Finite Group Databasebeta

← #16945010

Subgroups — #16945010

Order 4352.

478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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#14528864C211yesmaximal, characteristic
2#14527114C211yesmaximal, characteristic
3#14526790C214yesmaximal, complemented
4C2×C17×#398C211yesmaximal, characteristic
5#11762773—21no—
6#11762773—21no—
7#11762578—21no—
8#11762578C2212yes—
9#11762535—21no—
10#11762535C2212yes—
11C22×C4⋊C4×C17—21no—
12C22×C4⋊C4×C17C411yescharacteristic
13C22×C4⋊C4×C17C2211yescharacteristic
14C17×#398—21no—
15C17×#398—21no—
16C17×#398C412yes—
17C17×#398C2212yes—
18C2×C17×#95—21no—
19C2×C17×#95C411yescharacteristic
20C23×C4×C17—21no—
21C23×C4×C17—21no—
22C23×C4×C17C2×C411yescharacteristic
23C23×C4×C17D411yescharacteristic
24C23×C4×C17D411yescharacteristic
25C2×C4⋊C4×C17—22no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—22no—
28C2×C4⋊C4×C17—41no—
29C2×C4⋊C4×C17—41no—
30C2×C4⋊C4×C17—44no—
31C2×C4⋊C4×C17—41no—
32C2×C4⋊C4×C17—41no—
33C2×C4⋊C4×C17C2×C412yes—
34C2×C4⋊C4×C17C2×C411yescharacteristic
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C4⋊C4×C17C2311yescharacteristic
38C2×#63223—22no—
39C2×#63223—41no—
40C17×#95—22no—
41C17×#95—21no—
42C17×#95—22no—
43C17×#95C2×C412yes—
44C22⋊#3622—22no—
45C22⋊#3622—41no—
46C22⋊#3622—41no—
47C22⋊#3622—41no—
48C24×C17C22⋊C411yescharacteristic
49C22×C4×C17—24no—
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—21no—
55C22×C4×C17—22no—
56C22×C4×C17—21no—
57C22×C4×C17—22no—
58C22×C4×C17—22no—
59C22×C4×C17—41no—
60C22×C4×C17—42no—
61C22×C4×C17—42no—
62C22×C4×C17—42no—
63C22×C4×C17—42no—
64C22×C4×C17—42no—
65C22×C4×C17—42no—
66C22×C4×C17—41no—
67C22×C4×C17—41no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22×C411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C22×C4×C17C2×D411yescharacteristic
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—42no—
79C4⋊C4×C17—42no—
80C4⋊C4×C17—44no—
81C4⋊C4×C17—44no—
82#63223—42no—
83#63223—42no—
84#63223—82no—
85C2×#3622—42no—
86C2×#3622—42no—
87#11803—171nomaximal, Sylow
88C23×C17—22no—
89C23×C17—22no—
90C23×C17—21no—
91C23×C17—21no—
92C23×C17#9911yescharacteristic
93C23×C17#9911yescharacteristic
94C23×C17C2×C22⋊C411yescharacteristic
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—24no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—42no—
106C2×C4×C17—42no—
107C2×C4×C17—48no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—42no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—42no—
118C2×C4×C17—42no—
119C2×C4×C17—42no—
120C2×C4×C17—81no—
121C2×C4×C17—82no—
122C2×C4×C17—82no—
123C2×C4×C17AGL(1,ℤ/8)12yes—
124#3622—82no—
125#3622—82no—
126C2×#398D1711yescharacteristic
127#1821—171no—
128#1463—171no—
129#1346—174no—
130C22×C17—24no—
131C22×C17—24no—
132C22×C17—21no—
133C22×C17—21no—
134C22×C17—21no—
135C22×C17—21no—
136C22×C17—21no—
137C22×C17—21no—
138C22×C17#35212yes—
139C22×C17#35612yes—
140C22×C17C2×#9911yescharacteristic
141C22×C17#41811yescharacteristic
142C22×C17#42111yescharacteristic
143C4×C17—22no—
144C4×C17—44no—
145C4×C17—41no—
146C4×C17—41no—
147C4×C17—41no—
148C4×C17—41no—
149C4×C17—41no—
150C4×C17—82no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4Dic1711yescharacteristic
153C22×C4⋊C4C2×D1711yescharacteristic
154#407—341no—
155#407—341no—
156#398—21no—
157#398—21no—
158#398Dic1712yes—
159#398C2×D1712yes—
160C2×#95—21no—
161C2×#95Dic1711yescharacteristic
162#343—172no—
163#343—341no—
164#324—172no—
165#324—341no—
166C2×C17—21no—
167C2×C17—22no—
168C2×C17—22no—
169C2×C17—21no—
170C2×C17#151011yescharacteristic
171C2×C17C2×#35211yescharacteristic
172C2×C17C2×#35611yescharacteristic
173C23×C4—21no—
174C23×C4—21no—
175C23×C4C2×Dic1711yescharacteristic
176C23×C4C22⋊D1711yescharacteristic
177C23×C4C22⋊D1711yescharacteristic
178C2×M16—342no—
179C2×M16—681no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—41no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4C2×Dic1712yes—
189C2×C4⋊C4C2×Dic1711yescharacteristic
190C2×C4⋊C4C22⋊D1711yescharacteristic
191C2×C4⋊C4C22⋊D1711yescharacteristic
192C2×C4⋊C4C22×D1711yescharacteristic
193C22⋊C8—342no—
194C22⋊C8—681no—
195C22⋊C8—681no—
196C22⋊C8—681no—
197#95—22no—
198#95—21no—
199#95—22no—
200#95C2×Dic1712yes—
201C17#1180311yescharacteristic, complemented, Sylow
202C24C22⋊Dic1711yescharacteristic
203C22×C4—24no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4C22⋊Dic1711yescharacteristic
223C22×C4C22⋊Dic1711yescharacteristic
224C22×C4C22⋊Dic1711yescharacteristic
225C22×C4C22×Dic1711yescharacteristic
226C22×C4C2×C22⋊D1711yescharacteristic
227C22×C4C2×C22⋊D1711yescharacteristic
228M16—682no—
229M16—682no—
230M16—1362no—
231C2×C8—682no—
232C2×C8—682no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—44no—
240C4⋊C4—44no—
241C23—21no—
242C23—21no—
243C23—22no—
244C23—22no—
245C23#1058750511yescharacteristic
246C23#1058750511yescharacteristic
247C23C2×C22⋊Dic1711yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—48no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4#1058761812yes—
277C8—1362no—
278C8—1362no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22#1176259912yes—
288C22#1176260812yes—
289C22C2×#1058750511yescharacteristic
290C22#1176281411yescharacteristic
291C22#1176282611yescharacteristic
292C4—22no—
293C4—44no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—22no—
304C2#1452731311yescharacteristic
305C2C2×#1176259911yescharacteristic
306C2C2×#1176260811yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC2×C17×#398C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenterC2×#398D17
hypocenterC17#11803
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. #14526790C2semidirect
201. C17#11803semidirect

Maximal subgroups

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

subgroupindex
#145288642
#145271142
#145267902
C2×C17×#3982
#1180317