yescharacteristic, complemented
44#14579082C2211yescharacteristic, complemented
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52#121×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic, complemented
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×D316—21no—
62C2×D316—21no—
63C2×D316—22no—
64C2×D316—21no—
65C2×D316—41no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79D411yescharacteristic
74D4×D79—22no—
75D4×D79—44no—
76D4×D79—41no—
77C2×C4×D79—21no—
78C2×C4×D79—21no—
79C2×C4×D79—21no—
80C2×C4×D79C2311yescharacteristic
81D632—22no—
82D632—41no—
83#11929609—41no—
84#11929608—41no—
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C8×D79—41no—
88C4⋊Dic79—21no—
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91Dic79⋊C4—21no—
92Dic79⋊C4D411yescharacteristic
93C22⋊Dic79D411yescharacteristic
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—
99(C2×D79)⋊C4D411yescharacteristic
100C4×Dic79C2311yescharacteristic
101C2×D4×C79—21no—
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C42×C79—21no—
112C23×C79—21no—
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—
123C22×D79C2×D411yescharacteristic
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—42no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—22no—
135C22⋊D79—42no—
136C22⋊D79—42no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C2×Dic79—21no—
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143D316—21no—
144D316—21no—
145D316—21no—
146D316—21no—
147D316—21no—
148D316—42no—
149D316—42no—
150D316—42no—
151D316#4112yes—
152C4×D79—21no—
153C4×D79—21no—
154C4×D79—42no—
155C4×D79—81no—
156C4×D79—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×C79C22×D411yescharacteristic
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—22no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—84no—
180C2×D79—84no—
181C2×D79AGL(1,ℤ/8)12yes—
182C4×C79—21no—
183C4×C79—41no—
184C4×C79—41no—
185C4×C79—41no—
186C4×C79C2×#4111yescharacteristic
187C4×C79H(5,𝔽2)11yescharacteristic
188Dic79—21no—
189Dic79—21no—
190Dic79—21no—
191Dic79—41no—
192C2×C79—41no—
193C2×C79—81no—
194C2×C79#54611yescharacteristic
195C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C79#57611yescharacteristic
197D79—22no—
198D79—42no—
199D79—81no—
200D79—81no—
201#3318—791nomaximal, Sylow
202C79#331811yescharacteristic, complemented, Sylow
203#553—791no—
204D42—791no—
205#490—791no—
206#482D7911yescharacteristic, complemented
207#481—791no—
208#478—791no—
209#469—791no—
210#466—791no—
211#459—791no—
212#447—791no—
213#447—791no—
214#442—791no—
215#435—791no—
216#418—791no—
217C2×#102—791no—
218C22×D4—791no—
219C22×D4—791no—
220C22×D4—1581no—
221C2×D8—791no—
222C2×D8—791no—
223C2×D8—791no—
224C2×M16—791no—
225C22×C8—791no—
226#127—791no—
227#126—1581no—
228#125—791no—
229#123—1581no—
230#121—791no—
231#121—791no—
232#121—791no—
233#121—1581no—
234#121—1581no—
235#121C2×D7911yescharacteristic
236#120—1581no—
237#120—1581no—
238C4×D4—791no—
239C4×D4—791no—
240C4×D4—791no—
241C4×D4—1581no—
242#117C2×D7911yescharacteristic, complemented
243C2×C4⋊C4—791no—
244#107C2×D7911yescharacteristic, complemented
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⋊C8C2×D7911yescharacteristic, complemented
260#97—791no—
261C24—1581no—
262C24—1581no—
263C2×D4—21no—
264C2×D4—3161no—
265C2×D4—3164no—
266C2×D4—3161no—
267C2×D4—791no—
268C2×D4—791no—
269C2×D4—791no—
270C2×D4—791no—
271C2×D4—1581no—
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
281C22×C4—791no—
282C22×C4—1581no—
283C22×C4—1581no—
284C22×C4—1581no—
285C22×C4C22×D7911yescharacteristic
286D8—3161no—
287D8—3161no—
288D8—1582no—
289M16—3161no—
290C2×C8—3161no—
291C2×C8—791no—
292C2×C8—791no—
293C2×C8C22×D7911yescharacteristic
294C2×C8C22×D7911yescharacteristic
295C4⋊C4—791no—
296C4⋊C4—791no—
297C4⋊C4—1581no—
298C4⋊C4—1581no—
299C4⋊C4—1581no—
300C4⋊C4C22×D7911yescharacteristic
301C4⋊C4C22×D7911yescharacteristic
302C4⋊C4C22×D7911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—791no—
306C22⋊C4—791no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C42—21no—
313C42—791no—
314C23—21no—
315C23—3162no—
316C23—3162no—
317C23—3162no—
318C23—3162no—
319C23—791no—
320C23—6321no—
321C23—6321no—
322C23—1581no—
323C23—1581no—
324C23—1581no—
325C23D4×D7911yescharacteristic
326D4—21no—
327D4—21no—
328D4—42no—
329D4—3162no—
330D4—3162no—
331D4—3162no—
332D4—3162no—
333D4—3162no—
334D4—792no—
335D4—6321no—
336D4—6321no—
337D4—1582no—
338D4—1581no—
339D4—1581no—
340D4—1581no—
341D4—1581no—
342D4—1581no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—3162no—
349C2×C4—791no—
350C2×C4—791no—
351C2×C4—791no—
352C2×C4—6321no—
353C2×C4—6321no—
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—3161no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22—3161no—
374C22—3161no—
375C22—3161no—
376C22—3161no—
377C22—792no—
378C22—6324no—
379C22—6324no—
380C22—1582no—
381C22—1581no—
382C22—1581no—
383C22C2×D4×D7911yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—41no—
388C4—3161no—
389C4—1581no—
390C4—1581no—
391C4—1581no—
392C4#41×D7911yescharacteristic
393C4#1457920711yescharacteristic
394C2—41no—
395C2—81no—
396C2—3162no—
397C2—6321no—
398C2—6321no—
399C2—1582no—
400C2#1909920511yescharacteristic
401C2AGL(1,ℤ/8)×D7911yescharacteristic
402C2#1909936511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#482×C79C2
socleC22×C79C22×D4
hypercenter#482D79
hypocenterC79#3318
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #19099257C2semidirect
2. #19099197C2semidirect
3. #19098926C2semidirect
4. #19098883C2semidirect
5. #19098866C2semidirect
6. #19098814C2semidirect
7. #19098800C2semidirect
8. #19098757C2semidirect
9. #19098699C2semidirect
10. #19098698C2semidirect
11. #19098674C2semidirect
12. #19098637C2semidirect
13. #19098567C2semidirect
14. #102×D79C2semidirect
15. #482×C79C2semidirect
20. C2×D632C22semidirect
21. C2×#11929609C22semidirect
22. C2×#11929608C22semidirect
23. C2×C8×D79C22semidirect
26. #14579152C22semidirect
29. #14579136C22semidirect
30. #14579135C22semidirect
37. #14579123C22semidirect
39. C4⋊C4×D79C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
43. #14579083C22semidirect
44. #14579082C22semidirect
47. #14579081C22semidirect
48. #14579081C22semidirect
49. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579071C22semidirect
53. #117×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. #102×C79C22semidirect
57. #102×C79C22semidirect
58. C22⋊C8×C79C22semidirect
202. C79#3318semidirect
206. #482D79semidirect
242. #117C2×D79semidirect
244. #107C2×D79semidirect
246. #106C2×D79semidirect
256. #102C2×D79semidirect
257. #102C2×D79semidirect
259. C22⋊C8C2×D79semidirect