Finite Group Databasebeta

← #23775099

Subgroups — #23775099

Order 10112.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D79C212yesmaximal, complemented
2#19099228C211yesmaximal, characteristic, complemented
3D4×D316C211yesmaximal, characteristic
4#19098937C211yesmaximal, characteristic, complemented
5#19098795C212yesmaximal, complemented
6#19098764C211yesmaximal, characteristic, complemented
7#19098712C212yesmaximal, complemented
8#19098703C212yesmaximal, complemented
9C4×#11929612C211yesmaximal, characteristic, complemented
10#19098628C211yesmaximal, characteristic, complemented
11#461×C79C211yesmaximal, characteristic, complemented
12C2×Q8×D79C2212yescomplemented
13C22×D316—21no—
14C2×D4×D79C2212yes—
15C2×#11929613C2212yescomplemented
16C2×#11929612C2211yescharacteristic
17C2×#11929611C2212yescomplemented
18C2×#11929611C2212yescomplemented
19SD16×D79—28no—
20C2×C8×D79C2212yescomplemented
21#14579160—21no—
22#14579158C2211yescharacteristic
23#14579139—22no—
24#14579137C2212yescomplemented
25#14579136C2212yes—
26#14579135—21no—
27#14579131—22no—
28C4×Dic158C2211yescharacteristic, complemented
29C4×D316C2211yescharacteristic
30#14579123—21no—
31#14579092C2211yescharacteristic, complemented
32#14579084C2211yescharacteristic, complemented
33#14579083C2212yescomplemented
34#14579082C2211yescharacteristic
35(C2×D79)⋊C8C2212yescomplemented
36C4×C79⋊C8C2211yescharacteristic, complemented
37C2×SD16×C79C2212yes—
38C4⋊Q8×C79C2211yescharacteristic, complemented
39C4×D4×C79C2211yescharacteristic
40C4⋊C8×C79C2211yescharacteristic, complemented
41#103×C79C2212yescomplemented
42C23×D79—22no—
43C2×Dic158—22no—
44C2×Dic158C2311yescharacteristic
45Q8×D79—24no—
46Q8×D79—42no—
47C2×D316—22no—
48C2×D316—21no—
49C2×D316—21no—
50C2×D316—44no—
51C2×D316D411yescharacteristic
52C2×D316C2312yes—
53C2×C22⋊D79—22no—
54D4×D79—24no—
55D4×D79—42no—
56C2×C4×D79—22no—
57C2×C4×D79C2312yes—
58#11929613—24no—
59#11929612D414yescomplemented
60#11929611—24no—
61#11929611—42no—
62C2×C79⋊C8C2311yescharacteristic
63C2×C79⋊C8C2311yescharacteristic
64C8×D79—24no—
65C4⋊Dic79D411yescharacteristic
66C4⋊Dic79C2311yescharacteristic
67Dic79⋊C4—22no—
68Dic79⋊C4—21no—
69(C2×D79)⋊C4—22no—
70(C2×D79)⋊C4—22no—
71(C2×D79)⋊C4D412yes—
72C4×Dic79—21no—
73C2×Q8×C79C2312yes—
74C2×D4×C79C2311yescharacteristic
75C22×C4×C79—21no—
76SD16×C79—24no—
77C2×C8×C79C2312yes—
78C4⋊C4×C79—21no—
79C4⋊C4×C79—21no—
80C4⋊C4×C79C2311yescharacteristic
81C22⋊C4×C79—21no—
82C42×C79C2311yescharacteristic
83C23×C79—21no—
84C22×D79—22no—
85C22×D79—44no—
86C22×D79—44no—
87C22×D79—82no—
88C22×D79C2×D412yes—
89Q8×C79—22no—
90Q8×C79—22no—
91D4×C79—21no—
92D4×C79C2×D412yes—
93C2×C4×C79—21no—
94C2×C4×C79—22no—
95C2×C4×C79—42no—
96C2×C4×C79C2×D411yescharacteristic
97C2×C4×C79C2×D411yescharacteristic
98C2×C4×C79C2411yescharacteristic
99C22⋊D79—44no—
100C2×Dic79—21no—
101C2×Dic79—21no—
102C2×Dic79C2×D412yes—
103D316—22no—
104D316—22no—
105D316—44no—
106D316—42no—
107D316—81no—
108D316SD1614yescomplemented
109C4×D79—22no—
110C4×D79—22no—
111C4×D79—44no—
112Dic158—21no—
113Dic158—44no—
114Dic158C2×D412yescomplemented
115C8×C79—22no—
116C79⋊C8—21no—
117C79⋊C8C2×D412yescomplemented
118C22×C79—22no—
119C22×C79—41no—
120C22×C79—41no—
121C22×C79C22×D411yescharacteristic
122C2×D79—22no—
123C2×D79—22no—
124C2×D79—42no—
125C2×D79—42no—
126C2×D79—42no—
127C2×D79—88no—
128C2×D79C2×SD1614yescomplemented
129C4×C79—21no—
130C4×C79—42no—
131C4×C79—41no—
132C4×C79C2×SD1612yescomplemented
133C4×C79C22×D411yescharacteristic
134C4×C79H(5,𝔽2)11yescharacteristic
135Dic79—22no—
136Dic79—22no—
137Dic79—41no—
138C2×C79—42no—
139C2×C79D4211yescharacteristic
140C2×C79C22×SD1611yescharacteristic
141C2×C79#57711yescharacteristic
142D79—24no—
143D79—82no—
144D4×SD16—791nomaximal, Sylow
145C79D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—792no—
147D4×Q8—791no—
148D42—791no—
149#492—791no—
150#465—792no—
151#461D7911yescharacteristic, complemented
152#460—791no—
153#450—792no—
154#448—792no—
155C4×SD16—791no—
156C8×D4—791no—
157C22×Q8—792no—
158C22×D4—792no—
159C22×D4—1581no—
160C2×SD16—792no—
161C2×SD16—791no—
162C2×SD16—792no—
163C2×SD16—792no—
164C2×SD16—1588no—
165C2×SD16C2×D7912yes—
166C22×C8—792no—
167C4⋊Q8—1581no—
168C4⋊Q8C2×D7911yescharacteristic, complemented
169#127—791no—
170C22⋊Q8—792no—
171C22⋊Q8—1582no—
172#121—792no—
173#121—1581no—
174#120—1582no—
175C4×Q8—791no—
176C4×D4—791no—
177C4×D4—1581no—
178C4×D4C2×D7911yescharacteristic
179#106—791no—
180C4⋊C8C2×D7911yescharacteristic, complemented
181#103—791no—
182#103C2×D7912yescomplemented
183#102—791no—
184#102—792no—
185C22⋊C8—792no—
186C4×C8—791no—
187C24—1582no—
188C2×Q8—3162no—
189C2×Q8—791no—
190C2×Q8—1582no—
191C2×Q8—1584no—
192C2×Q8C22×D7912yes—
193C2×D4—3164no—
194C2×D4—3162no—
195C2×D4—791no—
196C2×D4—792no—
197C2×D4—1582no—
198C2×D4—1582no—
199C2×D4—1584no—
200C2×D4—1581no—
201C2×D4—1581no—
202C2×D4C22×D7911yescharacteristic
203C22×C4—21no—
204C22×C4—792no—
205C22×C4—1582no—
206SD16—24no—
207SD16—3162no—
208SD16—794no—
209SD16—1584no—
210SD16—1584no—
211C2×C8—791no—
212C2×C8—791no—
213C2×C8—1584no—
214C2×C8C22×D7912yes—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—791no—
218C4⋊C4—791no—
219C4⋊C4—1582no—
220C4⋊C4—1581no—
221C4⋊C4C22×D7911yescharacteristic
222C22⋊C4—21no—
223C22⋊C4—792no—
224C22⋊C4—1582no—
225C22⋊C4—1582no—
226C42—1581no—
227C42C22×D7911yescharacteristic
228C23—21no—
229C23—3164no—
230C23—3164no—
231C23—792no—
232C23—6322no—
233C23—1582no—
234Q8—22no—
235Q8—22no—
236Q8—3164no—
237Q8—792no—
238Q8—1581no—
239D4—21no—
240D4—3164no—
241D4—3164no—
242D4—3162no—
243D4—794no—
244D4—6321no—
245D4—1582no—
246D4—1582no—
247D4D4×D7912yes—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—3164no—
252C2×C4—792no—
253C2×C4—1581no—
254C2×C4—1581no—
255C2×C4—1582no—
256C2×C4—1582no—
257C2×C4D4×D7911yescharacteristic
258C2×C4D4×D7911yescharacteristic
259C2×C4C23×D7911yescharacteristic
260C8—22no—
261C8—792no—
262C8—1581no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—3162no—
267C22—3162no—
268C22—3162no—
269C22—794no—
270C22—6328no—
271C22—1582no—
272C22—1582no—
273C22C2×D4×D7911yescharacteristic
274C4—21no—
275C4—42no—
276C4—41no—
277C4—3161no—
278C4—1582no—
279C4—1582no—
280C4SD16×D7912yescomplemented
281C4C2×D4×D7911yescharacteristic
282C4#1457920711yescharacteristic
283C2—42no—
284C2—6322no—
285C2—1584no—
286C2#1909919711yescharacteristic
287C2C2×SD16×D7911yescharacteristic
288C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#461×C79C2
socleC22×C79C22×D4
prime radicalD4×D316C2
hypercenter#461D79
hypocenterC79D4×SD16
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D79C2semidirect
2. #19099228C2semidirect
4. #19098937C2semidirect
5. #19098795C2semidirect
6. #19098764C2semidirect
7. #19098712C2semidirect
8. #19098703C2semidirect
9. C4×#11929612C2semidirect
10. #19098628C2semidirect
11. #461×C79C2semidirect
12. C2×Q8×D79C22semidirect
15. C2×#11929613C22semidirect
17. C2×#11929611C22semidirect
18. C2×#11929611C22semidirect
20. C2×C8×D79C22semidirect
24. #14579137C22semidirect
28. C4×Dic158C22semidirect
31. #14579092C22semidirect
32. #14579084C22semidirect
33. #14579083C22semidirect
35. (C2×D79)⋊C8C22semidirect
36. C4×C79⋊C8C22semidirect
38. C4⋊Q8×C79C22semidirect
40. C4⋊C8×C79C22semidirect
41. #103×C79C22semidirect
59. #11929612D4semidirect
108. D316SD16semidirect
114. Dic158C2×D4semidirect
117. C79⋊C8C2×D4semidirect
128. C2×D79C2×SD16semidirect
132. C4×C79C2×SD16semidirect
145. C79D4×SD16semidirect
151. #461D79semidirect
168. C4⋊Q8C2×D79semidirect
180. C4⋊C8C2×D79semidirect
182. #103C2×D79semidirect
280. C4SD16×D79semidirect