Finite Group Databasebeta

← #34100348

Subgroups — #34100348

Order 20096.

324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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#23757748C211yesmaximal, characteristic
2#23757315C212yesmaximal, complemented
3#23757176C211yesmaximal, characteristic
4#23757034C212yesmaximal, complemented
5C2×#100×C157C211yesmaximal, characteristic
6D4×Dic157—22no—
7D4×Dic157—22no—
8#19097730C2212yes—
9C2×C4⋊Dic157C2211yescharacteristic
10C2×C22⋊Dic157—22no—
11C2×C22⋊Dic157—22no—
12C2×C4×Dic157C2211yescharacteristic
13#19097705—22no—
14#19097703—22no—
15C22×D4×C157C2211yescharacteristic
16C2×M16×C157C2212yes—
17#100×C157C414yescomplemented
18C22×Dic157—22no—
19C22×Dic157—22no—
20C22×Dic157—21no—
21C22×Dic157—21no—
22C4⋊Dic157—22no—
23C4⋊Dic157D412yes—
24C4⋊Dic157D412yes—
25C22⋊Dic157—24no—
26C22⋊Dic157—22no—
27C22⋊Dic157—44no—
28C4×Dic157—22no—
29C4×Dic157—22no—
30C24×C157D412yes—
31C2×D4×C157—22no—
32C2×D4×C157—22no—
33C2×D4×C157C2×C412yes—
34C2×D4×C157Q812yes—
35C22×C4×C157C2311yescharacteristic
36M16×C157—22no—
37M16×C157C2×C414yescomplemented
38C2×C8×C157—22no—
39C2×Dic157—22no—
40C2×Dic157—22no—
41C2×Dic157—22no—
42C2×Dic157—41no—
43C2×Dic157—41no—
44C2×Dic157—42no—
45C2×Dic157—41no—
46C2×Dic157—82no—
47C2×Dic157—82no—
48C23×C157—22no—
49C23×C157—22no—
50C23×C157—42no—
51C23×C157—42no—
52C23×C157C4⋊C414yes—
53C23×C157C2×D411yescharacteristic
54D4×C157—24no—
55D4×C157—24no—
56C2×C4×C157C22×C411yescharacteristic
57C2×C4×C157C2×D412yes—
58C2×C4×C157C2×Q811yescharacteristic
59C2×C4×C157#4112yes—
60C8×C157—24no—
61C22×C157—21no—
62C22×C157—21no—
63C22×C157—24no—
64C22×C157—44no—
65C22×C157—42no—
66C22×C157—42no—
67C22×C157—82no—
68C22×C157C2×C4⋊C411yescharacteristic
69C22×C157#12011yescharacteristic
70C22×C157#12311yescharacteristic
71C4×C157C4×D412yes—
72C4×C157C22⋊Q812yes—
73Dic157—42no—
74Dic157—42no—
75Dic157—42no—
76Dic157—81no—
77C2×C157—21no—
78C2×C157—21no—
79C2×C157—44no—
80C2×C157#38511yescharacteristic
81C2×C157#45311yescharacteristic
82C2×C157#45511yescharacteristic
83C157#185611yescharacteristic, complemented, Sylow
84#1856—1571nomaximal, Sylow
85#518—1571no—
86#428—1572no—
87C2×#100D15711yescharacteristic
88#390—1571no—
89#339—1572no—
90C22×D4C2×D15711yescharacteristic
91C2×M16C2×D15712yes—
92C4×D4—3142no—
93C4×D4—3142no—
94#117—1572no—
95C2×C4⋊C4—1571no—
96C2×C22⋊C4—3142no—
97C2×C22⋊C4—3142no—
98C2×C42—1571no—
99#107—3142no—
100#106—3142no—
101#100Dic15714yescomplemented
102C24D62812yes—
103C2×D4—22no—
104C2×D4—22no—
105C2×D4C2×Dic15712yes—
106C2×D4Dic31412yes—
107C22×C4—3141no—
108C22×C4—3142no—
109C22×C4—3142no—
110C22×C4—3141no—
111C22×C4C22×D15711yescharacteristic
112M16—22no—
113M16C2×Dic15714yescomplemented
114C2×C8—22no—
115C4⋊C4—3142no—
116C4⋊C4—1572no—
117C4⋊C4—1572no—
118C22⋊C4—3144no—
119C22⋊C4—3142no—
120C22⋊C4—6284no—
121C42—3142no—
122C42—3142no—
123C23—22no—
124C23—22no—
125C23—42no—
126C23—42no—
127C23C4⋊Dic15714yes—
128C23C2×D62811yescharacteristic
129D4—24no—
130D4—24no—
131C2×C4—3142no—
132C2×C4—3142no—
133C2×C4—3142no—
134C2×C4—6281no—
135C2×C4—6281no—
136C2×C4—6282no—
137C2×C4—6281no—
138C2×C4—12562no—
139C2×C4—12562no—
140C2×C4C22×Dic15711yescharacteristic
141C2×C4D4×D15712yes—
142C2×C4C2×Dic31411yescharacteristic
143C2×C4#1457895312yes—
144C8—24no—
145C22—21no—
146C22—21no—
147C22—24no—
148C22—44no—
149C22—42no—
150C22—42no—
151C22—82no—
152C22C2×C4⋊Dic15711yescharacteristic
153C22#1909774111yescharacteristic
154C22#1909775511yescharacteristic
155C4—6282no—
156C4—6282no—
157C4—6282no—
158C4—12561no—
159C4D4×Dic15712yes—
160C4#1909774812yes—
161C2—21no—
162C2—21no—
163C2—44no—
164C2#2375714811yescharacteristic
165C2#2375744311yescharacteristic
166C2#2375745311yescharacteristic
subgroupG/H
centerC22#19097741
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#100×C157C2
socleC22×C157#120
prime radicalC22×D4×C157C22
cosocleC22×C4×C157C23
hypercenterC2×#100D157
hypocenterC157#1856
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #23757315C2semidirect
4. #23757034C2semidirect
17. #100×C157C4semidirect
37. M16×C157C2×C4semidirect
83. C157#1856semidirect
101. #100Dic157semidirect
113. M16C2×Dic157semidirect

Maximal subgroups

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

subgroupindex
#237577482
#237573152
#237571762
#237570342
C2×#100×C1572
#1856157