Finite Group Databasebeta

← #17949035

Subgroups — #17949035

Order 4352.

518 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 62 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#14544618C212yesmaximal
2#14527054C211yesmaximal, characteristic
3C2×#10587545—22no—
4C2×#10587545C414yescomplemented
5#11763779—22no—
6C23×Dic34C2211yescharacteristic
7C2×#10587502—22no—
8C2×#10587502C411yescharacteristic
9C2×C17×#95C411yescharacteristic
10C23×C4×C17—21no—
11C23×C4×C17C2×C411yescharacteristic
12C23×Dic17—21no—
13C23×Dic17D412yes—
14C22×Dic34—44no—
15C22×Dic34—41no—
16C22×Dic34—41no—
17C22×Dic34C2×C412yes—
18C22×Dic34D411yescharacteristic
19C22×Dic34Q811yescharacteristic
20C2×#63247—24no—
21C22⋊#3624—42no—
22C22⋊#3624—42no—
23#10587545—44no—
24#10587545—44no—
25C17×#95—41no—
26#10587502—44no—
27#10587502—41no—
28C24×C17C22⋊C411yescharacteristic
29C22×C4×C17—21no—
30C22×C4×C17—21no—
31C22×C4×C17—22no—
32C22×C4×C17—42no—
33C22×C4×C17—41no—
34C22×C4×C17—42no—
35C22×C4×C17—42no—
36C22×C4×C17—41no—
37C22×C4×C17C4211yescharacteristic
38C22×C4×C17C4⋊C411yescharacteristic
39C22×Dic17—22no—
40C22×Dic17—22no—
41C22×Dic17—24no—
42C22×Dic17—22no—
43C22×Dic17—42no—
44C22×Dic17—41no—
45C22×Dic17—42no—
46C22×Dic17—42no—
47C22×Dic17—41no—
48C22×Dic17C22⋊C412yes—
49C22×Dic17C4⋊C412yes—
50C2×Dic34—24no—
51C2×Dic34—24no—
52C2×Dic34—42no—
53C2×Dic34—42no—
54C2×Dic34—41no—
55C2×Dic34—42no—
56C2×Dic34—41no—
57C2×Dic34—48no—
58C2×Dic34—48no—
59#63247—44no—
60#63247—44no—
61C2×#3624—44no—
62#7308—171nomaximal, Sylow
63C23×C17—22no—
64C23×C17—21no—
65C23×C17—21no—
66C23×C17—21no—
67C23×C17—21no—
68C23×C17#9511yescharacteristic
69C23×C17#9911yescharacteristic
70C23×C17#9911yescharacteristic
71C2×C4×C17—22no—
72C2×C4×C17—22no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—42no—
76C2×C4×C17—42no—
77C2×C4×C17—44no—
78C2×C4×C17—42no—
79C2×C4×C17—82no—
80C2×C4×C17—81no—
81C2×C4×C17—81no—
82C2×Dic17—22no—
83C2×Dic17—22no—
84C2×Dic17—22no—
85C2×Dic17—22no—
86C2×Dic17—22no—
87C2×Dic17—44no—
88C2×Dic17—44no—
89C2×Dic17—44no—
90C2×Dic17—42no—
91C2×Dic17—82no—
92C2×Dic17—81no—
93C2×Dic17—81no—
94C2×Dic17#9914yes—
95Dic34—44no—
96Dic34—48no—
97Dic34—44no—
98#3624—84no—
99#1784—172no—
100#1446—171no—
101C22×C17—22no—
102C22×C17—22no—
103C22×C17—22no—
104C22×C17—22no—
105C22×C17—21no—
106C22×C17—21no—
107C22×C17—21no—
108C22×C17—21no—
109C22×C17—21no—
110C22×C17—21no—
111C22×C17#34212yes—
112C22×C17#34211yescharacteristic
113C22×C17#35511yescharacteristic
114C22×C17#35511yescharacteristic
115C22×C17#35611yescharacteristic
116C22×C17#35611yescharacteristic
117C4×C17—41no—
118C4×C17—41no—
119C4×C17—82no—
120Dic17—24no—
121Dic17—42no—
122Dic17—82no—
123C23×Q8—171no—
124C2×#101—174no—
125C2×#101—342no—
126#407—342no—
127C2×#95—171no—
128C2×#95—342no—
129C2×#95#59511yescharacteristic
130C2×C17—21no—
131C2×C17—21no—
132C2×C17—22no—
133C2×C17—21no—
134C2×C17—21no—
135C2×C17#130411yescharacteristic
136C2×C17#139411yescharacteristic
137C2×C17#139411yescharacteristic
138C22×Q8—172no—
139C22×Q8—171no—
140C22×Q8—171no—
141C22×Q8—681no—
142C22×Q8—681no—
143C22×Q8—684no—
144C23×C4—21no—
145C23×C4—172no—
146C23×C4—341no—
147C23×C4C2×#59511yescharacteristic
148C2×M16—344no—
149#101—684no—
150#101—684no—
151C22⋊C8—682no—
152C22⋊C8—682no—
153#95—41no—
154#95—681no—
155#95—684no—
156C17#730811yescharacteristic, complemented, Sylow
157C24C22⋊#59511yescharacteristic
158C2×Q8—344no—
159C2×Q8—344no—
160C2×Q8—682no—
161C2×Q8—682no—
162C2×Q8—682no—
163C2×Q8—681no—
164C2×Q8—681no—
165C2×Q8—688no—
166C2×Q8—688no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—22no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—41no—
173C22×C4—42no—
174C22×C4—41no—
175C22×C4—172no—
176C22×C4—172no—
177C22×C4—344no—
178C22×C4—342no—
179C22×C4—342no—
180C22×C4—342no—
181C22×C4—682no—
182C22×C4—682no—
183C22×C4—681no—
184C22×C4—682no—
185C22×C4—681no—
186C22×C4C4×#59511yescharacteristic
187C22×C4C4⋊#59511yescharacteristic
188M16—684no—
189M16—684no—
190C2×C8—684no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23—22no—
196C23#1058753911yescharacteristic
197C23(C2×#595)⋊C411yescharacteristic
198C23#1058755111yescharacteristic
199Q8—684no—
200Q8—688no—
201Q8—684no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4—82no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4—174no—
214C2×C4—342no—
215C2×C4—342no—
216C2×C4—342no—
217C2×C4—342no—
218C2×C4—342no—
219C2×C4—684no—
220C2×C4—684no—
221C2×C4—684no—
222C2×C4—682no—
223C2×C4—1362no—
224C2×C4—1361no—
225C2×C4—1361no—
226C8—1364no—
227C22—22no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—21no—
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22#1176368612yes—
238C22#1176368711yescharacteristic
239C22#1176371711yescharacteristic
240C22#1176371811yescharacteristic
241C22#1176371911yescharacteristic
242C22#1176372011yescharacteristic
243C4—41no—
244C4—41no—
245C4—82no—
246C4—344no—
247C4—682no—
248C4—1362no—
249C2—21no—
250C2—21no—
251C2—21no—
252C2—21no—
253C2—22no—
254C2#1454368311yescharacteristic
255C2#1454388111yescharacteristic
256C2#1454388211yescharacteristic
subgroupG/H
centerC22#11763687
commutatorC22×C4×C17C42
FrattiniC23×C4C2×#595
FittingC2×C17×#95C4
socleC22×C17#342
prime radicalC24×C17C22⋊C4
cosocleC23×Dic34C22
hypercenterC2×#95#595
hypocenterC17#7308
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C2×#10587545C4semidirect
156. C17#7308semidirect

Maximal subgroups

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

subgroupindex
#145446182
#145270542
#730817