Finite Group Databasebeta

← #17949888

Subgroups — #17949888

Order 4352.

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

normal subgroups only

This group has 658 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#14543605C214yesmaximal, complemented
3C2×#11762714C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5C2×#10587542—22no—
6#11763675C2214yes—
7C23×Dic34C411yescharacteristic
8C22×C4×Dic17C2211yescharacteristic
9#11762714—22no—
10#11762714C412yes—
11#11762714C2212yes—
12C2×#10587502—22no—
13C22×C4⋊C4×C17C411yescharacteristic
14C23×C4×C17—21no—
15C23×C4×C17C2×C411yescharacteristic
16C23×Dic17—21no—
17C23×Dic17D412yes—
18C22×Dic34—21no—
19C22×Dic34—24no—
20C22×Dic34—42no—
21C22×Dic34—42no—
22C22×Dic34C2×C412yes—
23C22×#3624—24no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17—42no—
26C2×C4⋊C4×C17C2×C412yes—
27C2×C4×Dic17—42no—
28C2×C4×Dic17C2×C411yescharacteristic
29C2×C4×Dic17D412yes—
30C2×C4×Dic17C2311yescharacteristic
31C22⋊#3624—28no—
32#10587542—44no—
33#10587502—24no—
34#10587502—24no—
35C24×C17C22⋊C411yescharacteristic
36C22×C4×C17—22no—
37C22×C4×C17—22no—
38C22×C4×C17—22no—
39C22×C4×C17—22no—
40C22×C4×C17—42no—
41C22×C4×C17—44no—
42C22×C4×C17C22⋊C411yescharacteristic
43C22×C4×C17C22×C411yescharacteristic
44C22×Dic17—24no—
45C22×Dic17—24no—
46C22×Dic17—22no—
47C22×Dic17—24no—
48C22×Dic17—42no—
49C22×Dic17—42no—
50C22×Dic17—42no—
51C22×Dic17C22⋊C412yes—
52C22×Dic17C2×D412yes—
53C2×Dic34—24no—
54C2×Dic34—22no—
55C2×Dic34—42no—
56C2×Dic34—416no—
57C2×Dic34—42no—
58C2×Dic34—42no—
59C2×Dic34—42no—
60C2×Dic34M1614yes—
61C2×#3624—28no—
62C2×#3624—44no—
63C2×#3624—44no—
64C4⋊C4×C17—42no—
65C4⋊C4×C17—42no—
66C4×Dic17—24no—
67C4×Dic17—41no—
68C4×Dic17—41no—
69#7629—171nomaximal, Sylow
70C23×C17—21no—
71C23×C17—21no—
72C23×C17—22no—
73C23×C17#10012yes—
74C23×C17#10414yes—
75C23×C17C2×C22⋊C411yescharacteristic
76C2×C4×C17—28no—
77C2×C4×C17—21no—
78C2×C4×C17—21no—
79C2×C4×C17—21no—
80C2×C4×C17—21no—
81C2×C4×C17—42no—
82C2×C4×C17—44no—
83C2×C4×C17—84no—
84C2×C4×C17#9912yes—
85C2×C4×C17C2×M1612yes—
86C2×Dic17—22no—
87C2×Dic17—22no—
88C2×Dic17—24no—
89C2×Dic17—22no—
90C2×Dic17—22no—
91C2×Dic17—22no—
92C2×Dic17—48no—
93C2×Dic17—48no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96C2×Dic17#13714yes—
97Dic34—48no—
98Dic34—44no—
99Dic34—44no—
100#3624—48no—
101C2×#391—171no—
102#1749—172no—
103#1272—174no—
104C22×C17—22no—
105C22×C17—22no—
106C22×C17—24no—
107C22×C17—24no—
108C22×C17#32914yes—
109C22×C17#40711yescharacteristic
110C22×C17C2×#9911yescharacteristic
111C22×C17C2×#10011yescharacteristic
112C22×C17#41912yes—
113C22×C17C2×#10412yes—
114C4×C17—22no—
115C4×C17—22no—
116C4×C17—82no—
117Dic17—24no—
118Dic17—44no—
119Dic17—42no—
120C23×Q8—171no—
121C22×C4⋊C4#59511yescharacteristic
122C22×C42—171no—
123C2×C22⋊C8—342no—
124C2×#97—342no—
125#391—172no—
126#391—172no—
127#391—342no—
128C2×#95—342no—
129#336—174no—
130C2×C17—24no—
131C2×C17#146211yescharacteristic
132C2×C17#149112yes—
133C2×C17#150812yes—
134C2×C17C2×#32911yescharacteristic
135C2×C17#155811yescharacteristic
136C22×Q8—172no—
137C22×Q8—344no—
138C22×Q8—341no—
139C22×Q8—682no—
140C22×Q8—682no—
141C23×C4—21no—
142C23×C4—172no—
143C23×C4—341no—
144C23×C4C2×#59511yescharacteristic
145C22×C8—344no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—42no—
148C2×C4⋊C4C2×#59512yes—
149C2×C42—172no—
150C2×C42—171no—
151C2×C42—171no—
152C2×C42—682no—
153C22⋊C8—348no—
154#97—684no—
155#95—344no—
156#95—344no—
157C17#762911yescharacteristic, complemented, Sylow
158C24C22⋊#59511yescharacteristic
159C2×Q8—174no—
160C2×Q8—344no—
161C2×Q8—342no—
162C2×Q8—6816no—
163C2×Q8—682no—
164C2×Q8—682no—
165C2×Q8—682no—
166C2×Q8—682no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—44no—
172C22×C4—42no—
173C22×C4—172no—
174C22×C4—172no—
175C22×C4—344no—
176C22×C4—344no—
177C22×C4—342no—
178C22×C4—344no—
179C22×C4—682no—
180C22×C4—682no—
181C22×C4—682no—
182C22×C4C22⋊#59511yescharacteristic
183C22×C4C22×#59511yescharacteristic
184C2×C8—348no—
185C2×C8—684no—
186C2×C8—684no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C42—344no—
190C42—681no—
191C42—681no—
192C23—21no—
193C23—21no—
194C23—22no—
195C23#1058754814yes—
196C23#1058755312yes—
197C23C2×C22⋊#59511yescharacteristic
198Q8—684no—
199Q8—684no—
200Q8—688no—
201C2×C4—28no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—44no—
208C2×C4—84no—
209C2×C4—174no—
210C2×C4—342no—
211C2×C4—342no—
212C2×C4—344no—
213C2×C4—342no—
214C2×C4—342no—
215C2×C4—342no—
216C2×C4—688no—
217C2×C4—688no—
218C2×C4—682no—
219C2×C4—682no—
220C2×C4#1058753912yes—
221C2×C4D17⋊M1612yes—
222C8—688no—
223C22—24no—
224C22—24no—
225C22—22no—
226C22—22no—
227C22#1176366414yes—
228C22#1176378111yescharacteristic
229C22C2×#1058753911yescharacteristic
230C22C2×#1058755311yescharacteristic
231C22#1176380212yes—
232C22C2×#1058754812yes—
233C4—22no—
234C4—22no—
235C4—82no—
236C4—344no—
237C4—682no—
238C4—684no—
239C2—24no—
240C2#1454403111yescharacteristic
241C2#1454412812yes—
242C2#1454418312yes—
243C2C2×#1176366411yescharacteristic
244C2#1454431711yescharacteristic
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#7629
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. #14543605C2semidirect
157. C17#7629semidirect

Maximal subgroups

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

subgroupindex
#145445102
#145436052
C2×#117627142
#762917