Finite Group Databasebeta

← #11870876

Subgroups — #11870876

Order 1152.

967 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594965C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic, complemented
3#10592417C211yesmaximal, characteristic, complemented
4C3×#4735C211yesmaximal, characteristic, complemented
5C3×#4731C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic
7#10591132C211yesmaximal, characteristic, complemented
8#10590782C212yesmaximal, complemented
9#10590775C212yesmaximal, complemented
10#10590750C212yesmaximal, complemented
11#10590740C212yesmaximal, complemented
12#81309—31nomaximal
13#80133—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C3×#930C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C3×#924C2211yescharacteristic
20C2×C3×#204C2212yes—
21#67⋊Dic3—21no—
22#63962—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63898—21no—
25#63898—21no—
26#63898C2212yes—
27#63898C2212yes—
28#63898C2211yescharacteristic, complemented
29#63878—21no—
30#63872C2211yescharacteristic, complemented
31#63863C2211yescharacteristic, complemented
32#63862—21no—
33#63843C2211yescharacteristic, complemented
34C2×#3713C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63657C2211yescharacteristic
37#63641C2212yescomplemented
38C8×C3⋊Dic3C2212yescomplemented
39C3×#821C2212yes—
40C3×#821C2212yescomplemented
41C3×#817C2212yescomplemented
42#63576C2212yescomplemented
43#63565C2212yescomplemented
44#63562C2212yes—
45C2×D4×Dic3—31no—
46#5624—31no—
47#5600—31no—
48C2×#893—31no—
49C3×#481—31no—
50C3×#450—31no—
51#5217—31no—
52#5165—32no—
53Dic3×SD16—32no—
54#5044—31no—
55#5036—31no—
56#4970—31no—
57#4871—32no—
58#4852—32no—
59#4787—32no—
60#4763—32no—
61#4756—32no—
62#4756—32no—
63#4735D311yescharacteristic, complemented
64#4731D311yescharacteristic, complemented
65#4718—31no—
66#4718—31no—
67#4718—61no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3D411yescharacteristic
71C22×C3⋊Dic3D411yescharacteristic
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C2×C3×D12—21no—
75C2×C3×D12—24no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×Dic6C2311yescharacteristic
79C2×D3×Dic3—22no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—21no—
82C2×D3×Dic3—44no—
83C2×C32×C8C2312yes—
84C4×C3⋊Dic3D411yescharacteristic
85C4×C3⋊Dic3D411yescharacteristic
86C4×C3⋊Dic3C2311yescharacteristic
87C4×C3⋊Dic3C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2312yes—
89C3×#217—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×C4⋊Dic3C2312yes—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—21no—
96C3×#204—24no—
97Dic3⋊Dic3—21no—
98Dic3⋊Dic3—21no—
99Dic3⋊Dic3—21no—
100(C2×D3)⋊Dic3—21no—
101(C2×D3)⋊Dic3—21no—
102(C2×D3)⋊Dic3—21no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105Dic32—21no—
106#3713—24no—
107#3105—91noSylow
108C22×C3×D4—31no—
109C23×Dic3—61no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—61no—
112C2×C3×SD16—32no—
113C3×C22⋊Q8—31no—
114C3×#121—31no—
115C2×C3×C4⋊C4—31no—
116C2×#217—61no—
117#947—31no—
118Q8×Dic3—31no—
119#936—31no—
120#935—61no—
121D4×Dic3—32no—
122D4×Dic3—32no—
123D4×Dic3—31no—
124D4×Dic3—61no—
125D4×Dic3—61no—
126D4×Dic3—61no—
127C2×#213—32no—
128C2×#213—32no—
129#930C2×D311yescharacteristic
130C2×(C2×D3)⋊C4—61no—
131C2×C4⋊Dic3C2×D311yescharacteristic
132#924C2×D311yescharacteristic
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—61no—
136C2×#204C2×D312yes—
137#898—61no—
138#893—32no—
139#893—32no—
140#893—31no—
141#893—61no—
142#893—61no—
143#892—61no—
144#890—31no—
145#890—31no—
146#887—31no—
147#886—61no—
148#67⋊C4—61no—
149#879—61no—
150#877—61no—
151C3×#106—32no—
152C3×#102—32no—
153C3×#102—32no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8C2×D311yescharacteristic
156C3×C22⋊C8C2×D311yescharacteristic
157#835—32no—
158#832—32no—
159#830—31no—
160#830—31no—
161#830—61no—
162#821C2×D312yes—
163#821C2×D312yescomplemented
164#817C2×D312yescomplemented
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—62no—
168C8×Dic3—32no—
169C8×Dic3—32no—
170C8×Dic3—62no—
171#810—32no—
172#809—32no—
173#807—32no—
174#807—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—22no—
178C22×C3×D3—21no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3C2×D411yescharacteristic
187C2×C3⋊Dic3C2×D411yescharacteristic
188C2×C3⋊Dic3C2×D411yescharacteristic
189C2×C3⋊Dic3C2×D411yescharacteristic
190C3×#67—42no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—42no—
196C3×D12—24no—
197C3×D12—22no—
198C3×D12—22no—
199C3×D12#4114yes—
200C3×Dic6—22no—
201D3×Dic3—44no—
202D3×Dic3—42no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3⋊(C3⋊C8)—22no—
206#529—91no—
207C2×C4×D4—91no—
208#484—91no—
209#481—31no—
210#478—92no—
211#463—92no—
212#450—31no—
213#447—91no—
214C4×SD16—92no—
215C4×D8—92no—
216#431—91no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×Q8—31no—
220C2×C3×D4—32no—
221C2×C3×D4—31no—
222C2×C3×D4—64no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—21no—
230C22×Dic3—21no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—62no—
239C22×Dic3—62no—
240C22×Dic3—124no—
241C2×D12—21no—
242C2×D12—24no—
243C2×D12C22×D311yescharacteristic
244C2×D12C22×D312yes—
245C2×C4×D3—61no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—124no—
249C2×Dic6C22×D311yescharacteristic
250C3×SD16—64no—
251C2×C3×C8—22no—
252C2×C3×C8C22×D312yes—
253C2×C3×C8C22×D312yes—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C22⋊C4—61no—
260C3×C22⋊C4—61no—
261#217—21no—
262#217—61no—
263#217—61no—
264#217—61no—
265#217—62no—
266#217—62no—
267#213—64no—
268#213—64no—
269(C2×D3)⋊C4—21no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275C4⋊Dic3—21no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3C22×D311yescharacteristic
280C4⋊Dic3C22×D312yes—
281C4⋊Dic3C22×D311yescharacteristic
282Dic3⋊C4—21no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285Dic3⋊C4—61no—
286C4×Dic3—31no—
287C4×Dic3—31no—
288C4×Dic3—31no—
289C4×Dic3—31no—
290C4×Dic3—31no—
291C4×Dic3—31no—
292C4×Dic3—31no—
293C4×Dic3—31no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3—61no—
298C4×Dic3—61no—
299C4×Dic3—61no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—62no—
303#204—24no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32#13512yes—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—24no—
309C2×C3×D3—48no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—21no—
316C32×C4C2×#4112yes—
317C3⋊Dic3—21no—
318C3⋊Dic3—21no—
319C3⋊Dic3—21no—
320C3⋊Dic3AGL(1,ℤ/8)12yes—
321C3×Dic3—41no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C3×Dic3—41no—
325C22×D4—31no—
326C23×C4—181no—
327C2×SD16—32no—
328C2×D8—92no—
329#126—181no—
330#125—91no—
331#124—91no—
332#123—181no—
333C22⋊Q8—31no—
334#121—31no—
335C4×Q8—91no—
336C4×D4—92no—
337C4×D4—92no—
338C4×D4—91no—
339C4×D4—181no—
340C4×D4—181no—
341C4×D4—181no—
342#117—181no—
343C2×C4⋊C4—31no—
344C2×C22⋊C4—181no—
345C2×C42—91no—
346#107—92no—
347#106—32no—
348C4⋊C8—92no—
349#103—92no—
350#102—32no—
351#102—32no—
352#102—92no—
353C22⋊C8—91no—
354C22⋊C8D3211yescharacteristic
355C4×C8—92no—
356C23×C3—21no—
357C23×C3—64no—
358C23×C3—62no—
359C23×C3—61no—
360C23×C3—122no—
361C23×C3—122no—
362C23×C3D3×D411yescharacteristic
363C23×C3D3×D411yescharacteristic
364C22×D3—24no—
365C22×D3—22no—
366C22×D3—21no—
367C22×D3—42no—
368C22×D3—42no—
369C3×Q8—62no—
370C3×D4—34no—
371C3×D4—64no—
372C3×D4—62no—
373C3×D4—62no—
374C3×D4—122no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—42no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—62no—
384C2×C3×C4—122no—
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389#67—42no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—31no—
395C2×Dic3—31no—
396C2×Dic3—31no—
397C2×Dic3—31no—
398C2×Dic3—31no—
399C2×Dic3—31no—
400C2×Dic3—31no—
401C2×Dic3—31no—
402C2×Dic3—42no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—64no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—124no—
415C2×Dic3—124no—
416D12—24no—
417D12—22no—
418D12—22no—
419D12#23714yes—
420C4×D3—122no—
421C4×D3—124no—
422C4×D3—124no—
423Dic6—22no—
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—42no—
427C3⋊C8—62no—
428C3⋊C8—62no—
429C3⋊C8—122no—
430C2×C32—22no—
431C2×C32#52511yescharacteristic
432C2×C32C2×#13511yescharacteristic
433C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
434C3×D3—44no—
435C3×D3—81no—
436C24—61no—
437C2×Q8—31no—
438C2×D4—32no—
439C2×D4—31no—
440C2×D4—64no—
441C2×D4—61no—
442C2×D4—61no—
443C22×C4—61no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—181no—
447C22×C4—182no—
448C22×C4—182no—
449C22×C4—364no—
450C22×C4C2×D3211yescharacteristic
451SD16—64no—
452D8—184no—
453C2×C8—92no—
454C2×C8C2×D3212yes—
455C4⋊C4—31no—
456C4⋊C4—32no—
457C4⋊C4—31no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C4⋊C4—181no—
463C22⋊C4—61no—
464C22⋊C4—61no—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22⋊C4—181no—
468C22⋊C4—181no—
469C22⋊C4—181no—
470C42—91no—
471C42—91no—
472C42—91no—
473C42—91no—
474C42—181no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—64no—
484C22×C3—128no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3#91612yes—
491C22×C3#91612yes—
492C22×C3C2×D3×D411yescharacteristic
493C22×C3C2×D3×D411yescharacteristic
494C2×D3—24no—
495C2×D3—48no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—22no—
504C3×C4—41no—
505C3×C4—121no—
506C3×C4—121no—
507C3×C4—122no—
508C3×C4—121no—
509C3×C4C2×#23712yes—
510C3×C4D3×#4112yes—
511Dic3—32no—
512Dic3—32no—
513Dic3—41no—
514Dic3—42no—
515Dic3—41no—
516Dic3—41no—
517Dic3—62no—
518Dic3—62no—
519Dic3—62no—
520Dic3—61no—
521Dic3—61no—
522Dic3—61no—
523Dic3—61no—
524Dic3—61no—
525Dic3—61no—
526Dic3—121no—
527C32#310511yescharacteristic, complemented, Sylow
528C23—64no—
529C23—62no—
530C23—61no—
531C23—122no—
532C23—122no—
533C23#380211yescharacteristic
534Q8—62no—
535D4—34no—
536D4—64no—
537D4—62no—
538D4—62no—
539D4—122no—
540C2×C4—22no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—91no—
546C2×C4—91no—
547C2×C4—91no—
548C2×C4—91no—
549C2×C4—122no—
550C2×C4—182no—
551C2×C4—182no—
552C2×C4—364no—
553C2×C4—362no—
554C2×C4—364no—
555C2×C4#380211yescharacteristic
556C2×C4C22×D3211yescharacteristic
557C8—22no—
558C8—182no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—42no—
565C2×C3—124no—
566C2×C3—241no—
567C2×C3#558611yescharacteristic
568C2×C3#565611yescharacteristic
569C2×C3C2×#91611yescharacteristic
570C2×C3C2×#91611yescharacteristic
571C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
572C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
573D3—44no—
574D3—81no—
575C22—21no—
576C22—21no—
577C22—64no—
578C22—128no—
579C22—122no—
580C22—122no—
581C22—121no—
582C22—121no—
583C22—121no—
584C22#6380912yes—
585C22C2×#380211yescharacteristic
586C4—21no—
587C4—92no—
588C4—121no—
589C4—121no—
590C4—122no—
591C4—121no—
592C4—181no—
593C4—181no—
594C4—181no—
595C4D3×#23712yes—
596C3—21no—
597C3#8013311yescharacteristic, complemented
598C3#8130911yescharacteristic, complemented
599C2—22no—
600C2—124no—
601C2—241no—
602C2#1059408211yescharacteristic
603C2C2×#6380911yescharacteristic
604C2#1059471611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10591160C2
hypercenterC22⋊C8D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594965C2semidirect
2. C2×#63898C2semidirect
3. #10592417C2semidirect
4. C3×#4735C2semidirect
5. C3×#4731C2semidirect
7. #10591132C2semidirect
8. #10590782C2semidirect
9. #10590775C2semidirect
10. #10590750C2semidirect
11. #10590740C2semidirect
28. #63898C22semidirect
30. #63872C22semidirect
31. #63863C22semidirect
33. #63843C22semidirect
37. #63641C22semidirect
38. C8×C3⋊Dic3C22semidirect
40. C3×#821C22semidirect
41. C3×#817C22semidirect
42. #63576C22semidirect
43. #63565C22semidirect
63. #4735D3semidirect
64. #4731D3semidirect
163. #821C2×D3semidirect
164. #817C2×D3semidirect
527. C32#3105semidirect
597. C3#80133semidirect
598. C3#81309semidirect

Maximal subgroups

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

subgroupindex
#105949652
C2×#638982
#105924172
C3×#47352
C3×#47312
#105911602
#105911322
#105907822
#105907752
#105907502
#105907402
#813093
#801333