Finite Group Databasebeta

← #14544697

Subgroups — #14544697

Order 2176.

272 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#10587553C212yesmaximal
2#11763690C214yesmaximal, complemented
3#11763282C211yesmaximal, characteristic
4C22×C22⋊D17C2211yescharacteristic
5C2×#63247C2214yes—
6C2×C22⋊C4×C17C411yescharacteristic
7C2×C22⋊Dic17C411yescharacteristic
8C4×C22⋊D17—22no—
9#10587567—22no—
10C22⋊C4×D17C412yes—
11#10587563C2212yes—
12#10587553—22no—
13#10587553—22no—
14C24×C17C2×C411yescharacteristic
15C23×D17C2×C411yescharacteristic
16C22×C4×C17—21no—
17C2×C22⋊D17—24no—
18C2×C22⋊D17D412yes—
19C2×C22⋊D17D412yes—
20C22×Dic17—21no—
21C22×Dic17C2311yescharacteristic
22C2×C4×D17—22no—
23#63247—24no—
24#63247—24no—
25C2×#3624—24no—
26C22⋊C4×C17—21no—
27C22⋊C4×C17C2×C412yes—
28C22⋊Dic17—21no—
29C22⋊Dic17C2×C412yes—
30#63227—22no—
31#63225—22no—
32C4×Dic17—22no—
33C23×C17—22no—
34C23×C17—81no—
35C23×C17C22⋊C411yescharacteristic
36C23×C17C22⋊C411yescharacteristic
37C23×C17C22×C411yescharacteristic
38C22×D17—22no—
39C22×D17—81no—
40C22×D17C22⋊C412yes—
41C2×C4×C17—22no—
42C2×C4×C17—81no—
43C22⋊D17—24no—
44C22⋊D17—24no—
45C2×Dic17—22no—
46C2×Dic17—81no—
47C2×Dic17C2×D412yes—
48C2×Dic17#4114yes—
49C4×D17—82no—
50#3624—44no—
51#1829—171nomaximal, Sylow
52C22×C17—21no—
53C22×C17—21no—
54C22×C17—41no—
55C22×C17—41no—
56C22×C17—41no—
57C22×C17—82no—
58C22×C17C2×C22⋊C411yescharacteristic
59C22×C17#11712yes—
60C2×D17—22no—
61C2×D17—42no—
62C2×D17—82no—
63C4×C17—42no—
64Dic17—42no—
65Dic17#12314yes—
66#518—171no—
67C2×#100—172no—
68#344—174no—
69C2×C17—21no—
70C2×C17—22no—
71C2×C17—41no—
72C2×C17—41no—
73C2×C17#38111yescharacteristic
74D17—42no—
75C22×D4—171no—
76C2×M16—174no—
77C4×D4—342no—
78C4×D4—342no—
79#117—172no—
80C2×C22⋊C4—171no—
81C2×C22⋊C4—172no—
82C2×C22⋊C4#59511yescharacteristic
83#100—342no—
84#100—342no—
85C17#182911yescharacteristic, complemented, Sylow
86C24—171no—
87C24C2×#59511yescharacteristic
88C2×D4—172no—
89C2×D4—172no—
90C2×D4—344no—
91C22×C4—21no—
92C22×C4—171no—
93C22×C4—342no—
94C22×C4—341no—
95M16—344no—
96M16—344no—
97C2×C8—344no—
98C4⋊C4—342no—
99C22⋊C4—21no—
100C22⋊C4—172no—
101C22⋊C4—342no—
102C22⋊C4—341no—
103C22⋊C4C2×#59512yes—
104C42—342no—
105C23—22no—
106C23—81no—
107C23—172no—
108C23—342no—
109C23—1361no—
110C23C22⋊#59511yescharacteristic
111C23C22⋊#59511yescharacteristic
112C23C22×#59511yescharacteristic
113D4—344no—
114D4—344no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—174no—
118C2×C4—172no—
119C2×C4—342no—
120C2×C4—1362no—
121C2×C4—1361no—
122C8—684no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—342no—
130C22—682no—
131C22—1362no—
132C22#1058767712yes—
133C22C2×C22⋊#59511yescharacteristic
134C4—42no—
135C4—174no—
136C4—682no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—682no—
142C2#1176375211yescharacteristic
subgroupG/H
centerC2#11763752
commutatorC23×C17C22×C4
FrattiniC23C22×#595
FittingC2×C22⋊C4×C17C4
socleC2×C17#381
prime radicalC22×C22⋊D17C22
cosocleC22×Dic17C23
hypercenterC2×C22⋊C4#595
hypocenterC17#1829
LCSG ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11763690C2semidirect
85. C17#1829semidirect

Maximal subgroups

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

subgroupindex
C2×#105875532
#117636902
#117632822
#182917