Finite Group Databasebeta

← #28399839

Subgroups — #28399839

Order 14464.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813668C211yesmaximal, characteristic, complemented
2C2×#16813649C211yesmaximal, characteristic, complemented
3C2×D8×D113C211yesmaximal, characteristic, complemented
4#20299164C211yesmaximal, characteristic, complemented
5#20298746C211yesmaximal, characteristic, complemented
6#20298743C211yesmaximal, characteristic, complemented
7#20298742C211yesmaximal, characteristic, complemented
8#20298734C211yesmaximal, characteristic, complemented
9#20298733C211yesmaximal, characteristic, complemented
10#20298731C211yesmaximal, characteristic, complemented
11#20298730C211yesmaximal, characteristic, complemented
12#20298601C211yesmaximal, characteristic, complemented
13#20298593C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16#16813668—24no—
17#16813668—24no—
18C2×#14268648C2211yescharacteristic
19C2×#14268648C2211yescharacteristic, complemented
20C2×#14268647—21no—
21C2×#14268647C2211yescharacteristic
22C22×D452—21no—
23C22×D452C2211yescharacteristic, complemented
24C2×D4×D113—21no—
25C2×D4×D113—21no—
26C2×D4×D113C2211yescharacteristic
27C2×D4×D113C2211yescharacteristic, complemented
28C2×D4×D113C2211yescharacteristic, complemented
29#16813649—24no—
30C2×#14268634C2211yescharacteristic, complemented
31C2×D904C2211yescharacteristic, complemented
32C2×D904C2211yescharacteristic, complemented
33C2×#14268632C2211yescharacteristic, complemented
34C2×#14268632C2211yescharacteristic, complemented
35C2×#14268632C2211yescharacteristic, complemented
36D8×D113—24no—
37C2×#14268630C2211yescharacteristic, complemented
38C2×C8×D113C2211yescharacteristic, complemented
39#16813618—21no—
40#16813608—21no—
41#16813597C2211yescharacteristic, complemented
42#16813596C2211yescharacteristic, complemented
43#16813593C2211yescharacteristic, complemented
44#16813592—21no—
45#16813590—21no—
46#16813580C2211yescharacteristic, complemented
47#16813546C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813543C2211yescharacteristic, complemented
51#16813542C2211yescharacteristic, complemented
52#16813542C2211yescharacteristic, complemented
53C22⋊#11744751C2211yescharacteristic, complemented
54#16813534C2211yescharacteristic, complemented
55#16813534C2211yescharacteristic, complemented
56C2×#41×C113C2211yescharacteristic, complemented
57C2×SD16×C113C2211yescharacteristic, complemented
58C2×D8×C113C2211yescharacteristic, complemented
59#121×C113C2211yescharacteristic, complemented
60#103×C113C2211yescharacteristic, complemented
61#102×C113C2211yescharacteristic, complemented
62C22⋊C8×C113C2211yescharacteristic, complemented
63C23×D113—21no—
64C23×D113—21no—
65C23×D113—21no—
66C23×D113—21no—
67#14268648—22no—
68#14268648—22no—
69#14268648—22no—
70#14268648D414yescomplemented
71#14268647—28no—
72#14268647—22no—
73#14268647—22no—
74C2×Dic226D411yescharacteristic
75C2×D452—28no—
76C2×D452—21no—
77C2×D452—21no—
78C2×D452—21no—
79C2×D452—22no—
80C2×D452—22no—
81C2×D452—21no—
82C2×D452D411yescharacteristic
83C2×D452C2311yescharacteristic
84C2×D452C2311yescharacteristic
85C2×D452C2311yescharacteristic
86C2×C22⋊D113—21no—
87C2×C22⋊D113—21no—
88C2×C22⋊D113—21no—
89C2×C22⋊D113—21no—
90C2×C22⋊D113—21no—
91C2×C22⋊D113D411yescharacteristic
92C2×C22⋊D113D411yescharacteristic
93D4×D113—28no—
94D4×D113—28no—
95D4×D113—22no—
96D4×D113—22no—
97D4×D113—22no—
98D4×D113—22no—
99D4×D113—22no—
100D4×D113D414yescomplemented
101C2×C4×D113—21no—
102C2×C4×D113—21no—
103C2×C4×D113C2311yescharacteristic
104C2×C4×D113C2311yescharacteristic
105#14268634—22no—
106D904—22no—
107D904—22no—
108#14268632—22no—
109#14268632—22no—
110#14268632—22no—
111#14268630—22no—
112C2×#11744751C2311yescharacteristic
113C2×#11744751C2311yescharacteristic
114C8×D113—22no—
115C4⋊Dic113C2311yescharacteristic
116C22⋊Dic113—21no—
117#14268624—21no—
118#14268624—21no—
119#14268624—21no—
120C4×Dic113—21no—
121#41×C113—22no—
122#41×C113—22no—
123C2×Q8×C113C2311yescharacteristic
124C2×D4×C113—21no—
125C2×D4×C113—21no—
126C2×D4×C113C2311yescharacteristic
127C2×D4×C113C2311yescharacteristic
128C22×C4×C113—21no—
129C22×C4×C113C2311yescharacteristic
130SD16×C113—22no—
131D8×C113—22no—
132C2×C8×C113C2311yescharacteristic
133C2×C8×C113C2311yescharacteristic
134C4⋊C4×C113C2311yescharacteristic
135C22⋊C4×C113—21no—
136C23×C113—21no—
137C23×C113—21no—
138C23×C113C2×D411yescharacteristic
139C22×D113—21no—
140C22×D113—21no—
141C22×D113—24no—
142C22×D113—24no—
143C22×D113—24no—
144C22×D113—21no—
145C22×D113—42no—
146C22×D113—81no—
147C22×D113—81no—
148C22×D113—81no—
149C22×D113—81no—
150C22×D113—81no—
151C22×D113—81no—
152C22×D113—81no—
153C22×D113—81no—
154C22×D113C2×D411yescharacteristic
155C22×D113C2×D411yescharacteristic
156Q8×C113—21no—
157Q8×C113C2×D412yes—
158D4×C113—24no—
159D4×C113—21no—
160D4×C113—21no—
161D4×C113—21no—
162D4×C113—81no—
163D4×C113C2×D412yes—
164C2×C4×C113—24no—
165C2×C4×C113—21no—
166C2×C4×C113—21no—
167C2×C4×C113—21no—
168C2×C4×C113—21no—
169C2×C4×C113C2×D411yescharacteristic
170C2×C4×C113C2411yescharacteristic
171C22⋊D113—24no—
172C22⋊D113—22no—
173C22⋊D113—22no—
174C22⋊D113—24no—
175C22⋊D113—42no—
176C22⋊D113—81no—
177C22⋊D113—81no—
178C2×Dic113—21no—
179C2×Dic113C2×D411yescharacteristic
180C2×Dic113C2×D411yescharacteristic
181D452—24no—
182D452—24no—
183D452—24no—
184D452—22no—
185D452—21no—
186D452—21no—
187D452—21no—
188D452—21no—
189D452—81no—
190D452C2×D412yes—
191D452C2×D412yes—
192C4×D113—24no—
193C4×D113—21no—
194C4×D113—21no—
195C4×D113—24no—
196C4×D113C2×D412yes—
197C4×D113C2×D412yes—
198Dic226—22no—
199C8×C113—21no—
200C8×C113—21no—
201#11744751—21no—
202#11744751—21no—
203C22×C113—21no—
204C22×C113—22no—
205C22×C113—21no—
206C22×C113—21no—
207C22×C113—41no—
208C22×C113—41no—
209C22×C113—41no—
210C22×C113—41no—
211C22×C113—41no—
212C22×C113C22×D411yescharacteristic
213C2×D113—21no—
214C2×D113—21no—
215C2×D113—21no—
216C2×D113—22no—
217C2×D113—22no—
218C2×D113—21no—
219C2×D113—21no—
220C2×D113—41no—
221C2×D113—41no—
222C2×D113—41no—
223C2×D113—41no—
224C2×D113—41no—
225C2×D113—41no—
226C2×D113—41no—
227C2×D113—84no—
228C2×D113—84no—
229C2×D113—84no—
230C2×D113—84no—
231C2×D113#12012yes—
232C4×C113—21no—
233C4×C113—22no—
234C4×C113—41no—
235C4×C113C22×D411yescharacteristic
236C4×C113C22×D411yescharacteristic
237Dic113—21no—
238Dic113—41no—
239Dic113#12012yes—
240C2×C113—41no—
241C2×C113—42no—
242C2×C113—81no—
243C2×C113C2×#12011yescharacteristic
244C2×C113#57611yescharacteristic
245C2×C113#57611yescharacteristic
246D113—22no—
247D113—41no—
248D113—42no—
249D113—42no—
250D113—81no—
251#3008—1131nomaximal, Sylow
252C113#300811yescharacteristic, complemented, Sylow
253C2×H(5,𝔽2)—1131no—
254C2×AGL(1,ℤ/8)—1131no—
255C22×D8—1131no—
256#535—1131no—
257#449—1131no—
258#449—1131no—
259#449—1131no—
260#449D11311yescharacteristic, complemented
261#447—1131no—
262#447—1131no—
263#447—1131no—
264#447—1131no—
265#418—1131no—
266#416—1131no—
267#408—1131no—
268H(5,𝔽2)—2264no—
269H(5,𝔽2)—2264no—
270C2×#41—1131no—
271C2×#41—1131no—
272C2×#41—1131no—
273C2×#41—2261no—
274C2×#41C2×D11311yescharacteristic, complemented
275C22×D4—1131no—
276C22×D4—1131no—
277C22×D4—1131no—
278C22×D4—1131no—
279C22×D4—2261no—
280C22×D4—2261no—
281C22×D4—2261no—
282AGL(1,ℤ/8)—2264no—
283C2×SD16—1131no—
284C2×SD16C2×D11311yescharacteristic, complemented
285C2×D8—1131no—
286C2×D8—1131no—
287C2×D8—1131no—
288C2×D8—1131no—
289C2×D8—1131no—
290C2×D8—2264no—
291C2×D8C2×D11311yescharacteristic, complemented
292C2×M16—1131no—
293C22×C8—1131no—
294#127—2261no—
295#124—2261no—
296#121—1131no—
297#121—1131no—
298#121—1131no—
299#121C2×D11311yescharacteristic, complemented
300#120—2261no—
301#120—2261no—
302#117—1131no—
303#103—1131no—
304#103C2×D11311yescharacteristic, complemented
305#102—1131no—
306#102—1131no—
307#102—1131no—
308#102—1131no—
309#102—1131no—
310#102C2×D11311yescharacteristic, complemented
311C22⋊C8—1131no—
312C22⋊C8—1131no—
313C22⋊C8—1131no—
314C22⋊C8C2×D11311yescharacteristic, complemented
315C24—2261no—
316C24—2261no—
317C24—2261no—
318C24—2261no—
319#41—22no—
320#41—22no—
321#41—1134no—
322#41—2262no—
323#41—2262no—
324#41—2268no—
325#41—2262no—
326#41—2262no—
327#41—2262no—
328C2×Q8—1131no—
329C2×Q8C22×D11311yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—1134no—
333C2×D4—1131no—
334C2×D4—1131no—
335C2×D4—1131no—
336C2×D4—1131no—
337C2×D4—1131no—
338C2×D4—1131no—
339C2×D4—2262no—
340C2×D4—2262no—
341C2×D4—2261no—
342C2×D4—2261no—
343C2×D4—2261no—
344C2×D4—2268no—
345C2×D4—2262no—
346C2×D4—2262no—
347C2×D4—2262no—
348C2×D4—2261no—
349C2×D4—2261no—
350C2×D4—2261no—
351C2×D4—2262no—
352C2×D4—2268no—
353C2×D4—2268no—
354C2×D4—2261no—
355C2×D4—2261no—
356C2×D4—2262no—
357C2×D4—2261no—
358C2×D4C22×D11311yescharacteristic
359C2×D4C22×D11311yescharacteristic
360C22×C4—21no—
361C22×C4—1131no—
362C22×C4—1131no—
363C22×C4—2261no—
364C22×C4—2261no—
365C22×C4C22×D11311yescharacteristic
366SD16—22no—
367SD16—2262no—
368D8—22no—
369D8—2262no—
370D8—2262no—
371D8—2262no—
372D8—2262no—
373D8—2262no—
374M16—2262no—
375C2×C8—1131no—
376C2×C8—1131no—
377C2×C8—2262no—
378C2×C8C22×D11311yescharacteristic
379C2×C8C22×D11311yescharacteristic
380C4⋊C4—1131no—
381C4⋊C4C22×D11311yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—2261no—
384C22⋊C4—2261no—
385C22⋊C4—2261no—
386C22⋊C4—2261no—
387C42—2261no—
388C23—21no—
389C23—21no—
390C23—1131no—
391C23—1131no—
392C23—9041no—
393C23—9041no—
394C23—9041no—
395C23—9041no—
396C23—9041no—
397C23—9041no—
398C23—9041no—
399C23—9041no—
400C23—4522no—
401C23—2264no—
402C23—2264no—
403C23—2264no—
404C23—2261no—
405C23—2261no—
406C23—2261no—
407C23D4×D11311yescharacteristic
408Q8—21no—
409Q8—2262no—
410Q8D4×D11312yes—
411D4—24no—
412D4—21no—
413D4—21no—
414D4—21no—
415D4—81no—
416D4—1132no—
417D4—1132no—
418D4—9041no—
419D4—9041no—
420D4—9041no—
421D4—4522no—
422D4—2262no—
423D4—2264no—
424D4—2264no—
425D4—2264no—
426D4—2262no—
427D4—2264no—
428D4—2262no—
429D4—2264no—
430D4—2261no—
431D4—2261no—
432D4—2261no—
433D4—2261no—
434D4D4×D11312yes—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—1131no—
441C2×C4—1132no—
442C2×C4—1132no—
443C2×C4—1131no—
444C2×C4—2264no—
445C2×C4—2264no—
446C2×C4—2261no—
447C2×C4—2261no—
448C2×C4—2261no—
449C2×C4D4×D11311yescharacteristic
450C2×C4C23×D11311yescharacteristic
451C8—21no—
452C8—21no—
453C8—2261no—
454C8—2261no—
455C22—21no—
456C22—22no—
457C22—21no—
458C22—21no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—1132no—
465C22—9044no—
466C22—9044no—
467C22—9044no—
468C22—9044no—
469C22—4521no—
470C22—4521no—
471C22—4521no—
472C22—4521no—
473C22—4521no—
474C22—4521no—
475C22—4521no—
476C22—2262no—
477C22—2262no—
478C22—2261no—
479C22—2261no—
480C22—2261no—
481C22—2261no—
482C22—2261no—
483C22C2×D4×D11311yescharacteristic
484C4—21no—
485C4—22no—
486C4—41no—
487C4—1132no—
488C4—4521no—
489C4—2261no—
490C4C2×D4×D11311yescharacteristic
491C4C2×D4×D11311yescharacteristic
492C2—41no—
493C2—42no—
494C2—81no—
495C2—9041no—
496C2—4522no—
497C2—4522no—
498C2—4521no—
499C2—2262no—
500C2#120×D11311yescharacteristic
501C2#2029940011yescharacteristic
502C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3008
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×#16813668C2semidirect
2. C2×#16813649C2semidirect
3. C2×D8×D113C2semidirect
4. #20299164C2semidirect
5. #20298746C2semidirect
6. #20298743C2semidirect
7. #20298742C2semidirect
8. #20298734C2semidirect
9. #20298733C2semidirect
10. #20298731C2semidirect
11. #20298730C2semidirect
12. #20298601C2semidirect
13. #20298593C2semidirect
14. #20298563C2semidirect
15. #449×C113C2semidirect
19. C2×#14268648C22semidirect
23. C22×D452C22semidirect
27. C2×D4×D113C22semidirect
28. C2×D4×D113C22semidirect
30. C2×#14268634C22semidirect
31. C2×D904C22semidirect
32. C2×D904C22semidirect
33. C2×#14268632C22semidirect
34. C2×#14268632C22semidirect
35. C2×#14268632C22semidirect
37. C2×#14268630C22semidirect
38. C2×C8×D113C22semidirect
41. #16813597C22semidirect
42. #16813596C22semidirect
43. #16813593C22semidirect
46. #16813580C22semidirect
47. #16813546C22semidirect
48. #16813544C22semidirect
49. #16813544C22semidirect
50. #16813543C22semidirect
51. #16813542C22semidirect
52. #16813542C22semidirect
53. C22⋊#11744751C22semidirect
54. #16813534C22semidirect
55. #16813534C22semidirect
56. C2×#41×C113C22semidirect
57. C2×SD16×C113C22semidirect
58. C2×D8×C113C22semidirect
59. #121×C113C22semidirect
60. #103×C113C22semidirect
61. #102×C113C22semidirect
62. C22⋊C8×C113C22semidirect
70. #14268648D4semidirect
100. D4×D113D4semidirect
252. C113#3008semidirect
260. #449D113semidirect
274. C2×#41C2×D113semidirect
284. C2×SD16C2×D113semidirect
291. C2×D8C2×D113semidirect
299. #121C2×D113semidirect
304. #103C2×D113semidirect
310. #102C2×D113semidirect
314. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136682
C2×#168136492
C2×D8×D1132
#202991642
#202987462
#202987432
#202987422
#202987342
#202987332
#202987312
#202987302
#202986012
#202985932
#202985632
#449×C1132
#3008113