Finite Group Databasebeta

← #11870866

Subgroups — #11870866

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5600C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3#10592735C211yesmaximal, characteristic
4C3×#5034C211yesmaximal, characteristic, complemented
5#10591432C212yesmaximal, complemented
6#10591400C212yesmaximal, complemented
7#10591183C211yesmaximal, characteristic, complemented
8#10591132C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590470C212yesmaximal, complemented
11#10590458C212yesmaximal, complemented
12#83141—31nomaximal
13#81309—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624—21no—
16C32×#121C2211yescharacteristic
17C2×#3753C2212yes—
18C3×#936C2211yescharacteristic, complemented
19C3×#935—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2211yescharacteristic, complemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26C3×#887C2211yescharacteristic, complemented
27C3×#879—21no—
28C3×#877—21no—
29C2×#3722—21no—
30#63894—21no—
31#63894—21no—
32#63894C2212yes—
33#63894C2212yes—
34C2×#3717C2212yes—
35#63657C2211yescharacteristic
36#63636C2212yes—
37C3×#832C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#808C2212yescomplemented
40#63576C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63565C2212yescomplemented
43#63564C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C3×#529—31no—
46#5600D311yescharacteristic, complemented
47C2×#893—31no—
48C2×C4×D12—31no—
49C3×#481—31no—
50#5066—32no—
51#5057—32no—
52#5046—31no—
53#5044—31no—
54#5036—31no—
55#5036—31no—
56#5036—61no—
57#5034D311yescharacteristic, complemented
58C4×#215—32no—
59C4×#213—32no—
60#4970—31no—
61#4925—31no—
62#4871—32no—
63#4852—32no—
64#4787—32no—
65#4756—32no—
66#4731—31no—
67#4718—31no—
68C23×C3⋊D3—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—24no—
74C2×C4⋊(C3⋊D3)C2312yes—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×C3×Dic6C2311yescharacteristic
80C2×#624—22no—
81C2×#624—22no—
82C2×#624—44no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85#3753—24no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—21no—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2312yes—
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
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#3717—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—31no—
118C3×#121—21no—
119C3×#121C2×D311yescharacteristic
120C3×#121C2×D311yescharacteristic
121C3×C4×Q8—31no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C3×#117—61no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C42—31no—
127C2×#215—32no—
128#936C2×D311yescharacteristic, complemented
129#935—21no—
130D4×Dic3—21no—
131D4×Dic3C2×D311yescharacteristic, complemented
132C2×#213—32no—
133C2×#213—32no—
134C2×#213—62no—
135C2×(C2×D3)⋊C4—61no—
136C2×(C2×D3)⋊C4—61no—
137C2×C4⋊Dic3C2×D311yescharacteristic
138#924C2×D311yescharacteristic
139C2×C4×Dic3C2×D311yescharacteristic
140C2×#204—32no—
141#893—32no—
142#893—32no—
143#893—61no—
144#893—61no—
145#890C2×D311yescharacteristic, complemented
146#887C2×D311yescharacteristic, complemented
147#879—21no—
148#877—21no—
149C4×D12—32no—
150C4×D12—32no—
151C4×D12—61no—
152C4×D12—61no—
153C3×#106—32no—
154C3×#102—32no—
155C3×C22⋊C8—31no—
156#835—32no—
157#832C2×D312yescomplemented
158#830—31no—
159#830—31no—
160#830—61no—
161#830C2×D311yescharacteristic
162#821—32no—
163Dic3⋊C8—32no—
164C8×Dic3—32no—
165#810—32no—
166#809—32no—
167#809—32no—
168#809—32no—
169#809—62no—
170#808C2×D312yescomplemented
171#807—32no—
172#807—32no—
173C4⋊(C3⋊C8)—32no—
174C4×C3⋊C8—32no—
175C23×C32—21no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—24no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—42no—
180C22×C3⋊D3—42no—
181C32×D4—22no—
182C32×D4—42no—
183C2×C32×C4—22no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)#4114yes—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C3×Dic6—22no—
202#624—44no—
203#624—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#529—31no—
207C2×C4×D4—91no—
208#484—91no—
209#481—31no—
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—31no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—41no—
225C2×C3×D4C22×D311yescharacteristic
226C2×C3×D4C22×D311yescharacteristic
227C22×C3×C4—21no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—61no—
231C22×C3×C4—61no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3#6711yescharacteristic
237C22×Dic3#6711yescharacteristic
238C2×D12—32no—
239C2×D12—32no—
240C2×D12—62no—
241C2×D12—64no—
242C2×D12—64no—
243C2×D12—61no—
244C2×D12—61no—
245C2×D12—124no—
246C2×D12—121no—
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×Dic6C22×D311yescharacteristic
254C2×C3×C8—32no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—61no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C22⋊C4—21no—
266C3×C22⋊C4—21no—
267C3×C22⋊C4—41no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—31no—
276C3×C42—61no—
277#217—21no—
278#217—21no—
279#217—21no—
280#217—21no—
281#215—64no—
282#213—64no—
283#213—64no—
284#213—124no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288(C2×D3)⋊C4—62no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3C22×D311yescharacteristic
292C4⋊Dic3C22×D312yes—
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
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—
305#204—64no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32—41no—
311C22×C32#13512yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—24no—
314C2×C3⋊D3—48no—
315C2×C3⋊D3—42no—
316C2×C3⋊D3—42no—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4C2×#4112yes—
320C3×Dic3—21no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3—41no—
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⋊Q8—31no—
336#121D3211yescharacteristic
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—92no—
349#106—32no—
350C4⋊C8—92no—
351#103—92no—
352#102—32no—
353#102—92no—
354#102—92no—
355C22⋊C8—31no—
356C22⋊C8—91no—
357C4×C8—92no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—41no—
362C23×C3D3×D411yescharacteristic
363C23×C3C2×#6711yescharacteristic
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—122no—
369C22×D3—124no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—242no—
375C22×D3—242no—
376C3×Q8—62no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—42no—
380C3×D4—42no—
381C3×D4—42no—
382C3×D4—82no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—31no—
390C2×C3×C4—31no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—42no—
394C2×C3×C4—41no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—62no—
400C2×C3×C4—122no—
401C2×C3×C4—122no—
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—42no—
412C2×Dic3—42no—
413C2×Dic3C2×#6711yescharacteristic
414C2×Dic3C2×#6711yescharacteristic
415C2×Dic3C2×#6711yescharacteristic
416C2×Dic3C2×#6711yescharacteristic
417D12—34no—
418D12—34no—
419D12—64no—
420D12—64no—
421D12—64no—
422D12—62no—
423D12—62no—
424D12—122no—
425D12—124no—
426C4×D3—124no—
427C4×D3—124no—
428C4×D3—124no—
429C4×D3—124no—
430Dic6—22no—
431C3×C8—62no—
432C3⋊C8—22no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C3⋊C8—122no—
436C2×C32—22no—
437C2×C32—81no—
438C2×C32#52511yescharacteristic
439C2×C32C2×#13511yescharacteristic
440C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
441C3⋊D3—44no—
442C24—181no—
443C2×Q8—31no—
444C2×D4—21no—
445C2×D4—92no—
446C2×D4—184no—
447C2×D4—181no—
448C2×D4C2×D3211yescharacteristic
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4—182no—
454C22×C4—182no—
455C22×C4—364no—
456C22×C4C2×D3211yescharacteristic
457SD16—184no—
458D8—184no—
459C2×C8—32no—
460C2×C8—92no—
461C4⋊C4—32no—
462C4⋊C4—31no—
463C4⋊C4—61no—
464C4⋊C4—61no—
465C4⋊C4—61no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4C2×D3211yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—61no—
471C22⋊C4—61no—
472C22⋊C4—61no—
473C22⋊C4—61no—
474C22⋊C4—182no—
475C22⋊C4—182no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—31no—
480C42—61no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—81no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3#91612yes—
499C22×C3#95012yes—
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C22×#6711yescharacteristic
502C2×D3—64no—
503C2×D3—64no—
504C2×D3—124no—
505C2×D3—128no—
506C2×D3—128no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—242no—
512C2×D3—242no—
513C2×D3—248no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—22no—
517C3×C4—32no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—61no—
522C3×C4—61no—
523C3×C4—61no—
524C3×C4—81no—
525C3×C4—121no—
526C3×C4—121no—
527C3×C4—122no—
528C3×C4D3×#4112yes—
529C3×C4D3×#4112yes—
530Dic3—21no—
531Dic3—21no—
532Dic3—21no—
533Dic3—42no—
534Dic3—41no—
535Dic3—41no—
536Dic3#94912yes—
537C32#310511yescharacteristic, complemented, Sylow
538C23—21no—
539C23—184no—
540C23—182no—
541C23—362no—
542C23—362no—
543C23D3×#6711yescharacteristic
544Q8—62no—
545D4—22no—
546D4—42no—
547D4—94no—
548D4—184no—
549D4—182no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—62no—
561C2×C4—122no—
562C2×C4—122no—
563C2×C4—364no—
564C2×C4—364no—
565C2×C4D3×#6711yescharacteristic
566C2×C4C22×D3211yescharacteristic
567C8—62no—
568C8—182no—
569C2×C3—22no—
570C2×C3—22no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—42no—
575C2×C3—81no—
576C2×C3—81no—
577C2×C3—161no—
578C2×C3#565611yescharacteristic
579C2×C3C2×#91611yescharacteristic
580C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
581C2×C3C2×#94911yescharacteristic
582C2×C3C2×#95011yescharacteristic
583C2×C3#582811yescharacteristic
584D3—124no—
585D3—124no—
586D3—244no—
587C22—21no—
588C22—21no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—184no—
593C22—368no—
594C22—362no—
595C22—362no—
596C22#6393512yes—
597C22C2×D3×#6711yescharacteristic
598C4—21no—
599C4—32no—
600C4—41no—
601C4—61no—
602C4—61no—
603C4—61no—
604C4—121no—
605C4—122no—
606C4—121no—
607C4#6431212yes—
608C3—21no—
609C3#8130911yescharacteristic, complemented
610C3#8314111yescharacteristic, complemented
611C2—22no—
612C2—81no—
613C2—364no—
614C2C2×#6393511yescharacteristic
615C2#1059515911yescharacteristic
616C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radical#10592735C2
hypercenter#121D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5600C2semidirect
2. C2×#63894C2semidirect
4. C3×#5034C2semidirect
5. #10591432C2semidirect
6. #10591400C2semidirect
7. #10591183C2semidirect
8. #10591132C2semidirect
9. #10591053C2semidirect
10. #10590470C2semidirect
11. #10590458C2semidirect
18. C3×#936C22semidirect
21. C3×D4×Dic3C22semidirect
25. C3×#890C22semidirect
26. C3×#887C22semidirect
37. C3×#832C22semidirect
39. C3×#808C22semidirect
40. #63576C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63565C22semidirect
44. Dic3×C3⋊C8C22semidirect
46. #5600D3semidirect
57. #5034D3semidirect
128. #936C2×D3semidirect
131. D4×Dic3C2×D3semidirect
145. #890C2×D3semidirect
146. #887C2×D3semidirect
157. #832C2×D3semidirect
170. #808C2×D3semidirect
537. C32#3105semidirect
609. C3#81309semidirect
610. C3#83141semidirect

Maximal subgroups

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

subgroupindex
C3×#56002
C2×#638942
#105927352
C3×#50342
#105914322
#105914002
#105911832
#105911322
#105910532
#105904702
#105904582
#831413
#813093