Finite Group Databasebeta

← #16943751

Subgroups — #16943751

Order 4352.

418 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 99 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#14527118C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526732C214yesmaximal
4C17×#2317C211yesmaximal, characteristic
5#11762866—21no—
6#11762866—21no—
7#11762535—21no—
8#11762535—21no—
9#11762533C2212yes—
10#11762533C2212yes—
11C2×C17×#117C411yescharacteristic
12C2×C17×#117C2211yescharacteristic
13C22×C4⋊C4×C17C411yescharacteristic
14C17×#389—21no—
15C17×#389—21no—
16C17×#385C412yes—
17C17×#385C2212yes—
18C17×#384—21no—
19C17×#382—21no—
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C412yes—
22C17×#117—24no—
23C17×#117—41no—
24C17×#117—41no—
25C2×C4⋊C4×C17—21no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—22no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17—41no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C22⋊C4×C17C2×C412yes—
35C2×C22⋊C4×C17C2×C411yescharacteristic
36C2×C22⋊C4×C17C2311yescharacteristic
37C2×C42×C17—21no—
38C2×C42×C17D411yescharacteristic
39C2×C42×C17D411yescharacteristic
40C17×#95—22no—
41C17×#95—22no—
42C22⋊#3622—22no—
43C22⋊#3622—22no—
44C4⋊#3622—41no—
45C4⋊#3622—41no—
46#10587474—41no—
47#10587474—41no—
48C24×C17C22×C411yescharacteristic
49C22×C4×C17—22no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—22no—
53C22×C4×C17—22no—
54C22×C4×C17—22no—
55C22×C4×C17—42no—
56C22×C4×C17—82no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17C22⋊C411yescharacteristic
61C22×C4×C17C2×D411yescharacteristic
62C22×C4×C17C2×D411yescharacteristic
63C4⋊C4×C17—24no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—42no—
67C4⋊C4×C17—41no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—82no—
70C4⋊C4×C17—82no—
71C22⋊C4×C17—22no—
72C22⋊C4×C17—41no—
73C22⋊C4×C17—41no—
74C22⋊C4×C17M1614yes—
75C42×C17—24no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—21no—
79C42×C17—21no—
80C2×#3622—42no—
81C2×#3622—42no—
82#11520—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—41no—
86C23×C17—41no—
87C23×C17C2×C22⋊C411yescharacteristic
88C23×C17C2×M1612yes—
89C2×C4×C17—24no—
90C2×C4×C17—24no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—24no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—42no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—84no—
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17#9911yescharacteristic
112C2×C4×C17#10112yes—
113#3622—82no—
114#3622—82no—
115#2317D1711yescharacteristic
116#1464—171no—
117#1464—171no—
118#1326—174no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17—22no—
122C22×C17—42no—
123C22×C17—42no—
124C22×C17—41no—
125C22×C17—41no—
126C22×C17#40711yescharacteristic
127C22×C17C2×#9911yescharacteristic
128C22×C17C2×#10111yescharacteristic
129C4×C17—21no—
130C4×C17—21no—
131C4×C17—22no—
132C4×C17—44no—
133C4×C17—41no—
134C4×C17—41no—
135C4×C17—41no—
136C4×C17—41no—
137C4×C17—82no—
138C2×#117Dic1711yescharacteristic
139C2×#117C2×D1711yescharacteristic
140C22×C4⋊C4Dic1711yescharacteristic
141#432—341no—
142#432—341no—
143#389—21no—
144#389—21no—
145#385Dic1712yes—
146#385C2×D1712yes—
147#384—21no—
148#382—21no—
149#324—341no—
150#324—341no—
151#323—172no—
152#323—172no—
153C2×C17—21no—
154C2×C17—21no—
155C2×C17—42no—
156C2×C17#146311yescharacteristic
157C2×C17#212211yescharacteristic
158C2×C17#212311yescharacteristic
159C23×C4C2×Dic1711yescharacteristic
160C23×C4C2×Dic1712yes—
161#117—24no—
162#117—41no—
163#117—41no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4C22⋊D1711yescharacteristic
172C2×C4⋊C4C22⋊D1711yescharacteristic
173C2×C22⋊C4C2×Dic1712yes—
174C2×C22⋊C4C2×Dic1711yescharacteristic
175C2×C22⋊C4C22×D1711yescharacteristic
176C2×C42—21no—
177C2×C42C22⋊D1711yescharacteristic
178C2×C42C22⋊D1711yescharacteristic
179C4⋊C8—681no—
180C4⋊C8—681no—
181C22⋊C8—342no—
182C22⋊C8—342no—
183#97—681no—
184#97—681no—
185#95—22no—
186#95—22no—
187C17#1152011yescharacteristic, complemented, Sylow
188C24C22×Dic1711yescharacteristic
189C22×C4—22no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—42no—
196C22×C4—82no—
197C22×C4C22⋊Dic1711yescharacteristic
198C22×C4C22⋊Dic1711yescharacteristic
199C22×C4C22⋊Dic1711yescharacteristic
200C22×C4C22⋊Dic1711yescharacteristic
201C22×C4C2×C22⋊D1711yescharacteristic
202C22×C4C2×C22⋊D1711yescharacteristic
203C2×C8—682no—
204C2×C8—682no—
205C4⋊C4—24no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—82no—
212C4⋊C4—82no—
213C22⋊C4—22no—
214C22⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4#6322314yes—
217C42—24no—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C23—21no—
223C23—21no—
224C23—41no—
225C23—41no—
226C23C2×#6322312yes—
227C23C2×C22⋊Dic1711yescharacteristic
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—84no—
249C2×C4#1058750511yescharacteristic
250C2×C4#1058750511yescharacteristic
251C2×C4#1058750712yes—
252C8—1362no—
253C8—1362no—
254C22—21no—
255C22—21no—
256C22—22no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22#1176277311yescharacteristic
262C22C2×#1058750511yescharacteristic
263C22C2×#1058750711yescharacteristic
264C4—21no—
265C4—21no—
266C4—22no—
267C4—44no—
268C4—41no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C2—21no—
274C2—21no—
275C2—42no—
276C2#1452711411yescharacteristic
277C2#1453043411yescharacteristic
278C2#1453043811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutator, prime radicalC24×C17C22×C4
FrattiniC2×C22⋊C4C22×D17
FittingC17×#2317C2
socleC22×C17C2×#99
cosocleC2×C22⋊C4×C17C23
hypercenter#2317D17
hypocenterC17#11520
LCSG ▷ C24×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
187. C17#11520semidirect

Maximal subgroups

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

subgroupindex
#145271182
#145267322
C17×#23172
#1152017