Finite Group Databasebeta

← #34100671

Subgroups — #34100671

Order 20096.

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

normal subgroups only

This group has 314 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#23757847C211yesmaximal, characteristic
2#23757751C211yesmaximal, characteristic, complemented
3#23757289C212yesmaximal
4#23757030C212yesmaximal, complemented
5C2×#101×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2211yescharacteristic
7#19097769C412yescomplemented
8#19097760C412yescomplemented
9#19097754—22no—
10#19097747—22no—
11Q8×Dic157—24no—
12#19097730—22no—
13#19097730C2211yescharacteristic
14#19097730C2212yes—
15#19097697—24no—
16C22×Q8×C157C2211yescharacteristic
17C2×M16×C157C2212yes—
18#101×C157—22no—
19#14578954—22no—
20#14578954—22no—
21C2×Dic314C2×C411yescharacteristic
22C2×D628C2×C411yescharacteristic
23C2×C22⋊D157—21no—
24C2×C4×D157—21no—
25C4⋊Dic157—24no—
26C4⋊Dic157—22no—
27C4⋊Dic157—21no—
28#14578933—24no—
29C22⋊Dic157—22no—
30C22⋊Dic157—21no—
31#14578931—24no—
32C4×Dic157—24no—
33C4×Dic157C2×C412yes—
34C4×Dic157D414yes—
35C2×Q8×C157—22no—
36C2×Q8×C157—22no—
37C2×Q8×C157C2×C412yes—
38C2×Q8×C157D412yes—
39C22×C4×C157D412yes—
40C22×C4×C157C2311yescharacteristic
41M16×C157—22no—
42M16×C157—22no—
43C2×C8×C157—22no—
44C22×D157—21no—
45Dic314—22no—
46D628—22no—
47C22⋊D157—41no—
48C22⋊D157—41no—
49C2×Dic157—21no—
50C2×Dic157—22no—
51C2×Dic157—24no—
52C4×D157—42no—
53C23×C157C2×D411yescharacteristic
54Q8×C157—24no—
55Q8×C157—24no—
56C2×C4×C157—22no—
57C2×C4×C157—22no—
58C2×C4×C157C22⋊C414yes—
59C2×C4×C157C22×C411yescharacteristic
60C2×C4×C157C2×D412yes—
61C2×C4×C157C2×D411yescharacteristic
62C2×C4×C157#4112yes—
63C8×C157—42no—
64C22×C157—41no—
65C22×C157C2×C22⋊C411yescharacteristic
66C22×C157#12011yescharacteristic
67C22×C157#12311yescharacteristic
68C2×D157—42no—
69C2×D157—41no—
70C4×C157—24no—
71C4×C157C4×D412yes—
72C4×C157#12112yes—
73Dic157—44no—
74Dic157—42no—
75Dic157—41no—
76C2×C157—21no—
77C2×C157—21no—
78C2×C157—21no—
79C2×C157#38611yescharacteristic
80D157—81no—
81C157#191211yescharacteristic, complemented, Sylow
82#1912—1571nomaximal, Sylow
83#536—1571no—
84#519—1571no—
85#421—1572no—
86C2×#101D15711yescharacteristic, complemented
87H(3,ℤ/4)—1572no—
88C2×#41—1571no—
89C22×Q8C2×D15711yescharacteristic
90C2×M16C2×D15712yes—
91C4⋊Q8—1572no—
92#124—1572no—
93#123—3142no—
94C22⋊Q8—3142no—
95C4×Q8—3144no—
96#117—3142no—
97#117—1572no—
98#117—1571no—
99#104—3144no—
100#101—22no—
101#41—3142no—
102#41—3142no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—1571no—
106C2×Q8C4×D15712yes—
107C2×Q8C22⋊D15712yes—
108C2×D4—3141no—
109C2×D4—1571no—
110C22×C4—3141no—
111C22×C4D62812yes—
112C22×C4C22×D15711yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—3144no—
117C4⋊C4—3142no—
118C4⋊C4—3141no—
119C4⋊C4—3144no—
120C22⋊C4—3142no—
121C22⋊C4—3141no—
122C22⋊C4—3144no—
123C42—3144no—
124C42—1572no—
125C42—1574no—
126C23—3141no—
127C23C2×D62811yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—3142no—
131D4—3142no—
132D4—6281no—
133D4—6281no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—3142no—
137C2×C4—3141no—
138C2×C4—3144no—
139C2×C4—6282no—
140C2×C4#1457893114yes—
141C2×C4C2×C4×D15711yescharacteristic
142C2×C4D4×D15712yes—
143C2×C4C2×C22⋊D15711yescharacteristic
144C2×C4#1457895312yes—
145C8—42no—
146C22—41no—
147C22—6282no—
148C22—6281no—
149C22C2×#1457893111yescharacteristic
150C22#1909774111yescharacteristic
151C22#1909775511yescharacteristic
152C4—24no—
153C4—6284no—
154C4—6282no—
155C4—6281no—
156C4#1909773112yes—
157C4#1909774312yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—12561no—
162C2#2375715011yescharacteristic
subgroupG/H
centerC2#23757150
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#101×C157C2
socleC2×C157#386
prime radicalC2×#14578954C22
cosocleC22×C4×C157C23
hypercenterC2×#101D157
hypocenterC157#1912
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #23757751C2semidirect
4. #23757030C2semidirect
5. C2×#101×C157C2semidirect
7. #19097769C4semidirect
8. #19097760C4semidirect
81. C157#1912semidirect
86. C2×#101D157semidirect

Maximal subgroups

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

subgroupindex
#237578472
#237577512
#237572892
#237570302
C2×#101×C1572
#1912157