Finite Group Databasebeta

← #17958417

Subgroups — #17958417

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#14543712C214yesmaximal, complemented
3#14531366C211yesmaximal, characteristic
4#11763829—22no—
5#11763654C2214yescomplemented
6#11763652—22no—
7C2×#10587612C411yescharacteristic
8C2×#10587612C2211yescharacteristic
9#11762712—22no—
10#11762712C412yes—
11#11762712C2212yes—
12#11762665—22no—
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
21C2×C22⋊Dic17—21no—
22C2×C22⋊Dic17—24no—
23C2×C22⋊Dic17—24no—
24C2×C22⋊Dic17D412yes—
25#10587612—42no—
26#10587612—42no—
27C2×C4⋊Dic17—21no—
28C2×C4⋊Dic17C2×C411yescharacteristic
29C2×C4⋊Dic17C2311yescharacteristic
30C2×C4×Dic17C2×C412yes—
31C2×C4×Dic17D412yes—
32C22⋊#3624—24no—
33#10587544—42no—
34#10587542—42no—
35C24×C17—24no—
36C24×C17—22no—
37C24×C17—42no—
38C24×C17—42no—
39C24×C17—82no—
40C24×C17—82no—
41C24×C17C22⋊C411yescharacteristic
42C2×D4×C17—24no—
43C2×D4×C17—22no—
44C2×D4×C17—42no—
45C2×D4×C17—42no—
46C2×D4×C17—416no—
47C2×D4×C17—42no—
48C2×D4×C17—42no—
49C2×D4×C17M1614yes—
50C22×C4×C17—22no—
51C22×C4×C17—22no—
52C22×C4×C17—22no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22×C411yescharacteristic
55C22×Dic17—22no—
56C22×Dic17C22⋊C412yes—
57C22×Dic17C2×D412yes—
58C2×#3624—44no—
59C22⋊Dic17—42no—
60C22⋊Dic17—42no—
61C22⋊Dic17—84no—
62C22⋊Dic17—84no—
63C4⋊Dic17—41no—
64C4⋊Dic17—41no—
65C4⋊Dic17—42no—
66C4×Dic17—22no—
67C4×Dic17—22no—
68C4×Dic17—42no—
69#11509—171nomaximal, Sylow
70C23×C17—21no—
71C23×C17—21no—
72C23×C17—24no—
73C23×C17—41no—
74C23×C17—41no—
75C23×C17—44no—
76C23×C17—44no—
77C23×C17—48no—
78C23×C17—42no—
79C23×C17—42no—
80C23×C17—88no—
81C23×C17—88no—
82C23×C17—84no—
83C23×C17—84no—
84C23×C17#10012yes—
85C23×C17C2×C22⋊C411yescharacteristic
86D4×C17—44no—
87D4×C17—48no—
88D4×C17—44no—
89C2×C4×C17—28no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17#9912yes—
95C2×C4×C17C2×M1612yes—
96C2×Dic17—22no—
97C2×Dic17—22no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103#3624—84no—
104#2309—171no—
105#1464—172no—
106#1318—174no—
107C22×C17—21no—
108C22×C17—21no—
109C22×C17—22no—
110C22×C17—42no—
111C22×C17—42no—
112C22×C17—48no—
113C22×C17—41no—
114C22×C17—41no—
115C22×C17—44no—
116C22×C17—84no—
117C22×C17—816no—
118C22×C17—82no—
119C22×C17—82no—
120C22×C17#40711yescharacteristic
121C22×C17C2×#9911yescharacteristic
122C22×C17C2×#10011yescharacteristic
123C4×C17—22no—
124C4×C17—22no—
125Dic17—42no—
126Dic17—42no—
127Dic17—82no—
128C23×D4#59511yescharacteristic
129C2×#117—171no—
130C2×#117—171no—
131#432—342no—
132#390—172no—
133#390—172no—
134#390—342no—
135#379—342no—
136#324—174no—
137#323—342no—
138C2×C17—21no—
139C2×C17—21no—
140C2×C17—42no—
141C2×C17—84no—
142C2×C17#146211yescharacteristic
143C2×C17#212811yescharacteristic
144C2×C17#213411yescharacteristic
145C25—21no—
146C22×D4—24no—
147C22×D4—21no—
148C22×D4—42no—
149C22×D4—42no—
150C22×D4C2×#59512yes—
151C23×C4C2×#59511yescharacteristic
152#117—682no—
153#117—682no—
154C2×C4⋊C4—171no—
155C2×C4⋊C4—171no—
156C2×C4⋊C4—341no—
157C2×C22⋊C4—172no—
158C2×C22⋊C4—341no—
159C2×C22⋊C4—344no—
160C2×C22⋊C4—344no—
161C2×C42—172no—
162C2×C42—172no—
163C4⋊C8—682no—
164C22⋊C8—344no—
165#97—682no—
166C17#1150911yescharacteristic, complemented, Sylow
167C24—24no—
168C24—22no—
169C24—42no—
170C24—42no—
171C24—82no—
172C24—82no—
173C24C22⋊#59511yescharacteristic
174C2×D4—24no—
175C2×D4—22no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—416no—
179C2×D4—42no—
180C2×D4—42no—
181C2×D4#6324714yes—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—172no—
186C22×C4—172no—
187C22×C4—342no—
188C22×C4C22⋊#59511yescharacteristic
189C22×C4C22×#59511yescharacteristic
190C2×C8—684no—
191C4⋊C4—681no—
192C4⋊C4—681no—
193C4⋊C4—682no—
194C22⋊C4—682no—
195C22⋊C4—682no—
196C22⋊C4—1364no—
197C22⋊C4—1364no—
198C42—342no—
199C42—342no—
200C42—682no—
201C23—21no—
202C23—21no—
203C23—24no—
204C23—41no—
205C23—41no—
206C23—44no—
207C23—44no—
208C23—48no—
209C23—42no—
210C23—42no—
211C23—88no—
212C23—88no—
213C23—84no—
214C23—84no—
215C23#1058755312yes—
216C23C2×C22⋊#59511yescharacteristic
217D4—44no—
218D4—44no—
219D4—48no—
220C2×C4—28no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—342no—
226C2×C4—342no—
227C2×C4—682no—
228C2×C4—682no—
229C2×C4—682no—
230C2×C4—682no—
231C2×C4—682no—
232C2×C4#1058755112yes—
233C2×C4C2×#6324712yes—
234C8—1364no—
235C22—21no—
236C22—21no—
237C22—22no—
238C22—42no—
239C22—42no—
240C22—48no—
241C22—41no—
242C22—41no—
243C22—44no—
244C22—84no—
245C22—816no—
246C22—82no—
247C22—82no—
248C22#1176377911yescharacteristic
249C22C2×#1058755111yescharacteristic
250C22C2×#1058755311yescharacteristic
251C4—22no—
252C4—22no—
253C4—682no—
254C4—682no—
255C4—1362no—
256C2—21no—
257C2—21no—
258C2—42no—
259C2—84no—
260C2#1454402911yescharacteristic
261C2#1454506311yescharacteristic
262C2#1454508311yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
Fitting, prime radicalC23×D4×C17C4
socleC22×C17C2×#99
cosocleC2×C4⋊Dic17C23
hypercenterC23×D4#595
hypocenterC17#11509
LCSG ▷ C22×C4×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. #14543712C2semidirect
5. #11763654C22semidirect
166. C17#11509semidirect

Maximal subgroups

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

subgroupindex
#145440352
#145437122
#145313662
#1150917