Finite Group Databasebeta

← #28400084

Subgroups — #28400084

Order 14464.

494 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic
2C2×SD16×D113C211yesmaximal, characteristic, complemented
3#20299168C211yesmaximal, characteristic, complemented
4#20299070C211yesmaximal, characteristic, complemented
5#20298812C211yesmaximal, characteristic, complemented
6#20298811C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298804C211yesmaximal, characteristic, complemented
9#20298803C211yesmaximal, characteristic, complemented
10#20298802C211yesmaximal, characteristic, complemented
11#20298801C211yesmaximal, characteristic, complemented
12#20298623C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298591C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813646—24no—
20C2×#14268636C2211yescharacteristic
21C2×#14268636C2211yescharacteristic
22C2×#14268635C2211yescharacteristic
23C2×#14268635C2211yescharacteristic
24C2×#14268634C2211yescharacteristic
25SD16×D113—24no—
26C2×#14268632C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic
29#16813622C2211yescharacteristic, complemented
30#16813620C2211yescharacteristic, complemented
31#16813609C2211yescharacteristic, complemented
32#16813604—21no—
33#16813604—21no—
34#16813599—21no—
35#16813599—21no—
36C4×D452C2211yescharacteristic
37D4×Dic113C2211yescharacteristic
38#16813584C2211yescharacteristic
39C4×C22⋊D113—21no—
40#16813582—21no—
41#16813580C2211yescharacteristic
42#16813579C2211yescharacteristic
43C2×#14268624—21no—
44C22⋊C4×D113—21no—
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813551C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813547C2211yescharacteristic, complemented
50#16813546C2211yescharacteristic, complemented
51#16813545C2211yescharacteristic, complemented
52#16813545C2211yescharacteristic, complemented
53#16813543C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268646—22no—
63#14268646—22no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—22no—
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72D4×D113—22no—
73D4×D113D414yes—
74C22×Dic113—21no—
75C22×Dic113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113C2311yescharacteristic
80#14268636—22no—
81#14268636—22no—
82#14268635—22no—
83#14268635—22no—
84#14268634—22no—
85#14268632—22no—
86#14268630—22no—
87C2×#11744751C2311yescharacteristic
88C2×#11744751C2311yescharacteristic
89C8×D113—22no—
90C4⋊Dic113—21no—
91C4⋊Dic113—21no—
92C4⋊Dic113C2311yescharacteristic
93#14268626—21no—
94#14268626—21no—
95#14268626D411yescharacteristic
96#14268626D411yescharacteristic
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100#14268624—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624D411yescharacteristic
104#14268624D411yescharacteristic
105C4×Dic113—21no—
106C4×Dic113C2311yescharacteristic
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110C22×C4×C113—21no—
111SD16×C113—22no—
112D8×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C42×C113C2311yescharacteristic
120C23×C113—21no—
121C23×C113—21no—
122C22×D113—21no—
123C22×D113—24no—
124C22×D113—81no—
125C22×D113—81no—
126C22×D113C2×D411yescharacteristic
127Q8×C113—21no—
128Q8×C113—21no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113C2×D412yes—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—81no—
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2411yescharacteristic
139C22⋊D113—24no—
140C22⋊D113—42no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—42no—
145C2×Dic113—81no—
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149D452—21no—
150D452C2×D412yes—
151C4×D113—42no—
152C4×D113—81no—
153C4×D113—81no—
154C4×D113C2×D412yes—
155C4×D113#4112yes—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—21no—
160Dic226—42no—
161C8×C113—21no—
162C8×C113—21no—
163#11744751—21no—
164#11744751—21no—
165C22×C113—22no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113C22×D411yescharacteristic
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—22no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—84no—
178C2×D113#12112yes—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—41no—
182C4×C113—41no—
183C4×C113C22×D411yescharacteristic
184C4×C113C2×#4111yescharacteristic
185Dic113—21no—
186Dic113—21no—
187Dic113—41no—
188Dic113—41no—
189Dic113—41no—
190Dic113#12112yes—
191C2×C113—42no—
192C2×C113—81no—
193C2×C113C2×#12111yescharacteristic
194C2×C113#57711yescharacteristic
195C2×C113#57711yescharacteristic
196D113—22no—
197D113—42no—
198#3042—1131nomaximal, Sylow
199C113#304211yescharacteristic, complemented, Sylow
200C2×AGL(1,ℤ/8)—1131no—
201C22×SD16—1131no—
202#536—1131no—
203#518—1131no—
204#463—1131no—
205#463—1131no—
206#463—1131no—
207#463D11311yescharacteristic, complemented
208#461—1131no—
209#461—1131no—
210#461—1131no—
211#461—1131no—
212#424—1131no—
213#419—1131no—
214#416—1131no—
215C2×#41—1131no—
216C22×Q8—1131no—
217C22×D4—1131no—
218AGL(1,ℤ/8)—2264no—
219C2×SD16—1131no—
220C2×SD16—1131no—
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×SD16—1131no—
224C2×SD16—2264no—
225C2×SD16C2×D11311yescharacteristic
226C2×D8—1131no—
227C2×D8C2×D11311yescharacteristic
228C2×M16—1131no—
229C22×C8—1131no—
230C4⋊Q8—1131no—
231C4⋊Q8—1131no—
232#124—1131no—
233#124C2×D11311yescharacteristic, complemented
234#123—2261no—
235#123—2261no—
236C22⋊Q8—2261no—
237C22⋊Q8—2261no—
238C4×D4—1131no—
239C4×D4—1131no—
240C4×D4—1131no—
241C4×D4—2261no—
242C4×D4—2261no—
243C4×D4C2×D11311yescharacteristic
244#117—1131no—
245#117—1131no—
246C2×C22⋊C4—2261no—
247C2×C22⋊C4—2261no—
248C4⋊C8—1131no—
249C4⋊C8—1131no—
250C4⋊C8—1131no—
251C4⋊C8C2×D11311yescharacteristic, complemented
252#103—1131no—
253#103—1131no—
254#103—1131no—
255#103—1131no—
256#103—1131no—
257#103C2×D11311yescharacteristic, complemented
258#102—1131no—
259#102C2×D11311yescharacteristic, complemented
260C24—2261no—
261#41—2262no—
262#41—2262no—
263C2×Q8—1131no—
264C2×Q8—1131no—
265C2×Q8—2261no—
266C2×Q8—2262no—
267C2×Q8—2262no—
268C2×Q8C22×D11311yescharacteristic
269C2×D4—1134no—
270C2×D4—1131no—
271C2×D4—2262no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4C22×D11311yescharacteristic
275C2×D4C22×D11311yescharacteristic
276C22×C4—21no—
277C22×C4—1131no—
278C22×C4—2261no—
279C22×C4—2261no—
280C22×C4—2261no—
281C22×C4—2261no—
282C22×C4—2261no—
283SD16—22no—
284SD16—2262no—
285SD16—2262no—
286SD16—2262no—
287SD16—2262no—
288SD16—2262no—
289D8—22no—
290D8—2262no—
291M16—2262no—
292C2×C8—1131no—
293C2×C8—1131no—
294C2×C8—2262no—
295C2×C8C22×D11311yescharacteristic
296C2×C8C22×D11311yescharacteristic
297C4⋊C4—1131no—
298C4⋊C4—1131no—
299C4⋊C4—1131no—
300C4⋊C4—2261no—
301C4⋊C4—2261no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4C22×D11311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—1131no—
309C22⋊C4—1131no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C42—1131no—
317C42—2261no—
318C42C22×D11311yescharacteristic
319C23—21no—
320C23—21no—
321C23—1131no—
322C23—9041no—
323C23—9041no—
324C23—2264no—
325C23—2261no—
326Q8—21no—
327Q8—21no—
328Q8—4522no—
329Q8—2261no—
330Q8—2261no—
331Q8—2261no—
332Q8—2261no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—1132no—
337D4—4522no—
338D4—2264no—
339D4—2261no—
340D4D4×D11312yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—81no—
344C2×C4—1131no—
345C2×C4—1132no—
346C2×C4—1132no—
347C2×C4—1131no—
348C2×C4—1131no—
349C2×C4—9041no—
350C2×C4—9041no—
351C2×C4—9041no—
352C2×C4—4522no—
353C2×C4—4522no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4D4×D11311yescharacteristic
358C2×C4D4×D11311yescharacteristic
359C2×C4C23×D11311yescharacteristic
360C8—21no—
361C8—21no—
362C8—2261no—
363C8—2261no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—1132no—
371C22—9044no—
372C22—4521no—
373C22—4521no—
374C22—2262no—
375C22—2261no—
376C22—2261no—
377C22C2×D4×D11311yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—1132no—
383C4—4521no—
384C4—4521no—
385C4—4521no—
386C4—2261no—
387C4—2261no—
388C4C2×D4×D11311yescharacteristic
389C4#41×D11311yescharacteristic
390C2—42no—
391C2—81no—
392C2—4522no—
393C2—2262no—
394C2#121×D11311yescharacteristic
395C2#2029940511yescharacteristic
396C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813646C2
hypercenter#463D113
hypocenterC113#3042
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D113C2semidirect
3. #20299168C2semidirect
4. #20299070C2semidirect
5. #20298812C2semidirect
6. #20298811C2semidirect
7. #20298810C2semidirect
8. #20298804C2semidirect
9. #20298803C2semidirect
10. #20298802C2semidirect
11. #20298801C2semidirect
12. #20298623C2semidirect
13. #20298605C2semidirect
14. #20298591C2semidirect
15. #463×C113C2semidirect
29. #16813622C22semidirect
30. #16813620C22semidirect
31. #16813609C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813551C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813547C22semidirect
50. #16813546C22semidirect
51. #16813545C22semidirect
52. #16813545C22semidirect
53. #16813543C22semidirect
56. #124×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
199. C113#3042semidirect
207. #463D113semidirect
233. #124C2×D113semidirect
251. C4⋊C8C2×D113semidirect
257. #103C2×D113semidirect
259. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×SD16×D1132
#202991682
#202990702
#202988122
#202988112
#202988102
#202988042
#202988032
#202988022
#202988012
#202986232
#202986052
#202985912
#463×C1132
#3042113