Finite Group Databasebeta

← #23771663

Subgroups — #23771663

Order 10112.

548 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 125 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#19098500C211yesmaximal, characteristic, complemented
2#19098498C213yesmaximal, complemented
3#19098487C211yesmaximal, characteristic, complemented
4#19098486C213yesmaximal, complemented
5#19098485C213yesmaximal, complemented
6#19098418C213yesmaximal
7#396×C79C211yesmaximal, characteristic, complemented
8C24×D79C2211yescharacteristic
9C2×C4⋊Dic79C2213yescomplemented
10C2×Dic79⋊C4C2213yescomplemented
11C2×Dic79⋊C4C2213yescomplemented
12C2×C22⋊Dic79C2213yes—
13C2×(C2×D79)⋊C4C2213yes—
14C2×(C2×D79)⋊C4C2213yes—
15C2×(C2×D79)⋊C4C2213yes—
16C2×(C2×D79)⋊C4C2213yes—
17C79⋊#95C2213yescomplemented
18C2×C4⋊C4×C79C2213yescomplemented
19C2×C22⋊C4×C79C2213yes—
20#95×C79C2211yescharacteristic, complemented
21C23×D79—43no—
22C23×D79—43no—
23C23×D79Q814yes—
24C23×D79C2311yescharacteristic
25C23×D79C2311yescharacteristic
26C22×Dic79C2313yes—
27C22×Dic79C2313yes—
28C4⋊Dic79—43no—
29Dic79⋊C4—43no—
30Dic79⋊C4—43no—
31C22⋊Dic79—43no—
32(C2×D79)⋊C4—43no—
33(C2×D79)⋊C4—43no—
34(C2×D79)⋊C4—43no—
35(C2×D79)⋊C4—43no—
36C24×C79C2311yescharacteristic
37C22×C4×C79C2313yes—
38C22×C4×C79C2313yes—
39C4⋊C4×C79—43no—
40C22⋊C4×C79—43no—
41C23×C79—23no—
42C23×C79—23no—
43C23×C79C2×Q812yes—
44C23×C79C2411yescharacteristic
45C22×D79—23no—
46C22×D79—23no—
47C22×D79—23no—
48C22×D79—23no—
49C22×D79—412no—
50C22×D79—412no—
51C22×D79—44no—
52C22×D79C2×Q812yes—
53C22×D79C2×Q812yes—
54C2×C4×C79—23no—
55C2×C4×C79—23no—
56C2×C4×C79—23no—
57C2×C4×C79—23no—
58C2×C4×C79—23no—
59C2×C4×C79—23no—
60C2×Dic79—23no—
61C2×Dic79—23no—
62C2×Dic79—23no—
63C2×Dic79—23no—
64C2×Dic79—23no—
65C2×Dic79—23no—
66C22×C79—26no—
67C22×C79—43no—
68C22×C79—41no—
69C22×C79C22×Q811yescharacteristic
70C22×C79H(5,𝔽2)13yes—
71C22×C79H(5,𝔽2)13yes—
72C2×D79—26no—
73C2×D79—26no—
74C2×D79—416no—
75C2×D79—43no—
76C2×D79—43no—
77C2×D79—41no—
78C2×D79—41no—
79C4×C79—43no—
80C4×C79—43no—
81Dic79—43no—
82Dic79—43no—
83C2×C79—42no—
84C2×C79#54313yes—
85C2×C79#56013yes—
86C2×C79#56011yescharacteristic
87D79—42no—
88D79—42no—
89#2842—791nomaximal, Sylow
90C79#284211yescharacteristic, complemented, Sylow
91#399—793no—
92#399—791no—
93#396—793no—
94#396—793no—
95#396—791no—
96#396D7911yescharacteristic, complemented
97#379—793no—
98C25—791no—
99C2×C4⋊C4—793no—
100C2×C4⋊C4—793no—
101C2×C4⋊C4—793no—
102C2×C4⋊C4C2×D7913yescomplemented
103C2×C22⋊C4—793no—
104C2×C22⋊C4—793no—
105C2×C22⋊C4—793no—
106C2×C22⋊C4—793no—
107C2×C22⋊C4—793no—
108C2×C22⋊C4C2×D7913yes—
109#95—793no—
110#95C2×D7911yescharacteristic, complemented
111C24—3163no—
112C24—3163no—
113C24—794no—
114C24—791no—
115C24—791no—
116C24C22×D7911yescharacteristic
117C22×C4—793no—
118C22×C4—793no—
119C22×C4C22×D7913yes—
120C22×C4C22×D7913yes—
121C4⋊C4—43no—
122C4⋊C4—3163no—
123C4⋊C4—3163no—
124C4⋊C4—3163no—
125C22⋊C4—43no—
126C22⋊C4—3163no—
127C22⋊C4—3163no—
128C22⋊C4—3163no—
129C22⋊C4—3163no—
130C22⋊C4—3163no—
131C23—23no—
132C23—23no—
133C23—31612no—
134C23—31612no—
135C23—3164no—
136C23—792no—
137C23—792no—
138C23—1583no—
139C23—1583no—
140C23—1583no—
141C23—1583no—
142C23Q8×D7912yes—
143C23C23×D7911yescharacteristic
144C2×C4—23no—
145C2×C4—23no—
146C2×C4—23no—
147C2×C4—23no—
148C2×C4—23no—
149C2×C4—23no—
150C2×C4—1583no—
151C2×C4—1583no—
152C2×C4—1583no—
153C2×C4—1583no—
154C2×C4—1583no—
155C2×C4—1583no—
156C22—26no—
157C22—43no—
158C22—41no—
159C22—31616no—
160C22—3163no—
161C22—3163no—
162C22—3161no—
163C22—3161no—
164C22—1586no—
165C22—1586no—
166C22C2×Q8×D7911yescharacteristic
167C22#1457920613yes—
168C22#1457920713yes—
169C4—43no—
170C4—43no—
171C4—3163no—
172C4—3163no—
173C2—42no—
174C2—3162no—
175C2—3162no—
176C2#1909918813yes—
177C2#1909930113yes—
178C2#1909930411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#396×C79C2
prime radicalC24×D79C22
hypercenter#396D79
hypocenterC79#2842
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #19098500C2semidirect
2. #19098498C2semidirect
3. #19098487C2semidirect
4. #19098486C2semidirect
5. #19098485C2semidirect
7. #396×C79C2semidirect
9. C2×C4⋊Dic79C22semidirect
10. C2×Dic79⋊C4C22semidirect
11. C2×Dic79⋊C4C22semidirect
17. C79⋊#95C22semidirect
18. C2×C4⋊C4×C79C22semidirect
20. #95×C79C22semidirect
90. C79#2842semidirect
96. #396D79semidirect
102. C2×C4⋊C4C2×D79semidirect
110. #95C2×D79semidirect