Finite Group Databasebeta

← #16935280

Subgroups — #16935280

Order 4352.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 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#14540129C211yesmaximal, characteristic, complemented
2#14538883C212yesmaximal
3#14527398C212yesmaximal, complemented
4#14526654C211yesmaximal, characteristic, complemented
5C17×#1955C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763144—22no—
8#11763105—22no—
9#11763089—22no—
10#11763050—22no—
11#11763020—22no—
12#11763014—22no—
13#11762960—22no—
14#11762909—24no—
15#11762866C2212yes—
16#11762550—24no—
17C2×C4×D4×C17C2211yescharacteristic
18C2×C17×C4⋊C8C2211yescharacteristic
19C2×C17×C22⋊C8—22no—
20C2×C17×#97C2211yescharacteristic
21C22×D4×C17D411yescharacteristic
22C23×C4×C17—21no—
23C22×C8×C17—21no—
24C22×C8×C17D412yes—
25C4×D4×C17—22no—
26C4×D4×C17—22no—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C22⋊C4×C17—21no—
29C2×C42×C17C2311yescharacteristic
30C2×#63229—24no—
31#10587612—22no—
32#10587610—22no—
33#10587610—22no—
34C2×Dic68—22no—
35#10587556—22no—
36#10587555D412yes—
37#10587555D412yes—
38C4×Dic34—22no—
39C4×Dic34—22no—
40C17×C4⋊C8—22no—
41C17×C22⋊C8—44no—
42C17×#97—22no—
43#10587503—24no—
44C22⋊#3622—22no—
45#10587489—22no—
46#10587487—24no—
47#10587481—24no—
48#10587478—24no—
49C4⋊#3622—22no—
50#10587474D414yes—
51C24×C17—21no—
52C2×D4×C17—22no—
53C2×D4×C17—42no—
54C22×C4×C17—21no—
55C22×C4×C17—42no—
56C22×C4×C17—42no—
57C22×C4×C17—41no—
58C22×C4×C17—41no—
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×C4×C17#4111yescharacteristic
62C2×Dic34—22no—
63C2×Dic34—22no—
64C2×C8×C17—22no—
65C2×C8×C17—22no—
66C2×C8×C17—41no—
67C2×C8×C17—41no—
68C2×C8×C17—42no—
69C4⋊C4×C17—22no—
70C22⋊C4×C17—42no—
71C42×C17C2×D412yes—
72C42×C17C2×D412yes—
73C22⋊Dic17—42no—
74#63229—48no—
75C4⋊Dic17—22no—
76C4⋊Dic17—22no—
77C4⋊Dic17—22no—
78C4⋊Dic17—22no—
79#63225—42no—
80#63225—42no—
81C4×Dic17—42no—
82C2×#3622—24no—
83Dic68—82no—
84#10030—171nomaximal, Sylow
85C23×C17—22no—
86C23×C17—42no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17—42no—
90C23×C17#12111yescharacteristic
91D4×C17—24no—
92D4×C17—42no—
93C2×C4×C17—22no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—41no—
97C2×C4×C17—42no—
98C2×C4×C17—41no—
99C2×C4×C17—82no—
100C2×C4×C17—81no—
101C2×C4×C17—81no—
102C2×C4×C17#12012yes—
103C2×C4×C17#12011yescharacteristic
104C2×C4×C17#12112yes—
105C2×C4×C17#12711yescharacteristic
106C2×Dic17—42no—
107C2×Dic17—42no—
108Dic34—44no—
109Dic34—42no—
110Dic34—42no—
111C8×C17—42no—
112C8×C17—42no—
113#3622—44no—
114#3249—171no—
115#3110—172no—
116#1955D1711yescharacteristic
117#1531—172no—
118#1290—171no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17—44no—
122C22×C17—42no—
123C22×C17—82no—
124C22×C17—81no—
125C22×C17—81no—
126C22×C17#39211yescharacteristic
127C22×C17#47312yes—
128C4×C17—21no—
129C4×C17—22no—
130C4×C17—22no—
131C4×C17—81no—
132C4×C17#45311yescharacteristic
133C4×C17#45411yescharacteristic
134Dic17—82no—
135Dic17—82no—
136#533—172no—
137C2×C4×D4C2×D1711yescharacteristic
138#484—342no—
139#477—342no—
140#474—342no—
141#467—342no—
142#462—342no—
143#461—342no—
144#450—342no—
145#440—344no—
146#432—172no—
147C2×C4⋊C8C2×D1711yescharacteristic
148C2×C22⋊C8—22no—
149C2×#97C2×D1711yescharacteristic
150#330—344no—
151C2×C17—22no—
152C2×C17—82no—
153C2×C17#200611yescharacteristic
154C2×C17#201011yescharacteristic
155C2×C17#202011yescharacteristic
156C22×D4D6811yescharacteristic
157C23×C4—21no—
158C2×Q16—342no—
159C2×SD16—344no—
160C22×C8—21no—
161C22×C8C22⋊D1712yes—
162C4⋊Q8—172no—
163C4⋊Q8—172no—
164#125—342no—
165C22⋊Q8—342no—
166C22⋊Q8—342no—
167C4×Q8—342no—
168C4×Q8—342no—
169C4×D4—22no—
170C4×D4—22no—
171#117—342no—
172C2×C4⋊C4D6811yescharacteristic
173C2×C22⋊C4—21no—
174C2×C42C22×D1711yescharacteristic
175#107—344no—
176#107—342no—
177C4⋊C8—22no—
178C4⋊C8—342no—
179#103—344no—
180#103—344no—
181#102—344no—
182C22⋊C8—44no—
183C22⋊C8—342no—
184#97—22no—
185#97—174no—
186C17#1003011yescharacteristic, complemented, Sylow
187C24—21no—
188C2×Q8—342no—
189C2×Q8—342no—
190C2×D4—22no—
191C2×D4—42no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4C2×D6811yescharacteristic
198C22×C4#6325211yescharacteristic
199C22×C4C2×C22⋊D1711yescharacteristic
200Q16—1362no—
201SD16—688no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—344no—
208C4⋊C4—22no—
209C4⋊C4—342no—
210C4⋊C4—342no—
211C4⋊C4—342no—
212C4⋊C4—342no—
213C4⋊C4—682no—
214C4⋊C4—682no—
215C22⋊C4—42no—
216C22⋊C4—682no—
217C42—682no—
218C42D4×D1712yes—
219C42D4×D1712yes—
220C23—22no—
221C23—42no—
222C23—41no—
223C23—41no—
224C23—42no—
225C23#1058761611yescharacteristic
226Q8—684no—
227Q8—682no—
228Q8—682no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—682no—
241C2×C4—682no—
242C2×C4#1058756812yes—
243C2×C4#1058757012yes—
244C2×C4#1058762311yescharacteristic
245C2×C4#1058762611yescharacteristic
246C8—42no—
247C8—42no—
248C8—684no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#1176271811yescharacteristic
257C22#1176308412yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—81no—
262C4—1362no—
263C4—1362no—
264C4#1176297611yescharacteristic
265C4#1176298111yescharacteristic
266C2—22no—
267C2—82no—
268C2#1452982511yescharacteristic
269C2#1452985111yescharacteristic
270C2#1452990511yescharacteristic
subgroupG/H
centerC22#11762718
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1955C2
socleC22×C17#392
prime radicalC22×D4×C17D4
hypercenter#1955D17
hypocenterC17#10030
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #14540129C2semidirect
3. #14527398C2semidirect
4. #14526654C2semidirect
186. C17#10030semidirect

Maximal subgroups

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

subgroupindex
#145401292
#145388832
#145273982
#145266542
C17×#19552
#1003017