Finite Group Databasebeta

← #17949339

Subgroups — #17949339

Order 4352.

174 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 32 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#14543873C211yesmaximal, characteristic
2#14543707C211yesmaximal, characteristic
3#14530338C211yesmaximal, characteristic
4#11763788—21no—
5C22⋊#63216—21no—
6#11762858C411yescharacteristic, complemented
7#11762836—21no—
8#11762827—21no—
9#11762777C2211yescharacteristic
10C17×H(3,ℤ/4)C411yescharacteristic, complemented
11C2×#63252D411yescharacteristic
12#10587677—41no—
13C2×M16×C17C2×C411yescharacteristic
14C17×#117—21no—
15C2×#63223—21no—
16C22×#3622D411yescharacteristic
17#10587551—22no—
18#10587539—41no—
19C2×#63216—41no—
20#10587491—41no—
21#10587490—41no—
22#10587476—42no—
23C4⋊#3622—42no—
24C22×C4×C17C22⋊C411yescharacteristic
25C2×C22⋊D17—21no—
26#63252—41no—
27#63252—41no—
28C2×D68SD1611yescharacteristic
29C2×C4×D17—21no—
30C2×Dic34Q1611yescharacteristic
31C22⋊#595—42no—
32C4⋊#595—81no—
33C4×#595—81no—
34M16×C17—41no—
35C2×C8×C17—21no—
36C4⋊C4×C17—41no—
37C22⋊C4×C17—41no—
38C42×C17—22no—
39#63223—41no—
40#63223—41no—
41C2×#3622—21no—
42C2×#3622—41no—
43C2×#3622—41no—
44#63216—81no—
45#7438—171nomaximal, Sylow
46C23×C17#10411yescharacteristic
47C22×D17—21no—
48C2×#595—82no—
49C2×C4×C17—21no—
50C2×C4×C17—21no—
51C2×C4×C17—42no—
52C2×C4×C17#9911yescharacteristic
53C2×C4×C17#10311yescharacteristic
54C22⋊D17—81no—
55C2×Dic17—21no—
56D68—41no—
57C4×D17—41no—
58C4×D17—41no—
59Dic34—41no—
60C8×C17—41no—
61#3622—41no—
62#3622—81no—
63#2098—171no—
64#1391—171no—
65#1315—171no—
66C22×C17—21no—
67C22×C17—41no—
68C22×C17#32811yescharacteristic
69C2×D17—41no—
70C2×D17—81no—
71#595—162no—
72C4×C17—21no—
73C4×C17—82no—
74C4×C17#35211yescharacteristic
75C4×C17#35311yescharacteristic
76Dic17—41no—
77#430—171no—
78#424—341no—
79#421—341no—
80#410—341no—
81#408—171no—
82C22⋊C16—341no—
83H(3,ℤ/4)#59511yescharacteristic, complemented
84C2×C17—21no—
85C2×C17—41no—
86C2×C17#135211yescharacteristic
87D17—81no—
88C2×#41—171no—
89C2×M16—341no—
90C2×M16C2×#59511yescharacteristic
91C22×C8—171no—
92#117—21no—
93#117—681no—
94C2×C16—681no—
95#108—681no—
96C4⋊C8—682no—
97#104—682no—
98#99—342no—
99#99—681no—
100C22⋊C8—681no—
101C17#743811yescharacteristic, complemented, Sylow
102#41—681no—
103#41—681no—
104C2×Q8—171no—
105C2×D4—171no—
106C2×D4—341no—
107C22×C4—341no—
108C22×C4C22⋊#59511yescharacteristic
109M16—41no—
110M16—681no—
111M16—681no—
112C2×C8—21no—
113C2×C8—341no—
114C2×C8—681no—
115C2×C8—681no—
116C4⋊C4—41no—
117C4⋊C4—1361no—
118C22⋊C4—41no—
119C22⋊C4—682no—
120C42—22no—
121C42—1361no—
122C16—1361no—
123C23—341no—
124C23#1058754811yescharacteristic
125Q8—681no—
126D4—681no—
127D4—1361no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—42no—
131C2×C4—341no—
132C2×C4—681no—
133C2×C4—681no—
134C2×C4—1362no—
135C2×C4#1058753911yescharacteristic
136C2×C4#1058754911yescharacteristic
137C8—41no—
138C8—681no—
139C8—1361no—
140C22—21no—
141C22—41no—
142C22—681no—
143C22—1361no—
144C22#1176366211yescharacteristic
145C4—21no—
146C4—82no—
147C4—2722no—
148C4—681no—
149C4#1176371211yescharacteristic
150C4#1176371411yescharacteristic
151C2—21no—
152C2—41no—
153C2—1361no—
154C2#1454378011yescharacteristic
subgroupG/H
centerC4#11763714
commutatorC2×M16×C17C2×C4
FrattiniC2×M16C2×#595
FittingC17×H(3,ℤ/4)C4
socleC2×C17#1352
prime radicalC2×#63252D4
cosocle#11762777C22
hypercenterH(3,ℤ/4)#595
hypocenterC17#7438
LCSG ▷ C2×M16×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
6. #11762858C4semidirect
10. C17×H(3,ℤ/4)C4semidirect
83. H(3,ℤ/4)#595semidirect
101. C17#7438semidirect

Maximal subgroups

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

subgroupindex
#145438732
#145437072
#145303382
#743817