Finite Group Databasebeta

← #17958635

Subgroups — #17958635

Order 4352.

462 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 74 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#14544046C211yesmaximal, characteristic, complemented
2#14544026C211yesmaximal, characteristic, complemented
3#14543713C214yesmaximal, complemented
4#14533786C211yesmaximal, characteristic
5#11763830—21no—
6#11763826—21no—
7#11763655—21no—
8#11763655—21no—
9#11763654C2212yes—
10#11763654C2212yes—
11C2×#10587560C411yescharacteristic
12C2×#10587561C412yes—
13C2×C4×Dic34C2211yescharacteristic
14#11762727—21no—
15#11762727—21no—
16#11762711C2212yes—
17#11762710—21no—
18#11762710—21no—
19C4×C4⋊C4×C17C411yescharacteristic
20C22×D68—21no—
21C22×D68—21no—
22C22×D68C2×C412yes—
23C22×Dic34C2×C411yescharacteristic
24C2×C4⋊C4×C17—21no—
25C2×C42×C17C2×C411yescharacteristic
26C2×C42×C17C2×C412yes—
27C2×#63227—22no—
28C2×#63227—22no—
29C2×#63227—22no—
30C2×#63227—22no—
31C2×C4⋊Dic17C2311yescharacteristic
32C2×#63225D411yescharacteristic
33C2×#63225D411yescharacteristic
34C2×C4×Dic17D411yescharacteristic
35C2×C4×Dic17D411yescharacteristic
36#10587561—44no—
37#10587560—41no—
38#10587560—41no—
39C4×Dic34—41no—
40C4×Dic34—41no—
41C22⋊#3624—22no—
42C22⋊#3624—22no—
43#10587544—41no—
44#10587542—41no—
45C4⋊#3624—41no—
46C4×#3624—41no—
47C17×#95—21no—
48C23×D17—22no—
49C22×C4×C17—22no—
50C22×C4×C17C22⋊C411yescharacteristic
51C22×C4×C17C22⋊C411yescharacteristic
52C22×C4×C17C22×C411yescharacteristic
53C22×Dic17C22⋊C411yescharacteristic
54C22×Dic17C22⋊C411yescharacteristic
55C22×Dic17C2×D411yescharacteristic
56C22×Dic17C2×D411yescharacteristic
57C2×D68—24no—
58C2×D68—42no—
59C2×D68—42no—
60C2×D68—42no—
61C2×D68—42no—
62C2×D68—42no—
63C2×D68—41no—
64C2×D68—41no—
65C2×D68—82no—
66C2×Dic34—22no—
67C2×Dic34—22no—
68C2×Dic34—41no—
69C2×#3624—42no—
70C2×#3624—42no—
71C4⋊C4×C17—42no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—42no—
75#63227—44no—
76#63227—44no—
77#63227—82no—
78#63227—82no—
79C4⋊Dic17—41no—
80#63225—41no—
81#63225—41no—
82C4×Dic17—21no—
83C4×Dic17—21no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86#11567—171nomaximal, Sylow
87C23×C17C2×C22⋊C411yescharacteristic
88C22×D17—42no—
89C22×D17—42no—
90C22×D17—42no—
91C22×D17—42no—
92C22×D17—42no—
93C22×D17—42no—
94C22×D17—42no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—22no—
98C2×C4×C17—21no—
99C2×C4×C17—41no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—42no—
103C2×C4×C17#9911yescharacteristic
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17#13112yes—
106C2×Dic17—21no—
107C2×Dic17—21no—
108C2×Dic17—21no—
109C2×Dic17—21no—
110C2×Dic17—21no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—41no—
114C2×Dic17—41no—
115C2×Dic17#10012yes—
116D68—84no—
117D68—82no—
118D68—84no—
119D68—82no—
120Dic34—44no—
121#3624—82no—
122#3624—82no—
123#2548—171no—
124#1467—171no—
125#1461—171no—
126#1318—174no—
127C22×C17—21no—
128C22×C17—21no—
129C22×C17#40811yescharacteristic
130C22×C17C2×#9911yescharacteristic
131C22×C17C2×#10011yescharacteristic
132C2×D17—82no—
133C2×D17—82no—
134C2×D17—82no—
135C2×D17—82no—
136C2×D17—82no—
137C2×D17—82no—
138C2×D17—82no—
139C4×C17—21no—
140C4×C17—22no—
141C4×C17—41no—
142C4×C17—82no—
143C4×C17#35512yes—
144Dic17—22no—
145Dic17—41no—
146Dic17—41no—
147Dic17—41no—
148C2×#127—171no—
149C2×#124—172no—
150C2×C4×Q8—171no—
151#432—341no—
152#431—341no—
153#394—341no—
154#394—341no—
155#390—172no—
156#390—341no—
157#390—341no—
158C4×C4⋊C4#59511yescharacteristic
159#324—172no—
160#324—172no—
161#324—341no—
162#324—341no—
163C2×C17—21no—
164C2×C17—21no—
165C2×C17#147111yescharacteristic
166C2×C17#212811yescharacteristic
167C2×C17C2×#35511yescharacteristic
168D17—162no—
169C22×Q8—171no—
170C22×D4—172no—
171C22×D4—341no—
172C22×D4—341no—
173#127—681no—
174#127—681no—
175#124—684no—
176C4×Q8—681no—
177C4×Q8—681no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—171no—
180C2×C4⋊C4—171no—
181C2×C4⋊C4—171no—
182C2×C22⋊C4—342no—
183C2×C22⋊C4—342no—
184C2×C22⋊C4—342no—
185C2×C22⋊C4—342no—
186C2×C42—171no—
187C2×C42—171no—
188C2×C42C2×#59512yes—
189C2×C42C2×#59511yescharacteristic
190C4⋊C8—681no—
191C4⋊C8—681no—
192C22⋊C8—342no—
193C22⋊C8—342no—
194#97—681no—
195C4×C8—681no—
196#95—21no—
197C17#1156711yescharacteristic, complemented, Sylow
198C24—342no—
199C2×Q8—342no—
200C2×Q8—342no—
201C2×Q8—681no—
202C2×D4—344no—
203C2×D4—682no—
204C2×D4—682no—
205C2×D4—682no—
206C2×D4—682no—
207C2×D4—682no—
208C2×D4—681no—
209C2×D4—681no—
210C2×D4—1362no—
211C22×C4—22no—
212C22×C4—171no—
213C22×C4—171no—
214C22×C4—171no—
215C22×C4—171no—
216C22×C4C22⋊#59511yescharacteristic
217C22×C4C22⋊#59511yescharacteristic
218C22×C4C22×#59511yescharacteristic
219C2×C8—682no—
220C2×C8—682no—
221C4⋊C4—42no—
222C4⋊C4—681no—
223C4⋊C4—681no—
224C4⋊C4—681no—
225C22⋊C4—684no—
226C22⋊C4—684no—
227C22⋊C4—1362no—
228C22⋊C4—1362no—
229C42—21no—
230C42—21no—
231C42—42no—
232C42—341no—
233C42—341no—
234C42—341no—
235C42—341no—
236C23—682no—
237C23—682no—
238C23—682no—
239C23—682no—
240C23—682no—
241C23—682no—
242C23—682no—
243C23C2×C22⋊#59511yescharacteristic
244Q8—684no—
245D4—1364no—
246D4—1362no—
247D4—1364no—
248D4—1362no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—172no—
258C2×C4—341no—
259C2×C4—341no—
260C2×C4—341no—
261C2×C4—341no—
262C2×C4—341no—
263C2×C4—341no—
264C2×C4—341no—
265C2×C4—681no—
266C2×C4—681no—
267C2×C4#1058753911yescharacteristic
268C2×C4#1058753911yescharacteristic
269C2×C4#1058768012yes—
270C8—1362no—
271C8—1362no—
272C22—21no—
273C22—21no—
274C22—1362no—
275C22—1362no—
276C22—1362no—
277C22—1362no—
278C22—1362no—
279C22—1362no—
280C22—1362no—
281C22#1176378411yescharacteristic
282C22C2×#1058753911yescharacteristic
283C22D17⋊#10011yescharacteristic
284C4—21no—
285C4—22no—
286C4—41no—
287C4—82no—
288C4—342no—
289C4—681no—
290C4—681no—
291C4—681no—
292C4#1176371812yes—
293C2—21no—
294C2—21no—
295C2—2722no—
296C2#1454406111yescharacteristic
297C2#1454506511yescharacteristic
298C2C2×#1176371811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC4×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC2×#10587560C4
cosocleC2×C4⋊Dic17C23
hypercenterC4×C4⋊C4#595
hypocenterC17#11567
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14544046C2semidirect
2. #14544026C2semidirect
3. #14543713C2semidirect
197. C17#11567semidirect

Maximal subgroups

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

subgroupindex
#145440462
#145440262
#145437132
#145337862
#1156717