Finite Group Databasebeta

← #13241666

Subgroups — #13241666

Order 1792.

128 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 25 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#11729053C211yesmaximal, characteristic
2C7×#1411C211yesmaximal, characteristic
3#11725601C211yesmaximal, characteristic
4C7×#494C2211yescharacteristic
5#89865—21no—
6#89851—21no—
7#89452C411yescharacteristic
8C7×#356—21no—
9#89343—21no—
10#89250C411yescharacteristic
11#7534—71nomaximal, Sylow
12C2×C7×Q16—41no—
13C7×C4⋊Q8D411yescharacteristic
14C7×C4⋊Q8D411yescharacteristic
15#6432—21no—
16C7×#101—41no—
17C4×C7×C8C2×C411yescharacteristic
18#6410—41no—
19#6391—41no—
20#6384—42no—
21#6382—42no—
22C4×C7⋊C8—21no—
23#1716—71no—
24#1411—71no—
25#1411D711yescharacteristic
26C2×C7×Q8—21no—
27C2×C7×Q8—21no—
28C2×Dic14—41no—
29C7×Q16—82no—
30C7×M16—81no—
31C2×C7×C8—21no—
32C7×C4⋊C4—41no—
33C7×C4⋊C4—41no—
34C42×C7C22⋊C411yescharacteristic
35C4⋊Dic7—41no—
36C4⋊Dic7—41no—
37#1136—81no—
38C2×C7⋊C8—22no—
39#498—71no—
40#498—141no—
41#494C2×D711yescharacteristic
42#487—141no—
43#356—21no—
44#356—141no—
45#322—71no—
46C7×Q8—81no—
47C7×Q8—81no—
48C2×C4×C7—21no—
49C2×C4×C7—41no—
50C2×C4×C7—41no—
51C2×C4×C7#9911yescharacteristic
52C2×Dic7—81no—
53Dic14—82no—
54C7×C8—22no—
55C7×C8—161no—
56C7⋊C8—42no—
57C7⋊C8—161no—
58C2×Q16—41no—
59C4⋊Q8—141no—
60C4⋊Q8D2811yescharacteristic
61C4⋊Q8C22⋊D711yescharacteristic
62#106—282no—
63#106—281no—
64#103—282no—
65#101—41no—
66#101—281no—
67C4×C8—141no—
68C4×C8C4×D711yescharacteristic
69C22×C7#35311yescharacteristic
70C4×C7—22no—
71C4×C7—21no—
72C4×C7—81no—
73C4×C7—81no—
74Dic7—161no—
75C2×Q8—21no—
76C2×Q8—21no—
77C2×Q8—281no—
78Q16—82no—
79M16—81no—
80M16—561no—
81C2×C8—21no—
82C2×C8—142no—
83C4⋊C4—41no—
84C4⋊C4—41no—
85C4⋊C4—281no—
86C4⋊C4—281no—
87C42(C2×D7)⋊C411yescharacteristic
88C2×C7—21no—
89C2×C7#140911yescharacteristic
90Q8—81no—
91Q8—81no—
92Q8—562no—
93C2×C4—21no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—561no—
97C2×C4#638011yescharacteristic
98C8—22no—
99C8—161no—
100C8—282no—
101C8—1121no—
102C7#753411yescharacteristic, complemented, Sylow
103C22#8926911yescharacteristic
104C4—22no—
105C4—21no—
106C4—81no—
107C4—81no—
108C4—1121no—
109C2—21no—
110C2#1172534611yescharacteristic
subgroupG/H
centerC2#11725346
commutatorC4×C7×C8C2×C4
Frattini#494C2×D7
FittingC7×#1411C2
socleC2×C7#1409
prime radicalC22×C7#353
cosocleC7×#494C22
hypercenter#1411D7
hypocenterC7#7534
LCSG ▷ C4×C7×C8 ▷ C42×C7 ▷ C2×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
102. C7#7534semidirect

Maximal subgroups

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

subgroupindex
#117290532
C7×#14112
#117256012
#75347