Finite Group Databasebeta

← #11870868

Subgroups — #11870868

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5600C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3#10592733C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic
5#10591431C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10591169C211yesmaximal, characteristic, complemented
8#10591103C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590469C212yesmaximal, complemented
11#10590453C212yesmaximal, complemented
12#83141—31nomaximal
13#79989—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C32×#121C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#936C2211yescharacteristic, complemented
19C3×#935—21no—
20C3×D4×Dic3—21no—
21C3×D4×Dic3C2211yescharacteristic, complemented
22C2×C3×#213C2212yes—
23C3×#924C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26C3×#887C2211yescharacteristic, complemented
27C3×#879—21no—
28C3×#877—21no—
29C2×(C2×D3)⋊Dic3—21no—
30Dic3×D12—21no—
31Dic3×D12—21no—
32Dic3×D12C2212yes—
33Dic3×D12C2212yes—
34C2×#3715C2212yes—
35#63659C2212yescomplemented
36#63657C2211yescharacteristic
37#63635C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#809C2212yes—
40#63575C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63566C2212yescomplemented
43#63562C2212yes—
44Dic3×C3⋊C8C2212yescomplemented
45C3×#529—31no—
46C2×D4×Dic3—31no—
47#5600D311yescharacteristic, complemented
48C2×C4×D12—31no—
49C3×#447—31no—
50#5218—31no—
51#5153—32no—
52Dic3×D8—32no—
53#5066—32no—
54#5057—32no—
55#5046—31no—
56#5044—31no—
57#5036D311yescharacteristic
58#5034—31no—
59#5034—31no—
60#5034—61no—
61C4×#215—32no—
62C4×#213—32no—
63#4925—31no—
64#4766—32no—
65#4758—32no—
66#4722—31no—
67#4718—31no—
68C23×C3×D3—21no—
69C2×C32×D4—21no—
70C2×C32×D4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C3⋊Dic3—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3D411yescharacteristic
75C22×C3×Dic3D411yescharacteristic
76C2×C3×D12—21no—
77C2×C3×D12—24no—
78C2×C3×D12C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C2×D3×Dic3—22no—
81C2×D3×Dic3—22no—
82C2×D3×Dic3—44no—
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217—21no—
91C3×#217—21no—
92C3×#213—24no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
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(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106#3715—24no—
107#3105—91noSylow
108C22×C3×D4—31no—
109C23×Dic3—61no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—61no—
112C2×C3×D8—32no—
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×C42—31no—
126C2×#217—61no—
127C2×#215—32no—
128#936C2×D311yescharacteristic, complemented
129#935—21no—
130D4×Dic3—21no—
131D4×Dic3—32no—
132D4×Dic3—32no—
133D4×Dic3—61no—
134D4×Dic3—61no—
135D4×Dic3C2×D311yescharacteristic, complemented
136C2×#214—32no—
137C2×#213C2×D312yes—
138C2×(C2×D3)⋊C4—61no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—61no—
142#924C2×D311yescharacteristic
143C2×C4×Dic3C2×D311yescharacteristic
144#890C2×D311yescharacteristic, complemented
145#887C2×D311yescharacteristic, complemented
146#879—21no—
147#877—21no—
148C4×D12—32no—
149C4×D12—32no—
150C4×D12—61no—
151C4×D12—61no—
152C3×#102—32no—
153C3×C22⋊C8—31no—
154#835—32no—
155#832—32no—
156#832—32no—
157#832—32no—
158#832—62no—
159#830—31no—
160#830—31no—
161#830—61no—
162#830C2×D311yescharacteristic
163#818—32no—
164#816—32no—
165Dic3⋊C8—32no—
166C8×Dic3—32no—
167#809—32no—
168#809C2×D312yes—
169#808—32no—
170#808—32no—
171#808—62no—
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
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—42no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C3×D12—24no—
199C3×D12—22no—
200C3×D12#4114yes—
201C3×Dic6—22no—
202D3×Dic3—44no—
203D3×Dic3—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#529—31no—
207C2×C4×D4—91no—
208#484—91no—
209#481—91no—
210#478—92no—
211#463—92no—
212#450—91no—
213#447—31no—
214C4×SD16—92no—
215C4×D8—92no—
216#431—91no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×Q8—31no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—32no—
224C2×C3×D4—41no—
225C2×C3×D4—64no—
226C2×C3×D4—61no—
227C2×C3×D4C22×D311yescharacteristic
228C2×C3×D4C22×D311yescharacteristic
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—31no—
232C22×C3×C4—61no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C22×Dic3—21no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—62no—
239C22×Dic3—62no—
240C22×Dic3—121no—
241C22×Dic3—124no—
242C22×Dic3#6711yescharacteristic
243C22×Dic3#6711yescharacteristic
244C2×D12—21no—
245C2×D12—24no—
246C2×D12C22×D312yes—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—124no—
250C2×Dic6C22×D311yescharacteristic
251C3×D8—64no—
252C2×C3×C8—32no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—31no—
255C3×C4⋊C4—61no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4C22×D311yescharacteristic
260C3×C4⋊C4C22×D311yescharacteristic
261C3×C22⋊C4—21no—
262C3×C22⋊C4—21no—
263C3×C22⋊C4—41no—
264C3×C22⋊C4—61no—
265C3×C22⋊C4—61no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4—61no—
268C3×C42—31no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42—61no—
273#217—21no—
274#217—21no—
275#217—21no—
276#217—21no—
277#217—62no—
278#217—62no—
279#215—64no—
280#214—64no—
281#213—24no—
282(C2×D3)⋊C4—62no—
283(C2×D3)⋊C4—62no—
284C4⋊Dic3—21no—
285C4⋊Dic3—32no—
286C4⋊Dic3—32no—
287C4⋊Dic3—62no—
288C4⋊Dic3—61no—
289C4⋊Dic3—61no—
290C4⋊Dic3—121no—
291C4⋊Dic3C22×D311yescharacteristic
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294Dic3⋊C4—21no—
295C4×Dic3—21no—
296C4×Dic3#6711yescharacteristic
297C4×Dic3#6711yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8C22×D312yes—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32#13512yes—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—24no—
312C2×C3×D3—48no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C32×C4—21no—
316C32×C4—41no—
317C32×C4C2×#4112yes—
318C3⋊Dic3—42no—
319C3×Dic3—21no—
320C3×Dic3—21no—
321C3×Dic3—21no—
322C3×Dic3—41no—
323C3×Dic3—41no—
324C3×Dic3AGL(1,ℤ/8)12yes—
325C22×D4—31no—
326C23×C4—181no—
327C2×SD16—92no—
328C2×D8—32no—
329#126—61no—
330#125—31no—
331#124—31no—
332#123—61no—
333C22⋊Q8—31no—
334#121D3211yescharacteristic
335C4×Q8—31no—
336C4×D4—31no—
337C4×D4—61no—
338C4×D4—92no—
339C4×D4—92no—
340C4×D4—181no—
341C4×D4—181no—
342#117—61no—
343C2×C4⋊C4—91no—
344C2×C22⋊C4—181no—
345C2×C42—31no—
346#107—92no—
347#106—92no—
348C4⋊C8—92no—
349#103—92no—
350#102—32no—
351#102—92no—
352#102—92no—
353C22⋊C8—31no—
354C22⋊C8—91no—
355C4×C8—92no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—41no—
360C23×C3—64no—
361C23×C3—62no—
362C23×C3—122no—
363C23×C3—122no—
364C23×C3D3×D411yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C22×D3—24no—
367C22×D3—22no—
368C22×D3—42no—
369C22×D3—42no—
370C3×Q8—62no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—34no—
374C3×D4—42no—
375C3×D4—42no—
376C3×D4—42no—
377C3×D4—64no—
378C3×D4—62no—
379C3×D4—82no—
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—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—122no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—42no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—122no—
409C2×Dic3—124no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—124no—
413C2×Dic3—242no—
414C2×Dic3C2×#6711yescharacteristic
415C2×Dic3C2×#6711yescharacteristic
416C2×Dic3C2×#6711yescharacteristic
417C2×Dic3C2×#6711yescharacteristic
418D12—24no—
419D12—22no—
420D12#23714yes—
421C4×D3—124no—
422C4×D3—124no—
423Dic6—22no—
424C3×C8—62no—
425C3⋊C8—22no—
426C3⋊C8—62no—
427C3⋊C8—62no—
428C3⋊C8—122no—
429C2×C32—22no—
430C2×C32—81no—
431C2×C32#52511yescharacteristic
432C2×C32C2×#13511yescharacteristic
433C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
434C3×D3—44no—
435C24—61no—
436C2×Q8—31no—
437C2×D4—21no—
438C2×D4—32no—
439C2×D4—64no—
440C2×D4—61no—
441C2×D4C2×D3211yescharacteristic
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—61no—
445C22×C4—182no—
446C22×C4—182no—
447C22×C4—181no—
448C22×C4—364no—
449C22×C4C2×D3211yescharacteristic
450SD16—184no—
451D8—64no—
452C2×C8—32no—
453C2×C8—92no—
454C4⋊C4—31no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—92no—
460C4⋊C4—181no—
461C4⋊C4C2×D3211yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—61no—
464C22⋊C4—61no—
465C22⋊C4—61no—
466C22⋊C4—61no—
467C22⋊C4—182no—
468C22⋊C4—182no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—31no—
473C42—61no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—64no—
489C22×C3—81no—
490C22×C3—81no—
491C22×C3—81no—
492C22×C3—128no—
493C22×C3—122no—
494C22×C3—122no—
495C22×C3#91212yes—
496C22×C3#95012yes—
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C22×#6711yescharacteristic
499C2×D3—24no—
500C2×D3—48no—
501C2×D3—42no—
502C2×D3—42no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—22no—
506C3×C4—32no—
507C3×C4—41no—
508C3×C4—41no—
509C3×C4—41no—
510C3×C4—61no—
511C3×C4—61no—
512C3×C4—61no—
513C3×C4—81no—
514C3×C4—121no—
515C3×C4—121no—
516C3×C4C2×#23712yes—
517C3×C4D3×#4112yes—
518Dic3—21no—
519Dic3—21no—
520Dic3—21no—
521Dic3—41no—
522Dic3—41no—
523Dic3—122no—
524Dic3—122no—
525Dic3—242no—
526Dic3#94912yes—
527C32#310511yescharacteristic, complemented, Sylow
528C23—21no—
529C23—64no—
530C23—62no—
531C23—122no—
532C23—122no—
533C23D3×#6711yescharacteristic
534Q8—62no—
535D4—22no—
536D4—34no—
537D4—42no—
538D4—64no—
539D4—62no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—31no—
543C2×C4—31no—
544C2×C4—31no—
545C2×C4—31no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—122no—
551C2×C4—182no—
552C2×C4—364no—
553C2×C4—364no—
554C2×C4—362no—
555C2×C4D3×#6711yescharacteristic
556C2×C4C22×D3211yescharacteristic
557C8—62no—
558C8—182no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—42no—
565C2×C3—81no—
566C2×C3—81no—
567C2×C3—124no—
568C2×C3—161no—
569C2×C3#558611yescharacteristic
570C2×C3C2×#91211yescharacteristic
571C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
572C2×C3C2×#94911yescharacteristic
573C2×C3C2×#95011yescharacteristic
574C2×C3#582811yescharacteristic
575D3—44no—
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—64no—
582C22—128no—
583C22—122no—
584C22—122no—
585C22#6393312yes—
586C22C2×D3×#6711yescharacteristic
587C4—21no—
588C4—32no—
589C4—41no—
590C4—61no—
591C4—61no—
592C4—61no—
593C4—121no—
594C4—121no—
595C4—362no—
596C4D3×#23712yes—
597C3—21no—
598C3#7998911yescharacteristic, complemented
599C3#8314111yescharacteristic, complemented
600C2—22no—
601C2—81no—
602C2—124no—
603C2C2×#6393311yescharacteristic
604C2#1059515411yescharacteristic
605C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5036C2
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×Dic3×D12C2semidirect
3. #10592733C2semidirect
5. #10591431C2semidirect
6. Dic3×#213C2semidirect
7. #10591169C2semidirect
8. #10591103C2semidirect
9. #10591053C2semidirect
10. #10590469C2semidirect
11. #10590453C2semidirect
18. C3×#936C22semidirect
21. C3×D4×Dic3C22semidirect
25. C3×#890C22semidirect
26. C3×#887C22semidirect
35. #63659C22semidirect
37. #63635C22semidirect
40. #63575C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63566C22semidirect
44. Dic3×C3⋊C8C22semidirect
47. #5600D3semidirect
128. #936C2×D3semidirect
135. D4×Dic3C2×D3semidirect
144. #890C2×D3semidirect
145. #887C2×D3semidirect
527. C32#3105semidirect
598. C3#79989semidirect
599. 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×Dic3×D122
#105927332
C3×#50362
#105914312
Dic3×#2132
#105911692
#105911032
#105910532
#105904692
#105904532
#831413
#799893