Finite Group Databasebeta

← #16944643

Subgroups — #16944643

Order 4352.

432 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 115 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#14528523C211yesmaximal, characteristic
2#14527098C211yesmaximal, characteristic
3#14526814C214yesmaximal, complemented
4C17×#2628C211yesmaximal, characteristic
5C22×#63223—21no—
6#11762862—21no—
7#11762578—21no—
8#11762578C2212yes—
9#11762535C2212yes—
10#11762533—21no—
11C2×C17×C4⋊Q8C411yescharacteristic
12C2×C17×#117C2211yescharacteristic
13C17×#400—21no—
14C17×#399—21no—
15C17×#395C2212yes—
16C17×#393C412yes—
17C17×#389—21no—
18C17×#382C411yescharacteristic
19C17×#380—21no—
20C22×Q8×C17C2×C412yes—
21C23×C4×C17D411yescharacteristic
22C17×C4⋊Q8—41no—
23C17×C4⋊Q8—41no—
24C17×#117—41no—
25C17×#117—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—22no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17C2311yescharacteristic
32C2×C22⋊C4×C17—22no—
33C2×C22⋊C4×C17C2×C411yescharacteristic
34C2×C22⋊C4×C17D411yescharacteristic
35C2×C42×C17C2×C411yescharacteristic
36C2×C42×C17D411yescharacteristic
37C2×#63223—24no—
38C2×#63223—22no—
39C2×#63223—41no—
40C2×#63223—42no—
41C22×#3622—41no—
42C17×#95—21no—
43C17×#95—22no—
44C17×#95—22no—
45C17×#95C2×C412yes—
46C22⋊#3622—22no—
47C4⋊#3622—41no—
48C4×#3622—41no—
49C24×C17C22⋊C411yescharacteristic
50C2×Q8×C17—42no—
51C2×Q8×C17—82no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—22no—
55C22×C4×C17—22no—
56C22×C4×C17—22no—
57C22×C4×C17C22⋊C411yescharacteristic
58C22×C4×C17C22⋊C411yescharacteristic
59C22×C4×C17C22⋊C411yescharacteristic
60C22×C4×C17SD1612yes—
61C22×C4×C17Q1612yes—
62C22×C4×C17C22×C411yescharacteristic
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17C2×D411yescharacteristic
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17—42no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—42no—
71C4⋊C4×C17—82no—
72C22⋊C4×C17—41no—
73C22⋊C4×C17—41no—
74C22⋊C4×C17—82no—
75C42×C17—21no—
76C42×C17—21no—
77C42×C17—21no—
78C42×C17—21no—
79#63223—24no—
80#63223—44no—
81#63223—42no—
82C2×#3622—42no—
83C2×#3622—44no—
84C2×#3622—42no—
85#11724—171nomaximal, Sylow
86C23×C17—21no—
87C23×C17—21no—
88C23×C17—41no—
89C23×C17—41no—
90C23×C17#10312yes—
91C23×C17C2×C22⋊C411yescharacteristic
92Q8×C17—84no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—22no—
96C2×C4×C17—22no—
97C2×C4×C17—22no—
98C2×C4×C17—22no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17—42no—
111C2×C4×C17—42no—
112C2×C4×C17—42no—
113C2×C4×C17#9911yescharacteristic
114C2×C4×C17#9911yescharacteristic
115C2×C4×C17#10312yes—
116C2×C4×C17#10412yes—
117C2×C4×C17C2×SD1611yescharacteristic
118C2×C4×C17C2×Q1611yescharacteristic
119#3622—44no—
120#3622—82no—
121#2628D1711yescharacteristic
122#1742—171no—
123#1458—171no—
124#1354—174no—
125C22×C17—21no—
126C22×C17—21no—
127C22×C17—22no—
128C22×C17—42no—
129C22×C17—41no—
130C22×C17—41no—
131C22×C17—81no—
132C22×C17C2×#9911yescharacteristic
133C22×C17C2×#10311yescharacteristic
134C22×C17C2×#10411yescharacteristic
135C4×C17—21no—
136C4×C17—21no—
137C4×C17—41no—
138C4×C17—41no—
139C4×C17—41no—
140C4×C17—41no—
141C4×C17—82no—
142C4×C17—82no—
143C4×C17#32812yes—
144C4×C17#32812yes—
145C22×M16—341no—
146C2×C4⋊Q8Dic1711yescharacteristic
147C2×#117C2×D1711yescharacteristic
148#431—341no—
149#400—21no—
150#399—21no—
151#395C2×D1712yes—
152#393Dic1712yes—
153#389—21no—
154#382Dic1711yescharacteristic
155#380—21no—
156#343—172no—
157#343—341no—
158#324—172no—
159#323—341no—
160C2×C17—21no—
161C2×C17—21no—
162C2×C17—42no—
163C2×C17C2×#32811yescharacteristic
164C2×C17#212211yescharacteristic
165C2×C17#213511yescharacteristic
166C22×Q8C2×Dic1712yes—
167C23×C4C22⋊D1711yescharacteristic
168C2×M16—344no—
169C2×M16—342no—
170C2×M16—681no—
171C2×M16—682no—
172C22×C8—681no—
173C4⋊Q8—41no—
174C4⋊Q8—41no—
175#117—41no—
176#117—41no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4C22⋊D1711yescharacteristic
182C2×C4⋊C4C22×D1711yescharacteristic
183C2×C22⋊C4—22no—
184C2×C22⋊C4C2×Dic1711yescharacteristic
185C2×C22⋊C4C22⋊D1711yescharacteristic
186C2×C42C2×Dic1711yescharacteristic
187C2×C42C22⋊D1711yescharacteristic
188C4⋊C8—681no—
189C22⋊C8—342no—
190C4×C8—681no—
191#95—21no—
192#95—22no—
193#95—22no—
194#95C2×Dic1712yes—
195C17#1172411yescharacteristic, complemented, Sylow
196C24C22⋊Dic1711yescharacteristic
197C2×Q8—42no—
198C2×Q8—82no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4#6323012yes—
205C22×C4#6323112yes—
206C22×C4C22⋊Dic1711yescharacteristic
207C22×C4C22⋊Dic1711yescharacteristic
208C22×C4C22⋊Dic1711yescharacteristic
209C22×C4C22×Dic1711yescharacteristic
210C22×C4C2×C22⋊D1711yescharacteristic
211C22×C4C2×C22⋊D1711yescharacteristic
212M16—344no—
213M16—684no—
214M16—682no—
215C2×C8—682no—
216C2×C8—684no—
217C2×C8—682no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—82no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—82no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23#1058750612yes—
237C23C2×C22⋊Dic1711yescharacteristic
238Q8—84no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4#1058750511yescharacteristic
260C2×C4#1058750511yescharacteristic
261C2×C4#1058750612yes—
262C2×C4#1058750812yes—
263C2×C4C2×#6323011yescharacteristic
264C2×C4C2×#6323111yescharacteristic
265C8—684no—
266C8—1362no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#1058750511yescharacteristic
275C22C2×#1058750611yescharacteristic
276C22C2×#1058750811yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—82no—
284C4—82no—
285C4#1176254612yes—
286C4#1176254612yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#1176254611yescharacteristic
291C2#1453043411yescharacteristic
292C2#1453047911yescharacteristic
subgroupG/H
centerC22C2×#10587505
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2628C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#2628D17
hypocenterC17#11724
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
3. #14526814C2semidirect
195. C17#11724semidirect

Maximal subgroups

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

subgroupindex
#145285232
#145270982
#145268142
C17×#26282
#1172417