Finite Group Databasebeta

← #34100241

Subgroups — #34100241

Order 20096.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic157C211yesmaximal, characteristic
2#23757247C211yesmaximal, characteristic
3#23757034C212yesmaximal, complemented
4#23757030C212yesmaximal, complemented
5#413×C157C211yesmaximal, characteristic
6Q8×Dic157—21no—
7D4×Dic157—21no—
8D4×Dic157—22no—
9#19097730C412yescomplemented
10#19097730C2212yes—
11#19097730C2211yescharacteristic
12C2×C4×Dic157C412yescomplemented
13C2×C4×Dic157C2211yescharacteristic
14#19097686—22no—
15C2×#41×C157C2211yescharacteristic
16C2×M16×C157C2212yes—
17#101×C157—21no—
18#100×C157—21no—
19C22×Dic157—22no—
20C22×Dic157—21no—
21C4⋊Dic157—22no—
22C4⋊Dic157—21no—
23C4⋊Dic157—22no—
24C22⋊Dic157—22no—
25C22⋊Dic157—21no—
26C22⋊Dic157—22no—
27C4×Dic157—22no—
28C4×Dic157—21no—
29C4×Dic157—22no—
30C4×Dic157C2×C411yescharacteristic
31C4×Dic157C2×C412yes—
32C4×Dic157C2×C411yescharacteristic
33#41×C157—22no—
34#41×C157—22no—
35C2×Q8×C157D411yescharacteristic
36C2×D4×C157D411yescharacteristic
37C2×D4×C157D412yes—
38C22×C4×C157C2×C412yes—
39C22×C4×C157C2311yescharacteristic
40M16×C157—22no—
41M16×C157—22no—
42C2×C8×C157—22no—
43C2×Dic157—21no—
44C2×Dic157—22no—
45C2×Dic157—21no—
46C2×Dic157—42no—
47C2×Dic157—44no—
48C2×Dic157—42no—
49C23×C157C22⋊C412yes—
50C23×C157C2×D411yescharacteristic
51Q8×C157—22no—
52D4×C157—24no—
53D4×C157—22no—
54C2×C4×C157—22no—
55C2×C4×C157—22no—
56C2×C4×C157C22⋊C412yes—
57C2×C4×C157C22×C411yescharacteristic
58C2×C4×C157C2×D411yescharacteristic
59C2×C4×C157#4112yes—
60C2×C4×C157#4112yes—
61C8×C157—42no—
62C22×C157—22no—
63C22×C157—41no—
64C22×C157—42no—
65C22×C157C2×C22⋊C411yescharacteristic
66C22×C157#12312yes—
67C4×C157—22no—
68C4×C157#11711yescharacteristic
69C4×C157#11711yescharacteristic
70C4×C157#12312yes—
71Dic157—22no—
72Dic157—42no—
73Dic157—41no—
74Dic157—82no—
75C2×C157—21no—
76C2×C157—22no—
77C2×C157—42no—
78C2×C157#38111yescharacteristic
79C157#182711yescharacteristic, complemented, Sylow
80#1827—1571nomaximal, Sylow
81C4×#41—1571no—
82#413D15711yescharacteristic
83#410—1571no—
84#339—1572no—
85H(3,ℤ/4)—1572no—
86C2×#41C2×D15711yescharacteristic
87C2×M16C2×D15712yes—
88C4×Q8—3141no—
89C4×D4—3141no—
90C4×D4—3142no—
91#117—1572no—
92#117—1572no—
93#117—1571no—
94C2×C42—1572no—
95C2×C42—1571no—
96#101—21no—
97#100—21no—
98#99—3142no—
99#41—22no—
100#41—22no—
101C2×Q8C22⋊D15711yescharacteristic
102C2×D4C22⋊D15711yescharacteristic
103C2×D4D62812yes—
104C22×C4—3141no—
105C22×C4—3142no—
106C22×C4C4×D15712yes—
107C22×C4C22×D15711yescharacteristic
108M16—22no—
109M16—22no—
110C2×C8—22no—
111C4⋊C4—3141no—
112C4⋊C4—3142no—
113C4⋊C4—3142no—
114C22⋊C4—3141no—
115C22⋊C4—3142no—
116C22⋊C4—3142no—
117C42—3141no—
118C42—3142no—
119C42—3142no—
120C42—1571no—
121C42—1572no—
122C42—1571no—
123C23#1457893112yes—
124C23C2×D62811yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—3141no—
131C2×C4—3141no—
132C2×C4—3142no—
133C2×C4—6282no—
134C2×C4—6284no—
135C2×C4—6282no—
136C2×C4#1457893112yes—
137C2×C4C2×C4×D15711yescharacteristic
138C2×C4C2×C22⋊D15711yescharacteristic
139C2×C4#1457895312yes—
140C2×C4#1457895312yes—
141C8—42no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×#1457893111yescharacteristic
146C22#1909775512yes—
147C4—22no—
148C4—3142no—
149C4—6281no—
150C4—6282no—
151C4—12562no—
152C4#1909772711yescharacteristic
153C4#1909772711yescharacteristic
154C4#1909775212yes—
155C2—21no—
156C2—22no—
157C2—42no—
158C2#2375713411yescharacteristic
subgroupG/H
centerC4#19097727
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#413×C157C2
socleC2×C157#381
prime radicalC2×#41×C157C22
cosocleC22×C4×C157C23
hypercenter#413D157
hypocenterC157#1827
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #23757034C2semidirect
4. #23757030C2semidirect
9. #19097730C4semidirect
12. C2×C4×Dic157C4semidirect
79. C157#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1572
#237572472
#237570342
#237570302
#413×C1572
#1827157