Finite Group Databasebeta

← #34101240

Subgroups — #34101240

Order 20096.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#23758073C211yesmaximal, characteristic, complemented
2#23758071C212yesmaximal, complemented
3#23757239C212yesmaximal, complemented
4#23757031C211yesmaximal, characteristic, complemented
5#408×C157C211yesmaximal, characteristic, complemented
6C2×#14578954C2212yes—
7#19097804—22no—
8#19097802—22no—
9#19097801—22no—
10#19097799—22no—
11#19097797—22no—
12#19097796—22no—
13#19097793—22no—
14#19097791—24no—
15C2×#14578938C2212yes—
16#19097683—24no—
17C2×#41×C157C2211yescharacteristic
18C2×M16×C157C2211yescharacteristic
19C22×C8×C157C2211yescharacteristic
20C22⋊C8×C157—22no—
21#14578954—22no—
22#14578954—22no—
23#14578954—22no—
24#14578954—22no—
25C2×Dic314D412yes—
26C2×D628D412yes—
27C2×C22⋊D157—22no—
28C2×C4×D157—22no—
29Dic628—22no—
30#14578944—24no—
31#14578943—24no—
32#14578942—24no—
33#14578941—24no—
34D1256—22no—
35#14578939—24no—
36#14578938—22no—
37#14578938—22no—
38C2×#11929434D414yes—
39#41×C157—22no—
40#41×C157—22no—
41C2×Q8×C157D411yescharacteristic
42C2×D4×C157—21no—
43C2×D4×C157D411yescharacteristic
44C22×C4×C157—21no—
45C22×C4×C157C2311yescharacteristic
46M16×C157—22no—
47C2×C8×C157—21no—
48C2×C8×C157—22no—
49C2×C8×C157D412yes—
50C22×D157—22no—
51Dic314—22no—
52Dic314—22no—
53D628—22no—
54D628—22no—
55C22⋊D157—42no—
56C22⋊D157—42no—
57C2×Dic157—22no—
58C4×D157—42no—
59C4×D157—42no—
60#11929434—24no—
61C23×C157—21no—
62C23×C157#4111yescharacteristic
63Q8×C157—22no—
64D4×C157—22no—
65D4×C157—42no—
66C2×C4×C157—21no—
67C2×C4×C157—41no—
68C2×C4×C157—41no—
69C2×C4×C157C2×D412yes—
70C2×C4×C157C2×D412yes—
71C2×C4×C157C2×D411yescharacteristic
72C2×C4×C157C2×D411yescharacteristic
73C8×C157—22no—
74C8×C157—41no—
75C22×C157—41no—
76C22×C157—42no—
77C22×C157—41no—
78C22×C157#12112yes—
79C22×C157#12111yescharacteristic
80C2×D157—44no—
81C2×D157—42no—
82C4×C157—41no—
83C4×C157#12011yescharacteristic
84C4×C157#12012yes—
85C4×C157#12711yescharacteristic
86Dic157—42no—
87C2×C157—22no—
88C2×C157—21no—
89C2×C157—81no—
90C2×C157#39211yescharacteristic
91D157—82no—
92C157#201711yescharacteristic, complemented, Sylow
93#2017—1571nomaximal, Sylow
94#575—1572no—
95#575—1571no—
96#408—1572no—
97#408D15711yescharacteristic, complemented
98#338—1571no—
99C2×#41—1572no—
100C2×#41C2×D15711yescharacteristic
101#137—3142no—
102#137—3142no—
103#137—3142no—
104AGL(1,ℤ/8)—3142no—
105AGL(1,ℤ/8)—3142no—
106AGL(1,ℤ/8)—3142no—
107#135—3144no—
108#135—3142no—
109C2×M16—1572no—
110C2×M16C2×D15711yescharacteristic
111C22×C8C2×D15711yescharacteristic
112C22⋊C8—22no—
113C22⋊C8—3144no—
114#41—22no—
115#41—22no—
116#41—3142no—
117#41—3142no—
118#41—3142no—
119#41—3142no—
120C2×Q8—1572no—
121C2×Q8D62811yescharacteristic
122C2×D4—21no—
123C2×D4—3142no—
124C2×D4—1572no—
125C2×D4D62811yescharacteristic
126C22×C4—21no—
127C22×C4—3142no—
128C22×C4C22×D15711yescharacteristic
129Q16—3142no—
130Q16—3144no—
131SD16—3144no—
132SD16—3144no—
133SD16—3144no—
134D8—3142no—
135D8—3144no—
136M16—22no—
137M16—3142no—
138M16—3142no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—1574no—
142C2×C8C22⋊D15712yes—
143C23—21no—
144C23—3142no—
145C23#1457895411yescharacteristic
146Q8—22no—
147Q8—3142no—
148Q8—3142no—
149D4—22no—
150D4—42no—
151D4—3142no—
152D4—3142no—
153D4—6282no—
154D4—6282no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—3142no—
159C2×C4—6282no—
160C2×C4—6282no—
161C2×C4D4×D15712yes—
162C2×C4D4×D15712yes—
163C2×C4C2×C22⋊D15711yescharacteristic
164C2×C4C2×D62811yescharacteristic
165C8—22no—
166C8—41no—
167C8—3144no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—6284no—
172C22—6282no—
173C22#1909774412yes—
174C22#1909774511yescharacteristic
175C4—41no—
176C4—6282no—
177C4#1909773911yescharacteristic
178C4#1909774112yes—
179C4#1909776711yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—12562no—
184C2#2375718211yescharacteristic
subgroupG/H
centerC4#19097767
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#408×C157C2
socleC2×C157#392
hypercenter#408D157
hypocenterC157#2017
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #23758073C2semidirect
2. #23758071C2semidirect
3. #23757239C2semidirect
4. #23757031C2semidirect
5. #408×C157C2semidirect
92. C157#2017semidirect
97. #408D157semidirect

Maximal subgroups

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

subgroupindex
#237580732
#237580712
#237572392
#237570312
#408×C1572
#2017157