Finite Group Databasebeta

← #17949511

Subgroups — #17949511

Order 4352.

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

normal subgroups only

This group has 294 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#14545057C212yesmaximal
2#14529612C211yesmaximal, characteristic
3#11763788—22no—
4#11763716C414yescomplemented
5#11763714—22no—
6#11763359C2211yescharacteristic
7#11762833C411yescharacteristic, complemented
8C2×#10587476—22no—
9C43×C17C411yescharacteristic, complemented
10C2×#63252D412yes—
11#10587677—42no—
12C2×C42×C17—21no—
13C2×C42×C17—41no—
14C2×C42×C17C2×C411yescharacteristic
15#10587616—41no—
16C2×#63223—21no—
17#10587561C2×C412yes—
18#10587560D411yescharacteristic
19C4×D68—41no—
20#10587555Q811yescharacteristic
21#10587551—42no—
22#10587539—24no—
23#10587476—44no—
24C4⋊#3622—41no—
25C22×C4×C17—21no—
26C22×C4×C17—41no—
27C22×C4×C17C22⋊C411yescharacteristic
28C2×C22⋊D17—22no—
29#63252—42no—
30#63252—42no—
31C2×D68—41no—
32C2×D68C22⋊C412yes—
33C2×C4×D17—22no—
34C2×Dic34C4⋊C412yes—
35C22⋊#595—44no—
36C4⋊#595—82no—
37C4×#595—82no—
38C42×C17—21no—
39C42×C17—22no—
40C42×C17—41no—
41C42×C17—44no—
42C42×C17C4211yescharacteristic
43C42×C17C4⋊C411yescharacteristic
44#63227—42no—
45C4⋊Dic17—41no—
46#63223—42no—
47C2×#3622—41no—
48#7500—171nomaximal, Sylow
49C23×C17#9911yescharacteristic
50C22×D17—22no—
51C2×#595—84no—
52C2×C4×C17—21no—
53C2×C4×C17—21no—
54C2×C4×C17—21no—
55C2×C4×C17—21no—
56C2×C4×C17—42no—
57C2×C4×C17—42no—
58C2×C4×C17—44no—
59C2×C4×C17#9511yescharacteristic
60C2×C4×C17#9911yescharacteristic
61C22⋊D17—82no—
62C2×Dic17—22no—
63D68—42no—
64D68—82no—
65C4×D17—42no—
66C4×D17—42no—
67Dic34—42no—
68#3622—81no—
69#2126—172no—
70#1962—171no—
71C22×C17—21no—
72C22×C17—41no—
73C22×C17#34211yescharacteristic
74C2×D17—42no—
75C2×D17—82no—
76#595—164no—
77C4×C17—22no—
78C4×C17—21no—
79C4×C17—41no—
80C4×C17—44no—
81C4×C17#35311yescharacteristic
82C4×C17#35411yescharacteristic
83Dic17—42no—
84#532—171no—
85#423—171no—
86C2×#104—342no—
87#410—342no—
88C43#59511yescharacteristic, complemented
89#354—174no—
90#353—342no—
91C2×C17—21no—
92C2×C17—41no—
93C2×C17#139311yescharacteristic
94D17—82no—
95C2×#41—172no—
96C2×M16—341no—
97C4⋊Q8—171no—
98#127—171no—
99#124—172no—
100#121—681no—
101C4×D4—681no—
102#117—682no—
103C2×C42—21no—
104C2×C42—41no—
105C2×C42C2×#59511yescharacteristic
106C4⋊C8—681no—
107#104—684no—
108#99—344no—
109#99—682no—
110C17#750011yescharacteristic, complemented, Sylow
111#41—682no—
112#41—682no—
113C2×Q8—172no—
114C2×D4—172no—
115C2×D4—342no—
116C2×D4—681no—
117C22×C4—21no—
118C22×C4—41no—
119C22×C4—342no—
120C22×C4C22⋊#59511yescharacteristic
121M16—682no—
122C2×C8—681no—
123C4⋊C4—681no—
124C4⋊C4—1362no—
125C22⋊C4—682no—
126C22⋊C4—684no—
127C42—21no—
128C42—22no—
129C42—41no—
130C42—44no—
131C42—1362no—
132C42C4×#59511yescharacteristic
133C42C4⋊#59511yescharacteristic
134C23—342no—
135C23#1058755111yescharacteristic
136Q8—682no—
137D4—682no—
138D4—1362no—
139D4—1362no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—44no—
147C2×C4—342no—
148C2×C4—682no—
149C2×C4—682no—
150C2×C4—1364no—
151C2×C4#1058753911yescharacteristic
152C2×C4(C2×#595)⋊C411yescharacteristic
153C8—1361no—
154C22—21no—
155C22—41no—
156C22—682no—
157C22—1362no—
158C22#1176368711yescharacteristic
159C4—22no—
160C4—21no—
161C4—41no—
162C4—44no—
163C4—2724no—
164C4—682no—
165C4#1176371411yescharacteristic
166C4#1176371611yescharacteristic
167C2—21no—
168C2—41no—
169C2—1362no—
170C2#1454387811yescharacteristic
subgroupG/H
centerC4#11763716
commutatorC42×C17C42
FrattiniC2×C42C2×#595
FittingC43×C17C4
socleC2×C17#1393
prime radical, cosocle#11763359C22
hypercenterC43#595
hypocenterC17#7500
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
4. #11763716C4semidirect
7. #11762833C4semidirect
9. C43×C17C4semidirect
88. C43#595semidirect
110. C17#7500semidirect

Maximal subgroups

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

subgroupindex
#145450572
#145296122
#750017