Finite Group Databasebeta

← #11870877

Subgroups — #11870877

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
1#10594955C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3#10592434C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4718C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic
7#10591103C211yesmaximal, characteristic, complemented
8#10590772C212yesmaximal, complemented
9Dic3×#204C212yesmaximal, complemented
10#10590754C212yesmaximal, complemented
11#10590745C212yesmaximal, complemented
12#80133—31nomaximal
13#79300—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16#64139C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C3×#924C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#204C2212yes—
21#63966—21no—
22C2×(C2×D3)⋊Dic3—21no—
23#63952—21no—
24#63894C2211yescharacteristic, complemented
25Dic3×D12—21no—
26Dic3×D12—21no—
27Dic3×D12C2212yes—
28Dic3×D12C2212yes—
29#63869C2211yescharacteristic, complemented
30#63868—21no—
31#63864C2211yescharacteristic, complemented
32Dic3×Dic6C2211yescharacteristic, complemented
33#63836—21no—
34C2×#3714C2212yes—
35C32×C22⋊C8C2211yescharacteristic
36#63648C2212yescomplemented
37#63644C2212yescomplemented
38C3×#830C2211yescharacteristic
39C3×#821C2212yes—
40C3×Dic3⋊C8C2212yescomplemented
41C3×C8×Dic3C2212yescomplemented
42#63575C2212yescomplemented
43#63566C2212yescomplemented
44#63563C2212yes—
45C2×D4×Dic3—31no—
46#5624—31no—
47#5479—31no—
48C2×C4×D12—31no—
49C3×#450—31no—
50C3×#431—31no—
51#5217—31no—
52#5165—32no—
53Dic3×SD16—32no—
54#5044—31no—
55#4847—32no—
56#4844—32no—
57#4763—32no—
58#4756—32no—
59#4735—31no—
60#4735—31no—
61#4735—61no—
62#4732—31no—
63#4731D311yescharacteristic, complemented
64#4722—31no—
65#4718D311yescharacteristic, complemented
66C4×D24—32no—
67C4×#204—32no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C22×C3⋊Dic3—21no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C22×C3×Dic3D411yescharacteristic
74C22×C3×Dic3D411yescharacteristic
75C2×C3×D12—21no—
76C2×C3×D12—24no—
77C2×C3×D12C2312yes—
78C2×C3×Dic6C2311yescharacteristic
79C2×#624—21no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—22no—
82C2×D3×Dic3—44no—
83C2×C32×C8C2312yes—
84#3752—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88C3×#217—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3D411yescharacteristic
92C3×C4×Dic3D411yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C3×C4×Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C3×#204—24no—
97#3724—21no—
98Dic3⋊Dic3—21no—
99Dic3⋊Dic3—21no—
100#3722—21no—
101#3722—21no—
102#3722—21no—
103(C2×D3)⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105Dic32—21no—
106#3714—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—
114C2×C3×C42—31no—
115C2×#217—61no—
116#947—31no—
117Q8×Dic3—31no—
118D4×Dic3—32no—
119D4×Dic3—32no—
120D4×Dic3—61no—
121D4×Dic3—61no—
122C2×#213—32no—
123#930—31no—
124#930—31no—
125#930—61no—
126#929—61no—
127C4×#67—61no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—61no—
132#924C2×D311yescharacteristic
133C2×C4×Dic3C2×D311yescharacteristic
134C2×D24—32no—
135C2×#204C2×D312yes—
136#898—61no—
137#893—31no—
138#892—61no—
139#890—31no—
140#886—61no—
141#67⋊C4—61no—
142#876—61no—
143#875—31no—
144C4×D12—32no—
145C4×D12—32no—
146C4×D12—31no—
147C4×D12—61no—
148C4×D12—61no—
149#872—61no—
150#870—31no—
151C4×Dic6—31no—
152C3×C4⋊C8—32no—
153C3×#102—32no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—31no—
156C3×C22⋊C8C2×D311yescharacteristic
157C3×C22⋊C8C2×D311yescharacteristic
158C3×C4×C8—32no—
159#835—32no—
160#832—32no—
161#830C2×D311yescharacteristic
162#821—32no—
163#821—32no—
164#821—32no—
165#821—62no—
166#821C2×D312yes—
167#818—32no—
168#817—32no—
169#817—32no—
170#817—62no—
171#816—32no—
172Dic3⋊C8C2×D312yescomplemented
173C8×Dic3C2×D312yescomplemented
174#807—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3⋊D3—21no—
177C22×C3×D3—24no—
178C22×C3×D3—22no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184#638—42no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—42no—
188C4⋊(C3⋊D3)—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—24no—
198C3×D12—22no—
199C3×D12#4114yes—
200C3×Dic6—22no—
201#624—42no—
202D3×Dic3—44no—
203D3×Dic3—44no—
204C32×C8—22no—
205C3×C3⋊C8—22no—
206#529—91no—
207C2×C4×D4—91no—
208#484—91no—
209#481—91no—
210#478—92no—
211#463—92no—
212#450—31no—
213#447—91no—
214C4×SD16—92no—
215C4×D8—92no—
216#431—31no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×Q8—31no—
220C2×C3×D4—32no—
221C2×C3×D4—64no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—61no—
229C2×#67—61no—
230C2×#67—121no—
231C22×Dic3—61no—
232C22×Dic3—61no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3—121no—
236C22×Dic3—124no—
237C22×Dic3D1211yescharacteristic
238C22×Dic3D1211yescharacteristic
239C2×D12—21no—
240C2×D12—24no—
241C2×D12—31no—
242C2×D12—31no—
243C2×D12—61no—
244C2×D12C22×D312yes—
245C2×C4×D3—61no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—61no—
249C2×C4×D3—124no—
250C2×Dic6C22×D311yescharacteristic
251C3×SD16—64no—
252C2×C3×C8—22no—
253C2×C3×C8—32no—
254C2×C3×C8C22×D312yes—
255C2×C3×C8C22×D312yes—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—61no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—31no—
263#217—21no—
264#217—62no—
265#217—62no—
266#213—64no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—61no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—61no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275(C2×D3)⋊C4—61no—
276(C2×D3)⋊C4—61no—
277(C2×D3)⋊C4—121no—
278C4⋊Dic3—32no—
279C4⋊Dic3—32no—
280C4⋊Dic3—31no—
281C4⋊Dic3—31no—
282C4⋊Dic3—61no—
283C4⋊Dic3—62no—
284C4⋊Dic3—61no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—61no—
288C4⋊Dic3—121no—
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—61no—
292Dic3⋊C4—61no—
293Dic3⋊C4—61no—
294Dic3⋊C4—61no—
295C4×Dic3—61no—
296C4×Dic3—61no—
297C4×Dic3D1211yescharacteristic
298C4×Dic3D1211yescharacteristic
299C4×Dic3C22×D311yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C2×C3⋊C8C22×D312yes—
302D24—64no—
303#204—24no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32#13512yes—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—41no—
309C2×C3⋊D3—41no—
310C2×C3⋊D3—41no—
311C2×C3×D3—24no—
312C2×C3×D3—48no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C32×C4—21no—
316C32×C4C2×#4112yes—
317C3⋊Dic3—41no—
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—32no—
328C2×D8—92no—
329#126—181no—
330#125—91no—
331#124—91no—
332#123—181no—
333C22⋊Q8—31no—
334#121—91no—
335C4×Q8—91no—
336C4×D4—91no—
337C4×D4—92no—
338C4×D4—92no—
339C4×D4—181no—
340C4×D4—181no—
341C4×D4—181no—
342#117—181no—
343C2×C4⋊C4—91no—
344C2×C22⋊C4—181no—
345C2×C42—31no—
346#107—92no—
347#106—92no—
348C4⋊C8—32no—
349#103—92no—
350#102—32no—
351#102—92no—
352#102—92no—
353C22⋊C8—31no—
354C22⋊C8D3211yescharacteristic
355C4×C8—32no—
356C23×C3—21no—
357C23×C3—64no—
358C23×C3—62no—
359C23×C3—122no—
360C23×C3—122no—
361C23×C3C2×D1211yescharacteristic
362C23×C3D3×D411yescharacteristic
363C22×D3—24no—
364C22×D3—22no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3—61no—
368C22×D3—61no—
369C22×D3—121no—
370C3×Q8—62no—
371C3×D4—34no—
372C3×D4—64no—
373C3×D4—62no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—31no—
379C2×C3×C4—31no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—42no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4C2×D1211yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×C3×C4C23×D311yescharacteristic
391#67—122no—
392#67—122no—
393#67—242no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—61no—
401C2×Dic3—62no—
402C2×Dic3—122no—
403C2×Dic3—121no—
404C2×Dic3—124no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—124no—
408C2×Dic3—242no—
409C2×Dic3C2×D1211yescharacteristic
410C2×Dic3C2×D1211yescharacteristic
411C2×Dic3C2×D1211yescharacteristic
412C2×Dic3C2×D1211yescharacteristic
413D12—24no—
414D12—22no—
415D12—62no—
416D12—62no—
417D12—122no—
418D12#23714yes—
419C4×D3—122no—
420C4×D3—124no—
421C4×D3—124no—
422C4×D3—122no—
423Dic6—22no—
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—42no—
427C3×C8—62no—
428C3⋊C8—22no—
429C2×C32—22no—
430C2×C32#52511yescharacteristic
431C2×C32C2×#13511yescharacteristic
432C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
433C3⋊D3—81no—
434C3×D3—44no—
435C24—61no—
436C2×Q8—31no—
437C2×D4—32no—
438C2×D4—64no—
439C2×D4—61no—
440C2×D4—91no—
441C2×D4—181no—
442C22×C4—31no—
443C22×C4—31no—
444C22×C4—181no—
445C22×C4—182no—
446C22×C4—182no—
447C22×C4—181no—
448C22×C4—364no—
449C22×C4C2×D3211yescharacteristic
450SD16—64no—
451D8—184no—
452C2×C8—32no—
453C2×C8C2×D3212yes—
454C4⋊C4—31no—
455C4⋊C4—61no—
456C4⋊C4—91no—
457C4⋊C4—92no—
458C4⋊C4—181no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C4⋊C4—181no—
462C22⋊C4—61no—
463C22⋊C4—181no—
464C22⋊C4—181no—
465C22⋊C4—181no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C22⋊C4—181no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—31no—
473C42—181no—
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—64no—
483C22×C3—128no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3#90412yes—
487C22×C3#91612yes—
488C22×C3C22×D1211yescharacteristic
489C22×C3C2×D3×D411yescharacteristic
490C2×D3—24no—
491C2×D3—48no—
492C2×D3—42no—
493C2×D3—42no—
494C2×D3—121no—
495C2×D3—121no—
496C2×D3—121no—
497C2×D3—121no—
498C2×D3—121no—
499C2×D3—121no—
500C2×D3—241no—
501C2×D3—241no—
502C2×D3—241no—
503C3×C4—21no—
504C3×C4—21no—
505C3×C4—22no—
506C3×C4—32no—
507C3×C4—41no—
508C3×C4—61no—
509C3×C4—61no—
510C3×C4—61no—
511C3×C4—121no—
512C3×C4—121no—
513C3×C4C2×#23712yes—
514C3×C4D3×#4112yes—
515Dic3—21no—
516Dic3—21no—
517Dic3—21no—
518Dic3—41no—
519Dic3—41no—
520Dic3—121no—
521Dic3—122no—
522Dic3—121no—
523Dic3—122no—
524Dic3—242no—
525Dic3—241no—
526Dic3#90812yes—
527C32#310511yescharacteristic, complemented, Sylow
528C23—64no—
529C23—62no—
530C23—122no—
531C23—122no—
532C23—181no—
533C23D3×D1211yescharacteristic
534Q8—62no—
535D4—34no—
536D4—64no—
537D4—62no—
538D4—182no—
539D4—362no—
540C2×C4—22no—
541C2×C4—31no—
542C2×C4—31no—
543C2×C4—31no—
544C2×C4—31no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—181no—
550C2×C4—182no—
551C2×C4—362no—
552C2×C4—364no—
553C2×C4—364no—
554C2×C4—362no—
555C2×C4D3×D1211yescharacteristic
556C2×C4C22×D3211yescharacteristic
557C8—22no—
558C8—62no—
559C2×C3—22no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—42no—
565C2×C3—124no—
566C2×C3#552411yescharacteristic
567C2×C3#558611yescharacteristic
568C2×C3C2×#90411yescharacteristic
569C2×C3C2×#90811yescharacteristic
570C2×C3C2×#91611yescharacteristic
571C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
572D3—44no—
573D3—241no—
574D3—241no—
575D3—481no—
576C22—21no—
577C22—21no—
578C22—64no—
579C22—128no—
580C22—122no—
581C22—122no—
582C22—361no—
583C22—361no—
584C22—361no—
585C22#6380612yes—
586C22C2×D3×D1211yescharacteristic
587C4—21no—
588C4—32no—
589C4—61no—
590C4—61no—
591C4—61no—
592C4—121no—
593C4—121no—
594C4—361no—
595C4—362no—
596C4D3×#23712yes—
597C3—21no—
598C3#7930011yescharacteristic, complemented
599C3#8013311yescharacteristic, complemented
600C2—22no—
601C2—124no—
602C2—721no—
603C2#1059407811yescharacteristic
604C2C2×#6380611yescharacteristic
605C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10591162C2
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. #10594955C2semidirect
2. C2×Dic3×D12C2semidirect
3. #10592434C2semidirect
4. C3×#4731C2semidirect
5. C3×#4718C2semidirect
7. #10591103C2semidirect
8. #10590772C2semidirect
9. Dic3×#204C2semidirect
10. #10590754C2semidirect
11. #10590745C2semidirect
24. #63894C22semidirect
29. #63869C22semidirect
31. #63864C22semidirect
32. Dic3×Dic6C22semidirect
36. #63648C22semidirect
37. #63644C22semidirect
40. C3×Dic3⋊C8C22semidirect
41. C3×C8×Dic3C22semidirect
42. #63575C22semidirect
43. #63566C22semidirect
63. #4731D3semidirect
65. #4718D3semidirect
172. Dic3⋊C8C2×D3semidirect
173. C8×Dic3C2×D3semidirect
527. C32#3105semidirect
598. C3#79300semidirect
599. C3#80133semidirect

Maximal subgroups

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

subgroupindex
#105949552
C2×Dic3×D122
#105924342
C3×#47312
C3×#47182
#105911622
#105911032
#105907722
Dic3×#2042
#105907542
#105907452
#801333
#793003