Finite Group Databasebeta

← #17953590

Subgroups — #17953590

Order 4352.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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
3#14531187C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5C2×#10587542C2214yes—
6#11763675—22no—
7C2×#10587612C411yescharacteristic
8C22×C4×Dic17C2211yescharacteristic
9#11762678C412yes—
10#11762674C2212yes—
11#11762667—22no—
12C4×#63225—22no—
13C2×C17×#117C411yescharacteristic
14C23×C4×C17C2×C411yescharacteristic
15C23×Dic17D412yes—
16C22×#3624—24no—
17C17×#117—42no—
18C2×C4⋊C4×C17C2×C412yes—
19C2×C22⋊C4×C17—21no—
20C2×C42×C17—21no—
21C2×C22⋊Dic17—21no—
22#10587612—42no—
23C2×C4⋊Dic17C2×C412yes—
24C2×#63225—22no—
25C2×#63225—22no—
26C2×C4×Dic17—24no—
27C2×C4×Dic17—21no—
28C2×C4×Dic17C2×C411yescharacteristic
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31C22⋊#3624—28no—
32#10587542—28no—
33#10587502—24no—
34C24×C17C22⋊C411yescharacteristic
35C22×C4×C17—22no—
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17C22⋊C411yescharacteristic
40C22×C4×C17C22×C411yescharacteristic
41C22×Dic17—24no—
42C22×Dic17—24no—
43C22×Dic17—22no—
44C22×Dic17—42no—
45C22×Dic17C22⋊C412yes—
46C22×Dic17C2×D412yes—
47C2×#3624—28no—
48C2×#3624—44no—
49C2×#3624—44no—
50C4⋊C4×C17—42no—
51C22⋊C4×C17—42no—
52C42×C17—42no—
53C22⋊Dic17—42no—
54C4⋊Dic17—42no—
55#63225—44no—
56#63225—44no—
57C4×Dic17—22no—
58C4×Dic17—24no—
59C4×Dic17—42no—
60C4×Dic17#4114yes—
61#8722—171nomaximal, Sylow
62C23×C17—21no—
63C23×C17—21no—
64C23×C17—22no—
65C23×C17—22no—
66C23×C17#10012yes—
67C23×C17C2×C22⋊C411yescharacteristic
68C2×C4×C17—28no—
69C2×C4×C17—21no—
70C2×C4×C17—21no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—42no—
74C2×C4×C17—42no—
75C2×C4×C17—42no—
76C2×C4×C17#10112yes—
77C2×C4×C17#11712yes—
78C2×Dic17—22no—
79C2×Dic17—22no—
80C2×Dic17—22no—
81C2×Dic17—22no—
82C2×Dic17—48no—
83C2×Dic17—42no—
84C2×Dic17—42no—
85C2×Dic17—42no—
86C2×Dic17#10414yes—
87C2×Dic17#12314yes—
88#3624—48no—
89#2285—171no—
90#1749—172no—
91#1295—174no—
92C22×C17—22no—
93C22×C17—24no—
94C22×C17—41no—
95C22×C17—42no—
96C22×C17—41no—
97C22×C17#38111yescharacteristic
98C22×C17C2×#10011yescharacteristic
99C22×C17C2×#10111yescharacteristic
100C22×C17C2×#10412yes—
101C22×C17#42112yes—
102C4×C17—22no—
103C4×C17—22no—
104C4×C17—82no—
105Dic17—24no—
106Dic17—24no—
107Dic17—82no—
108C2×#117—171no—
109C2×#117#59511yescharacteristic
110C22×C42—171no—
111C2×C22⋊C8—342no—
112C2×#97—174no—
113#384—172no—
114#382—172no—
115#380—342no—
116C4×C4⋊C4—342no—
117#336—342no—
118C2×C17—42no—
119C2×C17#152611yescharacteristic
120C2×C17#153012yes—
121C2×C17#153711yescharacteristic
122C2×C17#182111yescharacteristic
123C2×C17#182612yes—
124C23×C4—172no—
125C23×C4C2×#59511yescharacteristic
126C22×C8—344no—
127#117—42no—
128#117—682no—
129C2×C4⋊C4—172no—
130C2×C4⋊C4—342no—
131C2×C4⋊C4—342no—
132C2×C4⋊C4C2×#59512yes—
133C2×C22⋊C4—21no—
134C2×C22⋊C4—341no—
135C2×C42—21no—
136C2×C42—171no—
137C2×C42—172no—
138C2×C42—171no—
139C2×C42—344no—
140C2×C42—341no—
141C22⋊C8—348no—
142#97—348no—
143#95—344no—
144C17#872211yescharacteristic, complemented, Sylow
145C24C22⋊#59511yescharacteristic
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—172no—
151C22×C4—172no—
152C22×C4—344no—
153C22×C4—344no—
154C22×C4—342no—
155C22×C4—682no—
156C22×C4C22⋊#59511yescharacteristic
157C22×C4C22×#59511yescharacteristic
158C2×C8—348no—
159C2×C8—684no—
160C2×C8—684no—
161C4⋊C4—42no—
162C4⋊C4—682no—
163C4⋊C4—684no—
164C4⋊C4—684no—
165C22⋊C4—42no—
166C22⋊C4—682no—
167C42—42no—
168C42—174no—
169C42—344no—
170C42—342no—
171C42—682no—
172C23—21no—
173C23—21no—
174C23—22no—
175C23—22no—
176C23#1058755312yes—
177C23C2×C22⋊#59511yescharacteristic
178C2×C4—28no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—174no—
187C2×C4—174no—
188C2×C4—342no—
189C2×C4—342no—
190C2×C4—342no—
191C2×C4—342no—
192C2×C4—688no—
193C2×C4—682no—
194C2×C4—682no—
195C2×C4—682no—
196C2×C4#1058754512yes—
197C2×C4#1058767712yes—
198C8—688no—
199C22—22no—
200C22—24no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22#1176375211yescharacteristic
205C22C2×#1058755311yescharacteristic
206C22C2×#1058754511yescharacteristic
207C22D17⋊#10412yes—
208C22#1176380612yes—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—344no—
213C4—344no—
214C4—1362no—
215C2—42no—
216C2#1454424111yescharacteristic
217C2#1454425312yes—
218C2#1454427511yescharacteristic
219C2#1454468311yescharacteristic
220C2#1454469212yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC2×C17×#117C4
socleC23×C17C2×C22⋊C4
prime radicalC24×C17C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC2×#117#595
hypocenterC17#8722
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #14543660C2semidirect
144. C17#8722semidirect

Maximal subgroups

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

subgroupindex
#145445102
#145436602
#145311872
#872217