Finite Group Databasebeta

← #15845749

Subgroups — #15845749

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125229C211yesmaximal, characteristic, complemented
2C2×#11718669C211yesmaximal, characteristic, complemented
3D4×#6099C211yesmaximal, characteristic, complemented
4#13114409C212yesmaximal, complemented
5#13114367C212yesmaximal, complemented
6#13114285C212yesmaximal, complemented
7#13114243C212yesmaximal, complemented
8#13113589C211yesmaximal, characteristic, complemented
9#13113516C211yesmaximal, characteristic, complemented
10#13113513C211yesmaximal, characteristic, complemented
11C13×#3100C211yesmaximal, characteristic
12C13×#532C2211yescharacteristic
13C2×C4×D4×C13C2211yescharacteristic
14C22×#6099—21no—
15C2×#88123C2211yescharacteristic
16C13×#480—21no—
17C13×#474C2211yescharacteristic
18C13×#474C2211yescharacteristic
19C13×#459C2211yescharacteristic
20C13×#459C2211yescharacteristic
21C13×#447—21no—
22C4×C13×D8—21no—
23C4×C13×D8—21no—
24C13×#431C2211yescharacteristic
25#11718893—21no—
26#11718893—21no—
27C2×#88072—21no—
28#11718868—21no—
29#11718742C2212yescomplemented
30#11718731C2212yescomplemented
31#11718716—22no—
32#11718673C2212yes—
33#11718672—22no—
34D4×#1055C2212yes—
35#11718669—21no—
36#11718669—21no—
37#11718669C2212yes—
38#11718669C2212yes—
39C2×#88048—21no—
40#11718585C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718139C2212yescomplemented
44#11718136C2212yescomplemented
45#11718073C2212yescomplemented
46#11718073C2212yescomplemented
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×C4⋊Dic13—21no—
72C2×C4⋊Dic13—21no—
73C2×#6099—21no—
74C2×#6099—22no—
75C2×#6099—44no—
76C2×#6099D411yescharacteristic
77C2×#6099D411yescharacteristic
78C22×#1055—21no—
79C22×#1055—22no—
80#88123—21no—
81#88123—21no—
82#88123—21no—
83#88123C2312yes—
84C13×#107—21no—
85C13×#107—21no—
86C13×C4⋊C8C2311yescharacteristic
87C13×C4⋊C8C2311yescharacteristic
88C13×#102—21no—
89C13×#102—21no—
90C13×#102—21no—
91C13×#102—21no—
92C13×C22⋊C8—21no—
93C4×C8×C13—21no—
94#88075—22no—
95#88075—22no—
96#88072—22no—
97#88072—22no—
98#88072—22no—
99#88072—22no—
100C22⋊#1055—22no—
101C22⋊#1055—22no—
102#88048—22no—
103#88048—22no—
104C4⋊#1055—21no—
105C4⋊#1055—21no—
106C4⋊#1055C2312yes—
107C4⋊#1055C2312yes—
108#88043D412yes—
109C4×#1055C2312yes—
110#19168—131nomaximal, Sylow
111C24×C13—21no—
112C13×#41—42no—
113C13×#41—42no—
114C2×Q8×C13—21no—
115C2×D4×C13—22no—
116C2×D4×C13—21no—
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—41no—
121C2×D4×C13—41no—
122C2×D4×C13C2×D411yescharacteristic
123C2×D4×C13C2×D411yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—42no—
130C22×C4×C13—42no—
131C22×C4×C13—41no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13#4111yescharacteristic
135C22×Dic13—41no—
136C2×Dic26—22no—
137C2×Dic26—41no—
138C2×Dic26—82no—
139C13×D8—42no—
140C13×D8—42no—
141C2×C8×C13—21no—
142C2×C8×C13—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4C2×D411yescharacteristic
147C13×C4⋊C4C2×D411yescharacteristic
148C13×C22⋊C4—21no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—21no—
151C13×C22⋊C4—21no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C42×C13C2×D411yescharacteristic
155C42×C13C2×D411yescharacteristic
156C42×C13#4111yescharacteristic
157C42×C13C2411yescharacteristic
158C4⋊Dic13—22no—
159C4⋊Dic13—22no—
160C4⋊Dic13—41no—
161C4⋊Dic13—41no—
162#6099—22no—
163#6099—22no—
164#6099—44no—
165#6099—42no—
166C2×#1055—22no—
167C2×#1055—22no—
168C2×#1055—44no—
169C2×#1055—42no—
170C2×#1055C2×D412yes—
171C2×#1055C2×D412yes—
172#3141—131no—
173#3100D1311yescharacteristic
174C2×#476—131no—
175D4×M16—131no—
176#1703—132no—
177#1697—132no—
178#1683—132no—
179#1677—132no—
180#1565—131no—
181#1548—131no—
182#1547—131no—
183C23×C13—21no—
184C23×C13—21no—
185C23×C13—42no—
186C23×C13—42no—
187C23×C13—41no—
188C23×C13—81no—
189C23×C13#12111yescharacteristic
190Q8×C13—41no—
191Q8×C13—41no—
192D4×C13—21no—
193D4×C13—21no—
194D4×C13—21no—
195D4×C13—42no—
196D4×C13—41no—
197D4×C13—41no—
198D4×C13—41no—
199D4×C13—41no—
200D4×C13—81no—
201D4×C13—82no—
202D4×C13#13712yes—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—41no—
208C2×C4×C13—42no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—42no—
214C2×C4×C13—42no—
215C2×C4×C13—41no—
216C2×C4×C13—82no—
217C2×C4×C13#12111yescharacteristic
218C2×C4×C13#12111yescharacteristic
219C2×C4×C13#12111yescharacteristic
220C2×C4×C13#13512yes—
221C2×C4×C13AGL(1,ℤ/8)12yes—
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C22×D411yescharacteristic
224C2×C4×C13C2×#4111yescharacteristic
225C2×Dic13—42no—
226C2×Dic13—82no—
227Dic26—82no—
228Dic26—82no—
229C8×C13—41no—
230C8×C13—41no—
231#1055—22no—
232#1055—22no—
233#1055—42no—
234#1055—42no—
235C22×M16—261no—
236#532C2×D1311yescharacteristic
237C2×C4⋊Q8—131no—
238C2×C4×D4C2×D1311yescharacteristic
239#489—262no—
240#487—132no—
241#486—132no—
242#480—21no—
243#476—132no—
244#476—132no—
245#476—261no—
246#476—261no—
247#474C2×D1311yescharacteristic
248#474C2×D1311yescharacteristic
249#459C2×D1311yescharacteristic
250#459C2×D1311yescharacteristic
251#447—21no—
252C4×D8—21no—
253C4×D8—21no—
254#436—132no—
255#435—262no—
256C8×D4—132no—
257#431C2×D1311yescharacteristic
258C2×#106—261no—
259#423—131no—
260C2×C4⋊C8—131no—
261#417—261no—
262#417—261no—
263C2×#102—261no—
264#407—261no—
265C4×M16—131no—
266#335—132no—
267#334—132no—
268#333—132no—
269#333—132no—
270#332—132no—
271#331—132no—
272C22×C13—21no—
273C22×C13—21no—
274C22×C13—22no—
275C22×C13—41no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—84no—
281C22×C13—81no—
282C22×C13—81no—
283C22×C13—81no—
284C22×C13#46312yes—
285C22×C13C2×#12111yescharacteristic
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—41no—
290C4×C13—41no—
291C4×C13—81no—
292C4×C13#46312yes—
293C4×C13C2×#13511yescharacteristic
294C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C13C2×#13711yescharacteristic
296C4×C13#57511yescharacteristic
297Dic13—82no—
298C2×#41—21no—
299C22×Q8—261no—
300C22×D4C22⋊D1311yescharacteristic
301C23×C4—21no—
302C2×D8—21no—
303C2×D8—21no—
304C2×M16—131no—
305C2×M16—131no—
306C2×M16—262no—
307C2×M16—261no—
308C2×M16—524no—
309C22×C8—262no—
310C22×C8—261no—
311C4⋊Q8—132no—
312C4⋊Q8—261no—
313C4⋊Q8—261no—
314C4⋊Q8—261no—
315C4⋊Q8C22×D1311yescharacteristic
316#127C22×D1311yescharacteristic
317#124—21no—
318#121—21no—
319#121—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4C22⋊D1311yescharacteristic
325C4×D4C22⋊D1311yescharacteristic
326C4×D4C22×D1311yescharacteristic
327C4×D4C22×D1311yescharacteristic
328C2×C4⋊C4—261no—
329C2×C4⋊C4—261no—
330C2×C4⋊C4C22⋊D1311yescharacteristic
331C2×C22⋊C4—21no—
332C2×C42C22×D1311yescharacteristic
333#107—21no—
334#107—21no—
335#106—262no—
336#106—262no—
337C4⋊C8—132no—
338C4⋊C8—132no—
339C4⋊C8—261no—
340C4⋊C8—261no—
341C4⋊C8C22×D1311yescharacteristic
342C4⋊C8C22×D1311yescharacteristic
343#103—262no—
344#103—262no—
345#102—21no—
346#102—21no—
347#102—21no—
348#102—21no—
349#102—262no—
350#102—262no—
351#102—262no—
352#102—262no—
353C22⋊C8—21no—
354C22⋊C8—262no—
355C22⋊C8—262no—
356#97—132no—
357C4×C8—21no—
358C4×C8—132no—
359C2×C13—22no—
360C2×C13—42no—
361C2×C13—81no—
362C2×C13—161no—
363C2×C13C2×#46311yescharacteristic
364C2×C13#305611yescharacteristic
365C2×C13#306811yescharacteristic
366C24—21no—
367#41—42no—
368#41—42no—
369C2×Q8—21no—
370C2×Q8—262no—
371C2×Q8—521no—
372C2×Q8—1042no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4C2×C22⋊D1311yescharacteristic
381C2×D4C2×C22⋊D1311yescharacteristic
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—521no—
391C22×C4D4×D1311yescharacteristic
392C22×C4#612911yescharacteristic
393C22×C4C2×C22⋊D1311yescharacteristic
394D8—42no—
395D8—42no—
396M16—262no—
397M16—262no—
398M16—524no—
399M16—522no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—132no—
403C2×C8—132no—
404C2×C8—262no—
405C2×C8—262no—
406C2×C8—524no—
407C2×C8—522no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—262no—
412C4⋊C4—262no—
413C4⋊C4—521no—
414C4⋊C4—521no—
415C4⋊C4C2×C22⋊D1311yescharacteristic
416C4⋊C4C2×C22⋊D1311yescharacteristic
417C22⋊C4—21no—
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C42D4×D1311yescharacteristic
424C42#612911yescharacteristic
425C42C2×C22⋊D1311yescharacteristic
426C42C23×D1311yescharacteristic
427C13#1916811yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—41no—
433C23—81no—
434C23#8819311yescharacteristic
435Q8—41no—
436Q8—41no—
437Q8—1042no—
438Q8—1042no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—41no—
447D4—81no—
448D4—82no—
449D4#8820512yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—82no—
464C2×C4—522no—
465C2×C4—1042no—
466C2×C4#8816512yes—
467C2×C4#8816612yes—
468C2×C4#8819311yescharacteristic
469C2×C4#8819311yescharacteristic
470C2×C4#8819311yescharacteristic
471C2×C4C2×D4×D1311yescharacteristic
472C2×C4C2×#612911yescharacteristic
473C2×C4C22×C22⋊D1311yescharacteristic
474C8—41no—
475C8—41no—
476C8—262no—
477C8—262no—
478C8—522no—
479C8—522no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—81no—
490C22—81no—
491C22—81no—
492C22#1171881412yes—
493C22C2×#8819311yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—81no—
500C4—1042no—
501C4#1171881412yes—
502C4C2×#8816511yescharacteristic
503C4C2×#8816611yescharacteristic
504C4#1171952711yescharacteristic
505C4C2×#8820511yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—161no—
510C2C2×#1171881411yescharacteristic
511C2#1312446811yescharacteristic
512C2#1312456611yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3100C2
socleC22×C13C2×#121
hypercenter#3100D13
hypocenterC13#19168
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×#11718669C2semidirect
3. D4×#6099C2semidirect
4. #13114409C2semidirect
5. #13114367C2semidirect
6. #13114285C2semidirect
7. #13114243C2semidirect
8. #13113589C2semidirect
9. #13113516C2semidirect
10. #13113513C2semidirect
29. #11718742C22semidirect
30. #11718731C22semidirect
43. #11718139C22semidirect
44. #11718136C22semidirect
45. #11718073C22semidirect
46. #11718073C22semidirect
47. #11718072C22semidirect
48. #11718071C22semidirect
427. C13#19168semidirect

Maximal subgroups

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

subgroupindex
#131252292
C2×#117186692
D4×#60992
#131144092
#131143672
#131142852
#131142432
#131135892
#131135162
#131135132
C13×#31002
#1916813