Finite Group Databasebeta

← #16016254

Subgroups — #16016254

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718572C211yesmaximal, characteristic
2#13123706C211yesmaximal, characteristic, complemented
3#13123683C211yesmaximal, characteristic, complemented
4#13116712C211yesmaximal, characteristic, complemented
5#13116710C211yesmaximal, characteristic, complemented
6#13116700C211yesmaximal, characteristic, complemented
7#13116699C211yesmaximal, characteristic, complemented
8#13116691C211yesmaximal, characteristic, complemented
9C4×#88040C211yesmaximal, characteristic, complemented
10#13116680C211yesmaximal, characteristic, complemented
11#13116621C211yesmaximal, characteristic, complemented
12#13116540C211yesmaximal, characteristic, complemented
13D13×#357C211yesmaximal, characteristic, complemented
14#13116431C211yesmaximal, characteristic, complemented
15C4×C13×D16C211yesmaximal, characteristic, complemented
16C2×#88166C2211yescharacteristic
17C2×D8×D13C2211yescharacteristic
18#11719251—21no—
19#11719250—21no—
20C2×C13×D16C2211yescharacteristic
21C4×C13×D8C2211yescharacteristic
22C4×C13×D8C2211yescharacteristic, complemented
23D8×Dic13C2211yescharacteristic
24D8×Dic13C2211yescharacteristic, complemented
25C2×#88067C2211yescharacteristic
26C2×#88066C2211yescharacteristic
27#11718679—21no—
28#11718675—21no—
29#11718572C418yescomplemented
30C2×#88040C2211yescharacteristic
31C2×#88038C2211yescharacteristic
32C2×C16×D13C2211yescharacteristic
33#11718541C2211yescharacteristic
34D13×#107C2211yescharacteristic
35#11718534C2211yescharacteristic, complemented
36#11718533C2211yescharacteristic
37#11718446—21no—
38#11718432—21no—
39#11718431—21no—
40#11718418—21no—
41C4×Dic52C2211yescharacteristic, complemented
42C4×D104C2211yescharacteristic
43#11718350C2211yescharacteristic
44C13×#366C2211yescharacteristic, complemented
45C13×#357C2211yescharacteristic
46C13×#357C2211yescharacteristic, complemented
47C4×C13×C16C2211yescharacteristic, complemented
48#11718154C2211yescharacteristic
49#11718154C2211yescharacteristic, complemented
50#11718101C2211yescharacteristic
51#11718097C2211yescharacteristic, complemented
52#11718095C2211yescharacteristic, complemented
53#11718094C2211yescharacteristic, 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—
62C2×C13×D8C2311yescharacteristic
63C2×C13×D8C2311yescharacteristic
64C4×D4×C13—21no—
65C4×D4×C13—21no—
66D4×Dic13—21no—
67D4×Dic13—21no—
68C2×#6105—21no—
69C2×#6104—21no—
70C4×C22⋊D13—41no—
71C4×C22⋊D13—41no—
72C2×#6103—41no—
73C2×#6101—41no—
74#88166—22no—
75#88166C2×C414yescomplemented
76D8×D13—22no—
77D8×D13C2×C414yescomplemented
78C2×Dic52C2311yescharacteristic
79C2×D104C2311yescharacteristic
80C2×#6094D411yescharacteristic
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—
91#88126D411yescharacteristic
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—
109#88055D411yescharacteristic
110C8×Dic13C2311yescharacteristic
111C2×#6090C2311yescharacteristic
112C2×#6090C2311yescharacteristic
113#88050—21no—
114#88049—21no—
115#88048—21no—
116#88047—21no—
117#88043D411yescharacteristic
118#88040C2×C414yescomplemented
119#88038C2×C414yescomplemented
120C16×D13—22no—
121#33454—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×D13C2×D411yescharacteristic
141C2×Dic26—21no—
142C13×D8—21no—
143C13×D8—21no—
144C13×D8C22×C412yes—
145C13×D8C22×C412yes—
146C2×C8×C13C2×D411yescharacteristic
147C2×C8×C13C2411yescharacteristic
148C13×C4⋊C4—21no—
149C13×C4⋊C4—21no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C42×C13C2×D411yescharacteristic
153C22⋊Dic13—41no—
154C22⋊Dic13—41no—
155#6105—24no—
156#6104—24no—
157#6103—41no—
158#6103—41no—
159#6103—41no—
160#6103D811yescharacteristic
161#6103D811yescharacteristic
162C4⋊Dic13—21no—
163C4⋊Dic13—21no—
164#6101—41no—
165#6101—41no—
166#6101—41no—
167#6101D811yescharacteristic
168#6101D811yescharacteristic
169C4×Dic13—41no—
170C4×Dic13—41no—
171C4×Dic13—41no—
172C4×Dic13C2×D411yescharacteristic
173C2×#1055C2×D411yescharacteristic
174C2×#1055C2×D411yescharacteristic
175Dic52—21no—
176Dic52C22×C412yes—
177D104—21no—
178D104C22×C412yes—
179#6094—22no—
180C8×D13C22×C412yes—
181C8×D13#4112yes—
182C13×C16—21no—
183C13×C16C22×C412yes—
184#6090—21no—
185#6090C22×C412yes—
186C2×#509—131no—
187#2951—131no—
188#2948—131no—
189#2177—131no—
190#2177—131no—
191#2175—131no—
192#2175—131no—
193C4×SD32—131no—
194C4×SD32—131no—
195C4×D16—131no—
196C4×D16D1311yescharacteristic, complemented
197#2159—131no—
198#2138—131no—
199C2×#357—131no—
200#2108—131no—
201C23×C13—41no—
202C23×C13—41no—
203C22×D13—41no—
204C22×D13—44no—
205C22×D13—161no—
206C22×D13—161no—
207C22×D13C2×D811yescharacteristic
208D4×C13—22no—
209D4×C13—22no—
210D4×C13—41no—
211D4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—161no—
215C2×C4×C13—161no—
216C2×C4×C13C2×D811yescharacteristic
217C2×C4×C13C2×D811yescharacteristic
218C2×C4×C13C22×D411yescharacteristic
219C22⋊D13—44no—
220C22⋊D13—44no—
221C2×Dic13—41no—
222C2×Dic13—44no—
223C2×Dic13—41no—
224C2×Dic13—41no—
225C2×Dic13—161no—
226C2×Dic13—161no—
227C2×Dic13C2×D811yescharacteristic
228C2×Dic13C2×D811yescharacteristic
229C2×Dic13C2×D811yescharacteristic
230D52—22no—
231D52—41no—
232C4×D13—161no—
233C4×D13—161no—
234C4×D13—161no—
235C4×D13C4×D412yes—
236C4×D13#13512yes—
237Dic26—22no—
238Dic26—41no—
239C8×C13—21no—
240C8×C13C23×C411yescharacteristic
241C8×C13C2×#4111yescharacteristic
242#1055—21no—
243#1055C4×D412yes—
244C2×#135—131no—
245C22×D8—131no—
246#520—261no—
247#518—261no—
248#509—138no—
249C2×SD32—131no—
250C2×SD32—131no—
251C2×D16—131no—
252C2×D16C2×D1311yescharacteristic
253C2×M32—131no—
254C22×C16—131no—
255#442—261no—
256#442—261no—
257#440—261no—
258#440—261no—
259C4×Q16—131no—
260C4×Q16—131no—
261C4×D8—131no—
262C4×D8—131no—
263C4×D8—131no—
264C4×D8—131no—
265C4×D8C2×D1311yescharacteristic
266C4×D8C2×D1311yescharacteristic, complemented
267#427—131no—
268C2×#107—131no—
269#418—261no—
270#417—261no—
271#405—131no—
272#367—131no—
273#367—131no—
274#366—131no—
275#366C2×D1311yescharacteristic, complemented
276#358—131no—
277#358—131no—
278#357—131no—
279#357—131no—
280#357—131no—
281#357—131no—
282#357C2×D1311yescharacteristic
283#357C2×D1311yescharacteristic, complemented
284#346—131no—
285#346—131no—
286C4×C16—131no—
287C4×C16C2×D1311yescharacteristic, complemented
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13—81no—
293C22×C13—81no—
294C22×C13C22×D811yescharacteristic
295C2×D13—21no—
296C2×D13—21no—
297C2×D13—42no—
298C2×D13—81no—
299C2×D13—81no—
300C2×D13—164no—
301C2×D13C4×D812yes—
302C4×C13—21no—
303C4×C13—21no—
304C4×C13—81no—
305C4×C13—81no—
306C4×C13C2×C4×D411yescharacteristic
307C4×C13C2×#13511yescharacteristic
308Dic13—21no—
309Dic13—21no—
310Dic13—42no—
311Dic13—81no—
312Dic13—81no—
313Dic13C4×D812yes—
314C2×#41—261no—
315C22×D4—261no—
316#135—134no—
317#135—262no—
318C2×Q16—131no—
319C2×SD16—261no—
320C2×D8—134no—
321C2×D8—131no—
322C2×D8—262no—
323C2×D8—261no—
324C2×D8C22×D1311yescharacteristic
325C2×D8C22×D1311yescharacteristic
326C2×M16—131no—
327C22×C8—131no—
328C4×Q8—261no—
329C4×Q8—261no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—261no—
333C4×D4—261no—
334C4×D4—261no—
335C4×D4—261no—
336C4×D4—521no—
337C4×D4—521no—
338C4×D4—521no—
339C4×D4—521no—
340#117—131no—
341#117—261no—
342#117—521no—
343C2×C4⋊C4—261no—
344C2×C4⋊C4—521no—
345C2×C22⋊C4—521no—
346C2×C22⋊C4—521no—
347SD32—134no—
348SD32—134no—
349D16—134no—
350D16C4×D1314yescomplemented
351M32—134no—
352C2×C16—131no—
353C2×C16—131no—
354C2×C16—262no—
355C2×C16C22×D1311yescharacteristic
356C2×C16C22×D1311yescharacteristic
357#107—131no—
358#107—131no—
359#107—261no—
360#107C22×D1311yescharacteristic
361#107C22×D1311yescharacteristic
362#106—261no—
363#103—261no—
364#103—261no—
365#102—21no—
366#102—21no—
367#102—261no—
368#102—261no—
369#102—261no—
370#102—261no—
371#97—131no—
372#97—131no—
373C4×C8—131no—
374C4×C8C22×D1311yescharacteristic
375C2×C13—82no—
376C2×C13—82no—
377C2×C13C2×C4×D811yescharacteristic
378C2×C13#341511yescharacteristic
379C2×C13#341611yescharacteristic
380D13—22no—
381D13—82no—
382C24—521no—
383#41—264no—
384#41—522no—
385C2×Q8—261no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—264no—
389C2×D4—261no—
390C2×D4—522no—
391C2×D4—521no—
392C2×D4—521no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—131no—
396C22×C4—521no—
397C22×C4—521no—
398C22×C4—521no—
399C22×C4—521no—
400C22×C4—521no—
401C22×C4—521no—
402Q16—132no—
403Q16—261no—
404SD16—264no—
405D8—21no—
406D8—21no—
407D8—132no—
408D8—264no—
409D8—261no—
410D8C2×C4×D1312yes—
411D8C2×C4×D1312yes—
412M16—262no—
413C2×C8—131no—
414C2×C8—132no—
415C2×C8—132no—
416C2×C8—131no—
417C2×C8D4×D1311yescharacteristic
418C2×C8C23×D1311yescharacteristic
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—131no—
422C4⋊C4—131no—
423C4⋊C4—261no—
424C4⋊C4—261no—
425C4⋊C4—521no—
426C4⋊C4—521no—
427C4⋊C4—521no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—131no—
431C22⋊C4—131no—
432C22⋊C4—521no—
433C22⋊C4—521no—
434C22⋊C4—521no—
435C22⋊C4—521no—
436C22⋊C4—521no—
437C42—131no—
438C42—521no—
439C42—521no—
440C42—521no—
441C42D4×D1311yescharacteristic
442C16—21no—
443C16—132no—
444C16—261no—
445C16C2×C4×D1312yes—
446C13#3345411yescharacteristic, complemented, Sylow
447C23—41no—
448C23—41no—
449C23—131no—
450C23—524no—
451C23—521no—
452C23—2081no—
453C23—2081no—
454Q8—262no—
455Q8—521no—
456D4—22no—
457D4—22no—
458D4—41no—
459D4—41no—
460D4—262no—
461D4—524no—
462D4—524no—
463D4—521no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—131no—
467C2×C4—132no—
468C2×C4—132no—
469C2×C4—131no—
470C2×C4—131no—
471C2×C4—161no—
472C2×C4—161no—
473C2×C4—524no—
474C2×C4—521no—
475C2×C4—521no—
476C2×C4—521no—
477C2×C4—2081no—
478C2×C4—2081no—
479C2×C4—2081no—
480C2×C4—2081no—
481C2×C4—2081no—
482C2×C4D8×D1311yescharacteristic
483C2×C4D8×D1311yescharacteristic
484C2×C4C2×D4×D1311yescharacteristic
485C8—21no—
486C8—132no—
487C8—261no—
488C8C22×C4×D1311yescharacteristic
489C8#41×D1311yescharacteristic
490C22—42no—
491C22—42no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—132no—
497C22—261no—
498C22—261no—
499C22—522no—
500C22—1041no—
501C22—1041no—
502C22—2084no—
503C22C2×D8×D1311yescharacteristic
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—132no—
509C4—261no—
510C4—261no—
511C4—522no—
512C4—1041no—
513C4—1041no—
514C4C4×D4×D1311yescharacteristic
515C4D13×#13511yescharacteristic
516C2—82no—
517C2—82no—
518C2—262no—
519C2—1042no—
520C2C4×D8×D1311yescharacteristic
521C2#1312797311yescharacteristic
522C2#1312797911yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC4×C13×D16C2
socleC22×C13C22×D8
prime radicalC2×#11718572C2
cosocleC2×C8×C13C24
hypercenterC4×D16D13
hypocenterC13#33454
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
2. #13123706C2semidirect
3. #13123683C2semidirect
4. #13116712C2semidirect
5. #13116710C2semidirect
6. #13116700C2semidirect
7. #13116699C2semidirect
8. #13116691C2semidirect
9. C4×#88040C2semidirect
10. #13116680C2semidirect
11. #13116621C2semidirect
12. #13116540C2semidirect
13. D13×#357C2semidirect
14. #13116431C2semidirect
15. C4×C13×D16C2semidirect
22. C4×C13×D8C22semidirect
24. D8×Dic13C22semidirect
29. #11718572C4semidirect
35. #11718534C22semidirect
41. C4×Dic52C22semidirect
44. C13×#366C22semidirect
46. C13×#357C22semidirect
47. C4×C13×C16C22semidirect
49. #11718154C22semidirect
51. #11718097C22semidirect
52. #11718095C22semidirect
53. #11718094C22semidirect
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
119. #88038C2×C4semidirect
196. C4×D16D13semidirect
266. C4×D8C2×D13semidirect
275. #366C2×D13semidirect
283. #357C2×D13semidirect
287. C4×C16C2×D13semidirect
350. D16C4×D13semidirect
446. C13#33454semidirect

Maximal subgroups

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

subgroupindex
C2×#117185722
#131237062
#131236832
#131167122
#131167102
#131167002
#131166992
#131166912
C4×#880402
#131166802
#131166212
#131165402
D13×#3572
#131164312
C4×C13×D162
#3345413