Finite Group Databasebeta

← #28402074

Subgroups — #28402074

Order 14464.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813650C211yesmaximal, characteristic, complemented
2C22×#14268636C211yesmaximal, characteristic, complemented
3#20299257C211yesmaximal, characteristic, complemented
4D4×D452C211yesmaximal, characteristic, complemented
5#20298987C211yesmaximal, characteristic, complemented
6#20298844C211yesmaximal, characteristic, complemented
7#20298834C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298799C211yesmaximal, characteristic, complemented
10#20298751C211yesmaximal, characteristic, complemented
11#20298745C211yesmaximal, characteristic, complemented
12#20298739C211yesmaximal, characteristic, complemented
13#20298734C211yesmaximal, characteristic, complemented
14#20298700C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic, complemented
17C22×Dic226C2211yescharacteristic, complemented
18C22×D452C2211yescharacteristic
19C22×D452C2211yescharacteristic
20C2×D4×D113—21no—
21#16813650—24no—
22C2×#14268636—24no—
23C2×#14268636C2211yescharacteristic
24C2×#14268636C2211yescharacteristic
25C2×#14268636C2211yescharacteristic, complemented
26C2×#14268636C2211yescharacteristic, complemented
27C2×#14268636C2211yescharacteristic, complemented
28C2×#14268636C2211yescharacteristic, complemented
29C2×D904C2211yescharacteristic
30C2×D904C2211yescharacteristic, complemented
31C2×D904C2211yescharacteristic, complemented
32#16813619C2211yescharacteristic
33#16813610C2211yescharacteristic, complemented
34#16813608—21no—
35#16813601C2211yescharacteristic, complemented
36#16813600—21no—
37#16813597—21no—
38#16813596C2211yescharacteristic
39#16813596C2211yescharacteristic
40#16813596C2211yescharacteristic, complemented
41#16813594—21no—
42#16813592—21no—
43#16813592—21no—
44C4×Dic226C2211yescharacteristic, complemented
45C4×D452C2211yescharacteristic
46#16813582—21no—
47#16813556C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813547C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic, complemented
52#16813544C2211yescharacteristic, complemented
53#16813544C2211yescharacteristic, complemented
54C2×M16×C113C2211yescharacteristic, complemented
55C22×C8×C113C2211yescharacteristic, complemented
56C4×D4×C113C2211yescharacteristic
57C4⋊C8×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C22⋊C8×C113C2211yescharacteristic, complemented
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268647—22no—
64#14268647—41no—
65C2×Dic226—22no—
66C2×Dic226—21no—
67C2×Dic226—41no—
68C2×Dic226C2311yescharacteristic
69C2×Dic226C2311yescharacteristic
70C2×D452—22no—
71C2×D452—22no—
72C2×D452—21no—
73C2×D452—21no—
74C2×D452—21no—
75C2×D452—21no—
76C2×D452—41no—
77C2×D452—41no—
78C2×D452C2311yescharacteristic
79C2×D452C2311yescharacteristic
80C2×D452C2311yescharacteristic
81C2×D452C2311yescharacteristic
82C2×C22⋊D113—21no—
83C2×C22⋊D113—21no—
84C2×C22⋊D113—21no—
85C2×C22⋊D113—21no—
86D4×D113—44no—
87C22×Dic113—21no—
88C2×C4×D113—21no—
89C2×C4×D113—21no—
90#14268636—22no—
91#14268636—22no—
92#14268636—22no—
93#14268636—22no—
94#14268636—41no—
95#14268636D414yescomplemented
96D904—22no—
97D904—22no—
98D904—41no—
99C4⋊Dic113C2311yescharacteristic
100C4⋊Dic113C2311yescharacteristic
101#14268626—21no—
102#14268626—21no—
103C22⋊Dic113—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624—21no—
110C4×Dic113—21no—
111C2×D4×C113D411yescharacteristic
112C22×C4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
114M16×C113—22no—
115C2×C8×C113—22no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C22⋊C4×C113D411yescharacteristic
123C42×C113C2311yescharacteristic
124C23×C113C2×D411yescharacteristic
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—21no—
130C22×D113—42no—
131C22×D113—42no—
132C22×D113—42no—
133C22×D113—42no—
134C22×D113—81no—
135C22×D113—81no—
136D4×C113—22no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113C2×D411yescharacteristic
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2411yescharacteristic
146C22⋊D113—42no—
147C22⋊D113—42no—
148C22⋊D113—42no—
149C22⋊D113—42no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—42no—
155D452—21no—
156D452—21no—
157D452—21no—
158D452—21no—
159D452—21no—
160D452—21no—
161D452—21no—
162D452—42no—
163D452—42no—
164D452—42no—
165D452—81no—
166D452C2×D412yes—
167C4×D113—42no—
168C4×D113—42no—
169Dic226—21no—
170Dic226—21no—
171Dic226—21no—
172Dic226—42no—
173Dic226C2×D412yescomplemented
174C8×C113—21no—
175C8×C113—21no—
176C8×C113—21no—
177C8×C113C2×D412yescomplemented
178C22×C113—21no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—21no—
182C22×C113—21no—
183C22×C113AGL(1,ℤ/8)12yescomplemented
184C22×C113C22×D411yescharacteristic
185C2×D113—22no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—41no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—41no—
195C2×D113—41no—
196C2×D113—41no—
197C2×D113—84no—
198C2×D113—84no—
199C4×C113—21no—
200C4×C113—21no—
201C4×C113—21no—
202C4×C113—21no—
203C4×C113C22×D411yescharacteristic
204C4×C113H(5,𝔽2)11yescharacteristic
205Dic113—22no—
206Dic113—41no—
207Dic113—41no—
208Dic113—41no—
209C2×C113—22no—
210C2×C113—41no—
211C2×C113D4211yescharacteristic
212C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C113#57711yescharacteristic
214D113—42no—
215D113—81no—
216D113—81no—
217D113—81no—
218#3265—1131nomaximal, Sylow
219C113#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—1131no—
221C22×SD16—1131no—
222#548—1131no—
223D42—1131no—
224#496—1131no—
225#468—1131no—
226#466—1131no—
227#463—1131no—
228#460—1131no—
229#450—1131no—
230#449—1131no—
231#448—1131no—
232#447—1131no—
233#440—1131no—
234#435D11311yescharacteristic, complemented
235C2×#41—1131no—
236C22×Q8—1131no—
237C22×D4—1131no—
238C22×D4—1131no—
239C22×D4—2261no—
240AGL(1,ℤ/8)—2264no—
241C2×SD16—1131no—
242C2×SD16—1131no—
243C2×SD16—1131no—
244C2×SD16—1131no—
245C2×SD16—1131no—
246C2×SD16—1131no—
247C2×SD16—2264no—
248C2×D8—1131no—
249C2×D8—1131no—
250C2×D8—1131no—
251C2×M16C2×D11311yescharacteristic, complemented
252C22×C8C2×D11311yescharacteristic, complemented
253#127—1131no—
254#124—1131no—
255#124—2261no—
256C22⋊Q8—1131no—
257C22⋊Q8—2261no—
258#121—1131no—
259#121—1131no—
260#121—1131no—
261#121—2261no—
262#121—2261no—
263#120—2261no—
264#120—2261no—
265C4×Q8—1131no—
266C4×D4—1131no—
267C4×D4—2261no—
268C4×D4C2×D11311yescharacteristic
269#107—1131no—
270C4⋊C8C2×D11311yescharacteristic, complemented
271#103—1131no—
272#103—1131no—
273#102—1131no—
274#102—1131no—
275#102—1131no—
276#102—1131no—
277C22⋊C8C2×D11311yescharacteristic, complemented
278C22⋊C8C2×D11311yescharacteristic, complemented
279#97C2×D11311yescharacteristic, complemented
280C24—2261no—
281C24—2261no—
282#41—4521no—
283#41—2262no—
284C2×Q8—1131no—
285C2×Q8—1131no—
286C2×Q8—4521no—
287C2×Q8—2262no—
288C2×Q8—2261no—
289C2×D4—1131no—
290C2×D4—1131no—
291C2×D4—1131no—
292C2×D4—1131no—
293C2×D4—4521no—
294C2×D4—4521no—
295C2×D4—4524no—
296C2×D4—2262no—
297C2×D4—2262no—
298C2×D4—2261no—
299C2×D4—2261no—
300C2×D4—2261no—
301C2×D4—2261no—
302C2×D4—2261no—
303C2×D4—2261no—
304C2×D4—2261no—
305C2×D4—2261no—
306C2×D4D45211yescharacteristic
307C22×C4—2261no—
308C22×C4—2261no—
309C22×C4—2261no—
310C22×C4C22×D11311yescharacteristic
311C22×C4C22×D11311yescharacteristic
312SD16—1134no—
313SD16—4521no—
314SD16—2262no—
315SD16—2262no—
316SD16—2262no—
317SD16—2262no—
318D8—4521no—
319D8—2262no—
320D8—2262no—
321M16—22no—
322C2×C8—22no—
323C2×C8C22×D11311yescharacteristic
324C2×C8C22×D11311yescharacteristic
325C2×C8C22×D11311yescharacteristic
326C2×C8C22×D11311yescharacteristic
327C4⋊C4—1131no—
328C4⋊C4—1131no—
329C4⋊C4—2261no—
330C4⋊C4—2261no—
331C4⋊C4D45211yescharacteristic
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C22⋊C4—2261no—
337C22⋊C4—2261no—
338C22⋊C4—2261no—
339C22⋊C4D45211yescharacteristic
340C22⋊C4D45211yescharacteristic
341C42—2261no—
342C42C22×D11311yescharacteristic
343C23—9041no—
344C23—9041no—
345C23—4522no—
346C23—4522no—
347C23—4522no—
348C23—4522no—
349C23—2261no—
350C23—2261no—
351C23—2261no—
352C23—2261no—
353C23C2×D45211yescharacteristic
354C23C2×D45211yescharacteristic
355Q8—1132no—
356Q8—4522no—
357Q8—2261no—
358Q8—2261no—
359Q8—2261no—
360D4—22no—
361D4—1132no—
362D4—9041no—
363D4—4522no—
364D4—4522no—
365D4—4522no—
366D4—4522no—
367D4—4522no—
368D4—4522no—
369D4—4522no—
370D4—2261no—
371D4—2261no—
372D4—2261no—
373D4—2261no—
374D4—2261no—
375D4—2261no—
376D4—2261no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—4522no—
382C2×C4—4522no—
383C2×C4—4522no—
384C2×C4—2261no—
385C2×C4—2261no—
386C2×C4—2261no—
387C2×C4—2261no—
388C2×C4C2×D45211yescharacteristic
389C2×C4C2×D45211yescharacteristic
390C2×C4C2×D45211yescharacteristic
391C2×C4C2×D45211yescharacteristic
392C2×C4C23×D11311yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8D4×D11312yescomplemented
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—9044no—
403C22—9044no—
404C22—4521no—
405C22—4521no—
406C22—4521no—
407C22—4521no—
408C22—4521no—
409C22—4521no—
410C22—4521no—
411C22—4521no—
412C22—4521no—
413C22—4521no—
414C22—4521no—
415C22—2262no—
416C22#1681365012yescomplemented
417C22C22×D45211yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—4521no—
423C4—4521no—
424C4—4521no—
425C4—2262no—
426C4C2×D4×D11311yescharacteristic
427C4#1681366811yescharacteristic
428C2—22no—
429C2—41no—
430C2—9041no—
431C2—9041no—
432C2—9041no—
433C2—4522no—
434C2D4×D45211yescharacteristic
435C2C2×#1681365011yescharacteristic
436C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3265
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C22×#14268636C2semidirect
3. #20299257C2semidirect
4. D4×D452C2semidirect
5. #20298987C2semidirect
6. #20298844C2semidirect
7. #20298834C2semidirect
8. #20298814C2semidirect
9. #20298799C2semidirect
10. #20298751C2semidirect
11. #20298745C2semidirect
12. #20298739C2semidirect
13. #20298734C2semidirect
14. #20298700C2semidirect
15. #435×C113C2semidirect
16. C2×#14268647C22semidirect
17. C22×Dic226C22semidirect
25. C2×#14268636C22semidirect
26. C2×#14268636C22semidirect
27. C2×#14268636C22semidirect
28. C2×#14268636C22semidirect
30. C2×D904C22semidirect
31. C2×D904C22semidirect
33. #16813610C22semidirect
35. #16813601C22semidirect
40. #16813596C22semidirect
44. C4×Dic226C22semidirect
47. #16813556C22semidirect
48. #16813547C22semidirect
49. #16813547C22semidirect
51. #16813544C22semidirect
52. #16813544C22semidirect
53. #16813544C22semidirect
54. C2×M16×C113C22semidirect
55. C22×C8×C113C22semidirect
57. C4⋊C8×C113C22semidirect
58. C22⋊C8×C113C22semidirect
59. C22⋊C8×C113C22semidirect
60. #97×C113C22semidirect
95. #14268636D4semidirect
173. Dic226C2×D4semidirect
177. C8×C113C2×D4semidirect
183. C22×C113AGL(1,ℤ/8)semidirect
219. C113#3265semidirect
234. #435D113semidirect
251. C2×M16C2×D113semidirect
252. C22×C8C2×D113semidirect
270. C4⋊C8C2×D113semidirect
277. C22⋊C8C2×D113semidirect
278. C22⋊C8C2×D113semidirect
279. #97C2×D113semidirect
396. C8D4×D113semidirect
416. C22#16813650semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C22×#142686362
#202992572
D4×D4522
#202989872
#202988442
#202988342
#202988142
#202987992
#202987512
#202987452
#202987392
#202987342
#202987002
#435×C1132
#3265113