Finite Group Databasebeta

← #17949535

Subgroups — #17949535

Order 4352.

266 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 46 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#14545077C212yesmaximal
2#14529615C211yesmaximal, characteristic
3#11763795—22no—
4#11763720—22no—
5#11763718C414yescomplemented
6#11763359C2211yescharacteristic
7C2×#10587496—22no—
8#11762655C411yescharacteristic
9C17×#423C411yescharacteristic
10C2×#63252D412yes—
11D17⋊M16—42no—
12C2×M16×C17—21no—
13C2×C42×C17C2×C411yescharacteristic
14#10587616—41no—
15C2×C4×Dic17—21no—
16#10587561C2×C412yes—
17#10587560Q811yescharacteristic
18C4×D68—41no—
19#10587555D411yescharacteristic
20#10587553—42no—
21#10587545—24no—
22C17×C4⋊C8—41no—
23#10587502—41no—
24#10587496—44no—
25C22×C4×C17—21no—
26C22×C4×C17C22⋊C411yescharacteristic
27C2×C22⋊D17—22no—
28C22×Dic17—41no—
29#63252—42no—
30#63252—42no—
31C2×D68—41no—
32C2×D68C4⋊C412yes—
33C2×C4×D17—22no—
34C2×Dic34C22⋊C412yes—
35#63247—44no—
36#63243—82no—
37#63242—82no—
38M16×C17—42no—
39C2×C8×C17—41no—
40C42×C17—21no—
41C42×C17C4211yescharacteristic
42C42×C17C4⋊C411yescharacteristic
43#63227—42no—
44C4⋊Dic17—41no—
45C4×Dic17—22no—
46C4×Dic17—41no—
47#7507—171nomaximal, Sylow
48C23×C17#9911yescharacteristic
49C22×D17—22no—
50C2×C4×C17—21no—
51C2×C4×C17—21no—
52C2×C4×C17—21no—
53C2×C4×C17—21no—
54C2×C4×C17—81no—
55C2×C4×C17#9511yescharacteristic
56C2×C4×C17#9911yescharacteristic
57C22⋊D17—82no—
58C2×Dic17—22no—
59C2×Dic17—42no—
60C2×Dic17—82no—
61D68—42no—
62D68—82no—
63C4×D17—42no—
64C4×D17—42no—
65Dic34—42no—
66#3624—84no—
67C8×C17—81no—
68#2132—172no—
69#1963—171no—
70C22×C17—21no—
71C22×C17—41no—
72C22×C17#34211yescharacteristic
73C2×D17—42no—
74C2×D17—82no—
75C4×C17—21no—
76C4×C17—41no—
77C4×C17—41no—
78C4×C17#35311yescharacteristic
79C4×C17#35411yescharacteristic
80Dic17—42no—
81Dic17—82no—
82#532—171no—
83#423#59511yescharacteristic
84C2×#104—342no—
85#413—342no—
86#376—171no—
87#356—342no—
88#355—174no—
89C2×C17—21no—
90C2×C17—41no—
91C2×C17#139311yescharacteristic
92D17—82no—
93C2×#41—172no—
94C2×M16—21no—
95C2×M16—682no—
96C4⋊Q8—171no—
97#127—171no—
98#124—172no—
99#121—681no—
100C4×D4—681no—
101C2×C42—341no—
102C2×C42C2×#59511yescharacteristic
103C4⋊C8—41no—
104#104—684no—
105#101—344no—
106#100—682no—
107#95—681no—
108C17#750711yescharacteristic, complemented, Sylow
109#41—682no—
110#41—682no—
111C2×Q8—172no—
112C2×D4—172no—
113C2×D4—342no—
114C2×D4—681no—
115C22×C4—21no—
116C22×C4—342no—
117C22×C4—681no—
118C22×C4C22⋊#59511yescharacteristic
119M16—42no—
120M16—684no—
121M16—1362no—
122C2×C8—41no—
123C2×C8—1362no—
124C4⋊C4—681no—
125C22⋊C4—682no—
126C42—21no—
127C42—342no—
128C42—681no—
129C42C4×#59511yescharacteristic
130C42C4⋊#59511yescharacteristic
131C23—342no—
132C23#1058753911yescharacteristic
133Q8—682no—
134D4—682no—
135D4—1362no—
136D4—1362no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—81no—
142C2×C4—342no—
143C2×C4—682no—
144C2×C4—682no—
145C2×C4—682no—
146C2×C4—1362no—
147C2×C4(C2×#595)⋊C411yescharacteristic
148C2×C4#1058755111yescharacteristic
149C8—81no—
150C8—1364no—
151C22—21no—
152C22—41no—
153C22—682no—
154C22—1362no—
155C22#1176368711yescharacteristic
156C4—21no—
157C4—41no—
158C4—41no—
159C4—682no—
160C4—1362no—
161C4#1176371311yescharacteristic
162C4#1176371511yescharacteristic
163C2—21no—
164C2—41no—
165C2—1362no—
166C2#1454387911yescharacteristic
subgroupG/H
centerC4#11763713
commutatorC42×C17C42
FrattiniC2×C42C2×#595
FittingC17×#423C4
socleC2×C17#1393
prime radical, cosocle#11763359C22
hypercenter#423#595
hypocenterC17#7507
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
5. #11763718C4semidirect
108. C17#7507semidirect

Maximal subgroups

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

subgroupindex
#145450772
#145296152
#750717