Finite Group Databasebeta

← #15904224

Subgroups — #15904224

Order 3328.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718748C211yesmaximal, characteristic, complemented
2C2×#11718587C211yesmaximal, characteristic, complemented
3C4×#88184C211yesmaximal, characteristic
4#13116267C212yesmaximal, complemented
5#13116025C212yesmaximal
6#13115789C211yesmaximal, characteristic, complemented
7#13115597C211yesmaximal, characteristic, complemented
8#13115576C212yesmaximal, complemented
9#13115532C212yesmaximal, complemented
10#13114833C211yesmaximal, characteristic, complemented
11C13×#2857C211yesmaximal, characteristic, complemented
12C2×C13×C4⋊Q8C2211yescharacteristic
13C2×C13×C22⋊Q8—21no—
14C22×C42×C13C2211yescharacteristic
15C2×#88184C2211yescharacteristic
16C2×C4×C22⋊D13—21no—
17C2×C4×D52C2211yescharacteristic
18C13×#391—21no—
19C13×#389—21no—
20C13×#389C2212yes—
21C13×#384C2211yescharacteristic
22C13×#380—21no—
23C13×#380C2212yes—
24#11718874—21no—
25#11718873C2211yescharacteristic
26C2×C22⋊#1055C2212yes—
27#11718748—24no—
28C2×#88049C2212yes—
29C2×#88049C2212yes—
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32#11718601—21no—
33#11718600C2211yescharacteristic
34C4×#6103—21no—
35C4×C4⋊Dic13C2211yescharacteristic
36#11718589C2211yescharacteristic
37#11718587—24no—
38C2×C4⋊#1055C2211yescharacteristic
39C2×C4⋊#1055C2211yescharacteristic
40C2×#88043C2212yes—
41#11718121C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45C22×Q8×C13—21no—
46C23×C4×C13D411yescharacteristic
47C23×C4×C13D411yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C22×C22⋊D13—21no—
50C22×D52C2311yescharacteristic
51C22×C4×D13—21no—
52C13×C4⋊Q8—22no—
53C13×C4⋊Q8—22no—
54C13×C22⋊Q8—44no—
55C2×C13×C4⋊C4—21no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C22⋊C4—22no—
62C2×C42×C13—22no—
63C2×C42×C13—22no—
64C2×C42×C13D411yescharacteristic
65C2×C42×C13D411yescharacteristic
66C2×C42×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C22⋊Dic13—21no—
69#88184—22no—
70#88184—22no—
71C4×C22⋊D13—44no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×#6103—21no—
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×#6101—21no—
80C2×C4×Dic13—21no—
81C22×#1055C2312yes—
82C22×#1055C2312yes—
83C4×D52—22no—
84C4×D52—22no—
85C13×#95—22no—
86C13×#95—22no—
87#88071—21no—
88#88071—21no—
89#88071—21no—
90C22⋊#1055—24no—
91#88049—24no—
92#88049—24no—
93#88048—24no—
94#88047—24no—
95C4⋊#1055—22no—
96C4⋊#1055D414yescomplemented
97#88043—24no—
98#24709—131nomaximal, Sylow
99C24×C13C2×D411yescharacteristic
100C23×D13—21no—
101C2×Q8×C13—42no—
102C2×Q8×C13—42no—
103C2×Q8×C13—42no—
104C22×C4×C13—22no—
105C22×C4×C13—22no—
106C22×C4×C13—22no—
107C22×C4×C13—22no—
108C22×C4×C13—22no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—41no—
118C22×C4×C13C2×D411yescharacteristic
119C22×C4×C13C2×D411yescharacteristic
120C22×C4×C13C2×D411yescharacteristic
121C22×C4×C13C2×D411yescharacteristic
122C22×C4×C13C2×D411yescharacteristic
123C22×C4×C13C2411yescharacteristic
124C2×C22⋊D13—24no—
125C2×C22⋊D13—42no—
126C2×C22⋊D13—42no—
127C22×Dic13—21no—
128C22×Dic13—21no—
129C22×Dic13—21no—
130C2×D52—21no—
131C2×D52—21no—
132C2×D52—21no—
133C2×D52—21no—
134C2×D52—21no—
135C2×D52#4112yes—
136C2×C4×D13—42no—
137C2×C4×D13—42no—
138C2×C4×D13—42no—
139C13×C4⋊C4—22no—
140C13×C4⋊C4—22no—
141C13×C4⋊C4—22no—
142C13×C4⋊C4—22no—
143C13×C4⋊C4—42no—
144C13×C4⋊C4—44no—
145C13×C4⋊C4—42no—
146C13×C4⋊C4—42no—
147C13×C22⋊C4—44no—
148C42×C13—22no—
149C42×C13—22no—
150C42×C13—21no—
151C42×C13—21no—
152C42×C13C2×D412yes—
153C42×C13#4112yes—
154C22⋊Dic13—42no—
155#6103—24no—
156#6103—42no—
157#6103—42no—
158#6103—42no—
159C4⋊Dic13—21no—
160C4⋊Dic13—21no—
161C4⋊Dic13—21no—
162C4⋊Dic13—21no—
163C4⋊Dic13—21no—
164C4⋊Dic13#4112yes—
165#6101—42no—
166C4×Dic13—42no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055—22no—
171C2×#1055—22no—
172C2×#1055C2×D414yes—
173C2×#474—131no—
174C2×#432—131no—
175#2857D1311yescharacteristic, complemented
176C4×#121—131no—
177#2076—132no—
178#2034—132no—
179#1988—131no—
180#1948—131no—
181#1944—132no—
182#1936—132no—
183#1802—131no—
184C23×C13—21no—
185C23×C13—21no—
186C23×C13—21no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—21no—
190C23×C13#13712yes—
191C23×C13C22×D411yescharacteristic
192C22×D13—22no—
193C22×D13—41no—
194C22×D13—41no—
195C22×D13—41no—
196C22×D13—41no—
197C22×D13—41no—
198C22×D13—41no—
199Q8×C13—84no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—44no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—44no—
217C2×C4×C13—42no—
218C2×C4×C13—42no—
219C2×C4×C13—42no—
220C2×C4×C13—42no—
221C2×C4×C13—42no—
222C2×C4×C13—42no—
223C2×C4×C13#12112yes—
224C2×C4×C13#12112yes—
225C2×C4×C13AGL(1,ℤ/8)12yes—
226C2×C4×C13AGL(1,ℤ/8)12yes—
227C2×C4×C13C22×D411yescharacteristic
228C2×C4×C13C2×#4111yescharacteristic
229C2×C4×C13C2×#4111yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C2×C4×C132−1+411yescharacteristic
232C2×C4×C132−1+411yescharacteristic
233C22⋊D13—48no—
234C2×Dic13—22no—
235C2×Dic13—41no—
236C2×Dic13—41no—
237C2×Dic13—41no—
238C2×Dic13—41no—
239C2×Dic13—41no—
240C2×Dic13—41no—
241C2×Dic13—41no—
242C2×Dic13—41no—
243D52—22no—
244D52—22no—
245D52—41no—
246D52—41no—
247C4×D13—84no—
248#1055—24no—
249#1055—42no—
250C2×C4⋊Q8C2×D1311yescharacteristic
251C2×C22⋊Q8—21no—
252C2×#121—131no—
253C2×C4×D4—131no—
254C2×C4×D4—261no—
255C22×C42C2×D1311yescharacteristic
256#474—264no—
257#432—264no—
258C2×#107—132no—
259C2×#106—132no—
260C2×C4⋊C8—131no—
261C2×C4⋊C8—131no—
262C2×#102—132no—
263C2×#102—132no—
264C2×C22⋊C8—132no—
265C2×#97—132no—
266#391—21no—
267#390—131no—
268#389—21no—
269#389—131no—
270#389C2×D1312yes—
271#388—261no—
272#386—261no—
273#384C2×D1311yescharacteristic
274#380—21no—
275#380—131no—
276#380C2×D1312yes—
277C4×C4⋊C4—131no—
278C4×C22⋊C4—261no—
279#340—132no—
280#340—132no—
281#340—132no—
282#340—132no—
283C22×C13—22no—
284C22×C13—22no—
285C22×C13—22no—
286C22×C13—41no—
287C22×C13—41no—
288C22×C13—41no—
289C22×C13—41no—
290C22×C13C2×#12111yescharacteristic
291C22×C13#52511yescharacteristic
292C22×C13#53611yescharacteristic
293C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C13C2×#13711yescharacteristic
296C22×C13#57511yescharacteristic
297C2×D13—42no—
298C2×D13—42no—
299C2×D13—42no—
300C2×D13—81no—
301C2×D13—81no—
302C2×D13—81no—
303C2×D13—81no—
304C4×C13—22no—
305C4×C13—41no—
306C4×C13—41no—
307C4×C13—41no—
308C4×C13—82no—
309C4×C13—82no—
310C4×C13#46914yes—
311C4×C13#54711yescharacteristic
312C4×C13#54811yescharacteristic
313C4×C13#55211yescharacteristic
314C4×C13#55611yescharacteristic
315Dic13—42no—
316Dic13—81no—
317Dic13—81no—
318C22×Q8—21no—
319C22×D4—131no—
320C22×D4—261no—
321C23×C4—261no—
322C23×C4C22⋊D1311yescharacteristic
323C23×C4C22⋊D1311yescharacteristic
324C23×C4C22×D1311yescharacteristic
325C22×C8—132no—
326C22×C8—132no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C22⋊Q8—44no—
330#121—262no—
331#121—262no—
332C4×D4—262no—
333C4×D4—262no—
334C4×D4—524no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—131no—
340C2×C4⋊C4—131no—
341C2×C4⋊C4—131no—
342C2×C4⋊C4—261no—
343C2×C4⋊C4C22×D1312yes—
344C2×C4⋊C4C22×D1312yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—261no—
347C2×C22⋊C4—261no—
348C2×C22⋊C4—261no—
349C2×C22⋊C4—261no—
350C2×C22⋊C4—261no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—261no—
354C2×C42C22⋊D1311yescharacteristic
355C2×C42C22⋊D1311yescharacteristic
356C2×C42C22×D1311yescharacteristic
357C2×C42C22×D1311yescharacteristic
358#107—264no—
359#106—264no—
360C4⋊C8—134no—
361C4⋊C8—262no—
362#102—264no—
363#102—264no—
364C22⋊C8—264no—
365#97—264no—
366#95—22no—
367#95—22no—
368#95—261no—
369#95—261no—
370#95—261no—
371C2×C13—42no—
372C2×C13#241511yescharacteristic
373C2×C13C2×#46911yescharacteristic
374C2×C13#305611yescharacteristic
375C2×C13#311011yescharacteristic
376C2×C13#311511yescharacteristic
377C2×C13#323511yescharacteristic
378C2×C13#323911yescharacteristic
379D13—82no—
380C24—261no—
381C24C2×C22⋊D1311yescharacteristic
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×D4—132no—
386C2×D4—264no—
387C2×D4—261no—
388C2×D4—261no—
389C2×D4—261no—
390C2×D4—261no—
391C2×D4—261no—
392C2×D4—522no—
393C2×D4—522no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—41no—
408C22×C4—261no—
409C22×C4—261no—
410C22×C4—261no—
411C22×C4—522no—
412C22×C4—522no—
413C22×C4—522no—
414C22×C4C2×C22⋊D1311yescharacteristic
415C22×C4C2×C22⋊D1311yescharacteristic
416C22×C4C2×C22⋊D1311yescharacteristic
417C22×C4C2×C22⋊D1311yescharacteristic
418C22×C4C2×C22⋊D1311yescharacteristic
419C22×C4C23×D1311yescharacteristic
420C2×C8—134no—
421C2×C8—262no—
422C2×C8—262no—
423C2×C8—262no—
424C2×C8—262no—
425C2×C8—262no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—44no—
431C4⋊C4—42no—
432C4⋊C4—42no—
433C4⋊C4—42no—
434C4⋊C4—132no—
435C4⋊C4—261no—
436C4⋊C4—261no—
437C4⋊C4—261no—
438C4⋊C4—261no—
439C4⋊C4—261no—
440C4⋊C4—522no—
441C22⋊C4—44no—
442C22⋊C4—264no—
443C22⋊C4—522no—
444C22⋊C4—522no—
445C22⋊C4—522no—
446C22⋊C4—522no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—522no—
452C42D4×D1312yes—
453C42#612912yes—
454C13#2470911yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—262no—
462C23—521no—
463C23—521no—
464C23—521no—
465C23—521no—
466C23—521no—
467C23—521no—
468C23#8819612yes—
469C23C22×C22⋊D1311yescharacteristic
470Q8—84no—
471D4—262no—
472D4—262no—
473D4—528no—
474D4—521no—
475D4—521no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—262no—
500C2×C4—521no—
501C2×C4—521no—
502C2×C4—521no—
503C2×C4—521no—
504C2×C4—521no—
505C2×C4—521no—
506C2×C4—521no—
507C2×C4—521no—
508C2×C4—1044no—
509C2×C4#8818612yes—
510C2×C4#8819312yes—
511C2×C4#8819312yes—
512C2×C4#8820312yes—
513C2×C4C2×D4×D1311yescharacteristic
514C2×C4C2×#612911yescharacteristic
515C2×C4#8825411yescharacteristic
516C2×C4#8825411yescharacteristic
517C2×C4#41×D1311yescharacteristic
518C2×C4#41×D1311yescharacteristic
519C8—264no—
520C8—522no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—522no—
529C22—522no—
530C22—522no—
531C22—1041no—
532C22—1041no—
533C22—1041no—
534C22—1041no—
535C22C2×#8818611yescharacteristic
536C22C2×#8819311yescharacteristic
537C22C2×#8819611yescharacteristic
538C22#1171952111yescharacteristic
539C22C2×#8820311yescharacteristic
540C22#1171952711yescharacteristic
541C22#1171953311yescharacteristic
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—82no—
547C4—82no—
548C4—522no—
549C4—1041no—
550C4—1041no—
551C4#1171870014yes—
552C4#1171933611yescharacteristic
553C4#1171933811yescharacteristic
554C4#1171934411yescharacteristic
555C4#1171934611yescharacteristic
556C2—42no—
557C2—1042no—
558C2#1311826611yescharacteristic
559C2C2×#1171870011yescharacteristic
560C2#1312446211yescharacteristic
561C2#1312493111yescharacteristic
562C2#1312498111yescharacteristic
563C2#1312603411yescharacteristic
564C2#1312606611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2857C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2857D13
hypocenterC13#24709
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#11718748C2semidirect
2. C2×#11718587C2semidirect
4. #13116267C2semidirect
6. #13115789C2semidirect
7. #13115597C2semidirect
8. #13115576C2semidirect
9. #13115532C2semidirect
10. #13114833C2semidirect
11. C13×#2857C2semidirect
96. C4⋊#1055D4semidirect
175. #2857D13semidirect
454. C13#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
C2×#117185872
C4×#881842
#131162672
#131160252
#131157892
#131155972
#131155762
#131155322
#131148332
C13×#28572
#2470913