Finite Group Databasebeta

← #34101239

Subgroups — #34101239

Order 20096.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#23758071C212yesmaximal, complemented
2#23757241C211yesmaximal, characteristic, complemented
3#23757240C212yesmaximal, complemented
4#23757031C211yesmaximal, characteristic, complemented
5#575×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2211yescharacteristic
7#19097802—22no—
8#19097801—22no—
9#19097797—22no—
10#19097796—22no—
11#19097791—24no—
12C2×#14578938C2212yes—
13C22×#11929434C2211yescharacteristic
14C22⋊#11929434—24no—
15#19097683—22no—
16C2×#41×C157C2212yes—
17#137×C157—22no—
18AGL(1,ℤ/8)×C157—22no—
19#135×C157—22no—
20C2×M16×C157C2211yescharacteristic
21#14578954—22no—
22#14578954—22no—
23C2×Dic314D411yescharacteristic
24C2×D628D411yescharacteristic
25C2×C22⋊D157—21no—
26C2×C4×D157—21no—
27#14578944—24no—
28#14578942—24no—
29#14578941—24no—
30#14578939—24no—
31#14578938—22no—
32#14578938—22no—
33C2×#11929434—21no—
34C2×#11929434—22no—
35C2×#11929434D414yes—
36#41×C157—22no—
37#41×C157—22no—
38#41×C157—22no—
39#41×C157—22no—
40C2×Q8×C157D412yes—
41C2×D4×C157—22no—
42C2×D4×C157D412yes—
43C22×C4×C157—22no—
44C22×C4×C157C2311yescharacteristic
45Q16×C157—22no—
46SD16×C157—24no—
47D8×C157—22no—
48M16×C157—22no—
49C2×C8×C157D412yes—
50C22×D157—21no—
51Dic314—22no—
52D628—22no—
53C22⋊D157—42no—
54C2×Dic157—21no—
55C4×D157—41no—
56C4×D157—41no—
57#11929434—24no—
58#11929434—41no—
59C23×C157—22no—
60C23×C157#4111yescharacteristic
61Q8×C157—22no—
62Q8×C157—22no—
63D4×C157—22no—
64D4×C157—22no—
65D4×C157—42no—
66D4×C157—42no—
67C2×C4×C157—22no—
68C2×C4×C157—42no—
69C2×C4×C157—42no—
70C2×C4×C157C2×D411yescharacteristic
71C2×C4×C157C2×D412yes—
72C2×C4×C157C2×D412yes—
73C2×C4×C157C2×D411yescharacteristic
74C8×C157—22no—
75C22×C157—41no—
76C22×C157—44no—
77C22×C157—42no—
78C22×C157#12111yescharacteristic
79C22×C157#12112yes—
80C2×D157—42no—
81C2×D157—41no—
82C4×C157—42no—
83C4×C157#12012yes—
84C4×C157#12011yescharacteristic
85C4×C157#12711yescharacteristic
86Dic157—41no—
87C2×C157—21no—
88C2×C157—22no—
89C2×C157—82no—
90C2×C157#39211yescharacteristic
91D157—81no—
92C157#201711yescharacteristic, complemented, Sylow
93#2017—1571nomaximal, Sylow
94#575—1572no—
95#575D15711yescharacteristic, complemented
96#408—1572no—
97#408—1571no—
98#338—1571no—
99C2×#41—1571no—
100C2×#41C2×D15712yes—
101#137—22no—
102#137—3142no—
103#137—3142no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—3142no—
106AGL(1,ℤ/8)—3142no—
107#135—22no—
108#135—3144no—
109C2×M16—1572no—
110C2×M16C2×D15711yescharacteristic
111C22×C8—1571no—
112C22⋊C8—3144no—
113C22⋊C8—3142no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—3142no—
119#41—3142no—
120C2×Q8—1571no—
121C2×Q8C22⋊D15712yes—
122C2×D4—22no—
123C2×D4—3141no—
124C2×D4—1571no—
125C2×D4C22⋊D15712yes—
126C22×C4—22no—
127C22×C4—3141no—
128C22×C4C22×D15711yescharacteristic
129Q16—22no—
130Q16—3144no—
131SD16—24no—
132SD16—3144no—
133SD16—3144no—
134D8—22no—
135D8—3144no—
136M16—22no—
137M16—3142no—
138M16—3142no—
139C2×C8—3142no—
140C2×C8—3141no—
141C2×C8—1574no—
142C2×C8C22⋊D15712yes—
143C23—22no—
144C23—3141no—
145C23#1457895311yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—3142no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—3142no—
154D4—6282no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—3141no—
159C2×C4—6281no—
160C2×C4—6281no—
161C2×C4D4×D15711yescharacteristic
162C2×C4D4×D15712yes—
163C2×C4C2×C22⋊D15712yes—
164C2×C4C2×C22⋊D15711yescharacteristic
165C8—22no—
166C8—3144no—
167C8—6281no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—6282no—
172C22—6281no—
173C22#1909774211yescharacteristic
174C22#1909774312yes—
175C4—42no—
176C4—6281no—
177C4#1909773912yes—
178C4#1909774011yescharacteristic
179C4#1909776711yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—12561no—
184C2#2375718111yescharacteristic
subgroupG/H
centerC4#19097767
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#575×C157C2
socleC2×C157#392
hypercenter#575D157
hypocenterC157#2017
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23758071C2semidirect
2. #23757241C2semidirect
3. #23757240C2semidirect
4. #23757031C2semidirect
5. #575×C157C2semidirect
92. C157#2017semidirect
95. #575D157semidirect

Maximal subgroups

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

subgroupindex
#237580712
#237572412
#237572402
#237570312
#575×C1572
#2017157