Finite Group Databasebeta

← #15765234

Subgroups — #15765234

Order 3328.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718668C211yesmaximal, characteristic, complemented
2C2×#11718680C211yesmaximal, characteristic, complemented
3#13115796C211yesmaximal, characteristic, complemented
4C2×D4⋊#1055C211yesmaximal, characteristic, complemented
5C2×D4⋊#1055C211yesmaximal, characteristic, complemented
6#13112719C211yesmaximal, characteristic, complemented
7C13×#2537C211yesmaximal, characteristic
8C2×C13×#121—21no—
9C2×C13×#121—21no—
10C2×C4×D4×C13C2211yescharacteristic
11C2×C4×D4×C13C2211yescharacteristic
12C22×#6105—21no—
13C2×#88123C2211yescharacteristic
14C13×#394—22no—
15C13×#384C2211yescharacteristic
16C13×#380—21no—
17C13×#380—21no—
18C2×#88072—21no—
19#11718680—22no—
20#11718680—22no—
21#11718668—22no—
22#11718668—22no—
23C2×#88050—21no—
24C2×#88047—21no—
25C2×C4⋊#1055C2211yescharacteristic
26C2×C4⋊#1055C2211yescharacteristic
27C2×C4×#1055C2211yescharacteristic
28D4⋊#1055—22no—
29D4⋊#1055—22no—
30#11718121—22no—
31C22×D4×C13—22no—
32C22×D4×C13D411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C23×C4×C13—21no—
35C23×C4×C13—21no—
36C22×Dic26—21no—
37C13×#121—42no—
38C13×#121—42no—
39C13×#121—42no—
40C13×#121—42no—
41C4×D4×C13—21no—
42C4×D4×C13—21no—
43C4×D4×C13—21no—
44C4×D4×C13—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C4×D4×C13—21no—
48C4×D4×C13—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C13×C4⋊C4D412yes—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—22no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C42×C13C2311yescharacteristic
59C2×#6105—24no—
60C2×#6105—42no—
61C2×#6105—42no—
62C2×C4⋊Dic13—21no—
63C2×C4⋊Dic13—21no—
64C22×#1055—21no—
65C22×#1055—21no—
66C22×#1055—21no—
67#88123—21no—
68#88123—21no—
69#88123—21no—
70#88123D412yescomplemented
71C13×#95—22no—
72#88072—24no—
73#88050—24no—
74#88047—24no—
75C4⋊#1055—21no—
76C4⋊#1055—21no—
77C4⋊#1055D412yescomplemented
78C4⋊#1055D412yescomplemented
79C4×#1055—21no—
80C4×#1055—21no—
81#10231—131nomaximal, Sylow
82C24×C13—21no—
83C24×C13—21no—
84C2×D4×C13—21no—
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13—21no—
88C2×D4×C13—21no—
89C2×D4×C13—21no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—21no—
93C2×D4×C13—21no—
94C2×D4×C13—44no—
95C2×D4×C13—44no—
96C2×D4×C13—82no—
97C2×D4×C13D812yes—
98C2×D4×C13SD1612yescomplemented
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—22no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—41no—
106C22×C4×C13—41no—
107C22×C4×C13—41no—
108C22×C4×C13—41no—
109C22×C4×C13—41no—
110C22×C4×C13—41no—
111C22×C4×C13—41no—
112C22×C4×C13—41no—
113C22×C4×C13—41no—
114C22×C4×C13C2×D411yescharacteristic
115C22×C4×C13C2×D411yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×Dic13—41no—
118C2×Dic26—22no—
119C2×Dic26—41no—
120C2×Dic26—41no—
121C2×Dic26—41no—
122C2×Dic26—41no—
123C2×Dic26—41no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—21no—
126C13×C4⋊C4—21no—
127C13×C4⋊C4—21no—
128C13×C4⋊C4—42no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C22⋊C4—44no—
134C13×C22⋊C4—44no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—41no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C42×C13C2×D411yescharacteristic
140C42×C13C2×D411yescharacteristic
141C42×C13C2×D411yescharacteristic
142C42×C13#4111yescharacteristic
143#6105—48no—
144C4⋊Dic13—22no—
145C4⋊Dic13—22no—
146C4⋊Dic13—41no—
147C4⋊Dic13—41no—
148C2×#1055—22no—
149C2×#1055—22no—
150C2×#1055—22no—
151C2×#1055—41no—
152C2×#1055—41no—
153C2×#1055—41no—
154C2×#1055—41no—
155C2×#1055—41no—
156C2×#1055—41no—
157C2×#474—131no—
158C2×#461—131no—
159#2537D1311yescharacteristic
160#1990—131no—
161C2×D4⋊C8—131no—
162C2×D4⋊C8—131no—
163#1296—131no—
164C23×C13—22no—
165C23×C13—22no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13#12011yescharacteristic
179D4×C13—22no—
180D4×C13—22no—
181D4×C13—22no—
182D4×C13—22no—
183D4×C13—41no—
184D4×C13—41no—
185D4×C13—41no—
186D4×C13—41no—
187D4×C13—88no—
188C2×C4×C13—21no—
189C2×C4×C13—21no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—41no—
193C2×C4×C13—42no—
194C2×C4×C13—41no—
195C2×C4×C13—41no—
196C2×C4×C13—42no—
197C2×C4×C13—41no—
198C2×C4×C13—42no—
199C2×C4×C13—81no—
200C2×C4×C13—81no—
201C2×C4×C13—81no—
202C2×C4×C13—81no—
203C2×C4×C13—81no—
204C2×C4×C13—81no—
205C2×C4×C13—81no—
206C2×C4×C13—81no—
207C2×C4×C13#12011yescharacteristic
208C2×C4×C13#12011yescharacteristic
209C2×C4×C13#12111yescharacteristic
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12111yescharacteristic
212C2×C4×C13#12711yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C2×SD1611yescharacteristic
215C2×C4×C13#13511yescharacteristic
216C2×C4×C13#13511yescharacteristic
217C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
218C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
219C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C13#13711yescharacteristic
221C2×Dic13—42no—
222C2×Dic13—81no—
223C2×Dic13—81no—
224Dic26—42no—
225Dic26—42no—
226Dic26—81no—
227Dic26—81no—
228#1055—42no—
229#1055—42no—
230#1055—42no—
231C22×SD16—261no—
232C2×C4⋊Q8—131no—
233C2×#121—21no—
234C2×#121—21no—
235C2×C4×D4C2×D1311yescharacteristic
236C2×C4×D4C2×D1311yescharacteristic
237#474—262no—
238#474—262no—
239#461—262no—
240#461—262no—
241C2×#107—261no—
242C2×C4⋊C8—131no—
243C2×C4⋊C8—131no—
244C2×#103—261no—
245C2×#102—261no—
246C2×C4×C8—131no—
247#394—22no—
248#384C2×D1311yescharacteristic
249#380—21no—
250#380—21no—
251#340—262no—
252D4⋊C8—262no—
253D4⋊C8—262no—
254C22×C13—42no—
255C22×C13—42no—
256C22×C13—42no—
257C22×C13—42no—
258C22×C13—42no—
259C22×C13—42no—
260C22×C13—81no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13#39211yescharacteristic
269C22×C13#44711yescharacteristic
270C22×C13#44911yescharacteristic
271C22×C13#45011yescharacteristic
272C22×C13#45211yescharacteristic
273C22×C13#45511yescharacteristic
274C22×C13#45611yescharacteristic
275C4×C13—21no—
276C4×C13—21no—
277C4×C13—82no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13#44711yescharacteristic
281C4×C13#44811yescharacteristic
282C4×C13#44911yescharacteristic
283C4×C13#44911yescharacteristic
284C4×C13#46511yescharacteristic
285C4×C13#46611yescharacteristic
286C4×C13#46811yescharacteristic
287C4×C13#46911yescharacteristic
288Dic13—82no—
289C22×Q8—261no—
290C22×D4—22no—
291C22×D4C22⋊D1311yescharacteristic
292C22×D4C22⋊D1311yescharacteristic
293C23×C4—21no—
294C23×C4—21no—
295C2×SD16—264no—
296C2×SD16—522no—
297C2×SD16—522no—
298C22×C8—261no—
299C22×C8—261no—
300C22×C8—261no—
301C4⋊Q8—132no—
302C4⋊Q8—261no—
303C4⋊Q8—261no—
304C4⋊Q8—261no—
305#121—42no—
306#121—42no—
307#121—42no—
308#121—42no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—261no—
320C2×C4⋊C4—261no—
321C2×C4⋊C4C22⋊D1311yescharacteristic
322C2×C4⋊C4C22⋊D1311yescharacteristic
323C2×C4⋊C4C22⋊D1312yes—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C42C22×D1311yescharacteristic
329#107—264no—
330C4⋊C8—132no—
331C4⋊C8—132no—
332C4⋊C8—261no—
333C4⋊C8—261no—
334#103—264no—
335#102—264no—
336C4×C8—261no—
337C4×C8—261no—
338#95—22no—
339C2×C13—82no—
340C2×C13—82no—
341C2×C13#163911yescharacteristic
342C2×C13#164611yescharacteristic
343C2×C13#164711yescharacteristic
344C2×C13#165411yescharacteristic
345C2×C13#199911yescharacteristic
346C2×C13#200011yescharacteristic
347C2×C13#200711yescharacteristic
348C24—21no—
349C24—21no—
350C2×Q8—262no—
351C2×Q8—521no—
352C2×Q8—521no—
353C2×Q8—521no—
354C2×Q8—521no—
355C2×Q8—521no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—44no—
367C2×D4—44no—
368C2×D4—82no—
369C2×D4#610412yes—
370C2×D4#610512yescomplemented
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—521no—
387C22×C4C2×C22⋊D1311yescharacteristic
388C22×C4C2×C22⋊D1311yescharacteristic
389C22×C4C2×C22⋊D1311yescharacteristic
390SD16—528no—
391C2×C8—262no—
392C2×C8—262no—
393C2×C8—262no—
394C2×C8—521no—
395C2×C8—521no—
396C2×C8—521no—
397C2×C8—521no—
398C2×C8—521no—
399C2×C8—521no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—42no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—262no—
410C4⋊C4—262no—
411C4⋊C4—521no—
412C4⋊C4—521no—
413C22⋊C4—44no—
414C22⋊C4—44no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C42D4×D1311yescharacteristic
420C42D4×D1311yescharacteristic
421C42D4×D1311yescharacteristic
422C42#612911yescharacteristic
423C13#1023111yescharacteristic, complemented, Sylow
424C23—22no—
425C23—22no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#8820711yescharacteristic
439Q8—522no—
440Q8—522no—
441Q8—1041no—
442Q8—1041no—
443D4—22no—
444D4—22no—
445D4—22no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—88no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—81no—
464C2×C4—81no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—522no—
472C2×C4—1041no—
473C2×C4—1041no—
474C2×C4C2×#610411yescharacteristic
475C2×C4#8818611yescharacteristic
476C2×C4#8818611yescharacteristic
477C2×C4C2×#610511yescharacteristic
478C2×C4#8819111yescharacteristic
479C2×C4#8819111yescharacteristic
480C2×C4#8819211yescharacteristic
481C2×C4#8819311yescharacteristic
482C2×C4#8819311yescharacteristic
483C2×C4#8819411yescharacteristic
484C2×C4#8820311yescharacteristic
485C2×C4#8820411yescharacteristic
486C2×C4#8820411yescharacteristic
487C2×C4#8820511yescharacteristic
488C8—522no—
489C8—522no—
490C8—522no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22#1171887811yescharacteristic
506C22#1171887911yescharacteristic
507C22#1171888411yescharacteristic
508C22#1171889911yescharacteristic
509C22#1171890011yescharacteristic
510C22#1171890311yescharacteristic
511C22#1171890711yescharacteristic
512C4—21no—
513C4—21no—
514C4—82no—
515C4—81no—
516C4—81no—
517C4—1042no—
518C4#1171869711yescharacteristic
519C4#1171869811yescharacteristic
520C4#1171869811yescharacteristic
521C4#1171869911yescharacteristic
522C4#1171870011yescharacteristic
523C4#1171870111yescharacteristic
524C4#1171870211yescharacteristic
525C4#1171870311yescharacteristic
526C2—82no—
527C2—82no—
528C2#1311401511yescharacteristic
529C2#1311406411yescharacteristic
530C2#1311407111yescharacteristic
531C2#1311412011yescharacteristic
532C2#1311583211yescharacteristic
533C2#1311583911yescharacteristic
534C2#1311588311yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2537C2
socleC23×C13#120
hypercenter#2537D13
hypocenterC13#10231
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#11718668C2semidirect
2. C2×#11718680C2semidirect
3. #13115796C2semidirect
4. C2×D4⋊#1055C2semidirect
5. C2×D4⋊#1055C2semidirect
6. #13112719C2semidirect
70. #88123D4semidirect
77. C4⋊#1055D4semidirect
78. C4⋊#1055D4semidirect
98. C2×D4×C13SD16semidirect
370. C2×D4#6105semidirect
423. C13#10231semidirect

Maximal subgroups

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

subgroupindex
C2×#117186682
C2×#117186802
#131157962
C2×D4⋊#10552
#131127192
C13×#25372
#1023113