Finite Group Databasebeta

← #15845700

Subgroups — #15845700

Order 3328.

760 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
1#13125296C211yesmaximal, characteristic, complemented
2C2×#11718668C211yesmaximal, characteristic, complemented
3D4×#6099C211yesmaximal, characteristic, complemented
4#13114323C212yesmaximal, complemented
5#13114299C212yesmaximal, complemented
6#13114199C212yesmaximal, complemented
7#13114175C212yesmaximal, complemented
8#13113589C211yesmaximal, characteristic, complemented
9#13113513C211yesmaximal, characteristic, complemented
10#13113507C211yesmaximal, characteristic, complemented
11C13×#3100C211yesmaximal, characteristic
12C13×#532C2211yescharacteristic
13C2×C4×D4×C13C2211yescharacteristic
14C2×#88205—21no—
15C2×#88205—21no—
16C22×#6099—21no—
17C2×#88123C2211yescharacteristic
18C13×#480—21no—
19C13×#474C2211yescharacteristic
20C13×#474C2211yescharacteristic
21C13×#459C2211yescharacteristic
22C13×#459C2211yescharacteristic
23C13×#447—21no—
24C4×C13×D8—21no—
25C4×C13×D8—21no—
26C13×#431C2211yescharacteristic
27C2×#88072—21no—
28#11718868—21no—
29#11718753C2212yescomplemented
30#11718737C2212yescomplemented
31#11718721—22no—
32#11718673C2212yes—
33#11718672—22no—
34D4×#1055C2212yes—
35#11718668—21no—
36#11718668—21no—
37#11718668C2212yes—
38#11718668C2212yes—
39C2×#88047—21no—
40#11718585C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718139C2212yescomplemented
44#11718136C2212yescomplemented
45#11718078C2212yescomplemented
46#11718078C2212yescomplemented
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
71#88205—44no—
72#88205—44no—
73C2×#6107—22no—
74C2×#6107—22no—
75C2×#6105—22no—
76C2×#6105—22no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×#6099—21no—
80C2×#6099—22no—
81C2×#6099—44no—
82C2×#6099D411yescharacteristic
83C2×#6099D411yescharacteristic
84C22×#1055—21no—
85C22×#1055—22no—
86#88123—21no—
87#88123—21no—
88#88123—21no—
89#88123C2312yes—
90C13×#107—21no—
91C13×#107—21no—
92C13×C4⋊C8C2311yescharacteristic
93C13×C4⋊C8C2311yescharacteristic
94C13×#102—21no—
95C13×#102—21no—
96C13×#102—21no—
97C13×#102—21no—
98C13×C22⋊C8—21no—
99C4×C8×C13—21no—
100#88072—22no—
101#88072—22no—
102C22⋊#1055—22no—
103C22⋊#1055—22no—
104#88047—22no—
105#88047—22no—
106C4⋊#1055—21no—
107C4⋊#1055—21no—
108C4⋊#1055C2312yes—
109C4⋊#1055C2312yes—
110#88043D412yes—
111C4×#1055C2312yes—
112#19163—131nomaximal, Sylow
113C24×C13—21no—
114C13×#41—42no—
115C13×#41—42no—
116C2×Q8×C13—21no—
117C2×D4×C13—22no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—21no—
122C2×D4×C13—41no—
123C2×D4×C13—41no—
124C2×D4×C13C2×D411yescharacteristic
125C2×D4×C13C2×D411yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13—41no—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13#4111yescharacteristic
137C22×Dic13—41no—
138C2×Dic26—22no—
139C2×Dic26—42no—
140C2×Dic26—42no—
141C2×Dic26—41no—
142C13×D8—42no—
143C13×D8—42no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—21no—
148C13×C4⋊C4—21no—
149C13×C4⋊C4C2×D411yescharacteristic
150C13×C4⋊C4C2×D411yescharacteristic
151C13×C22⋊C4—21no—
152C13×C22⋊C4—21no—
153C13×C22⋊C4—21no—
154C13×C22⋊C4—21no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4—41no—
157C42×C13C2×D411yescharacteristic
158C42×C13C2×D411yescharacteristic
159C42×C13#4111yescharacteristic
160C42×C13C2411yescharacteristic
161#6107—44no—
162#6107—44no—
163#6105—44no—
164#6105—44no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13—41no—
168C4⋊Dic13—41no—
169#6099—22no—
170#6099—42no—
171#6099—44no—
172#6099D814yescomplemented
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055—42no—
176C2×#1055—44no—
177C2×#1055C2×D412yes—
178C2×#1055C2×D412yes—
179#3152—131no—
180#3100D1311yescharacteristic
181C2×#474—131no—
182D4×M16—131no—
183#1689—132no—
184#1685—132no—
185#1669—132no—
186#1665—132no—
187#1565—131no—
188#1547—131no—
189#1546—131no—
190C23×C13—21no—
191C23×C13—21no—
192C23×C13—42no—
193C23×C13—42no—
194C23×C13—41no—
195C23×C13—81no—
196C23×C13#12111yescharacteristic
197Q8×C13—41no—
198Q8×C13—41no—
199D4×C13—21no—
200D4×C13—21no—
201D4×C13—21no—
202D4×C13—42no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—41no—
207D4×C13—81no—
208D4×C13—82no—
209D4×C13#13712yescomplemented
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—41no—
215C2×C4×C13—42no—
216C2×C4×C13—41no—
217C2×C4×C13—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—41no—
223C2×C4×C13—82no—
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13C2×D812yes—
228C2×C4×C13AGL(1,ℤ/8)12yes—
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C13C22×D411yescharacteristic
231C2×C4×C13C2×#4111yescharacteristic
232C2×Dic13—42no—
233C2×Dic13—82no—
234Dic26—42no—
235Dic26—42no—
236Dic26—82no—
237C8×C13—41no—
238C8×C13—41no—
239#1055—22no—
240#1055—42no—
241#1055—42no—
242#1055C2×D814yes—
243C2×#137—261no—
244C2×#137—261no—
245C22×M16—261no—
246#532C2×D1311yescharacteristic
247C2×C4⋊Q8—131no—
248C2×C4×D4C2×D1311yescharacteristic
249#497—262no—
250#494—132no—
251#492—132no—
252#480—21no—
253#474—132no—
254#474—132no—
255#474—261no—
256#474—261no—
257#474C2×D1311yescharacteristic
258#474C2×D1311yescharacteristic
259#459C2×D1311yescharacteristic
260#459C2×D1311yescharacteristic
261#447—21no—
262C4×D8—21no—
263C4×D8—21no—
264#436—132no—
265#435—262no—
266C8×D4—132no—
267#431C2×D1311yescharacteristic
268C2×#107—261no—
269#423—131no—
270C2×C4⋊C8—131no—
271C2×#102—261no—
272#407—261no—
273C4×M16—131no—
274#335—132no—
275#334—132no—
276#332—132no—
277#332—132no—
278#332—132no—
279#331—132no—
280C22×C13—21no—
281C22×C13—21no—
282C22×C13—22no—
283C22×C13—41no—
284C22×C13—41no—
285C22×C13—41no—
286C22×C13—41no—
287C22×C13—41no—
288C22×C13—84no—
289C22×C13—81no—
290C22×C13—81no—
291C22×C13—81no—
292C22×C13#45912yes—
293C22×C13C2×#12111yescharacteristic
294C4×C13—21no—
295C4×C13—21no—
296C4×C13—21no—
297C4×C13—41no—
298C4×C13—41no—
299C4×C13—81no—
300C4×C13#45912yes—
301C4×C13C22×D811yescharacteristic
302C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C13C2×#13711yescharacteristic
304C4×C13#57511yescharacteristic
305Dic13—82no—
306C2×#41—21no—
307C22×Q8—261no—
308C22×D4C22⋊D1311yescharacteristic
309C23×C4—21no—
310#137—524no—
311#137—524no—
312C2×Q16—262no—
313C2×Q16—262no—
314C2×SD16—262no—
315C2×SD16—262no—
316C2×D8—21no—
317C2×D8—21no—
318C2×M16—131no—
319C2×M16—131no—
320C2×M16—262no—
321C2×M16—261no—
322C2×M16—524no—
323C22×C8—262no—
324C22×C8—261no—
325C4⋊Q8—132no—
326C4⋊Q8—261no—
327C4⋊Q8—261no—
328C4⋊Q8—261no—
329C4⋊Q8C22×D1311yescharacteristic
330#127C22×D1311yescharacteristic
331#124—21no—
332#121—21no—
333#121—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4C22⋊D1311yescharacteristic
339C4×D4C22⋊D1311yescharacteristic
340C4×D4C22×D1311yescharacteristic
341C4×D4C22×D1311yescharacteristic
342C2×C4⋊C4—261no—
343C2×C4⋊C4—261no—
344C2×C4⋊C4C22⋊D1311yescharacteristic
345C2×C22⋊C4—21no—
346C2×C42C22×D1311yescharacteristic
347#107—21no—
348#107—21no—
349#107—262no—
350#107—262no—
351C4⋊C8—132no—
352C4⋊C8—132no—
353C4⋊C8—261no—
354C4⋊C8—261no—
355C4⋊C8C22×D1311yescharacteristic
356C4⋊C8C22×D1311yescharacteristic
357#102—21no—
358#102—21no—
359#102—21no—
360#102—21no—
361#102—262no—
362#102—262no—
363C22⋊C8—21no—
364C22⋊C8—262no—
365C22⋊C8—262no—
366#97—132no—
367C4×C8—21no—
368C4×C8—132no—
369C2×C13—22no—
370C2×C13—42no—
371C2×C13—81no—
372C2×C13—161no—
373C2×C13C2×#45911yescharacteristic
374C2×C13#305611yescharacteristic
375C2×C13#306911yescharacteristic
376C24—21no—
377#41—42no—
378#41—42no—
379C2×Q8—21no—
380C2×Q8—262no—
381C2×Q8—521no—
382C2×Q8—522no—
383C2×Q8—522no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4C2×C22⋊D1311yescharacteristic
392C2×D4C2×C22⋊D1311yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—42no—
399C22×C4—42no—
400C22×C4—41no—
401C22×C4—521no—
402C22×C4D4×D1311yescharacteristic
403C22×C4#612911yescharacteristic
404C22×C4C2×C22⋊D1311yescharacteristic
405Q16—524no—
406Q16—524no—
407SD16—524no—
408SD16—524no—
409D8—42no—
410D8—42no—
411M16—134no—
412M16—262no—
413M16—524no—
414M16—522no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—132no—
418C2×C8—132no—
419C2×C8—262no—
420C2×C8—262no—
421C2×C8—524no—
422C2×C8—522no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—262no—
427C4⋊C4—262no—
428C4⋊C4—521no—
429C4⋊C4—521no—
430C4⋊C4C2×C22⋊D1311yescharacteristic
431C4⋊C4C2×C22⋊D1311yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C42D4×D1311yescharacteristic
439C42#612911yescharacteristic
440C42C2×C22⋊D1311yescharacteristic
441C42C23×D1311yescharacteristic
442C13#1916311yescharacteristic, complemented, Sylow
443C23—21no—
444C23—21no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—81no—
449C23#8819311yescharacteristic
450Q8—41no—
451Q8—41no—
452Q8—522no—
453Q8—522no—
454Q8—1042no—
455D4—21no—
456D4—21no—
457D4—21no—
458D4—42no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—81no—
464D4—82no—
465D4#8820512yescomplemented
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—82no—
480C2×C4—522no—
481C2×C4—1042no—
482C2×C4D8×D1312yes—
483C2×C4#8816512yes—
484C2×C4#8819311yescharacteristic
485C2×C4#8819311yescharacteristic
486C2×C4#8819311yescharacteristic
487C2×C4C2×D4×D1311yescharacteristic
488C2×C4C2×#612911yescharacteristic
489C2×C4C22×C22⋊D1311yescharacteristic
490C8—41no—
491C8—41no—
492C8—134no—
493C8—262no—
494C8—522no—
495C8—522no—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—84no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22#1171881112yes—
509C22C2×#8819311yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—81no—
516C4—1042no—
517C4#1171881112yes—
518C4C2×D8×D1311yescharacteristic
519C4C2×#8816511yescharacteristic
520C4#1171952711yescharacteristic
521C4C2×#8820511yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—161no—
526C2C2×#1171881111yescharacteristic
527C2#1312446811yescharacteristic
528C2#1312457511yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3100C2
socleC22×C13C2×#121
hypercenter#3100D13
hypocenterC13#19163
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. #13125296C2semidirect
2. C2×#11718668C2semidirect
3. D4×#6099C2semidirect
4. #13114323C2semidirect
5. #13114299C2semidirect
6. #13114199C2semidirect
7. #13114175C2semidirect
8. #13113589C2semidirect
9. #13113513C2semidirect
10. #13113507C2semidirect
29. #11718753C22semidirect
30. #11718737C22semidirect
43. #11718139C22semidirect
44. #11718136C22semidirect
45. #11718078C22semidirect
46. #11718078C22semidirect
47. #11718072C22semidirect
48. #11718071C22semidirect
172. #6099D8semidirect
209. D4×C13#137semidirect
442. C13#19163semidirect
465. D4#88205semidirect

Maximal subgroups

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

subgroupindex
#131252962
C2×#117186682
D4×#60992
#131143232
#131142992
#131141992
#131141752
#131135892
#131135132
#131135072
C13×#31002
#1916313