Finite Group Databasebeta

← #17953578

Subgroups — #17953578

Order 4352.

554 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 112 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#14544510C212yesmaximal
2#14543660C214yesmaximal, complemented
3C2×#11762674C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5C2×#10587542C2214yes—
6#11763675—22no—
7C22×C4⋊Dic17C411yescharacteristic
8C22×C4×Dic17C2211yescharacteristic
9#11762674—22no—
10#11762674C412yes—
11#11762674C2212yes—
12C2×#10587502—22no—
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×C4×Dic17—24no—
26C2×C4×Dic17C2×C411yescharacteristic
27C2×C4×Dic17D412yes—
28C2×C4×Dic17C2311yescharacteristic
29C22⋊#3624—28no—
30#10587542—28no—
31#10587502—24no—
32#10587502—24no—
33C24×C17C22⋊C411yescharacteristic
34C22×C4×C17—22no—
35C22×C4×C17—22no—
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—42no—
39C22×C4×C17—44no—
40C22×C4×C17C22⋊C411yescharacteristic
41C22×C4×C17C22×C411yescharacteristic
42C22×Dic17—24no—
43C22×Dic17—24no—
44C22×Dic17—22no—
45C22×Dic17—42no—
46C22×Dic17—44no—
47C22×Dic17—42no—
48C22×Dic17C22⋊C412yes—
49C22×Dic17C2×D412yes—
50C2×#3624—28no—
51C2×#3624—44no—
52C2×#3624—44no—
53C4⋊C4×C17—42no—
54C4⋊C4×C17—42no—
55C4⋊Dic17—42no—
56C4⋊Dic17—42no—
57C4×Dic17—22no—
58C4×Dic17—24no—
59C4×Dic17#4114yes—
60#8718—171nomaximal, Sylow
61C23×C17—21no—
62C23×C17—21no—
63C23×C17—22no—
64C23×C17#10012yes—
65C23×C17#10414yes—
66C23×C17C2×C22⋊C411yescharacteristic
67C2×C4×C17—28no—
68C2×C4×C17—21no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—42no—
73C2×C4×C17—44no—
74C2×C4×C17—84no—
75C2×C4×C17#10112yes—
76C2×C4×C17#11712yes—
77C2×Dic17—22no—
78C2×Dic17—22no—
79C2×Dic17—22no—
80C2×Dic17—22no—
81C2×Dic17—22no—
82C2×Dic17—48no—
83C2×Dic17—42no—
84C2×Dic17—44no—
85C2×Dic17—84no—
86C2×Dic17#12314yes—
87#3624—48no—
88C2×#382—171no—
89#1749—172no—
90#1295—174no—
91C22×C17—22no—
92C22×C17—24no—
93C22×C17—24no—
94C22×C17—22no—
95C22×C17#32914yes—
96C22×C17#38111yescharacteristic
97C22×C17C2×#10011yescharacteristic
98C22×C17C2×#10111yescharacteristic
99C22×C17C2×#10412yes—
100C22×C17#42112yes—
101C4×C17—22no—
102C4×C17—22no—
103C4×C17—82no—
104Dic17—24no—
105Dic17—42no—
106Dic17—82no—
107C22×C4⋊C4—171no—
108C22×C4⋊C4#59511yescharacteristic
109C22×C42—171no—
110C2×C22⋊C8—342no—
111C2×#97—174no—
112#382—172no—
113#382—172no—
114#382—342no—
115C2×#95—342no—
116#336—342no—
117C2×C17—24no—
118C2×C17C2×#32911yescharacteristic
119C2×C17#152812yes—
120C2×C17#153311yescharacteristic
121C2×C17#182111yescharacteristic
122C2×C17#182612yes—
123C23×C4—21no—
124C23×C4—172no—
125C23×C4—341no—
126C23×C4C2×#59511yescharacteristic
127C22×C8—344no—
128C2×C4⋊C4—21no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—172no—
131C2×C4⋊C4—341no—
132C2×C4⋊C4—682no—
133C2×C4⋊C4C2×#59512yes—
134C2×C42—171no—
135C2×C42—172no—
136C2×C42—171no—
137C2×C42—344no—
138C22⋊C8—348no—
139#97—348no—
140#95—344no—
141#95—344no—
142C17#871811yescharacteristic, complemented, Sylow
143C24C22⋊#59511yescharacteristic
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—44no—
149C22×C4—42no—
150C22×C4—172no—
151C22×C4—172no—
152C22×C4—344no—
153C22×C4—344no—
154C22×C4—342no—
155C22×C4—682no—
156C22×C4—684no—
157C22×C4—682no—
158C22×C4C22⋊#59511yescharacteristic
159C22×C4C22×#59511yescharacteristic
160C2×C8—348no—
161C2×C8—684no—
162C2×C8—684no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—682no—
166C4⋊C4—682no—
167C42—174no—
168C42—344no—
169C42—342no—
170C23—21no—
171C23—21no—
172C23—22no—
173C23#1058754814yes—
174C23#1058755312yes—
175C23C2×C22⋊#59511yescharacteristic
176C2×C4—28no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—44no—
183C2×C4—84no—
184C2×C4—174no—
185C2×C4—342no—
186C2×C4—342no—
187C2×C4—342no—
188C2×C4—342no—
189C2×C4—342no—
190C2×C4—688no—
191C2×C4—682no—
192C2×C4—684no—
193C2×C4—1364no—
194C2×C4#1058754512yes—
195C2×C4#1058767712yes—
196C8—688no—
197C22—22no—
198C22—24no—
199C22—24no—
200C22—22no—
201C22#1176366414yes—
202C22#1176375211yescharacteristic
203C22C2×#1058755311yescharacteristic
204C22C2×#1058754511yescharacteristic
205C22C2×#1058754812yes—
206C22#1176380812yes—
207C4—22no—
208C4—22no—
209C4—82no—
210C4—344no—
211C4—682no—
212C4—1362no—
213C2—24no—
214C2C2×#1176366411yescharacteristic
215C2#1454424612yes—
216C2#1454426511yescharacteristic
217C2#1454468311yescharacteristic
218C2#1454469012yes—
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#8718
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. #14543660C2semidirect
142. C17#8718semidirect

Maximal subgroups

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

subgroupindex
#145445102
#145436602
C2×#117626742
#871817