Finite Group Databasebeta

← #17958397

Subgroups — #17958397

Order 4352.

670 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544035C212yesmaximal, complemented
2#14543708C214yesmaximal, complemented
3#14531366C211yesmaximal, characteristic
4#11763829—22no—
5#11763654—22no—
6#11763652C2214yes—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762712—22no—
10#11762712—22no—
11#11762665C412yes—
12#11762665C2212yes—
13C23×D4×C17C411yescharacteristic
14C25×C17C2×C412yes—
15C22×D4×C17—24no—
16C22×D4×C17—21no—
17C22×D4×C17—21no—
18C22×D4×C17—41no—
19C22×D4×C17—41no—
20C22×D4×C17—42no—
21C23×C4×C17C2×C411yescharacteristic
22C2×C22⋊Dic17—24no—
23C2×C22⋊Dic17—24no—
24C2×C22⋊Dic17C2×C412yes—
25C2×C22⋊Dic17C2×C411yescharacteristic
26C2×C22⋊Dic17C2311yescharacteristic
27#10587612—41no—
28#10587612—41no—
29#10587612—42no—
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17D412yes—
32C2×C4×Dic17—21no—
33C2×C4×Dic17D412yes—
34C22⋊#3624—24no—
35#10587544—42no—
36#10587542—42no—
37C24×C17—22no—
38C24×C17—22no—
39C24×C17—42no—
40C24×C17—42no—
41C24×C17—84no—
42C24×C17M1614yes—
43C24×C17C22×C411yescharacteristic
44C2×D4×C17—24no—
45C2×D4×C17—24no—
46C2×D4×C17—48no—
47C2×D4×C17—48no—
48C2×D4×C17—42no—
49C2×D4×C17—42no—
50C2×D4×C17—41no—
51C2×D4×C17—41no—
52C2×D4×C17—42no—
53C22×C4×C17—22no—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—22no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×Dic17—22no—
60C22×Dic17C22⋊C412yes—
61C22×Dic17C2×D412yes—
62C2×#3624—44no—
63C22⋊Dic17—41no—
64C22⋊Dic17—41no—
65C22⋊Dic17—42no—
66C22⋊Dic17—84no—
67C22⋊Dic17—84no—
68C4⋊Dic17—42no—
69C4⋊Dic17—42no—
70C4×Dic17—22no—
71C4×Dic17—22no—
72C4×Dic17—42no—
73#11503—171nomaximal, Sylow
74C23×C17—21no—
75C23×C17—21no—
76C23×C17—24no—
77C23×C17—42no—
78C23×C17—44no—
79C23×C17—44no—
80C23×C17—44no—
81C23×C17—44no—
82C23×C17—42no—
83C23×C17—42no—
84C23×C17—84no—
85C23×C17—84no—
86C23×C17—88no—
87C23×C17—88no—
88C23×C17C2×C22⋊C411yescharacteristic
89C23×C17C2×M1612yes—
90D4×C17—44no—
91D4×C17—44no—
92D4×C17—48no—
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#9911yescharacteristic
100C2×C4×C17#9911yescharacteristic
101C2×C4×C17#10012yes—
102C2×Dic17—22no—
103C2×Dic17—22no—
104C2×Dic17—42no—
105C2×Dic17—42no—
106C2×Dic17—44no—
107C2×Dic17—42no—
108#3624—84no—
109#2309—171no—
110#1464—172no—
111#1316—174no—
112C22×C17—22no—
113C22×C17—22no—
114C22×C17—42no—
115C22×C17—42no—
116C22×C17—44no—
117C22×C17—44no—
118C22×C17—42no—
119C22×C17—44no—
120C22×C17—84no—
121C22×C17—88no—
122C22×C17—88no—
123C22×C17—84no—
124C22×C17#40711yescharacteristic
125C22×C17C2×#9911yescharacteristic
126C22×C17C2×#10011yescharacteristic
127C4×C17—21no—
128C4×C17—21no—
129C4×C17—22no—
130Dic17—42no—
131Dic17—42no—
132Dic17—82no—
133C23×D4#59511yescharacteristic
134C2×#117—171no—
135C2×#117—171no—
136#432—342no—
137#390—342no—
138#390—342no—
139#379—172no—
140#379—172no—
141#324—342no—
142#323—174no—
143C2×C17—21no—
144C2×C17—21no—
145C2×C17—42no—
146C2×C17—84no—
147C2×C17#146211yescharacteristic
148C2×C17#212212yes—
149C25C2×#59512yes—
150C22×D4—24no—
151C22×D4—21no—
152C22×D4—21no—
153C22×D4—41no—
154C22×D4—41no—
155C22×D4—42no—
156C23×C4C2×#59511yescharacteristic
157#117—681no—
158#117—681no—
159#117—682no—
160C2×C4⋊C4—172no—
161C2×C4⋊C4—341no—
162C2×C22⋊C4—171no—
163C2×C22⋊C4—171no—
164C2×C22⋊C4—172no—
165C2×C22⋊C4—344no—
166C2×C22⋊C4—344no—
167C2×C42—172no—
168C2×C42—341no—
169C4⋊C8—682no—
170C22⋊C8—344no—
171#97—682no—
172C17#1150311yescharacteristic, complemented, Sylow
173C24—22no—
174C24—22no—
175C24—42no—
176C24—42no—
177C24—84no—
178C24#6324714yes—
179C24C22×#59511yescharacteristic
180C2×D4—24no—
181C2×D4—24no—
182C2×D4—48no—
183C2×D4—48no—
184C2×D4—42no—
185C2×D4—42no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—42no—
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—172no—
194C22×C4—172no—
195C22×C4—342no—
196C22×C4C22⋊#59511yescharacteristic
197C22×C4C22⋊#59511yescharacteristic
198C2×C8—684no—
199C4⋊C4—682no—
200C4⋊C4—682no—
201C22⋊C4—681no—
202C22⋊C4—681no—
203C22⋊C4—682no—
204C22⋊C4—1364no—
205C22⋊C4—1364no—
206C42—342no—
207C42—342no—
208C42—682no—
209C23—21no—
210C23—21no—
211C23—24no—
212C23—42no—
213C23—44no—
214C23—44no—
215C23—44no—
216C23—44no—
217C23—42no—
218C23—42no—
219C23—84no—
220C23—84no—
221C23—88no—
222C23—88no—
223C23C2×#6324712yes—
224C23C2×C22⋊#59511yescharacteristic
225D4—44no—
226D4—44no—
227D4—48no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—342no—
235C2×C4—342no—
236C2×C4—682no—
237C2×C4—682no—
238C2×C4—684no—
239C2×C4—682no—
240C2×C4#1058755111yescharacteristic
241C2×C4#1058755111yescharacteristic
242C2×C4#1058755312yes—
243C8—1364no—
244C22—22no—
245C22—22no—
246C22—42no—
247C22—42no—
248C22—44no—
249C22—44no—
250C22—42no—
251C22—44no—
252C22—84no—
253C22—88no—
254C22—88no—
255C22—84no—
256C22#1176377911yescharacteristic
257C22C2×#1058755111yescharacteristic
258C22C2×#1058755311yescharacteristic
259C4—21no—
260C4—21no—
261C4—22no—
262C4—682no—
263C4—682no—
264C4—1362no—
265C2—21no—
266C2—21no—
267C2—42no—
268C2—84no—
269C2#1454402911yescharacteristic
270C2#1454504312yes—
subgroupG/H
centerC22C2×#10587551
commutatorC24×C17C22×C4
FrattiniC24C22×#595
Fitting, prime radicalC23×D4×C17C4
socleC22×C17C2×#99
cosocleC2×C22⋊Dic17C23
hypercenterC23×D4#595
hypocenterC17#11503
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #14544035C2semidirect
2. #14543708C2semidirect
172. C17#11503semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437082
#145313662
#1150317