Finite Group Databasebeta

← #16947849

Subgroups — #16947849

Order 4352.

322 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 67 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#14541789C211yesmaximal, characteristic, complemented
2#14531040C211yesmaximal, characteristic
3#14530824C211yesmaximal, characteristic
4#14528145C211yesmaximal, characteristic
5#14526832C211yesmaximal, characteristic, complemented
6#14526764C211yesmaximal, characteristic, complemented
7C17×#1332C211yesmaximal, characteristic, complemented
8#11763537—21no—
9C2×#10587471—22no—
10C2×#10587499—21no—
11#11763189C2211yescharacteristic
12#11763187—21no—
13#11763186C2211yescharacteristic
14#11763019—21no—
15#11763018—22no—
16#11763010—21no—
17C8×Dic34C2211yescharacteristic
18#11762903—21no—
19C4⋊#63214C2211yescharacteristic
20#11762609—21no—
21#11762552—21no—
22C4×Q16×C17C2211yescharacteristic
23C4×C16×C17C2211yescharacteristic
24C17×#335C2211yescharacteristic
25C2×Q16×C17D411yescharacteristic
26C4×Q8×C17—21no—
27#10587630—22no—
28C2×#63231—22no—
29C2×Dic68—21no—
30C2×Dic68D412yes—
31C2×D136—21no—
32C2×D136—21no—
33C2×#63219—41no—
34#10587575—42no—
35#10587573—22no—
36#10587560—21no—
37#10587556—41no—
38#10587555—21no—
39C4×Dic34—41no—
40C4×Dic34D411yescharacteristic
41C2×C16×C17—21no—
42C17×#107D411yescharacteristic
43C17×C4⋊C8—21no—
44C17×#103—21no—
45C4×C8×C17C2311yescharacteristic
46#10587499—42no—
47#10587492—41no—
48#10587485—21no—
49C8×Dic17—21no—
50C2×#63214—21no—
51#10587481—22no—
52C4⋊#3622D411yescharacteristic
53#10587471—44no—
54C2×Q8×C17—21no—
55C2×D68—41no—
56C2×D68—41no—
57C2×D68—41no—
58C2×Dic34—22no—
59C2×Dic34D811yescharacteristic
60Q16×C17—21no—
61Q16×C17—21no—
62C2×C8×C17—41no—
63C2×C8×C17C2×D411yescharacteristic
64C2×C8×C17C2×D411yescharacteristic
65C4⋊C4×C17—21no—
66C4⋊C4×C17—41no—
67C42×C17—41no—
68C42×C17C2×D411yescharacteristic
69#63231—82no—
70C4⋊Dic17—41no—
71C4⋊Dic17—41no—
72C4⋊Dic17D811yescharacteristic
73#63225—21no—
74#63225—42no—
75#63225—42no—
76#63225—42no—
77C4×Dic17—21no—
78C4×Dic17—42no—
79C2×#3622—21no—
80Dic68—42no—
81Dic68—41no—
82Dic68—41no—
83D136—42no—
84D136—41no—
85D136—41no—
86#63219—82no—
87C16×C17—22no—
88#63214—41no—
89#12330—171nomaximal, Sylow
90C22×D17—81no—
91Q8×C17—41no—
92Q8×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17#12011yescharacteristic
96C2×C4×C17C2×D811yescharacteristic
97C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
98C2×Dic17—21no—
99C2×Dic17—21no—
100C2×Dic17—42no—
101D68—81no—
102D68—81no—
103D68—81no—
104D68—81no—
105D68—161no—
106Dic34—21no—
107Dic34—42no—
108Dic34—42no—
109Dic34SD3212yescomplemented
110C8×C17—21no—
111C8×C17—81no—
112C8×C17#13511yescharacteristic
113C8×C17AGL(1,ℤ/8)11yescharacteristic
114#3622—41no—
115#3395—171no—
116#2248—171no—
117#2207—171no—
118#1668—171no—
119#1362—171no—
120Q8⋊C16—171no—
121#1332D1711yescharacteristic, complemented
122C22×C17#44711yescharacteristic
123C2×D17—161no—
124C2×D17—161no—
125C2×D17—161no—
126C4×C17—21no—
127C4×C17—81no—
128C4×C17—81no—
129C4×C17#44911yescharacteristic
130C4×C17#45311yescharacteristic
131C4×C17C2×SD3211yescharacteristic
132C4×C17#51011yescharacteristic
133Dic17—22no—
134Dic17—41no—
135Dic17—82no—
136#557—341no—
137C2×SD32—342no—
138C2×SD32—341no—
139#494—171no—
140#494—341no—
141#493—171no—
142#462—342no—
143#462—341no—
144#460—341no—
145C8×Q8—171no—
146C4×Q16—341no—
147C4×Q16C2×D1711yescharacteristic
148C4⋊C16—171no—
149#357—341no—
150C4×C16C2×D1711yescharacteristic
151#335C2×D1711yescharacteristic
152#331—341no—
153C2×C17#162111yescharacteristic
154C2×C17#218511yescharacteristic
155C2×C17#219311yescharacteristic
156D17—321no—
157C2×Q16—172no—
158C2×Q16—342no—
159C2×Q16—341no—
160C2×Q16D6811yescharacteristic
161C2×SD16—681no—
162C2×D8—341no—
163C2×D8—341no—
164C4⋊Q8—342no—
165C4⋊Q8—341no—
166#127—341no—
167#125—681no—
168#125—682no—
169C4×Q8—21no—
170C4×Q8—171no—
171C4×Q8—342no—
172C4×Q8—681no—
173SD32—684no—
174SD32—682no—
175C2×C16—21no—
176C2×C16—341no—
177#107D6811yescharacteristic
178C4⋊C8—21no—
179C4⋊C8—171no—
180C4⋊C8—341no—
181#103—21no—
182#103—342no—
183#102—681no—
184C4×C8—341no—
185C4×C8C22×D1711yescharacteristic
186C17#1233011yescharacteristic, complemented, Sylow
187C2×Q8—21no—
188C2×Q8—171no—
189C2×Q8—342no—
190C2×D4—681no—
191C2×D4—681no—
192C2×D4—681no—
193Q16—21no—
194Q16—21no—
195Q16—682no—
196Q16—681no—
197Q16—681no—
198Q16—1362no—
199SD16—1362no—
200D8—682no—
201D8—681no—
202D8—681no—
203C2×C8—41no—
204C2×C8—341no—
205C2×C8C2×D6811yescharacteristic
206C2×C8D4×D1711yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—171no—
210C4⋊C4—341no—
211C4⋊C4—682no—
212C4⋊C4—682no—
213C4⋊C4—682no—
214C4⋊C4—681no—
215C4⋊C4—681no—
216C42—41no—
217C42—341no—
218C42—682no—
219C42D4×D1711yescharacteristic
220C16—22no—
221C16—681no—
222C23—1361no—
223Q8—41no—
224Q8—41no—
225Q8—172no—
226Q8—341no—
227Q8—682no—
228Q8—682no—
229D4—2721no—
230D4—1361no—
231D4—1361no—
232D4—1361no—
233D4—1361no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—341no—
237C2×C4—341no—
238C2×C4—682no—
239C2×C4#1058756811yescharacteristic
240C2×C4D8×D1711yescharacteristic
241C2×C4#1058760011yescharacteristic
242C8—21no—
243C8—81no—
244C8—681no—
245C8#1058759011yescharacteristic
246C8#1058759411yescharacteristic
247C22—2721no—
248C22—2721no—
249C22—2721no—
250C22#1176294411yescharacteristic
251C4—21no—
252C4—81no—
253C4—81no—
254C4—342no—
255C4—681no—
256C4—1362no—
257C4#1176295611yescharacteristic
258C4#1176297811yescharacteristic
259C4SD32×D1711yescharacteristic
260C4#1176325111yescharacteristic
261C2—5441no—
262C2#1452785211yescharacteristic
263C2#1453070211yescharacteristic
264C2#1453074911yescharacteristic
subgroupG/H
centerC22#11762944
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1332C2
socleC22×C17#447
prime radical#11763186C22
hypercenter#1332D17
hypocenterC17#12330
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1332

Complements

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

NH ≅ G/Ntype
1. #14541789C2semidirect
5. #14526832C2semidirect
6. #14526764C2semidirect
7. C17×#1332C2semidirect
109. Dic34SD32semidirect
121. #1332D17semidirect
186. C17#12330semidirect

Maximal subgroups

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

subgroupindex
#145417892
#145310402
#145308242
#145281452
#145268322
#145267642
C17×#13322
#1233017