Finite Group Databasebeta

← #17969675

Subgroups — #17969675

Order 4352.

1126 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763819C214yesmaximal
2#14545233C212yesmaximal
3#14544721C214yesmaximal, complemented
4#14544720C212yesmaximal, complemented
5#14544719C212yesmaximal, complemented
6C2×C4×C8×D17C211yesmaximal, characteristic
7C2×#10587677C2214yes—
8#11763819—216no—
9C2×#10587534C2218yes—
10C2×#10587533C2218yes—
11#11763755C2214yes—
12#11763753C2214yes—
13#11763751—24no—
14C4×C4⋊#595—24no—
15C22×C8×D17C2212yes—
16C2×C42×D17C2211yescharacteristic
17C2×C4×#3622C411yescharacteristic, complemented
18C2×C8×Dic17C412yescomplemented
19C4×C8×D17C411yescharacteristic, complemented
20C4×C8×D17C411yescharacteristic, complemented
21C4×C8×D17C412yescomplemented
22C4×C8×D17C2211yescharacteristic
23C4×C8×D17C2211yescharacteristic
24C4×C8×D17C2212yes—
25C2×C4×C8×C17C411yescharacteristic, complemented
26C22×C4×D17D412yes—
27C22×C4×D17C2311yescharacteristic
28C2×C22⋊#595—24no—
29#10587677—216no—
30C2×C4⋊#595—28no—
31C2×C4⋊#595C2318yes—
32C2×C4×#595—24no—
33C22×C8×C17C2×C412yes—
34C2×C42×C17C2×C411yescharacteristic
35C2×C4×Dic17C2×C411yescharacteristic
36C2×C4×Dic17Q812yes—
37C22×#3622C2×C412yes—
38C2×C8×D17C2×C412yes—
39C2×C8×D17C2×C412yes—
40C2×C8×D17D418yes—
41C2×C8×D17Q818yes—
42C2×C8×D17C2312yes—
43C2×C8×D17C2312yes—
44C42×D17C2×C411yescharacteristic
45C42×D17C2×C411yescharacteristic
46C42×D17D412yes—
47C42×D17Q812yes—
48C42×D17C2311yescharacteristic
49C42×D17C2311yescharacteristic
50(C2×#595)⋊C4—28no—
51#10587534—216no—
52#10587533—216no—
53C4×C8×C17C2×C411yescharacteristic
54C4×C8×C17C2×C411yescharacteristic
55C4×C8×C17C2×C412yes—
56C8×Dic17C2×C412yes—
57C8×Dic17C2×C412yes—
58C8×Dic17C2×C412yes—
59C8×Dic17C2×C412yes—
60C4×#3622C2×C411yescharacteristic
61C4×#3622C2×C411yescharacteristic
62C4×#3622C2×C412yes—
63C23×D17C2×D411yescharacteristic
64C22×#595—28no—
65C22×C4×C17C4⋊C412yes—
66C22×C4×C17C22×C411yescharacteristic
67C22×Dic17C4⋊C412yes—
68C22×Dic17C2×Q811yescharacteristic
69C2×C4×D17—28no—
70C2×C4×D17C4⋊C412yes—
71C2×C4×D17C4⋊C412yes—
72C2×C4×D17C22×C411yescharacteristic
73C2×C4×D17C2×D412yes—
74C2×C4×D17C2×D414yes—
75C2×C4×D17C2×D411yescharacteristic
76C2×C4×D17C2×D412yes—
77C2×C4×D17C2×Q814yes—
78C2×C4×D17C2×Q811yescharacteristic
79C2×C4×D17C2411yescharacteristic
80C22⋊#595—48no—
81C4⋊#595—216no—
82C4⋊#595—416no—
83C4×#595—48no—
84C2×C8×C17C4⋊C418yescomplemented
85C2×C8×C17C22×C412yes—
86C2×C8×C17C22×C412yes—
87C42×C17C4⋊C412yes—
88C42×C17C22×C411yescharacteristic
89C42×C17C22×C411yescharacteristic
90C4×Dic17C4⋊C412yes—
91C4×Dic17C4⋊C412yes—
92C4×Dic17C4⋊C412yes—
93C4×Dic17C22×C411yescharacteristic
94C4×Dic17C22×C411yescharacteristic
95C4×Dic17C2×Q812yes—
96C4×Dic17C2×Q812yes—
97C2×#3622C4⋊C418yescomplemented
98C2×#3622C22×C412yes—
99C2×#3622C22×C412yes—
100C8×D17C4⋊C418yescomplemented
101C8×D17C4⋊C418yescomplemented
102C8×D17C2×D414yes—
103C8×D17C2×D414yes—
104C8×D17C2×Q814yes—
105C8×D17C2×Q814yes—
106#20797—171nomaximal, Sylow
107C23×C17C2×C4⋊C411yescharacteristic
108C22×D17—24no—
109C22×D17C2×C4⋊C411yescharacteristic
110C22×D17#12712yes—
111C22×D17C4⋊Q812yes—
112C22×D17C22×D411yescharacteristic
113C2×#595—48no—
114C2×#595—416no—
115C2×C4×C17—24no—
116C2×C4×C17C2×C4⋊C412yes—
117C2×C4×C17C2×C4⋊C414yes—
118C2×C4×C17C2×C4⋊C412yes—
119C2×C4×C17C2×C4⋊C411yescharacteristic
120C2×C4×C17C23×C411yescharacteristic
121C2×Dic17—24no—
122C2×Dic17C2×C4⋊C412yes—
123C2×Dic17C2×C4⋊C411yescharacteristic
124C2×Dic17C2×C4⋊C412yes—
125C2×Dic17C4⋊Q814yes—
126C2×Dic17C22×Q811yescharacteristic
127C4×D17—24no—
128C4×D17—24no—
129C4×D17—24no—
130C4×D17C2×C4⋊C414yes—
131C4×D17#12712yes—
132C4×D17C4⋊Q814yes—
133C4×D17C4⋊Q812yes—
134C4×D17#13518yes—
135C4×D17C22×D412yes—
136C4×D17C22×Q812yes—
137C8×C17C2×C4⋊C414yes—
138C8×C17C2×C4⋊C414yes—
139#3622C2×C4⋊C414yes—
140#3622C2×C4⋊C414yes—
141C2×#427—174no—
142C22×C4×C8—171no—
143#2285—172no—
144#1846—174no—
145#1845—172no—
146#1844—172no—
147C22×C17—22no—
148C22×C17#38412yes—
149C22×C17C22×C4⋊C411yescharacteristic
150C2×D17—22no—
151C2×D17—24no—
152C2×D17—24no—
153C2×D17#38412yes—
154C2×D17C2×#12711yescharacteristic
155C2×D17C2×C4⋊Q811yescharacteristic
156C2×D17C2×#13514yes—
157#595—88no—
158C4×C17—22no—
159C4×C17#38412yes—
160C4×C17#42714yescomplemented
161C4×C17C22×C4⋊C412yes—
162Dic17—22no—
163Dic17#38412yes—
164Dic17#42714yescomplemented
165Dic17C2×C4⋊Q812yes—
166C23×C8—172no—
167C2×#117—174no—
168C22×C42—171no—
169#427—3416no—
170C2×#107—178no—
171C2×#106—178no—
172C2×C4×C8—172no—
173C2×C4×C8—171no—
174C2×C4×C8—171no—
175C2×C4×C8—171no—
176C2×C4×C8—172no—
177C2×C4×C8—172no—
178C2×C4×C8—171no—
179C2×C4×C8—171no—
180C2×C4×C8#59511yescharacteristic, complemented
181#384—174no—
182#382—174no—
183#380—344no—
184C4×C4⋊C4—344no—
185C2×C17—22no—
186C2×C17C2×#38411yescharacteristic
187C2×C17C2×#42712yes—
188D17—22no—
189D17#314712yes—
190D17#316012yes—
191C23×C4—171no—
192C23×C4—172no—
193C22×C8—172no—
194C22×C8—178no—
195C22×C8—178no—
196C22×C8—172no—
197C22×C8—172no—
198C22×C8—172no—
199C22×C8—172no—
200C22×C8C2×#59512yes—
201#117—3416no—
202C2×C4⋊C4—178no—
203C2×C4⋊C4—348no—
204C2×C22⋊C4—344no—
205C2×C42—172no—
206C2×C42—171no—
207C2×C42—172no—
208C2×C42—172no—
209C2×C42—171no—
210C2×C42—171no—
211C2×C42—171no—
212C2×C42—171no—
213C2×C42—344no—
214C2×C42C2×#59511yescharacteristic
215#107—3416no—
216#106—3416no—
217C4×C8—172no—
218C4×C8—172no—
219C4×C8—172no—
220C4×C8—172no—
221C4×C8—171no—
222C4×C8—171no—
223C4×C8—172no—
224C4×C8C2×#59511yescharacteristic
225C4×C8C2×#59511yescharacteristic
226C4×C8C2×#59512yes—
227#95—348no—
228C17#2079711yescharacteristic, complemented, Sylow
229C24—171no—
230C22×C4—171no—
231C22×C4—172no—
232C22×C4—174no—
233C22×C4—174no—
234C22×C4—171no—
235C22×C4—171no—
236C22×C4—171no—
237C22×C4—171no—
238C22×C4—172no—
239C22×C4—172no—
240C22×C4—172no—
241C22×C4—172no—
242C22×C4—348no—
243C22×C4—348no—
244C22×C4C4⋊#59512yes—
245C22×C4C22×#59511yescharacteristic
246C2×C8—178no—
247C2×C8—172no—
248C2×C8—172no—
249C2×C8—174no—
250C2×C8—174no—
251C2×C8—178no—
252C2×C8—178no—
253C2×C8—174no—
254C2×C8—174no—
255C2×C8C4⋊#59518yescomplemented
256C2×C8C22×#59512yes—
257C2×C8C22×#59512yes—
258C4⋊C4—3416no—
259C4⋊C4—6816no—
260C22⋊C4—688no—
261C42—172no—
262C42—172no—
263C42—172no—
264C42—172no—
265C42—172no—
266C42—171no—
267C42—171no—
268C42—688no—
269C42C4⋊#59512yes—
270C42C22×#59511yescharacteristic
271C42C22×#59511yescharacteristic
272C23—171no—
273C23—172no—
274C23—172no—
275C23—171no—
276C23—344no—
277C23C2×C4⋊#59511yescharacteristic
278C2×C4—24no—
279C2×C4—174no—
280C2×C4—172no—
281C2×C4—171no—
282C2×C4—171no—
283C2×C4—172no—
284C2×C4—174no—
285C2×C4—172no—
286C2×C4—178no—
287C2×C4—172no—
288C2×C4—174no—
289C2×C4—172no—
290C2×C4—172no—
291C2×C4—344no—
292C2×C4—344no—
293C2×C4—344no—
294C2×C4—344no—
295C2×C4—688no—
296C2×C4—6816no—
297C2×C4C2×C4⋊#59512yes—
298C2×C4C2×C4⋊#59514yes—
299C2×C4C2×C4⋊#59512yes—
300C2×C4C2×C4⋊#59511yescharacteristic
301C2×C4C23×#59511yescharacteristic
302C8—174no—
303C8—174no—
304C8C2×C4⋊#59514yes—
305C8C2×C4⋊#59514yes—
306C22—22no—
307C22—174no—
308C22—171no—
309C22—171no—
310C22—172no—
311C22—344no—
312C22—344no—
313C22—342no—
314C22#1176375512yes—
315C22C22×C4⋊#59511yescharacteristic
316C4—22no—
317C4—174no—
318C4—172no—
319C4—172no—
320C4—342no—
321C4—1368no—
322C4#1176375512yes—
323C4#1176381914yescomplemented
324C4C22×C4⋊#59512yes—
325C2—22no—
326C2—172no—
327C2—172no—
328C2—342no—
329C2C2×#1176375511yescharacteristic
330C2C2×#1176381912yes—
subgroupG/H
centerC2×C4C2×C4⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C4×C8×C17C4
socleC22×C17C22×C4⋊C4
prime radicalC23×D17C2×D4
cosocleC2×C4×D17C24
hypercenterC2×C4×C8#595
hypocenterC17#20797
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
3. #14544721C2semidirect
4. #14544720C2semidirect
5. #14544719C2semidirect
17. C2×C4×#3622C4semidirect
18. C2×C8×Dic17C4semidirect
19. C4×C8×D17C4semidirect
20. C4×C8×D17C4semidirect
21. C4×C8×D17C4semidirect
25. C2×C4×C8×C17C4semidirect
84. C2×C8×C17C4⋊C4semidirect
97. C2×#3622C4⋊C4semidirect
100. C8×D17C4⋊C4semidirect
101. C8×D17C4⋊C4semidirect
160. C4×C17#427semidirect
164. Dic17#427semidirect
180. C2×C4×C8#595semidirect
228. C17#20797semidirect
255. C2×C8C4⋊#595semidirect
323. C4#11763819semidirect

Maximal subgroups

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

subgroupindex
C2×#117638192
#145452332
#145447212
#145447202
#145447192
C2×C4×C8×D172
#2079717