Finite Group Databasebeta

← #28402107

Subgroups — #28402107

Order 14464.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813649C211yesmaximal, characteristic, complemented
2C2×#16813642C211yesmaximal, characteristic, complemented
3#20299267C211yesmaximal, characteristic, complemented
4#20299245C211yesmaximal, characteristic, complemented
5#20298986C211yesmaximal, characteristic, complemented
6#20298843C211yesmaximal, characteristic, complemented
7#20298832C211yesmaximal, characteristic, complemented
8#20298818C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298763C211yesmaximal, characteristic, complemented
11#20298745C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298701C211yesmaximal, characteristic, complemented
14#20298666C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813649—24no—
20#16813642—24no—
21C2×#14268637C2211yescharacteristic, complemented
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268634C2211yescharacteristic
25C2×D904C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C2×#14268630C2211yescharacteristic
29C22×#11744751C2211yescharacteristic, complemented
30#16813618—21no—
31#16813618C2211yescharacteristic, complemented
32#16813609C2211yescharacteristic
33#16813604—21no—
34#16813602C2211yescharacteristic
35#16813596—21no—
36#16813596C2211yescharacteristic, complemented
37#16813593—21no—
38#16813593—21no—
39#16813593C2211yescharacteristic
40#16813590—21no—
41Q8×Dic113C2211yescharacteristic, complemented
42#16813584C2211yescharacteristic
43C4×C22⋊D113—21no—
44C4×C22⋊D113C2211yescharacteristic
45C22⋊C4×D113—21no—
46#16813555C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic
50#16813543C2211yescharacteristic
51#16813542C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic
53#16813532C2211yescharacteristic, complemented
54C2×#41×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic
56C2×D8×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268648—22no—
63#14268648—41no—
64#14268647—22no—
65#14268647—41no—
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—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113D411yescharacteristic
77D4×D113—22no—
78D4×D113—41no—
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113C2311yescharacteristic
83#14268637—22no—
84#14268636—41no—
85#14268635—22no—
86#14268634D414yescomplemented
87D904—22no—
88#14268632—22no—
89#14268632—22no—
90#14268630—22no—
91C2×#11744751—22no—
92C2×#11744751C2311yescharacteristic
93C2×#11744751C2311yescharacteristic
94C4⋊Dic113—21no—
95C4⋊Dic113—21no—
96C4⋊Dic113C2311yescharacteristic
97#14268626D411yescharacteristic
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113D411yescharacteristic
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624D411yescharacteristic
106C4×Dic113—21no—
107C4×Dic113C2311yescharacteristic
108#41×C113—22no—
109#41×C113—41no—
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113—21no—
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C22×C4×C113—21no—
116C22×C4×C113C2311yescharacteristic
117SD16×C113—22no—
118D8×C113—41no—
119C2×C8×C113C2311yescharacteristic
120C2×C8×C113C2311yescharacteristic
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—81no—
131C22×D113C2×D411yescharacteristic
132Q8×C113—21no—
133Q8×C113C2×D412yes—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—21no—
138D4×C113—42no—
139D4×C113—81no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—21no—
144C2×C4×C113—42no—
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2411yescharacteristic
147C22⋊D113—41no—
148C22⋊D113—42no—
149C22⋊D113—42no—
150C22⋊D113—42no—
151C22⋊D113—81no—
152C22⋊D113—81no—
153C22⋊D113—81no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156C2×Dic113C2×D411yescharacteristic
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159D452—21no—
160D452—21no—
161D452—21no—
162D452—42no—
163D452C2×D412yes—
164C4×D113—21no—
165C4×D113—21no—
166C4×D113—42no—
167C4×D113—42no—
168C4×D113—81no—
169Dic226—21no—
170Dic226—21no—
171C8×C113—21no—
172C8×C113—21no—
173#11744751—21no—
174#11744751C2×D412yes—
175C22×C113—21no—
176C22×C113—21no—
177C22×C113—21no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113C22×D411yescharacteristic
185C2×D113—21no—
186C2×D113—22no—
187C2×D113—21no—
188C2×D113—21no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—84no—
195C4×C113—21no—
196C4×C113—22no—
197C4×C113—41no—
198C4×C113C22×D411yescharacteristic
199C4×C113H(5,𝔽2)11yescharacteristic
200Dic113—21no—
201Dic113—21no—
202Dic113—21no—
203Dic113—41no—
204Dic113—41no—
205C2×C113—41no—
206C2×C113—81no—
207C2×C113—81no—
208C2×C113D4211yescharacteristic
209C2×C113#57511yescharacteristic
210C2×C113#57611yescharacteristic
211D113—41no—
212D113—42no—
213D113—81no—
214#3268—1131nomaximal, Sylow
215C113#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—1131no—
217C2×#135—1131no—
218#550—1131no—
219#546—1131no—
220#496—1131no—
221#468—1131no—
222#466—1131no—
223#464—1131no—
224#459—1131no—
225#452—1131no—
226#449—1131no—
227#449D11311yescharacteristic, complemented
228#447—1131no—
229#440—1131no—
230#435—1131no—
231C2×#41—1131no—
232C2×#41—1131no—
233C2×#41C2×D11311yescharacteristic, complemented
234C22×D4—1131no—
235AGL(1,ℤ/8)—2264no—
236#135—2264no—
237C2×Q16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16C2×D11311yescharacteristic
242C2×D8—1131no—
243C2×D8—1131no—
244C2×D8—1131no—
245C2×D8C2×D11311yescharacteristic
246C2×M16—1131no—
247C22×C8—1131no—
248#127—1131no—
249#127—2261no—
250#124—1131no—
251#123—2261no—
252C22⋊Q8—1131no—
253#121—1131no—
254#121—1131no—
255#121—2261no—
256#121—2261no—
257#121—2261no—
258#121C2×D11311yescharacteristic
259#120—2261no—
260C4×Q8—1131no—
261C4×D4—1131no—
262C4×D4—1131no—
263C4×D4—2261no—
264C2×C22⋊C4—2261no—
265#107—1131no—
266C4⋊C8—1131no—
267#103—1131no—
268#103C2×D11311yescharacteristic, complemented
269#102—1131no—
270#102—1131no—
271#102—1131no—
272#102C2×D11311yescharacteristic, complemented
273C22⋊C8—1131no—
274C22⋊C8C2×D11311yescharacteristic, complemented
275#97—1131no—
276C24—2261no—
277#41—22no—
278#41—41no—
279#41—4521no—
280#41—4521no—
281#41—2262no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8C22×D11311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—1131no—
288C2×D4—1131no—
289C2×D4—1131no—
290C2×D4—4521no—
291C2×D4—2261no—
292C2×D4—2261no—
293C2×D4—2261no—
294C2×D4—2261no—
295C2×D4—2262no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4—2261no—
299C2×D4C22×D11311yescharacteristic
300C2×D4C22×D11311yescharacteristic
301C22×C4—21no—
302C22×C4—1131no—
303C22×C4—2261no—
304C22×C4—2261no—
305C22×C4—2261no—
306C22×C4C22×D11311yescharacteristic
307Q16—2262no—
308SD16—22no—
309SD16—1134no—
310SD16—4521no—
311SD16—2262no—
312D8—41no—
313D8—2262no—
314D8—2262no—
315D8—2262no—
316M16—2262no—
317C2×C8—1131no—
318C2×C8—1131no—
319C2×C8—2262no—
320C2×C8C22×D11311yescharacteristic
321C2×C8C22×D11311yescharacteristic
322C4⋊C4—1131no—
323C4⋊C4—1131no—
324C4⋊C4—2261no—
325C4⋊C4—2261no—
326C4⋊C4C22×D11311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—1131no—
329C22⋊C4—1131no—
330C22⋊C4—2261no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C42—1131no—
337C42—2261no—
338C23—21no—
339C23—21no—
340C23—1131no—
341C23—9041no—
342C23—4522no—
343C23—4522no—
344C23—2261no—
345C23—2261no—
346C23D4×D11311yescharacteristic
347Q8—21no—
348Q8—2261no—
349Q8—2261no—
350Q8D4×D11312yes—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—42no—
356D4—81no—
357D4—1132no—
358D4—9041no—
359D4—9041no—
360D4—9041no—
361D4—4522no—
362D4—4522no—
363D4—4521no—
364D4—4522no—
365D4—4522no—
366D4—2261no—
367D4—2261no—
368D4—2261no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—1131no—
375C2×C4—1131no—
376C2×C4—1131no—
377C2×C4—9041no—
378C2×C4—4522no—
379C2×C4—4522no—
380C2×C4—2261no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4D4×D11311yescharacteristic
385C2×C4C23×D11311yescharacteristic
386C8—21no—
387C8—21no—
388C8—1132no—
389C8—2261no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—9044no—
400C22—4521no—
401C22—4521no—
402C22—4521no—
403C22—4521no—
404C22—4521no—
405C22—2261no—
406C22—2261no—
407C22—2262no—
408C22—2261no—
409C22C2×D4×D11311yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—4521no—
414C4—4521no—
415C4—2261no—
416C4—2261no—
417C4—2261no—
418C4C2×D4×D11311yescharacteristic
419C4#1681366711yescharacteristic
420C2—41no—
421C2—81no—
422C2—81no—
423C2—9041no—
424C2—4521no—
425C2—4522no—
426C2#2029923011yescharacteristic
427C2#2029939511yescharacteristic
428C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3268
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C2×#16813642C2semidirect
3. #20299267C2semidirect
4. #20299245C2semidirect
5. #20298986C2semidirect
6. #20298843C2semidirect
7. #20298832C2semidirect
8. #20298818C2semidirect
9. #20298792C2semidirect
10. #20298763C2semidirect
11. #20298745C2semidirect
12. #20298730C2semidirect
13. #20298701C2semidirect
14. #20298666C2semidirect
15. #449×C113C2semidirect
21. C2×#14268637C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268635C22semidirect
29. C22×#11744751C22semidirect
31. #16813618C22semidirect
36. #16813596C22semidirect
41. Q8×Dic113C22semidirect
46. #16813555C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
51. #16813542C22semidirect
53. #16813532C22semidirect
54. C2×#41×C113C22semidirect
58. #103×C113C22semidirect
59. #102×C113C22semidirect
60. C22⋊C8×C113C22semidirect
86. #14268634D4semidirect
215. C113#3268semidirect
227. #449D113semidirect
233. C2×#41C2×D113semidirect
268. #103C2×D113semidirect
272. #102C2×D113semidirect
274. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×#168136422
#202992672
#202992452
#202989862
#202988432
#202988322
#202988182
#202987922
#202987632
#202987452
#202987302
#202987012
#202986662
#449×C1132
#3268113