Finite Group Databasebeta

← #17952463

Subgroups — #17952463

Order 4352.

874 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 124 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#14544674C212yesmaximal, complemented
2C2×#11763655C212yesmaximal, complemented
3C2×#11763652C212yesmaximal
4C22×#10587565C211yesmaximal, characteristic
5C2×C22⋊#3624C2214yes—
6#11763675—24no—
7#11763655—24no—
8#11763652—24no—
9C2×#10587565—24no—
10C2×#10587565—24no—
11C2×#10587565—24no—
12C22×C4⋊Dic17C411yescharacteristic
13C22×#63225C411yescharacteristic
14C22×#63225C2211yescharacteristic
15C22×C22⋊Dic17C411yescharacteristic
16C22×C22⋊Dic17C2211yescharacteristic
17C22×C4×Dic17C2211yescharacteristic
18C22×C22⋊C4×C17C411yescharacteristic
19C25×C17C2×C411yescharacteristic
20C23×C4×C17C2×C411yescharacteristic
21C23×C4×C17C2×C411yescharacteristic
22C23×Dic17C2×C411yescharacteristic
23C23×Dic17C2×C411yescharacteristic
24C23×Dic17C2×C411yescharacteristic
25C23×Dic17C2311yescharacteristic
26C22×#3624—24no—
27C2×C22⋊C4×C17—22no—
28C2×C22⋊C4×C17—22no—
29C2×C22⋊C4×C17—22no—
30C2×C22⋊Dic17—22no—
31C2×C22⋊Dic17—22no—
32C2×C22⋊Dic17—22no—
33C2×C22⋊Dic17—22no—
34C2×C22⋊Dic17—22no—
35C2×C22⋊Dic17D414yes—
36C2×C4⋊Dic17—22no—
37C2×C4⋊Dic17—22no—
38C2×C4⋊Dic17—22no—
39C2×#63225—22no—
40C2×#63225—22no—
41C2×#63225—22no—
42C2×#63225—22no—
43C2×#63225—22no—
44C2×#63225D414yes—
45C2×C4×Dic17—22no—
46C2×C4×Dic17—22no—
47C2×C4×Dic17D414yes—
48#10587565—232no—
49C22⋊#3624—24no—
50C22⋊#3624—24no—
51C24×C17—21no—
52C24×C17—21no—
53C24×C17—24no—
54C24×C17—42no—
55C24×C17—42no—
56C24×C17C22⋊C412yes—
57C24×C17C22×C411yescharacteristic
58C22×C4×C17—21no—
59C22×C4×C17—21no—
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—24no—
63C22×C4×C17—42no—
64C22×C4×C17C22⋊C412yes—
65C22×C4×C17C22⋊C412yes—
66C22×Dic17—21no—
67C22×Dic17—21no—
68C22×Dic17—21no—
69C22×Dic17—21no—
70C22×Dic17—21no—
71C22×Dic17—21no—
72C22×Dic17—24no—
73C22×Dic17—42no—
74C22×Dic17—42no—
75C22×Dic17—42no—
76C22×Dic17C22⋊C412yes—
77C22×Dic17C22⋊C412yes—
78C22×Dic17C22⋊C412yes—
79C22×Dic17C2×D412yes—
80C22×Dic17C2×D412yes—
81C22×Dic17C2×D412yes—
82C2×#3624—48no—
83C2×#3624—44no—
84C22⋊C4×C17—28no—
85C22⋊Dic17—28no—
86C22⋊Dic17—28no—
87C4⋊Dic17—28no—
88#63225—28no—
89#63225—28no—
90C4×Dic17—28no—
91#8309—171nomaximal, Sylow
92C23×C17—22no—
93C23×C17—22no—
94C23×C17—22no—
95C23×C17—24no—
96C23×C17—42no—
97C23×C17—42no—
98C23×C17—42no—
99C23×C17—42no—
100C23×C17—42no—
101C23×C17—42no—
102C23×C17—42no—
103C23×C17—42no—
104C23×C17—88no—
105C23×C17C2×C22⋊C411yescharacteristic
106C23×C17C2×C22⋊C411yescharacteristic
107C23×C17C2×C22⋊C411yescharacteristic
108C23×C17#13114yes—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—24no—
112C2×C4×C17—42no—
113C2×C4×C17—42no—
114C2×C4×C17—42no—
115C2×C4×C17—42no—
116C2×C4×C17—42no—
117C2×Dic17—24no—
118C2×Dic17—22no—
119C2×Dic17—22no—
120C2×Dic17—22no—
121C2×Dic17—24no—
122C2×Dic17—24no—
123C2×Dic17—42no—
124C2×Dic17—42no—
125C2×Dic17—42no—
126C2×Dic17—42no—
127C2×Dic17—42no—
128C2×Dic17—42no—
129C2×Dic17—42no—
130C2×Dic17—42no—
131C2×Dic17—42no—
132C2×Dic17#12014yes—
133#3624—84no—
134C22×#126—171no—
135#1817—172no—
136C2×#324—172no—
137C2×#323—172no—
138C22×C17—28no—
139C22×C17—21no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17—21no—
143C22×C17—42no—
144C22×C17—42no—
145C22×C17—42no—
146C22×C17—84no—
147C22×C17—84no—
148C22×C17—84no—
149C22×C17#37911yescharacteristic
150C22×C17#40812yes—
151C22×C17#40812yes—
152C22×C17#40812yes—
153C22×C17#41012yes—
154C22×C17#41312yes—
155C4×C17—42no—
156C4×C17—42no—
157Dic17—24no—
158Dic17—42no—
159Dic17—42no—
160Dic17—42no—
161C2×#126—344no—
162C2×#126—344no—
163C2×#126—344no—
164C22×C4⋊C4—171no—
165C22×C4⋊C4—171no—
166C22×C4⋊C4—171no—
167C22×C22⋊C4—171no—
168C22×C22⋊C4—171no—
169C22×C22⋊C4#59511yescharacteristic
170C22×C42—171no—
171C2×C22⋊C8—174no—
172#336—344no—
173#324—344no—
174#323—344no—
175C2×C17—22no—
176C2×C17—22no—
177C2×C17—82no—
178C2×C17#147314yes—
179C2×C17#178011yescharacteristic
180C2×C17#178211yescharacteristic
181C2×C17#178511yescharacteristic
182C25C2×#59511yescharacteristic
183C23×C4—171no—
184C23×C4—171no—
185C23×C4—171no—
186C23×C4—171no—
187C23×C4C2×#59511yescharacteristic
188C23×C4C2×#59511yescharacteristic
189C22×C8—344no—
190#126—3432no—
191C2×C4⋊C4—174no—
192C2×C4⋊C4—342no—
193C2×C4⋊C4—342no—
194C2×C4⋊C4—342no—
195C2×C4⋊C4—342no—
196C2×C4⋊C4—342no—
197C2×C4⋊C4—342no—
198C2×C4⋊C4—342no—
199C2×C4⋊C4—342no—
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—174no—
204C2×C22⋊C4—342no—
205C2×C22⋊C4—342no—
206C2×C22⋊C4—342no—
207C2×C22⋊C4—342no—
208C2×C22⋊C4—342no—
209C2×C42—174no—
210C2×C42—342no—
211C2×C42—342no—
212C22⋊C8—344no—
213C22⋊C8—344no—
214C17#830911yescharacteristic, complemented, Sylow
215C24—21no—
216C24—21no—
217C24—24no—
218C24—42no—
219C24—42no—
220C24C22⋊#59512yes—
221C24C22×#59511yescharacteristic
222C22×C4—24no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—42no—
228C22×C4—172no—
229C22×C4—172no—
230C22×C4—172no—
231C22×C4—172no—
232C22×C4—172no—
233C22×C4—172no—
234C22×C4—344no—
235C22×C4—341no—
236C22×C4—341no—
237C22×C4—341no—
238C22×C4—341no—
239C22×C4—341no—
240C22×C4—341no—
241C22×C4—682no—
242C22×C4—682no—
243C22×C4—682no—
244C22×C4C22⋊#59512yes—
245C22×C4C22⋊#59512yes—
246C2×C8—684no—
247C2×C8—688no—
248C4⋊C4—348no—
249C4⋊C4—348no—
250C4⋊C4—348no—
251C22⋊C4—28no—
252C22⋊C4—348no—
253C22⋊C4—348no—
254C42—348no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—24no—
259C23—42no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—42no—
265C23—42no—
266C23—42no—
267C23—88no—
268C23#1058767814yes—
269C23C2×C22⋊#59511yescharacteristic
270C23C2×C22⋊#59511yescharacteristic
271C23C2×C22⋊#59511yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—174no—
281C2×C4—344no—
282C2×C4—342no—
283C2×C4—342no—
284C2×C4—342no—
285C2×C4—344no—
286C2×C4—344no—
287C2×C4—682no—
288C2×C4—682no—
289C2×C4—682no—
290C2×C4—682no—
291C2×C4—682no—
292C2×C4—682no—
293C2×C4—682no—
294C2×C4—682no—
295C2×C4—682no—
296C8—1364no—
297C22—28no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—84no—
306C22—84no—
307C22—84no—
308C22#1176375011yescharacteristic
309C22#1176378212yes—
310C22#1176378212yes—
311C22#1176378312yes—
312C22#1176378912yes—
313C22#1176379512yes—
314C4—42no—
315C4—42no—
316C4—344no—
317C4—682no—
318C4—682no—
319C4—682no—
320C2—22no—
321C2—22no—
322C2—82no—
323C2#1454406614yes—
324C2#1454460811yescharacteristic
325C2#1454461411yescharacteristic
326C2#1454462011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17C2×C22⋊C4
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17#8309
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #14544674C2semidirect
2. C2×#11763655C2semidirect
214. C17#8309semidirect

Maximal subgroups

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

subgroupindex
#145446742
C2×#117636552
C2×#117636522
C22×#105875652
#830917