Finite Group Databasebeta

← #34100661

Subgroups — #34100661

Order 20096.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#23758040C211yesmaximal, characteristic, complemented
2#23757837C211yesmaximal, characteristic
3#23757277C212yesmaximal, complemented
4#23757029C212yesmaximal, complemented
5#410×C157C211yesmaximal, characteristic, complemented
6C22×D628C2211yescharacteristic
7#19097778—24no—
8C2×#14578938—22no—
9C2×#14578938C2212yes—
10#19097767C412yescomplemented
11#19097760C412yescomplemented
12#19097745—22no—
13#19097739—22no—
14#19097730C2211yescharacteristic
15#19097691—24no—
16C2×#41×C157C2211yescharacteristic
17#117×C157C2212yes—
18#99×C157—22no—
19C23×D157—21no—
20C2×D628—22no—
21C2×D628—21no—
22C2×D628—22no—
23C2×D628C2×C412yes—
24C2×C22⋊D157—24no—
25#14578938—24no—
26#14578938—22no—
27#14578938—22no—
28C2×#11929434—24no—
29C2×#11929434D414yescomplemented
30C4⋊Dic157—21no—
31C22⋊Dic157—21no—
32#14578931—24no—
33C4×Dic157C2×C412yes—
34#41×C157—22no—
35#41×C157—22no—
36C2×Q8×C157C2×C411yescharacteristic
37C2×D4×C157C2×C411yescharacteristic
38C2×D4×C157D412yes—
39C22×C4×C157D412yes—
40C22×C4×C157C2311yescharacteristic
41C4⋊C4×C157—22no—
42C22⋊C4×C157—22no—
43C42×C157—22no—
44C22×D157—22no—
45C22×D157—42no—
46C22×D157—82no—
47D628—24no—
48D628—41no—
49D628—41no—
50C22⋊D157—84no—
51C2×Dic157—22no—
52#11929434—24no—
53C23×C157C22⋊C412yes—
54C23×C157C2×D411yescharacteristic
55Q8×C157—22no—
56D4×C157—24no—
57D4×C157—22no—
58C2×C4×C157—22no—
59C2×C4×C157—22no—
60C2×C4×C157—42no—
61C2×C4×C157C22⋊C412yes—
62C2×C4×C157C22×C411yescharacteristic
63C2×C4×C157C2×D412yes—
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157#4112yes—
66C22×C157—22no—
67C22×C157—41no—
68C22×C157—42no—
69C22×C157C2×C22⋊C411yescharacteristic
70C22×C157#12112yes—
71C2×D157—44no—
72C2×D157—42no—
73C2×D157—84no—
74C4×C157—22no—
75C4×C157—82no—
76C4×C157C4×D412yes—
77C4×C157#12011yescharacteristic
78C4×C157#12311yescharacteristic
79Dic157—42no—
80C2×C157—21no—
81C2×C157—22no—
82C2×C157—42no—
83C2×C157#38611yescharacteristic
84D157—82no—
85C157#191011yescharacteristic, complemented, Sylow
86#1910—1571nomaximal, Sylow
87#568—1571no—
88#535—1571no—
89#418—1572no—
90#410D15711yescharacteristic, complemented
91H(3,ℤ/4)—1572no—
92C2×#41C2×D15711yescharacteristic
93C22×D4—1571no—
94#131—3144no—
95C2×M16—3142no—
96C2×M16—1572no—
97#127—1572no—
98#124—1572no—
99#121—3142no—
100#120—3142no—
101#117—1571no—
102#117C2×D15712yes—
103#102—3144no—
104#99—22no—
105C24—3141no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D15711yescharacteristic
109C2×D4—3144no—
110C2×D4—3142no—
111C2×D4—3141no—
112C2×D4—3142no—
113C2×D4—1572no—
114C2×D4C4×D15711yescharacteristic
115C2×D4C22⋊D15712yes—
116C22×C4D62812yes—
117C22×C4C22×D15711yescharacteristic
118M16—3144no—
119M16—3142no—
120M16—3142no—
121C2×C8—3144no—
122C2×C8—1574no—
123C4⋊C4—22no—
124C4⋊C4—3141no—
125C22⋊C4—22no—
126C22⋊C4—3141no—
127C22⋊C4—3144no—
128C42—22no—
129C42—1572no—
130C23—3142no—
131C23—6282no—
132C23—12562no—
133C23#1457893112yes—
134C23C2×C22⋊D15711yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—3144no—
139D4—6281no—
140D4—6281no—
141D4—12564no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—3142no—
146C2×C4#1457893112yes—
147C2×C4C2×C4×D15711yescharacteristic
148C2×C4D4×D15712yes—
149C2×C4C2×D62811yescharacteristic
150C2×C4#1457895312yes—
151C8—3144no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—6284no—
156C22—6282no—
157C22—12564no—
158C22C2×#1457893111yescharacteristic
159C22#1909774312yes—
160C4—22no—
161C4—82no—
162C4—6282no—
163C4#1909773112yes—
164C4#1909774111yescharacteristic
165C4#1909775511yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—12562no—
170C2#2375715011yescharacteristic
subgroupG/H
centerC2#23757150
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#410×C157C2
socleC2×C157#386
prime radical#23757837C2
cosocleC22×C4×C157C23
hypercenter#410D157
hypocenterC157#1910
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #23758040C2semidirect
3. #23757277C2semidirect
4. #23757029C2semidirect
5. #410×C157C2semidirect
10. #19097767C4semidirect
11. #19097760C4semidirect
29. C2×#11929434D4semidirect
85. C157#1910semidirect
90. #410D157semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237580402
#237578372
#237572772
#237570292
#410×C1572
#1910157