Finite Group Databasebeta

← #23775091

Subgroups — #23775091

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
2Q8×D316C211yesmaximal, characteristic, complemented
3#19099198C211yesmaximal, characteristic
4#19098935C211yesmaximal, characteristic, complemented
5#19098791C212yesmaximal, complemented
6#19098769C211yesmaximal, characteristic, complemented
7#19098715C212yesmaximal, complemented
8#19098700C212yesmaximal, complemented
9C4×#11929611C211yesmaximal, characteristic, complemented
10#19098628C211yesmaximal, characteristic, complemented
11#460×C79C211yesmaximal, characteristic, complemented
12C2×Q8×D79C2212yescomplemented
13C2×D4×D79—21no—
14C2×D4×D79C2212yes—
15C2×#11929613C2212yes—
16C2×#11929612C2212yescomplemented
17C2×#11929612C2212yescomplemented
18C2×#11929611C2211yescharacteristic
19SD16×D79—28no—
20C2×C8×D79C2212yescomplemented
21#14579161—21no—
22#14579161C2211yescharacteristic, complemented
23#14579141—22no—
24#14579141C2212yescomplemented
25#14579132—21no—
26#14579132C2212yes—
27#14579129—22no—
28C4×D316—21no—
29C4×D316C2211yescharacteristic
30C4×D316C2211yescharacteristic
31#14579092C2211yescharacteristic, complemented
32#14579086C2212yescomplemented
33#14579085C2211yescharacteristic, complemented
34#14579081C2211yescharacteristic
35(C2×D79)⋊C8C2212yescomplemented
36C4×C79⋊C8C2211yescharacteristic, complemented
37C2×SD16×C79C2212yescomplemented
38#127×C79C2211yescharacteristic
39C4×Q8×C79C2211yescharacteristic, complemented
40C4⋊C8×C79C2211yescharacteristic, complemented
41#102×C79C2212yescomplemented
42C23×D79—22no—
43C2×Dic158—22no—
44C2×Dic158C2312yes—
45Q8×D79—24no—
46Q8×D79—42no—
47C2×D316D411yescharacteristic
48C2×D316C2311yescharacteristic
49C2×C22⋊D79—22no—
50C2×C22⋊D79—22no—
51D4×D79—24no—
52D4×D79—42no—
53D4×D79—44no—
54C2×C4×D79—22no—
55C2×C4×D79—21no—
56C2×C4×D79C2312yes—
57#11929613—24no—
58#11929612—24no—
59#11929612—42no—
60#11929611D414yescomplemented
61C2×C79⋊C8C2311yescharacteristic
62C2×C79⋊C8C2311yescharacteristic
63C8×D79—24no—
64C4⋊Dic79—22no—
65C4⋊Dic79—21no—
66C4⋊Dic79—21no—
67C4⋊Dic79D411yescharacteristic
68C4⋊Dic79C2311yescharacteristic
69C22⋊Dic79—22no—
70(C2×D79)⋊C4—22no—
71(C2×D79)⋊C4—21no—
72(C2×D79)⋊C4D412yes—
73C2×Q8×C79C2311yescharacteristic
74C2×D4×C79—21no—
75C2×D4×C79—21no—
76C2×D4×C79C2312yes—
77SD16×C79—24no—
78C2×C8×C79C2312yes—
79C4⋊C4×C79—21no—
80C4⋊C4×C79C2311yescharacteristic
81C42×C79—21no—
82C42×C79C2311yescharacteristic
83C23×C79—22no—
84C22×D79—21no—
85C22×D79—44no—
86C22×D79—44no—
87C22×D79—82no—
88C22×D79C2×D412yes—
89Q8×C79—21no—
90Q8×C79C2×D412yescomplemented
91D4×C79—22no—
92D4×C79—22no—
93D4×C79—42no—
94D4×C79—81no—
95C2×C4×C79—21no—
96C2×C4×C79—21no—
97C2×C4×C79C2×D411yescharacteristic
98C2×C4×C79C2×D411yescharacteristic
99C2×C4×C79C2411yescharacteristic
100C22⋊D79—44no—
101C22⋊D79—44no—
102C2×Dic79—21no—
103C2×Dic79—22no—
104C2×Dic79C2×D412yes—
105D316—21no—
106D316SD1614yescomplemented
107D316C2×D412yes—
108C4×D79—22no—
109C4×D79—22no—
110C4×D79—44no—
111C4×D79—42no—
112Dic158—22no—
113Dic158—22no—
114Dic158—44no—
115C8×C79—22no—
116C79⋊C8—21no—
117C79⋊C8C2×D412yescomplemented
118C22×C79—42no—
119C22×C79—42no—
120C22×C79—42no—
121C22×C79C22×D411yescharacteristic
122C2×D79—22no—
123C2×D79—22no—
124C2×D79—22no—
125C2×D79—41no—
126C2×D79—41no—
127C2×D79—88no—
128C2×D79C2×SD1614yescomplemented
129C4×C79—22no—
130C4×C79—21no—
131C4×C79—41no—
132C4×C79C2×SD1612yescomplemented
133C4×C79C22×D411yescharacteristic
134C4×C79H(5,𝔽2)11yescharacteristic
135Dic79—22no—
136Dic79—42no—
137Dic79—41no—
138C2×C79—82no—
139C2×C79D4211yescharacteristic
140C2×C79C22×SD1611yescharacteristic
141C2×C79#57711yescharacteristic
142D79—24no—
143D79—42no—
144D4×SD16—791nomaximal, Sylow
145C79D4×SD1611yescharacteristic, complemented, Sylow
146C22×SD16—792no—
147D4×Q8—791no—
148D42—791no—
149#492—791no—
150#465—792no—
151#461—791no—
152#460D7911yescharacteristic, complemented
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×D7912yescomplemented
166C22×C8—792no—
167C4⋊Q8—791no—
168C4⋊Q8—1581no—
169#127C2×D7911yescharacteristic
170C22⋊Q8—792no—
171C22⋊Q8—1582no—
172#121—792no—
173#121—1581no—
174#120—1582no—
175C4×Q8C2×D7911yescharacteristic, complemented
176C4×D4—791no—
177C4×D4—791no—
178C4×D4—1581no—
179#106—791no—
180C4⋊C8C2×D7911yescharacteristic, complemented
181#103—791no—
182#103—792no—
183#102—791no—
184#102C2×D7912yescomplemented
185C22⋊C8—792no—
186C4×C8—791no—
187C24—1582no—
188C2×Q8—3162no—
189C2×Q8—792no—
190C2×Q8—1582no—
191C2×Q8—1584no—
192C2×Q8C22×D7911yescharacteristic
193C2×D4—21no—
194C2×D4—21no—
195C2×D4—3164no—
196C2×D4—3162no—
197C2×D4—791no—
198C2×D4—791no—
199C2×D4—1582no—
200C2×D4—1584no—
201C2×D4—1582no—
202C2×D4C22×D7912yes—
203C22×C4—792no—
204C22×C4—1582no—
205C22×C4—1581no—
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—791no—
217C4⋊C4—791no—
218C4⋊C4—1582no—
219C4⋊C4—1581no—
220C4⋊C4—1581no—
221C4⋊C4C22×D7911yescharacteristic
222C22⋊C4—792no—
223C22⋊C4—1582no—
224C22⋊C4—1582no—
225C22⋊C4—1581no—
226C42—21no—
227C42C22×D7911yescharacteristic
228C23—22no—
229C23—3164no—
230C23—3164no—
231C23—792no—
232C23—6322no—
233C23—1581no—
234Q8—21no—
235Q8—3164no—
236Q8—1582no—
237Q8—1582no—
238Q8D4×D7912yescomplemented
239D4—22no—
240D4—22no—
241D4—42no—
242D4—81no—
243D4—3164no—
244D4—3164no—
245D4—794no—
246D4—792no—
247D4—1581no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—3164no—
251C2×C4—3162no—
252C2×C4—792no—
253C2×C4—1581no—
254C2×C4—1582no—
255C2×C4—1582no—
256C2×C4—1582no—
257C2×C4D4×D7911yescharacteristic
258C2×C4D4×D7911yescharacteristic
259C2×C4C23×D7911yescharacteristic
260C8—22no—
261C8—792no—
262C8—1581no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—3161no—
267C22—3161no—
268C22—794no—
269C22—6328no—
270C22—1582no—
271C22—1582no—
272C22—1582no—
273C22C2×D4×D7911yescharacteristic
274C4—22no—
275C4—21no—
276C4—41no—
277C4—3162no—
278C4—3161no—
279C4—1582no—
280C4SD16×D7912yescomplemented
281C4C2×D4×D7911yescharacteristic
282C4#1457920711yescharacteristic
283C2—82no—
284C2—3162no—
285C2—1584no—
286C2#1909919711yescharacteristic
287C2C2×SD16×D7911yescharacteristic
288C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#460×C79C2
socleC22×C79C22×D4
prime radical#19099198C2
hypercenter#460D79
hypocenterC79D4×SD16
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D79C2semidirect
2. Q8×D316C2semidirect
4. #19098935C2semidirect
5. #19098791C2semidirect
6. #19098769C2semidirect
7. #19098715C2semidirect
8. #19098700C2semidirect
9. C4×#11929611C2semidirect
10. #19098628C2semidirect
11. #460×C79C2semidirect
12. C2×Q8×D79C22semidirect
16. C2×#11929612C22semidirect
17. C2×#11929612C22semidirect
20. C2×C8×D79C22semidirect
22. #14579161C22semidirect
24. #14579141C22semidirect
31. #14579092C22semidirect
32. #14579086C22semidirect
33. #14579085C22semidirect
35. (C2×D79)⋊C8C22semidirect
36. C4×C79⋊C8C22semidirect
37. C2×SD16×C79C22semidirect
39. C4×Q8×C79C22semidirect
40. C4⋊C8×C79C22semidirect
41. #102×C79C22semidirect
60. #11929611D4semidirect
90. Q8×C79C2×D4semidirect
106. D316SD16semidirect
117. C79⋊C8C2×D4semidirect
128. C2×D79C2×SD16semidirect
132. C4×C79C2×SD16semidirect
145. C79D4×SD16semidirect
152. #460D79semidirect
165. C2×SD16C2×D79semidirect
175. C4×Q8C2×D79semidirect
180. C4⋊C8C2×D79semidirect
184. #102C2×D79semidirect
238. Q8D4×D79semidirect
280. C4SD16×D79semidirect