Finite Group Databasebeta

← #17948335

Subgroups — #17948335

Order 4352.

194 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 44 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#14543704C212yesmaximal
2#14528853C211yesmaximal, characteristic
3C22⋊#63216—22no—
4C2×#10587612C411yescharacteristic
5C2×C22⋊#3622C2211yescharacteristic
6#11762563—22no—
7C2×C17×C22⋊C8C411yescharacteristic
8C23×C4×C17C2×C411yescharacteristic
9C22×C8×C17—21no—
10C2×C22⋊Dic17—21no—
11#10587612—41no—
12#10587612—41no—
13C2×C4⋊Dic17C811yescharacteristic
14C2×C4⋊Dic17C811yescharacteristic
15C2×C4×Dic17—21no—
16C22×#3622D412yes—
17C2×#63216—42no—
18C17×C22⋊C8—41no—
19C22⋊#3622—41no—
20C24×C17M1611yescharacteristic
21C22×C4×C17—21no—
22C22×C4×C17—21no—
23C22×C4×C17—42no—
24C22×C4×C17C22⋊C411yescharacteristic
25C22×C4×C17C2×C811yescharacteristic
26C22×Dic17—21no—
27C22×Dic17—21no—
28C2×C8×C17—42no—
29C2×C8×C17—41no—
30C22⋊Dic17—42no—
31C4⋊Dic17—41no—
32C4⋊Dic17—41no—
33C4×Dic17—41no—
34C4×Dic17—41no—
35C2×#3622—22no—
36C2×#3622—42no—
37#63216—82no—
38#7059—171nomaximal, Sylow
39C23×C17—21no—
40C23×C17—22no—
41C23×C17—41no—
42C23×C17—41no—
43C23×C17C22⋊C811yescharacteristic
44C2×C4×C17—22no—
45C2×C4×C17—21no—
46C2×C4×C17—42no—
47C2×C4×C17—42no—
48C2×C4×C17—41no—
49C2×C4×C17#9911yescharacteristic
50C2×C4×C17#10011yescharacteristic
51C2×Dic17—42no—
52C2×Dic17—41no—
53C2×Dic17—41no—
54C2×Dic17—42no—
55C8×C17—81no—
56#3622—42no—
57#1818—171no—
58#1314—172no—
59C22×C17—21no—
60C22×C17—21no—
61C22×C17—41no—
62C22×C17—41no—
63C22×C17—41no—
64C22×C17—82no—
65C22×C17#32311yescharacteristic
66C22×C17#35012yes—
67C4×C17—21no—
68C4×C17—41no—
69C4×C17#35212yes—
70Dic17—81no—
71Dic17—81no—
72C2×#117—171no—
73C2×C22⋊C8—171no—
74C2×C22⋊C8#59511yescharacteristic
75C22⋊C16—342no—
76#336—342no—
77C2×C17—22no—
78C2×C17—81no—
79C2×C17#131511yescharacteristic
80C2×C17#131711yescharacteristic
81C2×C17#132111yescharacteristic
82C23×C4C2×#59511yescharacteristic
83C22×C8—21no—
84C22×C8—172no—
85#117—681no—
86#117—681no—
87C2×C4⋊C4—171no—
88C2×C4⋊C4—171no—
89C2×C22⋊C4—341no—
90C2×C42—341no—
91C2×C16—682no—
92C22⋊C8—41no—
93C22⋊C8—681no—
94C17#705911yescharacteristic, complemented, Sylow
95C24#6324311yescharacteristic
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—42no—
99C22×C4—341no—
100C22×C4—341no—
101C22×C4#6324211yescharacteristic
102C22×C4C22⋊#59511yescharacteristic
103C2×C8—42no—
104C2×C8—41no—
105C2×C8—342no—
106C2×C8—682no—
107C4⋊C4—681no—
108C4⋊C4—681no—
109C22⋊C4—682no—
110C42—681no—
111C42—681no—
112C16—1362no—
113C23—21no—
114C23—22no—
115C23—41no—
116C23—41no—
117C23#1058754311yescharacteristic
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—682no—
124C2×C4—681no—
125C2×C4—681no—
126C2×C4—682no—
127C2×C4#1058753911yescharacteristic
128C2×C4#1058755311yescharacteristic
129C8—81no—
130C8—682no—
131C22—21no—
132C22—21no—
133C22—41no—
134C22—41no—
135C22—41no—
136C22—82no—
137C22#1176365311yescharacteristic
138C22#1176370812yes—
139C4—21no—
140C4—41no—
141C4—1361no—
142C4—1361no—
143C4#1176371212yes—
144C2—22no—
145C2—81no—
146C2#1454370711yescharacteristic
147C2#1454371111yescharacteristic
148C2#1454371911yescharacteristic
subgroupG/H
centerC2×C4#10587539
commutatorC22×C4×C17C2×C8
FrattiniC23×C4C2×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17#323
prime radicalC24×C17M16
cosocleC2×C22⋊#3622C22
hypercenterC2×C22⋊C8#595
hypocenterC17#7059
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
94. C17#7059semidirect

Maximal subgroups

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

subgroupindex
#145437042
#145288532
#705917