Finite Group Databasebeta

← #34102097

Subgroups — #34102097

Order 20096.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#23758087C211yesmaximal, characteristic, complemented
2C2×#19097715C211yesmaximal, characteristic, complemented
3#23757540C211yesmaximal, characteristic, complemented
4#23757090C211yesmaximal, characteristic, complemented
5#23757080C211yesmaximal, characteristic, complemented
6#23757058C211yesmaximal, characteristic, complemented
7#509×C157C211yesmaximal, characteristic, complemented
8#19097818—21no—
9#19097801—21no—
10#19097800—22no—
11#19097797—21no—
12#19097790—21no—
13C2×Dic628C2211yescharacteristic
14Q16×D157—21no—
15#19097777C2211yescharacteristic
16#19097715—22no—
17C2×#14578929C2211yescharacteristic
18#19097707C2211yescharacteristic
19#19097688—21no—
20#135×C157C2211yescharacteristic
21C2×D8×C157C2211yescharacteristic
22SD32×C157—21no—
23D16×C157—21no—
24M32×C157C2211yescharacteristic
25#14578954—41no—
26#14578954D411yescharacteristic
27#14578953—22no—
28#14578953—42no—
29C2×Dic314—21no—
30C2×Dic314—41no—
31Q8×D157—22no—
32Dic628—21no—
33Dic628D412yes—
34#14578944—22no—
35#14578942—22no—
36#14578942—41no—
37#14578939—41no—
38#14578938—21no—
39#14578938D411yescharacteristic
40#14578937—21no—
41C8×D157—21no—
42#14578929—21no—
43#41×C157—21no—
44C2×D4×C157—21no—
45Q16×C157D411yescharacteristic
46SD16×C157—21no—
47D8×C157—21no—
48D8×C157—21no—
49D8×C157D411yescharacteristic
50C2×C8×C157C2311yescharacteristic
51C16×C157—21no—
52Dic314—22no—
53Dic314—42no—
54Dic314—41no—
55Dic314D811yescharacteristic
56D628D811yescharacteristic
57C22⋊D157—21no—
58C22⋊D157—42no—
59C2×Dic157—42no—
60C2×Dic157—41no—
61C4×D157—21no—
62C4×D157—42no—
63#11929434—21no—
64#11929434—41no—
65C23×C157—41no—
66Q8×C157—21no—
67D4×C157—21no—
68D4×C157—41no—
69D4×C157—41no—
70D4×C157—41no—
71C2×C4×C157—41no—
72C2×C4×C157C2×D411yescharacteristic
73C8×C157C2×D411yescharacteristic
74C8×C157C2×D411yescharacteristic
75C22×C157—41no—
76C22×C157—81no—
77C22×C157—161no—
78C22×C157AGL(1,ℤ/8)11yescharacteristic
79C2×D157—21no—
80C4×C157—41no—
81C4×C157#12011yescharacteristic
82C4×C157C2×D811yescharacteristic
83Dic157—21no—
84Dic157—42no—
85C2×C157—21no—
86C2×C157—81no—
87C2×C157—161no—
88C2×C157#44711yescharacteristic
89D157—41no—
90C157#219311yescharacteristic, complemented, Sylow
91#2193—1571nomaximal, Sylow
92#578—1571no—
93#509D15711yescharacteristic, complemented
94C2×SD32—1571no—
95#472—1571no—
96#362—1571no—
97#359—1571no—
98#350—1571no—
992−1+4—3141no—
100#137—3142no—
101#137—3141no—
102AGL(1,ℤ/8)—3141no—
103#135—3141no—
104#135C2×D15711yescharacteristic
105C2×Q16—3141no—
106C2×Q16—1571no—
107C2×D8C2×D15711yescharacteristic
108#131—1571no—
109SD32—21no—
110SD32—3142no—
111D16—21no—
112M32C2×D15711yescharacteristic
113C2×C16—1571no—
114#108—1571no—
115#100—3141no—
116#41—21no—
117#41—3142no—
118#41—6281no—
119#41—6282no—
120#41—1571no—
121C2×Q8—3142no—
122C2×Q8—3141no—
123C2×Q8—6281no—
124C2×D4—21no—
125Q16—3142no—
126Q16—3141no—
127Q16—1572no—
128Q16C22⋊D15711yescharacteristic
129SD16—21no—
130SD16—3142no—
131SD16—6281no—
132D8—21no—
133D8—21no—
134D8—6281no—
135D8C22⋊D15711yescharacteristic
136M16—3141no—
137M16—3141no—
138M16—1571no—
139C2×C8—3141no—
140C2×C8C22×D15711yescharacteristic
141C16—21no—
142C16—3141no—
143C23—41no—
144Q8—21no—
145Q8—3142no—
146Q8—6282no—
147Q8—6281no—
148Q8—1571no—
149D4—21no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—3141no—
154D4—6282no—
155D4—1571no—
156C2×C4—41no—
157C2×C4—3141no—
158C2×C4—6282no—
159C2×C4—6282no—
160C2×C4—6281no—
161C2×C4D4×D15711yescharacteristic
162C8—3141no—
163C8—6281no—
164C8D4×D15711yescharacteristic
165C8C2×C22⋊D15711yescharacteristic
166C22—41no—
167C22—81no—
168C22—161no—
169C22—3141no—
170C22#1909779511yescharacteristic
171C4—41no—
172C4—3141no—
173C4—6282no—
174C4#1909773911yescharacteristic
175C4D8×D15711yescharacteristic
176C2—21no—
177C2—81no—
178C2—161no—
179C2—6281no—
180C2#2375740511yescharacteristic
subgroupG/H
centerC2#23757405
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#509×C157C2
socleC2×C157#447
hypercenter#509D157
hypocenterC157#2193
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #23758087C2semidirect
2. C2×#19097715C2semidirect
3. #23757540C2semidirect
4. #23757090C2semidirect
5. #23757080C2semidirect
6. #23757058C2semidirect
7. #509×C157C2semidirect
90. C157#2193semidirect
93. #509D157semidirect

Maximal subgroups

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

subgroupindex
#237580872
C2×#190977152
#237575402
#237570902
#237570802
#237570582
#509×C1572
#2193157