Finite Group Databasebeta

← #34102131

Subgroups — #34102131

Order 20096.

246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 41 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#23758009C211yesmaximal, characteristic, complemented
2#23757463C212yesmaximal, complemented
3#23757066C211yesmaximal, characteristic, complemented
4#23757064C212yesmaximal, complemented
5#453×C157C211yesmaximal, characteristic
6#19097758—22no—
7#19097752—21no—
8#19097752—22no—
9#19097752C2212yes—
10C4×Dic314—21no—
11D4×Dic157—22no—
12#19097686—22no—
13#19097686C2212yes—
14H(5,𝔽2)×C157C2211yescharacteristic
15AGL(1,ℤ/8)×C157—21no—
16#127×C157C2211yescharacteristic
17#104×C157—21no—
18#100×C157C2211yescharacteristic
19C2×Dic314—21no—
20C22×Dic157—21no—
21C22×Dic157D412yes—
22C4⋊Dic157—21no—
23#14578933—22no—
24#14578933—42no—
25C22⋊Dic157—22no—
26C22⋊Dic157—21no—
27C22⋊Dic157—22no—
28C22⋊Dic157—22no—
29C22⋊Dic157—42no—
30C22⋊Dic157D412yes—
31C4×Dic157—22no—
32#41×C157—21no—
33#41×C157—41no—
34C2×D4×C157—22no—
35C2×D4×C157—22no—
36C2×D4×C157—41no—
37C2×D4×C157D411yescharacteristic
38C2×D4×C157C2311yescharacteristic
39SD16×C157—41no—
40D8×C157—41no—
41M16×C157—21no—
42C42×C157D411yescharacteristic
43Dic314—42no—
44C2×Dic157—22no—
45C2×Dic157—22no—
46C2×Dic157—42no—
47C2×Dic157—42no—
48C2×Dic157—81no—
49C23×C157—22no—
50C23×C157—21no—
51C23×C157C2×D412yes—
52Q8×C157—21no—
53D4×C157—21no—
54D4×C157—41no—
55D4×C157—41no—
56D4×C157—44no—
57D4×C157—42no—
58D4×C157—41no—
59C2×C4×C157—21no—
60C2×C4×C157—22no—
61C2×C4×C157—41no—
62C2×C4×C157C2×D411yescharacteristic
63C8×C157—41no—
64C22×C157—22no—
65C22×C157—42no—
66C22×C157—42no—
67C22×C157—41no—
68C22×C157—41no—
69C22×C157—82no—
70C22×C157#12011yescharacteristic
71C4×C157—22no—
72C4×C157—21no—
73C4×C157—41no—
74Dic157—42no—
75Dic157—42no—
76Dic157—82no—
77C2×C157—21no—
78C2×C157—42no—
79C2×C157—81no—
80C2×C157—81no—
81C2×C157B(4,𝔽2)11yescharacteristic
82C157#219811yescharacteristic, complemented, Sylow
83#2198—1571nomaximal, Sylow
84#559—1571no—
85#458—1572no—
86#453D15711yescharacteristic
87#353—1571no—
88#352—1572no—
89H(5,𝔽2)C2×D15711yescharacteristic
90AGL(1,ℤ/8)—21no—
91#127C2×D15711yescharacteristic
92#124—3142no—
93#123—3141no—
94#123—3142no—
95#123—1572no—
96C4×Q8—3141no—
97C4×D4—3142no—
98#104—21no—
99#100C2×D15711yescharacteristic
100#99—3142no—
101#99—1572no—
102#41—21no—
103#41—41no—
104C2×Q8—3141no—
105C2×D4—22no—
106C2×D4—22no—
107C2×D4—41no—
108C2×D4C22⋊D15711yescharacteristic
109C2×D4C22×D15711yescharacteristic
110C22×C4—3141no—
111C22×C4—1572no—
112SD16—41no—
113D8—41no—
114M16—21no—
115C4⋊C4—3141no—
116C4⋊C4—3142no—
117C4⋊C4—6282no—
118C22⋊C4—3142no—
119C22⋊C4—3141no—
120C22⋊C4—3142no—
121C22⋊C4—3142no—
122C22⋊C4—6282no—
123C22⋊C4—1572no—
124C42—3142no—
125C42C22⋊D15711yescharacteristic
126C23—22no—
127C23—21no—
128C23D4×D15712yes—
129Q8—21no—
130Q8—6282no—
131D4—21no—
132D4—41no—
133D4—41no—
134D4—44no—
135D4—42no—
136D4—41no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—3142no—
141C2×C4—3142no—
142C2×C4—6282no—
143C2×C4—6282no—
144C2×C4—12561no—
145C2×C4C2×C22⋊D15711yescharacteristic
146C8—41no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—41no—
152C22—82no—
153C22#1909773911yescharacteristic
154C4—22no—
155C4—21no—
156C4—41no—
157C4—6282no—
158C4—6282no—
159C4—12562no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—81no—
164C2#2375745911yescharacteristic
subgroupG/H
centerC2#23757459
commutator, cosocleC2×D4×C157C23
FrattiniC2×D4C22×D157
Fitting, prime radical#453×C157C2
socleC2×C157B(4,𝔽2)
hypercenter#453D157
hypocenterC157#2198
LCSG ▷ C2×D4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #23758009C2semidirect
2. #23757463C2semidirect
3. #23757066C2semidirect
4. #23757064C2semidirect
82. C157#2198semidirect

Maximal subgroups

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

subgroupindex
#237580092
#237574632
#237570662
#237570642
#453×C1572
#2198157