Finite Group Databasebeta

← #15845760

Subgroups — #15845760

Order 3328.

728 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
1#13125229C211yesmaximal, characteristic, complemented
2C2×#11718680C211yesmaximal, characteristic, complemented
3D4×#6099C211yesmaximal, characteristic, complemented
4#13114395C212yesmaximal, complemented
5#13114381C212yesmaximal, complemented
6#13114271C212yesmaximal, complemented
7#13114257C212yesmaximal, complemented
8#13113589C211yesmaximal, characteristic, complemented
9#13113520C211yesmaximal, characteristic, complemented
10#13113513C211yesmaximal, characteristic, complemented
11C13×#3100C211yesmaximal, characteristic
12C13×#532C2211yescharacteristic
13C2×C4×D4×C13C2211yescharacteristic
14C22×#6105—21no—
15C22×#6099—21no—
16C2×#88123C2211yescharacteristic
17C13×#480—21no—
18C13×#474C2211yescharacteristic
19C13×#474C2211yescharacteristic
20C13×#459C2211yescharacteristic
21C13×#459C2211yescharacteristic
22C13×#447—21no—
23C4×C13×D8—21no—
24C4×C13×D8—21no—
25C13×#431C2211yescharacteristic
26#11718893—21no—
27#11718893—21no—
28#11718868—21no—
29#11718742C2212yescomplemented
30#11718731C2212yescomplemented
31#11718716—22no—
32#11718680—21no—
33#11718680—21no—
34#11718680C2212yes—
35#11718680C2212yes—
36#11718673C2212yes—
37#11718672—22no—
38D4×#1055C2212yes—
39C2×#88050—21no—
40#11718585C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718139C2212yescomplemented
44#11718136C2212yescomplemented
45#11718074C2212yescomplemented
46#11718074C2212yescomplemented
47#11718072C2212yescomplemented
48#11718071C2212yescomplemented
49C2×C13×#41—21no—
50C22×D4×C13D411yescharacteristic
51C23×C4×C13—21no—
52C22×Dic26—21no—
53C2×C13×D8—21no—
54C2×C13×D8—21no—
55C13×C4⋊Q8C2311yescharacteristic
56C13×#127C2311yescharacteristic
57C13×#124—21no—
58C13×#121—21no—
59C13×#121—21no—
60C4×D4×C13—21no—
61C4×D4×C13—21no—
62C4×D4×C13—21no—
63C4×D4×C13—21no—
64C4×D4×C13D411yescharacteristic
65C4×D4×C13D411yescharacteristic
66C4×D4×C13C2311yescharacteristic
67C4×D4×C13C2311yescharacteristic
68C2×C13×C4⋊C4D411yescharacteristic
69C2×C13×C22⋊C4—21no—
70C2×C42×C13C2311yescharacteristic
71C2×#6105—22no—
72C2×#6105—22no—
73C2×#6105—44no—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13—21no—
76C2×#6099—21no—
77C2×#6099—22no—
78C2×#6099—44no—
79C2×#6099D411yescharacteristic
80C2×#6099D411yescharacteristic
81C22×#1055—21no—
82C22×#1055—22no—
83#88123—21no—
84#88123—21no—
85#88123—21no—
86#88123C2312yes—
87C13×#107—21no—
88C13×#107—21no—
89C13×C4⋊C8C2311yescharacteristic
90C13×C4⋊C8C2311yescharacteristic
91C13×#102—21no—
92C13×#102—21no—
93C13×#102—21no—
94C13×#102—21no—
95C13×C22⋊C8—21no—
96C4×C8×C13—21no—
97#88075—22no—
98#88075—22no—
99#88072—22no—
100#88072—22no—
101C22⋊#1055—22no—
102C22⋊#1055—22no—
103#88050—22no—
104#88050—22no—
105C4⋊#1055—21no—
106C4⋊#1055—21no—
107C4⋊#1055C2312yes—
108C4⋊#1055C2312yes—
109#88043D412yes—
110C4×#1055C2312yes—
111#19169—131nomaximal, Sylow
112C24×C13—21no—
113C13×#41—42no—
114C13×#41—42no—
115C2×Q8×C13—21no—
116C2×D4×C13—22no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—41no—
122C2×D4×C13—41no—
123C2×D4×C13C2×D411yescharacteristic
124C2×D4×C13C2×D411yescharacteristic
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—42no—
131C22×C4×C13—42no—
132C22×C4×C13—41no—
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13#4111yescharacteristic
136C22×Dic13—41no—
137C2×Dic26—22no—
138C2×Dic26—42no—
139C2×Dic26—42no—
140C2×Dic26—41no—
141C13×D8—42no—
142C13×D8—42no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4C2×D411yescharacteristic
149C13×C4⋊C4C2×D411yescharacteristic
150C13×C22⋊C4—21no—
151C13×C22⋊C4—21no—
152C13×C22⋊C4—21no—
153C13×C22⋊C4—21no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C42×C13C2×D411yescharacteristic
157C42×C13C2×D411yescharacteristic
158C42×C13#4111yescharacteristic
159C42×C13C2411yescharacteristic
160#6105—44no—
161#6105—44no—
162C4⋊Dic13—22no—
163C4⋊Dic13—22no—
164C4⋊Dic13—41no—
165C4⋊Dic13—41no—
166#6099—22no—
167#6099—22no—
168#6099—44no—
169#6099—42no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055—44no—
173C2×#1055—42no—
174C2×#1055C2×D412yes—
175C2×#1055C2×D412yes—
176#3141—131no—
177#3100D1311yescharacteristic
178C2×#461—131no—
179D4×M16—131no—
180#1701—132no—
181#1699—132no—
182#1681—132no—
183#1679—132no—
184#1565—131no—
185#1549—131no—
186#1547—131no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—42no—
190C23×C13—42no—
191C23×C13—41no—
192C23×C13—81no—
193C23×C13#12111yescharacteristic
194Q8×C13—41no—
195Q8×C13—41no—
196D4×C13—21no—
197D4×C13—21no—
198D4×C13—21no—
199D4×C13—42no—
200D4×C13—41no—
201D4×C13—41no—
202D4×C13—41no—
203D4×C13—41no—
204D4×C13—81no—
205D4×C13—82no—
206D4×C13AGL(1,ℤ/8)12yes—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—41no—
212C2×C4×C13—42no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—41no—
220C2×C4×C13—82no—
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13#12111yescharacteristic
223C2×C4×C13#12111yescharacteristic
224C2×C4×C13#13512yes—
225C2×C4×C13AGL(1,ℤ/8)12yes—
226C2×C4×C13C22×D411yescharacteristic
227C2×C4×C13C22×D411yescharacteristic
228C2×C4×C13C2×#4111yescharacteristic
229C2×Dic13—42no—
230C2×Dic13—82no—
231Dic26—42no—
232Dic26—42no—
233Dic26—82no—
234C8×C13—41no—
235C8×C13—41no—
236#1055—22no—
237#1055—22no—
238#1055—42no—
239#1055—42no—
240C22×SD16—261no—
241C22×M16—261no—
242#532C2×D1311yescharacteristic
243C2×C4⋊Q8—131no—
244C2×C4×D4C2×D1311yescharacteristic
245#489—262no—
246#487—132no—
247#486—132no—
248#480—21no—
249#474C2×D1311yescharacteristic
250#474C2×D1311yescharacteristic
251#461—132no—
252#461—132no—
253#461—261no—
254#461—261no—
255#459C2×D1311yescharacteristic
256#459C2×D1311yescharacteristic
257#447—21no—
258C4×D8—21no—
259C4×D8—21no—
260#436—132no—
261#435—262no—
262C8×D4—132no—
263#431C2×D1311yescharacteristic
264#423—131no—
265C2×C4⋊C8—131no—
266#417—261no—
267#417—261no—
268C2×#103—261no—
269#407—261no—
270C4×M16—131no—
271#335—132no—
272#334—132no—
273#332—132no—
274#332—132no—
275#332—132no—
276#331—132no—
277C22×C13—21no—
278C22×C13—21no—
279C22×C13—22no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13—41no—
283C22×C13—41no—
284C22×C13—41no—
285C22×C13—84no—
286C22×C13—81no—
287C22×C13—81no—
288C22×C13—81no—
289C22×C13#46312yes—
290C22×C13C2×#12111yescharacteristic
291C4×C13—21no—
292C4×C13—21no—
293C4×C13—21no—
294C4×C13—41no—
295C4×C13—41no—
296C4×C13—81no—
297C4×C13#46312yes—
298C4×C13C2×#13511yescharacteristic
299C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C13#57511yescharacteristic
302Dic13—82no—
303C2×#41—21no—
304C22×Q8—261no—
305C22×D4C22⋊D1311yescharacteristic
306C23×C4—21no—
307C2×SD16—262no—
308C2×SD16—262no—
309C2×SD16—524no—
310C2×D8—21no—
311C2×D8—21no—
312C2×M16—131no—
313C2×M16—131no—
314C2×M16—262no—
315C2×M16—261no—
316C2×M16—524no—
317C22×C8—262no—
318C22×C8—261no—
319C4⋊Q8—132no—
320C4⋊Q8—261no—
321C4⋊Q8—261no—
322C4⋊Q8—261no—
323C4⋊Q8C22×D1311yescharacteristic
324#127C22×D1311yescharacteristic
325#124—21no—
326#121—21no—
327#121—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4C22⋊D1311yescharacteristic
333C4×D4C22⋊D1311yescharacteristic
334C4×D4C22×D1311yescharacteristic
335C4×D4C22×D1311yescharacteristic
336C2×C4⋊C4—261no—
337C2×C4⋊C4—261no—
338C2×C4⋊C4C22⋊D1311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C42C22×D1311yescharacteristic
341#107—21no—
342#107—21no—
343C4⋊C8—132no—
344C4⋊C8—132no—
345C4⋊C8—261no—
346C4⋊C8—261no—
347C4⋊C8C22×D1311yescharacteristic
348C4⋊C8C22×D1311yescharacteristic
349#103—262no—
350#103—262no—
351#103—262no—
352#103—262no—
353#102—21no—
354#102—21no—
355#102—21no—
356#102—21no—
357#102—262no—
358#102—262no—
359C22⋊C8—21no—
360C22⋊C8—262no—
361C22⋊C8—262no—
362#97—132no—
363C4×C8—21no—
364C4×C8—132no—
365C2×C13—22no—
366C2×C13—42no—
367C2×C13—81no—
368C2×C13—161no—
369C2×C13C2×#46311yescharacteristic
370C2×C13#305511yescharacteristic
371C2×C13#306911yescharacteristic
372C24—21no—
373#41—42no—
374#41—42no—
375C2×Q8—21no—
376C2×Q8—262no—
377C2×Q8—522no—
378C2×Q8—522no—
379C2×Q8—521no—
380C2×D4—22no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4C2×C22⋊D1311yescharacteristic
388C2×D4C2×C22⋊D1311yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—41no—
397C22×C4—521no—
398C22×C4D4×D1311yescharacteristic
399C22×C4#612911yescharacteristic
400C22×C4C2×C22⋊D1311yescharacteristic
401SD16—524no—
402SD16—524no—
403D8—42no—
404D8—42no—
405M16—262no—
406M16—262no—
407M16—524no—
408M16—522no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—132no—
412C2×C8—132no—
413C2×C8—262no—
414C2×C8—262no—
415C2×C8—524no—
416C2×C8—522no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—262no—
421C4⋊C4—262no—
422C4⋊C4—521no—
423C4⋊C4—521no—
424C4⋊C4C2×C22⋊D1311yescharacteristic
425C4⋊C4C2×C22⋊D1311yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C42D4×D1311yescharacteristic
433C42#612911yescharacteristic
434C42C2×C22⋊D1311yescharacteristic
435C42C23×D1311yescharacteristic
436C13#1916911yescharacteristic, complemented, Sylow
437C23—21no—
438C23—21no—
439C23—42no—
440C23—42no—
441C23—41no—
442C23—81no—
443C23#8819311yescharacteristic
444Q8—41no—
445Q8—41no—
446Q8—522no—
447Q8—522no—
448Q8—1042no—
449D4—21no—
450D4—21no—
451D4—21no—
452D4—42no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—81no—
458D4—82no—
459D4#8820312yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4—522no—
475C2×C4—1042no—
476C2×C4#8816512yes—
477C2×C4#8816612yes—
478C2×C4#8819311yescharacteristic
479C2×C4#8819311yescharacteristic
480C2×C4#8819311yescharacteristic
481C2×C4C2×D4×D1311yescharacteristic
482C2×C4C2×#612911yescharacteristic
483C2×C4C22×C22⋊D1311yescharacteristic
484C8—41no—
485C8—41no—
486C8—262no—
487C8—262no—
488C8—522no—
489C8—522no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—84no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22#1171881412yes—
503C22C2×#8819311yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—81no—
510C4—1042no—
511C4#1171881412yes—
512C4C2×#8816511yescharacteristic
513C4C2×#8816611yescharacteristic
514C4C2×#8820311yescharacteristic
515C4#1171952711yescharacteristic
516C2—22no—
517C2—42no—
518C2—81no—
519C2—161no—
520C2C2×#1171881411yescharacteristic
521C2#1312445711yescharacteristic
522C2#1312457511yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3100C2
socleC22×C13C2×#121
hypercenter#3100D13
hypocenterC13#19169
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #13125229C2semidirect
2. C2×#11718680C2semidirect
3. D4×#6099C2semidirect
4. #13114395C2semidirect
5. #13114381C2semidirect
6. #13114271C2semidirect
7. #13114257C2semidirect
8. #13113589C2semidirect
9. #13113520C2semidirect
10. #13113513C2semidirect
29. #11718742C22semidirect
30. #11718731C22semidirect
43. #11718139C22semidirect
44. #11718136C22semidirect
45. #11718074C22semidirect
46. #11718074C22semidirect
47. #11718072C22semidirect
48. #11718071C22semidirect
436. C13#19169semidirect

Maximal subgroups

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

subgroupindex
#131252292
C2×#117186802
D4×#60992
#131143952
#131143812
#131142712
#131142572
#131135892
#131135202
#131135132
C13×#31002
#1916913