Finite Group Databasebeta

← #17949758

Subgroups — #17949758

Order 4352.

846 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 846 conjugacy classes of subgroups — too many to draw. Only its 124 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#14544674C212yesmaximal, complemented
2#14543601C214yesmaximal, complemented
3C2×#11762710C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5#11763675—22no—
6#11763675C2214yescomplemented
7C23×D68C411yescharacteristic
8C22×#63227—22no—
9C22×C4×Dic17C2211yescharacteristic
10#11762710—22no—
11#11762710C412yes—
12#11762710C2212yes—
13C22×C4⋊C4×C17C411yescharacteristic
14C24×D17—21no—
15C23×C4×C17—21no—
16C23×C4×C17C2×C411yescharacteristic
17C23×Dic17D412yes—
18C22×D68—21no—
19C22×D68—22no—
20C22×D68—42no—
21C22×D68—42no—
22C22×D68C814yescomplemented
23C22×D68C2×C412yes—
24C22×#3624—24no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—42no—
27C2×C4⋊C4×C17C2×C412yes—
28C2×#63227—24no—
29C2×#63227—24no—
30C2×#63227—48no—
31C2×C4×Dic17—42no—
32C2×C4×Dic17C2×C411yescharacteristic
33C2×C4×Dic17D412yes—
34C2×C4×Dic17C2311yescharacteristic
35C22⋊#3624—44no—
36C24×C17C22⋊C411yescharacteristic
37C23×D17—24no—
38C23×D17—22no—
39C23×D17—44no—
40C23×D17—44no—
41C23×D17—42no—
42C23×D17—42no—
43C22×C4×C17—22no—
44C22×C4×C17—22no—
45C22×C4×C17—22no—
46C22×C4×C17—44no—
47C22×C4×C17—42no—
48C22×C4×C17C22⋊C411yescharacteristic
49C22×C4×C17C2×C812yes—
50C22×C4×C17M1612yes—
51C22×C4×C17C22×C411yescharacteristic
52C22×Dic17—24no—
53C22×Dic17—24no—
54C22×Dic17—42no—
55C22×Dic17C22⋊C412yes—
56C22×Dic17C2×D412yes—
57C2×D68—24no—
58C2×D68—22no—
59C2×D68—48no—
60C2×D68—42no—
61C2×D68—42no—
62C2×D68—48no—
63C2×D68—42no—
64C2×D68—42no—
65C2×D68C2×C814yes—
66C2×#3624—44no—
67C2×#3624—44no—
68C2×#3624—44no—
69C4⋊C4×C17—42no—
70C4⋊C4×C17—42no—
71#63227—48no—
72#63227—48no—
73C4×Dic17—41no—
74C4×Dic17—42no—
75C4×Dic17—41no—
76#7592—171nomaximal, Sylow
77C23×C17—22no—
78C23×C17—22no—
79C23×C17C22⋊C812yes—
80C23×C17#9912yes—
81C23×C17#10012yes—
82C23×C17C2×C22⋊C411yescharacteristic
83C22×D17—24no—
84C22×D17—416no—
85C22×D17—48no—
86C22×D17—42no—
87C22×D17—42no—
88C22×D17—44no—
89C22×D17—44no—
90C22×D17—84no—
91C22×D17—88no—
92C22×D17—84no—
93C2×C4×C17—24no—
94C2×C4×C17—24no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—42no—
100C2×C4×C17—44no—
101C2×C4×C17—84no—
102C2×C4×C17C22⋊C812yes—
103C2×C4×C17C22×C811yescharacteristic
104C2×C4×C17C2×M1611yescharacteristic
105C2×Dic17—22no—
106C2×Dic17—22no—
107C2×Dic17—22no—
108C2×Dic17—22no—
109C2×Dic17—22no—
110C2×Dic17—48no—
111C2×Dic17AGL(1,ℤ/8)14yes—
112D68—44no—
113D68—48no—
114D68—44no—
115#3624—84no—
116C2×#390—171no—
117#1817—172no—
118#1270—174no—
119C22×C17—22no—
120C22×C17—24no—
121C22×C17—24no—
122C22×C17—22no—
123C22×C17#32314yes—
124C22×C17C2×C22⋊C811yescharacteristic
125C22×C17C2×#9911yescharacteristic
126C22×C17C2×#10011yescharacteristic
127C22×C17#41812yes—
128C22×C17#42112yes—
129C2×D17—44no—
130C2×D17—48no—
131C2×D17—816no—
132C2×D17—82no—
133C2×D17—84no—
134C2×D17—82no—
135C4×C17—22no—
136C4×C17—21no—
137C4×C17—21no—
138C4×C17—82no—
139Dic17—24no—
140Dic17—42no—
141C23×D4—171no—
142C22×C4⋊C4#59511yescharacteristic
143C22×C22⋊C4—342no—
144C22×C42—171no—
145C2×C22⋊C8—342no—
146#390—172no—
147#390—172no—
148#390—342no—
149#336—174no—
150#336—342no—
151C2×C17—24no—
152C2×C17C2×#32311yescharacteristic
153C2×C17#147812yes—
154C2×C17#151012yes—
155C2×C17#153311yescharacteristic
156C2×C17#155511yescharacteristic
157D17—84no—
158C25—341no—
159C22×D4—174no—
160C22×D4—172no—
161C22×D4—342no—
162C22×D4—341no—
163C22×D4—682no—
164C22×D4—682no—
165C23×C4—21no—
166C23×C4—172no—
167C23×C4C2×#59511yescharacteristic
168C22×C8—344no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4C2×#59512yes—
172C2×C22⋊C4—344no—
173C2×C22⋊C4—344no—
174C2×C22⋊C4—688no—
175C2×C42—172no—
176C2×C42—171no—
177C2×C42—171no—
178C2×C42—682no—
179C22⋊C8—684no—
180C17#759211yescharacteristic, complemented, Sylow
181C24—342no—
182C24—344no—
183C24—684no—
184C24—684no—
185C24—682no—
186C24—682no—
187C24C22⋊#59511yescharacteristic
188C2×D4—174no—
189C2×D4—342no—
190C2×D4—344no—
191C2×D4—682no—
192C2×D4—682no—
193C2×D4—688no—
194C2×D4—682no—
195C2×D4—682no—
196C2×D4—688no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—44no—
201C22×C4—42no—
202C22×C4—172no—
203C22×C4—172no—
204C22×C4—344no—
205C22×C4—344no—
206C22×C4—682no—
207C22×C4#6324212yes—
208C22×C4#6324312yes—
209C22×C4C22⋊#59511yescharacteristic
210C22×C4C22×#59511yescharacteristic
211C2×C8—684no—
212C2×C8—684no—
213C2×C8—684no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C22⋊C4—688no—
217C22⋊C4—688no—
218C42—682no—
219C42—681no—
220C42—681no—
221C23—22no—
222C23—22no—
223C23—344no—
224C23—6816no—
225C23—682no—
226C23—682no—
227C23—684no—
228C23—684no—
229C23—688no—
230C23—1368no—
231C23—1364no—
232C23—1364no—
233C23#1058753912yes—
234C23#1058754312yes—
235C23#1058755312yes—
236C23C2×C22⋊#59511yescharacteristic
237D4—684no—
238D4—684no—
239D4—688no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—24no—
245C2×C4—24no—
246C2×C4—42no—
247C2×C4—44no—
248C2×C4—84no—
249C2×C4—174no—
250C2×C4—342no—
251C2×C4—342no—
252C2×C4—342no—
253C2×C4—342no—
254C2×C4—342no—
255C2×C4—688no—
256C2×C4#1058754312yes—
257C2×C4C2×#6324211yescharacteristic
258C2×C4C2×#6324311yescharacteristic
259C8—1364no—
260C22—24no—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—684no—
265C22—688no—
266C22—13616no—
267C22—1364no—
268C22—1362no—
269C22—1362no—
270C22#1176365314yes—
271C22C2×#1058754311yescharacteristic
272C22C2×#1058753911yescharacteristic
273C22C2×#1058755311yescharacteristic
274C22#1176380112yes—
275C22#1176380812yes—
276C4—21no—
277C4—21no—
278C4—22no—
279C4—82no—
280C4—344no—
281C4—682no—
282C2—24no—
283C2—1364no—
284C2C2×#1176365311yescharacteristic
285C2#1454408512yes—
286C2#1454419112yes—
287C2#1454426511yescharacteristic
288C2#1454431111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C22×C8
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D68C4
cosocleC2×C4×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#7592
LCSG ▷ C2×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
1. #14544674C2semidirect
2. #14543601C2semidirect
6. #11763675C22semidirect
22. C22×D68C8semidirect
180. C17#7592semidirect

Maximal subgroups

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

subgroupindex
#145446742
#145436012
C2×#117627102
#759217