Finite Group Databasebeta

← #16937566

Subgroups — #16937566

Order 4352.

594 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 75 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#14534454C211yesmaximal, characteristic, complemented
2#14528728C212yesmaximal
3#14526692C211yesmaximal, characteristic, complemented
4#14526636C212yesmaximal, complemented
5C17×#1782C211yesmaximal, characteristic
6C2×#10587508—22no—
7C2×#10587508—22no—
8#11762773C2212yes—
9#11762732—22no—
10#11762706—22no—
11#11762692—22no—
12C4×C22⋊Dic17C2212yes—
13C22×#41×C17C2211yescharacteristic
14C2×C17×#99—22no—
15C17×#381C2211yescharacteristic
16C17×#381C2211yescharacteristic
17C2×#41×C17—22no—
18C2×#41×C17—22no—
19C2×#41×C17—44no—
20C22×Q8×C17Q811yescharacteristic
21C22×D4×C17—21no—
22C22×D4×C17Q811yescharacteristic
23C23×C4×C17—21no—
24C23×C4×C17C2311yescharacteristic
25C2×C22⋊C4×C17—21no—
26C2×C22⋊C4×C17D412yes—
27C2×C22⋊Dic17—22no—
28C2×C4⋊Dic17—22no—
29C2×#63225—22no—
30C2×#63225—22no—
31C2×C4×Dic17D412yes—
32C2×C4×Dic17D412yes—
33C2×#63223—22no—
34C17×#99—44no—
35C17×#95—22no—
36C17×#95—22no—
37#10587508—44no—
38#10587508—44no—
39#10587502—22no—
40#10587502—22no—
41C22⋊#3622—22no—
42C22⋊#3622—22no—
43C24×C17—21no—
44C24×C17C2×D411yescharacteristic
45#41×C17—24no—
46#41×C17—24no—
47#41×C17—42no—
48#41×C17—42no—
49#41×C17—44no—
50#41×C17—44no—
51C2×Q8×C17—22no—
52C2×Q8×C17—42no—
53C2×D4×C17—24no—
54C2×D4×C17—22no—
55C2×D4×C17—42no—
56C2×D4×C17—42no—
57C2×D4×C17—41no—
58C2×D4×C17—41no—
59C22×C4×C17—21no—
60C22×C4×C17—22no—
61C22×C4×C17—42no—
62C22×C4×C17—42no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17—41no—
66C22×C4×C17C2×D412yes—
67C22×C4×C17C2×Q811yescharacteristic
68C22×C4×C17#4111yescharacteristic
69C22×C4×C17#4112yes—
70C22×Dic17—22no—
71C22×Dic17—22no—
72C22⋊C4×C17—42no—
73C22⋊C4×C17—42no—
74C22⋊Dic17—44no—
75C4⋊Dic17—44no—
76#63225—44no—
77#63225—82no—
78C4×Dic17—42no—
79C4×Dic17—42no—
80#63223—42no—
81#63223—42no—
82C2×#3622—42no—
83#10388—171nomaximal, Sylow
84C23×C17—22no—
85C23×C17—22no—
86C23×C17—42no—
87C23×C17—41no—
88C23×C17—41no—
89C23×C17—82no—
90C23×C17#12011yescharacteristic
91C23×C17C22⋊Q811yescharacteristic
92C23×C17#12411yescharacteristic
93Q8×C17—24no—
94Q8×C17—42no—
95D4×C17—24no—
96D4×C17—42no—
97D4×C17—44no—
98D4×C17—44no—
99C2×C4×C17—22no—
100C2×C4×C17—22no—
101C2×C4×C17—22no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—42no—
105C2×C4×C17—44no—
106C2×C4×C17—44no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—81no—
113C2×C4×C17—82no—
114C2×C4×C17C22⋊Q812yes—
115C2×C4×C17#12412yes—
116C2×Dic17—24no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120C2×Dic17—42no—
121C2×Dic17—42no—
122#3622—82no—
123#2608—171no—
124#1789—172no—
125#1782D1711yescharacteristic
126#1306—171no—
127#1284—172no—
128C22×C17—22no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—22no—
132C22×C17—22no—
133C22×C17—42no—
134C22×C17—82no—
135C22×C17—82no—
136C22×C17—82no—
137C22×C17—82no—
138C22×C17#39311yescharacteristic
139C22×C17B(4,𝔽2)12yes—
140C4×C17—22no—
141C4×C17—22no—
142C4×C17—42no—
143C4×C17—82no—
144C4×C17—161no—
145Dic17—44no—
146Dic17—82no—
147C22×#41C2×D1711yescharacteristic
148C2×#104—342no—
149C2×#104—342no—
150C2×#99—22no—
151#407—172no—
152#396—342no—
153#389—342no—
154#387—342no—
155#381C2×D1711yescharacteristic
156#381C2×D1711yescharacteristic
157C4×C22⋊C4—172no—
158C2×C17—22no—
159C2×C17—41no—
160C2×C17—41no—
161C2×C17—82no—
162C2×C17#202911yescharacteristic
163C2×C17#203112yes—
164C2×#41—22no—
165C2×#41—22no—
166C2×#41—44no—
167C22×Q8Dic3411yescharacteristic
168C22×D4—21no—
169C22×D4Dic3411yescharacteristic
170C23×C4—21no—
171C23×C4C22×D1711yescharacteristic
172C2×M16—342no—
173C2×C4⋊C4—342no—
174C2×C4⋊C4—342no—
175C2×C4⋊C4—342no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—342no—
178C2×C22⋊C4C22⋊D1712yes—
179C2×C42—172no—
180C2×C42—172no—
181#104—684no—
182#104—684no—
183#99—44no—
184C22⋊C8—342no—
185C22⋊C8—342no—
186#95—22no—
187#95—22no—
188#95—342no—
189#95—342no—
190C17#1038811yescharacteristic, complemented, Sylow
191C24—21no—
192C24C2×C22⋊D1711yescharacteristic
193#41—24no—
194#41—24no—
195#41—42no—
196#41—42no—
197#41—44no—
198#41—44no—
199C2×Q8—22no—
200C2×Q8—42no—
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—41no—
206C2×D4—41no—
207C22×C4—21no—
208C22×C4—22no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—41no—
214C22×C4—342no—
215C22×C4—342no—
216C22×C4C2×Dic3411yescharacteristic
217C22×C4#6325211yescharacteristic
218C22×C4D4×D1712yes—
219C22×C4#6325412yes—
220M16—682no—
221M16—682no—
222C2×C8—682no—
223C4⋊C4—684no—
224C4⋊C4—684no—
225C4⋊C4—1362no—
226C22⋊C4—42no—
227C22⋊C4—42no—
228C22⋊C4—684no—
229C42—682no—
230C42—682no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23—82no—
237C23#1058761011yescharacteristic
238C23#1058762211yescharacteristic
239C23#1058762311yescharacteristic
240Q8—24no—
241Q8—42no—
242D4—24no—
243D4—42no—
244D4—44no—
245D4—44no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—44no—
253C2×C4—44no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—81no—
260C2×C4—82no—
261C2×C4—344no—
262C2×C4—682no—
263C2×C4—682no—
264C2×C4—682no—
265C2×C4—682no—
266C2×C4—682no—
267C2×C4#1058756412yes—
268C2×C4#1058757112yes—
269C8—1362no—
270C22—22no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22#1176272111yescharacteristic
281C22#1176299512yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—82no—
286C4—161no—
287C4—684no—
288C4—1362no—
289C2—22no—
290C2—41no—
291C2—41no—
292C2—82no—
293C2#1452994811yescharacteristic
294C2#1452995812yes—
subgroupG/H
centerC22#11762721
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1782C2
socleC22×C17#393
prime radicalC22×#41×C17C22
hypercenter#1782D17
hypocenterC17#10388
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
1. #14534454C2semidirect
3. #14526692C2semidirect
4. #14526636C2semidirect
190. C17#10388semidirect

Maximal subgroups

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

subgroupindex
#145344542
#145287282
#145266922
#145266362
C17×#17822
#1038817