Finite Group Databasebeta

← #17962720

Subgroups — #17962720

Order 4352.

318 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 60 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#14543927C214yesmaximal, complemented
3#14539187C211yesmaximal, characteristic
4#11763795—22no—
5#11763720C2214yes—
6#11763718—22no—
7#11763359C2211yescharacteristic
8#11763179C2212yes—
9#11763175C412yes—
10#11763166—22no—
11#11762808—22no—
12C4×#63223C411yescharacteristic
13C2×C17×#125C411yescharacteristic
14C2×#63252D412yes—
15D17⋊M16—42no—
16C17×#125—21no—
17C17×#125—41no—
18C17×#125C2×C412yes—
19C2×C4⋊C4×C17—21no—
20C2×C4⋊C4×C17—41no—
21C2×C42×C17C2×C411yescharacteristic
22#10587616—41no—
23C2×#63223—21no—
24#10587561D412yes—
25#10587560C2×C411yescharacteristic
26C4×D68—41no—
27#10587555C2311yescharacteristic
28#10587553—42no—
29#10587545—24no—
30#10587481—24no—
31#10587480—24no—
32#10587474C2×C412yes—
33C4×#3622—21no—
34C22×C4×C17—21no—
35C22×C4×C17—41no—
36C22×C4×C17C22⋊C411yescharacteristic
37C2×C22⋊D17—22no—
38#63252—42no—
39#63252—42no—
40C2×D68—41no—
41C2×D68C22⋊C412yes—
42C2×C4×D17—22no—
43C2×Dic34C2×D412yes—
44#63247—44no—
45#63243—82no—
46#63242—82no—
47C4⋊C4×C17—22no—
48C4⋊C4×C17—42no—
49C4⋊C4×C17—42no—
50C4⋊C4×C17—41no—
51C42×C17—21no—
52C42×C17C22⋊C411yescharacteristic
53C42×C17C22×C411yescharacteristic
54#63227—42no—
55C4⋊Dic17—41no—
56#63223—42no—
57C2×#3622—22no—
58#13600—171nomaximal, Sylow
59C23×C17#9911yescharacteristic
60C22×D17—22no—
61C2×C4×C17—22no—
62C2×C4×C17—21no—
63C2×C4×C17—21no—
64C2×C4×C17—42no—
65C2×C4×C17—81no—
66C2×C4×C17—82no—
67C2×C4×C17#9911yescharacteristic
68C2×C4×C17C2×C22⋊C411yescharacteristic
69C22⋊D17—82no—
70C2×Dic17—22no—
71D68—42no—
72D68—82no—
73C4×D17—42no—
74C4×D17—42no—
75Dic34—42no—
76#3624—84no—
77#3622—42no—
78#3142—171no—
79#2132—172no—
80#1413—174no—
81C22×C17—21no—
82C22×C17—41no—
83C22×C17C2×#9911yescharacteristic
84C2×D17—42no—
85C2×D17—82no—
86C4×C17—21no—
87C4×C17—41no—
88C4×C17—41no—
89C4×C17—82no—
90C4×C17#35412yes—
91Dic17—42no—
92#532—171no—
93C2×#125#59511yescharacteristic
94#491—172no—
95#490—172no—
96#488—342no—
97#417—342no—
98#413—342no—
99C4×M16—171no—
100#356—174no—
101#355—342no—
102C2×C17—21no—
103C2×C17—41no—
104C2×C17C2×#35411yescharacteristic
105D17—82no—
106C2×#41—172no—
107C2×M16—341no—
108C2×M16—682no—
109C4⋊Q8—171no—
110#127—171no—
111#125—21no—
112#125—41no—
113#125C2×#59512yes—
114#124—172no—
115#121—681no—
116C4×D4—681no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—41no—
119C2×C42C2×#59511yescharacteristic
120#103—344no—
121#102—344no—
122#101—344no—
123#100—682no—
124#97—172no—
125C4×C8—341no—
126C17#1360011yescharacteristic, complemented, Sylow
127#41—682no—
128#41—682no—
129C2×Q8—172no—
130C2×D4—172no—
131C2×D4—342no—
132C2×D4—681no—
133C22×C4—21no—
134C22×C4—41no—
135C22×C4—342no—
136C22×C4C22⋊#59511yescharacteristic
137M16—682no—
138M16—684no—
139M16—1362no—
140C2×C8—342no—
141C2×C8—1362no—
142C4⋊C4—22no—
143C4⋊C4—42no—
144C4⋊C4—42no—
145C4⋊C4—41no—
146C4⋊C4—681no—
147C22⋊C4—682no—
148C42—21no—
149C42C22⋊#59511yescharacteristic
150C42C22×#59511yescharacteristic
151C23—342no—
152C23#1058755111yescharacteristic
153Q8—682no—
154D4—682no—
155D4—1362no—
156D4—1362no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—42no—
161C2×C4—81no—
162C2×C4—82no—
163C2×C4—342no—
164C2×C4—682no—
165C2×C4—682no—
166C2×C4#1058755111yescharacteristic
167C2×C4C2×C22⋊#59511yescharacteristic
168C8—682no—
169C8—1364no—
170C22—21no—
171C22—41no—
172C22—682no—
173C22—1362no—
174C22C2×#1058755111yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—682no—
180C4#1176371512yes—
181C2—21no—
182C2—41no—
183C2—1362no—
184C2C2×#1176371511yescharacteristic
subgroupG/H
centerC2C2×#11763715
commutatorC42×C17C22×C4
FrattiniC42C22×#595
FittingC2×C17×#125C4
socleC2×C17C2×#354
prime radical#11763359C22
cosocle#10587555C23
hypercenterC2×#125#595
hypocenterC17#13600
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #14543927C2semidirect
126. C17#13600semidirect

Maximal subgroups

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

subgroupindex
#145450772
#145439272
#145391872
#1360017