Finite Group Databasebeta

← #34101297

Subgroups — #34101297

Order 20096.

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

normal subgroups only

This group has 246 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#23757904C211yesmaximal, characteristic
2#23757282C212yesmaximal
3#23757042C211yesmaximal, characteristic
4#23757033C212yesmaximal
5#391×C157C211yesmaximal, characteristic
6C2×#14578938C2212yes—
7#19097770—22no—
8#19097762—22no—
9#19097750—22no—
10#19097730C2212yes—
11#19097695—22no—
12#19097695—22no—
13C22×Q8×C157C2211yescharacteristic
14C2×C4⋊C4×C157C2211yescharacteristic
15C2×C42×C157C2211yescharacteristic
16#95×C157—22no—
17C2×Dic314—22no—
18#14578938—22no—
19#14578938—22no—
20C2×#11929434—22no—
21C4⋊Dic157—22no—
22C4⋊Dic157D412yes—
23C4⋊Dic157D412yes—
24#14578933—24no—
25C22⋊Dic157—22no—
26C4×Dic157—22no—
27C2×Q8×C157—21no—
28C2×Q8×C157—22no—
29C2×Q8×C157—22no—
30C2×Q8×C157Q812yescomplemented
31C22×C4×C157—21no—
32C22×C4×C157—21no—
33C22×C4×C157D412yes—
34C22×C4×C157C2311yescharacteristic
35C4⋊C4×C157—22no—
36C42×C157—22no—
37Dic314—82no—
38C2×Dic157—22no—
39C2×Dic157—22no—
40#11929434—42no—
41C23×C157C2×D411yescharacteristic
42Q8×C157—24no—
43Q8×C157—42no—
44C2×C4×C157—22no—
45C2×C4×C157—22no—
46C2×C4×C157—22no—
47C2×C4×C157—41no—
48C2×C4×C157—41no—
49C2×C4×C157—41no—
50C2×C4×C157—41no—
51C2×C4×C157—42no—
52C2×C4×C157C2×D412yes—
53C2×C4×C157C2×Q811yescharacteristic
54C2×C4×C157#4112yes—
55C2×C4×C157#4111yescharacteristic
56C22×C157—21no—
57C22×C157—21no—
58C22×C157#12011yescharacteristic
59C22×C157C22⋊Q811yescharacteristic
60C22×C157#12411yescharacteristic
61C4×C157—42no—
62C4×C157—42no—
63C4×C157—42no—
64C4×C157C22⋊Q812yes—
65C4×C157#12412yes—
66Dic157—42no—
67Dic157—42no—
68C2×C157—21no—
69C2×C157—21no—
70C2×C157#39311yescharacteristic
71C2×C157#45511yescharacteristic
72C2×C157#45611yescharacteristic
73C157#202811yescharacteristic, complemented, Sylow
74#2028—1571nomaximal, Sylow
75#544—1571no—
76#419—1572no—
77#391D15711yescharacteristic
78#343—1571no—
79#339—1572no—
80C22×Q8C2×D15711yescharacteristic
81C2×M16—1572no—
82C4⋊Q8—3142no—
83#125—3142no—
84C22⋊Q8—3142no—
85#117—1572no—
86C2×C4⋊C4C2×D15711yescharacteristic
87C2×C42C2×D15711yescharacteristic
88#103—3142no—
89#103—3142no—
90#95—22no—
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—3142no—
95C2×Q8Dic31412yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D15712yes—
99C22×C4C22×D15711yescharacteristic
100M16—3142no—
101M16—3142no—
102C2×C8—3142no—
103C4⋊C4—22no—
104C4⋊C4—3142no—
105C4⋊C4—3144no—
106C4⋊C4—1572no—
107C4⋊C4—1572no—
108C22⋊C4—3142no—
109C42—22no—
110C42—3142no—
111C23C2×C22⋊D15711yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—12562no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—3142no—
124C2×C4—3142no—
125C2×C4D4×D15712yes—
126C2×C4C2×Dic31411yescharacteristic
127C2×C4#1457895312yes—
128C2×C4#1457895411yescharacteristic
129C8—6282no—
130C22—21no—
131C22—21no—
132C22#1909773911yescharacteristic
133C22#1909775011yescharacteristic
134C22#1909775811yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—6282no—
139C4—6282no—
140C4#1909774812yes—
141C4#1909775712yes—
142C2—21no—
143C2—21no—
144C2#2375718511yescharacteristic
145C2#2375745011yescharacteristic
146C2#2375745511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#391×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#391D157
hypocenterC157#2028
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C157Q8semidirect
73. C157#2028semidirect
95. C2×Q8Dic314semidirect

Maximal subgroups

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

subgroupindex
#237579042
#237572822
#237570422
#237570332
#391×C1572
#2028157