Finite Group Databasebeta

← #16016285

Subgroups — #16016285

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×SD32C211yesmaximal, characteristic
2#13123699C211yesmaximal, characteristic, complemented
3#13123683C211yesmaximal, characteristic
4#13116702C211yesmaximal, characteristic, complemented
5#13116701C211yesmaximal, characteristic, complemented
6#13116699C211yesmaximal, characteristic, complemented
7#13116691C211yesmaximal, characteristic, complemented
8C4×#88068C211yesmaximal, characteristic, complemented
9C4×#88067C211yesmaximal, characteristic, complemented
10#13116685C211yesmaximal, characteristic, complemented
11#13116617C211yesmaximal, characteristic, complemented
12#13116554C211yesmaximal, characteristic, complemented
13#13116550C211yesmaximal, characteristic
14#13116434C211yesmaximal, characteristic, complemented
15C13×#2175C211yesmaximal, characteristic, complemented
16C2×Q16×D13C2211yescharacteristic
17C2×D8×D13C2211yescharacteristic
18#11719277—21no—
19#11719250—21no—
20C2×C13×SD32C2211yescharacteristic
21C4×C13×Q16C2211yescharacteristic, complemented
22C4×C13×D8C2211yescharacteristic
23Q16×Dic13C2211yescharacteristic, complemented
24C2×#88068C2211yescharacteristic
25D8×Dic13C2211yescharacteristic
26C2×#88067C2211yescharacteristic
27#11718691—21no—
28#11718675—21no—
29D13×SD32C418yescomplemented
30C2×#88040C2211yescharacteristic
31C2×#88038C2211yescharacteristic
32C2×C16×D13C2211yescharacteristic
33#11718541C2211yescharacteristic
34#11718541C2211yescharacteristic
35#11718534C2211yescharacteristic, complemented
36#11718533C2211yescharacteristic
37#11718463—21no—
38#11718450—21no—
39#11718446—21no—
40#11718431—21no—
41C4×Dic52C2211yescharacteristic, complemented
42C4×D104C2211yescharacteristic
43#11718350C2211yescharacteristic
44C13×#366C2211yescharacteristic, complemented
45C13×#358C2211yescharacteristic, complemented
46C13×#357C2211yescharacteristic
47C13×#346C2211yescharacteristic, complemented
48#11718156C2211yescharacteristic, complemented
49#11718154C2211yescharacteristic
50#11718101C2211yescharacteristic
51#11718096C2211yescharacteristic, complemented
52#11718095C2211yescharacteristic, complemented
53#11718094C2211yescharacteristic, complemented
54C16×Dic13C2211yescharacteristic, complemented
55#11718084C2211yescharacteristic, complemented
56#11718083C2211yescharacteristic
57#11718082C2211yescharacteristic, complemented
58#11718082C2211yescharacteristic, complemented
59C4×#6090C2211yescharacteristic, complemented
60C2×Q8×D13—21no—
61C2×D4×D13—21no—
62C2×C13×Q16C2311yescharacteristic
63C2×C13×D8C2311yescharacteristic
64C4×Q8×C13—21no—
65C4×D4×C13—21no—
66Q8×Dic13—21no—
67C2×#6107—21no—
68D4×Dic13—21no—
69C2×#6104—21no—
70C4×C22⋊D13—41no—
71C2×#6103—41no—
72Q16×D13—22no—
73Q16×D13C2×C414yescomplemented
74D8×D13—22no—
75D8×D13C2×C414yes—
76C2×Dic52C2311yescharacteristic
77C2×D104C2311yescharacteristic
78C2×#6094D411yescharacteristic
79C2×C8×D13C2311yescharacteristic
80#88147—21no—
81#88146—21no—
82#88146—21no—
83#88146—41no—
84#88141—21no—
85#88141—41no—
86#88135—41no—
87C22⋊C4×D13—41no—
88C4×D52—21no—
89#88126—41no—
90#88126D411yescharacteristic
91C4×Dic26—21no—
92C4×Dic26—41no—
93C13×SD32C2×C414yescomplemented
94C2×C13×C16C2311yescharacteristic
95C2×C13×C16C2311yescharacteristic
96C13×#107C2311yescharacteristic
97C13×#107C2311yescharacteristic
98C13×#103—21no—
99C13×#102—21no—
100C4×C8×C13C2311yescharacteristic
101#88075—21no—
102#88072—21no—
103#88068C2×C414yescomplemented
104#88067C2×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#88048—21no—
117#88043D411yescharacteristic
118#88040C2×C414yescomplemented
119#88038—22no—
120C16×D13C2×C414yescomplemented
121#33457—131nomaximal, Sylow
122C23×D13—41no—
123C2×Q8×C13—21no—
124C2×D4×C13—21no—
125C22×C4×C13—41no—
126C2×C22⋊D13—41no—
127C22×Dic13—41no—
128Q8×D13—24no—
129Q8×D13—42no—
130D4×D13—24no—
131D4×D13—42no—
132C2×D52—21no—
133C2×C4×D13—41no—
134C2×C4×D13—41no—
135C2×C4×D13—41no—
136C2×C4×D13C2×D411yescharacteristic
137C2×Dic26—21no—
138C2×Dic26—41no—
139C13×Q16—21no—
140C13×Q16C22×C412yes—
141C13×D8—21no—
142C13×D8C22×C412yes—
143C2×C8×C13C2×D411yescharacteristic
144C2×C8×C13C2411yescharacteristic
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—41no—
148C13×C22⋊C4—41no—
149C42×C13—41no—
150C42×C13C2×D411yescharacteristic
151C22⋊Dic13—41no—
152#6107—24no—
153#6104—24no—
154#6103—41no—
155#6103—41no—
156#6103—41no—
157#6103—41no—
158#6103D811yescharacteristic
159#6103D811yescharacteristic
160C4⋊Dic13—21no—
161C4⋊Dic13—21no—
162C4⋊Dic13—41no—
163#6101—41no—
164#6101—41no—
165#6101D811yescharacteristic
166#6101D811yescharacteristic
167C4×Dic13—41no—
168C4×Dic13—41no—
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—
186C22×SD32—131no—
187#2950—131no—
188#2948—131no—
189#2175—131no—
190#2175—131no—
191#2175—131no—
192#2175D1311yescharacteristic, complemented
193C4×SD32—131no—
194C4×SD32—131no—
195C4×SD32—131no—
196C4×SD32—131no—
197#2158—131no—
198#2141—131no—
199#2140—131no—
200#2108—131no—
201C23×C13—41no—
202C22×D13—41no—
203C22×D13—44no—
204C22×D13—161no—
205C22×D13—161no—
206C22×D13C2×D811yescharacteristic
207Q8×C13—22no—
208Q8×C13—41no—
209D4×C13—22no—
210D4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—161no—
215C2×C4×C13C2×D811yescharacteristic
216C2×C4×C13C2×D811yescharacteristic
217C2×C4×C13C22×D411yescharacteristic
218C22⋊D13—44no—
219C2×Dic13—41no—
220C2×Dic13—41no—
221C2×Dic13—41no—
222C2×Dic13—161no—
223C2×Dic13C2×D811yescharacteristic
224C2×Dic13C2×D811yescharacteristic
225C2×Dic13C2×D811yescharacteristic
226D52—22no—
227D52—41no—
228C4×D13—44no—
229C4×D13—161no—
230C4×D13—161no—
231C4×D13C4×D412yes—
232C4×D13#13512yes—
233Dic26—22no—
234Dic26—41no—
235Dic26—44no—
236C8×C13—21no—
237C8×C13C23×C411yescharacteristic
238C8×C13C2×#4111yescharacteristic
239#1055—21no—
240#1055C4×D412yes—
241C22×Q16—131no—
242C22×D8—131no—
243#519—261no—
244#518—261no—
245C2×SD32—131no—
246C2×SD32—131no—
247C2×SD32—138no—
248C2×SD32—131no—
249C2×SD32C2×D1311yescharacteristic
250C2×M32—131no—
251C22×C16—131no—
252#442—261no—
253#442—261no—
254#441—261no—
255#441—261no—
256C4×Q16—131no—
257C4×Q16—131no—
258C4×Q16—131no—
259C4×Q16C2×D1311yescharacteristic, complemented
260C4×D8—131no—
261C4×D8—131no—
262C4×D8—131no—
263C4×D8C2×D1311yescharacteristic
264#427—131no—
265#427—131no—
266#419—261no—
267#418—261no—
268#405—131no—
269#367—131no—
270#367—131no—
271#366—131no—
272#366C2×D1311yescharacteristic, complemented
273#358—131no—
274#358—131no—
275#358—131no—
276#358C2×D1311yescharacteristic, complemented
277#357—131no—
278#357—131no—
279#357—131no—
280#357C2×D1311yescharacteristic
281#346—131no—
282#346C2×D1311yescharacteristic, complemented
283C4×C16—131no—
284C4×C16—131no—
285C22×C13—42no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13C22×D811yescharacteristic
289C2×D13—21no—
290C2×D13—21no—
291C2×D13—42no—
292C2×D13—81no—
293C2×D13—81no—
294C2×D13—164no—
295C2×D13C4×D812yes—
296C4×C13—21no—
297C4×C13—21no—
298C4×C13—42no—
299C4×C13—81no—
300C4×C13—81no—
301C4×C13C2×C4×D411yescharacteristic
302C4×C13C2×#13511yescharacteristic
303Dic13—21no—
304Dic13—21no—
305Dic13—42no—
306Dic13—81no—
307Dic13—81no—
308Dic13C4×D812yes—
309C22×Q8—261no—
310C22×D4—261no—
311C2×Q16—134no—
312C2×Q16—131no—
313C2×Q16—262no—
314C2×Q16—261no—
315C2×Q16C22×D1311yescharacteristic
316C2×D8—134no—
317C2×D8—131no—
318C2×D8—262no—
319C2×D8—261no—
320C2×D8C22×D1311yescharacteristic
321C2×M16—131no—
322C22×C8—131no—
323C4×Q8—21no—
324C4×Q8—261no—
325C4×Q8—261no—
326C4×Q8—261no—
327C4×Q8—521no—
328C4×Q8—521no—
329C4×D4—21no—
330C4×D4—261no—
331C4×D4—261no—
332C4×D4—261no—
333C4×D4—521no—
334C4×D4—521no—
335#117—131no—
336#117—261no—
337#117—261no—
338#117—521no—
339#117—521no—
340C2×C22⋊C4—521no—
341C2×C22⋊C4—521no—
342SD32—134no—
343SD32—134no—
344SD32—134no—
345SD32C4×D1314yescomplemented
346M32—262no—
347C2×C16—131no—
348C2×C16—134no—
349C2×C16—131no—
350C2×C16C22×D1311yescharacteristic
351C2×C16C22×D1311yescharacteristic
352#107—131no—
353#107—131no—
354#107C22×D1311yescharacteristic
355#107C22×D1311yescharacteristic
356#106—261no—
357#106—261no—
358#103—21no—
359#103—261no—
360#103—261no—
361#103—261no—
362#102—21no—
363#102—261no—
364#102—261no—
365#102—261no—
366#97—131no—
367#97—131no—
368C4×C8—131no—
369C4×C8C22×D1311yescharacteristic
370C2×C13—82no—
371C2×C13C2×C4×D811yescharacteristic
372C2×C13#341611yescharacteristic
373C2×C13#341611yescharacteristic
374D13—22no—
375D13—82no—
376C24—521no—
377C2×Q8—21no—
378C2×Q8—264no—
379C2×Q8—261no—
380C2×Q8—521no—
381C2×Q8—522no—
382C2×D4—21no—
383C2×D4—264no—
384C2×D4—261no—
385C2×D4—522no—
386C2×D4—521no—
387C22×C4—41no—
388C22×C4—131no—
389C22×C4—521no—
390C22×C4—521no—
391C22×C4—521no—
392C22×C4—521no—
393Q16—21no—
394Q16—132no—
395Q16—264no—
396Q16—261no—
397Q16C2×C4×D1312yes—
398D8—21no—
399D8—132no—
400D8—264no—
401D8—261no—
402D8C2×C4×D1312yes—
403M16—262no—
404C2×C8—131no—
405C2×C8—132no—
406C2×C8—132no—
407C2×C8—131no—
408C2×C8D4×D1311yescharacteristic
409C2×C8C23×D1311yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—131no—
414C4⋊C4—131no—
415C4⋊C4—261no—
416C4⋊C4—261no—
417C4⋊C4—521no—
418C4⋊C4—521no—
419C4⋊C4—521no—
420C22⋊C4—41no—
421C22⋊C4—131no—
422C22⋊C4—131no—
423C22⋊C4—521no—
424C22⋊C4—521no—
425C22⋊C4—521no—
426C22⋊C4—521no—
427C22⋊C4—521no—
428C42—41no—
429C42—131no—
430C42—521no—
431C42—521no—
432C42—521no—
433C42—521no—
434C42—521no—
435C42D4×D1311yescharacteristic
436C16—21no—
437C16—132no—
438C16—261no—
439C16C2×C4×D1312yes—
440C13#3345711yescharacteristic, complemented, Sylow
441C23—41no—
442C23—131no—
443C23—524no—
444C23—521no—
445C23—2081no—
446C23—2081no—
447Q8—22no—
448Q8—41no—
449Q8—262no—
450Q8—524no—
451Q8—521no—
452D4—22no—
453D4—41no—
454D4—262no—
455D4—524no—
456D4—521no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—131no—
461C2×C4—132no—
462C2×C4—132no—
463C2×C4—131no—
464C2×C4—131no—
465C2×C4—161no—
466C2×C4—524no—
467C2×C4—521no—
468C2×C4—521no—
469C2×C4—521no—
470C2×C4—2081no—
471C2×C4—2081no—
472C2×C4—2081no—
473C2×C4D8×D1311yescharacteristic
474C2×C4D8×D1311yescharacteristic
475C2×C4C2×D4×D1311yescharacteristic
476C8—21no—
477C8—132no—
478C8—261no—
479C8C22×C4×D1311yescharacteristic
480C8#41×D1311yescharacteristic
481C22—42no—
482C22—81no—
483C22—81no—
484C22—132no—
485C22—261no—
486C22—261no—
487C22—522no—
488C22—1041no—
489C22—1041no—
490C22—2084no—
491C22C2×D8×D1311yescharacteristic
492C4—21no—
493C4—21no—
494C4—42no—
495C4—81no—
496C4—81no—
497C4—132no—
498C4—261no—
499C4—261no—
500C4—522no—
501C4—1041no—
502C4—1041no—
503C4C4×D4×D1311yescharacteristic
504C4D13×#13511yescharacteristic
505C2—82no—
506C2—262no—
507C2—1042no—
508C2C4×D8×D1311yescharacteristic
509C2#1312798111yescharacteristic
510C2#1312798211yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC13×#2175C2
socleC22×C13C22×D8
prime radicalC2×D8×D13C22
cosocleC2×C8×C13C24
hypercenter#2175D13
hypocenterC13#33457
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
2. #13123699C2semidirect
4. #13116702C2semidirect
5. #13116701C2semidirect
6. #13116699C2semidirect
7. #13116691C2semidirect
8. C4×#88068C2semidirect
9. C4×#88067C2semidirect
10. #13116685C2semidirect
11. #13116617C2semidirect
12. #13116554C2semidirect
14. #13116434C2semidirect
15. C13×#2175C2semidirect
21. C4×C13×Q16C22semidirect
23. Q16×Dic13C22semidirect
29. D13×SD32C4semidirect
35. #11718534C22semidirect
41. C4×Dic52C22semidirect
44. C13×#366C22semidirect
45. C13×#358C22semidirect
47. C13×#346C22semidirect
48. #11718156C22semidirect
51. #11718096C22semidirect
52. #11718095C22semidirect
53. #11718094C22semidirect
54. C16×Dic13C22semidirect
55. #11718084C22semidirect
57. #11718082C22semidirect
58. #11718082C22semidirect
59. C4×#6090C22semidirect
73. Q16×D13C2×C4semidirect
93. C13×SD32C2×C4semidirect
103. #88068C2×C4semidirect
104. #88067C2×C4semidirect
118. #88040C2×C4semidirect
120. C16×D13C2×C4semidirect
192. #2175D13semidirect
259. C4×Q16C2×D13semidirect
272. #366C2×D13semidirect
276. #358C2×D13semidirect
282. #346C2×D13semidirect
345. SD32C4×D13semidirect
440. C13#33457semidirect

Maximal subgroups

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

subgroupindex
C2×D13×SD322
#131236992
#131236832
#131167022
#131167012
#131166992
#131166912
C4×#880682
C4×#880672
#131166852
#131166172
#131165542
#131165502
#131164342
C13×#21752
#3345713