Finite Group Databasebeta

← #15874135

Subgroups — #15874135

Order 3328.

1080 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718888C211yesmaximal, characteristic
2C4×#88184C211yesmaximal, characteristic
3#13115720C212yesmaximal, complemented
4#13115529C212yesmaximal, complemented
5#13115474C212yesmaximal, complemented
6#13115173C212yesmaximal, complemented
7#13115153C211yesmaximal, characteristic
8#13115024C211yesmaximal, characteristic, complemented
9#13114771C211yesmaximal, characteristic, complemented
10#13114598C211yesmaximal, characteristic, complemented
11C2×C13×#391C211yesmaximal, characteristic, complemented
12C23×Q8×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C42×C13C2211yescharacteristic
15C22×#6106C2212yes—
16C2×#88184C2211yescharacteristic
17C2×C4×C22⋊D13—21no—
18C2×C4×D52C2211yescharacteristic
19C13×#391—21no—
20C13×#391—21no—
21C13×#391C2212yes—
22C13×#391C2212yes—
23C2×C13×#95—21no—
24C2×C13×#95—21no—
25#11718888C418yescomplemented
26C2×#88075C2212yes—
27C2×#88075C2212yes—
28C2×#88075C2212yes—
29#11718874—21no—
30#11718873C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88049C2212yes—
34C2×#88047C2212yes—
35#11718601—21no—
36#11718600C2211yescharacteristic
37C4×#6103—21no—
38C4×C4⋊Dic13C2211yescharacteristic
39#11718589C2211yescharacteristic
40C2×#88043C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718116C2212yes—
44C22×Q8×C13—21no—
45C22×Q8×C13—22no—
46C22×Q8×C13—42no—
47C22×Q8×C13—42no—
48C22×Q8×C13C2×C414yescomplemented
49C22×Q8×C13C2312yes—
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13D411yescharacteristic
53C23×C4×C13D411yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C22×C22⋊D13—21no—
56C22×D52C2311yescharacteristic
57C22×C4×D13—21no—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—42no—
60C2×C13×C4⋊C4C2312yes—
61C2×C42×C13—42no—
62C2×C42×C13D411yescharacteristic
63C2×C42×C13D411yescharacteristic
64C2×C42×C13C2311yescharacteristic
65C2×C42×C13C2311yescharacteristic
66C2×C22⋊Dic13—21no—
67C2×#6106—42no—
68C2×#6106—42no—
69C2×#6106C2×C418yescomplemented
70#88184—22no—
71#88184C2×C414yes—
72C4×C22⋊D13—44no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×#6103—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×#6101—21no—
81C2×C4×Dic13—21no—
82C22×#1055C2312yes—
83C22×#1055C2312yes—
84C4×D52—42no—
85C13×#95—22no—
86C13×#95—22no—
87C13×#95—22no—
88C13×#95—22no—
89#88075—42no—
90#88075—42no—
91#88075C2×C418yescomplemented
92#88071—21no—
93#88071—21no—
94#88071—21no—
95C22⋊#1055—22no—
96C22⋊#1055C2×C414yescomplemented
97#88049—42no—
98#88047—42no—
99#88043—42no—
100#22047—131nomaximal, Sylow
101C24×C13C2×D411yescharacteristic
102C23×D13—21no—
103C2×Q8×C13—24no—
104C2×Q8×C13—22no—
105C2×Q8×C13—22no—
106C2×Q8×C13—22no—
107C2×Q8×C13—22no—
108C2×Q8×C13—22no—
109C2×Q8×C13—48no—
110C2×Q8×C13—42no—
111C2×Q8×C13—42no—
112C2×Q8×C13—48no—
113C2×Q8×C13C22×C414yes—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—24no—
117C22×C4×C13—22no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—22no—
121C22×C4×C13—22no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—42no—
126C22×C4×C13—42no—
127C22×C4×C13—42no—
128C22×C4×C13—42no—
129C22×C4×C13—42no—
130C22×C4×C13C22×C412yes—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13#4112yes—
137C22×C4×C13C2411yescharacteristic
138C2×C22⋊D13—24no—
139C2×C22⋊D13—42no—
140C2×C22⋊D13—42no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C2×D52—22no—
145C2×D52—22no—
146C2×D52—21no—
147C2×D52C22×C412yes—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—42no—
154C42×C13—22no—
155C42×C13—22no—
156C42×C13—41no—
157C42×C13—41no—
158C22⋊Dic13—42no—
159#6106—48no—
160#6103—24no—
161#6103—42no—
162#6103—42no—
163#6103—42no—
164C4⋊Dic13—21no—
165C4⋊Dic13—22no—
166C4⋊Dic13—22no—
167C4⋊Dic13C22×C412yes—
168#6101—42no—
169C4×Dic13—42no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055—22no—
173C2×#1055—22no—
174C2×#1055—22no—
175C2×#1055C22×C414yes—
176C2×#448—131no—
177C4×#121—131no—
178C2×#391D1311yescharacteristic, complemented
179#1973—132no—
180#1935—132no—
181#1928—132no—
182#1877—132no—
183#1874—131no—
184#1852—131no—
185#1787—131no—
186#1749—131no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—21no—
190C23×C13—21no—
191C23×C13C4×D412yes—
192C23×C13AGL(1,ℤ/8)12yes—
193C23×C13#13712yes—
194C23×C13C22×D411yescharacteristic
195C22×D13—22no—
196C22×D13—41no—
197C22×D13—41no—
198C22×D13—41no—
199C22×D13—41no—
200C22×D13—41no—
201C22×D13—41no—
202Q8×C13—24no—
203Q8×C13—24no—
204Q8×C13—48no—
205Q8×C13—42no—
206Q8×C13—42no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—24no—
212C2×C4×C13—24no—
213C2×C4×C13—24no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—44no—
224C2×C4×C13—44no—
225C2×C4×C13—48no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
229C2×C4×C13—42no—
230C2×C4×C13—42no—
231C2×C4×C13—84no—
232C2×C4×C13C4×D412yes—
233C2×C4×C13#13712yes—
234C2×C4×C13C23×C411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×C4×C13H(5,𝔽2)12yes—
237C2×C4×C13H(5,𝔽2)12yes—
238C22⋊D13—48no—
239C2×Dic13—22no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243C2×Dic13—41no—
244C2×Dic13—41no—
245C2×Dic13—41no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248D52—24no—
249D52—42no—
250C4×D13—84no—
251#1055—24no—
252#1055—42no—
253C23×Q8C2×D1311yescharacteristic
254C22×SD16—132no—
255C2×#121—131no—
256C2×C4×D4—131no—
257C2×C4×D4—261no—
258C22×C4⋊C4C2×D1311yescharacteristic
259C22×C42C2×D1311yescharacteristic
260#448—138no—
261C2×#107—132no—
262C2×#103—132no—
263C2×#103—132no—
264C2×#103—132no—
265C2×#102—132no—
266C2×C22⋊C8—131no—
267C2×C22⋊C8—131no—
268C2×#97—132no—
269#391—21no—
270#391—21no—
271#391C2×D1312yes—
272#391C2×D1312yes—
273#390—131no—
274#389—131no—
275#388—261no—
276#386—261no—
277#380—131no—
278C4×C4⋊C4—131no—
279C4×C22⋊C4—261no—
280C2×#95—21no—
281C2×#95—21no—
282#340—132no—
283#340—132no—
284#336—132no—
285C22×C13—22no—
286C22×C13—22no—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—22no—
290C22×C13—22no—
291C22×C13#44014yes—
292C22×C13C2×C4×D411yescharacteristic
293C22×C13#53411yescharacteristic
294C22×C13#53511yescharacteristic
295C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C13C2×#13711yescharacteristic
297C22×C13C2×#13711yescharacteristic
298C22×C13#57511yescharacteristic
299C2×D13—42no—
300C2×D13—42no—
301C2×D13—42no—
302C2×D13—81no—
303C2×D13—81no—
304C2×D13—81no—
305C2×D13—81no—
306C4×C13—22no—
307C4×C13—22no—
308C4×C13—44no—
309C4×C13—41no—
310C4×C13—41no—
311C4×C13—41no—
312C4×C13—82no—
313C4×C13#51812yes—
314C4×C13#53812yes—
315Dic13—42no—
316Dic13—81no—
317Dic13—81no—
318C22×Q8—22no—
319C22×Q8—21no—
320C22×Q8—42no—
321C22×Q8—42no—
322C22×Q8C4×D1314yescomplemented
323C22×Q8C22×D1312yes—
324C22×D4—131no—
325C22×D4—261no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4—261no—
329C23×C4C22⋊D1311yescharacteristic
330C23×C4C22⋊D1311yescharacteristic
331C23×C4C22×D1311yescharacteristic
332C2×SD16—138no—
333C2×SD16—522no—
334C2×SD16—522no—
335C22×C8—132no—
336C22×C8—132no—
337#121—134no—
338#121—262no—
339C4×D4—522no—
340C4×D4—524no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—131no—
344C2×C4⋊C4—131no—
345C2×C4⋊C4—131no—
346C2×C4⋊C4—261no—
347C2×C4⋊C4C22×D1312yes—
348C2×C22⋊C4—261no—
349C2×C22⋊C4—261no—
350C2×C22⋊C4—261no—
351C2×C22⋊C4—261no—
352C2×C22⋊C4—261no—
353C2×C42—42no—
354C2×C42—261no—
355C2×C42C22⋊D1311yescharacteristic
356C2×C42C22⋊D1311yescharacteristic
357C2×C42C22×D1311yescharacteristic
358C2×C42C22×D1311yescharacteristic
359#107—522no—
360#103—138no—
361#103—522no—
362#103—522no—
363#102—522no—
364C22⋊C8—134no—
365C22⋊C8—262no—
366#97—522no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—261no—
372#95—261no—
373#95—261no—
374C2×C13—24no—
375C2×C13#232111yescharacteristic
376C2×C13C2×#44011yescharacteristic
377C2×C13C4×#13711yescharacteristic
378C2×C13#319311yescharacteristic
379C2×C13#319611yescharacteristic
380C2×C13#321311yescharacteristic
381C2×C13#321811yescharacteristic
382D13—82no—
383C24—261no—
384C24C2×C22⋊D1311yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—48no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—48no—
395C2×Q8C2×C4×D1314yes—
396C2×D4—132no—
397C2×D4—264no—
398C2×D4—261no—
399C2×D4—262no—
400C2×D4—262no—
401C2×D4—522no—
402C2×D4—522no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—261no—
420C22×C4—261no—
421C22×C4—261no—
422C22×C4—522no—
423C22×C4—522no—
424C22×C4—522no—
425C22×C4C2×C4×D1312yes—
426C22×C4#612712yes—
427C22×C4C2×C22⋊D1311yescharacteristic
428C22×C4C2×C22⋊D1311yescharacteristic
429C22×C4C2×C22⋊D1311yescharacteristic
430C22×C4C2×C22⋊D1311yescharacteristic
431C22×C4C2×C22⋊D1311yescharacteristic
432C22×C4C23×D1311yescharacteristic
433SD16—528no—
434C2×C8—134no—
435C2×C8—262no—
436C2×C8—262no—
437C2×C8—262no—
438C2×C8—262no—
439C2×C8—262no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—42no—
443C4⋊C4—132no—
444C4⋊C4—261no—
445C4⋊C4—262no—
446C4⋊C4—262no—
447C4⋊C4—522no—
448C22⋊C4—264no—
449C22⋊C4—522no—
450C22⋊C4—522no—
451C22⋊C4—522no—
452C22⋊C4—522no—
453C42—22no—
454C42—22no—
455C42—41no—
456C42—41no—
457C42—522no—
458C13#2204711yescharacteristic, complemented, Sylow
459C23—21no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—262no—
464C23—521no—
465C23—521no—
466C23—521no—
467C23—521no—
468C23—521no—
469C23—521no—
470C23C4×C22⋊D1312yes—
471C23#8819612yes—
472C23#8820312yes—
473C23C22×C22⋊D1311yescharacteristic
474Q8—24no—
475Q8—24no—
476Q8—48no—
477Q8—42no—
478Q8—42no—
479D4—264no—
480D4—528no—
481D4—522no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—48no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4—262no—
508C2×C4—521no—
509C2×C4—521no—
510C2×C4—521no—
511C2×C4—521no—
512C2×C4—521no—
513C2×C4—521no—
514C2×C4—521no—
515C2×C4—521no—
516C2×C4—1044no—
517C2×C4C4×C22⋊D1312yes—
518C2×C4#8819612yes—
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C2×#612711yescharacteristic
521C2×C4#8825112yes—
522C2×C4#8825112yes—
523C8—264no—
524C8—522no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—522no—
532C22—522no—
533C22—522no—
534C22—1041no—
535C22—1041no—
536C22—1041no—
537C22—1041no—
538C22#1171868714yes—
539C22C2×C4×C22⋊D1311yescharacteristic
540C22#1171950911yescharacteristic
541C22#1171951011yescharacteristic
542C22C2×#8819611yescharacteristic
543C22C2×#8819611yescharacteristic
544C22C2×#8820311yescharacteristic
545C22#1171952711yescharacteristic
546C4—22no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—44no—
552C4—82no—
553C4—522no—
554C4—1041no—
555C4—1041no—
556C4#1171919112yes—
557C4#1171919912yes—
558C2—24no—
559C2—1042no—
560C2#1311749411yescharacteristic
561C2C2×#1171868711yescharacteristic
562C2C4×#8819611yescharacteristic
563C2#1312563811yescharacteristic
564C2#1312566611yescharacteristic
565C2#1312582311yescharacteristic
566C2#1312586311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#391C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
cosocleC22×C4×C13C24
hypercenterC2×#391D13
hypocenterC13#22047
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #13115720C2semidirect
4. #13115529C2semidirect
5. #13115474C2semidirect
6. #13115173C2semidirect
8. #13115024C2semidirect
9. #13114771C2semidirect
10. #13114598C2semidirect
11. C2×C13×#391C2semidirect
25. #11718888C4semidirect
48. C22×Q8×C13C2×C4semidirect
69. C2×#6106C2×C4semidirect
91. #88075C2×C4semidirect
96. C22⋊#1055C2×C4semidirect
178. C2×#391D13semidirect
322. C22×Q8C4×D13semidirect
458. C13#22047semidirect

Maximal subgroups

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

subgroupindex
C2×#117188882
C4×#881842
#131157202
#131155292
#131154742
#131151732
#131151532
#131150242
#131147712
#131145982
C2×C13×#3912
#2204713