Finite Group Databasebeta

← #16935319

Subgroups — #16935319

Order 4352.

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

normal subgroups only

This group has 476 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#14539308C211yesmaximal, characteristic
2#14538823C212yesmaximal
3#14527186C212yesmaximal
4#14526615C211yesmaximal, characteristic
5C17×#1985C211yesmaximal, characteristic
6#11763366C2212yes—
7#11763218—22no—
8#11763218—22no—
9#11763144—22no—
10#11763104—22no—
11#11763019—22no—
12#11762965—22no—
13C4×#63231—24no—
14#11762862C2212yes—
15#11762847—22no—
16#11762539—24no—
17C2×C4×Q8×C17C2211yescharacteristic
18C2×C17×C4⋊C8C2211yescharacteristic
19C2×C17×#97C2211yescharacteristic
20C17×#336—22no—
21C22×Q8×C17D411yescharacteristic
22C22×C8×C17—21no—
23C22×C8×C17D412yes—
24C4×Q8×C17—22no—
25C4×Q8×C17—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17D411yescharacteristic
28C2×C42×C17—21no—
29C2×C42×C17C2311yescharacteristic
30C2×#63231—24no—
31#10587612—22no—
32#10587610—22no—
33#10587610—22no—
34#10587556—22no—
35#10587555D412yes—
36#10587555D412yes—
37C4×Dic34—22no—
38C4×Dic34—22no—
39C17×C4⋊C8—22no—
40C17×#97—22no—
41#10587506—24no—
42C22⋊#3622—22no—
43#10587489—22no—
44#10587489—22no—
45#10587488—24no—
46#10587481—24no—
47#10587478—24no—
48C4⋊#3622—22no—
49C4×#3622D414yes—
50C2×Q8×C17—22no—
51C2×Q8×C17—42no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17C2×D411yescharacteristic
55C22×C4×C17C2×D411yescharacteristic
56C22×C4×C17#4111yescharacteristic
57C2×Dic34—22no—
58C2×Dic34—22no—
59C2×C8×C17—22no—
60C2×C8×C17—22no—
61C2×C8×C17—41no—
62C2×C8×C17—42no—
63C2×C8×C17Q1614yescomplemented
64C4⋊C4×C17—22no—
65C4⋊C4×C17—42no—
66C42×C17—41no—
67C42×C17—41no—
68C42×C17C2×D412yes—
69C42×C17C2×D412yes—
70C22⋊Dic17—42no—
71#63231—48no—
72C4⋊Dic17—22no—
73C4⋊Dic17—22no—
74C4⋊Dic17—22no—
75C4⋊Dic17—22no—
76#63225—42no—
77#63225—42no—
78C4×Dic17—42no—
79C2×#3622—24no—
80#10037—171nomaximal, Sylow
81C23×C17#12111yescharacteristic
82Q8×C17—24no—
83Q8×C17—42no—
84C2×C4×C17—22no—
85C2×C4×C17—41no—
86C2×C4×C17—41no—
87C2×C4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—42no—
90C2×C4×C17—41no—
91C2×C4×C17#12012yes—
92C2×C4×C17#12011yescharacteristic
93C2×C4×C17#12112yes—
94C2×C4×C17#12711yescharacteristic
95C2×C4×C17C2×Q1612yes—
96C2×C4×C17#13712yes—
97C2×Dic17—42no—
98C2×Dic17—42no—
99Dic34—44no—
100Dic34—44no—
101C8×C17—24no—
102C8×C17—81no—
103#3622—44no—
104#3162—171no—
105#3104—172no—
106#1985D1711yescharacteristic
107#1481—172no—
108#1275—171no—
109C22×C17—21no—
110C22×C17—21no—
111C22×C17#39211yescharacteristic
112C22×C17#46212yes—
113C4×C17—22no—
114C4×C17—22no—
115C4×C17—42no—
116C4×C17—81no—
117C4×C17#45112yes—
118C4×C17#49411yescharacteristic
119C4×C17#49711yescharacteristic
120Dic17—82no—
121Dic17—82no—
122#533—172no—
123C2×C4×Q8C2×D1711yescharacteristic
124#501—342no—
125#501—342no—
126#484—342no—
127#477—342no—
128#462—342no—
129#451—342no—
130C4×Q16—344no—
131#431—172no—
132#427—342no—
133C2×C4⋊C8C2×D1711yescharacteristic
134C2×#97C2×D1711yescharacteristic
135#336—22no—
136Q8⋊C8—344no—
137C2×C17—22no—
138C2×C17#201011yescharacteristic
139C2×C17#201611yescharacteristic
140C2×C17#201711yescharacteristic
141C22×Q8D6811yescharacteristic
142C2×Q16—344no—
143C22×C8—21no—
144C22×C8C22⋊D1712yes—
145C4⋊Q8—172no—
146C4⋊Q8—172no—
147#125—342no—
148C22⋊Q8—342no—
149C22⋊Q8—342no—
150C4×Q8—22no—
151C4×Q8—22no—
152C4×Q8—342no—
153C4×Q8—342no—
154#117—342no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4D6811yescharacteristic
157C2×C42—21no—
158C2×C42C22×D1711yescharacteristic
159#107—344no—
160#107—342no—
161#107—342no—
162#106—344no—
163C4⋊C8—22no—
164C4⋊C8—342no—
165#103—344no—
166#103—344no—
167C22⋊C8—342no—
168#97—22no—
169C4×C8—174no—
170C17#1003711yescharacteristic, complemented, Sylow
171C2×Q8—22no—
172C2×Q8—42no—
173C2×Q8—342no—
174C2×Q8—342no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C2×D6811yescharacteristic
178C22×C4#6325211yescharacteristic
179C22×C4C2×C22⋊D1711yescharacteristic
180Q16—688no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—41no—
184C2×C8—42no—
185C2×C8—344no—
186C2×C8#6323114yescomplemented
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—342no—
190C4⋊C4—342no—
191C4⋊C4—342no—
192C4⋊C4—342no—
193C4⋊C4—682no—
194C4⋊C4—682no—
195C22⋊C4—682no—
196C42—41no—
197C42—41no—
198C42—682no—
199C42D4×D1712yes—
200C42D4×D1712yes—
201C23#1058761611yescharacteristic
202Q8—24no—
203Q8—42no—
204Q8—684no—
205Q8—684no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—682no—
214C2×C4—682no—
215C2×C4#1058756812yes—
216C2×C4#1058757012yes—
217C2×C4#1058762311yescharacteristic
218C2×C4#1058762611yescharacteristic
219C2×C4C2×#6323112yes—
220C2×C4#1058763712yes—
221C8—24no—
222C8—81no—
223C8—684no—
224C22—21no—
225C22—21no—
226C22#1176271811yescharacteristic
227C22#1176301912yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—81no—
232C4—1362no—
233C4—1362no—
234C4#1176296412yes—
235C4#1176318811yescharacteristic
236C4#1176320411yescharacteristic
237C2—22no—
238C2#1452985111yescharacteristic
239C2#1452988311yescharacteristic
240C2#1452988811yescharacteristic
subgroupG/H
centerC2×C4#10587626
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1985C2
socleC22×C17#392
prime radicalC23×C17#121
hypercenter#1985D17
hypocenterC17#10037
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
63. C2×C8×C17Q16semidirect
170. C17#10037semidirect
186. C2×C8#63231semidirect

Maximal subgroups

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

subgroupindex
#145393082
#145388232
#145271862
#145266152
C17×#19852
#1003717