Finite Group Databasebeta

← #34100656

Subgroups — #34100656

Order 20096.

312 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 85 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
2#23757844C211yesmaximal, characteristic
3#23757281C212yesmaximal, complemented
4#23757029C212yesmaximal, complemented
5#410×C157C211yesmaximal, characteristic
6C22×Dic314C2211yescharacteristic
7#19097778—24no—
8C2×#14578938—22no—
9C2×#14578938C2212yes—
10#19097769C412yescomplemented
11#19097758C412yescomplemented
12#19097752—22no—
13#19097750—22no—
14#19097730C2211yescharacteristic
15#19097694—24no—
16C2×#41×C157C2211yescharacteristic
17#117×C157C2212yes—
18#99×C157—22no—
19C2×Dic314—21no—
20C2×Dic314—22no—
21C2×Dic314—22no—
22C2×Dic314C2×C412yes—
23C22×Dic157—21no—
24#14578938—24no—
25#14578938—22no—
26#14578938—22no—
27C2×#11929434—24no—
28C2×#11929434D414yes—
29C4⋊Dic157—21no—
30#14578933—24no—
31C22⋊Dic157—24no—
32C22⋊Dic157—21no—
33C4×Dic157C2×C412yes—
34#41×C157—22no—
35#41×C157—22no—
36C2×Q8×C157C2×C411yescharacteristic
37C2×D4×C157C2×C411yescharacteristic
38C2×D4×C157D412yes—
39C22×C4×C157D412yes—
40C22×C4×C157C2311yescharacteristic
41C4⋊C4×C157—22no—
42C22⋊C4×C157—22no—
43C42×C157—22no—
44Dic314—24no—
45Dic314—41no—
46Dic314—41no—
47C2×Dic157—22no—
48C2×Dic157—22no—
49C2×Dic157—42no—
50#11929434—24no—
51C23×C157C22⋊C412yes—
52C23×C157C2×D411yescharacteristic
53Q8×C157—22no—
54D4×C157—24no—
55D4×C157—22no—
56C2×C4×C157—22no—
57C2×C4×C157—22no—
58C2×C4×C157—42no—
59C2×C4×C157C22⋊C412yes—
60C2×C4×C157C22×C411yescharacteristic
61C2×C4×C157C2×D412yes—
62C2×C4×C157C2×D411yescharacteristic
63C2×C4×C157#4112yes—
64C22×C157—22no—
65C22×C157—41no—
66C22×C157—42no—
67C22×C157C2×C22⋊C411yescharacteristic
68C22×C157#12112yes—
69C4×C157—22no—
70C4×C157—82no—
71C4×C157C4×D412yes—
72C4×C157#12011yescharacteristic
73C4×C157#12311yescharacteristic
74Dic157—42no—
75Dic157—42no—
76C2×C157—21no—
77C2×C157—22no—
78C2×C157—42no—
79C2×C157#38611yescharacteristic
80C157#190911yescharacteristic, complemented, Sylow
81#1909—1571nomaximal, Sylow
82#568—1571no—
83#536—1571no—
84#419—1572no—
85#410D15711yescharacteristic
86H(3,ℤ/4)—1572no—
87C2×#41C2×D15711yescharacteristic
88C22×Q8—1571no—
89#131—3144no—
90C2×M16—3142no—
91C2×M16—1572no—
92C4⋊Q8—1572no—
93#124—1572no—
94#123—3142no—
95C22⋊Q8—3142no—
96#117—1571no—
97#117C2×D15712yes—
98#103—3144no—
99#99—22no—
100#41—22no—
101#41—22no—
102C2×Q8—3141no—
103C2×Q8—3142no—
104C2×Q8—3142no—
105C2×Q8—1572no—
106C2×Q8C4×D15711yescharacteristic
107C2×D4C4×D15711yescharacteristic
108C2×D4C22⋊D15712yes—
109C22×C4—3141no—
110C22×C4D62812yes—
111C22×C4C22×D15711yescharacteristic
112M16—3144no—
113M16—3142no—
114M16—3142no—
115C2×C8—3144no—
116C2×C8—1574no—
117C4⋊C4—22no—
118C4⋊C4—3141no—
119C4⋊C4—3144no—
120C22⋊C4—22no—
121C22⋊C4—3141no—
122C22⋊C4—3144no—
123C42—22no—
124C42—1572no—
125C23#1457893112yes—
126C23C2×C22⋊D15711yescharacteristic
127Q8—22no—
128Q8—3144no—
129Q8—6281no—
130Q8—6281no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—42no—
136C2×C4—3142no—
137C2×C4—3142no—
138C2×C4—6282no—
139C2×C4#1457893112yes—
140C2×C4C2×C4×D15711yescharacteristic
141C2×C4D4×D15712yes—
142C2×C4C2×D62811yescharacteristic
143C2×C4#1457895312yes—
144C8—3144no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×#1457893111yescharacteristic
149C22#1909774312yes—
150C4—22no—
151C4—82no—
152C4—6282no—
153C4—6282no—
154C4#1909773112yes—
155C4#1909774111yescharacteristic
156C4#1909775511yescharacteristic
157C2—22no—
158C2—21no—
159C2—42no—
160C2#2375715011yescharacteristic
subgroupG/H
centerC2#23757150
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#410×C157C2
socleC2×C157#386
prime radicalC2×#41×C157C22
cosocleC22×C4×C157C23
hypercenter#410D157
hypocenterC157#1909
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #23757281C2semidirect
4. #23757029C2semidirect
10. #19097769C4semidirect
11. #19097758C4semidirect
80. C157#1909semidirect

Maximal subgroups

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

subgroupindex
#237580402
#237578442
#237572812
#237570292
#410×C1572
#1909157