Finite Group Databasebeta

← #123×D157 #23757773

Subgroups — #123×D157 #23757773

Order 10048.

342 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 111 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×D4×D157C211yesmaximal, characteristic
2C22×C4×D157C211yesmaximal, characteristic, complemented
3#19097756C212yesmaximal, complemented
4#19097755C211yesmaximal, characteristic, complemented
5#19097754C211yesmaximal, characteristic, complemented
6#19097753C212yesmaximal, complemented
7#19097752C211yesmaximal, characteristic, complemented
8C4⋊C4×D157C212yesmaximal, complemented
9C22⋊C4×D157C211yesmaximal, characteristic, complemented
10C22⋊C4×D157C212yesmaximal, complemented
11#123×C157C211yesmaximal, characteristic, complemented
12C23×D157C2211yescharacteristic
13C23×D157C2211yescharacteristic
14C2×D628C2211yescharacteristic
15C2×C22⋊D157C2211yescharacteristic
16C2×C22⋊D157C2211yescharacteristic
17D4×D157—24no—
18C22×Dic157C2211yescharacteristic, complemented
19C2×C4×D157—24no—
20C2×C4×D157C2212yes—
21C2×C4×D157C2212yes—
22C2×C4×D157C2211yescharacteristic
23C2×C4×D157C2212yescomplemented
24C4⋊Dic157C2212yescomplemented
25#14578933C2212yescomplemented
26#14578933C2212yescomplemented
27C22⋊Dic157C2212yescomplemented
28C22⋊Dic157C2211yescharacteristic, complemented
29#14578931C2212yescomplemented
30#14578931C2212yescomplemented
31#14578931C2212yescomplemented
32C2×D4×C157C2211yescharacteristic
33C22×C4×C157C2211yescharacteristic, complemented
34C4⋊C4×C157C2212yescomplemented
35C22⋊C4×C157C2212yescomplemented
36C22⋊C4×C157C2211yescharacteristic, complemented
37C22×D157—24no—
38C22×D157—22no—
39C22×D157—24no—
40C22×D157D414yes—
41C22×D157C2311yescharacteristic
42C22×D157C2311yescharacteristic
43C22×D157C2311yescharacteristic
44D628—22no—
45C22⋊D157—22no—
46C22⋊D157—22no—
47C2×Dic157—22no—
48C2×Dic157C2312yes—
49C2×Dic157C2311yescharacteristic
50C2×Dic157C2312yes—
51C4×D157—24no—
52C4×D157—24no—
53C4×D157—22no—
54C4×D157—24no—
55C23×C157C2311yescharacteristic
56C23×C157C2311yescharacteristic
57D4×C157—22no—
58C2×C4×C157—22no—
59C2×C4×C157C2312yes—
60C2×C4×C157C2311yescharacteristic
61C2×C4×C157C2312yes—
62C22×C157—22no—
63C22×C157—21no—
64C22×C157—22no—
65C22×C157C2×D412yes—
66C22×C157C2411yescharacteristic
67C2×D157—22no—
68C2×D157—28no—
69C2×D157—21no—
70C2×D157—22no—
71C2×D157—44no—
72C2×D157C2×D412yes—
73C2×D157C2×D412yes—
74C2×D157#4114yes—
75C4×C157—22no—
76C4×C157—21no—
77C4×C157—22no—
78Dic157—22no—
79Dic157—21no—
80Dic157—22no—
81C2×C157—22no—
82C2×C157—41no—
83C2×C157C22×D411yescharacteristic
84C2×C157C2×#4112yes—
85D157—22no—
86D157—41no—
87D157#12314yesdirect product factor
88C157C2×#12311yescharacteristic, complemented, Sylow
89C2×#123—1571nomaximal, Sylow
90C22×D4—1571no—
91C23×C4—1571no—
92#123—1571no—
93#123—1571no—
94#123—1572no—
95#123—1572no—
96#123—1571no—
97#123D15711yescharacteristic, direct product factor
98C2×C4⋊C4—1572no—
99C2×C22⋊C4—1571no—
100C2×C22⋊C4—1572no—
101C24—1571no—
102C24—1571no—
103C2×D4—3144no—
104C2×D4—1571no—
105C2×D4—1571no—
106C2×D4—1571no—
107C2×D4C2×D15711yescharacteristic
108C22×C4—3144no—
109C22×C4—1571no—
110C22×C4—1572no—
111C22×C4—1572no—
112C22×C4—1571no—
113C22×C4—1572no—
114C22×C4C2×D15711yescharacteristic, complemented
115C4⋊C4—1572no—
116C4⋊C4—1572no—
117C4⋊C4—1572no—
118C4⋊C4C2×D15712yescomplemented
119C22⋊C4—1571no—
120C22⋊C4—1572no—
121C22⋊C4—1572no—
122C22⋊C4—1572no—
123C22⋊C4—1572no—
124C22⋊C4C2×D15711yescharacteristic, complemented
125C22⋊C4C2×D15712yescomplemented
126C23—3144no—
127C23—3142no—
128C23—3144no—
129C23—1571no—
130C23—1574no—
131C23—1571no—
132C23—1571no—
133C23C22×D15711yescharacteristic
134C23C22×D15711yescharacteristic
135D4—22no—
136D4—3142no—
137D4—3142no—
138D4—3142no—
139C2×C4—22no—
140C2×C4—3144no—
141C2×C4—3144no—
142C2×C4—3142no—
143C2×C4—3144no—
144C2×C4—3142no—
145C2×C4—1572no—
146C2×C4—1572no—
147C2×C4—1571no—
148C2×C4C22×D15712yes—
149C2×C4C22×D15712yes—
150C2×C4C22×D15711yescharacteristic
151C22—22no—
152C22—21no—
153C22—22no—
154C22—3148no—
155C22—3142no—
156C22—3141no—
157C22—3142no—
158C22—6284no—
159C22—1572no—
160C22—1572no—
161C22—1574no—
162C22D4×D15712yes—
163C22C23×D15711yescharacteristic
164C4—22no—
165C4—21no—
166C4—22no—
167C4—3142no—
168C4—3141no—
169C4—3142no—
170C2—22no—
171C2—41no—
172C2—3142no—
173C2—6281no—
174C2—1574no—
175C2C2×D4×D15711yescharacteristic
176C2#41×D15712yes—
subgroupG/H
center, FrattiniC22C23×D157
commutator, socle, cosocleC22×C157C24
Fitting#123×C157C2
prime radicalC2×D4×D157C2
hypercenter#123D157
hypocenterC157C2×#123
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C22×C4×D157C2semidirect
3. #19097756C2semidirect
4. #19097755C2semidirect
5. #19097754C2semidirect
6. #19097753C2semidirect
7. #19097752C2semidirect
8. C4⋊C4×D157C2semidirect
9. C22⋊C4×D157C2semidirect
10. C22⋊C4×D157C2semidirect
11. #123×C157C2semidirect
18. C22×Dic157C22semidirect
23. C2×C4×D157C22semidirect
24. C4⋊Dic157C22semidirect
25. #14578933C22semidirect
26. #14578933C22semidirect
27. C22⋊Dic157C22semidirect
28. C22⋊Dic157C22semidirect
29. #14578931C22semidirect
30. #14578931C22semidirect
31. #14578931C22semidirect
33. C22×C4×C157C22semidirect
34. C4⋊C4×C157C22semidirect
35. C22⋊C4×C157C22semidirect
36. C22⋊C4×C157C22semidirect
87. D157#123direct (N × H)
88. C157C2×#123semidirect
97. #123D157direct (N × H)
114. C22×C4C2×D157semidirect
118. C4⋊C4C2×D157semidirect
124. C22⋊C4C2×D157semidirect
125. C22⋊C4C2×D157semidirect