Finite Group Databasebeta

← #16931999

Subgroups — #16931999

Order 4352.

424 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 107 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#14537869C211yesmaximal, characteristic
2#14527411C212yesmaximal
3#14527128C211yesmaximal, characteristic
4#14526640C212yesmaximal
5C17×#2565C211yesmaximal, characteristic
6#11762940—24no—
7#11762866—21no—
8#11762866C2212yes—
9#11762866C2212yes—
10#11762862—21no—
11#11762551—24no—
12#11762535—21no—
13#11762535—21no—
14C2×C17×#125C2211yescharacteristic
15C2×C4×Q8×C17C2211yescharacteristic
16C17×#398—21no—
17C17×#398—21no—
18C17×#391C411yescharacteristic
19C17×#391C411yescharacteristic
20C17×#387—21no—
21C17×#387—21no—
22C17×#384C411yescharacteristic
23C17×#382C411yescharacteristic
24C4×C4⋊C4×C17C2211yescharacteristic
25C22×Q8×C17C2×C411yescharacteristic
26C17×#125—22no—
27C17×#125—22no—
28C4×Q8×C17—22no—
29C4×Q8×C17—22no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17C2×C411yescharacteristic
36C2×C4⋊C4×C17C2×C411yescharacteristic
37C2×C4⋊C4×C17C2×C411yescharacteristic
38C2×C4⋊C4×C17D411yescharacteristic
39C2×C4⋊C4×C17D411yescharacteristic
40C2×C42×C17C2×C411yescharacteristic
41C2×C42×C17C2×C411yescharacteristic
42C2×C42×C17D411yescharacteristic
43C2×C42×C17D411yescharacteristic
44C2×C42×C17C2311yescharacteristic
45C17×#95—21no—
46C17×#95—21no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C22⋊#3622—22no—
53C22⋊#3622—22no—
54C4⋊#3622—22no—
55C4⋊#3622—22no—
56C4⋊#3622—22no—
57C4⋊#3622—22no—
58#10587474—22no—
59#10587474—22no—
60#10587474D414yes—
61C4×#3622—22no—
62C2×Q8×C17—22no—
63C2×Q8×C17—22no—
64C2×Q8×C17—41no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22⋊C411yescharacteristic
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C22×C411yescharacteristic
74C22×C4×C17C2×D411yescharacteristic
75C22×C4×C17C2×D411yescharacteristic
76C4⋊C4×C17—22no—
77C4⋊C4×C17—22no—
78C4⋊C4×C17—22no—
79C4⋊C4×C17—22no—
80C4⋊C4×C17—22no—
81C4⋊C4×C17—42no—
82C4⋊C4×C17—42no—
83C4⋊C4×C17—42no—
84C4⋊C4×C17—41no—
85C4⋊C4×C17—42no—
86C4⋊C4×C17—41no—
87C42×C17—21no—
88C42×C17—21no—
89C42×C17—21no—
90C42×C17—21no—
91C42×C17—41no—
92C42×C17—41no—
93C42×C17C2×D412yes—
94C42×C17#4112yes—
95C2×#3622—24no—
96C2×#3622—42no—
97#9450—171nomaximal, Sylow
98C23×C17C2×C22⋊C411yescharacteristic
99Q8×C17—44no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—22no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—42no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17#10112yes—
125C2×C4×C17C4×D412yes—
126C2×C4×C17#12011yescharacteristic
127C2×C4×C17#12112yes—
128C2×C4×C17#12311yescharacteristic
129#3622—44no—
130#3622—82no—
131#2983—171no—
132#2565D1711yescharacteristic
133#1534—172no—
134#1467—171no—
135#1285—172no—
136C22×C17—21no—
137C22×C17—21no—
138C22×C17#38611yescharacteristic
139C22×C17C2×#10111yescharacteristic
140C22×C17#41311yescharacteristic
141C4×C17—22no—
142C4×C17—22no—
143C4×C17—22no—
144C4×C17—21no—
145C4×C17—21no—
146C4×C17—42no—
147C4×C17—41no—
148C4×C17—41no—
149C4×C17—41no—
150C4×C17—81no—
151C4×C17—81no—
152C4×C17—81no—
153C2×#125C2×D1711yescharacteristic
154C2×C4×Q8C2×D1711yescharacteristic
155#446—344no—
156#432—172no—
157#432—172no—
158#432—341no—
159#431—341no—
160#398—21no—
161#398—21no—
162#391Dic1711yescharacteristic
163#391Dic1711yescharacteristic
164#387—21no—
165#387—21no—
166#384Dic1711yescharacteristic
167#382Dic1711yescharacteristic
168C4×C4⋊C4C2×D1711yescharacteristic
169#330—344no—
170#324—341no—
171#324—341no—
172C2×C17—21no—
173C2×C17—21no—
174C2×C17#188411yescharacteristic
175C2×C17#190111yescharacteristic
176C2×C17#191211yescharacteristic
177C22×Q8C2×Dic1711yescharacteristic
178#125—22no—
179#125—22no—
180C4×Q8—22no—
181C4×Q8—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4C2×Dic1711yescharacteristic
188C2×C4⋊C4C2×Dic1711yescharacteristic
189C2×C4⋊C4C2×Dic1711yescharacteristic
190C2×C4⋊C4C22⋊D1711yescharacteristic
191C2×C4⋊C4C22⋊D1711yescharacteristic
192C2×C42C2×Dic1711yescharacteristic
193C2×C42C2×Dic1711yescharacteristic
194C2×C42C22⋊D1711yescharacteristic
195C2×C42C22⋊D1711yescharacteristic
196C2×C42C22×D1711yescharacteristic
197C4⋊C8—342no—
198C4⋊C8—342no—
199C4⋊C8—342no—
200C4⋊C8—342no—
201C22⋊C8—342no—
202C22⋊C8—342no—
203#97—174no—
204#97—342no—
205#97—342no—
206C4×C8—342no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214C17#945011yescharacteristic, complemented, Sylow
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊Dic1711yescharacteristic
223C22×C4C22⋊Dic1711yescharacteristic
224C22×C4C22⋊Dic1711yescharacteristic
225C22×C4C22⋊Dic1711yescharacteristic
226C22×C4C22×Dic1711yescharacteristic
227C22×C4C2×C22⋊D1711yescharacteristic
228C22×C4C2×C22⋊D1711yescharacteristic
229C2×C8—344no—
230C2×C8—682no—
231C4⋊C4—22no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C42D4×D1712yes—
249C42#6325412yes—
250C23C2×C22⋊Dic1711yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#1058750712yes—
277C2×C4D4×Dic1712yes—
278C2×C4#1058762111yescharacteristic
279C2×C4#1058762311yescharacteristic
280C2×C4#1058762512yes—
281C8—684no—
282C8—1362no—
283C22—21no—
284C22—21no—
285C22#1176268911yescharacteristic
286C22C2×#1058750711yescharacteristic
287C22#1176279311yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—42no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#1452916811yescharacteristic
303C2#1452925311yescharacteristic
304C2#1452932211yescharacteristic
subgroupG/H
centerC22#11762689
commutatorC22×C4×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#2565C2
socleC22×C17#386
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C42×C17C23
hypercenter#2565D17
hypocenterC17#9450
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2565

Complements

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

NH ≅ G/Ntype
214. C17#9450semidirect

Maximal subgroups

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

subgroupindex
#145378692
#145274112
#145271282
#145266402
C17×#25652
#945017