Finite Group Databasebeta

← #17949878

Subgroups — #17949878

Order 4352.

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

normal subgroups only

This group has 874 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, complemented
2#14543601C214yesmaximal, complemented
3C2×#11762710C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5C2×#10587542—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—24no—
20C22×D68—42no—
21C22×D68—42no—
22C22×D68C2×C412yes—
23C22×#3624—24no—
24C2×C4⋊C4×C17—21no—
25C2×C4⋊C4×C17—42no—
26C2×C4⋊C4×C17C2×C412yes—
27C2×#63227—24no—
28C2×#63227—24no—
29C2×#63227—48no—
30C2×C4×Dic17—42no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17D412yes—
33C2×C4×Dic17C2311yescharacteristic
34C22⋊#3624—28no—
35#10587542—44no—
36C24×C17C22⋊C411yescharacteristic
37C23×D17—24no—
38C23×D17—22no—
39C23×D17—42no—
40C23×D17—44no—
41C23×D17—42no—
42C23×D17—44no—
43C22×C4×C17—22no—
44C22×C4×C17—22no—
45C22×C4×C17—22no—
46C22×C4×C17—22no—
47C22×C4×C17—44no—
48C22×C4×C17—42no—
49C22×C4×C17C22⋊C411yescharacteristic
50C22×C4×C17C22×C411yescharacteristic
51C22×Dic17—24no—
52C22×Dic17—24no—
53C22×Dic17—42no—
54C22×Dic17C22⋊C412yes—
55C22×Dic17C2×D412yes—
56C2×D68—24no—
57C2×D68—22no—
58C2×D68—42no—
59C2×D68—42no—
60C2×D68—416no—
61C2×D68—42no—
62C2×D68—42no—
63C2×D68M1614yes—
64C2×#3624—28no—
65C2×#3624—44no—
66C2×#3624—44no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—42no—
69#63227—48no—
70#63227—48no—
71C4×Dic17—24no—
72C4×Dic17—41no—
73C4×Dic17—41no—
74#7626—171nomaximal, Sylow
75C23×C17—21no—
76C23×C17—21no—
77C23×C17—22no—
78C23×C17#10012yes—
79C23×C17#10414yes—
80C23×C17C2×C22⋊C411yescharacteristic
81C22×D17—24no—
82C22×D17—48no—
83C22×D17—416no—
84C22×D17—42no—
85C22×D17—42no—
86C22×D17—44no—
87C22×D17—44no—
88C22×D17—84no—
89C22×D17—88no—
90C22×D17—84no—
91C2×C4×C17—28no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—42no—
97C2×C4×C17—44no—
98C2×C4×C17—84no—
99C2×C4×C17#9912yes—
100C2×C4×C17C2×M1612yes—
101C2×Dic17—22no—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—22no—
105C2×Dic17—22no—
106C2×Dic17—48no—
107C2×Dic17AGL(1,ℤ/8)14yes—
108D68—44no—
109D68—48no—
110D68—44no—
111#3624—48no—
112C2×#390—171no—
113#1749—172no—
114#1270—174no—
115C22×C17—22no—
116C22×C17—22no—
117C22×C17—24no—
118C22×C17—24no—
119C22×C17#32914yes—
120C22×C17#40711yescharacteristic
121C22×C17C2×#9911yescharacteristic
122C22×C17C2×#10011yescharacteristic
123C22×C17#41812yes—
124C22×C17C2×#10412yes—
125C2×D17—44no—
126C2×D17—48no—
127C2×D17—816no—
128C2×D17—82no—
129C2×D17—84no—
130C2×D17—82no—
131C4×C17—22no—
132C4×C17—22no—
133C4×C17—82no—
134Dic17—24no—
135Dic17—42no—
136C23×D4—171no—
137C22×C4⋊C4#59511yescharacteristic
138C22×C22⋊C4—342no—
139C22×C42—171no—
140C2×C22⋊C8—342no—
141C2×#97—342no—
142#390—172no—
143#390—172no—
144#390—342no—
145#336—174no—
146C2×C17—24no—
147C2×C17#146211yescharacteristic
148C2×C17#149012yes—
149C2×C17#150712yes—
150C2×C17C2×#32911yescharacteristic
151C2×C17#155511yescharacteristic
152D17—84no—
153C25—341no—
154C22×D4—172no—
155C22×D4—344no—
156C22×D4—341no—
157C22×D4—682no—
158C22×D4—682no—
159C23×C4—21no—
160C23×C4—172no—
161C23×C4C2×#59511yescharacteristic
162C22×C8—344no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—42no—
165C2×C4⋊C4C2×#59512yes—
166C2×C22⋊C4—344no—
167C2×C22⋊C4—344no—
168C2×C22⋊C4—688no—
169C2×C42—172no—
170C2×C42—171no—
171C2×C42—171no—
172C2×C42—682no—
173C22⋊C8—348no—
174#97—684no—
175C17#762611yescharacteristic, complemented, Sylow
176C24—344no—
177C24—342no—
178C24—684no—
179C24—682no—
180C24—684no—
181C24—682no—
182C24C22⋊#59511yescharacteristic
183C2×D4—174no—
184C2×D4—344no—
185C2×D4—342no—
186C2×D4—682no—
187C2×D4—682no—
188C2×D4—6816no—
189C2×D4—682no—
190C2×D4—682no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—44no—
196C22×C4—42no—
197C22×C4—172no—
198C22×C4—172no—
199C22×C4—344no—
200C22×C4—344no—
201C22×C4—682no—
202C22×C4C22⋊#59511yescharacteristic
203C22×C4C22×#59511yescharacteristic
204C2×C8—348no—
205C2×C8—684no—
206C2×C8—684no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—688no—
210C22⋊C4—688no—
211C42—344no—
212C42—681no—
213C42—681no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—344no—
218C23—688no—
219C23—6816no—
220C23—682no—
221C23—682no—
222C23—684no—
223C23—684no—
224C23—1368no—
225C23—1364no—
226C23—1364no—
227C23#1058755014yes—
228C23#1058755312yes—
229C23C2×C22⋊#59511yescharacteristic
230D4—684no—
231D4—684no—
232D4—688no—
233C2×C4—28no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—44no—
240C2×C4—84no—
241C2×C4—174no—
242C2×C4—342no—
243C2×C4—342no—
244C2×C4—342no—
245C2×C4—342no—
246C2×C4—342no—
247C2×C4—688no—
248C2×C4#1058753912yes—
249C2×C4D17⋊M1612yes—
250C8—688no—
251C22—24no—
252C22—22no—
253C22—22no—
254C22—24no—
255C22—684no—
256C22—688no—
257C22—13616no—
258C22—1364no—
259C22—1362no—
260C22—1362no—
261C22#1176366514yes—
262C22#1176378111yescharacteristic
263C22C2×#1058753911yescharacteristic
264C22C2×#1058755311yescharacteristic
265C22#1176380112yes—
266C22C2×#1058755012yes—
267C4—22no—
268C4—22no—
269C4—82no—
270C4—344no—
271C4—682no—
272C2—24no—
273C2—1364no—
274C2#1454403111yescharacteristic
275C2#1454412512yes—
276C2#1454418112yes—
277C2C2×#1176366511yescharacteristic
278C2#1454431111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D68C4
cosocleC2×C4×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#7626
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
1. #14544510C2semidirect
2. #14543601C2semidirect
6. #11763675C22semidirect
175. C17#7626semidirect

Maximal subgroups

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

subgroupindex
#145445102
#145436012
C2×#117627102
#762617