Finite Group Databasebeta

← #16937397

Subgroups — #16937397

Order 4352.

400 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 91 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#14537056C211yesmaximal, characteristic
2#14529758C212yesmaximal
3#14526666C212yesmaximal
4#14526665C211yesmaximal, characteristic
5C17×#1960C211yesmaximal, characteristic
6C2×#10587474C2212yes—
7#11762751—22no—
8#11762748—21no—
9#11762730—22no—
10#11762729—21no—
11#11762675C2212yes—
12#11762571—22no—
13#11762571—22no—
14C2×C17×C4⋊Q8C2211yescharacteristic
15C2×C17×#103—21no—
16C2×C17×#103—21no—
17C2×C17×#97C2211yescharacteristic
18C17×#382C2211yescharacteristic
19C22×Q8×C17—21no—
20C22×Dic34—21no—
21C22×C8×C17—21no—
22C17×C4⋊Q8—22no—
23C17×C4⋊Q8—21no—
24C17×C4⋊Q8Q812yescomplemented
25C2×C4⋊C4×C17—22no—
26C2×C4⋊C4×C17D411yescharacteristic
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C42×C17C2311yescharacteristic
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17D412yes—
31C2×C4⋊Dic17D412yes—
32C2×#63225—22no—
33C22×#3622—22no—
34C17×#103—42no—
35C17×#103—42no—
36C17×#97—22no—
37C17×#95—22no—
38#10587502—21no—
39#10587502—22no—
40#10587502—21no—
41#10587502—22no—
42#10587502—22no—
43#10587474—22no—
44#10587474—22no—
45C2×Q8×C17—22no—
46C2×Q8×C17—41no—
47C2×Q8×C17—41no—
48C2×Q8×C17—41no—
49C2×Q8×C17—41no—
50C2×Q8×C17—41no—
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17—41no—
54C22×C4×C17C2×D412yes—
55C22×C4×C17C2×D411yescharacteristic
56C22×Dic17—22no—
57C22×Dic17—22no—
58C2×Dic34—81no—
59C2×Dic34—82no—
60C2×C8×C17—22no—
61C2×C8×C17—41no—
62C2×C8×C17—41no—
63C4⋊C4×C17—24no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—42no—
67C42×C17C2×Q811yescharacteristic
68C42×C17#4111yescharacteristic
69C42×C17#4112yes—
70C4⋊Dic17—42no—
71C4⋊Dic17—42no—
72C4⋊Dic17—81no—
73#63225—82no—
74C2×#3622—24no—
75C2×#3622—42no—
76C2×#3622—42no—
77#10359—171nomaximal, Sylow
78C23×C17#12011yescharacteristic
79Q8×C17—42no—
80Q8×C17—42no—
81Q8×C17—81no—
82Q8×C17—81no—
83C2×C4×C17—21no—
84C2×C4×C17—21no—
85C2×C4×C17—22no—
86C2×C4×C17—22no—
87C2×C4×C17—42no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17—42no—
91C2×C4×C17—42no—
92C2×C4×C17—81no—
93C2×C4×C17—81no—
94C2×C4×C17C22⋊Q812yes—
95C2×C4×C17C22⋊Q811yescharacteristic
96C2×C4×C17#12412yes—
97C2×C4×C17#12411yescharacteristic
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—42no—
104Dic34—84no—
105C8×C17—42no—
106#3622—44no—
107#2844—171no—
108#1993—172no—
109#1960D1711yescharacteristic
110#1295—172no—
111#1295—171no—
112C22×C17#39311yescharacteristic
113C22×C17#45311yescharacteristic
114C22×C17#45411yescharacteristic
115C22×C17#45512yes—
116C22×C17#45612yes—
117C4×C17—21no—
118C4×C17—21no—
119C4×C17—22no—
120C4×C17—22no—
121C4×C17—81no—
122C4×C17—81no—
123C4×C17—82no—
124Dic17—82no—
125Dic17—82no—
126C2×C4⋊Q8C2×D1711yescharacteristic
127C2×#103—21no—
128C2×#103—21no—
129C2×#97—172no—
130C2×#97C2×D1711yescharacteristic
131#400—342no—
132#400—341no—
133#395—342no—
134#395—341no—
135#382—172no—
136#382C2×D1711yescharacteristic
137#340—342no—
138#340—342no—
139C2×C17#165911yescharacteristic
140C2×C17#166011yescharacteristic
141C2×C17#166412yes—
142C2×C17#202711yescharacteristic
143C2×C17#202812yes—
144C22×Q8—21no—
145C22×Q8—341no—
146C22×C8—21no—
147C22×C8—342no—
148C4⋊Q8—21no—
149C4⋊Q8—22no—
150C4⋊Q8Dic3412yescomplemented
151C2×C4⋊C4—22no—
152C2×C4⋊C4—172no—
153C2×C4⋊C4—172no—
154C2×C4⋊C4—342no—
155C2×C4⋊C4—341no—
156C2×C4⋊C4C22⋊D1711yescharacteristic
157C2×C4⋊C4C22⋊D1711yescharacteristic
158C2×C42C22×D1711yescharacteristic
159#103—42no—
160#103—42no—
161#97—22no—
162#97—342no—
163#97—342no—
164#95—22no—
165#95—342no—
166#95—341no—
167#95—341no—
168#95—342no—
169#95—342no—
170C17#1035911yescharacteristic, complemented, Sylow
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—1361no—
178C2×Q8—1362no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—342no—
183C22×C4—342no—
184C22×C4D4×D1712yes—
185C22×C4C2×C22⋊D1711yescharacteristic
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—344no—
190C2×C8—682no—
191C2×C8—682no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—682no—
197C4⋊C4—682no—
198C4⋊C4—1362no—
199C4⋊C4—1361no—
200C42C2×Dic3411yescharacteristic
201C42#6325211yescharacteristic
202C42#6325412yes—
203C23#1058762311yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—1364no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—682no—
221C2×C4—682no—
222C2×C4—682no—
223C2×C4—682no—
224C2×C4—682no—
225C2×C4—682no—
226C2×C4#1058756412yes—
227C2×C4#1058757112yes—
228C2×C4#1058761011yescharacteristic
229C2×C4#1058762211yescharacteristic
230C8—42no—
231C8—684no—
232C22#1176272111yescharacteristic
233C22#1176297611yescharacteristic
234C22#1176298111yescharacteristic
235C22#1176298512yes—
236C22#1176299012yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—82no—
244C4—1362no—
245C4—1362no—
246C2#1452808811yescharacteristic
247C2#1452809311yescharacteristic
248C2#1452811512yes—
249C2#1452994011yescharacteristic
250C2#1452994312yes—
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1960C2
socle, prime radicalC23×C17#120
hypercenter#1960D17
hypocenterC17#10359
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
24. C17×C4⋊Q8Q8semidirect
150. C4⋊Q8Dic34semidirect
170. C17#10359semidirect

Maximal subgroups

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

subgroupindex
#145370562
#145297582
#145266662
#145266652
C17×#19602
#1035917