Finite Group Databasebeta

← #17949317

Subgroups — #17949317

Order 4352.

226 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 36 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#14543878C211yesmaximal, characteristic
2#14543713C211yesmaximal, characteristic
3#14529927C211yesmaximal, characteristic
4C2×#10587539—21no—
5#11763654—21no—
6C2×#10587480—21no—
7#11762711C2211yescharacteristic
8#11762571—21no—
9#11762564C411yescharacteristic, complemented
10C2×C17×#125C411yescharacteristic, complemented
11C22×D68D411yescharacteristic
12C2×C22⋊#595—41no—
13C17×#125—42no—
14C2×C4⋊C4×C17—21no—
15C2×C4⋊C4×C17—41no—
16C2×C42×C17C2×C411yescharacteristic
17C2×#63227—41no—
18C2×C4⋊Dic17D411yescharacteristic
19C22×#3622—21no—
20C22⋊#3624—41no—
21#10587539—22no—
22#10587539—41no—
23#10587480—42no—
24C23×D17—21no—
25C22×#595—81no—
26C22×C4×C17—21no—
27C22×C4×C17—41no—
28C22×C4×C17C22⋊C411yescharacteristic
29C22×Dic17—21no—
30C2×D68—21no—
31C2×D68—41no—
32C2×D68—41no—
33C2×D68SD1611yescharacteristic
34C2×D68Q1611yescharacteristic
35C22⋊#595—42no—
36C22⋊#595—81no—
37C2×#3624—81no—
38C4⋊C4×C17—22no—
39C4⋊C4×C17—41no—
40C4⋊C4×C17—42no—
41C4⋊C4×C17—42no—
42C42×C17—41no—
43#63227—82no—
44C4⋊Dic17—41no—
45C2×#3622—41no—
46C2×#3622—41no—
47C2×#3622—41no—
48#7428—171nomaximal, Sylow
49C23×C17#9911yescharacteristic
50C22×D17—21no—
51C22×D17—21no—
52C22×D17—41no—
53C22×D17—41no—
54C22×D17—81no—
55C22×D17—81no—
56C2×#595—82no—
57C2×#595—161no—
58C2×#595—161no—
59C2×C4×C17—21no—
60C2×C4×C17—21no—
61C2×C4×C17—41no—
62C2×C4×C17—41no—
63C2×C4×C17—41no—
64C2×C4×C17—42no—
65C2×C4×C17—81no—
66C2×C4×C17—81no—
67C2×C4×C17#10311yescharacteristic
68C2×C4×C17#10411yescharacteristic
69C2×Dic17—41no—
70C2×Dic17—81no—
71D68—41no—
72D68—41no—
73D68—81no—
74#3624—161no—
75#3622—81no—
76#2025—171no—
77#1393—171no—
78#1318—171no—
79C22×C17—21no—
80C22×C17—21no—
81C22×C17#32811yescharacteristic
82C22×C17AΣL(1,𝔽16)11yescharacteristic
83C22×C17#35411yescharacteristic
84C2×D17—41no—
85C2×D17—41no—
86C2×D17—81no—
87C2×D17—81no—
88C2×D17—81no—
89C2×D17—81no—
90C2×D17—161no—
91#595—162no—
92C4×C17—21no—
93C4×C17—21no—
94C4×C17—81no—
95C4×C17—82no—
96Dic17—81no—
97C2×#125#59511yescharacteristic, complemented
98C2×#102—341no—
99C2×#99—341no—
100#390—171no—
101#340—341no—
102#336—171no—
103#324—341no—
104C2×C17—21no—
105C2×C17—21no—
106C2×C17#135111yescharacteristic
107C2×C17#141211yescharacteristic
108C2×C17#141411yescharacteristic
109D17—81no—
110D17—81no—
111C22×D4—171no—
112C22×C8—341no—
113#125—42no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—171no—
117C2×C22⋊C4—681no—
118C2×C22⋊C4—681no—
119C2×C42C2×#59511yescharacteristic
120#102—682no—
121#99—342no—
122#99—681no—
123C22⋊C8—681no—
124C17#742811yescharacteristic, complemented, Sylow
125C24—341no—
126C2×D4—171no—
127C2×D4—171no—
128C2×D4—341no—
129C2×D4—681no—
130C2×D4—681no—
131C22×C4—21no—
132C22×C4—41no—
133C22×C4—341no—
134C22×C4—1361no—
135C22×C4C22⋊#59511yescharacteristic
136C2×C8—681no—
137C2×C8—681no—
138C2×C8—681no—
139C2×C8—1361no—
140C4⋊C4—22no—
141C4⋊C4—41no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C4⋊C4—681no—
145C22⋊C4—682no—
146C22⋊C4—1362no—
147C22⋊C4—1361no—
148C42—41no—
149C23—341no—
150C23—341no—
151C23—681no—
152C23—681no—
153C23—1361no—
154C23—1361no—
155C23#1058755111yescharacteristic
156D4—681no—
157D4—681no—
158D4—1361no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—2721no—
168C2×C4—2721no—
169C2×C4—681no—
170C2×C4—1362no—
171C2×C4—1361no—
172C2×C4#1058754911yescharacteristic
173C2×C4#1058755011yescharacteristic
174C8—2721no—
175C8—1361no—
176C22—21no—
177C22—21no—
178C22—2721no—
179C22—681no—
180C22—681no—
181C22—1361no—
182C22—1361no—
183C22—1361no—
184C22—1361no—
185C22#1176366311yescharacteristic
186C22#1176370911yescharacteristic
187C22#1176371511yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—82no—
192C4—2722no—
193C4—1361no—
194C2—21no—
195C2—21no—
196C2—1361no—
197C2—1361no—
198C2#1454377911yescharacteristic
199C2#1454392311yescharacteristic
200C2#1454393011yescharacteristic
subgroupG/H
centerC22#11763715
commutatorC2×C42×C17C2×C4
FrattiniC2×C42C2×#595
FittingC2×C17×#125C4
socleC22×C17#354
prime radicalC22×D68D4
cosocle#11762711C22
hypercenterC2×#125#595
hypocenterC17#7428
LCSG ▷ C2×C42×C17 ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
9. #11762564C4semidirect
10. C2×C17×#125C4semidirect
97. C2×#125#595semidirect
124. C17#7428semidirect

Maximal subgroups

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

subgroupindex
#145438782
#145437132
#145299272
#742817