Finite Group Databasebeta

← #17949876

Subgroups — #17949876

Order 4352.

874 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 116 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#14543600C214yesmaximal, complemented
3C2×#11762712C211yesmaximal, characteristic
4C2×C22⋊#3624—22no—
5C2×#10587542—22no—
6#11763675C2214yescomplemented
7C22×C4⋊Dic17C411yescharacteristic
8C22×C22⋊Dic17—22no—
9C22×C4×Dic17C2211yescharacteristic
10#11762712—22no—
11#11762712C412yes—
12#11762712C2212yes—
13C23×D4×C17C411yescharacteristic
14C25×C17—21no—
15C22×D4×C17—24no—
16C22×D4×C17—21no—
17C22×D4×C17—42no—
18C22×D4×C17—42no—
19C22×D4×C17C2×C412yes—
20C23×C4×C17C2×C411yescharacteristic
21C23×Dic17—21no—
22C23×Dic17D412yes—
23C22×#3624—24no—
24C2×C22⋊Dic17—24no—
25C2×C22⋊Dic17—24no—
26C2×C22⋊Dic17—48no—
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17—42no—
29C2×C4⋊Dic17C2×C412yes—
30C2×C4×Dic17—42no—
31C2×C4×Dic17C2×C411yescharacteristic
32C2×C4×Dic17D412yes—
33C2×C4×Dic17C2311yescharacteristic
34C22⋊#3624—28no—
35#10587542—44no—
36C24×C17—24no—
37C24×C17—22no—
38C24×C17—42no—
39C24×C17—44no—
40C24×C17—42no—
41C24×C17—44no—
42C24×C17C22⋊C411yescharacteristic
43C2×D4×C17—24no—
44C2×D4×C17—22no—
45C2×D4×C17—42no—
46C2×D4×C17—42no—
47C2×D4×C17—416no—
48C2×D4×C17—42no—
49C2×D4×C17—42no—
50C2×D4×C17M1614yes—
51C22×C4×C17—22no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22×C411yescharacteristic
56C22×Dic17—24no—
57C22×Dic17—24no—
58C22×Dic17—22no—
59C22×Dic17—42no—
60C22×Dic17—44no—
61C22×Dic17—42no—
62C22×Dic17C22⋊C412yes—
63C22×Dic17C2×D412yes—
64C2×#3624—28no—
65C2×#3624—44no—
66C2×#3624—44no—
67C22⋊Dic17—48no—
68C22⋊Dic17—48no—
69C4⋊Dic17—42no—
70C4⋊Dic17—42no—
71C4×Dic17—24no—
72C4×Dic17—41no—
73C4×Dic17—41no—
74#7626—171nomaximal, Sylow
75C23×C17—21no—
76C23×C17—21no—
77C23×C17—22no—
78C23×C17—24no—
79C23×C17—48no—
80C23×C17—416no—
81C23×C17—42no—
82C23×C17—42no—
83C23×C17—44no—
84C23×C17—44no—
85C23×C17—84no—
86C23×C17—88no—
87C23×C17—84no—
88C23×C17#10012yes—
89C23×C17#10414yes—
90C23×C17C2×C22⋊C411yescharacteristic
91D4×C17—44no—
92D4×C17—48no—
93D4×C17—44no—
94C2×C4×C17—28no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
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×Dic17—42no—
108C2×Dic17—44no—
109C2×Dic17—84no—
110C2×Dic17AGL(1,ℤ/8)14yes—
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—44no—
120C22×C17—48no—
121C22×C17—816no—
122C22×C17—82no—
123C22×C17—84no—
124C22×C17—82no—
125C22×C17#32914yes—
126C22×C17#40711yescharacteristic
127C22×C17C2×#9911yescharacteristic
128C22×C17C2×#10011yescharacteristic
129C22×C17#41812yes—
130C22×C17C2×#10412yes—
131C4×C17—22no—
132C4×C17—22no—
133Dic17—24no—
134Dic17—42no—
135Dic17—82no—
136C23×D4#59511yescharacteristic
137C22×C4⋊C4—171no—
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—84no—
148C2×C17#146211yescharacteristic
149C2×C17#149012yes—
150C2×C17#150712yes—
151C2×C17C2×#32911yescharacteristic
152C2×C17#155511yescharacteristic
153C25—21no—
154C22×D4—24no—
155C22×D4—21no—
156C22×D4—42no—
157C22×D4—42no—
158C22×D4C2×#59512yes—
159C23×C4—172no—
160C23×C4—341no—
161C23×C4C2×#59511yescharacteristic
162C22×C8—344no—
163C2×C4⋊C4—172no—
164C2×C4⋊C4—341no—
165C2×C4⋊C4—682no—
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—24no—
177C24—22no—
178C24—44no—
179C24—42no—
180C24—44no—
181C24—42no—
182C24C22⋊#59511yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—416no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4#6324714yes—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—172no—
195C22×C4—172no—
196C22×C4—344no—
197C22×C4—344no—
198C22×C4—342no—
199C22×C4—682no—
200C22×C4—684no—
201C22×C4—682no—
202C22×C4C22⋊#59511yescharacteristic
203C22×C4C22×#59511yescharacteristic
204C2×C8—348no—
205C2×C8—684no—
206C2×C8—684no—
207C4⋊C4—682no—
208C4⋊C4—682no—
209C22⋊C4—688no—
210C22⋊C4—688no—
211C42—344no—
212C42—681no—
213C42—681no—
214C23—21no—
215C23—21no—
216C23—22no—
217C23—24no—
218C23—48no—
219C23—416no—
220C23—42no—
221C23—42no—
222C23—44no—
223C23—44no—
224C23—88no—
225C23—84no—
226C23—84no—
227C23#1058754814yes—
228C23#1058755312yes—
229C23C2×C22⋊#59511yescharacteristic
230D4—44no—
231D4—44no—
232D4—48no—
233C2×C4—28no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—174no—
239C2×C4—342no—
240C2×C4—342no—
241C2×C4—342no—
242C2×C4—342no—
243C2×C4—342no—
244C2×C4—688no—
245C2×C4—682no—
246C2×C4—684no—
247C2×C4—1364no—
248C2×C4#1058755112yes—
249C2×C4C2×#6324712yes—
250C8—688no—
251C22—24no—
252C22—22no—
253C22—22no—
254C22—24no—
255C22—44no—
256C22—48no—
257C22—816no—
258C22—84no—
259C22—82no—
260C22—82no—
261C22#1176366414yes—
262C22#1176377911yescharacteristic
263C22C2×#1058755111yescharacteristic
264C22C2×#1058755311yescharacteristic
265C22#1176380112yes—
266C22C2×#1058754812yes—
267C4—22no—
268C4—22no—
269C4—344no—
270C4—682no—
271C4—1362no—
272C2—24no—
273C2—84no—
274C2#1454402911yescharacteristic
275C2#1454412312yes—
276C2#1454418012yes—
277C2C2×#1176366411yescharacteristic
278C2#1454431111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC23×D4×C17C4
socleC23×C17C2×C22⋊C4
cosocleC2×C4×Dic17C23
hypercenterC23×D4#595
hypocenterC17#7626
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #14544510C2semidirect
2. #14543600C2semidirect
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
#145436002
C2×#117627122
#762617