Finite Group Databasebeta

← #23775610

Subgroups — #23775610

Order 10112.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099209C211yesmaximal, characteristic
2#19098920C211yesmaximal, characteristic, complemented
3#19098904C211yesmaximal, characteristic, complemented
4#19098881C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098785C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098713C211yesmaximal, characteristic, complemented
11C4×#11929611C211yesmaximal, characteristic, complemented
12#19098641C211yesmaximal, characteristic, complemented
13#19098567C211yesmaximal, characteristic, complemented
14#19098562C211yesmaximal, characteristic, complemented
15#552×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C2×#11929608C2211yescharacteristic, complemented
23#14579149C2211yescharacteristic
24#14579146—21no—
25#14579140C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579134—21no—
28#14579129—21no—
29C4×D316C2211yescharacteristic
30C22⋊C4×D79—21no—
31#14579094C2211yescharacteristic, complemented
32#14579092C2211yescharacteristic, complemented
33#14579092C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35#14579085C2211yescharacteristic, complemented
36#14579084C2211yescharacteristic, complemented
37#14579084C2211yescharacteristic, complemented
38#14579084C2211yescharacteristic, complemented
39#14579081C2211yescharacteristic
40#14579081C2211yescharacteristic
41#14579081C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47C4×C79⋊C8C2211yescharacteristic, complemented
48#126×C79—21no—
49#125×C79—21no—
50#125×C79C2211yescharacteristic, complemented
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic, complemented
54C4×Q8×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56#117×C79—21no—
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×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×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72#11929614—41no—
73#11929611—22no—
74#11929611—41no—
75#11929608—41no—
76#11929608—41no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88C2×Q8×C79C2311yescharacteristic
89C2×D4×C79D411yescharacteristic
90C22×C4×C79—21no—
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79D411yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79D411yescharacteristic
107C22⋊C4×C79D411yescharacteristic
108C42×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118Q8×C79—21no—
119Q8×C79—21no—
120D4×C79—41no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—42no—
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—42no—
136C22⋊D79—81no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139D316—21no—
140D316—21no—
141D316—21no—
142D316—42no—
143D316#4112yes—
144C4×D79—42no—
145C4×D79—81no—
146Dic158—21no—
147Dic158—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79C22×D411yescharacteristic
159C2×D79—22no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—84no—
166C4×C79—21no—
167C4×C79—21no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79C2×#4111yescharacteristic
175C4×C79H(5,𝔽2)11yescharacteristic
176Dic79—41no—
177Dic79—41no—
178C2×C79—41no—
179C2×C79—41no—
180C2×C79#54611yescharacteristic
181C2×C79#57511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—42no—
184D79—81no—
185#3323—791nomaximal, Sylow
186C79#332311yescharacteristic, complemented, Sylow
187#552D7911yescharacteristic, complemented
188#546—791no—
189#488—791no—
190#485—791no—
191#481—791no—
192#478—791no—
193#470—791no—
194#468—791no—
195#464—791no—
196#452—791no—
197#450—791no—
198C4×SD16—791no—
199#436—791no—
200#418—791no—
201#417—791no—
202C2×#41—791no—
203C22×D4—791no—
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16—791no—
207C2×M16—791no—
208C2×M16—791no—
209#126—21no—
210#125—21no—
211#125C2×D7911yescharacteristic, complemented
212#124—791no—
213#123—21no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8C2×D7911yescharacteristic
217C22⋊Q8C2×D7911yescharacteristic, complemented
218#121—791no—
219#121—1581no—
220#120—1581no—
221C4×Q8C2×D7911yescharacteristic, complemented
222C4×D4—791no—
223C4×D4C2×D7911yescharacteristic
224#117—21no—
225#117C2×D7911yescharacteristic
226C2×C4⋊C4C2×D7911yescharacteristic, complemented
227C2×C22⋊C4—1581no—
228#107—791no—
229#106—791no—
230#106—791no—
231C4⋊C8—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242C22⋊C8—791no—
243C22⋊C8—791no—
244C4×C8—791no—
245C24—1581no—
246#41—3161no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—3161no—
251C2×D4—791no—
252C2×D4—791no—
253C2×D4—1582no—
254C2×D4—1581no—
255C2×D4—1581no—
256C2×D4—1581no—
257C2×D4C22⋊D7911yescharacteristic
258C22×C4—21no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4C22×D7911yescharacteristic
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—3161no—
265SD16—1582no—
266M16—3161no—
267M16—3161no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—791no—
279C4⋊C4—1581no—
280C4⋊C4C22⋊D7911yescharacteristic
281C4⋊C4C22×D7911yescharacteristic
282C4⋊C4C22×D7911yescharacteristic
283C4⋊C4C22×D7911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4C22⋊D7911yescharacteristic
293C22⋊C4C22⋊D7911yescharacteristic
294C42—21no—
295C42—21no—
296C42C22×D7911yescharacteristic
297C23—3162no—
298C23—3162no—
299C23—6321no—
300C23—1581no—
301C23—1581no—
302C23C2×C22⋊D7911yescharacteristic
303C23C2×C22⋊D7911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1581no—
307Q8—1581no—
308D4—41no—
309D4—3162no—
310D4—3162no—
311D4—792no—
312D4—6321no—
313D4—1581no—
314D4—1581no—
315D4—1581no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—3162no—
326C2×C4—6321no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4C2×C22⋊D7911yescharacteristic
330C2×C4C2×C22⋊D7911yescharacteristic
331C2×C4C2×C22⋊D7911yescharacteristic
332C2×C4C2×C22⋊D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—1581no—
335C8—1581no—
336C8—1581no—
337C8—1581no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—3161no—
345C22—3161no—
346C22—3161no—
347C22—3161no—
348C22—3161no—
349C22—6324no—
350C22—1582no—
351C22C22×C22⋊D7911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3161no—
361C4—3161no—
362C4#41×D7911yescharacteristic
363C4#1457920711yescharacteristic
364C2—41no—
365C2—41no—
366C2—3162no—
367C2—6321no—
368C2#1909920111yescharacteristic
369C2#1909936111yescharacteristic
370C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#552×C79C2
socleC22×C79C22×D4
prime radical#19099209C2
hypercenter#552D79
hypocenterC79#3323
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #19098920C2semidirect
3. #19098904C2semidirect
4. #19098881C2semidirect
5. #19098860C2semidirect
6. #19098819C2semidirect
7. #19098811C2semidirect
8. #19098785C2semidirect
9. #19098723C2semidirect
10. #19098713C2semidirect
11. C4×#11929611C2semidirect
12. #19098641C2semidirect
13. #19098567C2semidirect
14. #19098562C2semidirect
15. #552×C79C2semidirect
18. C2×#11929614C22semidirect
22. C2×#11929608C22semidirect
31. #14579094C22semidirect
32. #14579092C22semidirect
33. #14579092C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579085C22semidirect
36. #14579084C22semidirect
37. #14579084C22semidirect
38. #14579084C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. C4×C79⋊C8C22semidirect
50. #125×C79C22semidirect
53. C22⋊Q8×C79C22semidirect
54. C4×Q8×C79C22semidirect
58. C2×C4⋊C4×C79C22semidirect
186. C79#3323semidirect
187. #552D79semidirect
211. #125C2×D79semidirect
217. C22⋊Q8C2×D79semidirect
221. C4×Q8C2×D79semidirect
226. C2×C4⋊C4C2×D79semidirect