Finite Group Databasebeta

← #16936550

Subgroups — #16936550

Order 4352.

468 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 79 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#14540178C211yesmaximal, characteristic, complemented
2#14539978C212yesmaximal
3#14527295C212yesmaximal, complemented
4#14526695C211yesmaximal, characteristic, complemented
5C17×#1963C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763215—22no—
8#11763173—22no—
9#11763130—24no—
10#11763099—22no—
11#11763095—22no—
12#11763089—22no—
13#11763067—22no—
14#11763020—22no—
15#11762866C2212yes—
16#11762545—24no—
17C17×#532C2211yescharacteristic
18C17×#423C2211yescharacteristic
19C2×C17×#104—22no—
20C17×#376C2211yescharacteristic
21C2×#41×C17—21no—
22C2×M16×C17D412yes—
23C17×C4⋊Q8D411yescharacteristic
24C17×#127D411yescharacteristic
25C17×#124—21no—
26C17×#121—22no—
27C4×D4×C17—22no—
28C2×C42×C17—21no—
29C2×C42×C17C2311yescharacteristic
30#10587612—22no—
31#10587610—22no—
32#10587610—22no—
33C2×Dic68—22no—
34#10587556—22no—
35#10587555D412yes—
36#10587555D412yes—
37C4×Dic34—22no—
38C4×Dic34—22no—
39C17×C4⋊C8—22no—
40C17×#104—44no—
41C17×#95—22no—
42#10587503—24no—
43#10587503—24no—
44C22⋊#3622D414yes—
45#10587488—22no—
46#10587487—24no—
47#10587479—24no—
48#10587478—24no—
49C4⋊#3622—22no—
50#10587474—22no—
51#41×C17—42no—
52#41×C17—42no—
53C2×Q8×C17—21no—
54C2×D4×C17—22no—
55C2×D4×C17—21no—
56C2×D4×C17—41no—
57C22×C4×C17—41no—
58C22×C4×C17—41no—
59C22×C4×C17C2×D412yes—
60C22×C4×C17C2×D411yescharacteristic
61C2×Dic34—22no—
62C2×Dic34—22no—
63M16×C17—42no—
64C2×C8×C17—22no—
65C4⋊C4×C17—22no—
66C22⋊C4×C17—42no—
67C42×C17—22no—
68C42×C17—41no—
69C42×C17C2×D411yescharacteristic
70C42×C17C2×D412yes—
71C42×C17#4111yescharacteristic
72C22⋊Dic17—42no—
73C4⋊Dic17—22no—
74C4⋊Dic17—22no—
75C4⋊Dic17—22no—
76C4⋊Dic17—22no—
77#63225—42no—
78#63225—42no—
79C4×Dic17—42no—
80C2×#3622—24no—
81Dic68—82no—
82#10216—171nomaximal, Sylow
83C23×C17—41no—
84C23×C17#12711yescharacteristic
85Q8×C17—42no—
86D4×C17—44no—
87D4×C17—42no—
88D4×C17—82no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—42no—
92C2×C4×C17—42no—
93C2×C4×C17—41no—
94C2×C4×C17—82no—
95C2×C4×C17—81no—
96C2×C4×C17—81no—
97C2×C4×C17#12012yes—
98C2×C4×C17#12011yescharacteristic
99C2×C4×C17#12112yes—
100C2×C4×C17#12111yescharacteristic
101C2×Dic17—42no—
102C2×Dic17—42no—
103Dic34—42no—
104Dic34—42no—
105Dic34—82no—
106C8×C17—42no—
107#3622—44no—
108#3255—171no—
109#3235—172no—
110#1963D1711yescharacteristic
111#1506—172no—
112#1307—171no—
113C22×C17—21no—
114C22×C17—22no—
115C22×C17—81no—
116C22×C17—82no—
117C22×C17#39211yescharacteristic
118C4×C17—21no—
119C4×C17—22no—
120C4×C17—22no—
121C4×C17—82no—
122C4×C17—81no—
123C4×C17#45311yescharacteristic
124C4×C17#45411yescharacteristic
125Dic17—82no—
126Dic17—82no—
127#533—172no—
128#532C2×D1711yescharacteristic
129#501—342no—
130#490—342no—
131#482—344no—
132#476—342no—
133#475—342no—
134#474—342no—
135#470—342no—
136#462—342no—
137#432—172no—
138#423C2×D1711yescharacteristic
139C2×#104—22no—
140#376C2×D1711yescharacteristic
141#328—344no—
142C2×C17—41no—
143C2×C17—161no—
144C2×C17#200611yescharacteristic
145C2×C17#200912yes—
146C2×#41—21no—
147C2×Q16—342no—
148C2×M16C22⋊D1712yes—
149C4⋊Q8—172no—
150C4⋊Q8—172no—
151C4⋊Q8D6811yescharacteristic
152#127D6811yescharacteristic
153#125—342no—
154#124—21no—
155C22⋊Q8—342no—
156C22⋊Q8—342no—
157#121—22no—
158C4×Q8—342no—
159C4×Q8—342no—
160C4×D4—22no—
161#117—342no—
162C2×C42—21no—
163C2×C42C22×D1711yescharacteristic
164#107—344no—
165#106—344no—
166#106—342no—
167C4⋊C8—22no—
168C4⋊C8—342no—
169#104—44no—
170#103—344no—
171#102—344no—
172#102—344no—
173C22⋊C8—174no—
174#97—342no—
175#95—22no—
176C17#1021611yescharacteristic, complemented, Sylow
177#41—42no—
178#41—42no—
179C2×Q8—21no—
180C2×Q8—342no—
181C2×Q8—342no—
182C2×D4—22no—
183C2×D4—21no—
184C2×D4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4D4×D1712yes—
188C22×C4C2×C22⋊D1711yescharacteristic
189Q16—1362no—
190M16—42no—
191C2×C8—22no—
192C2×C8—344no—
193C4⋊C4—22no—
194C4⋊C4—342no—
195C4⋊C4—342no—
196C4⋊C4—342no—
197C4⋊C4—342no—
198C4⋊C4—682no—
199C4⋊C4—682no—
200C22⋊C4—42no—
201C22⋊C4—682no—
202C42—22no—
203C42—41no—
204C42—682no—
205C42C2×D6811yescharacteristic
206C42#6325211yescharacteristic
207C42D4×D1712yes—
208C23—41no—
209C23#1058762611yescharacteristic
210Q8—42no—
211Q8—682no—
212Q8—682no—
213Q8—1362no—
214D4—42no—
215D4—44no—
216D4—82no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—82no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—682no—
226C2×C4—682no—
227C2×C4#1058756812yes—
228C2×C4#1058757012yes—
229C2×C4#1058761611yescharacteristic
230C2×C4#1058762311yescharacteristic
231C8—42no—
232C8—684no—
233C22—21no—
234C22—22no—
235C22—81no—
236C22—82no—
237C22#1176271811yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—82no—
242C4—81no—
243C4—1362no—
244C4—1362no—
245C4#1176297611yescharacteristic
246C4#1176298111yescharacteristic
247C2—41no—
248C2—161no—
249C2#1452982511yescharacteristic
250C2#1452984512yes—
subgroupG/H
centerC22#11762718
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1963C2
socleC22×C17#392
prime radicalC17×#532C22
hypercenter#1963D17
hypocenterC17#10216
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #14540178C2semidirect
3. #14527295C2semidirect
4. #14526695C2semidirect
176. C17#10216semidirect

Maximal subgroups

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

subgroupindex
#145401782
#145399782
#145272952
#145266952
C17×#19632
#1021617