Finite Group Databasebeta

← #11874440

Subgroups — #11874440

Order 1152.

1200 conjugacy classes of subgroups.

The subgroup lattice has 575 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5668C211yesmaximal, characteristic, complemented
2C2×#63949C212yesmaximal, complemented
3C2×#63935C212yesmaximal, complemented
4#10593970C211yesmaximal, characteristic, complemented
5#10592757C211yesmaximal, characteristic, complemented
6C3×#5060C211yesmaximal, characteristic, complemented
7#10591608C212yesmaximal, complemented
8#10591472C212yesmaximal, complemented
9#10590376C211yesmaximal, characteristic, complemented
10#10590351C211yesmaximal, characteristic, complemented
11D3×#803C211yesmaximal, characteristic, complemented
12#83286—31nomaximal
13#81869—31nomaximal
14C2×C3×#239C2211yescharacteristic
15C2×C3×#237C2211yescharacteristic
16C2×#3799C2212yes—
17C32×#124C2211yescharacteristic
18C2×#3755C2212yes—
19C2×#3753C2212yes—
20#64083C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C2×C3×#216C2212yes—
23C3×#940C2211yescharacteristic
24C2×C3×#214C2212yes—
25C3×#884—22no—
26C3×#67⋊C4—22no—
27C3×#875C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×#869C2211yescharacteristic
30#63949—28no—
31#63935—28no—
32#63909—22no—
33#63894—22no—
34#63864C2212yes—
35C2×#3718C2212yes—
36C2×#3717C2212yes—
37C2×#3715C2212yes—
38C2×#3714C2212yes—
39C2×D3×C3⋊C8C2212yes—
40#63630C2211yescharacteristic
41C3×#803C2211yescharacteristic
42#63554C2212yes—
43C3×#532—31no—
44C2×#950—32no—
45C2×#950—32no—
46C2×#919—32no—
47C2×#916—32no—
48#5725—31no—
49#5668D311yescharacteristic, complemented
50#5477—31no—
51C3×#497—31no—
52#5190—32no—
53#5176—32no—
54#5086—32no—
55#5086—31no—
56#5074—32no—
57#5060—31no—
58#5060D311yescharacteristic, complemented
59#5058—31no—
60#5058—31no—
61#5058—31no—
62#5058—61no—
63C2×#803—31no—
64#4712—31no—
65D3×#97—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C3×#67—21no—
71C2×C3×#67—22no—
72C22×C3×Dic3—21no—
73C3×#239—24no—
74C3×#237—24no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3D412yes—
79C2×C3×C4×D3C2311yescharacteristic
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2311yescharacteristic
82C2×#626—22no—
83C2×#624—22no—
84#3799—24no—
85#3799—24no—
86C32×C22⋊C4—22no—
87C32×C42C2311yescharacteristic
88#3755—24no—
89#3753—24no—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×#216—24no—
92C3×#214—24no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3—22no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3D412yes—
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99#3722—24no—
100#3718—24no—
101#3717—24no—
102#3715—24no—
103#3714—24no—
104D3×C3⋊C8D418yescomplemented
105#3150—91noSylow
106C2×C3×#41—31no—
107C2×C3×#41—31no—
108C2×#239—32no—
109C2×#239C2×D311yescharacteristic
110C2×#237C2×D311yescharacteristic
111C2×#235—32no—
112C2×C3×Q16—32no—
113C2×C3×SD16—32no—
114C3×C4⋊Q8—31no—
115C3×C4⋊Q8—31no—
116C3×#127—31no—
117C3×#124—21no—
118C3×#124—31no—
119C3×#124C2×D311yescharacteristic
120C3×#124C2×D311yescharacteristic
121C3×#121—62no—
122C3×C4×D4—62no—
123C2×C3×C42—31no—
124#950—68no—
125#950—68no—
126#947—32no—
127#944C2×D311yescharacteristic
128C2×#216—32no—
129C2×#216—32no—
130C2×#216C2×D312yes—
131C2×#215—32no—
132C2×#215—32no—
133C2×#215—32no—
134C2×#215—32no—
135C2×#215—62no—
136#940C2×D311yescharacteristic
137C2×#214—32no—
138C2×#214C2×D312yes—
139C2×#213—32no—
140C2×#213—32no—
141C2×#213—32no—
142C2×#213—62no—
143#930—62no—
144C22×C3⋊C8—32no—
145#919—68no—
146#916—68no—
147C2×D24—32no—
148C2×#204—32no—
149C2×D3×C8—32no—
150#895—62no—
151#893—62no—
152#884—22no—
153#67⋊C4—22no—
154#875—32no—
155#875C2×D311yescharacteristic
156#874—31no—
157#874—31no—
158#874—61no—
159C4×D12—62no—
160C42×D3C2×D311yescharacteristic
161#869C2×D311yescharacteristic
162C3×#97—31no—
163#815—32no—
164#803—31no—
165#803—31no—
166#803—32no—
167#803—61no—
168#803C2×D311yescharacteristic
169C23×C32—21no—
170C22×C3⋊D3—22no—
171C22×C3×D3—21no—
172C22×C3×D3C2×D411yescharacteristic
173C32×Q8—22no—
174C32×D4—22no—
175C2×C32×C4—21no—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2411yescharacteristic
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—44no—
181C3×#67—44no—
182C3×#67—42no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—42no—
186C2×C3×Dic3C2×D412yes—
187C2×C3×Dic3C2×D411yescharacteristic
188C3×D12—22no—
189C3×D12—42no—
190C3×C4×D3—42no—
191C3×C4×D3—42no—
192C3×C4×D3C2×D414yes—
193C3×Dic6—22no—
194C3×Dic6—22no—
195C3×Dic6—22no—
196#626—44no—
197#624—44no—
198C3⋊(C3⋊C8)C2×D414yes—
199C3×C3⋊C8C2×D414yes—
200C2×#135—92no—
201C2×#135—92no—
202#532—31no—
203#532—91no—
204#497—31no—
205#497—91no—
206#497—92no—
207#496—91no—
208#496—92no—
209#496—91no—
210C2×#97—91no—
211C3×#41—64no—
212C3×#41—64no—
213C2×C3×Q8—21no—
214C2×C3×Q8—31no—
215C2×C3×Q8—32no—
216C2×C3×Q8C22×D311yescharacteristic
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×D4—21no—
219C2×C3×D4—31no—
220C2×C3×D4—61no—
221C2×C3×D4—62no—
222C2×C3×D4—61no—
223C2×C3×D4C22×D311yescharacteristic
224C2×C3×D4C22×D311yescharacteristic
225C22×C3×C4—31no—
226C22×C3×C4—32no—
227C22×C3×C4—61no—
228C22×C3×C4—61no—
229C2×#67—21no—
230C2×#67—22no—
231C2×#67—62no—
232C22×Dic3—21no—
233#239—24no—
234#239—64no—
235#239—64no—
236#237—24no—
237#235—64no—
238#235—64no—
239C2×D12—21no—
240C2×D12—32no—
241C2×D12—32no—
242C2×D12—62no—
243C2×D12—62no—
244C2×D12—62no—
245C2×D12—62no—
246C2×D12—122no—
247C2×D12C22×D311yescharacteristic
248C2×C4×D3—21no—
249C2×C4×D3—62no—
250C2×C4×D3—62no—
251C2×C4×D3#6712yes—
252C2×C4×D3C22×D311yescharacteristic
253C2×Dic6C22×D312yes—
254C2×Dic6C22×D311yescharacteristic
255C3×Q16—64no—
256C3×SD16—64no—
257C2×C3×C8—32no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—62no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—62no—
264C3×C42—21no—
265C3×C42—32no—
266C3×C42—31no—
267C3×C42C22×D311yescharacteristic
268C3×C42C22×D311yescharacteristic
269#216—24no—
270#216—64no—
271#216—64no—
272#215—64no—
273#215—64no—
274#215—64no—
275#215—64no—
276#215—124no—
277#214—24no—
278#214—64no—
279#213—64no—
280#213—64no—
281#213—64no—
282#213—124no—
283(C2×D3)⋊C4—22no—
284(C2×D3)⋊C4—64no—
285(C2×D3)⋊C4—64no—
286C4⋊Dic3—22no—
287Dic3⋊C4—22no—
288C4×Dic3#6712yes—
289C4×Dic3C22×D311yescharacteristic
290C2×C3⋊C8—32no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—38no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8C22×D312yes—
295D24—64no—
296#204—64no—
297D3×C8—38no—
298C22×C32—41no—
299C22×C32—42no—
300C22×C32C22×D411yescharacteristic
301C2×C3⋊D3—42no—
302C2×C3⋊D3—44no—
303C2×C3×D3—22no—
304C2×C3×D3—41no—
305C2×C3×D3—42no—
306C2×C3×D3#12712yes—
307C32×C4—22no—
308C32×C4—41no—
309C32×C4C22×D412yes—
310C3×Dic3—22no—
311C3×Dic3—42no—
312C3×Dic3—41no—
313C3×Dic3#12712yes—
314C2×#41—31no—
315C2×#41—31no—
316C2×#41—92no—
317#135—188no—
318#135—188no—
319C2×Q16—32no—
320C2×Q16—92no—
321C2×SD16—32no—
322C2×SD16—92no—
323C2×SD16—92no—
324C2×SD16—92no—
325C2×D8—92no—
326C2×D8—92no—
327C22×C8—92no—
328C4⋊Q8—31no—
329C4⋊Q8—31no—
330#127—31no—
331#127—91no—
332#124—31no—
333#124—92no—
334#124D3211yescharacteristic
335#121—62no—
336#121—182no—
337C4×D4—62no—
338C4×D4—182no—
339C2×C42—31no—
340#97—31no—
341#97—92no—
342#97—91no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—31no—
346C23×C3—41no—
347C23×C3—61no—
348C22×D3—21no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—122no—
352C22×D3C2×#6711yescharacteristic
353C3×Q8—22no—
354C3×Q8—22no—
355C3×Q8—42no—
356C3×Q8—62no—
357C3×Q8—62no—
358C3×Q8—62no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—42no—
362C3×D4—62no—
363C3×D4—122no—
364C3×D4—124no—
365C3×D4—122no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—22no—
370C2×C3×C4—31no—
371C2×C3×C4—34no—
372C2×C3×C4—32no—
373C2×C3×C4—41no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—122no—
377C2×C3×C4—122no—
378C2×C3×C4—122no—
379C2×C3×C4D3×D412yes—
380C2×C3×C4C2×#6712yes—
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—44no—
384#67—42no—
385#67—124no—
386C2×Dic3—22no—
387C2×Dic3—21no—
388C2×Dic3—42no—
389C2×Dic3C2×#6712yes—
390C2×Dic3C2×#6711yescharacteristic
391D12—22no—
392D12—42no—
393D12—62no—
394D12—62no—
395D12—62no—
396D12—62no—
397D12—122no—
398D12—122no—
399D12—124no—
400D12—124no—
401D12—124no—
402D12—244no—
403C4×D3—42no—
404C4×D3—42no—
405C4×D3—124no—
406C4×D3—124no—
407C4×D3D3×D414yes—
408Dic6—22no—
409Dic6—22no—
410Dic6—22no—
411C3×C8—34no—
412C3⋊C8—34no—
413C3⋊C8—34no—
414C3⋊C8—64no—
415C3⋊C8D3×D414yes—
416C2×C32—81no—
417C2×C32C2×#12711yescharacteristic
418C2×C32#57512yes—
419C3⋊D3—82no—
420C3×D3—22no—
421C3×D3—81no—
422#41—64no—
423#41—64no—
424#41—184no—
425#41—184no—
426C2×Q8—31no—
427C2×Q8—32no—
428C2×Q8C2×D3211yescharacteristic
429C2×D4—31no—
430C2×D4—61no—
431C2×D4—62no—
432C2×D4—61no—
433C2×D4—92no—
434C2×D4—182no—
435C2×D4—182no—
436C2×D4C2×D3211yescharacteristic
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—182no—
442Q16—64no—
443Q16—184no—
444SD16—64no—
445SD16—184no—
446SD16—184no—
447SD16—184no—
448D8—184no—
449D8—184no—
450C2×C8—32no—
451C2×C8—98no—
452C2×C8—92no—
453C4⋊C4—62no—
454C4⋊C4—62no—
455C22⋊C4—22no—
456C22⋊C4—62no—
457C22⋊C4—184no—
458C42—31no—
459C42—32no—
460C42C2×D3211yescharacteristic
461C22×C3—21no—
462C22×C3—32no—
463C22×C3—41no—
464C22×C3—42no—
465C22×C3—41no—
466C22×C3—42no—
467C22×C3—62no—
468C22×C3—81no—
469C22×C3—82no—
470C22×C3—121no—
471C22×C3—122no—
472C22×C3C2×D3×D411yescharacteristic
473C22×C3C22×#6711yescharacteristic
474C2×D3—22no—
475C2×D3—41no—
476C2×D3—42no—
477C2×D3—122no—
478C2×D3—124no—
479C2×D3—122no—
480C2×D3—124no—
481C2×D3—242no—
482C2×D3—244no—
483C2×D3#94012yes—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—32no—
488C3×C4—42no—
489C3×C4—41no—
490C3×C4—41no—
491C3×C4—62no—
492C3×C4—81no—
493C3×C4—121no—
494C3×C4—122no—
495C3×C4C2×D3×D412yes—
496C3×C4C2×D3×D412yes—
497Dic3—22no—
498Dic3—42no—
499Dic3—41no—
500Dic3#94012yes—
501C32#315011yescharacteristic, complemented, Sylow
502C23—21no—
503C23—31no—
504C23—61no—
505C23—182no—
506Q8—22no—
507Q8—62no—
508Q8—62no—
509Q8—62no—
510D4—22no—
511D4—62no—
512D4—122no—
513D4—124no—
514D4—122no—
515D4—182no—
516D4—182no—
517D4—364no—
518D4—364no—
519C2×C4—21no—
520C2×C4—31no—
521C2×C4—34no—
522C2×C4—32no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—122no—
526C2×C4—122no—
527C2×C4—122no—
528C2×C4—364no—
529C2×C4D3×#6712yes—
530C2×C4C22×D3211yescharacteristic
531C8—34no—
532C8—94no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—62no—
536C2×C3—81no—
537C2×C3—81no—
538C2×C3—161no—
539C2×C3—241no—
540C2×C3D3×#12711yescharacteristic
541C2×C3#577712yes—
542C2×C3C2×#94011yescharacteristic
543C2×C3#582212yes—
544D3—22no—
545D3—81no—
546D3—242no—
547D3—242no—
548D3—482no—
549C22—32no—
550C22—42no—
551C22—41no—
552C22—62no—
553C22—122no—
554C22—121no—
555C22—364no—
556C22—362no—
557C22C2×D3×#6711yescharacteristic
558C4—22no—
559C4—32no—
560C4—41no—
561C4—62no—
562C4—121no—
563C4—122no—
564C4D32×D412yes—
565C3—21no—
566C3#8186911yescharacteristic, complemented
567C3#8328611yescharacteristic, complemented
568C2—62no—
569C2—81no—
570C2—241no—
571C2—722no—
572C2D3×#94011yescharacteristic
573C2#1059547012yes—
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
hypercenter#124D32
hypocenterC32#3150
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5668C2semidirect
2. C2×#63949C2semidirect
3. C2×#63935C2semidirect
4. #10593970C2semidirect
5. #10592757C2semidirect
6. C3×#5060C2semidirect
7. #10591608C2semidirect
8. #10591472C2semidirect
9. #10590376C2semidirect
10. #10590351C2semidirect
11. D3×#803C2semidirect
49. #5668D3semidirect
58. #5060D3semidirect
104. D3×C3⋊C8D4semidirect
501. C32#3150semidirect
566. C3#81869semidirect
567. C3#83286semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
C2×#639492
C2×#639352
#105939702
#105927572
C3×#50602
#105916082
#105914722
#105903762
#105903512
D3×#8032
#832863
#818693