Finite Group Databasebeta

← #17958139

Subgroups — #17958139

Order 4352.

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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#14544016C212yesmaximal
2#14543711C212yesmaximal
3#14543710C212yesmaximal
4#14531369C211yesmaximal, characteristic
5#11763826—22no—
6#11763655—22no—
7#11763652C2214yes—
8C23×Dic34C411yescharacteristic
9C2×#10587563C411yescharacteristic
10C2×#10587563C2211yescharacteristic
11#11762713—22no—
12#11762713—22no—
13#11762672C2211yescharacteristic
14#11762670C411yescharacteristic
15#11762670C2211yescharacteristic
16C17×#381C411yescharacteristic
17C23×C4×C17C2×C411yescharacteristic
18C23×Dic17C2×C411yescharacteristic
19C23×Dic17C2×C411yescharacteristic
20C22×Dic34—21no—
21C22×Dic34—21no—
22C22×Dic34—22no—
23C22×Dic34—42no—
24C22×Dic34—42no—
25C22×Dic34C814yescomplemented
26C2×C22⋊C4×C17C2×C411yescharacteristic
27C2×C22⋊C4×C17C2×C411yescharacteristic
28C2×C22⋊Dic17C2×C411yescharacteristic
29C2×C22⋊Dic17C2311yescharacteristic
30C2×#63225—21no—
31C2×#63225D412yes—
32C2×C4×Dic17—21no—
33C2×C4×Dic17D412yes—
34#10587563—42no—
35#10587563—42no—
36C22⋊#3624—24no—
37#10587544—42no—
38C4×#3624—42no—
39C17×#95—22no—
40#10587502—22no—
41#10587502—22no—
42#10587502—22no—
43C24×C17C22×C411yescharacteristic
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—21no—
47C22×C4×C17—41no—
48C22×C4×C17—41no—
49C22×C4×C17C22⋊C412yes—
50C22×C4×C17C2×C812yes—
51C22×Dic17—22no—
52C22×Dic17—22no—
53C22×Dic17—21no—
54C22×Dic17—21no—
55C22×Dic17—21no—
56C22×Dic17—41no—
57C22×Dic17—41no—
58C22×Dic17C22⋊C411yescharacteristic
59C22×Dic17C22⋊C411yescharacteristic
60C22×Dic17C2×C812yes—
61C22×Dic17C2×C812yes—
62C22×Dic17M1612yes—
63C22×Dic17C2×D412yes—
64C2×Dic34—24no—
65C2×Dic34—24no—
66C2×Dic34—42no—
67C2×Dic34—42no—
68C2×Dic34—48no—
69C2×Dic34—42no—
70C2×Dic34—42no—
71C2×Dic34—48no—
72C2×#3624—44no—
73C22⋊C4×C17—41no—
74C22⋊C4×C17—41no—
75C22⋊Dic17—41no—
76C22⋊Dic17—41no—
77#63225—42no—
78#63225—42no—
79C4×Dic17—22no—
80C4×Dic17—22no—
81C4×Dic17—42no—
82#11428—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—42no—
86C23×C17C2×C22⋊C411yescharacteristic
87C23×C17C22×C811yescharacteristic
88C23×C17C2×M1611yescharacteristic
89C2×C4×C17—22no—
90C2×C4×C17—22no—
91C2×C4×C17—42no—
92C2×C4×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—42no—
95C2×C4×C17—42no—
96C2×C4×C17—42no—
97C2×C4×C17—41no—
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—24no—
101C2×Dic17—24no—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—42no—
105C2×Dic17—41no—
106C2×Dic17—41no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—41no—
111C2×Dic17C22⋊C812yes—
112C2×Dic17C22⋊C812yes—
113C2×Dic17#9912yes—
114C2×Dic17#10012yes—
115Dic34—48no—
116Dic34—48no—
117#3624—84no—
118#2310—171no—
119#1458—172no—
120#1317—172no—
121#1317—172no—
122C22×C17—22no—
123C22×C17—21no—
124C22×C17—21no—
125C22×C17—41no—
126C22×C17—41no—
127C22×C17—42no—
128C22×C17—42no—
129C22×C17C2×C22⋊C811yescharacteristic
130C22×C17C2×#9911yescharacteristic
131C22×C17C2×#10011yescharacteristic
132C4×C17—42no—
133C4×C17—42no—
134C4×C17—81no—
135Dic17—22no—
136Dic17—42no—
137Dic17—42no—
138Dic17—81no—
139Dic17#32314yes—
140C23×Q8—171no—
141C2×#117—171no—
142C2×#117—171no—
143#431—342no—
144#391—342no—
145#391—342no—
146#381—171no—
147#381—171no—
148#381—171no—
149#381#59511yescharacteristic
150#324—342no—
151#323—174no—
152C2×C17—21no—
153C2×C17—21no—
154C2×C17—41no—
155C2×C17—41no—
156C2×C17C2×#32311yescharacteristic
157C2×C17#212312yes—
158C22×Q8—174no—
159C22×Q8—342no—
160C22×Q8—341no—
161C22×Q8—341no—
162C22×Q8—682no—
163C22×Q8—682no—
164C23×C4—171no—
165C23×C4—171no—
166C23×C4C2×#59511yescharacteristic
167#117—682no—
168#117—682no—
169C2×C4⋊C4—172no—
170C2×C4⋊C4—341no—
171C2×C22⋊C4—171no—
172C2×C22⋊C4—171no—
173C2×C22⋊C4C2×#59511yescharacteristic
174C2×C22⋊C4C2×#59511yescharacteristic
175C2×C42—172no—
176C2×C42—341no—
177C4⋊C8—682no—
178C22⋊C8—344no—
179C4×C8—682no—
180#95—22no—
181#95—342no—
182#95—342no—
183#95—342no—
184C17#1142811yescharacteristic, complemented, Sylow
185C24C22×#59511yescharacteristic
186C2×Q8—344no—
187C2×Q8—344no—
188C2×Q8—682no—
189C2×Q8—682no—
190C2×Q8—688no—
191C2×Q8—688no—
192C2×Q8—682no—
193C2×Q8—682no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—171no—
200C22×C4—172no—
201C22×C4—172no—
202C22×C4—171no—
203C22×C4—172no—
204C22×C4—172no—
205C22×C4—342no—
206C22×C4—342no—
207C22×C4—341no—
208C22×C4—341no—
209C22×C4—341no—
210C22×C4—681no—
211C22×C4—681no—
212C22×C4#6324212yes—
213C22×C4C22⋊#59512yes—
214C2×C8—684no—
215C4⋊C4—682no—
216C4⋊C4—682no—
217C22⋊C4—41no—
218C22⋊C4—41no—
219C22⋊C4—681no—
220C22⋊C4—681no—
221C42—342no—
222C42—342no—
223C42—682no—
224C23—21no—
225C23—21no—
226C23—42no—
227C23C2×#6324211yescharacteristic
228C23D17⋊M1611yescharacteristic
229C23C2×C22⋊#59511yescharacteristic
230Q8—688no—
231Q8—688no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—172no—
242C2×C4—172no—
243C2×C4—172no—
244C2×C4—172no—
245C2×C4—344no—
246C2×C4—344no—
247C2×C4—341no—
248C2×C4—341no—
249C2×C4—342no—
250C2×C4—342no—
251C2×C4—682no—
252C2×C4—681no—
253C2×C4—681no—
254C2×C4—682no—
255C2×C4—682no—
256C2×C4—682no—
257C2×C4—681no—
258C8—1364no—
259C22—22no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22#1176377711yescharacteristic
267C22D17⋊#9911yescharacteristic
268C22D17⋊#10011yescharacteristic
269C4—42no—
270C4—42no—
271C4—81no—
272C4—174no—
273C4—342no—
274C4—682no—
275C4—682no—
276C4—1361no—
277C2—21no—
278C2—21no—
279C2—41no—
280C2—41no—
281C2#1454401011yescharacteristic
282C2#1454504712yes—
subgroupG/H
centerC22D17⋊#99
commutatorC23×C17C22×C8
FrattiniC24C22×#595
FittingC17×#381C4
socleC22×C17C2×#99
prime radicalC24×C17C22×C4
cosocleC2×C22⋊Dic17C23
hypercenter#381#595
hypocenterC17#11428
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #381

Complements

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

NH ≅ G/Ntype
25. C22×Dic34C8semidirect
184. C17#11428semidirect

Maximal subgroups

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

subgroupindex
#145440162
#145437112
#145437102
#145313692
#1142817