Finite Group Databasebeta

← #34102117

Subgroups — #34102117

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#23758086C211yesmaximal, characteristic
2#23757716C211yesmaximal, characteristic, complemented
3C2×#19097717C211yesmaximal, characteristic, complemented
4#23757549C211yesmaximal, characteristic, complemented
5#23757079C211yesmaximal, characteristic, complemented
6#23757058C211yesmaximal, characteristic, complemented
7#362×C157C211yesmaximal, characteristic, complemented
8#19097819—21no—
9#19097804—21no—
10#19097803—22no—
11#19097802—21no—
12#19097794—21no—
13#19097793C2211yescharacteristic
14C2×Dic628C2211yescharacteristic
15Q16×D157—21no—
16#19097777C2211yescharacteristic
17Dic1256—21no—
18#19097717—22no—
19#19097716—21no—
20C2×#14578929C2211yescharacteristic
21#19097689—21no—
22C2×Q16×C157C2211yescharacteristic
23M32×C157C2211yescharacteristic
24#108×C157C2211yescharacteristic
25#14578955—22no—
26#14578955—41no—
27#14578954—21no—
28#14578954—42no—
29#14578954D411yescharacteristic
30C2×Dic314—21no—
31Q8×D157—22no—
32Q8×D157—41no—
33Dic628—21no—
34Dic628—21no—
35Dic628—41no—
36Dic628D411yescharacteristic
37#14578944—22no—
38#14578943—21no—
39#14578943—41no—
40#14578941—22no—
41D1256D411yescharacteristic
42#14578938D411yescharacteristic
43#14578937—21no—
44C8×D157—21no—
45#14578929—21no—
46C2×Q8×C157—21no—
47Q16×C157—21no—
48Q16×C157D412yes—
49M16×C157—21no—
50C2×C8×C157C2311yescharacteristic
51C16×C157—21no—
52Dic314—21no—
53Dic314—42no—
54Dic314—41no—
55Dic314—41no—
56Dic314D811yescharacteristic
57D628—21no—
58D628—42no—
59D628D811yescharacteristic
60C22⋊D157—21no—
61C22⋊D157—41no—
62C2×Dic157—41no—
63C4×D157—21no—
64C4×D157—42no—
65C4×D157—42no—
66C4×D157—41no—
67#11929434—21no—
68Q8×C157—22no—
69Q8×C157—41no—
70C2×C4×C157—41no—
71C2×C4×C157C2×D411yescharacteristic
72C8×C157—41no—
73C8×C157C2×D411yescharacteristic
74C8×C157C2×D411yescharacteristic
75C22×C157AGL(1,ℤ/8)11yescharacteristic
76C2×D157—21no—
77C2×D157—41no—
78C4×C157—42no—
79C4×C157#12011yescharacteristic
80C4×C157C2×D811yescharacteristic
81Dic157—21no—
82Dic157—41no—
83Dic157—81no—
84C2×C157—21no—
85C2×C157#44711yescharacteristic
86D157—41no—
87D157—81no—
88C157#219511yescharacteristic, complemented, Sylow
89#2195—1571nomaximal, Sylow
90#578—1571no—
91#510—1571no—
92C2×Q32—1571no—
93#473—1571no—
94#362D15711yescharacteristic, complemented
95#359—1571no—
96#350—1571no—
972−1+4—3141no—
98#137—3141no—
99#137—3142no—
100#137—3141no—
101#135—3141no—
102#135—1571no—
103C2×Q16—3141no—
104C2×Q16—1571no—
105C2×Q16C2×D15711yescharacteristic
106#131—1571no—
107Q32—3141no—
108Q32—3142no—
109SD32—3141no—
110M32C2×D15711yescharacteristic
111C2×C16—1571no—
112#108C2×D15711yescharacteristic
113#101—3141no—
114#41—3142no—
115#41—3141no—
116#41—6282no—
117#41—6281no—
118#41—1571no—
119C2×Q8—21no—
120C2×Q8—3142no—
121C2×Q8—3141no—
122C2×Q8—6281no—
123Q16—21no—
124Q16—3142no—
125Q16—3141no—
126Q16—3141no—
127Q16—6281no—
128Q16—1571no—
129Q16D62812yes—
130SD16—3142no—
131SD16—3141no—
132SD16—6281no—
133D8—1571no—
134M16—21no—
135M16—3141no—
136M16—1571no—
137C2×C8—3141no—
138C2×C8C22×D15711yescharacteristic
139C16—21no—
140C16—3141no—
141Q8—22no—
142Q8—41no—
143Q8—3141no—
144Q8—6282no—
145Q8—6281no—
146Q8—6281no—
147Q8—1571no—
148D4—3141no—
149D4—3141no—
150D4—6282no—
151D4—6281no—
152D4—1571no—
153C2×C4—41no—
154C2×C4—3141no—
155C2×C4—6282no—
156C2×C4—6282no—
157C2×C4—6281no—
158C2×C4—6281no—
159C2×C4D4×D15711yescharacteristic
160C8—41no—
161C8—3141no—
162C8D4×D15711yescharacteristic
163C8C2×D62811yescharacteristic
164C22—3141no—
165C22—6281no—
166C22#1909779811yescharacteristic
167C4—42no—
168C4—3141no—
169C4—6281no—
170C4—12561no—
171C4#1909774111yescharacteristic
172C4D8×D15711yescharacteristic
173C2—21no—
174C2—6281no—
175C2—12561no—
176C2#2375740811yescharacteristic
subgroupG/H
centerC2#23757408
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#362×C157C2
socleC2×C157#447
prime radical#23758086C2
hypercenter#362D157
hypocenterC157#2195
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
2. #23757716C2semidirect
3. C2×#19097717C2semidirect
4. #23757549C2semidirect
5. #23757079C2semidirect
6. #23757058C2semidirect
7. #362×C157C2semidirect
88. C157#2195semidirect
94. #362D157semidirect

Maximal subgroups

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

subgroupindex
#237580862
#237577162
C2×#190977172
#237575492
#237570792
#237570582
#362×C1572
#2195157