Finite Group Databasebeta

← #16937562

Subgroups — #16937562

Order 4352.

414 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 73 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#14534449C211yesmaximal, characteristic
2#14528881C212yesmaximal
3#14528859C211yesmaximal, characteristic
4#14526638C212yesmaximal
5C17×#1306C211yesmaximal, characteristic
6C2×#10587612C2211yescharacteristic
7#11762745—21no—
8#11762721—21no—
9#11762713—22no—
10#11762696—22no—
11#11762672C2211yescharacteristic
12C4×C22⋊Dic17C2212yes—
13#11762575—21no—
14#11762575—21no—
15#11762570—22no—
16#11762570—22no—
17C17×#407C2212yes—
18C17×#381C2211yescharacteristic
19C23×C4×C17C2311yescharacteristic
20C22×Dic34—21no—
21C2×M16×C17—22no—
22C2×C22⋊C4×C17D411yescharacteristic
23C2×C22⋊C4×C17D411yescharacteristic
24C2×C22⋊Dic17—22no—
25C2×C22⋊Dic17—21no—
26C2×C22⋊Dic17—21no—
27#10587612—22no—
28#10587612—22no—
29C2×C4⋊Dic17—21no—
30C2×C4⋊Dic17Q812yescomplemented
31C2×#63225—22no—
32C2×C4×Dic17—21no—
33C2×C4×Dic17D412yes—
34C2×C4×Dic17D412yes—
35C17×C22⋊C8—22no—
36C17×C22⋊C8—22no—
37C17×#95—22no—
38#10587502—21no—
39#10587502—22no—
40#10587502—21no—
41#10587502—22no—
42#10587502—22no—
43C24×C17C2×D411yescharacteristic
44C22×C4×C17—21no—
45C22×C4×C17—21no—
46C22×C4×C17—41no—
47C22×C4×C17—41no—
48C22×C4×C17C2×D412yes—
49C22×C4×C17C2×Q811yescharacteristic
50C22×C4×C17#4112yes—
51C22×C4×C17#4111yescharacteristic
52C22×Dic17—22no—
53C22×Dic17—22no—
54C22×Dic17—22no—
55C22×Dic17—41no—
56C2×Dic34—44no—
57C2×Dic34—81no—
58M16×C17—42no—
59M16×C17—42no—
60C2×C8×C17—42no—
61C22⋊C4×C17—41no—
62C22⋊C4×C17—41no—
63C22⋊Dic17—44no—
64C22⋊Dic17—41no—
65C22⋊Dic17—41no—
66C22⋊Dic17—41no—
67C22⋊Dic17—41no—
68C4⋊Dic17—24no—
69C4⋊Dic17—81no—
70#63225—44no—
71C4×Dic17—42no—
72C4×Dic17—42no—
73C4×Dic17—42no—
74#10387—171nomaximal, Sylow
75C23×C17—21no—
76C23×C17—21no—
77C23×C17—42no—
78C23×C17#12011yescharacteristic
79C23×C17C22⋊Q811yescharacteristic
80C23×C17#12411yescharacteristic
81C2×C4×C17—22no—
82C2×C4×C17—22no—
83C2×C4×C17—41no—
84C2×C4×C17—42no—
85C2×C4×C17—41no—
86C2×C4×C17—42no—
87C2×C4×C17—42no—
88C2×C4×C17—41no—
89C2×C4×C17—41no—
90C2×C4×C17C22⋊Q812yes—
91C2×C4×C17#12412yes—
92C2×Dic17—24no—
93C2×Dic17—42no—
94C2×Dic17—42no—
95C2×Dic17—42no—
96C2×Dic17—42no—
97C2×Dic17—42no—
98C2×Dic17—42no—
99C2×Dic17—82no—
100C2×Dic17—81no—
101C2×Dic17—82no—
102Dic34—84no—
103C8×C17—82no—
104#2607—171no—
105#1826—172no—
106#1820—171no—
107#1306D1711yescharacteristic
108#1284—172no—
109C22×C17—22no—
110C22×C17—21no—
111C22×C17—21no—
112C22×C17—22no—
113C22×C17—22no—
114C22×C17—81no—
115C22×C17—81no—
116C22×C17#39311yescharacteristic
117C22×C17#45811yescharacteristic
118C22×C17#45811yescharacteristic
119C4×C17—22no—
120C4×C17—22no—
121C4×C17—81no—
122C4×C17—81no—
123Dic17—44no—
124Dic17—82no—
125Dic17—82no—
126Dic17—161no—
127C2×#117—171no—
128#407C2×D1712yes—
129#399—341no—
130#393—341no—
131#391—342no—
132#387—342no—
133#381—171no—
134#381C2×D1711yescharacteristic
135C4×C22⋊C4—172no—
136#342—341no—
137#342—341no—
138#339—342no—
139#339—342no—
140C2×C17—21no—
141C2×C17—21no—
142C2×C17—41no—
143C2×C17—41no—
144C2×C17#203011yescharacteristic
145C2×C17#203112yes—
146C22×Q8—341no—
147C23×C4C22×D1711yescharacteristic
148C2×M16—22no—
149#117—342no—
150#117—342no—
151C2×C4⋊C4—172no—
152C2×C4⋊C4—342no—
153C2×C4⋊C4—341no—
154C2×C22⋊C4—341no—
155C2×C22⋊C4—342no—
156C2×C22⋊C4—341no—
157C2×C22⋊C4D6811yescharacteristic
158C2×C22⋊C4D6811yescharacteristic
159C2×C42—172no—
160C2×C42—172no—
161C2×C42—341no—
162C22⋊C8—22no—
163C22⋊C8—22no—
164#95—22no—
165#95—341no—
166#95—342no—
167#95—341no—
168#95—342no—
169#95—342no—
170C17#1038711yescharacteristic, complemented, Sylow
171C24C2×D6811yescharacteristic
172C2×Q8—684no—
173C2×Q8—1361no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—342no—
179C22×C4—342no—
180C22×C4—342no—
181C22×C4—681no—
182C22×C4#6325212yes—
183C22×C4D4×D1712yes—
184C22×C4#6325411yescharacteristic
185C22×C4Q8×D1711yescharacteristic
186M16—42no—
187M16—42no—
188C2×C8—42no—
189C4⋊C4—344no—
190C4⋊C4—684no—
191C4⋊C4—1361no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—684no—
195C22⋊C4—681no—
196C22⋊C4—681no—
197C22⋊C4—681no—
198C22⋊C4—681no—
199C42—682no—
200C42—682no—
201C42—682no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23#1058756111yescharacteristic
206C23#1058756811yescharacteristic
207C23#1058758311yescharacteristic
208Q8—1364no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—344no—
219C2×C4—682no—
220C2×C4—682no—
221C2×C4—682no—
222C2×C4—682no—
223C2×C4—682no—
224C2×C4—682no—
225C2×C4—1361no—
226C2×C4—1362no—
227C2×C4—1362no—
228C2×C4#1058757112yes—
229C2×C4#1058758212yes—
230C8—82no—
231C22—22no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—22no—
236C22—81no—
237C22—81no—
238C22#1176272211yescharacteristic
239C22#1176300011yescharacteristic
240C22#1176300011yescharacteristic
241C4—22no—
242C4—22no—
243C4—81no—
244C4—81no—
245C4—2721no—
246C4—684no—
247C4—1362no—
248C4—1362no—
249C2—21no—
250C2—21no—
251C2—41no—
252C2—41no—
253C2#1452995211yescharacteristic
254C2#1452995912yes—
subgroupG/H
centerC22#11762722
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1306C2
socleC22×C17#393
prime radicalC24×C17C2×D4
hypercenter#1306D17
hypocenterC17#10387
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
30. C2×C4⋊Dic17Q8semidirect
170. C17#10387semidirect

Maximal subgroups

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

subgroupindex
#145344492
#145288812
#145288592
#145266382
C17×#13062
#1038717