Finite Group Databasebeta

← #17953532

Subgroups — #17953532

Order 4352.

530 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 108 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#14544674C212yesmaximal
2#14543622C214yesmaximal
3C2×#11762673C211yesmaximal, characteristic
4C2×C22⋊#3624C2214yes—
5#11763675—22no—
6#11763675—22no—
7C22×#63225C412yes—
8C22×C4×Dic17C2211yescharacteristic
9#11762673—22no—
10#11762673—22no—
11C2×#10587502C411yescharacteristic
12C2×#10587502C2212yes—
13C2×C17×#95C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×C4×C17C2×C412yes—
16C23×Dic17C2×C411yescharacteristic
17C23×Dic17C2×C412yes—
18C23×Dic17C2311yescharacteristic
19C22×#3624—24no—
20C2×#63225—22no—
21C2×#63225—22no—
22C2×#63225—44no—
23C2×C4×Dic17—24no—
24C2×C4×Dic17D412yes—
25C2×C4×Dic17D412yes—
26C22⋊#3624—28no—
27C17×#95—22no—
28#10587502—22no—
29#10587502—24no—
30C24×C17C22×C411yescharacteristic
31C22×C4×C17—22no—
32C22×C4×C17—24no—
33C22×C4×C17—22no—
34C22×C4×C17—24no—
35C22×C4×C17—42no—
36C22×C4×C17—42no—
37C22×C4×C17C22⋊C412yes—
38C22×Dic17—22no—
39C22×Dic17—22no—
40C22×Dic17—22no—
41C22×Dic17—22no—
42C22×Dic17—24no—
43C22×Dic17—42no—
44C22×Dic17—42no—
45C22×Dic17—42no—
46C22×Dic17C22⋊C411yescharacteristic
47C22×Dic17C22⋊C411yescharacteristic
48C22×Dic17C2×D412yes—
49C22×Dic17#4114yes—
50C2×#3624—48no—
51C2×#3624—44no—
52#63225—44no—
53#63225—44no—
54C4×Dic17—24no—
55C4×Dic17—24no—
56#8703—171nomaximal, Sylow
57C23×C17—22no—
58C23×C17—21no—
59C23×C17—21no—
60C23×C17C2×C22⋊C411yescharacteristic
61C23×C17#11712yes—
62C23×C17#13114yes—
63C2×C4×C17—22no—
64C2×C4×C17—24no—
65C2×C4×C17—44no—
66C2×C4×C17—42no—
67C2×C4×C17—42no—
68C2×C4×C17—42no—
69C2×C4×C17—84no—
70C2×Dic17—28no—
71C2×Dic17—21no—
72C2×Dic17—21no—
73C2×Dic17—24no—
74C2×Dic17—21no—
75C2×Dic17—21no—
76C2×Dic17—44no—
77C2×Dic17—42no—
78C2×Dic17—42no—
79C2×Dic17—42no—
80C2×Dic17—84no—
81C2×Dic17#10012yes—
82C2×Dic17#10112yes—
83C2×Dic17#12314yes—
84#3624—84no—
85C2×#382—171no—
86#1817—172no—
87#1280—174no—
88C22×C17—22no—
89C22×C17—22no—
90C22×C17—24no—
91C22×C17—24no—
92C22×C17#38111yescharacteristic
93C22×C17#40812yes—
94C22×C17#41012yes—
95C22×C17C2×#10011yescharacteristic
96C22×C17C2×#10111yescharacteristic
97C22×C17#43314yes—
98C4×C17—42no—
99C4×C17—82no—
100Dic17—24no—
101Dic17—22no—
102Dic17—22no—
103Dic17—82no—
104C22×C4⋊C4—172no—
105C22×C42—171no—
106C2×C22⋊C8—174no—
107#382—342no—
108#382—342no—
109C2×#95—172no—
110C2×#95—171no—
111C2×#95#59511yescharacteristic
112#336—342no—
113#336—342no—
114C2×C17—24no—
115C2×C17#146912yes—
116C2×C17#147012yes—
117C2×C17#181811yescharacteristic
118C2×C17#182011yescharacteristic
119C2×C17#182111yescharacteristic
120C23×C4—171no—
121C23×C4—171no—
122C23×C4—172no—
123C23×C4C2×#59512yes—
124C23×C4C2×#59511yescharacteristic
125C22×C8—344no—
126C2×C4⋊C4—342no—
127C2×C4⋊C4—342no—
128C2×C4⋊C4—684no—
129C2×C42—172no—
130C2×C42—172no—
131C2×C42—344no—
132C22⋊C8—348no—
133#95—22no—
134#95—344no—
135#95—342no—
136C17#870311yescharacteristic, complemented, Sylow
137C24C22×#59511yescharacteristic
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—22no—
141C22×C4—24no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—171no—
145C22×C4—171no—
146C22×C4—172no—
147C22×C4—174no—
148C22×C4—342no—
149C22×C4—342no—
150C22×C4—342no—
151C22×C4—342no—
152C22×C4—344no—
153C22×C4—682no—
154C22×C4—682no—
155C22×C4—682no—
156C22×C4C22⋊#59512yes—
157C2×C8—684no—
158C2×C8—688no—
159C4⋊C4—684no—
160C4⋊C4—684no—
161C42—344no—
162C42—344no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23#1058767712yes—
167C23#1058767814yes—
168C23C2×C22⋊#59511yescharacteristic
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—84no—
176C2×C4—174no—
177C2×C4—172no—
178C2×C4—172no—
179C2×C4—348no—
180C2×C4—341no—
181C2×C4—341no—
182C2×C4—344no—
183C2×C4—341no—
184C2×C4—341no—
185C2×C4—684no—
186C2×C4—682no—
187C2×C4—682no—
188C2×C4—682no—
189C2×C4—1364no—
190C8—1364no—
191C22—22no—
192C22—22no—
193C22—24no—
194C22—24no—
195C22#1176375211yescharacteristic
196C22#1176378212yes—
197C22#1176378812yes—
198C22D17⋊#10011yescharacteristic
199C22D17⋊#10111yescharacteristic
200C22#1176383314yes—
201C4—42no—
202C4—82no—
203C4—344no—
204C4—342no—
205C4—342no—
206C4—1362no—
207C2—24no—
208C2#1454405312yes—
209C2#1454405612yes—
210C2#1454467711yescharacteristic
211C2#1454468111yescharacteristic
212C2#1454468411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC2×C17×#95C4
socleC23×C17C2×C22⋊C4
cosocleC23×Dic17C23
hypercenterC2×#95#595
hypocenterC17#8703
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
136. C17#8703semidirect

Maximal subgroups

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

subgroupindex
#145446742
#145436222
C2×#117626732
#870317