Finite Group Databasebeta

← #34102148

Subgroups — #34102148

Order 20096.

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

normal subgroups only

This group has 226 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#23758023C211yesmaximal, characteristic, complemented
2#23757463C212yesmaximal
3#23757068C211yesmaximal, characteristic, complemented
4#23757064C212yesmaximal, complemented
5#455×C157C211yesmaximal, characteristic
6#19097769—21no—
7#19097764—22no—
8#19097763—21no—
9#19097752—22no—
10#19097752C2212yes—
11#19097748—22no—
12#19097686—22no—
13#19097686C2212yes—
14H(5,𝔽2)×C157C2211yescharacteristic
15#137×C157—21no—
16#124×C157C2211yescharacteristic
17#104×C157—21no—
18#100×C157C2211yescharacteristic
19C2×Dic314—21no—
20C22×Dic157D412yes—
21C4⋊Dic157—21no—
22C4⋊Dic157—21no—
23#14578933—22no—
24#14578933—22no—
25#14578933—22no—
26#14578933—42no—
27C22⋊Dic157—22no—
28C22⋊Dic157—22no—
29C22⋊Dic157—42no—
30C22⋊Dic157D412yes—
31C4×Dic157—21no—
32#41×C157—21no—
33#41×C157—41no—
34C2×Q8×C157D411yescharacteristic
35C2×D4×C157—22no—
36C2×D4×C157—41no—
37C2×D4×C157C2311yescharacteristic
38Q16×C157—41no—
39SD16×C157—41no—
40M16×C157—21no—
41C22⋊C4×C157—22no—
42C42×C157D411yescharacteristic
43Dic314—81no—
44C2×Dic157—22no—
45C2×Dic157—22no—
46C2×Dic157—42no—
47C2×Dic157—42no—
48C23×C157—22no—
49C23×C157C2×D412yes—
50Q8×C157—21no—
51Q8×C157—41no—
52D4×C157—21no—
53D4×C157—41no—
54D4×C157—42no—
55D4×C157—41no—
56C2×C4×C157—22no—
57C2×C4×C157—21no—
58C2×C4×C157—21no—
59C2×C4×C157—41no—
60C2×C4×C157C2×D411yescharacteristic
61C8×C157—41no—
62C22×C157—22no—
63C22×C157—42no—
64C22×C157—41no—
65C22×C157—82no—
66C22×C157#12011yescharacteristic
67C4×C157—21no—
68C4×C157—41no—
69C4×C157—41no—
70C4×C157—41no—
71Dic157—42no—
72Dic157—42no—
73Dic157—82no—
74C2×C157—21no—
75C2×C157—42no—
76C2×C157—81no—
77C2×C157B(4,𝔽2)11yescharacteristic
78C157#220111yescharacteristic, complemented, Sylow
79#2201—1571nomaximal, Sylow
80#563—1571no—
81#458—1572no—
82#455D15711yescharacteristic
83#354—1571no—
84#352—1572no—
85H(5,𝔽2)C2×D15711yescharacteristic
86#137—21no—
87C4⋊Q8—3141no—
88#126—3142no—
89#125—3141no—
90#124C2×D15711yescharacteristic
91#123—3142no—
92#123—1572no—
93C22⋊Q8—3142no—
94#104—21no—
95#100C2×D15711yescharacteristic
96#99—3142no—
97#99—1572no—
98#41—21no—
99#41—41no—
100C2×Q8—3141no—
101C2×Q8C22⋊D15711yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D15711yescharacteristic
105C22×C4—1572no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—3141no—
110C4⋊C4—3142no—
111C4⋊C4—3142no—
112C4⋊C4—3141no—
113C4⋊C4—3142no—
114C4⋊C4—6282no—
115C22⋊C4—22no—
116C22⋊C4—3142no—
117C22⋊C4—3142no—
118C22⋊C4—6282no—
119C22⋊C4—1572no—
120C42—3141no—
121C42C22⋊D15711yescharacteristic
122C23—22no—
123C23D4×D15712yes—
124Q8—21no—
125Q8—41no—
126Q8—12561no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—3142no—
136C2×C4—3142no—
137C2×C4—6282no—
138C2×C4—6282no—
139C2×C4C2×C22⋊D15711yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#1909773911yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—6282no—
151C4—6282no—
152C4—12562no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#2375745911yescharacteristic
subgroupG/H
centerC2#23757459
commutator, cosocleC2×D4×C157C23
FrattiniC2×D4C22×D157
Fitting#455×C157C2
socleC2×C157B(4,𝔽2)
prime radicalH(5,𝔽2)×C157C22
hypercenter#455D157
hypocenterC157#2201
LCSG ▷ C2×D4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #23758023C2semidirect
3. #23757068C2semidirect
4. #23757064C2semidirect
78. C157#2201semidirect

Maximal subgroups

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

subgroupindex
#237580232
#237574632
#237570682
#237570642
#455×C1572
#2201157