Finite Group Databasebeta

← #28402138

Subgroups — #28402138

Order 14464.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D113C211yesmaximal, characteristic, complemented
2Q8×C22⋊D113C211yesmaximal, characteristic, complemented
3#20299255C211yesmaximal, characteristic
4#20298989C211yesmaximal, characteristic, complemented
5#20298856C211yesmaximal, characteristic, complemented
6#20298824C211yesmaximal, characteristic, complemented
7#20298818C211yesmaximal, characteristic, complemented
8#20298806C211yesmaximal, characteristic, complemented
9#20298760C211yesmaximal, characteristic, complemented
10#20298754C211yesmaximal, characteristic, complemented
11#20298752C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13#20298705C211yesmaximal, characteristic, complemented
14#20298667C211yesmaximal, characteristic, complemented
15C2×#137×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Dic452C2211yescharacteristic
19C2×#14268637C2211yescharacteristic
20C2×#14268637C2211yescharacteristic
21C2×#14268637C2211yescharacteristic
22Q16×D113—24no—
23C2×#14268635C2211yescharacteristic
24C2×C8×D113C2211yescharacteristic
25#16813620—21no—
26#16813620C2211yescharacteristic
27#16813609—21no—
28#16813609C2211yescharacteristic
29#16813601—21no—
30#16813601—21no—
31#16813601C2211yescharacteristic
32#16813601C2211yescharacteristic
33#16813598—21no—
34#16813598C2211yescharacteristic
35#16813593—21no—
36#16813593C2211yescharacteristic
37Q8×Dic113C2211yescharacteristic
38Q8×Dic113C2211yescharacteristic
39C4×C22⋊D113—21no—
40C4×C22⋊D113—21no—
41C4×C22⋊D113C2211yescharacteristic
42#16813554C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813546C2211yescharacteristic
49#16813543C2211yescharacteristic
50C22⋊#11744751C2211yescharacteristic
51#16813534C2211yescharacteristic
52#16813532C2211yescharacteristic
53C2×#41×C113C2211yescharacteristic
54C22×Q8×C113C2211yescharacteristic
55#137×C113—24no—
56C2×Q16×C113C2211yescharacteristic
57C2×Q16×C113C2211yescharacteristic
58C2×SD16×C113C2211yescharacteristic
59C2×SD16×C113C2211yescharacteristic
60C2×M16×C113C2211yescharacteristic
61C2×Dic226—21no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×Dic226C2311yescharacteristic
65Q8×D113—22no—
66Q8×D113—22no—
67Q8×D113—41no—
68Q8×D113—41no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113D411yescharacteristic
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74Dic452—22no—
75#14268637—22no—
76#14268637—22no—
77#14268637—41no—
78#14268635—41no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C8×D113—22no—
82C4⋊Dic113—21no—
83C4⋊Dic113—21no—
84C4⋊Dic113C2311yescharacteristic
85C4⋊Dic113C2311yescharacteristic
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626D411yescharacteristic
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113D411yescharacteristic
98#14268624—21no—
99#14268624D411yescharacteristic
100C4×Dic113—21no—
101C4×Dic113—21no—
102C4×Dic113C2311yescharacteristic
103#41×C113—22no—
104#41×C113—41no—
105C2×Q8×C113—21no—
106C2×Q8×C113—22no—
107C2×Q8×C113—41no—
108C2×Q8×C113C2311yescharacteristic
109C2×Q8×C113C2311yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113—21no—
114C22×C4×C113—21no—
115C22×C4×C113C2311yescharacteristic
116Q16×C113—22no—
117Q16×C113D414yescomplemented
118SD16×C113—22no—
119SD16×C113—22no—
120M16×C113—22no—
121C2×C8×C113C2311yescharacteristic
122C2×C8×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C22×D113C2×D411yescharacteristic
126Q8×C113—21no—
127Q8×C113—21no—
128Q8×C113—21no—
129Q8×C113—21no—
130Q8×C113—42no—
131Q8×C113C2×D412yes—
132Q8×C113C2×D412yes—
133D4×C113—21no—
134D4×C113—21no—
135D4×C113—42no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—42no—
142C2×C4×C113—42no—
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2411yescharacteristic
145C22⋊D113—22no—
146C22⋊D113—42no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—21no—
151C2×Dic113C2×D411yescharacteristic
152C2×Dic113C2×D411yescharacteristic
153C2×Dic113C2×D411yescharacteristic
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—42no—
157C4×D113—42no—
158Dic226—21no—
159Dic226—21no—
160Dic226—21no—
161Dic226—21no—
162Dic226—42no—
163Dic226—42no—
164C8×C113—21no—
165C8×C113C2×D412yes—
166#11744751—21no—
167#11744751—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113C22×D411yescharacteristic
175C2×D113—21no—
176C2×D113—21no—
177C2×D113#13712yescomplemented
178C4×C113—22no—
179C4×C113—22no—
180C4×C113—21no—
181C4×C113—41no—
182C4×C113C22×D411yescharacteristic
183C4×C113H(5,𝔽2)11yescharacteristic
184Dic113—21no—
185Dic113—21no—
186Dic113—21no—
187Dic113—41no—
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191C2×C113—41no—
192C2×C113—81no—
193C2×C113D4211yescharacteristic
194C2×C113C2×#13711yescharacteristic
195C2×C113#57811yescharacteristic
196D113—22no—
197#3270—1131nomaximal, Sylow
198C113#327011yescharacteristic, complemented, Sylow
199C2×#137D11311yescharacteristic, complemented
200C22×Q16—1131no—
201D4×Q8—1131no—
202#548—1131no—
203#497—1131no—
204#470—1131no—
205#465—1131no—
206#464—1131no—
207#462—1131no—
208#452—1131no—
209#451—1131no—
210#451—1131no—
211#448—1131no—
212#441—1131no—
213#435—1131no—
214C2×#41C2×D11311yescharacteristic
215C22×Q8—1131no—
216C22×Q8—1131no—
217C22×Q8C2×D11311yescharacteristic
218#137—24no—
219C2×Q16—1131no—
220C2×Q16—1131no—
221C2×Q16—1131no—
222C2×Q16—1131no—
223C2×Q16—2264no—
224C2×Q16C2×D11311yescharacteristic
225C2×Q16C2×D11311yescharacteristic
226C2×SD16—1131no—
227C2×SD16C2×D11311yescharacteristic
228C2×SD16C2×D11311yescharacteristic
229C2×M16C2×D11311yescharacteristic
230C22×C8—1131no—
231C4⋊Q8—1131no—
232C4⋊Q8—2261no—
233#124—1131no—
234#124—2261no—
235C22⋊Q8—1131no—
236C22⋊Q8—1131no—
237C22⋊Q8—1131no—
238C22⋊Q8—2261no—
239C22⋊Q8—2261no—
240C22⋊Q8—2261no—
241#121—1131no—
242#121—2261no—
243C4×Q8—1131no—
244C4×Q8—1131no—
245C4×D4—1131no—
246C4×D4—2261no—
247C4×D4—2261no—
248#106—1131no—
249C4⋊C8—1131no—
250#103—1131no—
251#103—1131no—
252#103—1131no—
253#103—1131no—
254#103—1131no—
255#102—1131no—
256C22⋊C8—1131no—
257C22⋊C8—1131no—
258#97—1131no—
259#41—22no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—1131no—
265C2×Q8—1131no—
266C2×Q8—4521no—
267C2×Q8—4521no—
268C2×Q8—2261no—
269C2×Q8—2261no—
270C2×Q8—2262no—
271C2×Q8—2262no—
272C2×Q8C22×D11311yescharacteristic
273C2×Q8C22×D11311yescharacteristic
274C2×Q8C22×D11311yescharacteristic
275C2×D4—21no—
276C2×D4—1131no—
277C2×D4—2261no—
278C2×D4C22×D11311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—1131no—
282C22×C4—2261no—
283C22×C4—2261no—
284C22×C4C22×D11311yescharacteristic
285Q16—22no—
286Q16—4521no—
287Q16—2262no—
288Q16—2262no—
289Q16—2262no—
290Q16C22⋊D11314yescomplemented
291SD16—22no—
292SD16—22no—
293SD16—4521no—
294M16—22no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8—2262no—
298C2×C8C22×D11311yescharacteristic
299C2×C8C22×D11311yescharacteristic
300C4⋊C4—1131no—
301C4⋊C4—1131no—
302C4⋊C4—1131no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4—2261no—
308C4⋊C4—2261no—
309C4⋊C4—2261no—
310C22⋊C4—1131no—
311C22⋊C4—1131no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C42—1131no—
319C42—2261no—
320C42—2261no—
321C23—21no—
322C23—1131no—
323C23D4×D11311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—42no—
329Q8—4522no—
330Q8—4522no—
331Q8—2261no—
332Q8—2261no—
333Q8—2261no—
334Q8—2261no—
335Q8C2×C22⋊D11312yes—
336Q8C2×C22⋊D11312yes—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—4522no—
341D4—2262no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—1131no—
350C2×C4—1131no—
351C2×C4—1131no—
352C2×C4—4522no—
353C2×C4—4522no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4D4×D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—21no—
363C8—2261no—
364C8—2261no—
365C8C2×C22⋊D11312yes—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—1132no—
373C22—2261no—
374C22—2261no—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—4521no—
381C4—4521no—
382C4—4521no—
383C4—4521no—
384C4—2261no—
385C4—2261no—
386C4—2261no—
387C4C22×C22⋊D11311yescharacteristic
388C4#1681366711yescharacteristic
389C2—41no—
390C2—81no—
391C2—2262no—
392C2D4×C22⋊D11311yescharacteristic
393C2#137×D11311yescharacteristic
394C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
prime radical#20299255C2
hypercenterC2×#137D113
hypocenterC113#3270
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D113C2semidirect
2. Q8×C22⋊D113C2semidirect
4. #20298989C2semidirect
5. #20298856C2semidirect
6. #20298824C2semidirect
7. #20298818C2semidirect
8. #20298806C2semidirect
9. #20298760C2semidirect
10. #20298754C2semidirect
11. #20298752C2semidirect
12. #20298735C2semidirect
13. #20298705C2semidirect
14. #20298667C2semidirect
15. C2×#137×C113C2semidirect
117. Q16×C113D4semidirect
177. C2×D113#137semidirect
198. C113#3270semidirect
199. C2×#137D113semidirect
290. Q16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D1132
Q8×C22⋊D1132
#202992552
#202989892
#202988562
#202988242
#202988182
#202988062
#202987602
#202987542
#202987522
#202987352
#202987052
#202986672
C2×#137×C1132
#3270113