Finite Group Databasebeta

← #28402105

Subgroups — #28402105

Order 14464.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813649C211yesmaximal, characteristic, complemented
2C2×#16813643C211yesmaximal, characteristic, complemented
3#20299251C211yesmaximal, characteristic, complemented
4#20299243C211yesmaximal, characteristic, complemented
5#20298990C211yesmaximal, characteristic, complemented
6#20298855C211yesmaximal, characteristic, complemented
7#20298830C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298763C211yesmaximal, characteristic, complemented
10#20298757C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298746C211yesmaximal, characteristic, complemented
13#20298708C211yesmaximal, characteristic, complemented
14#20298668C211yesmaximal, characteristic, complemented
15#461×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268648C2211yescharacteristic, complemented
18C2×#14268646C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic
20#16813649—24no—
21#16813643—24no—
22C2×#14268637C2211yescharacteristic, complemented
23C2×#14268637C2211yescharacteristic, complemented
24C2×#14268636C2211yescharacteristic, complemented
25C2×#14268634C2211yescharacteristic
26C2×#14268634C2211yescharacteristic
27C2×D904C2211yescharacteristic
28C2×#14268632C2211yescharacteristic
29C2×#14268630C2211yescharacteristic
30C2×C8×D113C2211yescharacteristic, complemented
31#16813610C2211yescharacteristic
32#16813607—21no—
33#16813607—21no—
34#16813606—21no—
35#16813602C2211yescharacteristic
36#16813598C2211yescharacteristic
37#16813598C2211yescharacteristic, complemented
38#16813597—21no—
39#16813597C2211yescharacteristic
40#16813596—21no—
41#16813592—21no—
42C4×D452C2211yescharacteristic
43C4×D452C2211yescharacteristic, complemented
44C4⋊C4×D113—21no—
45C2×#14268624—21no—
46#16813553C2211yescharacteristic, complemented
47#16813547C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813542C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic
52#16813534C2211yescharacteristic, complemented
53#16813533C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56C4⋊Q8×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#103×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268648—22no—
63#14268648—22no—
64#14268648—41no—
65#14268648—41no—
66#14268646—22no—
67#14268646—41no—
68C2×Dic226C2311yescharacteristic
69C2×D452—21no—
70C2×D452—21no—
71C2×D452—21no—
72C2×D452D411yescharacteristic
73C2×D452C2311yescharacteristic
74C2×D452C2311yescharacteristic
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77D4×D113—22no—
78D4×D113—41no—
79C22×Dic113—21no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113—21no—
83C2×C4×D113C2311yescharacteristic
84C2×C4×D113C2311yescharacteristic
85#14268637—22no—
86#14268637—41no—
87#14268636—22no—
88#14268634—22no—
89#14268634—41no—
90D904—22no—
91#14268632D414yescomplemented
92#14268630—22no—
93C2×#11744751C2311yescharacteristic
94C2×#11744751C2311yescharacteristic
95C8×D113—22no—
96C4⋊Dic113—21no—
97C4⋊Dic113D411yescharacteristic
98C4⋊Dic113C2311yescharacteristic
99#14268626—21no—
100#14268626—21no—
101#14268624—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624D411yescharacteristic
109#14268624D411yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×Q8×C113C2311yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113—21no—
114SD16×C113—22no—
115SD16×C113—22no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C22×D113—21no—
125C22×D113—21no—
126C22×D113—42no—
127C22×D113—42no—
128C22×D113—81no—
129C22×D113C2×D411yescharacteristic
130C22×D113C2×D411yescharacteristic
131Q8×C113—21no—
132Q8×C113—21no—
133Q8×C113—21no—
134Q8×C113—21no—
135D4×C113—21no—
136D4×C113C2×D412yes—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—81no—
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2411yescharacteristic
144C22⋊D113—42no—
145C22⋊D113—42no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151D452—21no—
152D452—21no—
153D452—21no—
154D452—41no—
155D452—42no—
156D452—42no—
157D452—81no—
158D452C2×D412yes—
159C4×D113—21no—
160C4×D113—21no—
161C4×D113—21no—
162C4×D113—21no—
163C4×D113—42no—
164C4×D113—42no—
165C4×D113—42no—
166Dic226—21no—
167Dic226—21no—
168C8×C113—21no—
169C8×C113—21no—
170#11744751—21no—
171#11744751C2×D412yes—
172C22×C113—22no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113C22×D411yescharacteristic
176C2×D113—21no—
177C2×D113—21no—
178C2×D113—22no—
179C2×D113—21no—
180C2×D113—21no—
181C2×D113—21no—
182C2×D113—21no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—84no—
189C4×C113—21no—
190C4×C113—21no—
191C4×C113—41no—
192C4×C113—41no—
193C4×C113—41no—
194C4×C113C22×D411yescharacteristic
195C4×C113H(5,𝔽2)11yescharacteristic
196Dic113—21no—
197Dic113—21no—
198Dic113—41no—
199Dic113—41no—
200C2×C113—42no—
201C2×C113D4211yescharacteristic
202C2×C113#57511yescharacteristic
203C2×C113#57711yescharacteristic
204D113—41no—
205D113—41no—
206D113—42no—
207D113—81no—
208#3267—1131nomaximal, Sylow
209C113#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—1131no—
211C2×#135—1131no—
212#547—1131no—
213#546—1131no—
214#497—1131no—
215#470—1131no—
216#465—1131no—
217#463—1131no—
218#461D11311yescharacteristic, complemented
219#452—1131no—
220#452—1131no—
221#450—1131no—
222#449—1131no—
223#442—1131no—
224#435—1131no—
225C2×#41—1131no—
226C2×#41—1131no—
227C2×#41—1131no—
228C22×D4—1131no—
229AGL(1,ℤ/8)—2264no—
230#135—2264no—
231C2×Q16—1131no—
232C2×Q16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—1131no—
236C2×SD16C2×D11311yescharacteristic
237C2×SD16C2×D11311yescharacteristic
238C2×D8—1131no—
239C2×D8—1131no—
240C2×M16—1131no—
241C22×C8—1131no—
242C4⋊Q8C2×D11311yescharacteristic, complemented
243#124—1131no—
244#123—2261no—
245#123—2261no—
246#123—2261no—
247C22⋊Q8—1131no—
248C22⋊Q8—1131no—
249C22⋊Q8—1131no—
250#121—1131no—
251#121—2261no—
252#121—2261no—
253#120—2261no—
254C4×D4—1131no—
255C4×D4—1131no—
256C4×D4C2×D11311yescharacteristic
257C2×C4⋊C4—2261no—
258C2×C22⋊C4—2261no—
259#106—1131no—
260C4⋊C8C2×D11311yescharacteristic, complemented
261#103—1131no—
262#103C2×D11311yescharacteristic, complemented
263#103C2×D11311yescharacteristic, complemented
264#102—1131no—
265#102—1131no—
266#102—1131no—
267C22⋊C8—1131no—
268C22⋊C8—1131no—
269#97—1131no—
270C24—2261no—
271#41—4521no—
272#41—4521no—
273#41—4521no—
274#41—2262no—
275#41—2262no—
276#41—2262no—
277C2×Q8—1131no—
278C2×Q8C22×D11311yescharacteristic
279C2×Q8C22×D11311yescharacteristic
280C2×D4—1131no—
281C2×D4—1131no—
282C2×D4—1131no—
283C2×D4—4521no—
284C2×D4—2261no—
285C2×D4—2261no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4—2262no—
290C2×D4C22×D11311yescharacteristic
291C22×C4—21no—
292C22×C4—1131no—
293C22×C4—1131no—
294C22×C4—2261no—
295C22×C4—2261no—
296C22×C4—2261no—
297C22×C4—2261no—
298Q16—4521no—
299Q16—2262no—
300SD16—22no—
301SD16—22no—
302SD16—4521no—
303SD16—2262no—
304SD16—2262no—
305D8—1134no—
306D8—2262no—
307M16—2262no—
308C2×C8—1131no—
309C2×C8—1131no—
310C2×C8—2262no—
311C2×C8C22×D11311yescharacteristic
312C2×C8C22×D11311yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—1131no—
316C4⋊C4—1131no—
317C4⋊C4—2261no—
318C4⋊C4—2261no—
319C4⋊C4—2261no—
320C4⋊C4C22×D11311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—1131no—
323C22⋊C4—1131no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4—2261no—
330C22⋊C4—2261no—
331C42C22×D11311yescharacteristic
332C23—21no—
333C23—1131no—
334C23—1131no—
335C23—9041no—
336C23—4522no—
337C23—4522no—
338C23—2261no—
339C23—2261no—
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—2261no—
345Q8—2261no—
346D4—21no—
347D4—1132no—
348D4—9041no—
349D4—4521no—
350D4—4522no—
351D4—4522no—
352D4—4522no—
353D4—4522no—
354D4—2261no—
355D4—2261no—
356D4—2261no—
357D4D4×D11312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—81no—
362C2×C4—1131no—
363C2×C4—1131no—
364C2×C4—4522no—
365C2×C4—4522no—
366C2×C4—4522no—
367C2×C4—4522no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4D4×D11311yescharacteristic
375C2×C4D4×D11311yescharacteristic
376C2×C4C23×D11311yescharacteristic
377C8—21no—
378C8—21no—
379C8—1132no—
380C8—2261no—
381C22—22no—
382C22—41no—
383C22—41no—
384C22—9044no—
385C22—4521no—
386C22—4521no—
387C22—4521no—
388C22—4521no—
389C22—4521no—
390C22—2261no—
391C22—2261no—
392C22—2261no—
393C22—2261no—
394C22—2262no—
395C22—2261no—
396C22—2261no—
397C22C2×D4×D11311yescharacteristic
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—4521no—
404C4—4521no—
405C4—2261no—
406C4—2261no—
407C4C2×D4×D11311yescharacteristic
408C4#1681366811yescharacteristic
409C2—42no—
410C2—9041no—
411C2—4521no—
412C2—4522no—
413C2—4521no—
414C2#2029923211yescharacteristic
415C2#2029939711yescharacteristic
416C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
hypercenter#461D113
hypocenterC113#3267
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C2×#16813643C2semidirect
3. #20299251C2semidirect
4. #20299243C2semidirect
5. #20298990C2semidirect
6. #20298855C2semidirect
7. #20298830C2semidirect
8. #20298814C2semidirect
9. #20298763C2semidirect
10. #20298757C2semidirect
11. #20298747C2semidirect
12. #20298746C2semidirect
13. #20298708C2semidirect
14. #20298668C2semidirect
15. #461×C113C2semidirect
17. C2×#14268648C22semidirect
22. C2×#14268637C22semidirect
23. C2×#14268637C22semidirect
24. C2×#14268636C22semidirect
30. C2×C8×D113C22semidirect
37. #16813598C22semidirect
43. C4×D452C22semidirect
46. #16813553C22semidirect
47. #16813547C22semidirect
50. #16813542C22semidirect
52. #16813534C22semidirect
53. #16813533C22semidirect
56. C4⋊Q8×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
60. #103×C113C22semidirect
91. #14268632D4semidirect
209. C113#3267semidirect
218. #461D113semidirect
242. C4⋊Q8C2×D113semidirect
260. C4⋊C8C2×D113semidirect
262. #103C2×D113semidirect
263. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×#168136432
#202992512
#202992432
#202989902
#202988552
#202988302
#202988142
#202987632
#202987572
#202987472
#202987462
#202987082
#202986682
#461×C1132
#3267113