Finite Group Databasebeta

← #11897564

Subgroups — #11897564

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596014C211yesmaximal, characteristic, complemented
2#10593904C211yesmaximal, characteristic, complemented
3C3×C4×#213C211yesmaximal, characteristic
4C3×#5007C211yesmaximal, characteristic, complemented
5#10591495C212yesmaximal, complemented
6#10591436C212yesmaximal
7#10590563C212yesmaximal, complemented
8#10590473C212yesmaximal, complemented
9#10590303C211yesmaximal, characteristic, complemented
10#10590296C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#80959—31nomaximal
13#79576—31nomaximal
14C2×D3×Dic6—21no—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17C2×C4⋊(C3⋊Dic3)—21no—
18#64133—21no—
19#64099C2212yes—
20#64087—22no—
21#64078C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63919C2212yes—
27#63899—22no—
28#63898C2212yes—
29#63856—21no—
30C3×#832C2211yescharacteristic
31C3×#832C2212yes—
32C3×#809C2211yescharacteristic
33C3×#807C2212yes—
34C3×#807C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2212yes—
38#63573C2212yes—
39#63573C2212yes—
40#63572C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#5727—31no—
44#5543—31no—
45#5543—31no—
46#5543—61no—
47D4×Dic6—31no—
48C3×#474—31no—
49C3×C4×D8—31no—
50#5152—32no—
51#5080—31no—
52C4×#213D311yescharacteristic
53#5008—31no—
54#5007D311yescharacteristic, complemented
55#4891—32no—
56#4876—32no—
57#4876—32no—
58#4842—31no—
59#4831—31no—
60#4785—32no—
61#4763—32no—
62#4761—32no—
63#4761—32no—
64#4680—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634D411yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6—21no—
74C2×#627—22no—
75C2×D3×Dic3—22no—
76D3×Dic6—44no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80#3757—22no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)—22no—
83C4⋊(C3⋊Dic3)D411yescharacteristic
84C4⋊(C3⋊Dic3)C2312yes—
85#3750—22no—
86#3750D412yes—
87C4×C3⋊Dic3C2312yes—
88C3×#213Q814yescomplemented
89C3×(C2×D3)⋊C4—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96#3724—22no—
97(C2×D3)⋊Dic3—22no—
98#3384—91noSylow
99C2×D3×Q8—61no—
100C22×Dic6—61no—
101C2×C3×D8—31no—
102C3×C4⋊Q8—31no—
103C3×C4×D4—21no—
104C3×C4×D4—31no—
105C3×C4×D4C2×D311yescharacteristic
106C3×C4×D4C2×D311yescharacteristic
107#946—61no—
108D4×Dic3—32no—
109D4×Dic3—32no—
110D4×Dic3—32no—
111D4×Dic3—62no—
112C2×#213C2×D311yescharacteristic
113C2×C4⋊Dic3—61no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3—62no—
116#924—61no—
117#924—61no—
118#924—61no—
119#924—62no—
120#896—62no—
121#893—32no—
122#890—32no—
123#890—32no—
124#890—62no—
125#888—32no—
126#888—32no—
127#878—62no—
128#878—62no—
129#878—62no—
130#878—64no—
131C4×D12C2×D311yescharacteristic
132#869—31no—
133#869—31no—
134#869—61no—
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C3×#107—31no—
140C3×#107—32no—
141C3×C4⋊C8—31no—
142C3×#102—31no—
143C3×#102—32no—
144C3×#102—31no—
145C3×C4×C8—31no—
146#832—32no—
147#832C2×D312yes—
148#832C2×D311yescharacteristic
149#821—32no—
150#817—32no—
151#817—32no—
152#817—32no—
153#815—32no—
154#815—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157#809C2×D311yescharacteristic
158#808—32no—
159#808—32no—
160#808—32no—
161#807C2×D311yescharacteristic
162#807C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C23×C32—21no—
166C22×C3×D3—21no—
167C32×D4—21no—
168C32×D4C2×Q812yescomplemented
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—82no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—22no—
179#634—81no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12C2×Q812yes—
184C3×C4×D3—42no—
185C3×Dic6—42no—
186#627—44no—
187D3×Dic3—44no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190C3×C3⋊C8C2×Q812yescomplemented
191#554—91no—
192D4×Q8—91no—
193#501—92no—
194#498—91no—
195#478—92no—
196#476—92no—
197#476—91no—
198#474—31no—
199#446—91no—
200#442—92no—
201C4×D8—31no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4—31no—
205C2×C3×D4C22×D311yescharacteristic
206C2×C3×D4C22×D311yescharacteristic
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—61no—
211C22×Dic3—62no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—64no—
215D3×Q8—124no—
216C2×D12C22×D311yescharacteristic
217C2×C4×D3—21no—
218C2×C4×D3—62no—
219C2×Dic6—21no—
220C2×Dic6—31no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—124no—
229C3×D8—34no—
230C2×C3×C8—31no—
231C2×C3×C8—31no—
232C2×C3×C8—32no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—22no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—61no—
243C3×C42—21no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#217—62no—
248#217—62no—
249#217—64no—
250#213Dic614yescomplemented
251(C2×D3)⋊C4—21no—
252(C2×D3)⋊C4—62no—
253C4⋊Dic3—21no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—32no—
257C4⋊Dic3—32no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3—64no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3C22×D312yes—
267C4⋊Dic3C22×D311yescharacteristic
268Dic3⋊C4—32no—
269Dic3⋊C4—32no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—64no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—62no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D312yes—
281C2×C3⋊C8C22×D311yescharacteristic
282C22×C32—22no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C22×D411yescharacteristic
286C2×C3×D3—22no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—21no—
290C32×C4—41no—
291C32×C4AGL(1,ℤ/8)12yes—
292C32×C4C22×Q811yescharacteristic
293C32×C42−1+411yescharacteristic
294C3⋊Dic3—22no—
295C3⋊Dic3—22no—
296C3⋊Dic3—42no—
297C3×Dic3—42no—
298C3×Dic3—41no—
299C22×Q8—181no—
300C2×D8—31no—
301C4⋊Q8—31no—
302C4⋊Q8—92no—
303C4⋊Q8—91no—
304#125—92no—
305C22⋊Q8—182no—
306C22⋊Q8—182no—
307C22⋊Q8—181no—
308C22⋊Q8—181no—
309C4×Q8—91no—
310C4×D4—31no—
311C4×D4—92no—
312C4×D4—92no—
313C4×D4D3211yescharacteristic
314C2×C4⋊C4—181no—
315#107—31no—
316#107—32no—
317#106—92no—
318#106—92no—
319#106—92no—
320C4⋊C8—31no—
321C4⋊C8—92no—
322#102—31no—
323#102—32no—
324#102—31no—
325#102—92no—
326#97—92no—
327C4×C8—31no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—61no—
332C22×D3—21no—
333C3×Q8—122no—
334C3×D4—22no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—22no—
338C3×D4—32no—
339C3×D4—61no—
340C3×D4C2×Dic612yescomplemented
341C3×D4D3×Q812yescomplemented
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—44no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—122no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—124no—
372C2×Dic3—242no—
373C2×Dic3—242no—
374C2×Dic3—244no—
375D12—21no—
376D12C2×Dic612yes—
377C4×D3—42no—
378C4×D3—124no—
379Dic6—42no—
380Dic6—62no—
381Dic6—62no—
382Dic6—122no—
383Dic6—124no—
384Dic6—124no—
385Dic6—241no—
386Dic6—241no—
387Dic6—242no—
388C3×C8—32no—
389C3×C8—61no—
390C3×C8—62no—
391C3⋊C8—22no—
392C3⋊C8—21no—
393C3⋊C8C2×Dic612yescomplemented
394C2×C32—42no—
395C2×C32D4×Q811yescharacteristic
396C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
397C2×C32#57711yescharacteristic
398C3×D3—42no—
399C2×Q8—61no—
400C2×Q8—91no—
401C2×Q8—182no—
402C2×Q8—181no—
403C2×Q8—364no—
404C2×D4—31no—
405C2×D4C2×D3211yescharacteristic
406C22×C4—21no—
407C22×C4—61no—
408C22×C4—182no—
409C22×C4—182no—
410D8—34no—
411C2×C8—31no—
412C2×C8—31no—
413C2×C8—32no—
414C4⋊C4—31no—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C4⋊C4—91no—
418C4⋊C4—92no—
419C4⋊C4—92no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—181no—
424C4⋊C4C2×D3211yescharacteristic
425C22⋊C4—21no—
426C22⋊C4—61no—
427C22⋊C4—182no—
428C22⋊C4—182no—
429C42—92no—
430C42C2×D3211yescharacteristic
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—62no—
442C22×C3—121no—
443C22×C3—121no—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—22no—
454C3×C4—41no—
455C3×C4—42no—
456C3×C4—41no—
457C3×C4—41no—
458C3×C4—121no—
459C3×C4—122no—
460C3×C4#91112yes—
461C3×C4#91112yes—
462C3×C4C22×Dic611yescharacteristic
463C3×C4C2×D3×Q811yescharacteristic
464C3×C4#101011yescharacteristic
465C3×C4#101011yescharacteristic
466Dic3—42no—
467Dic3—41no—
468Dic3—62no—
469Dic3—62no—
470Dic3—62no—
471Dic3—62no—
472Dic3—122no—
473Dic3—122no—
474Dic3—124no—
475Dic3—122no—
476Dic3—122no—
477C32#338411yescharacteristic, complemented, Sylow
478C23—21no—
479C23—61no—
480Q8—122no—
481Q8—182no—
482Q8—364no—
483Q8—721no—
484D4—21no—
485D4—32no—
486D4—61no—
487D4D3×Dic612yescomplemented
488C2×C4—21no—
489C2×C4—42no—
490C2×C4—61no—
491C2×C4—62no—
492C2×C4—92no—
493C2×C4—92no—
494C2×C4—122no—
495C2×C4—182no—
496C2×C4—364no—
497C2×C4—722no—
498C2×C4#381111yescharacteristic
499C2×C4#381111yescharacteristic
500C2×C4C22×D3211yescharacteristic
501C8—32no—
502C8—61no—
503C8—62no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—44no—
508C2×C3—42no—
509C2×C3—42no—
510C2×C3—122no—
511C2×C3D4×Dic611yescharacteristic
512C2×C3#563211yescharacteristic
513C2×C3C2×#91111yescharacteristic
514C2×C3C2×#91111yescharacteristic
515C2×C3#577011yescharacteristic
516C2×C3#577811yescharacteristic
517D3—42no—
518C22—22no—
519C22—41no—
520C22—41no—
521C22—62no—
522C22—121no—
523C22—121no—
524C22C2×#381111yescharacteristic
525C4—21no—
526C4—41no—
527C4—121no—
528C4—122no—
529C4—182no—
530C4—182no—
531C4—362no—
532C4#6392712yes—
533C4C2×D3×Dic611yescharacteristic
534C4#6429811yescharacteristic
535C3—21no—
536C3#7957611yescharacteristic, complemented
537C3#8095911yescharacteristic, complemented
538C2—42no—
539C2—122no—
540C2#1059491511yescharacteristic
541C2C2×#6392711yescharacteristic
542C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
2. #10593904C2semidirect
4. C3×#5007C2semidirect
5. #10591495C2semidirect
7. #10590563C2semidirect
8. #10590473C2semidirect
9. #10590303C2semidirect
10. #10590296C2semidirect
11. #10590268C2semidirect
54. #5007D3semidirect
88. C3×#213Q8semidirect
168. C32×D4C2×Q8semidirect
190. C3×C3⋊C8C2×Q8semidirect
250. #213Dic6semidirect
340. C3×D4C2×Dic6semidirect
341. C3×D4D3×Q8semidirect
393. C3⋊C8C2×Dic6semidirect
477. C32#3384semidirect
487. D4D3×Dic6semidirect
536. C3#79576semidirect
537. C3#80959semidirect

Maximal subgroups

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

subgroupindex
#105960142
#105939042
C3×C4×#2132
C3×#50072
#105914952
#105914362
#105905632
#105904732
#105903032
#105902962
#105902682
#809593
#795763