Finite Group Databasebeta

← #23775252

Subgroups — #23775252

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099259C211yesmaximal, characteristic, complemented
2#19099209C211yesmaximal, characteristic, complemented
3#19098918C211yesmaximal, characteristic, complemented
4#19098899C211yesmaximal, characteristic, complemented
5#19098888C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098799C211yesmaximal, characteristic, complemented
8#19098792C211yesmaximal, characteristic, complemented
9#19098779C211yesmaximal, characteristic, complemented
10#19098710C211yesmaximal, characteristic, complemented
11#19098699C211yesmaximal, characteristic, complemented
12C4×D632C211yesmaximal, characteristic, complemented
13#19098560C211yesmaximal, characteristic, complemented
14C2×#14579083C211yesmaximal, characteristic, complemented
15C8×D4×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929613C2211yescharacteristic, complemented
19C2×D632C2211yescharacteristic
20C2×D632C2211yescharacteristic
21#14579156—21no—
22#14579153C2211yescharacteristic, complemented
23#14579149C2211yescharacteristic
24#14579146—21no—
25#14579143—21no—
26#14579140C2211yescharacteristic
27#14579135C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579135C2211yescharacteristic, complemented
30#14579134—21no—
31#14579133—21no—
32#14579129—21no—
33C4×D316C2211yescharacteristic
34C4×D316C2211yescharacteristic, complemented
35(C22⋊D79)⋊C4—21no—
36#14579120C2211yescharacteristic, complemented
37C2×C4⋊Dic79C2211yescharacteristic
38C22⋊C4×D79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579095C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic, complemented
52C22×C8×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic, complemented
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic, complemented
56C22⋊C8×C79C2211yescharacteristic
57C22⋊C8×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
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—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77#11929613—41no—
78D632—22no—
79D632—41no—
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—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—
97C4×Dic79—21no—
98C2×D4×C79D411yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C2×C8×C79—41no—
102C2×C8×C79—41no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—81no—
119D4×C79—22no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—42no—
130C22⋊D79—42no—
131C22⋊D79—81no—
132C22⋊D79—81no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—81no—
139D316—21no—
140D316—21no—
141D316—21no—
142D316—21no—
143D316—21no—
144D316—42no—
145D316#4112yes—
146C4×D79—42no—
147C4×D79—81no—
148C4×D79—81no—
149Dic158—21no—
150Dic158—21no—
151C8×C79—21no—
152C8×C79—21no—
153C8×C79—21no—
154C8×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79#13512yes—
161C22×C79C22×D411yescharacteristic
162C2×D79—22no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—84no—
172C4×C79—21no—
173C4×C79—21no—
174C4×C79—21no—
175C4×C79—21no—
176C4×C79C2×#4111yescharacteristic
177C4×C79H(5,𝔽2)11yescharacteristic
178Dic79—41no—
179Dic79—41no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—22no—
184C2×C79—41no—
185C2×C79#54611yescharacteristic
186C2×C79C2×#13511yescharacteristic
187C2×C79#57611yescharacteristic
188D79—42no—
189D79—81no—
190D79—81no—
191#3297—791nomaximal, Sylow
192C79#329711yescharacteristic, complemented, Sylow
193#553—791no—
194#546—791no—
195#488—791no—
196#484—791no—
197#482—791no—
198#478—791no—
199#466—791no—
200#465—791no—
201#463—791no—
202#449—791no—
203#447—791no—
204C4×D8—791no—
205C8×D4D7911yescharacteristic, complemented
206#416—791no—
207C2×#102—791no—
208C2×#41—791no—
209C22×D4—791no—
210C2×SD16—791no—
211C2×D8—791no—
212C2×D8—791no—
213C22×C8C2×D7911yescharacteristic
214C22×C8C2×D7911yescharacteristic, complemented
215#126—1581no—
216#125—791no—
217#124—791no—
218#123—1581no—
219#123—1581no—
220C22⋊Q8—791no—
221#121—791no—
222#121—791no—
223#121—791no—
224#121—1581no—
225#121—1581no—
226#120—1581no—
227C4×D4—791no—
228C4×D4—791no—
229C4×D4—1581no—
230C4×D4C2×D7911yescharacteristic
231#117—791no—
232C2×C4⋊C4—791no—
233C2×C22⋊C4—1581no—
234#107—791no—
235#107—791no—
236#106—791no—
237C4⋊C8C2×D7911yescharacteristic, complemented
238#103—791no—
239#103—791no—
240#103—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248C22⋊C8C2×D7911yescharacteristic
249C22⋊C8C2×D7911yescharacteristic, complemented
250C4×C8C2×D7911yescharacteristic, complemented
251C24—1581no—
252#41—3161no—
253#41—1582no—
254C2×Q8—791no—
255C2×D4—3161no—
256C2×D4—791no—
257C2×D4—791no—
258C2×D4—791no—
259C2×D4—1582no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4D31611yescharacteristic
266C22×C4—1581no—
267C22×C4—1581no—
268C22×C4—1581no—
269C22×C4—1581no—
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272SD16—3161no—
273D8—3161no—
274D8—1582no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D7911yescharacteristic
278C2×C8C22×D7911yescharacteristic
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—791no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4—1581no—
288C4⋊C4—1581no—
289C4⋊C4D31611yescharacteristic
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⋊C4D31611yescharacteristic
300C22⋊C4D31611yescharacteristic
301C42—1581no—
302C42C22×D7911yescharacteristic
303C23—3162no—
304C23—3162no—
305C23—6321no—
306C23—1581no—
307C23—1581no—
308C23—1581no—
309C23C2×D31611yescharacteristic
310C23C2×D31611yescharacteristic
311Q8—1581no—
312Q8—1581no—
313D4—22no—
314D4—3162no—
315D4—3162no—
316D4—3162no—
317D4—792no—
318D4—6321no—
319D4—6321no—
320D4—1581no—
321D4—1581no—
322D4—1581no—
323D4—1581no—
324D4—1581no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3162no—
330C2×C4—6321no—
331C2×C4—6321no—
332C2×C4—6321no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4C2×D31611yescharacteristic
339C2×C4C2×D31611yescharacteristic
340C2×C4C2×D31611yescharacteristic
341C2×C4C2×D31611yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—3161no—
353C22—3161no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—6324no—
361C22—1582no—
362C22#1457918312yes—
363C22C22×D31611yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—3161no—
369C4—3161no—
370C4—3161no—
371C4—3161no—
372C4—3161no—
373C4#41×D7911yescharacteristic
374C4#1457920611yescharacteristic
375C2—22no—
376C2—41no—
377C2—3162no—
378C2—6321no—
379C2—6321no—
380C2#1909920811yescharacteristic
381C2C2×#1457918311yescharacteristic
382C2#1909936811yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC8×D4×C79C2
socleC22×C79C22×D4
hypercenterC8×D4D79
hypocenterC79#3297
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #19099259C2semidirect
2. #19099209C2semidirect
3. #19098918C2semidirect
4. #19098899C2semidirect
5. #19098888C2semidirect
6. #19098864C2semidirect
7. #19098799C2semidirect
8. #19098792C2semidirect
9. #19098779C2semidirect
10. #19098710C2semidirect
11. #19098699C2semidirect
12. C4×D632C2semidirect
13. #19098560C2semidirect
14. C2×#14579083C2semidirect
15. C8×D4×C79C2semidirect
18. C2×#11929613C22semidirect
22. #14579153C22semidirect
29. #14579135C22semidirect
34. C4×D316C22semidirect
36. #14579120C22semidirect
39. #14579095C22semidirect
40. #14579095C22semidirect
41. #14579093C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
51. #14579083C22semidirect
53. C22×C8×C79C22semidirect
55. C4⋊C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. C4×C8×C79C22semidirect
192. C79#3297semidirect
205. C8×D4D79semidirect
214. C22×C8C2×D79semidirect
237. C4⋊C8C2×D79semidirect
249. C22⋊C8C2×D79semidirect
250. C4×C8C2×D79semidirect