Finite Group Databasebeta

← #34102111

Subgroups — #34102111

Order 20096.

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

normal subgroups only

This group has 206 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
2C2×#19097717C211yesmaximal, characteristic, complemented
3#23757545C211yesmaximal, characteristic, complemented
4#23757090C211yesmaximal, characteristic, complemented
5#23757080C211yesmaximal, characteristic, complemented
6#23757058C211yesmaximal, characteristic, complemented
7#510×C157C211yesmaximal, characteristic, complemented
8#19097818—21no—
9#19097802—21no—
10#19097801—21no—
11#19097800—22no—
12#19097790—21no—
13C2×Dic628C2211yescharacteristic
14Q16×D157—21no—
15#19097777C2211yescharacteristic
16#19097717—22no—
17C2×#14578929C2211yescharacteristic
18#19097707C2211yescharacteristic
19#19097690—21no—
20#135×C157C2211yescharacteristic
21C2×Q16×C157C2211yescharacteristic
22Q32×C157—21no—
23SD32×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#14578944—41no—
36#14578942—22no—
37#14578941—41no—
38#14578938—21no—
39#14578938D411yescharacteristic
40#14578937—21no—
41C8×D157—21no—
42#14578929—21no—
43#41×C157—21no—
44C2×Q8×C157—21no—
45Q16×C157—21no—
46Q16×C157—21no—
47Q16×C157D411yescharacteristic
48SD16×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—
65Q8×C157—21no—
66Q8×C157—41no—
67Q8×C157—41no—
68D4×C157—21no—
69D4×C157—41no—
70C2×C4×C157—41no—
71C2×C4×C157—41no—
72C2×C4×C157C2×D411yescharacteristic
73C8×C157C2×D411yescharacteristic
74C8×C157C2×D411yescharacteristic
75C22×C157—41no—
76C22×C157AGL(1,ℤ/8)11yescharacteristic
77C2×D157—21no—
78C4×C157—41no—
79C4×C157—81no—
80C4×C157#12011yescharacteristic
81C4×C157C2×D811yescharacteristic
82Dic157—21no—
83Dic157—42no—
84C2×C157—21no—
85C2×C157—81no—
86C2×C157#44711yescharacteristic
87D157—41no—
88C157#219511yescharacteristic, complemented, Sylow
89#2195—1571nomaximal, Sylow
90#578—1571no—
91#510D15711yescharacteristic, complemented
92C2×Q32—1571no—
93#473—1571no—
94#362—1571no—
95#359—1571no—
96#350—1571no—
972−1+4—3141no—
98#137—3142no—
99#137—3141no—
100#137—3141no—
101#135—3141no—
102#135C2×D15711yescharacteristic
103C2×Q16—3141no—
104C2×Q16—1571no—
105C2×Q16C2×D15711yescharacteristic
106#131—1571no—
107Q32—21no—
108Q32—3142no—
109SD32—21no—
110M32C2×D15711yescharacteristic
111C2×C16—1571no—
112#108—1571no—
113#101—3141no—
114#41—21no—
115#41—3142no—
116#41—6281no—
117#41—6282no—
118#41—1571no—
119C2×Q8—21no—
120C2×Q8—3142no—
121C2×Q8—3141no—
122C2×Q8—6281no—
123Q16—21no—
124Q16—21no—
125Q16—3142no—
126Q16—3141no—
127Q16—6281no—
128Q16—1572no—
129Q16C22⋊D15711yescharacteristic
130SD16—21no—
131SD16—3142no—
132SD16—6281no—
133D8C22⋊D15711yescharacteristic
134M16—3141no—
135M16—3141no—
136M16—1571no—
137C2×C8—3141no—
138C2×C8C22×D15711yescharacteristic
139C16—21no—
140C16—3141no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—3142no—
145Q8—6282no—
146Q8—6281no—
147Q8—1571no—
148D4—21no—
149D4—41no—
150D4—3141no—
151D4—6282no—
152D4—1571no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—3141no—
156C2×C4—6282no—
157C2×C4—6282no—
158C2×C4—6281no—
159C2×C4D4×D15711yescharacteristic
160C8—3141no—
161C8—6281no—
162C8D4×D15711yescharacteristic
163C8C2×C22⋊D15711yescharacteristic
164C22—41no—
165C22—3141no—
166C22#1909779511yescharacteristic
167C4—41no—
168C4—81no—
169C4—3141no—
170C4—6282no—
171C4#1909773911yescharacteristic
172C4D8×D15711yescharacteristic
173C2—21no—
174C2—81no—
175C2—6281no—
176C2#2375740511yescharacteristic
subgroupG/H
centerC2#23757405
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#510×C157C2
socleC2×C157#447
prime radical#23758087C2
hypercenter#510D157
hypocenterC157#2195
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#19097717C2semidirect
3. #23757545C2semidirect
4. #23757090C2semidirect
5. #23757080C2semidirect
6. #23757058C2semidirect
7. #510×C157C2semidirect
88. C157#2195semidirect
91. #510D157semidirect

Maximal subgroups

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

subgroupindex
#237580872
C2×#190977172
#237575452
#237570902
#237570802
#237570582
#510×C1572
#2195157