Finite Group Databasebeta

← #28399879

Subgroups — #28399879

Order 14464.

764 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813667C211yesmaximal, characteristic, complemented
2C2×#16813649C211yesmaximal, characteristic, complemented
3C2×#16813643C211yesmaximal, characteristic, complemented
4#20299178C211yesmaximal, characteristic, complemented
5#20298758C211yesmaximal, characteristic, complemented
6#20298757C211yesmaximal, characteristic, complemented
7#20298747C211yesmaximal, characteristic, complemented
8#20298745C211yesmaximal, characteristic, complemented
9#20298744C211yesmaximal, characteristic, complemented
10#20298733C211yesmaximal, characteristic, complemented
11#20298732C211yesmaximal, characteristic, complemented
12#20298596C211yesmaximal, characteristic, complemented
13#102×D113C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16#16813667—24no—
17#16813667—24no—
18C2×#14268648C2211yescharacteristic, complemented
19C2×#14268647C2211yescharacteristic
20C2×#14268647C2211yescharacteristic
21C2×#14268646—21no—
22C2×#14268646C2211yescharacteristic
23C2×#14268646C2211yescharacteristic
24C22×C22⋊D113—21no—
25C22×C22⋊D113—21no—
26C2×D4×D113—21no—
27C2×D4×D113C2211yescharacteristic
28C2×D4×D113C2211yescharacteristic
29#16813649—24no—
30#16813643—24no—
31C2×#14268637C2211yescharacteristic, complemented
32C2×#14268636C2211yescharacteristic, complemented
33C2×#14268634C2211yescharacteristic, complemented
34C2×D904C2211yescharacteristic, complemented
35C2×#14268632C2211yescharacteristic, complemented
36C2×#14268632C2211yescharacteristic, complemented
37C2×#14268630C2211yescharacteristic, complemented
38C2×C8×D113C2211yescharacteristic, complemented
39#16813600—21no—
40#16813598C2211yescharacteristic, complemented
41#16813597—21no—
42#16813597C2211yescharacteristic, complemented
43#16813596C2211yescharacteristic, complemented
44#16813595—21no—
45#16813595—21no—
46C4⋊C4×D113C2211yescharacteristic, complemented
47#16813547C2211yescharacteristic, complemented
48#16813545C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic, complemented
50#16813543C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813542C2211yescharacteristic, complemented
53C22⋊#11744751C2211yescharacteristic, complemented
54#16813534C2211yescharacteristic, complemented
55#16813534C2211yescharacteristic, complemented
56C22×D4×C113C2211yescharacteristic
57C2×SD16×C113C2211yescharacteristic, complemented
58C2×SD16×C113C2211yescharacteristic, complemented
59C22⋊Q8×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61#102×C113C2211yescharacteristic, complemented
62C22⋊C8×C113C2211yescharacteristic, complemented
63C23×D113—21no—
64C23×D113—21no—
65#14268648—22no—
66#14268648—22no—
67#14268647—22no—
68#14268647—22no—
69#14268647—22no—
70#14268647—22no—
71#14268646—28no—
72#14268646—22no—
73#14268646—22no—
74#14268646—22no—
75#14268646D414yescomplemented
76C2×Dic226D411yescharacteristic
77C2×Dic226C2311yescharacteristic
78C2×D452—21no—
79C2×D452—21no—
80C2×D452D411yescharacteristic
81C2×D452C2311yescharacteristic
82C2×D452C2311yescharacteristic
83C2×C22⋊D113—28no—
84C2×C22⋊D113—28no—
85C2×C22⋊D113—21no—
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—22no—
95D4×D113—22no—
96D4×D113—22no—
97D4×D113D414yescomplemented
98C22×Dic113—21no—
99C22×Dic113—21no—
100C2×C4×D113—21no—
101C2×C4×D113—21no—
102C2×C4×D113—21no—
103C2×C4×D113C2311yescharacteristic
104C2×C4×D113C2311yescharacteristic
105#14268637—22no—
106#14268636—22no—
107#14268634—22no—
108D904—22no—
109#14268632—22no—
110#14268632—22no—
111#14268630—22no—
112C2×#11744751C2311yescharacteristic
113C2×#11744751C2311yescharacteristic
114C8×D113—22no—
115C4⋊Dic113C2311yescharacteristic
116#14268626—21no—
117#14268626—21no—
118#14268624—21no—
119#14268624—21no—
120#14268624—21no—
121C24×C113—21no—
122C2×Q8×C113C2311yescharacteristic
123C2×D4×C113—22no—
124C2×D4×C113—22no—
125C2×D4×C113—21no—
126C2×D4×C113C2311yescharacteristic
127C2×D4×C113C2311yescharacteristic
128C22×C4×C113C2311yescharacteristic
129SD16×C113—22no—
130SD16×C113—22no—
131C2×C8×C113C2311yescharacteristic
132C2×C8×C113C2311yescharacteristic
133C4⋊C4×C113—21no—
134C4⋊C4×C113C2311yescharacteristic
135C22⋊C4×C113—21no—
136C23×C113—24no—
137C23×C113—21no—
138C23×C113—21no—
139C23×C113—81no—
140C23×C113—81no—
141C23×C113C2×D411yescharacteristic
142C22×D113—21no—
143C22×D113—24no—
144C22×D113—24no—
145C22×D113—21no—
146C22×D113—81no—
147C22×D113—81no—
148C22×D113—81no—
149C22×D113—81no—
150C22×D113C2×D411yescharacteristic
151C22×D113C2×D411yescharacteristic
152Q8×C113—21no—
153Q8×C113—21no—
154D4×C113—24no—
155D4×C113—21no—
156D4×C113—21no—
157D4×C113C2×D412yes—
158D4×C113C2×D412yes—
159C2×C4×C113—21no—
160C2×C4×C113—21no—
161C2×C4×C113—21no—
162C2×C4×C113—21no—
163C2×C4×C113C2×D411yescharacteristic
164C2×C4×C113C2411yescharacteristic
165C22⋊D113—24no—
166C22⋊D113—24no—
167C22⋊D113—24no—
168C22⋊D113—24no—
169C22⋊D113—22no—
170C22⋊D113—24no—
171C22⋊D113—22no—
172C22⋊D113—81no—
173C2×Dic113—24no—
174C2×Dic113—21no—
175C2×Dic113—24no—
176C2×Dic113—21no—
177C2×Dic113C2×D411yescharacteristic
178C2×Dic113C2×D411yescharacteristic
179D452—22no—
180D452—21no—
181D452—21no—
182D452—21no—
183D452—42no—
184D452—81no—
185D452C2×D412yes—
186C4×D113—24no—
187C4×D113—21no—
188C4×D113—21no—
189C4×D113—42no—
190C4×D113—81no—
191C4×D113C2×D412yes—
192C4×D113C2×D412yes—
193Dic226—21no—
194Dic226—22no—
195Dic226C2×D412yes—
196C8×C113—21no—
197C8×C113—21no—
198#11744751—21no—
199#11744751—21no—
200C22×C113—22no—
201C22×C113—22no—
202C22×C113—21no—
203C22×C113—21no—
204C22×C113—21no—
205C22×C113—41no—
206C22×C113—41no—
207C22×C113—41no—
208C22×C113—41no—
209C22×C113—84no—
210C22×C113C22×D411yescharacteristic
211C2×D113—21no—
212C2×D113—21no—
213C2×D113—21no—
214C2×D113—22no—
215C2×D113—21no—
216C2×D113—21no—
217C2×D113—41no—
218C2×D113—41no—
219C2×D113—41no—
220C2×D113—41no—
221C2×D113—41no—
222C2×D113—84no—
223C2×D113—84no—
224C2×D113#12012yes—
225C4×C113—21no—
226C4×C113—41no—
227C4×C113—41no—
228C4×C113C22×D411yescharacteristic
229C4×C113C22×D411yescharacteristic
230Dic113—21no—
231Dic113—22no—
232Dic113—41no—
233Dic113#12012yes—
234C2×C113—42no—
235C2×C113—42no—
236C2×C113—41no—
237C2×C113C2×#12011yescharacteristic
238C2×C113#57611yescharacteristic
239C2×C113#57711yescharacteristic
240D113—22no—
241D113—41no—
242D113—42no—
243D113—81no—
244#3012—1131nomaximal, Sylow
245C113#301211yescharacteristic, complemented, Sylow
246C2×H(5,𝔽2)—1131no—
247C2×AGL(1,ℤ/8)—1131no—
248C2×#135—1131no—
249#537—1131no—
250#452—1131no—
251#452—1131no—
252#450—1131no—
253#450D11311yescharacteristic, complemented
254#449—1131no—
255#449—1131no—
256#447—1131no—
257#447—1131no—
258#417—1131no—
259C2×#102—1131no—
260#408—1131no—
261H(5,𝔽2)—2264no—
262H(5,𝔽2)—2264no—
263C2×#41—1131no—
264C2×#41—1131no—
265C2×#41—1131no—
266C2×#41—1131no—
267C2×#41—1131no—
268C2×#41—2261no—
269C22×D4—1131no—
270C22×D4—1131no—
271C22×D4—2261no—
272C22×D4—2261no—
273C22×D4—2261no—
274C22×D4C2×D11311yescharacteristic
275AGL(1,ℤ/8)—2264no—
276#135—2264no—
277C2×Q16—1131no—
278C2×SD16—1131no—
279C2×SD16—1131no—
280C2×SD16C2×D11311yescharacteristic, complemented
281C2×SD16C2×D11311yescharacteristic, complemented
282C2×D8—1131no—
283C2×D8—1131no—
284C2×D8—1131no—
285C2×M16—1131no—
286C22×C8—1131no—
287C22⋊Q8—1131no—
288C22⋊Q8—2261no—
289C22⋊Q8C2×D11311yescharacteristic, complemented
290#121—1131no—
291#121—1131no—
292#121—2261no—
293#121—2261no—
294#121—2261no—
295C2×C4⋊C4—1131no—
296#103—1131no—
297#103—1131no—
298#102—1131no—
299#102—1131no—
300#102—1131no—
301#102—1131no—
302#102C2×D11311yescharacteristic, complemented
303#102C2×D11311yescharacteristic, complemented
304C22⋊C8—1131no—
305C22⋊C8—1131no—
306C22⋊C8—1131no—
307C22⋊C8C2×D11311yescharacteristic, complemented
308C24—21no—
309C24—2261no—
310C24—2261no—
311#41—1134no—
312#41—2262no—
313#41—2262no—
314#41—2262no—
315#41—2262no—
316#41—2262no—
317#41—2262no—
318#41—2262no—
319#41—2262no—
320#41—2268no—
321#41—2262no—
322C2×Q8—1131no—
323C2×Q8—1131no—
324C2×Q8C22×D11311yescharacteristic
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—1134no—
329C2×D4—1131no—
330C2×D4—1131no—
331C2×D4—1131no—
332C2×D4—1131no—
333C2×D4—1131no—
334C2×D4—2261no—
335C2×D4—2261no—
336C2×D4—2262no—
337C2×D4—2261no—
338C2×D4—2261no—
339C2×D4—2262no—
340C2×D4—2268no—
341C2×D4—2261no—
342C2×D4—2261no—
343C2×D4—2261no—
344C2×D4—2268no—
345C2×D4—2268no—
346C2×D4—2261no—
347C2×D4—2262no—
348C2×D4C22×D11311yescharacteristic
349C2×D4C22×D11311yescharacteristic
350C22×C4—1131no—
351C22×C4—1131no—
352C22×C4—2261no—
353C22×C4—2261no—
354C22×C4—2261no—
355C22×C4—2261no—
356C22×C4—2261no—
357C22×C4C22×D11311yescharacteristic
358Q16—2262no—
359SD16—22no—
360SD16—22no—
361SD16—2262no—
362SD16—2262no—
363D8—2262no—
364D8—2262no—
365D8—2262no—
366M16—2262no—
367C2×C8—1131no—
368C2×C8—1131no—
369C2×C8—2262no—
370C2×C8C22×D11311yescharacteristic
371C2×C8C22×D11311yescharacteristic
372C4⋊C4—21no—
373C4⋊C4—1131no—
374C4⋊C4—2261no—
375C4⋊C4—2261no—
376C4⋊C4C22×D11311yescharacteristic
377C22⋊C4—21no—
378C22⋊C4—2261no—
379C22⋊C4—2261no—
380C22⋊C4—2261no—
381C23—24no—
382C23—21no—
383C23—21no—
384C23—81no—
385C23—81no—
386C23—1131no—
387C23—1131no—
388C23—9041no—
389C23—9041no—
390C23—9041no—
391C23—9041no—
392C23—2264no—
393C23—2264no—
394C23—2261no—
395C23—2261no—
396C23D4×D11311yescharacteristic
397Q8—21no—
398Q8—21no—
399Q8—1132no—
400Q8—2262no—
401Q8—2261no—
402D4—24no—
403D4—21no—
404D4—21no—
405D4—1132no—
406D4—9041no—
407D4—9041no—
408D4—4522no—
409D4—2262no—
410D4—2262no—
411D4—2264no—
412D4—2262no—
413D4—2264no—
414D4—2264no—
415D4—2264no—
416D4—2264no—
417D4—2261no—
418D4—2261no—
419D4—2261no—
420D4D4×D11312yes—
421D4D4×D11312yes—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—1131no—
427C2×C4—1132no—
428C2×C4—1132no—
429C2×C4—1131no—
430C2×C4—9041no—
431C2×C4—4522no—
432C2×C4—2264no—
433C2×C4—2264no—
434C2×C4—2261no—
435C2×C4—2264no—
436C2×C4—2261no—
437C2×C4—2261no—
438C2×C4—2261no—
439C2×C4D4×D11311yescharacteristic
440C2×C4C23×D11311yescharacteristic
441C8—21no—
442C8—21no—
443C8—2261no—
444C8—2261no—
445C22—21no—
446C22—22no—
447C22—22no—
448C22—21no—
449C22—21no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—84no—
455C22—1132no—
456C22—9044no—
457C22—9044no—
458C22—4521no—
459C22—4521no—
460C22—4521no—
461C22—4521no—
462C22—4521no—
463C22—2262no—
464C22—2261no—
465C22—2261no—
466C22—2261no—
467C22—2261no—
468C22—2261no—
469C22C2×D4×D11311yescharacteristic
470C4—21no—
471C4—41no—
472C4—41no—
473C4—1132no—
474C4—4521no—
475C4—2261no—
476C4—2262no—
477C4C2×D4×D11311yescharacteristic
478C4C2×D4×D11311yescharacteristic
479C2—41no—
480C2—42no—
481C2—42no—
482C2—9041no—
483C2—4522no—
484C2—4521no—
485C2—2262no—
486C2#120×D11311yescharacteristic
487C2#2029940211yescharacteristic
488C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
hypercenter#450D113
hypocenterC113#3012
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#16813667C2semidirect
2. C2×#16813649C2semidirect
3. C2×#16813643C2semidirect
4. #20299178C2semidirect
5. #20298758C2semidirect
6. #20298757C2semidirect
7. #20298747C2semidirect
8. #20298745C2semidirect
9. #20298744C2semidirect
10. #20298733C2semidirect
11. #20298732C2semidirect
12. #20298596C2semidirect
13. #102×D113C2semidirect
14. #20298563C2semidirect
15. #450×C113C2semidirect
18. C2×#14268648C22semidirect
31. C2×#14268637C22semidirect
32. C2×#14268636C22semidirect
33. C2×#14268634C22semidirect
34. C2×D904C22semidirect
35. C2×#14268632C22semidirect
36. C2×#14268632C22semidirect
37. C2×#14268630C22semidirect
38. C2×C8×D113C22semidirect
40. #16813598C22semidirect
42. #16813597C22semidirect
43. #16813596C22semidirect
46. C4⋊C4×D113C22semidirect
47. #16813547C22semidirect
48. #16813545C22semidirect
49. #16813544C22semidirect
50. #16813543C22semidirect
51. #16813543C22semidirect
52. #16813542C22semidirect
53. C22⋊#11744751C22semidirect
54. #16813534C22semidirect
55. #16813534C22semidirect
57. C2×SD16×C113C22semidirect
58. C2×SD16×C113C22semidirect
59. C22⋊Q8×C113C22semidirect
60. #102×C113C22semidirect
61. #102×C113C22semidirect
62. C22⋊C8×C113C22semidirect
75. #14268646D4semidirect
97. D4×D113D4semidirect
245. C113#3012semidirect
253. #450D113semidirect
280. C2×SD16C2×D113semidirect
281. C2×SD16C2×D113semidirect
289. C22⋊Q8C2×D113semidirect
302. #102C2×D113semidirect
303. #102C2×D113semidirect
307. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136672
C2×#168136492
C2×#168136432
#202991782
#202987582
#202987572
#202987472
#202987452
#202987442
#202987332
#202987322
#202985962
#102×D1132
#202985632
#450×C1132
#3012113