Finite Group Databasebeta

← #16937325

Subgroups — #16937325

Order 4352.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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#14534754C211yesmaximal, characteristic
2#14528871C212yesmaximal
3#14527051C211yesmaximal, characteristic
4#14526664C212yesmaximal
5C17×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic17C2211yescharacteristic
7#11762751—22no—
8#11762743—22no—
9#11762682—22no—
10#11762669C2212yes—
11C2×#10587502—22no—
12C2×#10587502C2211yescharacteristic
13#11762572—22no—
14#11762572—22no—
15C2×C17×C22⋊C8C2212yes—
16C2×C17×#95C2211yescharacteristic
17C23×C4×C17D412yes—
18C23×C4×C17C2311yescharacteristic
19C23×Dic17—21no—
20C23×Dic17—21no—
21C22×C8×C17—22no—
22C2×C22⋊Dic17—22no—
23C2×C4⋊Dic17—21no—
24C2×C4⋊Dic17—22no—
25C2×C4⋊Dic17—22no—
26C2×C4⋊Dic17D412yes—
27C2×C4⋊Dic17D412yes—
28C2×C4⋊Dic17Q812yes—
29C2×#63225—22no—
30C2×#63225—22no—
31C17×C22⋊C8—22no—
32C17×C22⋊C8—22no—
33C17×#95—22no—
34#10587502—22no—
35#10587502—22no—
36#10587502—22no—
37#10587502—22no—
38#10587502—44no—
39C24×C17C2×D411yescharacteristic
40C22×C4×C17—22no—
41C22×C4×C17—22no—
42C22×C4×C17—22no—
43C22×C4×C17—42no—
44C22×C4×C17—42no—
45C22×C4×C17—42no—
46C22×C4×C17C2×D412yes—
47C22×C4×C17C2×Q811yescharacteristic
48C22×C4×C17#4112yes—
49C22×C4×C17#4111yescharacteristic
50C22×Dic17—22no—
51C22×Dic17—22no—
52C22×Dic17—22no—
53C22×Dic17—22no—
54C22×Dic17—41no—
55C22×Dic17—42no—
56C22×Dic17—41no—
57C22×Dic17—41no—
58C22×Dic17—41no—
59C22×Dic17—42no—
60C22×Dic17—42no—
61C22×Dic17—42no—
62C2×C8×C17—42no—
63C2×C8×C17—42no—
64C2×C8×C17—42no—
65C22⋊Dic17—42no—
66C22⋊Dic17—42no—
67C4⋊Dic17—24no—
68C4⋊Dic17—42no—
69C4⋊Dic17—42no—
70C4⋊Dic17—42no—
71#63225—82no—
72#63225—82no—
73#10346—171nomaximal, Sylow
74C23×C17—21no—
75C23×C17—21no—
76C23×C17—22no—
77C23×C17#12011yescharacteristic
78C23×C17C22⋊Q811yescharacteristic
79C23×C17#12411yescharacteristic
80C23×C17#13512yes—
81C23×C17AGL(1,ℤ/8)12yes—
82C2×C4×C17—22no—
83C2×C4×C17—22no—
84C2×C4×C17—41no—
85C2×C4×C17—42no—
86C2×C4×C17—41no—
87C2×C4×C17—44no—
88C2×C4×C17—42no—
89C2×C4×C17—42no—
90C2×C4×C17—42no—
91C2×C4×C17—82no—
92C2×C4×C17C22⋊Q812yes—
93C2×C4×C17#12412yes—
94C2×Dic17—44no—
95C2×Dic17—42no—
96C2×Dic17—42no—
97C2×Dic17—42no—
98C2×Dic17—42no—
99C2×Dic17—42no—
100C2×Dic17—42no—
101C2×Dic17—42no—
102C2×Dic17—42no—
103C2×Dic17—44no—
104C2×Dic17—82no—
105C2×Dic17—81no—
106C2×Dic17—82no—
107C2×Dic17—81no—
108C2×Dic17—81no—
109C2×Dic17—81no—
110C8×C17—82no—
111#2646—171no—
112#1823—172no—
113#1445—171no—
114#1294—172no—
115#1280D1711yescharacteristic
116C22×C17—22no—
117C22×C17—22no—
118C22×C17—22no—
119C22×C17—22no—
120C22×C17—21no—
121C22×C17—21no—
122C22×C17—21no—
123C22×C17—21no—
124C22×C17#39311yescharacteristic
125C22×C17#44912yes—
126C22×C17#45511yescharacteristic
127C22×C17#45611yescharacteristic
128C22×C17#45812yes—
129C22×C17#47812yes—
130C22×C17#48811yescharacteristic
131C22×C17#49011yescharacteristic
132C4×C17—22no—
133C4×C17—22no—
134C4×C17—82no—
135Dic17—82no—
136Dic17—82no—
137Dic17—82no—
138Dic17—82no—
139C22×C4⋊C4—171no—
140C2×C22⋊C8C2×D1712yes—
141#400—342no—
142#398—342no—
143#385—342no—
144#380—172no—
145C2×#95—171no—
146C2×#95—342no—
147C2×#95C2×D1711yescharacteristic
148#340—342no—
149#340—342no—
150C2×C17—21no—
151C2×C17—22no—
152C2×C17—21no—
153C2×C17#160912yes—
154C2×C17#161212yes—
155C2×C17#202511yescharacteristic
156C2×C17#202811yescharacteristic
157C2×C17#203011yescharacteristic
158C23×C4—341no—
159C23×C4—341no—
160C23×C4D6812yes—
161C23×C4C22×D1711yescharacteristic
162C22×C8—22no—
163C2×C4⋊C4—172no—
164C2×C4⋊C4—172no—
165C2×C4⋊C4—172no—
166C2×C4⋊C4—342no—
167C2×C4⋊C4—342no—
168C2×C4⋊C4—341no—
169C2×C4⋊C4—342no—
170C2×C4⋊C4—342no—
171C2×C22⋊C4—342no—
172C22⋊C8—22no—
173C22⋊C8—22no—
174#95—22no—
175#95—342no—
176#95—342no—
177#95—342no—
178#95—342no—
179#95—684no—
180C17#1034611yescharacteristic, complemented, Sylow
181C24C2×D6811yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—342no—
189C22×C4—342no—
190C22×C4—342no—
191C22×C4—342no—
192C22×C4—681no—
193C22×C4—682no—
194C22×C4—681no—
195C22×C4—681no—
196C22×C4—681no—
197C22×C4—682no—
198C22×C4—682no—
199C22×C4—682no—
200C22×C4#6325212yes—
201C22×C4D4×D1712yes—
202C22×C4#6325411yescharacteristic
203C22×C4Q8×D1711yescharacteristic
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C4⋊C4—344no—
208C4⋊C4—682no—
209C4⋊C4—682no—
210C4⋊C4—682no—
211C4⋊C4—1362no—
212C4⋊C4—1362no—
213C22⋊C4—682no—
214C22⋊C4—682no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1058756111yescharacteristic
219C23#1058756811yescharacteristic
220C23#1058758311yescharacteristic
221C23#1058759012yes—
222C23#1058759412yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—684no—
234C2×C4—682no—
235C2×C4—682no—
236C2×C4—682no—
237C2×C4—682no—
238C2×C4—682no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4—682no—
242C2×C4—684no—
243C2×C4—1362no—
244C2×C4—1361no—
245C2×C4—1362no—
246C2×C4—1361no—
247C2×C4—1361no—
248C2×C4—1361no—
249C2×C4#1058757112yes—
250C2×C4#1058758212yes—
251C8—82no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—22no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22#1176272211yescharacteristic
261C22#1176295612yes—
262C22#1176298911yescharacteristic
263C22#1176299411yescharacteristic
264C22#1176300012yes—
265C22#1176311012yes—
266C22#1176316411yescharacteristic
267C22#1176317411yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—1362no—
272C4—1362no—
273C4—1362no—
274C4—1362no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#1452778312yes—
279C2#1452780012yes—
280C2#1452993111yescharacteristic
281C2#1452994611yescharacteristic
282C2#1452995211yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1280C2
socleC23×C17#120
prime radicalC24×C17C2×D4
hypercenter#1280D17
hypocenterC17#10346
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
180. C17#10346semidirect

Maximal subgroups

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

subgroupindex
#145347542
#145288712
#145270512
#145266642
C17×#12802
#1034617