Finite Group Databasebeta

← #11860407

Subgroups — #11860407

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic
4#10592703C211yesmaximal, characteristic, complemented
5C3×#4995C211yesmaximal, characteristic, complemented
6#10591087C211yesmaximal, characteristic
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590590C212yesmaximal, complemented
9#10590481C212yesmaximal, complemented
10#10590480C212yesmaximal, complemented
11#10590479C212yesmaximal, complemented
12C4×#951—31nomaximal
13#79200—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#67⋊C4—21no—
26C3×#67⋊C4—21no—
27C3×#872—21no—
28C3×C42×D3—21no—
29C2×#3724—21no—
30C2×Dic32—21no—
31#63844—21no—
32#63844—21no—
33#63844C2212yes—
34#63844C2212yes—
35C2×#3719C2212yes—
36#63831C418yescomplemented
37C2×#3716C2212yes—
38#63637C2212yes—
39#63637C2212yes—
40C3×#808C2212yes—
41C3×#807C2212yes—
42#63565C2212yes—
43#63562C2212yes—
44#63554C2212yes—
45Dic3×C3⋊C8C2212yes—
46C3×C4×#41—31no—
47C2×#951—31no—
48C2×#909—31no—
49#5522D311yescharacteristic
50C2×#887—31no—
51C2×C4×Dic6—31no—
52C3×#428—31no—
53#5232—31no—
54Dic3×M16—31no—
55#5030—32no—
56C4×#216—32no—
57#5018—32no—
58C4×#214—32no—
59#5004—31no—
60#5004—31no—
61#5004—61no—
62#4995D311yescharacteristic, complemented
63#4966—31no—
64C4×#208—31no—
65#4889—32no—
66#4873—32no—
67#4853—32no—
68#4852—32no—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—21no—
71C2×#634—21no—
72C2×#634—22no—
73C2×#634C2×C414yescomplemented
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C3×#235—22no—
80C3×#235C2×C414yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—21no—
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—21no—
85C2×C3×Dic6C2311yescharacteristic
86C32×C4⋊C4C2311yescharacteristic
87C32×C4⋊C4C2311yescharacteristic
88C32×C22⋊C4—21no—
89C32×C42—21no—
90#3748—22no—
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×(C2×D3)⋊C4—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—21no—
97C3×Dic3⋊C4—21no—
98C3×C4×Dic3—21no—
99C3×C4×Dic3—21no—
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3D411yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C3×C4×Dic3C2311yescharacteristic
104C3×#208C2×C414yescomplemented
105C2×C3×C3⋊C8C2312yes—
106#3724—22no—
107#3724—22no—
108Dic32—22no—
109Dic32—22no—
110#3719C2×C418yescomplemented
111#3716C2×C418yescomplemented
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C2×#235C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C2×C3×M16—31no—
119C3×C4×Q8—31no—
120C3×C4×Q8—31no—
121C3×C4×D4—31no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C3×C4×D4—61no—
125C3×#117—21no—
126C3×#117—61no—
127C3×#117C2×D311yescharacteristic
128C3×#117C2×D311yescharacteristic
129C2×C3×C4⋊C4—31no—
130C2×C3×C42—31no—
131C2×C3×C42—61no—
132#951—38no—
133C2×#216—32no—
134C2×#214—32no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×Dic3⋊C4—61no—
137C2×Dic3⋊C4—61no—
138C2×C4×Dic3—61no—
139C2×C4×Dic3—61no—
140C2×C4×Dic3C2×D311yescharacteristic
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—61no—
144C2×#208C2×D311yescharacteristic
145#909—38no—
146C2×Dic12—32no—
147C2×#204—32no—
148#893C2×D311yescharacteristic
149#893C2×D311yescharacteristic
150#887—32no—
151#887—32no—
152#887—61no—
153#887—61no—
154#887C2×D311yescharacteristic
155#887C2×D311yescharacteristic
156#67⋊C4—21no—
157#67⋊C4—21no—
158#872—21no—
159C42×D3—21no—
160C4×Dic6—32no—
161C4×Dic6—32no—
162C4×Dic6—61no—
163C4×Dic6—61no—
164C3×#107—32no—
165C3×#106—32no—
166#835—32no—
167#832—32no—
168#815—32no—
169C8×Dic3—32no—
170#810—32no—
171#810—32no—
172#810—32no—
173#810—32no—
174#810—32no—
175#810—62no—
176#810—62no—
177#809—32no—
178#808C2×D312yes—
179#807C2×D312yes—
180#803—32no—
181C4×C3⋊C8—32no—
182C23×C32C2×D411yescharacteristic
183C22×C3×D3—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—24no—
191C2×C3⋊Dic3—22no—
192#634—24no—
193#634—22no—
194#634C22×C414yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—41no—
200C2×C3×Dic3—42no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—21no—
206C3×D12C22×C412yes—
207C3×C4×D3—24no—
208C3×C4×D3—42no—
209C3×C4×D3—42no—
210C3×Dic6—21no—
211C3×Dic6C22×C412yes—
212C3⋊(C3⋊C8)—22no—
213C3×C3⋊C8C22×C414yes—
214C2×#137—91no—
215C4×#41—31no—
216C2×C4×Q8—91no—
217#441—92no—
218#440—92no—
219C4×Q16—92no—
220C4×SD16—92no—
221#428—31no—
222#419—91no—
223#417—91no—
224C4×M16—91no—
225C3×#41—34no—
226C3×#41—62no—
227C2×C3×Q8—31no—
228C2×C3×D4—31no—
229C2×C3×D4—61no—
230C22×C3×C4—21no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—21no—
240C22×Dic3—21no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—121no—
244C22×Dic3#6711yescharacteristic
245C22×Dic3#6711yescharacteristic
246#235—22no—
247#235C4×D314yes—
248C2×D12C22×D311yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×Dic6—34no—
253C2×Dic6—34no—
254C2×Dic6—32no—
255C2×Dic6—32no—
256C2×Dic6—62no—
257C2×Dic6—64no—
258C2×Dic6—62no—
259C2×Dic6—61no—
260C2×Dic6—62no—
261C2×Dic6—61no—
262C2×Dic6—122no—
263C2×Dic6—121no—
264C2×Dic6C22×D311yescharacteristic
265C3×M16—34no—
266C2×C3×C8—32no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—32no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4—61no—
273C3×C4⋊C4C22×D311yescharacteristic
274C3×C4⋊C4C22×D311yescharacteristic
275C3×C4⋊C4C22×D311yescharacteristic
276C3×C4⋊C4C22×D311yescharacteristic
277C3×C22⋊C4—21no—
278C3×C22⋊C4—21no—
279C3×C22⋊C4—41no—
280C3×C22⋊C4—61no—
281C3×C22⋊C4—61no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—31no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—41no—
289C3×C42—61no—
290C3×C42—61no—
291#216—38no—
292#214—38no—
293(C2×D3)⋊C4—21no—
294(C2×D3)⋊C4—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3C22×D312yes—
297Dic3⋊C4—21no—
298Dic3⋊C4—21no—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303C4×Dic3—21no—
304C4×Dic3—21no—
305C4×Dic3—62no—
306C4×Dic3—62no—
307C4×Dic3—62no—
308C4×Dic3—62no—
309C4×Dic3#6711yescharacteristic
310C4×Dic3#6711yescharacteristic
311C4×Dic3C22×D311yescharacteristic
312C4×Dic3C22×D311yescharacteristic
313#208—62no—
314#208—62no—
315#208—122no—
316#208C4×D314yescomplemented
317C2×C3⋊C8—32no—
318C2×C3⋊C8—32no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8C22×D312yes—
321Dic12—38no—
322#204—38no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32C4×D412yes—
326C22×C32C22×D411yescharacteristic
327C2×C3×D3—22no—
328C2×C3×D3—41no—
329C2×C3×D3—41no—
330C32×C4—41no—
331C32×C4—41no—
332C32×C4C4×D412yes—
333C32×C4C23×C411yescharacteristic
334C32×C4C2×#4111yescharacteristic
335C3⋊Dic3—24no—
336C3×Dic3—22no—
337C3×Dic3—21no—
338C3×Dic3—21no—
339C3×Dic3—21no—
340C3×Dic3—42no—
341C3×Dic3#13712yescomplemented
342C2×#41—31no—
343C22×Q8—91no—
344#137—98no—
345C2×Q16—92no—
346C2×SD16—92no—
347C2×M16—31no—
348C2×M16—91no—
349C4×Q8—31no—
350C4×Q8—31no—
351C4×Q8—92no—
352C4×Q8—92no—
353C4×Q8—181no—
354C4×Q8—181no—
355C4×D4—31no—
356C4×D4—31no—
357C4×D4—61no—
358C4×D4—61no—
359#117—61no—
360#117D3211yescharacteristic
361C2×C4⋊C4—31no—
362C2×C4⋊C4—181no—
363C2×C42—31no—
364C2×C42—61no—
365C2×C42—181no—
366#107—32no—
367#106—32no—
368#103—92no—
369#103—92no—
370#103—92no—
371#102—92no—
372#97—92no—
373C4×C8—92no—
374C23×C3—21no—
375C23×C3—61no—
376C23×C3D3×D411yescharacteristic
377C23×C3C2×#6711yescharacteristic
378C22×D3—21no—
379C3×Q8—32no—
380C3×Q8—61no—
381C3×D4—32no—
382C3×D4—64no—
383C3×D4—61no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—31no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—64no—
401C2×C3×C4—62no—
402C2×C3×C4—122no—
403C2×C3×C4—122no—
404C2×C3×C4—121no—
405C2×C3×C4—122no—
406C2×C3×C4C2×C4×D312yes—
407C2×C3×C4C2×C4×D312yes—
408C2×C3×C4#23512yes—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4#23912yes—
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414#67—24no—
415C2×Dic3—21no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—41no—
419C2×Dic3—42no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—122no—
425C2×Dic3—124no—
426C2×Dic3C2×#6711yescharacteristic
427C2×Dic3C2×#6711yescharacteristic
428C2×Dic3C2×#6711yescharacteristic
429C2×Dic3C2×#6711yescharacteristic
430D12—21no—
431D12C2×C4×D312yes—
432C4×D3—24no—
433C4×D3—42no—
434C4×D3—42no—
435Dic6—21no—
436Dic6—34no—
437Dic6—34no—
438Dic6—64no—
439Dic6—64no—
440Dic6—64no—
441Dic6—62no—
442Dic6—62no—
443Dic6—122no—
444Dic6—124no—
445Dic6C2×C4×D312yes—
446C3×C8—34no—
447C3⋊C8—62no—
448C3⋊C8—62no—
449C3⋊C8—122no—
450C3⋊C8C2×C4×D314yes—
451C2×C32—22no—
452C2×C32C2×C4×D411yescharacteristic
453C2×C32C2×#13711yescharacteristic
454C2×C32#57511yescharacteristic
455C3×D3—42no—
456#41—34no—
457#41—62no—
458C2×Q8—31no—
459C2×Q8—92no—
460C2×Q8—94no—
461C2×Q8—182no—
462C2×Q8—181no—
463C2×D4—31no—
464C2×D4—61no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—181no—
472C22×C4C2×D3211yescharacteristic
473Q16—98no—
474SD16—98no—
475M16—34no—
476M16—182no—
477C2×C8—32no—
478C2×C8—92no—
479C4⋊C4—32no—
480C4⋊C4—61no—
481C4⋊C4—61no—
482C4⋊C4—61no—
483C4⋊C4—182no—
484C4⋊C4—182no—
485C4⋊C4C2×D3211yescharacteristic
486C4⋊C4C2×D3211yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C42—21no—
491C42—31no—
492C42—31no—
493C42—31no—
494C42—31no—
495C42—61no—
496C42—61no—
497C42—182no—
498C42—182no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—62no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3#89312yes—
511C22×C3C4×#6712yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C22×#6711yescharacteristic
514C2×D3—22no—
515C2×D3—41no—
516C2×D3—41no—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—22no—
520C3×C4—32no—
521C3×C4—41no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4—41no—
525C3×C4—62no—
526C3×C4—61no—
527C3×C4—61no—
528C3×C4—61no—
529C3×C4—81no—
530C3×C4—81no—
531C3×C4—122no—
532C3×C4#89312yes—
533C3×C4C4×#6712yes—
534C3×C4C22×C4×D311yescharacteristic
535C3×C4C22×C4×D311yescharacteristic
536C3×C4C2×#23511yescharacteristic
537C3×C4C2×#23911yescharacteristic
538Dic3—22no—
539Dic3—21no—
540Dic3—21no—
541Dic3—21no—
542Dic3—42no—
543Dic3—64no—
544Dic3—64no—
545Dic3—124no—
546Dic3#95112yescomplemented
547C32C4×#13711yescharacteristic, complemented, Sylow
548C23—61no—
549C23D3×#6711yescharacteristic
550Q8—32no—
551Q8—61no—
552Q8—94no—
553Q8—182no—
554Q8—184no—
555D4—32no—
556D4—64no—
557D4—61no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—31no—
561C2×C4—31no—
562C2×C4—31no—
563C2×C4—31no—
564C2×C4—62no—
565C2×C4—61no—
566C2×C4—64no—
567C2×C4—62no—
568C2×C4—122no—
569C2×C4—122no—
570C2×C4—121no—
571C2×C4—122no—
572C2×C4—182no—
573C2×C4—184no—
574C2×C4#379912yes—
575C2×C4C4×D3212yes—
576C2×C4D3×#6711yescharacteristic
577C2×C4C22×D3211yescharacteristic
578C8—34no—
579C8—182no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—42no—
586C2×C3—122no—
587C2×C3C2×#89311yescharacteristic
588C2×C3#577311yescharacteristic
589C2×C3D3×#13711yescharacteristic
590C2×C3C2×C4×#6711yescharacteristic
591C2×C3#582211yescharacteristic
592C2×C3C2×#95111yescharacteristic
593D3—42no—
594C22—21no—
595C22—21no—
596C22—62no—
597C22—121no—
598C22—121no—
599C22#6390412yes—
600C22C2×D3×#6711yescharacteristic
601C4—32no—
602C4—41no—
603C4—41no—
604C4—61no—
605C4—61no—
606C4—61no—
607C4—62no—
608C4—122no—
609C4—184no—
610C4#6390412yes—
611C4C2×#379911yescharacteristic
612C4C2×C4×D3211yescharacteristic
613C3—21no—
614C3#7920011yescharacteristic, complemented
615C3C4×#95111yescharacteristic, complemented
616C2—22no—
617C2—122no—
618C2C2×#6390411yescharacteristic
619C2D3×#95111yescharacteristic
620C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
4. #10592703C2semidirect
5. C3×#4995C2semidirect
7. Dic3×#208C2semidirect
8. #10590590C2semidirect
9. #10590481C2semidirect
10. #10590480C2semidirect
11. #10590479C2semidirect
36. #63831C4semidirect
62. #4995D3semidirect
73. C2×#634C2×C4semidirect
104. C3×#208C2×C4semidirect
110. #3719C2×C4semidirect
111. #3716C2×C4semidirect
316. #208C4×D3semidirect
341. C3×Dic3#137semidirect
546. Dic3#951semidirect
547. C32C4×#137semidirect
614. C3#79200semidirect
615. C3C4×#951semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C2×#638442
C2×#638312
#105927032
C3×#49952
#105910872
Dic3×#2082
#105905902
#105904812
#105904802
#105904792
C4×#9513
#792003