Finite Group Databasebeta

← #11874442

Subgroups — #11874442

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5668C211yesmaximal, characteristic, complemented
2C2×#63947C212yesmaximal, complemented
3C2×#63933C212yesmaximal, complemented
4#10593897C211yesmaximal, characteristic, complemented
5#10592759C211yesmaximal, characteristic, complemented
6C3×#5058C211yesmaximal, characteristic, complemented
7#10591605C212yesmaximal, complemented
8#10591469C212yesmaximal, complemented
9#10590372C211yesmaximal, characteristic, complemented
10#10590354C211yesmaximal, characteristic, complemented
11D3×#803C211yesmaximal, characteristic, complemented
12#83286—31nomaximal
13#81844—31nomaximal
14C2×C3×#239C2211yescharacteristic
15C2×C3×#237C2211yescharacteristic
16C2×#3795C2212yes—
17C32×#124C2211yescharacteristic
18C2×#3756C2212yes—
19C2×#3754C2212yes—
20#64078C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C2×C3×#215C2212yes—
23C3×#940C2211yescharacteristic
24C2×C3×#213C2212yes—
25C3×#884—22no—
26C3×#67⋊C4—22no—
27C3×#875C2211yescharacteristic
28C3×#874C2211yescharacteristic
29C3×C42×D3C2211yescharacteristic
30#63947—28no—
31#63933—28no—
32#63908—22no—
33Dic3×D12—22no—
34#63860C2212yes—
35C2×#3719C2212yes—
36C2×#3716C2212yes—
37C2×#3715C2212yes—
38C2×#3713C2212yes—
39C2×D3×C3⋊C8C2212yes—
40#63630C2211yescharacteristic
41C3×#803C2211yescharacteristic
42#63554C2212yes—
43C3×#532—31no—
44C2×#950—32no—
45C2×#950—32no—
46C2×#916—32no—
47C2×#912—32no—
48#5716—31no—
49#5668D311yescharacteristic, complemented
50#5477—31no—
51C3×#496—31no—
52#5167—32no—
53#5154—32no—
54#5086—32no—
55#5074—32no—
56#5074—31no—
57#5060—31no—
58#5060—31no—
59#5060—31no—
60#5060—61no—
61#5058—31no—
62#5058D311yescharacteristic, complemented
63C2×#803—31no—
64#4715—31no—
65D3×#97—31no—
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C2×#634C2312yes—
69C2×C3×#67—21no—
70C2×C3×#67—22no—
71C22×C3×Dic3—21no—
72C3×#239—24no—
73C3×#237—24no—
74C2×C3×D12—21no—
75C2×C3×D12—22no—
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3D412yes—
80C2×C3×C4×D3C2311yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C2×#625—22no—
83C2×D3×Dic3—22no—
84#3795—24no—
85#3795—24no—
86C32×C22⋊C4—22no—
87C32×C42C2311yescharacteristic
88#3756—24no—
89#3754—24no—
90C4⋊(C3⋊Dic3)—22no—
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×#215—24no—
93C3×#213—24no—
94C3×(C2×D3)⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3D412yes—
97C3×C4×Dic3C2311yescharacteristic
98C2×C3×C3⋊C8C2312yes—
99(C2×D3)⋊Dic3—24no—
100#3719—24no—
101#3716—24no—
102#3715—24no—
103#3713—24no—
104D3×C3⋊C8D418yescomplemented
105#3150—91noSylow
106C2×C3×#41—31no—
107C2×C3×#41—31no—
108C2×#239C2×D311yescharacteristic
109C2×#237—32no—
110C2×#237C2×D311yescharacteristic
111C2×#235—32no—
112C2×C3×SD16—32no—
113C2×C3×D8—32no—
114C3×C4⋊Q8—31no—
115C3×#127—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#944C2×D311yescharacteristic
127C2×#216—32no—
128C2×#216—32no—
129C2×#216—32no—
130C2×#216—62no—
131C2×#215—32no—
132C2×#215C2×D312yes—
133#940C2×D311yescharacteristic
134#938—62no—
135#936—32no—
136D4×Dic3—62no—
137C2×#214—32no—
138C2×#214—32no—
139C2×#214—32no—
140C2×#214—32no—
141C2×#214—62no—
142C2×#213—32no—
143C2×#213—32no—
144C2×#213C2×D312yes—
145#930—62no—
146C22×C3⋊C8—32no—
147#916—68no—
148#912—68no—
149C2×Dic12—32no—
150C2×#204—32no—
151C2×D3×C8—32no—
152#884—22no—
153#67⋊C4—22no—
154#875—32no—
155#875C2×D311yescharacteristic
156#874C2×D311yescharacteristic
157C4×D12—62no—
158C42×D3C2×D311yescharacteristic
159#869—31no—
160#869—31no—
161#869—61no—
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
178C2×C3⋊Dic3—22no—
179#634—22no—
180#634—22no—
181C3×#67—44no—
182C3×#67—42no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—42no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D411yescharacteristic
187C3×D12—22no—
188C3×D12—22no—
189C3×D12—22no—
190C3×D12—44no—
191C3×D12—42no—
192C3×C4×D3—42no—
193C3×C4×D3—42no—
194C3×C4×D3C2×D414yes—
195C3×Dic6—22no—
196#625—44no—
197D3×Dic3—44no—
198C3⋊(C3⋊C8)C2×D414yes—
199C3×C3⋊C8C2×D414yes—
200C2×#135—92no—
201C2×#135—92no—
202#532—31no—
203#532—91no—
204#497—91no—
205#497—92no—
206#497—91no—
207#496—31no—
208#496—91no—
209#496—92no—
210C2×#97—91no—
211C3×#41—64no—
212C3×#41—64no—
213C2×C3×Q8—21no—
214C2×C3×Q8—31no—
215C2×C3×Q8C22×D311yescharacteristic
216C2×C3×Q8C22×D311yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4—31no—
219C2×C3×D4—32no—
220C2×C3×D4—61no—
221C2×C3×D4—62no—
222C2×C3×D4—61no—
223C2×C3×D4—62no—
224C2×C3×D4C22×D311yescharacteristic
225C2×C3×D4C22×D311yescharacteristic
226C22×C3×C4—31no—
227C22×C3×C4—32no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C2×#67—21no—
231C2×#67—22no—
232C2×#67—62no—
233C2×#67—62no—
234C22×Dic3—21no—
235C22×Dic3—62no—
236#239—24no—
237#237—24no—
238#237—64no—
239#237—64no—
240#235—64no—
241#235—64no—
242C2×D12—21no—
243C2×D12—22no—
244C2×D12C22×D312yes—
245C2×D12C22×D311yescharacteristic
246C2×C4×D3—21no—
247C2×C4×D3—62no—
248C2×C4×D3#6712yes—
249C2×C4×D3C22×D311yescharacteristic
250C2×Dic6—32no—
251C2×Dic6—32no—
252C2×Dic6—62no—
253C2×Dic6C22×D311yescharacteristic
254C3×SD16—64no—
255C3×D8—64no—
256C2×C3×C8—32no—
257C3×C4⋊C4—62no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—42no—
261C3×C22⋊C4—62no—
262C3×C42—21no—
263C3×C42—32no—
264C3×C42—31no—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D311yescharacteristic
267#217—64no—
268#216—64no—
269#216—64no—
270#216—64no—
271#216—124no—
272#215—24no—
273#215—64no—
274#214—64no—
275#214—64no—
276#214—64no—
277#214—64no—
278#214—124no—
279#213—24no—
280#213—64no—
281#213—64no—
282(C2×D3)⋊C4—22no—
283(C2×D3)⋊C4—64no—
284C4⋊Dic3—62no—
285C4⋊Dic3—62no—
286C4⋊Dic3—122no—
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—
295Dic12—64no—
296#204—64no—
297D3×C8—38no—
298C22×C32—41no—
299C22×C32—42no—
300C22×C32C22×D411yescharacteristic
301C2×C3×D3—22no—
302C2×C3×D3—42no—
303C2×C3×D3—41no—
304C2×C3×D3—44no—
305C2×C3×D3—42no—
306C2×C3×D3#12712yes—
307C32×C4—22no—
308C32×C4—41no—
309C32×C4C22×D412yes—
310C3⋊Dic3—42no—
311C3×Dic3—22no—
312C3×Dic3—41no—
313C3×Dic3#12712yes—
314C2×#41—31no—
315C2×#41—31no—
316C2×#41—92no—
317#135—188no—
318#135—188no—
319C2×Q16—92no—
320C2×Q16—92no—
321C2×SD16—32no—
322C2×SD16—92no—
323C2×SD16—92no—
324C2×SD16—92no—
325C2×D8—32no—
326C2×D8—92no—
327C22×C8—92no—
328C4⋊Q8—31no—
329C4⋊Q8—91no—
330#127—31no—
331#127—31no—
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—
348C23×C3—62no—
349C22×D3—22no—
350C22×D3—21no—
351C22×D3C2×#6711yescharacteristic
352C3×Q8—22no—
353C3×Q8—22no—
354C3×Q8—42no—
355C3×Q8—62no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—42no—
359C3×D4—62no—
360C3×D4—62no—
361C3×D4—62no—
362C3×D4—124no—
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—122no—
376C2×C3×C4—122no—
377C2×C3×C4—122no—
378C2×C3×C4D3×D412yes—
379C2×C3×C4C2×#6712yes—
380C2×C3×C4C23×D311yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382#67—44no—
383#67—42no—
384#67—124no—
385#67—124no—
386C2×Dic3—21no—
387C2×Dic3—42no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—122no—
391C2×Dic3—124no—
392C2×Dic3C2×#6712yes—
393C2×Dic3C2×#6711yescharacteristic
394D12—22no—
395D12—22no—
396D12—22no—
397D12—44no—
398D12—42no—
399C4×D3—42no—
400C4×D3—42no—
401C4×D3—124no—
402C4×D3D3×D414yes—
403Dic6—22no—
404Dic6—62no—
405Dic6—62no—
406Dic6—62no—
407Dic6—62no—
408Dic6—122no—
409Dic6—122no—
410C3×C8—34no—
411C3⋊C8—34no—
412C3⋊C8—34no—
413C3⋊C8—64no—
414C3⋊C8D3×D414yes—
415C2×C32—81no—
416C2×C32C2×#12711yescharacteristic
417C2×C32#57512yes—
418C3×D3—22no—
419C3×D3—81no—
420C3×D3—82no—
421#41—64no—
422#41—64no—
423#41—184no—
424#41—184no—
425C2×Q8—31no—
426C2×Q8—92no—
427C2×Q8C2×D3211yescharacteristic
428C2×D4—31no—
429C2×D4—32no—
430C2×D4—61no—
431C2×D4—62no—
432C2×D4—61no—
433C2×D4—62no—
434C2×D4—182no—
435C2×D4C2×D3211yescharacteristic
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—182no—
441Q16—184no—
442Q16—184no—
443SD16—64no—
444SD16—184no—
445SD16—184no—
446SD16—184no—
447D8—64no—
448D8—184no—
449C2×C8—32no—
450C2×C8—98no—
451C2×C8—92no—
452C4⋊C4—62no—
453C4⋊C4—182no—
454C22⋊C4—22no—
455C22⋊C4—62no—
456C22⋊C4—184no—
457C42—31no—
458C42—32no—
459C42C2×D3211yescharacteristic
460C22×C3—21no—
461C22×C3—32no—
462C22×C3—41no—
463C22×C3—42no—
464C22×C3—41no—
465C22×C3—42no—
466C22×C3—62no—
467C22×C3—81no—
468C22×C3—82no—
469C22×C3—121no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—124no—
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C22×#6711yescharacteristic
475C2×D3—22no—
476C2×D3—42no—
477C2×D3—44no—
478C2×D3—41no—
479C2×D3—42no—
480C2×D3#94012yes—
481C3×C4—22no—
482C3×C4—22no—
483C3×C4—22no—
484C3×C4—32no—
485C3×C4—42no—
486C3×C4—41no—
487C3×C4—41no—
488C3×C4—62no—
489C3×C4—81no—
490C3×C4—121no—
491C3×C4C2×D3×D412yes—
492C3×C4C2×D3×D412yes—
493Dic3—22no—
494Dic3—41no—
495Dic3—122no—
496Dic3—122no—
497Dic3—242no—
498Dic3#94012yes—
499C32#315011yescharacteristic, complemented, Sylow
500C23—21no—
501C23—31no—
502C23—61no—
503C23—62no—
504Q8—22no—
505Q8—62no—
506Q8—182no—
507Q8—182no—
508D4—22no—
509D4—62no—
510D4—62no—
511D4—62no—
512D4—124no—
513D4—122no—
514D4—124no—
515D4—122no—
516D4—364no—
517C2×C4—21no—
518C2×C4—31no—
519C2×C4—34no—
520C2×C4—32no—
521C2×C4—61no—
522C2×C4—122no—
523C2×C4—122no—
524C2×C4—122no—
525C2×C4—182no—
526C2×C4—364no—
527C2×C4D3×#6712yes—
528C2×C4C22×D3211yescharacteristic
529C8—34no—
530C8—94no—
531C2×C3—22no—
532C2×C3—21no—
533C2×C3—62no—
534C2×C3—81no—
535C2×C3—81no—
536C2×C3—161no—
537C2×C3—242no—
538C2×C3—241no—
539C2×C3D3×#12711yescharacteristic
540C2×C3#577312yes—
541C2×C3C2×#94011yescharacteristic
542C2×C3#582212yes—
543D3—22no—
544D3—81no—
545D3—82no—
546C22—32no—
547C22—42no—
548C22—41no—
549C22—62no—
550C22—124no—
551C22—122no—
552C22—121no—
553C22—122no—
554C22C2×D3×#6711yescharacteristic
555C4—22no—
556C4—32no—
557C4—41no—
558C4—62no—
559C4—121no—
560C4—362no—
561C4D32×D412yes—
562C3—21no—
563C3#8184411yescharacteristic, complemented
564C3#8328611yescharacteristic, complemented
565C2—62no—
566C2—81no—
567C2—241no—
568C2—242no—
569C2D3×#94011yescharacteristic
570C2#1059546912yes—
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×#63947C2semidirect
3. C2×#63933C2semidirect
4. #10593897C2semidirect
5. #10592759C2semidirect
6. C3×#5058C2semidirect
7. #10591605C2semidirect
8. #10591469C2semidirect
9. #10590372C2semidirect
10. #10590354C2semidirect
11. D3×#803C2semidirect
49. #5668D3semidirect
62. #5058D3semidirect
104. D3×C3⋊C8D4semidirect
499. C32#3150semidirect
563. C3#81844semidirect
564. 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×#639472
C2×#639332
#105938972
#105927592
C3×#50582
#105916052
#105914692
#105903722
#105903542
D3×#8032
#832863
#818443