Finite Group Databasebeta

← #17949274

Subgroups — #17949274

Order 4352.

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

normal subgroups only

This group has 166 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#14543872C211yesmaximal, characteristic
2#14543719C211yesmaximal, characteristic
3#14530231C211yesmaximal, characteristic
4#11763788—21no—
5#11763705—21no—
6C2×#10587488C411yescharacteristic, complemented
7#11762811—21no—
8#11762775C2211yescharacteristic
9#11762577—21no—
10C17×#341C411yescharacteristic, complemented
11C2×#63252D411yescharacteristic
12#10587677—41no—
13C2×M16×C17—21no—
14C22×C8×C17C2×C411yescharacteristic
15C2×C4⋊Dic17—21no—
16C2×#63223D411yescharacteristic
17#10587551—22no—
18#10587539—41no—
19#10587538—41no—
20#10587492—41no—
21#10587491—41no—
22#10587488—41no—
23#10587487—41no—
24C22×C4×C17C22⋊C411yescharacteristic
25C2×C22⋊D17—21no—
26C22×Dic17—41no—
27#63252—41no—
28#63252—41no—
29C2×D68D811yescharacteristic
30C2×C4×D17—21no—
31C2×Dic34SD1611yescharacteristic
32C22⋊#595—42no—
33C4⋊#595—81no—
34C4×#595—81no—
35M16×C17—41no—
36M16×C17—41no—
37C2×C8×C17—21no—
38C2×C8×C17—41no—
39C2×C8×C17—41no—
40C4⋊Dic17—41no—
41C4⋊Dic17—41no—
42#63223—41no—
43C2×#3622—21no—
44#63216—81no—
45#7410—171nomaximal, Sylow
46C23×C17#10411yescharacteristic
47C22×D17—21no—
48C2×#595—82no—
49C2×C4×C17—21no—
50C2×C4×C17—21no—
51C2×C4×C17#9911yescharacteristic
52C2×C4×C17#10211yescharacteristic
53C22⋊D17—81no—
54C2×Dic17—21no—
55C2×Dic17—81no—
56C2×Dic17—161no—
57D68—41no—
58C4×D17—41no—
59C4×D17—41no—
60Dic34—41no—
61C8×C17—41no—
62C8×C17—81no—
63#3622—41no—
64#2079—171no—
65#1391—171no—
66#1321—171no—
67C22×C17—21no—
68C22×C17—41no—
69C22×C17#32711yescharacteristic
70C2×D17—41no—
71C2×D17—81no—
72#595—162no—
73C4×C17—21no—
74C4×C17#35211yescharacteristic
75C4×C17#35411yescharacteristic
76Dic17—41no—
77Dic17—161no—
78C2×#106—171no—
79#417—341no—
80#410—341no—
81#408—171no—
82#349—341no—
83#343—341no—
84#341#59511yescharacteristic, complemented
85C2×C17—21no—
86C2×C17—41no—
87C2×C17#134411yescharacteristic
88D17—81no—
89C2×#41—171no—
90C2×M16—21no—
91C2×M16—171no—
92C22×C8C2×#59511yescharacteristic
93#117—681no—
94C2×C4⋊C4—341no—
95M32—681no—
96#106—681no—
97#103—681no—
98#102—681no—
99#99—342no—
100#99—681no—
101C22⋊C8—681no—
102C17#741011yescharacteristic, complemented, Sylow
103#41—681no—
104#41—681no—
105C2×Q8—171no—
106C2×D4—171no—
107C2×D4—341no—
108C22×C4—341no—
109C22×C4—681no—
110C22×C4C22⋊#59511yescharacteristic
111M16—41no—
112M16—41no—
113M16—681no—
114C2×C8—21no—
115C2×C8—41no—
116C2×C8—41no—
117C2×C8—341no—
118C4⋊C4—681no—
119C4⋊C4—681no—
120C4⋊C4—1361no—
121C22⋊C4—682no—
122C42—1361no—
123C16—1361no—
124C23—341no—
125C23#1058755011yescharacteristic
126Q8—681no—
127D4—681no—
128D4—1361no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—2721no—
132C2×C4—341no—
133C2×C4—681no—
134C2×C4—681no—
135C2×C4—1362no—
136C2×C4—1361no—
137C2×C4#1058753911yescharacteristic
138C2×C4#1058754711yescharacteristic
139C8—41no—
140C8—81no—
141C8—681no—
142C22—21no—
143C22—41no—
144C22—681no—
145C22—1361no—
146C22#1176366111yescharacteristic
147C4—21no—
148C4—2721no—
149C4—2722no—
150C4—681no—
151C4#1176371211yescharacteristic
152C4#1176371611yescharacteristic
153C2—21no—
154C2—41no—
155C2—1361no—
156C2#1454376511yescharacteristic
subgroupG/H
centerC2#14543765
commutatorC22×C8×C17C2×C4
FrattiniC22×C8C2×#595
FittingC17×#341C4
socleC2×C17#1344
prime radicalC2×#63252D4
cosocle#11762775C22
hypercenter#341#595
hypocenterC17#7410
LCSG ▷ C22×C8×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #341

Complements

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

NH ≅ G/Ntype
6. C2×#10587488C4semidirect
10. C17×#341C4semidirect
84. #341#595semidirect
102. C17#7410semidirect

Maximal subgroups

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

subgroupindex
#145438722
#145437192
#145302312
#741017