Finite Group Databasebeta

← #28400036

Subgroups — #28400036

Order 14464.

548 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813649C211yesmaximal, characteristic, complemented
2C2×#16813646C211yesmaximal, characteristic, complemented
3#20299147C211yesmaximal, characteristic, complemented
4C4×D4×D113C211yesmaximal, characteristic, complemented
5#20298814C211yesmaximal, characteristic, complemented
6#20298813C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298802C211yesmaximal, characteristic, complemented
9#20298801C211yesmaximal, characteristic, complemented
10#20298792C211yesmaximal, characteristic, complemented
11#20298791C211yesmaximal, characteristic, complemented
12#20298620C211yesmaximal, characteristic, complemented
13#20298598C211yesmaximal, characteristic, complemented
14#20298596C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19C22×C4×D113—21no—
20#16813649—24no—
21#16813646—24no—
22C2×#14268636C2211yescharacteristic
23C2×#14268635C2211yescharacteristic
24C2×#14268634C2211yescharacteristic
25C2×D904C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C2×#14268630C2211yescharacteristic
29C2×#14268630C2211yescharacteristic
30#16813620C2211yescharacteristic, complemented
31#16813618C2211yescharacteristic, complemented
32#16813610C2211yescharacteristic, complemented
33#16813595—21no—
34#16813595—21no—
35C4×D452C2211yescharacteristic
36D4×Dic113C2211yescharacteristic
37#16813584C2211yescharacteristic
38C4×C22⋊D113—21no—
39#16813582—21no—
40#16813582—21no—
41#16813582—21no—
42C4⋊C4×D113C2211yescharacteristic
43C22⋊C4×D113—21no—
44C42×D113C2211yescharacteristic
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813551C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813546C2211yescharacteristic, complemented
50#16813545C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic, complemented
52#16813543C2211yescharacteristic, complemented
53#16813542C2211yescharacteristic, 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#14268648—22no—
63#14268648—22no—
64#14268646—22no—
65#14268646—22no—
66C2×Dic226C2311yescharacteristic
67C2×D452—21no—
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74D4×D113—22no—
75D4×D113D414yescomplemented
76C22×Dic113—21no—
77C22×Dic113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113—44no—
83C2×C4×D113D411yescharacteristic
84C2×C4×D113D411yescharacteristic
85C2×C4×D113C2311yescharacteristic
86#14268636—22no—
87#14268635—22no—
88#14268634—22no—
89D904—22no—
90#14268632—22no—
91#14268632—22no—
92#14268630—22no—
93#14268630—22no—
94C2×#11744751C2311yescharacteristic
95C2×#11744751C2311yescharacteristic
96C4⋊Dic113C2311yescharacteristic
97#14268626—21no—
98#14268626—21no—
99#14268626—21no—
100C22⋊Dic113—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105C4×Dic113D411yescharacteristic
106C4×Dic113D411yescharacteristic
107C4×Dic113C2311yescharacteristic
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110C2×D4×C113C2311yescharacteristic
111C22×C4×C113—21no—
112SD16×C113—22no—
113D8×C113—22no—
114C2×C8×C113C2311yescharacteristic
115C2×C8×C113C2311yescharacteristic
116C4⋊C4×C113C2311yescharacteristic
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C42×C113C2311yescharacteristic
121C23×C113—21no—
122C23×C113—21no—
123C22×D113—21no—
124C22×D113—24no—
125C22×D113—21no—
126C22×D113—42no—
127C22×D113—42no—
128C22×D113C2×D411yescharacteristic
129Q8×C113—21no—
130Q8×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—21no—
134D4×C113C2×D412yes—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—42no—
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2411yescharacteristic
141C22⋊D113—24no—
142C22⋊D113—42no—
143C22⋊D113—42no—
144C22⋊D113—42no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—42no—
148C2×Dic113—42no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151C2×Dic113C2×D411yescharacteristic
152D452—21no—
153D452—21no—
154D452—21no—
155D452—42no—
156D452C2×D412yes—
157C4×D113—22no—
158C4×D113—41no—
159C4×D113—42no—
160C4×D113—42no—
161C4×D113—42no—
162C4×D113—42no—
163C4×D113C2×D412yes—
164C4×D113#4112yes—
165Dic226—21no—
166Dic226—21no—
167C8×C113—21no—
168C8×C113—21no—
169#11744751—21no—
170#11744751—21no—
171C22×C113—22no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113C22×D411yescharacteristic
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—22no—
181C2×D113—48no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113#12112yes—
188C4×C113—21no—
189C4×C113—21no—
190C4×C113—41no—
191C4×C113—41no—
192C4×C113C22×D411yescharacteristic
193C4×C113C2×#4111yescharacteristic
194Dic113—21no—
195Dic113—41no—
196Dic113—41no—
197Dic113#12112yes—
198Dic113AGL(1,ℤ/8)12yescomplemented
199C2×C113—42no—
200C2×C113—81no—
201C2×C113C2×#12111yescharacteristic
202C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
203C2×C113#57511yescharacteristic
204D113—22no—
205D113—42no—
206D113—81no—
207#3036—1131nomaximal, Sylow
208C113#303611yescharacteristic, complemented, Sylow
209C2×AGL(1,ℤ/8)—1131no—
210C2×AGL(1,ℤ/8)—1131no—
211#532—1131no—
212C2×C4×D4—1131no—
213#463—1131no—
214#463—1131no—
215#463—1131no—
216#463D11311yescharacteristic, complemented
217#461—1131no—
218#461—1131no—
219#459—1131no—
220#459—1131no—
221#423—1131no—
222#417—1131no—
223#417—1131no—
224C2×#41—1131no—
225C2×#41—1131no—
226C22×D4—1131no—
227C23×C4—2261no—
228AGL(1,ℤ/8)—2264no—
229AGL(1,ℤ/8)—2264no—
230C2×SD16—1131no—
231C2×SD16—1131no—
232C2×SD16—1131no—
233C2×SD16C2×D11311yescharacteristic
234C2×D8—1131no—
235C2×D8—1131no—
236C2×D8—1131no—
237C2×D8C2×D11311yescharacteristic
238C2×M16—1131no—
239C2×M16—1131no—
240C4⋊Q8—1131no—
241#127—1131no—
242#124—1131no—
243#124C2×D11311yescharacteristic, complemented
244#121—2261no—
245#121—2261no—
246C4×D4—1131no—
247C4×D4—1131no—
248C4×D4—1131no—
249C4×D4—2261no—
250C4×D4—2261no—
251C4×D4—2261no—
252C4×D4—2261no—
253C4×D4C2×D11311yescharacteristic
254C2×C4⋊C4—1131no—
255C2×C22⋊C4—2261no—
256C2×C42—1131no—
257C4⋊C8—1131no—
258C4⋊C8—1131no—
259C4⋊C8—1131no—
260C4⋊C8C2×D11311yescharacteristic, complemented
261#103—1131no—
262#103—1131no—
263#103—1131no—
264#103C2×D11311yescharacteristic, complemented
265#102—1131no—
266#102—1131no—
267#102—1131no—
268#102C2×D11311yescharacteristic, complemented
269C24—2261no—
270#41—2262no—
271#41—2262no—
272#41—2262no—
273#41—2262no—
274C2×Q8—1131no—
275C2×Q8C22×D11311yescharacteristic
276C2×D4—1134no—
277C2×D4—1131no—
278C2×D4—1131no—
279C2×D4—2261no—
280C2×D4—2262no—
281C2×D4—2261no—
282C2×D4—2261no—
283C2×D4—2261no—
284C2×D4—2261no—
285C2×D4C22×D11311yescharacteristic
286C2×D4C22×D11311yescharacteristic
287C22×C4—21no—
288C22×C4—1131no—
289C22×C4—1131no—
290C22×C4—1131no—
291C22×C4—4524no—
292C22×C4—2261no—
293C22×C4—2261no—
294C22×C4—2261no—
295C22×C4—2261no—
296C22×C4—2261no—
297C22×C4—2261no—
298SD16—22no—
299SD16—2262no—
300SD16—2262no—
301SD16—2262no—
302D8—22no—
303D8—2262no—
304D8—2262no—
305D8—2262no—
306M16—2262no—
307M16—2262no—
308C2×C8—1131no—
309C2×C8—1131no—
310C2×C8C22×D11311yescharacteristic
311C2×C8C22×D11311yescharacteristic
312C4⋊C4—1131no—
313C4⋊C4—2261no—
314C4⋊C4—2261no—
315C4⋊C4—2261no—
316C4⋊C4C22×D11311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C42—1131no—
326C42—1131no—
327C42—1131no—
328C42C22×D11311yescharacteristic
329C23—21no—
330C23—21no—
331C23—1131no—
332C23—4522no—
333C23—4522no—
334C23—2264no—
335C23—2261no—
336C23—2261no—
337Q8—21no—
338Q8—21no—
339Q8—2261no—
340Q8—2261no—
341D4—21no—
342D4—21no—
343D4—21no—
344D4—1132no—
345D4—4522no—
346D4—4522no—
347D4—4522no—
348D4—4522no—
349D4—2264no—
350D4—2261no—
351D4—2261no—
352D4—2261no—
353D4D4×D11312yes—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—1131no—
358C2×C4—1131no—
359C2×C4—1132no—
360C2×C4—1132no—
361C2×C4—1131no—
362C2×C4—4522no—
363C2×C4—4521no—
364C2×C4—4522no—
365C2×C4—4522no—
366C2×C4—4522no—
367C2×C4—4522no—
368C2×C4—4522no—
369C2×C4—2262no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4D4×D11311yescharacteristic
373C2×C4D4×D11311yescharacteristic
374C2×C4C23×D11311yescharacteristic
375C8—21no—
376C8—21no—
377C8—2261no—
378C8—2261no—
379C22—22no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—1132no—
386C22—4528no—
387C22—4521no—
388C22—4521no—
389C22—4521no—
390C22—4521no—
391C22—4521no—
392C22—2262no—
393C22—2261no—
394C22—2261no—
395C22C2×D4×D11311yescharacteristic
396C4—21no—
397C4—21no—
398C4—41no—
399C4—41no—
400C4—1132no—
401C4—1132no—
402C4—4521no—
403C4—4521no—
404C4—2261no—
405C4C2×D4×D11311yescharacteristic
406C4#41×D11311yescharacteristic
407C2—42no—
408C2—81no—
409C2—9041no—
410C2—4522no—
411C2—2262no—
412C2#121×D11311yescharacteristic
413C2AGL(1,ℤ/8)×D11311yescharacteristic
414C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
hypercenter#463D113
hypocenterC113#3036
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
1. C2×#16813649C2semidirect
2. C2×#16813646C2semidirect
3. #20299147C2semidirect
4. C4×D4×D113C2semidirect
5. #20298814C2semidirect
6. #20298813C2semidirect
7. #20298810C2semidirect
8. #20298802C2semidirect
9. #20298801C2semidirect
10. #20298792C2semidirect
11. #20298791C2semidirect
12. #20298620C2semidirect
13. #20298598C2semidirect
14. #20298596C2semidirect
15. #463×C113C2semidirect
30. #16813620C22semidirect
31. #16813618C22semidirect
32. #16813610C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813551C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813546C22semidirect
50. #16813545C22semidirect
51. #16813544C22semidirect
52. #16813543C22semidirect
53. #16813542C22semidirect
56. #124×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
75. D4×D113D4semidirect
198. Dic113AGL(1,ℤ/8)semidirect
208. C113#3036semidirect
216. #463D113semidirect
243. #124C2×D113semidirect
260. C4⋊C8C2×D113semidirect
264. #103C2×D113semidirect
268. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×#168136462
#202991472
C4×D4×D1132
#202988142
#202988132
#202988102
#202988022
#202988012
#202987922
#202987912
#202986202
#202985982
#202985962
#463×C1132
#3036113