Finite Group Databasebeta

← #34101185

Subgroups — #34101185

Order 20096.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C2×#19097804C212yesmaximal, complemented
2#23757854C211yesmaximal, characteristic
3C2×#19097697C212yesmaximal, complemented
4#23757178C211yesmaximal, characteristic, complemented
5#343×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2212yes—
7C22×Dic314C2211yescharacteristic
8#19097804—24no—
9#19097804—24no—
10C2×Dic628—22no—
11C2×#14578943—22no—
12#19097751—22no—
13#19097746—22no—
14#19097745—22no—
15C2×C4×Dic157C2211yescharacteristic
16#19097697—24no—
17#19097678—22no—
18C2×M16×C157C2212yes—
19C2×C4⋊C4×C157C2211yescharacteristic
20#14578954—22no—
21#14578954—22no—
22#14578954—22no—
23#14578954—22no—
24C2×Dic314—22no—
25C2×Dic314—22no—
26C2×Dic314—21no—
27C2×Dic314D412yes—
28C2×Dic314D412yescomplemented
29C2×D628—22no—
30C2×D628D412yes—
31C2×C22⋊D157—22no—
32C22×Dic157—21no—
33C22×Dic157—21no—
34C2×C4×D157—22no—
35Dic628—28no—
36#14578943—28no—
37C4⋊Dic157—22no—
38#14578931—24no—
39C4×Dic157—22no—
40C22×C4×C157D412yes—
41C22×C4×C157C2311yescharacteristic
42M16×C157—22no—
43M16×C157D414yescomplemented
44C2×C8×C157—22no—
45C4⋊C4×C157—22no—
46C22×D157—22no—
47Dic314—22no—
48Dic314—24no—
49Dic314—22no—
50Dic314—42no—
51D628—22no—
52D628—22no—
53D628—82no—
54C22⋊D157—42no—
55C22⋊D157—42no—
56C2×Dic157—22no—
57C2×Dic157—22no—
58C2×Dic157—22no—
59C2×Dic157—41no—
60C2×Dic157—41no—
61C2×Dic157—41no—
62C2×Dic157—41no—
63C4×D157—42no—
64C4×D157—42no—
65C23×C157C2×D411yescharacteristic
66C2×C4×C157—22no—
67C2×C4×C157—42no—
68C2×C4×C157C2×D411yescharacteristic
69C2×C4×C157C2×D412yes—
70C2×C4×C157C2×D412yes—
71C2×C4×C157#4111yescharacteristic
72C8×C157—24no—
73C22×C157—21no—
74C22×C157—21no—
75C22×C157#12011yescharacteristic
76C22×C157#12111yescharacteristic
77C22×C157#12711yescharacteristic
78C2×D157—42no—
79C2×D157—42no—
80C2×D157—42no—
81C4×C157—42no—
82C4×C157#12012yes—
83C4×C157#12112yes—
84Dic157—42no—
85Dic157—42no—
86Dic157—42no—
87C2×C157—21no—
88C2×C157—21no—
89C2×C157#39211yescharacteristic
90C2×C157#45511yescharacteristic
91C2×C157#45611yescharacteristic
92D157—82no—
93C157#200711yescharacteristic, complemented, Sylow
94#2007—1571nomaximal, Sylow
95C2×#137—1572no—
96#537—1571no—
97C2×#104—1572no—
98#391—1571no—
99#343D15711yescharacteristic, complemented
100C2×#41—1572no—
101C22×Q8—1571no—
102#137—3144no—
103#137—3144no—
104C2×Q16—3142no—
105C2×SD16—3142no—
106C2×M16C2×D15712yes—
107C22⋊Q8—3142no—
108#121—3142no—
109#121—3142no—
110C2×C4⋊C4C2×D15711yescharacteristic
111C2×C42—1571no—
112#104—3144no—
113#95—3142no—
114#41—3142no—
115#41—3142no—
116#41—3142no—
117#41—3142no—
118C2×Q8—3141no—
119C2×Q8—3142no—
120C2×Q8—3142no—
121C2×Q8—1572no—
122C2×Q8—1572no—
123C2×D4—3142no—
124C2×D4—3142no—
125C2×D4—1572no—
126C22×C4—3141no—
127C22×C4—3141no—
128C22×C4—3142no—
129C22×C4D62812yes—
130C22×C4C22×D15711yescharacteristic
131Q16—3148no—
132SD16—3148no—
133M16—22no—
134M16D62814yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—3142no—
138C22⋊C4—3144no—
139C42—3142no—
140C23—3142no—
141C23C2×D62811yescharacteristic
142Q8—3144no—
143Q8—3142no—
144Q8—3142no—
145Q8—6282no—
146D4—3142no—
147D4—3142no—
148D4—6282no—
149D4—6282no—
150D4—12562no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—3142no—
154C2×C4—3142no—
155C2×C4—3142no—
156C2×C4—6281no—
157C2×C4—6281no—
158C2×C4—6281no—
159C2×C4—6281no—
160C2×C4—6282no—
161C2×C4—6282no—
162C2×C4D4×D15711yescharacteristic
163C2×C4D4×D15712yes—
164C2×C4C2×D62812yes—
165C2×C4#1457895511yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—6282no—
170C22—6282no—
171C22—6282no—
172C22#1909774111yescharacteristic
173C22#1909774611yescharacteristic
174C22#1909776811yescharacteristic
175C4—42no—
176C4—6282no—
177C4—6282no—
178C4—6282no—
179C4#1909774112yes—
180C4#1909774612yes—
181C2—21no—
182C2—21no—
183C2—12562no—
184C2#2375718311yescharacteristic
185C2#2375745311yescharacteristic
186C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#343×C157C2
socleC22×C157#120
prime radical#23757854C2
hypercenter#343D157
hypocenterC157#2007
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
1. C2×#19097804C2semidirect
3. C2×#19097697C2semidirect
4. #23757178C2semidirect
5. #343×C157C2semidirect
28. C2×Dic314D4semidirect
43. M16×C157D4semidirect
93. C157#2007semidirect
99. #343D157semidirect
134. M16D628semidirect

Maximal subgroups

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

subgroupindex
C2×#190978042
#237578542
C2×#190976972
#237571782
#343×C1572
#2007157