Finite Group Databasebeta

← #23774643

Subgroups — #23774643

Order 10112.

328 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 109 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
1#19099118C211yesmaximal, characteristic, complemented
2#19099098C211yesmaximal, characteristic
3#19098973C211yesmaximal, characteristic, complemented
4#19098925C211yesmaximal, characteristic, complemented
5#19098923C211yesmaximal, characteristic, complemented
6#19098907C212yesmaximal, complemented
7#19098890C212yesmaximal
8#19098869C212yesmaximal, complemented
9#19098862C212yesmaximal, complemented
10#19098618C211yesmaximal, characteristic, complemented
11#501×C79C211yesmaximal, characteristic, complemented
12#14579161C2211yescharacteristic
13#14579156—21no—
14#14579152C2212yes—
15#14579149C2211yescharacteristic
16#14579146—21no—
17#14579141—21no—
18#14579141C2211yescharacteristic
19#14579137—21no—
20#14579136C2211yescharacteristic
21Q8×Dic79—21no—
22#14579126—21no—
23#14579126C2211yescharacteristic
24#14579123—21no—
25#14579123C2211yescharacteristic
26#14579119—21no—
27#14579119C2212yes—
28C42×D79C2211yescharacteristic
29#14579094C2212yes—
30#14579092C2212yes—
31Dic79⋊C8C2212yes—
32#14579086C2212yes—
33#14579084C2212yes—
34#14579083C2212yes—
35#14579081C2212yes—
36(C2×D79)⋊C8C2212yes—
37#14579072C2211yescharacteristic
38C4⋊Q8×C79C2211yescharacteristic
39#125×C79C2211yescharacteristic
40#107×C79C2212yes—
41#106×C79C2212yes—
42#97×C79C2211yescharacteristic
43C2×Dic158—21no—
44C2×Dic158C2311yescharacteristic
45C2×D316—21no—
46C2×D316C2311yescharacteristic
47C2×C4×D79—21no—
48C2×C4×D79D411yescharacteristic
49C2×C4×D79D411yescharacteristic
50C2×C4×D79C2311yescharacteristic
51C2×C79⋊C8C2312yes—
52C4⋊Dic79—21no—
53C4⋊Dic79—22no—
54C4⋊Dic79—21no—
55C4⋊Dic79C2312yes—
56Dic79⋊C4—22no—
57Dic79⋊C4—21no—
58(C2×D79)⋊C4—21no—
59(C2×D79)⋊C4—21no—
60(C2×D79)⋊C4—22no—
61(C2×D79)⋊C4—21no—
62(C2×D79)⋊C4—21no—
63(C2×D79)⋊C4—21no—
64C4×Dic79—21no—
65C4×Dic79—22no—
66C4×Dic79D411yescharacteristic
67C4×Dic79D411yescharacteristic
68C4×Dic79C2311yescharacteristic
69C2×Q8×C79—21no—
70C2×C8×C79C2312yes—
71C4⋊C4×C79—21no—
72C4⋊C4×C79—21no—
73C4⋊C4×C79—21no—
74C4⋊C4×C79C2311yescharacteristic
75C4⋊C4×C79C2312yes—
76C4⋊C4×C79C2311yescharacteristic
77C42×C79C2311yescharacteristic
78C22×D79—21no—
79C22×D79C2×D411yescharacteristic
80Q8×C79—42no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—21no—
84C2×C4×C79C2×D411yescharacteristic
85C2×C4×C79C2×D411yescharacteristic
86C2×C4×C79C2411yescharacteristic
87C2×Dic79—21no—
88C2×Dic79—22no—
89C2×Dic79C2×D411yescharacteristic
90C2×Dic79C2×D411yescharacteristic
91C2×Dic79C2×D411yescharacteristic
92D316—22no—
93D316—42no—
94C4×D79—22no—
95C4×D79—41no—
96C4×D79—41no—
97C4×D79—42no—
98Dic158—22no—
99Dic158—42no—
100C8×C79—22no—
101C79⋊C8—22no—
102C22×C79C22×D411yescharacteristic
103C2×D79—21no—
104C2×D79—21no—
105C2×D79—21no—
106C2×D79—41no—
107C2×D79—41no—
108C2×D79—41no—
109C4×C79—21no—
110C4×C79—21no—
111C4×C79—42no—
112C4×C79—41no—
113C4×C79—41no—
114C4×C792−1+412yes—
115Dic79—21no—
116Dic79—21no—
117Dic79—21no—
118Dic79—41no—
119Dic79—42no—
120C2×C79#53611yescharacteristic
121C2×C79#57511yescharacteristic
122C2×C79#57511yescharacteristic
123D79—41no—
124D79—81no—
125#3240—791nomaximal, Sylow
126C79#324011yescharacteristic, complemented, Sylow
127#533—791no—
128#529—791no—
129#501—791no—
130#501D7911yescharacteristic, complemented
131#489—791no—
132#489—791no—
133#485—792no—
134#482—792no—
135#479—792no—
136#478—792no—
137#432—791no—
138C4⋊Q8—791no—
139C4⋊Q8C2×D7911yescharacteristic
140#126—1581no—
141#125—792no—
142#125C2×D7911yescharacteristic
143#124—791no—
144#123—1581no—
145C22⋊Q8—791no—
146C22⋊Q8—1581no—
147C22⋊Q8—1581no—
148#121—791no—
149C4×Q8—791no—
150C4×Q8—1581no—
151C4×Q8—1581no—
152C4×D4—791no—
153C4×D4—1581no—
154#117—792no—
155#117—1581no—
156C2×C42—791no—
157#107—792no—
158#107C2×D7912yes—
159#106—792no—
160#106C2×D7912yes—
161C4⋊C8—792no—
162#103—792no—
163#103—792no—
164#102—792no—
165#102—792no—
166C22⋊C8—792no—
167#97—791no—
168#97C2×D7911yescharacteristic
169C2×Q8—21no—
170C2×Q8—791no—
171C2×Q8—1581no—
172C2×D4—791no—
173C2×D4—1581no—
174C22×C4—791no—
175C22×C4—791no—
176C22×C4—791no—
177C22×C4—1581no—
178C2×C8—792no—
179C2×C8C22×D7912yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—792no—
184C4⋊C4—1581no—
185C4⋊C4—1582no—
186C4⋊C4—1581no—
187C4⋊C4—1582no—
188C4⋊C4—1581no—
189C4⋊C4C22×D7912yes—
190C4⋊C4C22×D7911yescharacteristic
191C4⋊C4C22×D7911yescharacteristic
192C22⋊C4—1581no—
193C22⋊C4—1581no—
194C22⋊C4—1582no—
195C22⋊C4—1581no—
196C22⋊C4—1581no—
197C22⋊C4—1581no—
198C42—791no—
199C42—791no—
200C42—791no—
201C42—1582no—
202C42—1581no—
203C42C22×D7911yescharacteristic
204C23—791no—
205C23—1581no—
206Q8—42no—
207Q8—3162no—
208Q8—1582no—
209D4—3162no—
210D4—1582no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—3161no—
215C2×C4—3161no—
216C2×C4—3162no—
217C2×C4—791no—
218C2×C4—791no—
219C2×C4—791no—
220C2×C4—1581no—
221C2×C4—1582no—
222C2×C4—1582no—
223C2×C4D4×D7911yescharacteristic
224C2×C4D4×D7911yescharacteristic
225C2×C4C23×D7911yescharacteristic
226C8—22no—
227C8—1582no—
228C22—3161no—
229C22—3161no—
230C22—3161no—
231C22—1581no—
232C22—1581no—
233C22—1581no—
234C22C2×D4×D7911yescharacteristic
235C4—21no—
236C4—21no—
237C4—41no—
238C4—42no—
239C4—41no—
240C4—3161no—
241C4—3162no—
242C4—1581no—
243C4—1581no—
244C4—1581no—
245C4#1457920912yes—
246C2—3161no—
247C2—6321no—
248C2#1909913811yescharacteristic
249C2#1909935911yescharacteristic
250C2#1909936211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#501×C79C2
socleC22×C79C22×D4
prime radical#14579136C22
hypercenter#501D79
hypocenterC79#3240
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #19099118C2semidirect
3. #19098973C2semidirect
4. #19098925C2semidirect
5. #19098923C2semidirect
6. #19098907C2semidirect
8. #19098869C2semidirect
9. #19098862C2semidirect
10. #19098618C2semidirect
11. #501×C79C2semidirect
126. C79#3240semidirect
130. #501D79semidirect