Finite Group Databasebeta

← #16935193

Subgroups — #16935193

Order 4352.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#14538819C212yesmaximal
2#14532077C211yesmaximal, characteristic
3#14527212C212yesmaximal
4#14526613C211yesmaximal, characteristic
5C17×#1995C211yesmaximal, characteristic
6C2×C4×Dic34C2212yes—
7#11763142—22no—
8#11763101—22no—
9#11763016—22no—
10#11762964—22no—
11C4×#63231—24no—
12#11762862C2212yes—
13#11762741—22no—
14#11762730—22no—
15C4×C4⋊Dic17—22no—
16#11762539—24no—
17C17×#533C2211yescharacteristic
18C17×#423C2211yescharacteristic
19C17×#376C2211yescharacteristic
20C17×#339—22no—
21C22×Dic34D412yes—
22C2×M16×C17—21no—
23C17×C4⋊Q8D412yes—
24C17×#125—21no—
25C17×C22⋊Q8—22no—
26C4×Q8×C17—22no—
27C17×#117—21no—
28C2×C42×C17D412yes—
29C2×C42×C17C2311yescharacteristic
30C2×#63231—24no—
31C2×C4⋊Dic17—24no—
32C2×C4⋊Dic17D412yes—
33C2×#63225—22no—
34C2×C4×Dic17—22no—
35C4×Dic34—22no—
36C4×Dic34—22no—
37C4×Dic34—22no—
38C4×Dic34—22no—
39C17×C4⋊C8—22no—
40C17×#95—22no—
41#10587506—24no—
42#10587502—22no—
43#10587502—22no—
44C22⋊#3622—22no—
45#10587481—24no—
46#10587478—24no—
47C4⋊#3622—22no—
48C4×#3622D414yes—
49C2×Q8×C17—22no—
50C22×C4×C17—22no—
51C22×C4×C17C2×D412yes—
52C22×C4×C17C2×D411yescharacteristic
53C22×Dic17—22no—
54C22×Dic17—22no—
55C2×Dic34—22no—
56C2×Dic34—22no—
57C2×Dic34—44no—
58M16×C17—42no—
59C2×C8×C17—41no—
60C4⋊C4×C17—22no—
61C4⋊C4×C17—22no—
62C4⋊C4×C17—42no—
63C22⋊C4×C17—41no—
64C42×C17—22no—
65C42×C17—41no—
66C42×C17Q1614yescomplemented
67C42×C17C2×D411yescharacteristic
68C42×C17C2×D412yes—
69C42×C17#4111yescharacteristic
70#63231—48no—
71C4⋊Dic17—22no—
72C4⋊Dic17—22no—
73C4⋊Dic17—48no—
74#63225—42no—
75#63225—42no—
76C4×Dic17—42no—
77C4×Dic17—42no—
78C2×#3622—24no—
79#10017—171nomaximal, Sylow
80C23×C17#12011yescharacteristic
81Q8×C17—44no—
82C2×C4×C17—24no—
83C2×C4×C17—42no—
84C2×C4×C17—44no—
85C2×C4×C17—42no—
86C2×C4×C17#12012yes—
87C2×C4×C17#12112yes—
88C2×C4×C17#12111yescharacteristic
89C2×C4×C17#12711yescharacteristic
90C2×C4×C17C2×Q1612yes—
91C2×C4×C17#13712yes—
92C2×Dic17—24no—
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17—44no—
96C2×Dic17—42no—
97Dic34—24no—
98Dic34—24no—
99Dic34—42no—
100Dic34—42no—
101C8×C17—81no—
102#3622—44no—
103#3104—172no—
104#2399—171no—
105#1995D1711yescharacteristic
106#1487—172no—
107#1274—171no—
108C22×C17—22no—
109C22×C17#39211yescharacteristic
110C22×C17#45112yes—
111C4×C17—22no—
112C4×C17—22no—
113C4×C17—44no—
114C4×C17—82no—
115C4×C17#46212yes—
116C4×C17#49411yescharacteristic
117C4×C17#49711yescharacteristic
118Dic17—44no—
119Dic17—82no—
120#533C2×D1711yescharacteristic
121C2×C4×Q8—172no—
122#484—342no—
123#477—342no—
124#462—342no—
125#451—342no—
126C4×Q16—344no—
127#431—172no—
128#423C2×D1711yescharacteristic
129#398—342no—
130#395—342no—
131C4×C4⋊C4—342no—
132#376C2×D1711yescharacteristic
133#339—22no—
134Q8⋊C8—344no—
135C2×C17—22no—
136C2×C17#201012yes—
137C2×C17#201611yescharacteristic
138C22×Q8—172no—
139C2×Q16—344no—
140C2×M16—21no—
141C4⋊Q8D6812yes—
142#125—21no—
143C22⋊Q8—22no—
144C4×Q8—22no—
145C4×Q8—342no—
146C4×Q8—342no—
147C4×Q8—342no—
148C4×Q8—342no—
149#117—21no—
150C2×C4⋊C4—172no—
151C2×C4⋊C4—344no—
152C2×C4⋊C4—342no—
153C2×C42—342no—
154C2×C42C22⋊D1712yes—
155C2×C42C22×D1711yescharacteristic
156#107—344no—
157C4⋊C8—22no—
158C4⋊C8—342no—
159#103—344no—
160#103—344no—
161C22⋊C8—342no—
162C4×C8—174no—
163#95—22no—
164#95—342no—
165#95—342no—
166C17#1001711yescharacteristic, complemented, Sylow
167C2×Q8—22no—
168C2×Q8—342no—
169C2×Q8—342no—
170C2×Q8—684no—
171C22×C4—22no—
172C22×C4—342no—
173C22×C4—342no—
174C22×C4D4×D1712yes—
175C22×C4C2×C22⋊D1711yescharacteristic
176Q16—688no—
177M16—42no—
178C2×C8—41no—
179C2×C8—344no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—342no—
184C4⋊C4—342no—
185C4⋊C4—688no—
186C4⋊C4—682no—
187C4⋊C4—682no—
188C22⋊C4—41no—
189C42—22no—
190C42—41no—
191C42—682no—
192C42—682no—
193C42#6323114yescomplemented
194C42C2×D6811yescharacteristic
195C42#6325211yescharacteristic
196C42D4×D1712yes—
197C23#1058762311yescharacteristic
198Q8—44no—
199Q8—344no—
200Q8—344no—
201Q8—682no—
202Q8—682no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—344no—
208C2×C4—682no—
209C2×C4—682no—
210C2×C4—684no—
211C2×C4—682no—
212C2×C4#1058756812yes—
213C2×C4#1058757012yes—
214C2×C4#1058761611yescharacteristic
215C2×C4#1058762611yescharacteristic
216C2×C4C2×#6323112yes—
217C2×C4#1058763712yes—
218C8—81no—
219C8—684no—
220C22—22no—
221C22#1176271811yescharacteristic
222C22#1176296412yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—82no—
227C4—684no—
228C4—1362no—
229C4#1176301912yes—
230C4#1176318811yescharacteristic
231C4#1176320411yescharacteristic
232C2—22no—
233C2#1452985012yes—
234C2#1452988311yescharacteristic
subgroupG/H
centerC2×C4#10587626
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1995C2
socleC22×C17#392
prime radicalC23×C17#120
hypercenter#1995D17
hypocenterC17#10017
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
66. C42×C17Q16semidirect
166. C17#10017semidirect
193. C42#63231semidirect

Maximal subgroups

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

subgroupindex
#145388192
#145320772
#145272122
#145266132
C17×#19952
#1001717