Finite Group Databasebeta

← #34100684

Subgroups — #34100684

Order 20096.

340 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 93 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#23758040C211yesmaximal, characteristic, complemented
2#23757257C211yesmaximal, characteristic, complemented
3C2×#19097688C212yesmaximal, complemented
4#23757043C212yesmaximal, complemented
5#535×C157C211yesmaximal, characteristic
6#19097778—24no—
7C2×#14578938—22no—
8C2×#14578938C2212yes—
9C2×#14578938C2212yes—
10#19097690—21no—
11#19097688—24no—
12#19097688—21no—
13C2×#41×C157C2211yescharacteristic
14C22×D4×C157C2211yescharacteristic
15#127×C157—21no—
16#124×C157—21no—
17#121×C157—22no—
18#120×C157C414yes—
19#117×C157C2211yescharacteristic
20#14578938—24no—
21#14578938—22no—
22#14578938—22no—
23#14578938—22no—
24#14578938D414yescomplemented
25C2×#11929434—24no—
26C2×#11929434—22no—
27C2×#11929434—22no—
28C24×C157C2×C412yes—
29#41×C157—22no—
30#41×C157—22no—
31C2×Q8×C157D411yescharacteristic
32C2×D4×C157—24no—
33C2×D4×C157—21no—
34C2×D4×C157—21no—
35C2×D4×C157—22no—
36C2×D4×C157—22no—
37C2×D4×C157C2×C412yes—
38C2×D4×C157D411yescharacteristic
39C22×C4×C157D412yes—
40C22×C4×C157C2311yescharacteristic
41C4⋊C4×C157—21no—
42C22⋊C4×C157—24no—
43C22⋊C4×C157C2×C412yes—
44C42×C157—21no—
45#11929434—24no—
46#11929434—42no—
47C23×C157—22no—
48C23×C157—24no—
49C23×C157—82no—
50C23×C157C22⋊C412yes—
51C23×C157C22×C411yescharacteristic
52Q8×C157—22no—
53D4×C157—24no—
54D4×C157—22no—
55D4×C157—41no—
56D4×C157—42no—
57D4×C157—41no—
58D4×C157—84no—
59C2×C4×C157—22no—
60C2×C4×C157—22no—
61C2×C4×C157—22no—
62C2×C4×C157C22⋊C412yes—
63C2×C4×C157C2×D412yes—
64C2×C4×C157C2×D411yescharacteristic
65C2×C4×C157C2×D411yescharacteristic
66C2×C4×C157#4112yes—
67C22×C157—22no—
68C22×C157—41no—
69C22×C157—42no—
70C22×C157—44no—
71C22×C157—42no—
72C22×C157—84no—
73C22×C157C2×C22⋊C411yescharacteristic
74C22×C157C4×D412yes—
75C4×C157—22no—
76C4×C157—42no—
77C4×C157#12011yescharacteristic
78C4×C157#12112yes—
79C4×C157#12311yescharacteristic
80C2×C157—21no—
81C2×C157—22no—
82C2×C157—42no—
83C2×C157—82no—
84C2×C157#38611yescharacteristic
85C157#191411yescharacteristic, complemented, Sylow
86#1914—1571nomaximal, Sylow
87#568—1571no—
88#535D15711yescharacteristic
89#413—1571no—
90C2×#100—1572no—
91#344—1572no—
92C2×#41C2×D15711yescharacteristic
93C22×D4C2×D15711yescharacteristic
94#131—3144no—
95C2×M16—3142no—
96C2×M16—1572no—
97C2×M16—1572no—
98#127—21no—
99#124—21no—
100#121—22no—
101#120Dic15714yes—
102#117C2×D15711yescharacteristic
103#101—3141no—
104#100—3141no—
105#100—3144no—
106C24C2×Dic15712yes—
107#41—22no—
108#41—22no—
109C2×Q8C22⋊D15711yescharacteristic
110C2×D4—24no—
111C2×D4—22no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4C2×Dic15712yes—
116C2×D4C22⋊D15711yescharacteristic
117C22×C4C22⋊D15712yes—
118C22×C4C22×D15711yescharacteristic
119M16—3144no—
120M16—3142no—
121M16—3142no—
122M16—3142no—
123M16—1574no—
124C2×C8—3144no—
125C2×C8—3142no—
126C2×C8—3142no—
127C4⋊C4—21no—
128C22⋊C4—24no—
129C22⋊C4C2×Dic15712yes—
130C42—21no—
131C23—22no—
132C23—24no—
133C23—82no—
134C23C22⋊Dic15712yes—
135C23C22×Dic15711yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—41no—
140D4—42no—
141D4—41no—
142D4—84no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4C22⋊Dic15712yes—
147C2×C4D4×D15712yes—
148C2×C4C2×C22⋊D15711yescharacteristic
149C2×C4C2×C22⋊D15711yescharacteristic
150C2×C4#1457895312yes—
151C8—3144no—
152C8—6282no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—44no—
157C22—42no—
158C22—84no—
159C22C2×C22⋊Dic15711yescharacteristic
160C22D4×Dic15712yes—
161C4—22no—
162C4—42no—
163C4#1909773911yescharacteristic
164C4#1909774312yes—
165C4#1909775211yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—82no—
170C2#2375715311yescharacteristic
subgroupG/H
centerC2#23757153
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
Fitting, prime radical#535×C157C2
socleC2×C157#386
cosocleC22×C4×C157C23
hypercenter#535D157
hypocenterC157#1914
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #23758040C2semidirect
2. #23757257C2semidirect
3. C2×#19097688C2semidirect
4. #23757043C2semidirect
24. #14578938D4semidirect
85. C157#1914semidirect

Maximal subgroups

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

subgroupindex
#237580402
#237572572
C2×#190976882
#237570432
#535×C1572
#1914157