Finite Group Databasebeta

← #11868679

Subgroups — #11868679

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 597 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5517C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic
3#10592694C211yesmaximal, characteristic, complemented
4C3×#5001C211yesmaximal, characteristic
5#10591131C211yesmaximal, characteristic, complemented
6#10591115C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic
8#10590469C212yesmaximal, complemented
9#10590467C212yesmaximal, complemented
10#10590465C212yesmaximal, complemented
11#10590463C212yesmaximal, complemented
12#83350—31nomaximal
13#78917—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×D3×Dic3—21no—
16C32×#117C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C3×#890C2211yescharacteristic, complemented
23C3×#890C2211yescharacteristic, complemented
24C3×#888C2211yescharacteristic, complemented
25C3×#888C2211yescharacteristic, complemented
26C3×#878—21no—
27C3×#878—21no—
28C3×C4×Dic6—21no—
29C3×C4×Dic6—21no—
30C2×(C2×D3)⋊Dic3—21no—
31Dic3×D12—21no—
32Dic3×D12—21no—
33Dic3×D12C2212yes—
34Dic3×D12C2212yes—
35#63635C2212yescomplemented
36#63634C2212yescomplemented
37C3×#809C2212yes—
38C3×#809C2212yes—
39#63575C2212yescomplemented
40#63573C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42Dic3⋊(C3⋊C8)C2212yescomplemented
43#63562C2212yes—
44#63562C2212yes—
45C3×#533—31no—
46C2×D4×Dic3—31no—
47#5517D311yescharacteristic, complemented
48C2×C4×D12—31no—
49C3×#418—31no—
50#5215—31no—
51#5121—31no—
52#5118—31no—
53#5087—32no—
54#5084—32no—
55#5066—32no—
56#5066—32no—
57#5001—31no—
58#5001D311yescharacteristic
59#4995—31no—
60#4995—31no—
61#4995—31no—
62#4995—61no—
63#4924—31no—
64#4766—32no—
65#4763—32no—
66#4761—32no—
67#4759—32no—
68C23×C3×D3—21no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C22×C3×Dic3D411yescharacteristic
72C22×C3×Dic3D411yescharacteristic
73C2×C3×D12—21no—
74C2×C3×D12—22no—
75C2×C3×D12Q814yescomplemented
76C2×C3×D12C2312yes—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×D3×Dic3—22no—
80C2×D3×Dic3—22no—
81C2×D3×Dic3—44no—
82C32×C4⋊C4C2311yescharacteristic
83C32×C4⋊C4C2311yescharacteristic
84C32×C22⋊C4—21no—
85C32×C42—21no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88#3748—22no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×C4⋊Dic3C2311yescharacteristic
95C3×Dic3⋊C4—21no—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×#208—22no—
105C2×C3×C3⋊C8C2312yes—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3077—91noSylow
109C22×C3×D4—31no—
110C23×Dic3—61no—
111C22×D12C2×D311yescharacteristic
112C22×C4×D3—61no—
113C2×C3×M16—31no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×#125—31no—
117C3×#125—31no—
118C3×C22⋊Q8—61no—
119C3×C22⋊Q8—61no—
120C3×C4×Q8—61no—
121C3×C4×Q8—61no—
122C3×#117—21no—
123C3×#117—31no—
124C3×#117C2×D311yescharacteristic
125C3×#117C2×D311yescharacteristic
126C2×C3×C42—31no—
127C2×#217—61no—
128D4×Dic3—32no—
129D4×Dic3—32no—
130D4×Dic3—61no—
131D4×Dic3—61no—
132C2×(C2×D3)⋊C4—61no—
133#926C2×D311yescharacteristic
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—61no—
137C2×C4×Dic3C2×D311yescharacteristic
138C2×#208—31no—
139C2×#208—31no—
140C2×#208—61no—
141C2×#208C2×D311yescharacteristic
142#890C2×D311yescharacteristic, complemented
143#890C2×D311yescharacteristic, complemented
144#888C2×D311yescharacteristic, complemented
145#888C2×D311yescharacteristic, complemented
146#878—21no—
147#878—21no—
148C4×D12—32no—
149C4×D12—32no—
150C4×D12—61no—
151C4×D12—61no—
152C4×Dic6—21no—
153C4×Dic6—21no—
154C3×#102—32no—
155C3×#102—32no—
156#832—32no—
157#832—32no—
158#818—32no—
159#817—32no—
160Dic3⋊C8—32no—
161Dic3⋊C8—32no—
162#809—32no—
163#809—32no—
164#809C2×D312yes—
165#809C2×D312yes—
166#808—32no—
167#808—32no—
168#808—32no—
169#808—62no—
170#807—32no—
171#807—32no—
172#807—32no—
173#807—62no—
174C4⋊(C3⋊C8)—32no—
175C4⋊(C3⋊C8)—32no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—24no—
178C22×C3×D3—22no—
179C22×C3×D3—42no—
180C22×C3×D3—42no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×Q812yes—
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—42no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3C2×D411yescharacteristic
194C2×C3×Dic3C2×D411yescharacteristic
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C3×D12—24no—
198C3×D12—22no—
199C3×D12C2×Q814yes—
200C3×Dic6—42no—
201C3×Dic6—42no—
202D3×Dic3—44no—
203D3×Dic3—44no—
204C3⋊(C3⋊C8)—22no—
205C3×C3⋊C8—22no—
206#533—31no—
207C2×C4×D4—91no—
208#478—92no—
209#478—92no—
210#476—92no—
211#474—92no—
212#428—91no—
213#428—91no—
214#423—91no—
215#418—31no—
216#418—91no—
217C24×C3—61no—
218C23×D3—21no—
219C2×C3×Q8—61no—
220C2×C3×Q8—61no—
221C2×C3×D4—34no—
222C2×C3×D4—32no—
223C2×C3×D4—62no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—62no—
233C22×Dic3—62no—
234C22×Dic3—121no—
235C22×Dic3—124no—
236C22×Dic3#6711yescharacteristic
237C22×Dic3#6711yescharacteristic
238C2×D12—21no—
239C2×D12—22no—
240C2×D12Dic614yescomplemented
241C2×D12C22×D312yes—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—124no—
245C2×Dic6—21no—
246C2×Dic6—21no—
247C3×M16—62no—
248C2×C3×C8—32no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—31no—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—61no—
254C3×C4⋊C4—61no—
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×C4⋊C4C22×D311yescharacteristic
262C3×C4⋊C4C22×D311yescharacteristic
263C3×C22⋊C4—21no—
264C3×C22⋊C4—21no—
265C3×C22⋊C4—41no—
266C3×C22⋊C4—61no—
267C3×C42—21no—
268C3×C42—21no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—41no—
274C3×C42—61no—
275#217—21no—
276#217—62no—
277#217—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—32no—
283C4⋊Dic3—32no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3—121no—
288C4⋊Dic3C22×D311yescharacteristic
289C4⋊Dic3C22×D311yescharacteristic
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292Dic3⋊C4—21no—
293Dic3⋊C4—21no—
294C4×Dic3—21no—
295C4×Dic3#6711yescharacteristic
296C4×Dic3#6711yescharacteristic
297C4×Dic3C22×D311yescharacteristic
298C4×Dic3C22×D311yescharacteristic
299#208—22no—
300#208—64no—
301#208—62no—
302#208—62no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—32no—
305C2×C3⋊C8—62no—
306C2×C3⋊C8C22×D312yes—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C22⋊Q812yes—
310C22×C32C22×D411yescharacteristic
311C2×C3×D3—24no—
312C2×C3×D3—48no—
313C2×C3×D3—42no—
314C2×C3×D3—42no—
315C32×C4—41no—
316C32×C4—41no—
317C32×C4C22⋊Q812yes—
318C32×C4C22×Q811yescharacteristic
319C32×C4C2×#4111yescharacteristic
320C3⋊Dic3—42no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—21no—
324C3×Dic3—41no—
325C3×Dic3—41no—
326C3×Dic3AGL(1,ℤ/8)12yes—
327C22×D4—31no—
328C23×C4—181no—
329C2×M16—31no—
330C2×M16—91no—
331C4⋊Q8—31no—
332C4⋊Q8—31no—
333#125—31no—
334#125—31no—
335C22⋊Q8—61no—
336C22⋊Q8—61no—
337C4×Q8—61no—
338C4×Q8—61no—
339C4×D4—92no—
340C4×D4—92no—
341C4×D4—181no—
342C4×D4—181no—
343#117—31no—
344#117D3211yescharacteristic
345C2×C4⋊C4—91no—
346C2×C22⋊C4—181no—
347C2×C42—31no—
348#107—92no—
349#107—92no—
350#106—92no—
351#106—92no—
352C4⋊C8—92no—
353C4⋊C8—92no—
354#102—32no—
355#102—32no—
356#102—92no—
357#102—92no—
358C23×C3—21no—
359C23×C3—64no—
360C23×C3—62no—
361C23×C3—122no—
362C23×C3—122no—
363C23×C3D3×D411yescharacteristic
364C23×C3C2×#6711yescharacteristic
365C22×D3—24no—
366C22×D3—22no—
367C22×D3—42no—
368C22×D3—42no—
369C3×Q8—122no—
370C3×Q8—122no—
371C3×D4—34no—
372C3×D4—64no—
373C3×D4—62no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—62no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—121no—
392C2×C3×C4C2×Dic612yes—
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4#23712yes—
395C2×C3×C4D3×Q812yes—
396C2×C3×C4#23912yes—
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×Dic3—22no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—41no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—122no—
407C2×Dic3—124no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—124no—
411C2×Dic3—242no—
412C2×Dic3C2×#6711yescharacteristic
413C2×Dic3C2×#6711yescharacteristic
414C2×Dic3C2×#6711yescharacteristic
415C2×Dic3C2×#6711yescharacteristic
416D12—24no—
417D12—22no—
418D12C2×Dic614yes—
419C4×D3—124no—
420C4×D3—124no—
421Dic6—42no—
422Dic6—42no—
423C3×C8—62no—
424C3⋊C8—22no—
425C3⋊C8—64no—
426C3⋊C8—62no—
427C3⋊C8—62no—
428C2×C32—22no—
429C2×C32C2×C22⋊Q811yescharacteristic
430C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
431C2×C32#57511yescharacteristic
432C3×D3—44no—
433C24—61no—
434C2×Q8—61no—
435C2×Q8—61no—
436C2×D4—32no—
437C2×D4—34no—
438C2×D4—62no—
439C2×D4—61no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—182no—
443C22×C4—182no—
444C22×C4—181no—
445C22×C4—364no—
446C22×C4C2×D3211yescharacteristic
447M16—62no—
448M16—182no—
449C2×C8—32no—
450C2×C8—92no—
451C4⋊C4—31no—
452C4⋊C4—31no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4—61no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—92no—
460C4⋊C4—181no—
461C4⋊C4C2×D3211yescharacteristic
462C4⋊C4C2×D3211yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—61no—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C42—21no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42—31no—
472C42—61no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—64no—
482C22×C3—128no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3#87812yes—
486C22×C3#94612yes—
487C22×C3C2×D3×D411yescharacteristic
488C22×C3C22×#6711yescharacteristic
489C2×D3—24no—
490C2×D3—48no—
491C2×D3—42no—
492C2×D3—42no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—22no—
496C3×C4—32no—
497C3×C4—41no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—41no—
501C3×C4—61no—
502C3×C4—61no—
503C3×C4—61no—
504C3×C4—81no—
505C3×C4—81no—
506C3×C4—121no—
507C3×C4—121no—
508C3×C4#87812yes—
509C3×C4#94612yes—
510C3×C4C22×Dic611yescharacteristic
511C3×C4C2×#23711yescharacteristic
512C3×C4C2×D3×Q811yescharacteristic
513C3×C4C2×#23911yescharacteristic
514Dic3—21no—
515Dic3—21no—
516Dic3—21no—
517Dic3—41no—
518Dic3—41no—
519Dic3—122no—
520Dic3—122no—
521Dic3—242no—
522Dic3#94912yes—
523C32#307711yescharacteristic, complemented, Sylow
524C23—62no—
525C23—64no—
526C23—122no—
527C23—122no—
528C23D3×#6711yescharacteristic
529Q8—122no—
530Q8—122no—
531D4—34no—
532D4—62no—
533D4—64no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—31no—
537C2×C4—31no—
538C2×C4—31no—
539C2×C4—31no—
540C2×C4—62no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—121no—
544C2×C4—182no—
545C2×C4—364no—
546C2×C4—364no—
547C2×C4—362no—
548C2×C4D3×Dic612yes—
549C2×C4#379612yes—
550C2×C4D3×#6711yescharacteristic
551C2×C4C22×D3211yescharacteristic
552C8—62no—
553C8—182no—
554C2×C3—22no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3—124no—
561C2×C3C2×#87811yescharacteristic
562C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
563C2×C3#577311yescharacteristic
564C2×C3C2×#94611yescharacteristic
565C2×C3C2×#94911yescharacteristic
566C2×C3#582211yescharacteristic
567D3—44no—
568C22—21no—
569C22—21no—
570C22—64no—
571C22—128no—
572C22—122no—
573C22—122no—
574C22#6388712yes—
575C22C2×D3×#6711yescharacteristic
576C4—32no—
577C4—41no—
578C4—41no—
579C4—61no—
580C4—61no—
581C4—61no—
582C4—121no—
583C4—121no—
584C4—362no—
585C4#6388712yes—
586C4C2×D3×Dic611yescharacteristic
587C4C2×#379611yescharacteristic
588C3—21no—
589C3#7891711yescharacteristic, complemented
590C3#8335011yescharacteristic, complemented
591C2—22no—
592C2—124no—
593C2C2×#6388711yescharacteristic
594C2D3×#94911yescharacteristic
595C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5517C2semidirect
3. #10592694C2semidirect
5. #10591131C2semidirect
6. #10591115C2semidirect
8. #10590469C2semidirect
9. #10590467C2semidirect
10. #10590465C2semidirect
11. #10590463C2semidirect
22. C3×#890C22semidirect
23. C3×#890C22semidirect
24. C3×#888C22semidirect
25. C3×#888C22semidirect
35. #63635C22semidirect
36. #63634C22semidirect
39. #63575C22semidirect
40. #63573C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. Dic3⋊(C3⋊C8)C22semidirect
47. #5517D3semidirect
75. C2×C3×D12Q8semidirect
142. #890C2×D3semidirect
143. #890C2×D3semidirect
144. #888C2×D3semidirect
145. #888C2×D3semidirect
240. C2×D12Dic6semidirect
523. C32#3077semidirect
589. C3#78917semidirect
590. C3#83350semidirect

Maximal subgroups

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

subgroupindex
C3×#55172
C2×Dic3×D122
#105926942
C3×#50012
#105911312
#105911152
#105910852
#105904692
#105904672
#105904652
#105904632
#833503
#789173