Finite Group Databasebeta

← #11870872

Subgroups — #11870872

Order 1152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5624C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3#10592745C211yesmaximal, characteristic, complemented
4C3×#5044C211yesmaximal, characteristic, complemented
5#10591568C212yesmaximal, complemented
6#10591536C212yesmaximal, complemented
7#10591168C211yesmaximal, characteristic
8#10591091C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590468C212yesmaximal, complemented
11#10590456C212yesmaximal, complemented
12#83141—31nomaximal
13#81453—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624—21no—
16C32×C22⋊Q8C2211yescharacteristic
17C2×#3755C2212yes—
18C3×#947C2211yescharacteristic, complemented
19C3×Q8×Dic3C2211yescharacteristic, complemented
20C3×#930C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C3×#898—21no—
24C3×#893C2211yescharacteristic, complemented
25C3×#892—21no—
26C3×#890C2211yescharacteristic, complemented
27C3×#886—21no—
28C3×#67⋊C4—21no—
29C2×#3722—21no—
30#63894—21no—
31#63894—21no—
32#63894C2212yes—
33#63894C2212yes—
34C2×#3714C2212yes—
35#63657C2211yescharacteristic
36#63636C2212yes—
37C3×#835C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#807C2212yescomplemented
40#63574C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63564C2212yes—
43#63562C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C3×#529—31no—
46#5624D311yescharacteristic, complemented
47C2×#893—31no—
48C2×C4×D12—31no—
49C3×#484—31no—
50#5066—32no—
51#5057—32no—
52#5046—31no—
53#5046—31no—
54#5046—61no—
55#5044D311yescharacteristic, complemented
56#5036—31no—
57#5034—31no—
58C4×#215—32no—
59C4×#213—32no—
60#4968—31no—
61#4925—31no—
62#4891—32no—
63#4872—32no—
64#4819—32no—
65#4788—32no—
66#4732—31no—
67#4718—31no—
68C23×C3⋊D3—21no—
69C2×C32×Q8C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—24no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3D411yescharacteristic
77C22×C3×Dic3D411yescharacteristic
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×#624—22no—
81C2×#624—22no—
82C2×#624—44no—
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86#3755—24no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×(C2×D3)⋊C4—21no—
89C3×(C2×D3)⋊C4—21no—
90C3×(C2×D3)⋊C4—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4⋊Dic3C2312yes—
97C3×Dic3⋊C4—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104#3722—22no—
105#3722—22no—
106#3714—24no—
107#3105—91noSylow
108C22×D12—31no—
109C22×D12—31no—
110C22×D12—61no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C3×#126—61no—
114C3×#125—31no—
115C3×#124—31no—
116C3×#123—61no—
117C3×C22⋊Q8—21no—
118C3×C22⋊Q8C2×D311yescharacteristic
119C3×C22⋊Q8C2×D311yescharacteristic
120C3×#121—31no—
121C3×C4×Q8—31no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C3×#117—61no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C42—31no—
127#947C2×D311yescharacteristic, complemented
128Q8×Dic3C2×D311yescharacteristic, complemented
129C2×#215—32no—
130C2×#215—32no—
131C2×#215—62no—
132C2×#213—32no—
133#930C2×D311yescharacteristic
134C2×(C2×D3)⋊C4—61no—
135C2×(C2×D3)⋊C4—61no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×C4×Dic3C2×D311yescharacteristic
138C2×D24—32no—
139#898—21no—
140#893—32no—
141#893—32no—
142#893—61no—
143#893—61no—
144#893C2×D311yescharacteristic, complemented
145#892—21no—
146#890C2×D311yescharacteristic, complemented
147#886—21no—
148#67⋊C4—21no—
149C4×D12—32no—
150C4×D12—32no—
151C4×D12—61no—
152C4×D12—61no—
153C3×#107—32no—
154C3×#103—32no—
155C3×C22⋊C8—31no—
156#835C2×D312yescomplemented
157#832—32no—
158#830—31no—
159#830—31no—
160#830—61no—
161#830C2×D311yescharacteristic
162#821—32no—
163Dic3⋊C8—32no—
164C8×Dic3—32no—
165#809—32no—
166#809—32no—
167#809—32no—
168#809—32no—
169#809—62no—
170#808—32no—
171#808—32no—
172#807C2×D312yescomplemented
173C4⋊(C3⋊C8)—32no—
174C4×C3⋊C8—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3⋊D3—24no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—42no—
179C22×C3⋊D3—42no—
180C22×C3×D3—21no—
181C32×Q8—22no—
182C2×C32×C4—22no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)#4114yes—
190C3×#67—42no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×D12—22no—
201C3×C4×D3—42no—
202#624—44no—
203#624—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#529—31no—
207C2×C4×D4—91no—
208#484—31no—
209#481—91no—
210#478—92no—
211#463—92no—
212#450—91no—
213#447—91no—
214C4×SD16—92no—
215C4×D8—92no—
216#431—91no—
217C23×D3—61no—
218C23×D3—61no—
219C23×D3—121no—
220C2×C3×Q8—21no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×D4—31no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—21no—
233C22×Dic3—21no—
234C22×Dic3#6711yescharacteristic
235C22×Dic3#6711yescharacteristic
236C2×D12—32no—
237C2×D12—32no—
238C2×D12—62no—
239C2×D12—64no—
240C2×D12—64no—
241C2×D12—61no—
242C2×D12—61no—
243C2×D12—124no—
244C2×D12—121no—
245C2×D12C22×D311yescharacteristic
246C2×C4×D3—21no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×C4×D3—124no—
252C2×C4×D3—124no—
253C2×C3×C8—32no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—32no—
259C3×C4⋊C4—41no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C22×D311yescharacteristic
266C3×C22⋊C4—21no—
267C3×C22⋊C4—21no—
268C3×C22⋊C4—41no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—61no—
278#215—64no—
279#215—64no—
280#215—124no—
281#213—64no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—21no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—21no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3C22×D312yes—
294C4⋊Dic3C22×D311yescharacteristic
295Dic3⋊C4—21no—
296C4×Dic3—21no—
297C4×Dic3#6711yescharacteristic
298C4×Dic3#6711yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8—32no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—62no—
304C2×C3⋊C8C22×D312yes—
305D24—64no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32#13512yes—
309C22×C32C22×D411yescharacteristic
310C2×C3⋊D3—24no—
311C2×C3⋊D3—48no—
312C2×C3⋊D3—42no—
313C2×C3⋊D3—42no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4—41no—
320C32×C4C2×#4112yes—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3AGL(1,ℤ/8)12yes—
327C22×D4—91no—
328C23×C4—181no—
329C2×SD16—92no—
330C2×D8—92no—
331#126—61no—
332#125—31no—
333#124—31no—
334#123—61no—
335C22⋊Q8D3211yescharacteristic
336#121—31no—
337C4×Q8—31no—
338C4×D4—31no—
339C4×D4—61no—
340C4×D4—92no—
341C4×D4—92no—
342C4×D4—181no—
343C4×D4—181no—
344#117—61no—
345C2×C4⋊C4—31no—
346C2×C22⋊C4—181no—
347C2×C42—31no—
348#107—32no—
349#106—92no—
350C4⋊C8—92no—
351#103—32no—
352#102—92no—
353#102—92no—
354#102—92no—
355C22⋊C8—31no—
356C22⋊C8—91no—
357C4×C8—92no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3D3×D411yescharacteristic
361C23×C3C2×#6711yescharacteristic
362C22×D3—21no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—122no—
368C22×D3—124no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—242no—
374C22×D3—242no—
375C3×Q8—22no—
376C3×Q8—22no—
377C3×Q8—42no—
378C3×D4—62no—
379C3×D4—122no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—42no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—62no—
399C2×C3×C4—122no—
400C2×C3×C4—122no—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—42no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—42no—
411C2×Dic3C2×#6711yescharacteristic
412C2×Dic3C2×#6711yescharacteristic
413C2×Dic3C2×#6711yescharacteristic
414C2×Dic3C2×#6711yescharacteristic
415D12—22no—
416D12—34no—
417D12—34no—
418D12—64no—
419D12—64no—
420D12—64no—
421D12—62no—
422D12—62no—
423D12—122no—
424D12—124no—
425C4×D3—42no—
426C4×D3—124no—
427C4×D3—124no—
428C4×D3—124no—
429C4×D3—124no—
430C3×C8—62no—
431C3⋊C8—22no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C2×C32—22no—
436C2×C32#52511yescharacteristic
437C2×C32C2×#13511yescharacteristic
438C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
439C3⋊D3—44no—
440C3×D3—81no—
441C24—181no—
442C2×Q8C2×D3211yescharacteristic
443C2×D4—31no—
444C2×D4—61no—
445C2×D4—92no—
446C2×D4—184no—
447C2×D4—181no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—182no—
453C22×C4—182no—
454C22×C4—364no—
455C22×C4C2×D3211yescharacteristic
456SD16—184no—
457D8—184no—
458C2×C8—32no—
459C2×C8—92no—
460C4⋊C4—21no—
461C4⋊C4—31no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4C2×D3211yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—61no—
470C22⋊C4—61no—
471C22⋊C4—61no—
472C22⋊C4—61no—
473C22⋊C4—182no—
474C22⋊C4—182no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—61no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—22no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3#91912yes—
492C22×C3#95012yes—
493C22×C3C2×D3×D411yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—124no—
501C2×D3—128no—
502C2×D3—128no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—242no—
508C2×D3—242no—
509C2×D3—248no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—32no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4—41no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—61no—
520C3×C4—61no—
521C3×C4—61no—
522C3×C4—81no—
523C3×C4—81no—
524C3×C4—121no—
525C3×C4—122no—
526C3×C4D3×#4112yes—
527C3×C4D3×#4112yes—
528Dic3—21no—
529Dic3—21no—
530Dic3—21no—
531Dic3—42no—
532Dic3—41no—
533Dic3#94912yes—
534C32#310511yescharacteristic, complemented, Sylow
535C23—61no—
536C23—184no—
537C23—182no—
538C23—362no—
539C23—362no—
540C23D3×#6711yescharacteristic
541Q8—22no—
542D4—62no—
543D4—94no—
544D4—122no—
545D4—184no—
546D4—182no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—122no—
559C2×C4—122no—
560C2×C4—364no—
561C2×C4—364no—
562C2×C4D3×#6711yescharacteristic
563C2×C4C22×D3211yescharacteristic
564C8—62no—
565C8—182no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—241no—
573C2×C3#565611yescharacteristic
574C2×C3C2×#91911yescharacteristic
575C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
576C2×C3C2×#94911yescharacteristic
577C2×C3C2×#95011yescharacteristic
578C2×C3#582811yescharacteristic
579D3—81no—
580D3—124no—
581D3—124no—
582D3—244no—
583C22—21no—
584C22—21no—
585C22—121no—
586C22—121no—
587C22—121no—
588C22—184no—
589C22—368no—
590C22—362no—
591C22—362no—
592C22#6394912yes—
593C22C2×D3×#6711yescharacteristic
594C4—21no—
595C4—32no—
596C4—41no—
597C4—41no—
598C4—61no—
599C4—61no—
600C4—61no—
601C4—121no—
602C4—122no—
603C4#6431212yes—
604C3—21no—
605C3#8145311yescharacteristic, complemented
606C3#8314111yescharacteristic, complemented
607C2—22no—
608C2—241no—
609C2—364no—
610C2#1059515911yescharacteristic
611C2C2×#6394911yescharacteristic
612C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10591168C2
hypercenterC22⋊Q8D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5624C2semidirect
2. C2×#63894C2semidirect
3. #10592745C2semidirect
4. C3×#5044C2semidirect
5. #10591568C2semidirect
6. #10591536C2semidirect
8. #10591091C2semidirect
9. #10591053C2semidirect
10. #10590468C2semidirect
11. #10590456C2semidirect
18. C3×#947C22semidirect
19. C3×Q8×Dic3C22semidirect
24. C3×#893C22semidirect
26. C3×#890C22semidirect
37. C3×#835C22semidirect
39. C3×#807C22semidirect
40. #63574C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
43. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. #5624D3semidirect
55. #5044D3semidirect
127. #947C2×D3semidirect
128. Q8×Dic3C2×D3semidirect
144. #893C2×D3semidirect
146. #890C2×D3semidirect
156. #835C2×D3semidirect
172. #807C2×D3semidirect
534. C32#3105semidirect
605. C3#81453semidirect
606. C3#83141semidirect

Maximal subgroups

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

subgroupindex
C3×#56242
C2×#638942
#105927452
C3×#50442
#105915682
#105915362
#105911682
#105910912
#105910532
#105904682
#105904562
#831413
#814533