Finite Group Databasebeta

← #17959340

Subgroups — #17959340

Order 4352.

482 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C4×#10587551C211yesmaximal, characteristic
2#14544043C211yesmaximal, characteristic
3#14543765C214yesmaximal, complemented
4#14533093C211yesmaximal, characteristic
5#11763830—21no—
6C2×#10587551—21no—
7C4×C22⋊#595—21no—
8#11763687C2212yes—
9#11763653C2212yes—
10#11763652—21no—
11C2×#10587572—21no—
12C2×C4×C22⋊D17C2211yescharacteristic
13C22×C4⋊Dic17C411yescharacteristic, complemented
14#11762741C412yescomplemented
15#11762736C2212yes—
16#11762708—21no—
17#11762670—21no—
18#11762666—21no—
19C17×#380C411yescharacteristic, complemented
20C23×C4×C17C2×C411yescharacteristic
21C22×C22⋊D17D411yescharacteristic
22C23×Dic17—21no—
23C22×C4×D17D411yescharacteristic
24C2×C22⋊#595—22no—
25C2×C4×#595—41no—
26C2×C4⋊C4×C17—21no—
27C2×C22⋊C4×C17—21no—
28C2×C22⋊Dic17D411yescharacteristic
29C4×C22⋊D17—41no—
30C4×C22⋊D17—41no—
31C2×#63227—22no—
32C2×#63227C2311yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—22no—
35C2×C4⋊Dic17—41no—
36C2×C4⋊Dic17—41no—
37C2×C4⋊Dic17C2×C412yes—
38C2×#63225C2×C411yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40#10587572—44no—
41C22⋊#3624—22no—
42#10587551—24no—
43(C2×#595)⋊C4—41no—
44#10587542—41no—
45C4⋊#3624—41no—
46C17×#95C2×C412yes—
47#10587502—22no—
48#10587502—22no—
49C24×C17C22⋊C411yescharacteristic
50C23×D17C2×D411yescharacteristic
51C22×#595—42no—
52C22×C4×C17—21no—
53C22×C4×C17—21no—
54C22×C4×C17—22no—
55C22×C4×C17—42no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C2×C22⋊D17—22no—
59C2×C22⋊D17—22no—
60C2×C22⋊D17—41no—
61C22×Dic17—22no—
62C22×Dic17—42no—
63C22×Dic17—42no—
64C22×Dic17—42no—
65C22×Dic17C22⋊C411yescharacteristic
66C22×Dic17C22⋊C411yescharacteristic
67C22×Dic17C2×D411yescharacteristic
68C2×C4×D17—21no—
69C2×C4×D17—21no—
70C2×C4×D17—42no—
71C22⋊#595—24no—
72C22⋊#595—42no—
73C2×#3624—42no—
74C4×#595—82no—
75C4⋊C4×C17—42no—
76C22⋊C4×C17—42no—
77C22⋊Dic17—41no—
78#63227—41no—
79#63227—44no—
80C4⋊Dic17—44no—
81C4⋊Dic17—41no—
82C4⋊Dic17—41no—
83C4⋊Dic17—42no—
84#63225—41no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87#11773—171nomaximal, Sylow
88C23×C17—21no—
89C23×C17—21no—
90C23×C17—41no—
91C23×C17—41no—
92C23×C17#10412yes—
93C23×C17C2×C22⋊C411yescharacteristic
94C22×D17—21no—
95C22×D17—21no—
96C22×D17—41no—
97C22×D17—41no—
98C22×D17AGL(1,ℤ/8)12yes—
99C2×#595—44no—
100C2×#595—82no—
101C2×#595—82no—
102C2×C4×C17—22no—
103C2×C4×C17—21no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—41no—
107C2×C4×C17—42no—
108C2×C4×C17—42no—
109C2×C4×C17—42no—
110C2×C4×C17#9911yescharacteristic
111C2×C4×C17#9911yescharacteristic
112C22⋊D17—44no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—21no—
117C2×Dic17—21no—
118C2×Dic17—41no—
119C2×Dic17—41no—
120C2×Dic17—42no—
121C2×Dic17—42no—
122C2×Dic17—42no—
123C2×Dic17—84no—
124C4×D17—42no—
125C4×D17—81no—
126#3624—82no—
127#2486—171no—
128C4×#99—171no—
129#1466—171no—
130#1344—174no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17—22no—
134C22×C17—42no—
135C22×C17—42no—
136C22×C17—41no—
137C22×C17—41no—
138C22×C17C2×#9911yescharacteristic
139C22×C17#41811yescharacteristic
140C22×C17C2×#10411yescharacteristic
141C2×D17—22no—
142C2×D17—41no—
143C2×D17—41no—
144C2×D17—42no—
145C2×D17—81no—
146#595—84no—
147C4×C17—21no—
148C4×C17—41no—
149C4×C17—82no—
150C4×C17#35212yes—
151Dic17—41no—
152Dic17—41no—
153Dic17—41no—
154Dic17—82no—
155C2×#123—341no—
156C2×C4×D4—171no—
157C22×C4⋊C4—171no—
158#432—341no—
159C2×#99—341no—
160#398—172no—
161#397—172no—
162#389—341no—
163#381—341no—
164#380—341no—
165#380#59511yescharacteristic, complemented
166C4×C22⋊C4—341no—
167#342—172no—
168#323—172no—
169#323—341no—
170C2×C17—21no—
171C2×C17—21no—
172C2×C17—42no—
173C2×C17#150711yescharacteristic
174C2×C17C2×#35211yescharacteristic
175C2×C17#212911yescharacteristic
176D17—42no—
177C22×D4—171no—
178C23×C4—171no—
179C23×C4—341no—
180C23×C4C2×#59511yescharacteristic
181#123—684no—
182C4×D4—681no—
183C4×D4—681no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—171no—
186C2×C4⋊C4—172no—
187C2×C4⋊C4—342no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4—681no—
190C2×C4⋊C4—681no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—171no—
193C2×C22⋊C4—171no—
194C2×C22⋊C4—342no—
195C2×C22⋊C4—342no—
196C2×C42—171no—
197C2×C42—681no—
198C4⋊C8—681no—
199#99—344no—
200C22⋊C8—342no—
201#97—681no—
202#95—342no—
203#95—342no—
204#95—681no—
205#95C2×#59512yes—
206C17#1177311yescharacteristic, complemented, Sylow
207C24—171no—
208C24C22⋊#59511yescharacteristic
209C2×D4—342no—
210C2×D4—342no—
211C2×D4—681no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—42no—
216C22×C4—171no—
217C22×C4—171no—
218C22×C4—171no—
219C22×C4—341no—
220C22×C4—341no—
221C22×C4—342no—
222C22×C4—682no—
223C22×C4—682no—
224C22×C4—682no—
225C22×C4—682no—
226C22×C4—682no—
227C22×C4C22⋊#59511yescharacteristic
228C22×C4C22×#59511yescharacteristic
229C2×C8—682no—
230C4⋊C4—42no—
231C4⋊C4—681no—
232C4⋊C4—682no—
233C4⋊C4—684no—
234C4⋊C4—681no—
235C4⋊C4—681no—
236C22⋊C4—42no—
237C22⋊C4—344no—
238C22⋊C4—681no—
239C22⋊C4—684no—
240C22⋊C4—681no—
241C22⋊C4—682no—
242C42—341no—
243C42—341no—
244C42—1362no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—172no—
250C23—341no—
251C23—341no—
252C23—681no—
253C23—681no—
254C23#1058755012yes—
255C23C2×C22⋊#59511yescharacteristic
256D4—684no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—341no—
266C2×C4—341no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—682no—
271C2×C4—681no—
272C2×C4—681no—
273C2×C4—684no—
274C2×C4—682no—
275C2×C4—682no—
276C2×C4—682no—
277C2×C4—1361no—
278C2×C4—1364no—
279C2×C4—1362no—
280C2×C4—1362no—
281C2×C4#1058753911yescharacteristic
282C2×C4#1058753911yescharacteristic
283C8—1362no—
284C22—21no—
285C22—21no—
286C22—22no—
287C22—42no—
288C22—42no—
289C22—41no—
290C22—41no—
291C22—342no—
292C22—682no—
293C22—681no—
294C22—681no—
295C22—1361no—
296C22C2×#1058753911yescharacteristic
297C22#1176380111yescharacteristic
298C22C2×#1058755011yescharacteristic
299C4—21no—
300C4—41no—
301C4—82no—
302C4—681no—
303C4—681no—
304C4—681no—
305C4—1364no—
306C4—1362no—
307C4#1176371212yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—682no—
312C2#1454418111yescharacteristic
313C2C2×#1176371211yescharacteristic
314C2#1454506811yescharacteristic
subgroupG/H
centerC22C2×#10587539
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#380C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17D4
cosocleC2×#63227C23
hypercenter#380#595
hypocenterC17#11773
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14543765C2semidirect
13. C22×C4⋊Dic17C4semidirect
14. #11762741C4semidirect
19. C17×#380C4semidirect
165. #380#595semidirect
206. C17#11773semidirect

Maximal subgroups

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

subgroupindex
C4×#105875512
#145440432
#145437652
#145330932
#1177317