Finite Group Databasebeta

← #17949341

Subgroups — #17949341

Order 4352.

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

normal subgroups only

This group has 170 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#14543876C211yesmaximal, characteristic
2#14543707C211yesmaximal, characteristic
3#14530338C211yesmaximal, characteristic
4#11763795—21no—
5C22⋊#63216—21no—
6#11762858C411yescharacteristic
7#11762836—21no—
8#11762827—21no—
9#11762777C2211yescharacteristic
10C17×H(3,ℤ/4)C411yescharacteristic
11C2×#63252D411yescharacteristic
12D17⋊M16—41no—
13C2×M16×C17C2×C411yescharacteristic
14C17×#117—21no—
15C2×#63223—21no—
16C22×#3622D411yescharacteristic
17#10587553—22no—
18#10587545—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×D68Q1611yescharacteristic
29C2×C4×D17—21no—
30C2×Dic34SD1611yescharacteristic
31#63247—42no—
32#63243—81no—
33#63242—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#7439—171nomaximal, Sylow
46C23×C17#10411yescharacteristic
47C22×D17—21no—
48C2×C4×C17—21no—
49C2×C4×C17—21no—
50C2×C4×C17—42no—
51C2×C4×C17#9911yescharacteristic
52C2×C4×C17#10311yescharacteristic
53C22⋊D17—81no—
54C2×Dic17—21no—
55D68—41no—
56C4×D17—41no—
57C4×D17—41no—
58Dic34—41no—
59#3624—82no—
60C8×C17—41no—
61#3622—41no—
62#3622—81no—
63#2098—171no—
64#1392—171no—
65#1315—171no—
66C22×C17—21no—
67C22×C17—41no—
68C22×C17#32811yescharacteristic
69C2×D17—41no—
70C2×D17—81no—
71C4×C17—21no—
72C4×C17—82no—
73C4×C17#35211yescharacteristic
74C4×C17#35311yescharacteristic
75Dic17—41no—
76#430—171no—
77#424—341no—
78#421—341no—
79#413—341no—
80#408—171no—
81C22⋊C16—341no—
82H(3,ℤ/4)#59511yescharacteristic
83C2×C17—21no—
84C2×C17—41no—
85C2×C17#135211yescharacteristic
86D17—81no—
87C2×#41—171no—
88C2×M16—341no—
89C2×M16—681no—
90C2×M16C2×#59511yescharacteristic
91C22×C8—171no—
92#117—21no—
93C2×C16—681no—
94#108—681no—
95C4⋊C8—682no—
96#104—682no—
97#101—681no—
98#100—342no—
99C22⋊C8—681no—
100C17#743911yescharacteristic, complemented, Sylow
101#41—681no—
102#41—681no—
103C2×Q8—171no—
104C2×D4—171no—
105C2×D4—341no—
106C22×C4—341no—
107C22×C4C22⋊#59511yescharacteristic
108M16—41no—
109M16—681no—
110M16—682no—
111M16—681no—
112M16—1361no—
113C2×C8—21no—
114C2×C8—341no—
115C2×C8—681no—
116C2×C8—681no—
117C2×C8—1361no—
118C4⋊C4—41no—
119C22⋊C4—41no—
120C42—22no—
121C16—1361no—
122C23—341no—
123C23#1058754811yescharacteristic
124Q8—681no—
125D4—681no—
126D4—1361no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—42no—
130C2×C4—341no—
131C2×C4—681no—
132C2×C4—681no—
133C2×C4#1058753911yescharacteristic
134C2×C4#1058754911yescharacteristic
135C8—41no—
136C8—681no—
137C8—1362no—
138C8—1361no—
139C22—21no—
140C22—41no—
141C22—681no—
142C22—1361no—
143C22#1176366211yescharacteristic
144C4—21no—
145C4—82no—
146C4—681no—
147C4#1176371211yescharacteristic
148C4#1176371411yescharacteristic
149C2—21no—
150C2—41no—
151C2—1361no—
152C2#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#7439
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
100. C17#7439semidirect

Maximal subgroups

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

subgroupindex
#145438762
#145437072
#145303382
#743917