Finite Group Databasebeta

← #16016240

Subgroups — #16016240

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718572C211yesmaximal, characteristic
2C4×#88166C211yesmaximal, characteristic, complemented
3C4×D8×D13C211yesmaximal, characteristic, complemented
4#13116710C211yesmaximal, characteristic, complemented
5#13116702C211yesmaximal, characteristic, complemented
6#13116700C211yesmaximal, characteristic, complemented
7#13116691C211yesmaximal, characteristic, complemented
8#13116687C211yesmaximal, characteristic, complemented
9D16×Dic13C211yesmaximal, characteristic, complemented
10#13116680C211yesmaximal, characteristic, complemented
11#13116623C211yesmaximal, characteristic, complemented
12#13116550C211yesmaximal, characteristic, complemented
13#13116545C211yesmaximal, characteristic, complemented
14#13116429C211yesmaximal, characteristic, complemented
15C13×#2177C211yesmaximal, characteristic, complemented
16C2×#88166C2211yescharacteristic
17C2×D8×D13C2211yescharacteristic
18C4×D4×D13—21no—
19C4×#6129—21no—
20C2×C13×D16C2211yescharacteristic
21C4×C13×D8C2211yescharacteristic
22C4×C13×D8C2211yescharacteristic, complemented
23D8×Dic13C2211yescharacteristic
24D8×Dic13C2211yescharacteristic, complemented
25C2×#88067C2211yescharacteristic
26C2×#88066C2211yescharacteristic
27C4×#6105—21no—
28C4×#6104—21no—
29#11718572C418yescomplemented
30C2×#88040C2211yescharacteristic
31C2×#88038C2211yescharacteristic
32C2×#88038C2211yescharacteristic
33#11718541C2211yescharacteristic
34D13×#107C2211yescharacteristic
35#11718534C2211yescharacteristic, complemented
36#11718533C2211yescharacteristic
37#11718433—21no—
38D13×#102—21no—
39#11718419—21no—
40#11718417—21no—
41C4×Dic52C2211yescharacteristic, complemented
42C4×D104C2211yescharacteristic
43C4×C8×D13C2211yescharacteristic
44C13×#367C2211yescharacteristic, complemented
45C13×#357C2211yescharacteristic
46C13×#357C2211yescharacteristic, complemented
47C13×#346C2211yescharacteristic, complemented
48#11718154C2211yescharacteristic
49#11718154C2211yescharacteristic, complemented
50#11718101C2211yescharacteristic
51#11718096C2211yescharacteristic, complemented
52#11718095C2211yescharacteristic, complemented
53C16×Dic13C2211yescharacteristic, complemented
54C16×Dic13C2211yescharacteristic, complemented
55#11718084C2211yescharacteristic, complemented
56#11718083C2211yescharacteristic
57#11718082C2211yescharacteristic, complemented
58#11718081C2211yescharacteristic, complemented
59#11718053C2211yescharacteristic, complemented
60C2×#6129—21no—
61C2×D4×D13—21no—
62C22×C4×D13—41no—
63C2×C13×D8C2311yescharacteristic
64C2×C13×D8C2311yescharacteristic
65C4×D4×C13—21no—
66C4×D4×C13—21no—
67D4×Dic13—21no—
68D4×Dic13—21no—
69C2×#6105—21no—
70C2×#6104—21no—
71C4×C22⋊D13—41no—
72C4×C22⋊D13—41no—
73C2×C4×Dic13—41no—
74#88166—22no—
75#88166C2×C414yescomplemented
76D8×D13—22no—
77D8×D13C2×C414yescomplemented
78C2×Dic52C2311yescharacteristic
79C2×D104C2311yescharacteristic
80C2×C8×D13D411yescharacteristic
81C2×C8×D13C2311yescharacteristic
82#88147—21no—
83#88146—21no—
84C4⋊C4×D13—21no—
85#88141—21no—
86#88135—41no—
87#88135—41no—
88C22⋊C4×D13—41no—
89#88131—41no—
90C4×D52—21no—
91C42×D13D411yescharacteristic
92C4×Dic26—21no—
93C13×D16C2×C414yescomplemented
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#102—21no—
99C13×#102—21no—
100C4×C8×C13C2311yescharacteristic
101#88072—21no—
102#88072—21no—
103#88067C2×C414yescomplemented
104#88066C2×C414yescomplemented
105#88061—21no—
106#88058C2311yescharacteristic
107#88058C2311yescharacteristic
108#88056—21no—
109C8×Dic13D411yescharacteristic
110C8×Dic13C2311yescharacteristic
111C2×#6090C2311yescharacteristic
112C2×#6090C2311yescharacteristic
113#88050—21no—
114#88049—21no—
115#88048—21no—
116#88047—21no—
117C4×#1055D411yescharacteristic
118#88040C2×C414yescomplemented
119#88038—22no—
120#88038C2×C414yescomplemented
121C4×#509—131nomaximal, Sylow
122C23×D13—41no—
123C2×D4×C13—21no—
124C2×D4×C13—21no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C2×C22⋊D13—41no—
128C2×C22⋊D13—41no—
129C22×Dic13—41no—
130C22×Dic13—41no—
131C22×Dic13—41no—
132#6129—24no—
133#6129—42no—
134D4×D13—24no—
135D4×D13—42no—
136C2×D52—21no—
137C2×C4×D13—41no—
138C2×C4×D13—41no—
139C2×C4×D13—41no—
140C2×C4×D13—84no—
141C2×C4×D13D811yescharacteristic
142C2×C4×D13D811yescharacteristic
143C2×C4×D13C2×D411yescharacteristic
144C2×Dic26—21no—
145C13×D8—21no—
146C13×D8—21no—
147C13×D8C22×C412yes—
148C13×D8C22×C412yescomplemented
149C2×C8×C13C2×D411yescharacteristic
150C2×C8×C13C2411yescharacteristic
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C42×C13C2×D411yescharacteristic
156C22⋊Dic13—41no—
157C22⋊Dic13—41no—
158#6105—24no—
159#6104—24no—
160#6103—41no—
161#6103—41no—
162#6103—41no—
163C4⋊Dic13—21no—
164C4⋊Dic13—21no—
165#6101—41no—
166#6101—41no—
167#6101—41no—
168C4×Dic13—41no—
169C4×Dic13—41no—
170C4×Dic13—41no—
171C4×Dic13D811yescharacteristic
172C4×Dic13D811yescharacteristic
173C4×Dic13C2×D411yescharacteristic
174C2×#1055C2×D411yescharacteristic
175C2×#1055C2×D411yescharacteristic
176Dic52—21no—
177Dic52C22×C412yescomplemented
178D104—21no—
179D104C22×C412yes—
180C8×D13—22no—
181C8×D13C22×C412yes—
182C8×D13#4112yes—
183C13×C16—21no—
184C13×C16C22×C412yescomplemented
185#6090—21no—
186#6090C22×C412yescomplemented
187C2×#509—131no—
188C4×#135—131no—
189C2×C4×D8—131no—
190#2177—131no—
191#2177D1311yescharacteristic, complemented
192#2175—131no—
193#2175—131no—
194C4×SD32—131no—
195C4×SD32—131no—
196C4×D16—131no—
197C4×D16—131no—
198#2159—131no—
199#2140—131no—
200#2139—131no—
201C4×M32—131no—
202C23×C13—41no—
203C23×C13—41no—
204C22×D13—41no—
205C22×D13—44no—
206C22×D13—82no—
207C22×D13—82no—
208C22×D13C2×D811yescharacteristic
209D4×C13—22no—
210D4×C13—22no—
211D4×C13—41no—
212D4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—82no—
216C2×C4×C13—82no—
217C2×C4×C13C2×D811yescharacteristic
218C2×C4×C13C2×D811yescharacteristic
219C2×C4×C13C22×D411yescharacteristic
220C22⋊D13—44no—
221C22⋊D13—44no—
222C2×Dic13—41no—
223C2×Dic13—44no—
224C2×Dic13—41no—
225C2×Dic13—41no—
226C2×Dic13—82no—
227C2×Dic13—82no—
228C2×Dic13C2×D811yescharacteristic
229C2×Dic13C2×D811yescharacteristic
230C2×Dic13C2×D811yescharacteristic
231D52—22no—
232D52—41no—
233C4×D13—22no—
234C4×D13—41no—
235C4×D13—82no—
236C4×D13—82no—
237C4×D13—82no—
238C4×D13C4×D412yes—
239C4×D13#13512yes—
240Dic26—22no—
241Dic26—41no—
242C8×C13—21no—
243C8×C13C23×C411yescharacteristic
244C8×C13C2×#4111yescharacteristic
245#1055—21no—
246#1055C4×D412yes—
247C2×#135—131no—
248C22×D8—131no—
249C4×#41—261no—
250C2×C4×D4—261no—
251#509—138no—
252C2×SD32—131no—
253C2×SD32—131no—
254C2×D16—131no—
255C2×D16C2×D1311yescharacteristic
256C2×M32—131no—
257C2×M32—131no—
258C4×Q16—131no—
259C4×Q16—131no—
260C4×SD16—261no—
261C4×SD16—261no—
262C4×D8—131no—
263C4×D8—131no—
264C4×D8—131no—
265C4×D8—131no—
266C4×D8—261no—
267C4×D8—261no—
268C4×D8C2×D1311yescharacteristic
269C4×D8C2×D1311yescharacteristic, complemented
270#427—131no—
271C2×#107—131no—
272#416—261no—
273C2×#102—261no—
274C2×C4×C8—131no—
275#367—131no—
276#367C2×D1311yescharacteristic, complemented
277#366—131no—
278#366—131no—
279#358—131no—
280#358—131no—
281#357—131no—
282#357—131no—
283#357—131no—
284#357—131no—
285#357C2×D1311yescharacteristic
286#357C2×D1311yescharacteristic, complemented
287#346—131no—
288#346C2×D1311yescharacteristic, complemented
289C4×C16—131no—
290C4×C16—131no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—81no—
294C22×C13—81no—
295C22×C13—81no—
296C22×C13—81no—
297C22×C13C22×D811yescharacteristic
298C2×D13—21no—
299C2×D13—21no—
300C2×D13—42no—
301C2×D13—88no—
302C2×D13—81no—
303C2×D13—81no—
304C2×D13C4×D812yes—
305C4×C13—21no—
306C4×C13—21no—
307C4×C13—81no—
308C4×C13—81no—
309C4×C13C2×C4×D411yescharacteristic
310C4×C13C2×#13511yescharacteristic
311Dic13—21no—
312Dic13—42no—
313Dic13—81no—
314Dic13—81no—
315Dic13C4×D812yes—
316Dic13#50912yescomplemented
317C2×#41—261no—
318C22×D4—261no—
319C23×C4—521no—
320#135—134no—
321#135—262no—
322C2×Q16—131no—
323C2×SD16—261no—
324C2×D8—134no—
325C2×D8—131no—
326C2×D8—262no—
327C2×D8—261no—
328C2×D8C22×D1311yescharacteristic
329C2×D8C22×D1311yescharacteristic
330C22×C8—131no—
331C22×C8—131no—
332C4×Q8—261no—
333C4×Q8—261no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—261no—
337C4×D4—261no—
338C4×D4—261no—
339C4×D4—261no—
340C4×D4—521no—
341C4×D4—521no—
342C4×D4—521no—
343C4×D4—521no—
344#117—261no—
345#117—521no—
346C2×C4⋊C4—261no—
347C2×C22⋊C4—521no—
348C2×C42—131no—
349C2×C42—521no—
350SD32—134no—
351SD32—134no—
352D16—134no—
353D16C4×D1314yescomplemented
354M32—134no—
355M32—262no—
356C2×C16—131no—
357C2×C16—131no—
358C2×C16C22×D1311yescharacteristic
359C2×C16C22×D1311yescharacteristic
360#107—131no—
361#107—131no—
362#107—261no—
363#107C22×D1311yescharacteristic
364#107C22×D1311yescharacteristic
365#106—261no—
366#103—261no—
367#103—261no—
368#102—21no—
369#102—21no—
370#102—261no—
371#102—261no—
372#102—261no—
373#102—261no—
374C4×C8—131no—
375C4×C8—131no—
376C4×C8—131no—
377C4×C8C22×D1311yescharacteristic
378C2×C13—82no—
379C2×C13—82no—
380C2×C13C2×C4×D811yescharacteristic
381C2×C13C2×#50911yescharacteristic
382C2×C13#341411yescharacteristic
383D13—22no—
384D13—82no—
385C24—521no—
386#41—264no—
387#41—522no—
388C2×Q8—261no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—264no—
392C2×D4—261no—
393C2×D4—522no—
394C2×D4—521no—
395C2×D4—521no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—131no—
399C22×C4—131no—
400C22×C4—131no—
401C22×C4—521no—
402C22×C4—521no—
403C22×C4—521no—
404C22×C4—521no—
405C22×C4—521no—
406C22×C4—521no—
407C22×C4—1044no—
408Q16—132no—
409Q16—261no—
410SD16—264no—
411D8—21no—
412D8—21no—
413D8—132no—
414D8—264no—
415D8—261no—
416D8C2×C4×D1312yes—
417D8C2×C4×D1312yescomplemented
418C2×C8—131no—
419C2×C8—132no—
420C2×C8—132no—
421C2×C8—131no—
422C2×C8—262no—
423C2×C8D4×D1311yescharacteristic
424C2×C8C23×D1311yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—261no—
428C4⋊C4—261no—
429C4⋊C4—521no—
430C4⋊C4—521no—
431C4⋊C4—521no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—521no—
435C22⋊C4—521no—
436C22⋊C4—521no—
437C22⋊C4—521no—
438C22⋊C4—521no—
439C42—131no—
440C42—131no—
441C42—131no—
442C42—521no—
443C42—521no—
444C42—521no—
445C42D4×D1311yescharacteristic
446C16—21no—
447C16—132no—
448C16—261no—
449C16C2×C4×D1312yescomplemented
450C13C4×#50911yescharacteristic, complemented, Sylow
451C23—41no—
452C23—41no—
453C23—131no—
454C23—524no—
455C23—521no—
456C23—1042no—
457C23—1042no—
458Q8—262no—
459Q8—521no—
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—262no—
465D4—524no—
466D4—524no—
467D4—521no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—131no—
473C2×C4—131no—
474C2×C4—132no—
475C2×C4—132no—
476C2×C4—131no—
477C2×C4—262no—
478C2×C4—521no—
479C2×C4—524no—
480C2×C4—521no—
481C2×C4—521no—
482C2×C4—521no—
483C2×C4—1042no—
484C2×C4—1042no—
485C2×C4—1042no—
486C2×C4—1042no—
487C2×C4—1042no—
488C2×C4D8×D1311yescharacteristic
489C2×C4D8×D1311yescharacteristic
490C2×C4C2×D4×D1311yescharacteristic
491C8—21no—
492C8—132no—
493C8—261no—
494C8C22×C4×D1311yescharacteristic
495C8#41×D1311yescharacteristic
496C22—42no—
497C22—42no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—132no—
503C22—261no—
504C22—261no—
505C22—522no—
506C22—1048no—
507C22—1041no—
508C22—1041no—
509C22C2×D8×D1311yescharacteristic
510C4—21no—
511C4—21no—
512C4—81no—
513C4—81no—
514C4—132no—
515C4—132no—
516C4—261no—
517C4—522no—
518C4—1041no—
519C4—1041no—
520C4C4×D4×D1311yescharacteristic
521C4D13×#13511yescharacteristic
522C2—82no—
523C2—82no—
524C2—262no—
525C2—1042no—
526C2C4×D8×D1311yescharacteristic
527C2D13×#50911yescharacteristic
528C2#1312796811yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2177C2
socleC22×C13C22×D8
prime radicalC2×#11718572C2
cosocleC2×C8×C13C24
hypercenter#2177D13
hypocenterC13C4×#509
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

Complements

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

NH ≅ G/Ntype
2. C4×#88166C2semidirect
3. C4×D8×D13C2semidirect
4. #13116710C2semidirect
5. #13116702C2semidirect
6. #13116700C2semidirect
7. #13116691C2semidirect
8. #13116687C2semidirect
9. D16×Dic13C2semidirect
10. #13116680C2semidirect
11. #13116623C2semidirect
12. #13116550C2semidirect
13. #13116545C2semidirect
14. #13116429C2semidirect
15. C13×#2177C2semidirect
22. C4×C13×D8C22semidirect
24. D8×Dic13C22semidirect
29. #11718572C4semidirect
35. #11718534C22semidirect
41. C4×Dic52C22semidirect
44. C13×#367C22semidirect
46. C13×#357C22semidirect
47. C13×#346C22semidirect
49. #11718154C22semidirect
51. #11718096C22semidirect
52. #11718095C22semidirect
53. C16×Dic13C22semidirect
54. C16×Dic13C22semidirect
55. #11718084C22semidirect
57. #11718082C22semidirect
58. #11718081C22semidirect
59. #11718053C22semidirect
75. #88166C2×C4semidirect
77. D8×D13C2×C4semidirect
93. C13×D16C2×C4semidirect
103. #88067C2×C4semidirect
104. #88066C2×C4semidirect
118. #88040C2×C4semidirect
120. #88038C2×C4semidirect
148. C13×D8C22×C4semidirect
177. Dic52C22×C4semidirect
184. C13×C16C22×C4semidirect
186. #6090C22×C4semidirect
191. #2177D13semidirect
269. C4×D8C2×D13semidirect
276. #367C2×D13semidirect
286. #357C2×D13semidirect
288. #346C2×D13semidirect
316. Dic13#509semidirect
353. D16C4×D13semidirect
417. D8C2×C4×D13semidirect
449. C16C2×C4×D13semidirect
450. C13C4×#509semidirect

Maximal subgroups

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

subgroupindex
C2×#117185722
C4×#881662
C4×D8×D132
#131167102
#131167022
#131167002
#131166912
#131166872
D16×Dic132
#131166802
#131166232
#131165502
#131165452
#131164292
C13×#21772
C4×#50913