Finite Group Databasebeta

← #17953596

Subgroups — #17953596

Order 4352.

630 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 140 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#14544640C212yesmaximal
2#14543662C214yesmaximal, complemented
3C2×#11762678C211yesmaximal, characteristic
4C2×#10587544C2214yes—
5C2×C22⋊#3624—22no—
6#11763675—22no—
7C22×C4⋊Dic17C411yescharacteristic
8C22×#63225—22no—
9C22×C4×Dic17C2211yescharacteristic
10#11762678—22no—
11#11762678C412yes—
12#11762678C2212yes—
13C22×C4⋊C4×C17C411yescharacteristic
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17—21no—
17C23×Dic17D412yes—
18C22×#3624—24no—
19C2×C4⋊C4×C17—21no—
20C2×C4⋊C4×C17—42no—
21C2×C4⋊C4×C17C2×C412yes—
22C2×C4⋊Dic17—21no—
23C2×C4⋊Dic17—42no—
24C2×C4⋊Dic17C2×C412yes—
25C2×#63225—24no—
26C2×#63225—24no—
27C2×#63225—48no—
28C2×C4×Dic17—24no—
29C2×C4×Dic17C2×C411yescharacteristic
30C2×C4×Dic17D412yes—
31C2×C4×Dic17C2311yescharacteristic
32C22⋊#3624—44no—
33#10587544—28no—
34C24×C17C22⋊C411yescharacteristic
35C22×C4×C17—22no—
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—44no—
40C22×C4×C17—42no—
41C22×C4×C17C22⋊C411yescharacteristic
42C22×C4×C17C22×C411yescharacteristic
43C22×Dic17—24no—
44C22×Dic17—24no—
45C22×Dic17—22no—
46C22×Dic17—44no—
47C22×Dic17—42no—
48C22×Dic17C22⋊C412yes—
49C22×Dic17SD1614yes—
50C22×Dic17Q1614yes—
51C22×Dic17C2×D412yes—
52C2×#3624—44no—
53C2×#3624—44no—
54C2×#3624—44no—
55C4⋊C4×C17—42no—
56C4⋊C4×C17—42no—
57C4⋊Dic17—42no—
58C4⋊Dic17—42no—
59#63225—48no—
60#63225—48no—
61C4×Dic17—22no—
62C4×Dic17—24no—
63C4×Dic17#4114yes—
64#8725—171nomaximal, Sylow
65C23×C17—21no—
66C23×C17—21no—
67C23×C17—22no—
68C23×C17#10012yes—
69C23×C17#10314yes—
70C23×C17C2×C22⋊C411yescharacteristic
71C2×C4×C17—28no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—42no—
77C2×C4×C17—44no—
78C2×C4×C17—84no—
79C2×C4×C17#10112yes—
80C2×C4×C17#11712yes—
81C2×Dic17—22no—
82C2×Dic17—22no—
83C2×Dic17—28no—
84C2×Dic17—28no—
85C2×Dic17—42no—
86C2×Dic17—44no—
87C2×Dic17—84no—
88C2×Dic17#10314yes—
89C2×Dic17#12314yes—
90C2×Dic17C2×SD1612yes—
91C2×Dic17C2×Q1612yes—
92C2×Dic17AGL(1,ℤ/8)14yes—
93#3624—84no—
94C2×#384—171no—
95#1797—172no—
96#1296—174no—
97C22×C17—24no—
98C22×C17—22no—
99C22×C17—22no—
100C22×C17—24no—
101C22×C17#33314yes—
102C22×C17#38111yescharacteristic
103C22×C17C2×#10011yescharacteristic
104C22×C17C2×#10111yescharacteristic
105C22×C17C2×#10312yes—
106C22×C17#41812yes—
107C4×C17—22no—
108C4×C17—22no—
109C4×C17—82no—
110Dic17—24no—
111Dic17—82no—
112Dic17#48114yes—
113Dic17#48414yes—
114C22×C4⋊C4—171no—
115C22×C4⋊C4—342no—
116C22×C4⋊C4#59511yescharacteristic
117C22×C42—171no—
118C2×C4⋊C8—174no—
119C2×C22⋊C8—342no—
120#384—172no—
121#384—172no—
122#384—342no—
123#336—342no—
124C2×C17—24no—
125C2×C17C2×#33311yescharacteristic
126C2×C17#154912yes—
127C2×C17#155511yescharacteristic
128C2×C17#182111yescharacteristic
129C2×C17#182412yes—
130C23×C4—21no—
131C23×C4—172no—
132C23×C4—341no—
133C23×C4C2×#59511yescharacteristic
134C22×C8—344no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—42no—
137C2×C4⋊C4—172no—
138C2×C4⋊C4—344no—
139C2×C4⋊C4—344no—
140C2×C4⋊C4—341no—
141C2×C4⋊C4—682no—
142C2×C4⋊C4—688no—
143C2×C4⋊C4C2×#59512yes—
144C2×C42—171no—
145C2×C42—172no—
146C2×C42—171no—
147C2×C42—344no—
148C4⋊C8—348no—
149C22⋊C8—684no—
150C17#872511yescharacteristic, complemented, Sylow
151C24C22⋊#59511yescharacteristic
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—44no—
157C22×C4—42no—
158C22×C4—172no—
159C22×C4—172no—
160C22×C4—174no—
161C22×C4—174no—
162C22×C4—344no—
163C22×C4—344no—
164C22×C4—342no—
165C22×C4—684no—
166C22×C4—682no—
167C22×C4C22⋊#59511yescharacteristic
168C22×C4C22×#59511yescharacteristic
169C2×C8—684no—
170C2×C8—684no—
171C2×C8—684no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—682no—
175C4⋊C4—682no—
176C4⋊C4—688no—
177C4⋊C4—688no—
178C42—174no—
179C42—344no—
180C42—342no—
181C23—21no—
182C23—21no—
183C23—22no—
184C23#1058754914yes—
185C23#1058755312yes—
186C23C2×C22⋊#59511yescharacteristic
187C2×C4—28no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—84no—
195C2×C4—174no—
196C2×C4—172no—
197C2×C4—172no—
198C2×C4—174no—
199C2×C4—174no—
200C2×C4—348no—
201C2×C4—348no—
202C2×C4—342no—
203C2×C4—342no—
204C2×C4—682no—
205C2×C4—684no—
206C2×C4—1364no—
207C2×C4#1058754512yes—
208C2×C4#1058767712yes—
209C8—1364no—
210C22—22no—
211C22—24no—
212C22—24no—
213C22—22no—
214C22#1176366914yes—
215C22#1176375211yescharacteristic
216C22C2×#1058755311yescharacteristic
217C22C2×#1058754511yescharacteristic
218C22C2×#1058754912yes—
219C22#1176380112yes—
220C4—22no—
221C4—22no—
222C4—82no—
223C4—174no—
224C4—174no—
225C4—344no—
226C4—1362no—
227C2—24no—
228C2C2×#1176366911yescharacteristic
229C2#1454429912yes—
230C2#1454431111yescharacteristic
231C2#1454468311yescharacteristic
232C2#1454468812yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#8725
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14543662C2semidirect
150. C17#8725semidirect

Maximal subgroups

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

subgroupindex
#145446402
#145436622
C2×#117626782
#872517