Finite Group Databasebeta

← #34101366

Subgroups — #34101366

Order 20096.

290 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 67 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#23757854C211yesmaximal, characteristic
2C2×#19097697C212yesmaximal, complemented
3#23757275C212yesmaximal, complemented
4#23757138C211yesmaximal, characteristic, complemented
5#343×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2212yes—
7#19097751—22no—
8#19097746—22no—
9#19097745—22no—
10C2×C4⋊Dic157C2211yescharacteristic
11C2×C4×Dic157C2211yescharacteristic
12#19097697—24no—
13#19097696—22no—
14#19097693—22no—
15#19097678—22no—
16C2×M16×C157C2212yes—
17C2×C4⋊C4×C157C2211yescharacteristic
18#14578954—22no—
19#14578954—22no—
20#14578954—22no—
21#14578954—22no—
22C2×Dic314D412yes—
23C2×D628—22no—
24C2×D628D412yes—
25C2×C22⋊D157—22no—
26C22×Dic157—21no—
27C22×Dic157—21no—
28C2×C4×D157—22no—
29C4⋊Dic157—22no—
30C4⋊Dic157—22no—
31#14578931—24no—
32C4×Dic157—21no—
33C4×Dic157D412yescomplemented
34C22×C4×C157D412yes—
35C22×C4×C157C2311yescharacteristic
36M16×C157—22no—
37M16×C157—22no—
38C2×C8×C157—22no—
39C4⋊C4×C157—22no—
40C22×D157—22no—
41Dic314—22no—
42Dic314—22no—
43D628—22no—
44D628—22no—
45D628—82no—
46C22⋊D157—42no—
47C22⋊D157—42no—
48C2×Dic157—22no—
49C2×Dic157—22no—
50C2×Dic157—41no—
51C2×Dic157—41no—
52C2×Dic157—42no—
53C2×Dic157—41no—
54C4×D157—42no—
55C4×D157—42no—
56C23×C157C2×D411yescharacteristic
57C2×C4×C157—22no—
58C2×C4×C157—42no—
59C2×C4×C157C2×D411yescharacteristic
60C2×C4×C157C2×D412yes—
61C2×C4×C157#4112yes—
62C2×C4×C157#4111yescharacteristic
63C8×C157—42no—
64C22×C157—21no—
65C22×C157—21no—
66C22×C157#12011yescharacteristic
67C22×C157#12111yescharacteristic
68C22×C157#12411yescharacteristic
69C2×D157—42no—
70C2×D157—42no—
71C2×D157—42no—
72C4×C157—42no—
73C4×C157#12112yes—
74C4×C157#12312yes—
75Dic157—42no—
76Dic157—42no—
77Dic157—81no—
78C2×C157—21no—
79C2×C157—21no—
80C2×C157#39411yescharacteristic
81C2×C157#45411yescharacteristic
82C2×C157#45511yescharacteristic
83D157—82no—
84C157#204011yescharacteristic, complemented, Sylow
85#2040—1571nomaximal, Sylow
86#537—1571no—
87C2×#104—1572no—
88#417—1572no—
89#382—1571no—
90#343D15711yescharacteristic, complemented
91C2×#41—1572no—
92C2×M16C2×D15712yes—
93C22⋊Q8—3142no—
94#121—3142no—
95#121—3142no—
96C2×C4⋊C4—1571no—
97C2×C4⋊C4C2×D15711yescharacteristic
98C2×C42—1571no—
99#104—3144no—
100#103—3142no—
101#102—3142no—
102#95—3142no—
103#41—3142no—
104#41—3142no—
105#41—3142no—
106#41—3142no—
107C2×Q8—1572no—
108C2×D4—3142no—
109C2×D4—3142no—
110C2×D4—1572no—
111C22×C4—3141no—
112C22×C4—3142no—
113C22×C4—3141no—
114C22×C4D62812yes—
115C22×C4C22×D15711yescharacteristic
116M16—22no—
117M16—22no—
118C2×C8—22no—
119C4⋊C4—22no—
120C4⋊C4—3142no—
121C4⋊C4—3142no—
122C22⋊C4—3144no—
123C42—3141no—
124C42—1572no—
125C23—3142no—
126C23C2×D62811yescharacteristic
127Q8—3142no—
128Q8—3142no—
129D4—3142no—
130D4—3142no—
131D4—6282no—
132D4—6282no—
133D4—12562no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—3142no—
137C2×C4—3142no—
138C2×C4—6281no—
139C2×C4—6281no—
140C2×C4—6282no—
141C2×C4—6282no—
142C2×C4—6282no—
143C2×C4—6281no—
144C2×C4D4×D15711yescharacteristic
145C2×C4D4×D15712yes—
146C2×C4#1457895412yes—
147C2×C4#1457895511yescharacteristic
148C8—42no—
149C22—21no—
150C22—21no—
151C22—6282no—
152C22—6282no—
153C22—6282no—
154C22#1909774111yescharacteristic
155C22#1909774611yescharacteristic
156C22#1909775911yescharacteristic
157C4—42no—
158C4—6282no—
159C4—6282no—
160C4—12561no—
161C4#1909774412yes—
162C4#1909775612yes—
163C2—21no—
164C2—21no—
165C2—12562no—
166C2#2375719111yescharacteristic
167C2#2375744811yescharacteristic
168C2#2375745311yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#343×C157C2
socleC22×C157#120
prime radical#23757854C2
hypercenter#343D157
hypocenterC157#2040
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#19097697C2semidirect
3. #23757275C2semidirect
4. #23757138C2semidirect
5. #343×C157C2semidirect
33. C4×Dic157D4semidirect
84. C157#2040semidirect
90. #343D157semidirect

Maximal subgroups

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

subgroupindex
#237578542
C2×#190976972
#237572752
#237571382
#343×C1572
#2040157