Finite Group Databasebeta

← #23775618

Subgroups — #23775618

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#19099253C211yesmaximal, characteristic, complemented
2#19099209C211yesmaximal, characteristic
3#19098918C211yesmaximal, characteristic, complemented
4#19098905C211yesmaximal, characteristic, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098821C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098786C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098716C211yesmaximal, characteristic, complemented
12C4×#11929613C211yesmaximal, characteristic, complemented
13#19098569C211yesmaximal, characteristic, complemented
14#19098565C211yesmaximal, characteristic, complemented
15#436×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21#14579154—21no—
22#14579153C2211yescharacteristic, complemented
23#14579151—21no—
24#14579149C2211yescharacteristic
25#14579146—21no—
26#14579142—21no—
27#14579140C2211yescharacteristic
28#14579140C2211yescharacteristic
29#14579140C2211yescharacteristic, complemented
30#14579135C2211yescharacteristic
31#14579134—21no—
32#14579129—21no—
33C4×Dic158C2211yescharacteristic, complemented
34C4×D316C2211yescharacteristic
35#14579120C2211yescharacteristic
36#14579117—21no—
37C2×C4⋊Dic79C2211yescharacteristic, complemented
38C22⋊C4×D79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579086C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic
52C2×M16×C79C2211yescharacteristic
53C2×M16×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×Dic158C2311yescharacteristic
64C2×D316—22no—
65C2×D316—21no—
66C2×D316—41no—
67C2×D316C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74Dic316—41no—
75#11929613—22no—
76#11929613—41no—
77C4⋊Dic79—21no—
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96C4×Dic79—21no—
97C4×Dic79—21no—
98C2×D4×C79D411yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101M16×C79—41no—
102M16×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—42no—
116C22×D79—42no—
117C22×D79—81no—
118D4×C79—41no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2411yescharacteristic
128C22⋊D79—42no—
129C22⋊D79—81no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—42no—
137D316—21no—
138D316—21no—
139D316—21no—
140D316—42no—
141D316#4112yes—
142C4×D79—42no—
143C4×D79—81no—
144Dic158—21no—
145Dic158—21no—
146Dic158—21no—
147Dic158—21no—
148C8×C79—21no—
149C8×C79—21no—
150C8×C79—21no—
151C8×C79—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×C79C2×#4111yescharacteristic
171C4×C79H(5,𝔽2)11yescharacteristic
172Dic79—41no—
173Dic79—41no—
174Dic79—41no—
175Dic79—41no—
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#552—791no—
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#436D7911yescharacteristic, complemented
200#418—791no—
201#417—791no—
202C2×#41—791no—
203C22×D4—791no—
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16—791no—
207C2×M16C2×D7911yescharacteristic
208C2×M16C2×D7911yescharacteristic, complemented
209#126—1581no—
210#125—791no—
211#125—1581no—
212#124—791no—
213#123—1581no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—791no—
218#121—791no—
219#121—1581no—
220#120—1581no—
221C4×Q8—791no—
222C4×D4—791no—
223C4×D4C2×D7911yescharacteristic
224#117—791no—
225#117—1581no—
226C2×C4⋊C4—791no—
227C2×C22⋊C4—1581no—
228#107—791no—
229#106—791no—
230#106—791no—
231C4⋊C8C2×D7911yescharacteristic, complemented
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⋊C8C2×D7911yescharacteristic
243C22⋊C8C2×D7911yescharacteristic, complemented
244C4×C8C2×D7911yescharacteristic, complemented
245C24—1581no—
246#41—3161no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8—791no—
250C2×D4—3161no—
251C2×D4—791no—
252C2×D4—791no—
253C2×D4—1582no—
254C2×D4—1581no—
255C2×D4—1581no—
256C2×D4—1581no—
257C2×D4D31611yescharacteristic
258C22×C4—1581no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4C22×D7911yescharacteristic
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—3161no—
265SD16—1582no—
266M16—41no—
267M16—41no—
268C2×C8C22×D7911yescharacteristic
269C2×C8C22×D7911yescharacteristic
270C2×C8C22×D7911yescharacteristic
271C2×C8C22×D7911yescharacteristic
272C4⋊C4—791no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4D31611yescharacteristic
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4D31611yescharacteristic
293C22⋊C4D31611yescharacteristic
294C42—1581no—
295C42—1581no—
296C42C22×D7911yescharacteristic
297C23—3162no—
298C23—3162no—
299C23—6321no—
300C23—1581no—
301C23—1581no—
302C23C2×D31611yescharacteristic
303C23C2×D31611yescharacteristic
304Q8—1581no—
305Q8—1581no—
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—3162no—
321C2×C4—3162no—
322C2×C4—6321no—
323C2×C4—1581no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4C2×D31611yescharacteristic
330C2×C4C2×D31611yescharacteristic
331C2×C4C2×D31611yescharacteristic
332C2×C4C2×D31611yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
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×D31611yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—3161no—
360C4—3161no—
361C4—3161no—
362C4#41×D7911yescharacteristic
363C4#1457920611yescharacteristic
364C2—41no—
365C2—41no—
366C2—3162no—
367C2—6321no—
368C2#1909920811yescharacteristic
369C2#1909936311yescharacteristic
370C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#436×C79C2
socleC22×C79C22×D4
prime radical#19099209C2
hypercenter#436D79
hypocenterC79#3323
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #19099253C2semidirect
3. #19098918C2semidirect
4. #19098905C2semidirect
5. #19098882C2semidirect
6. #19098864C2semidirect
7. #19098821C2semidirect
8. #19098809C2semidirect
9. #19098786C2semidirect
10. #19098727C2semidirect
11. #19098716C2semidirect
12. C4×#11929613C2semidirect
13. #19098569C2semidirect
14. #19098565C2semidirect
15. #436×C79C2semidirect
18. C2×Dic316C22semidirect
22. #14579153C22semidirect
29. #14579140C22semidirect
33. C4×Dic158C22semidirect
37. C2×C4⋊Dic79C22semidirect
39. #14579095C22semidirect
40. #14579093C22semidirect
41. #14579093C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579086C22semidirect
53. C2×M16×C79C22semidirect
55. C4⋊C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. C4×C8×C79C22semidirect
186. C79#3323semidirect
199. #436D79semidirect
208. C2×M16C2×D79semidirect
231. C4⋊C8C2×D79semidirect
243. C22⋊C8C2×D79semidirect
244. C4×C8C2×D79semidirect