Finite Group Databasebeta

← #28402146

Subgroups — #28402146

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×#16813654C211yesmaximal, characteristic, complemented
2C2×Q16×D113C211yesmaximal, characteristic, complemented
3Q8×D452C211yesmaximal, characteristic, complemented
4#20299260C211yesmaximal, characteristic
5#20298992C211yesmaximal, characteristic, complemented
6#20298857C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298820C211yesmaximal, characteristic, complemented
9#20298808C211yesmaximal, characteristic, complemented
10#20298763C211yesmaximal, characteristic, complemented
11#20298755C211yesmaximal, characteristic, complemented
12#20298755C211yesmaximal, characteristic, complemented
13#20298738C211yesmaximal, characteristic, complemented
14#20298671C211yesmaximal, characteristic, complemented
15#441×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19C2×Q8×D113C2211yescharacteristic
20#16813654—24no—
21C2×Dic452C2211yescharacteristic
22C2×Dic452C2211yescharacteristic
23C2×#14268637C2211yescharacteristic
24C2×#14268637C2211yescharacteristic
25C2×#14268637C2211yescharacteristic
26Q16×D113—24no—
27C2×#14268636C2211yescharacteristic
28C2×#14268636C2211yescharacteristic
29C2×#14268634C2211yescharacteristic
30C2×#14268630C2211yescharacteristic
31C2×C8×D113C2211yescharacteristic
32#16813622—21no—
33#16813622C2211yescharacteristic
34#16813610—21no—
35#16813610C2211yescharacteristic
36#16813602—21no—
37#16813602—21no—
38#16813602—21no—
39#16813602C2211yescharacteristic
40#16813602C2211yescharacteristic
41#16813602C2211yescharacteristic
42#16813597—21no—
43#16813597C2211yescharacteristic
44C4×D452—21no—
45C4×D452—21no—
46C4×D452C2211yescharacteristic
47C4⋊#11744751C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813545C2211yescharacteristic
51#16813542C2211yescharacteristic
52#16813534C2211yescharacteristic
53#16813534C2211yescharacteristic
54C2×Q16×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4×Q8×C113C2211yescharacteristic
57#106×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60#97×C113C2211yescharacteristic
61#14268648—22no—
62#14268648—41no—
63C2×Dic226—21no—
64C2×Dic226—21no—
65C2×Dic226—21no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×Dic226C2311yescharacteristic
69Q8×D113—22no—
70Q8×D113—22no—
71Q8×D113—22no—
72Q8×D113—41no—
73Q8×D113—41no—
74Q8×D113—41no—
75C2×D452—21no—
76C2×D452—21no—
77C2×D452D411yescharacteristic
78C2×D452C2311yescharacteristic
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113—21no—
83C2×C4×D113C2311yescharacteristic
84C2×C4×D113C2311yescharacteristic
85Dic452—22no—
86Dic452—41no—
87#14268637—22no—
88#14268637—22no—
89#14268637—22no—
90#14268636—22no—
91#14268636—41no—
92#14268634—22no—
93#14268630—22no—
94C2×#11744751C2311yescharacteristic
95C2×#11744751C2311yescharacteristic
96C8×D113—22no—
97C4⋊Dic113—21no—
98C4⋊Dic113—21no—
99C4⋊Dic113—21no—
100C4⋊Dic113—21no—
101C4⋊Dic113—21no—
102C4⋊Dic113D411yescharacteristic
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624D411yescharacteristic
110#14268624D411yescharacteristic
111C2×Q8×C113C2311yescharacteristic
112C2×Q8×C113C2311yescharacteristic
113Q16×C113D414yescomplemented
114C2×C8×C113C2311yescharacteristic
115C2×C8×C113C2311yescharacteristic
116C4⋊C4×C113—21no—
117C4⋊C4×C113—21no—
118C4⋊C4×C113C2311yescharacteristic
119C4⋊C4×C113C2311yescharacteristic
120C42×C113—21no—
121C42×C113—21no—
122C42×C113C2311yescharacteristic
123C22×D113—21no—
124C22×D113C2×D411yescharacteristic
125C22×D113C2×D411yescharacteristic
126Q8×C113—21no—
127Q8×C113—21no—
128Q8×C113C2×D412yes—
129Q8×C113C2×D412yes—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142D452—22no—
143D452—21no—
144D452—21no—
145D452—42no—
146D452—42no—
147C4×D113—21no—
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—21no—
151C4×D113—42no—
152C4×D113—42no—
153C4×D113—42no—
154C4×D113—42no—
155Dic226—21no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226—21no—
161Dic226—42no—
162Dic226—42no—
163Dic226—42no—
164C8×C113—21no—
165C8×C113C2×D412yes—
166#11744751—21no—
167#11744751—21no—
168C22×C113C22×D411yescharacteristic
169C2×D113—21no—
170C2×D113—21no—
171C2×D113—21no—
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113#13712yescomplemented
178C4×C113—22no—
179C4×C113—22no—
180C4×C113—21no—
181C4×C113—21no—
182C4×C113—41no—
183C4×C113—41no—
184C4×C113C22×D411yescharacteristic
185C4×C113H(5,𝔽2)11yescharacteristic
186Dic113—21no—
187Dic113—21no—
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191C2×C113D4211yescharacteristic
192C2×C113C2×#13711yescharacteristic
193C2×C113#57811yescharacteristic
194D113—22no—
195D113—41no—
196D113—81no—
197#3270—1131nomaximal, Sylow
198C113#327011yescharacteristic, complemented, Sylow
199C2×#137—1131no—
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#441D11311yescharacteristic, complemented
213#435—1131no—
214C2×#41—1131no—
215C22×Q8—1131no—
216C22×Q8—1131no—
217C22×Q8—1131no—
218#137—2264no—
219C2×Q16—1131no—
220C2×Q16—1131no—
221C2×Q16—1131no—
222C2×Q16—1131no—
223C2×Q16—1131no—
224C2×Q16—2264no—
225C2×Q16C2×D11311yescharacteristic
226C2×SD16—1131no—
227C2×SD16—1131no—
228C2×SD16—1131no—
229C2×M16—1131no—
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×Q8C2×D11311yescharacteristic
244C4×Q8C2×D11311yescharacteristic
245C4×D4—1131no—
246C4×D4—2261no—
247C4×D4—2261no—
248#106C2×D11311yescharacteristic
249C4⋊C8—1131no—
250#103—1131no—
251#103—1131no—
252#103—1131no—
253#103C2×D11311yescharacteristic
254#103C2×D11311yescharacteristic
255#102—1131no—
256C22⋊C8—1131no—
257C22⋊C8—1131no—
258#97C2×D11311yescharacteristic
259#41—4521no—
260#41—2262no—
261C2×Q8—1131no—
262C2×Q8—1131no—
263C2×Q8—1131no—
264C2×Q8—4521no—
265C2×Q8—4521no—
266C2×Q8—4521no—
267C2×Q8—2261no—
268C2×Q8—2261no—
269C2×Q8—2261no—
270C2×Q8—2262no—
271C2×Q8—2262no—
272C2×Q8—2262no—
273C2×Q8C22×D11311yescharacteristic
274C2×Q8C22×D11311yescharacteristic
275C2×D4—1131no—
276C2×D4—1131no—
277C2×D4—2261no—
278C2×D4—2261no—
279C22×C4—1131no—
280C22×C4—1131no—
281C22×C4—2261no—
282C22×C4—2261no—
283C22×C4—2261no—
284C22×C4—2261no—
285Q16—4521no—
286Q16—2262no—
287Q16—2262no—
288Q16—2262no—
289Q16—2262no—
290Q16D45214yescomplemented
291SD16—4521no—
292SD16—2262no—
293SD16—2262no—
294M16—2262no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8—2262no—
298C2×C8C22×D11311yescharacteristic
299C2×C8C22×D11311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—1131no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4—2261no—
308C4⋊C4C22×D11311yescharacteristic
309C4⋊C4C22×D11311yescharacteristic
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—21no—
319C42—21no—
320C42C22×D11311yescharacteristic
321C23—1131no—
322C23—1131no—
323C23—2261no—
324Q8—21no—
325Q8—21no—
326Q8—4522no—
327Q8—4522no—
328Q8—4522no—
329Q8—2261no—
330Q8—2261no—
331Q8—2261no—
332Q8—2261no—
333Q8—2261no—
334Q8—2261no—
335Q8C2×D45212yes—
336Q8C2×D45212yes—
337D4—4522no—
338D4—4522no—
339D4—2262no—
340D4—2261no—
341D4—2261no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—1131no—
347C2×C4—1131no—
348C2×C4—4522no—
349C2×C4—4522no—
350C2×C4—4522no—
351C2×C4—4522no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4D4×D11311yescharacteristic
360C2×C4D4×D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—21no—
363C8—2261no—
364C8—2261no—
365C8C2×D45212yes—
366C22—1132no—
367C22—4521no—
368C22—4521no—
369C22—4521no—
370C22—2261no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22—2261no—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—4521no—
383C4—4521no—
384C4—4521no—
385C4—2261no—
386C4—2261no—
387C4C22×D45211yescharacteristic
388C4#1681366811yescharacteristic
389C2—9041no—
390C2—4521no—
391C2—2262no—
392C2D4×D45211yescharacteristic
393C2#137×D11311yescharacteristic
394C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#441×C113C2
socleC22×C113C22×D4
prime radical#20299260C2
hypercenter#441D113
hypocenterC113#3270
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C2×Q16×D113C2semidirect
3. Q8×D452C2semidirect
5. #20298992C2semidirect
6. #20298857C2semidirect
7. #20298828C2semidirect
8. #20298820C2semidirect
9. #20298808C2semidirect
10. #20298763C2semidirect
11. #20298755C2semidirect
12. #20298755C2semidirect
13. #20298738C2semidirect
14. #20298671C2semidirect
15. #441×C113C2semidirect
113. Q16×C113D4semidirect
177. C2×D113#137semidirect
198. C113#3270semidirect
212. #441D113semidirect
290. Q16D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×Q16×D1132
Q8×D4522
#202992602
#202989922
#202988572
#202988282
#202988202
#202988082
#202987632
#202987552
#202987382
#202986712
#441×C1132
#3270113