Finite Group Databasebeta

← #17949304

Subgroups — #17949304

Order 4352.

150 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 34 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#14543900C211yesmaximal, characteristic, complemented
2#14543852C211yesmaximal, characteristic, complemented
3#14530888C211yesmaximal, characteristic
4#11763819—21no—
5#11763741—21no—
6C2×D272C411yescharacteristic, complemented
7C2×#10587469C2211yescharacteristic
8#11763046—21no—
9#11762609—21no—
10C17×#367C411yescharacteristic, complemented
11#10587677—41no—
12C2×D136—21no—
13C2×C8×D17D411yescharacteristic
14#10587581—41no—
15#10587534—41no—
16#10587533—22no—
17C2×C16×C17C2×C411yescharacteristic
18C17×#107—21no—
19C2×#63214D411yescharacteristic
20#10587480—41no—
21D272—41no—
22#10587469—41no—
23#10587467—41no—
24C2×D68—41no—
25C2×D68—81no—
26C2×C4×D17D811yescharacteristic
27C22⋊#595—81no—
28C4⋊#595—42no—
29C4×#595—81no—
30C2×C8×C17C22⋊C411yescharacteristic
31C4⋊C4×C17—41no—
32#63227—81no—
33C2×#3622SD1611yescharacteristic
34D136—41no—
35D136—41no—
36C8×D17—21no—
37C8×D17—21no—
38C16×C17—21no—
39#63214—21no—
40#7422—171nomaximal, Sylow
41C22×D17—81no—
42C22×D17D1611yescharacteristic
43C2×#595—82no—
44C2×C4×C17—81no—
45C2×C4×C17#10211yescharacteristic
46C2×Dic17SD3211yescharacteristic
47D68—81no—
48D68—81no—
49D68—162no—
50C4×D17—21no—
51C4×D17—21no—
52C8×C17#9911yescharacteristic
53C8×C17#10411yescharacteristic
54#3622—21no—
55#2218—171no—
56#1400—171no—
57#1384—171no—
58C22×C17#35711yescharacteristic
59C2×D17—21no—
60C2×D17—41no—
61C2×D17—161no—
62C2×D17—161no—
63C2×D17—161no—
64#595—162no—
65C4×C17—161no—
66C4×C17#32711yescharacteristic
67C4×C17#36011yescharacteristic
68Dic17—21no—
69C2×D16—171no—
70C2×M32—171no—
71#466—341no—
72#427—341no—
73M64—341no—
74#367#59511yescharacteristic, complemented
75#357—341no—
76C2×C17—21no—
77C2×C17#134711yescharacteristic
78D17—41no—
79D17—321no—
80C2×D8—341no—
81C22×C8—171no—
82#121—681no—
83#117—681no—
84D16—681no—
85M32—681no—
86C2×C16—171no—
87C2×C16C2×#59511yescharacteristic
88#107—21no—
89#107—681no—
90#106—342no—
91#102—681no—
92C32—681no—
93C17#742211yescharacteristic, complemented, Sylow
94C2×D4—681no—
95C2×D4—1361no—
96C22×C4—171no—
97D8—681no—
98D8—681no—
99C2×C8—171no—
100C2×C8—341no—
101C2×C8—341no—
102C2×C8C22⋊#59511yescharacteristic
103C4⋊C4—41no—
104C4⋊C4—682no—
105C22⋊C4—1361no—
106C22⋊C4—1361no—
107C42—1361no—
108C16—21no—
109C16—341no—
110C23—171no—
111C23—1361no—
112D4—2722no—
113D4—1361no—
114D4—1361no—
115C2×C4—81no—
116C2×C4—171no—
117C2×C4—341no—
118C2×C4—341no—
119C2×C4—1362no—
120C2×C4#1058754711yescharacteristic
121C8—341no—
122C8#1058753911yescharacteristic
123C8#1058755011yescharacteristic
124C22—2721no—
125C22—2721no—
126C22—2721no—
127C22—341no—
128C22—681no—
129C22#1176372111yescharacteristic
130C4—161no—
131C4—2722no—
132C4—341no—
133C4#1176366111yescharacteristic
134C4#1176372611yescharacteristic
135C2—21no—
136C2—5441no—
137C2—681no—
138C2#1454377111yescharacteristic
subgroupG/H
centerC2#14543771
commutatorC2×C16×C17C2×C4
FrattiniC2×C16C2×#595
FittingC17×#367C4
socleC2×C17#1347
prime radical#14530888C2
cosocleC2×#10587469C22
hypercenter#367#595
hypocenterC17#7422
LCSG ▷ C2×C16×C17 ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #367

Complements

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

NH ≅ G/Ntype
1. #14543900C2semidirect
2. #14543852C2semidirect
6. C2×D272C4semidirect
10. C17×#367C4semidirect
74. #367#595semidirect
93. C17#7422semidirect

Maximal subgroups

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

subgroupindex
#145439002
#145438522
#145308882
#742217