Finite Group Databasebeta

← #11857959

Subgroups — #11857959

Order 1152.

1619 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C3×D3×#117C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592703C211yesmaximal, characteristic, complemented
5C3×#5001C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic, complemented
8#10590608C214yesmaximal, complemented
9#10590607C214yesmaximal, complemented
10#82213—31nomaximal
11#78924—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#625—21no—
16C22×D3×Dic3—21no—
17C2×#3795—21no—
18C2×#3795—21no—
19C2×#3795—24no—
20C2×#3795C418yescomplemented
21C2×#3795C2212yes—
22C2×#3795C2212yes—
23C32×#117C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×#892C2212yescomplemented
28C3×D3×C4⋊C4C2212yescomplemented
29C3×D3×C22⋊C4—21no—
30C3×#877—21no—
31C3×#872—21no—
32C3×C42×D3—21no—
33C2×#3711C2212yescomplemented
34D3×#208—24no—
35C2×D3×C3⋊C8C2212yescomplemented
36#63637C2214yescomplemented
37C3×#809C2214yescomplemented
38#63567C2214yescomplemented
39#63562C2214yescomplemented
40C22×#237—31no—
41C22×#235—31no—
42C2×C3×#117—31no—
43C22×#208—31no—
44C2×D3×M16—31no—
45D3×#117D311yescharacteristic, complemented
46C3×#418—31no—
47#5215—31no—
48#5120—31no—
49#5004—31no—
50#5004—31no—
51#5004—31no—
52#5004—61no—
53#5002—34no—
54#5001—31no—
55#5001D311yescharacteristic, complemented
56#4966—34no—
57#4772—34no—
58#4771—34no—
59C23×C3×D3—21no—
60C23×C3×D3D411yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3—21no—
63C2×#634—21no—
64C2×#634—22no—
65C2×#634C2×C414yescomplemented
66C2×#634C2312yes—
67C22×C3×Dic3D411yescharacteristic
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12C2×C414yescomplemented
71C2×C3×D12C2312yes—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3C2×C414yes—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3D414yes—
77C2×C3×C4×D3C2311yescharacteristic
78C2×C3×C4×D3C2311yescharacteristic
79C2×#625—28no—
80C2×#625—22no—
81C2×#625—22no—
82C2×D3×Dic3—28no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3—22no—
85#3795—28no—
86#3795—28no—
87#3795—24no—
88#3795—24no—
89#3795C2×C418yes—
90#3795C2×C418yescomplemented
91C32×C4⋊C4C2312yes—
92C32×C22⋊C4—21no—
93C32×C42—21no—
94#3748—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×C4×Dic3—22no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3711—24no—
105D3×C3⋊C8—24no—
106#2896—91noSylow
107C22×C3×D4—31no—
108C23×C3×C4—31no—
109C22×#67—61no—
110C22×#67—61no—
111C23×Dic3—61no—
112C2×#237—38no—
113C2×#237—32no—
114C2×#237—32no—
115C2×#237—64no—
116C2×#237—61no—
117C2×#237—61no—
118C2×#235—38no—
119C2×#235—32no—
120C2×#235—32no—
121C2×#235—64no—
122C2×#235—61no—
123C2×#235—61no—
124C22×D12C2×D311yescharacteristic
125C22×C4×D3—61no—
126C22×C4×D3C2×D311yescharacteristic
127C22×Dic6—31no—
128C22×Dic6—31no—
129C22×Dic6—61no—
130C2×C3×M16—31no—
131C3×#117—21no—
132C3×#117—31no—
133C3×#117—32no—
134C3×#117—61no—
135C3×#117—61no—
136C3×#117C2×D311yescharacteristic
137C3×#117C2×D311yescharacteristic
138C2×C3×C4⋊C4—32no—
139C2×C3×C22⋊C4—61no—
140C2×C3×C42—61no—
141#926C2×D311yescharacteristic
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—32no—
145C2×#208—61no—
146C2×#208—64no—
147C2×#208C2×D311yescharacteristic
148C22×C3⋊C8—32no—
149D3×M16—64no—
150C2×ΓL(1,𝔽25)—32no—
151C2×D3×C8—32no—
152#892C2×D312yescomplemented
153D3×C4⋊C4C2×D312yescomplemented
154D3×C22⋊C4—21no—
155#877—21no—
156#872—21no—
157C42×D3—21no—
158C3×#102—34no—
159#832—34no—
160#816—34no—
161#810—34no—
162#810—34no—
163#810—34no—
164#810—64no—
165#809—34no—
166#809C2×D314yescomplemented
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—24no—
169C22×C3×D3—22no—
170C22×C3×D3—42no—
171C22×C3×D3—44no—
172C22×C3×D3C22⋊C414yes—
173C22×C3×D3C2×D411yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C2×C32×C4—22no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2411yescharacteristic
180C2×C3⋊Dic3—24no—
181C2×C3⋊Dic3—22no—
182#634—24no—
183#634—22no—
184#634C22×C414yes—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C22⋊C414yes—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C3×D12—24no—
190C3×D12—22no—
191C3×D12C22×C414yes—
192C3×C4×D3—44no—
193C3×C4×D3C22⋊C414yes—
194C3×C4×D3C22⋊C414yes—
195C3×C4×D3C22×C412yes—
196C3×C4×D3C22×C412yes—
197C3×C4×D3C2×D412yes—
198C3×C4×D3C2×D412yes—
199#625—28no—
200#625—28no—
201D3×Dic3—28no—
202D3×Dic3—28no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C22×#41—91no—
206C22×M16—91no—
207C2×#117—31no—
208#419—91no—
209#419—91no—
210#418—31no—
211#418—91no—
212#417—94no—
213#416—94no—
214C24×C3—31no—
215C24×C3—61no—
216C23×D3—21no—
217C23×D3#6711yescharacteristic
218C2×C3×D4—34no—
219C2×C3×D4—32no—
220C2×C3×D4—62no—
221C2×C3×D4—61no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—34no—
225C22×C3×C4—34no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4—62no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—68no—
234C2×#67—62no—
235C2×#67—62no—
236C2×#67—68no—
237C2×#67—62no—
238C2×#67—62no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—68no—
242C22×Dic3—62no—
243C22×Dic3—62no—
244C22×Dic3—121no—
245C22×Dic3#6711yescharacteristic
246#237—38no—
247#237—38no—
248#237—68no—
249#237—68no—
250#237—64no—
251#237—64no—
252#235—38no—
253#235—38no—
254#235—68no—
255#235—68no—
256#235—64no—
257#235—64no—
258C2×D12—22no—
259C2×D12—21no—
260C2×D12C4×D314yescomplemented
261C2×D12C22×D312yes—
262C2×C4×D3—22no—
263C2×C4×D3—68no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3C4×D314yes—
267C2×C4×D3D1214yes—
268C2×C4×D3#6711yescharacteristic
269C2×C4×D3#6711yescharacteristic
270C2×C4×D3C22×D311yescharacteristic
271C2×C4×D3C22×D311yescharacteristic
272C2×Dic6—34no—
273C2×Dic6—34no—
274C2×Dic6—32no—
275C2×Dic6—32no—
276C2×Dic6—62no—
277C2×Dic6—64no—
278C2×Dic6—62no—
279C2×Dic6—62no—
280C2×Dic6—61no—
281C2×Dic6—61no—
282C2×Dic6—122no—
283C2×Dic6—121no—
284C3×M16—62no—
285C2×C3×C8—32no—
286C3×C4⋊C4—22no—
287C3×C4⋊C4—32no—
288C3×C4⋊C4—62no—
289C3×C4⋊C4C22×D312yes—
290C3×C4⋊C4C22×D312yes—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—41no—
294C3×C22⋊C4—62no—
295C3×C22⋊C4—61no—
296C3×C42—21no—
297C3×C42—21no—
298C3×C42—41no—
299C3×C42—62no—
300C3×C42—61no—
301#217—21no—
302(C2×D3)⋊C4—22no—
303C4⋊Dic3C22×D312yes—
304Dic3⋊C4—22no—
305C4×Dic3—21no—
306C4×Dic3—22no—
307#208—22no—
308#208—64no—
309#208—62no—
310#208—62no—
311#208—122no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8—64no—
316C2×C3⋊C8C22×D312yes—
317ΓL(1,𝔽25)—64no—
318D3×C8—64no—
319C22×C32—22no—
320C22×C32C2×C22⋊C412yes—
321C22×C32C22×D411yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—24no—
325C2×C3×D3—44no—
326C2×C3×D3—48no—
327C2×C3×D3—44no—
328C2×C3×D3C2×C22⋊C412yes—
329C2×C3×D3C2×C22⋊C412yes—
330C32×C4—42no—
331C32×C4C2×C22⋊C412yes—
332C32×C4C23×C411yescharacteristic
333C32×C4C22×D411yescharacteristic
334C3⋊Dic3—24no—
335C3×Dic3—42no—
336C3×Dic3C2×C22⋊C412yes—
337C3×Dic3C2×C22⋊C412yes—
338C2×#41—92no—
339C2×#41—92no—
340C2×#41—98no—
341C2×#41—184no—
342C2×#41—181no—
343C2×#41—181no—
344C22×Q8—91no—
345C22×D4—31no—
346C22×D4—181no—
347C23×C4—31no—
348C23×C4—181no—
349C2×M16—31no—
350C2×M16—92no—
351C2×M16—91no—
352C2×M16—184no—
353C22×C8—92no—
354#117—31no—
355#117—32no—
356#117—61no—
357#117—61no—
358#117D3211yescharacteristic
359C2×C4⋊C4—32no—
360C2×C22⋊C4—61no—
361C2×C42—61no—
362#103—94no—
363#103—94no—
364#102—34no—
365#102—94no—
366C23×C3—21no—
367C23×C3—31no—
368C23×C3—31no—
369C23×C3—34no—
370C23×C3—64no—
371C23×C3—62no—
372C23×C3—122no—
373C23×C3—124no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×#6711yescharacteristic
376C22×D3—24no—
377C22×D3—22no—
378C22×D3—42no—
379C22×D3—44no—
380C22×D3(C2×D3)⋊C414yes—
381C22×D3C2×#6711yescharacteristic
382C22×D3C2×#6711yescharacteristic
383C3×D4—34no—
384C3×D4—64no—
385C3×D4—62no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—34no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—34no—
396C2×C3×C4—34no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—32no—
400C2×C3×C4—32no—
401C2×C3×C4—42no—
402C2×C3×C4—62no—
403C2×C3×C4—124no—
404C2×C3×C4C2×C4×D312yes—
405C2×C3×C4C2×C4×D312yes—
406C2×C3×C4C2×D1212yes—
407C2×C3×C4D3×D412yes—
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412#67—68no—
413#67—68no—
414#67—68no—
415#67—68no—
416C2×Dic3—22no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—68no—
422C2×Dic3—68no—
423C2×Dic3—122no—
424C2×Dic3—124no—
425C2×Dic3(C2×D3)⋊C414yes—
426C2×Dic3C2×#6711yescharacteristic
427C2×Dic3C2×#6711yescharacteristic
428D12—24no—
429D12—22no—
430D12C2×C4×D314yes—
431C4×D3—44no—
432C4×D3—68no—
433C4×D3—68no—
434C4×D3(C2×D3)⋊C414yes—
435C4×D3(C2×D3)⋊C414yes—
436C4×D3C2×C4×D312yes—
437C4×D3C2×C4×D312yes—
438C4×D3C2×D1212yes—
439C4×D3C2×D1212yes—
440Dic6—34no—
441Dic6—34no—
442Dic6—64no—
443Dic6—64no—
444Dic6—64no—
445Dic6—62no—
446Dic6—62no—
447Dic6—122no—
448Dic6—124no—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—62no—
452C3⋊C8—62no—
453C3⋊C8—122no—
454C2×C32—22no—
455C2×C32C22×C22⋊C411yescharacteristic
456C2×C32#57512yes—
457C3×D3—22no—
458C3×D3—22no—
459C3×D3—44no—
460C24—31no—
461C24—61no—
462#41—98no—
463#41—98no—
464#41—184no—
465#41—184no—
466#41—188no—
467#41—188no—
468C2×Q8—92no—
469C2×Q8—94no—
470C2×Q8—182no—
471C2×Q8—181no—
472C2×D4—32no—
473C2×D4—34no—
474C2×D4—62no—
475C2×D4—61no—
476C2×D4—182no—
477C2×D4—182no—
478C2×D4—188no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—34no—
483C22×C4—34no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—62no—
487C22×C4—182no—
488C22×C4—182no—
489C22×C4—188no—
490C22×C4—181no—
491C22×C4C2×D3211yescharacteristic
492M16—62no—
493M16—184no—
494M16—182no—
495C2×C8—32no—
496C2×C8—92no—
497C2×C8—184no—
498C4⋊C4—32no—
499C4⋊C4—62no—
500C4⋊C4C2×D3212yes—
501C22⋊C4—21no—
502C22⋊C4—62no—
503C22⋊C4—61no—
504C42—21no—
505C42—62no—
506C42—61no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—22no—
511C22×C3—32no—
512C22×C3—32no—
513C22×C3—42no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—64no—
517C22×C3—124no—
518C22×C3—128no—
519C22×C3—124no—
520C22×C3D3×C22⋊C412yes—
521C22×C3C2×(C2×D3)⋊C412yes—
522C22×C3C2×D3×D411yescharacteristic
523C22×C3C22×#6711yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—24no—
527C2×D3—44no—
528C2×D3—48no—
529C2×D3—44no—
530C2×D3C2×(C2×D3)⋊C412yes—
531C2×D3C2×(C2×D3)⋊C412yes—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—22no—
535C3×C4—32no—
536C3×C4—32no—
537C3×C4—42no—
538C3×C4—42no—
539C3×C4—82no—
540C3×C4—122no—
541C3×C4D3×C22⋊C412yes—
542C3×C4C2×(C2×D3)⋊C412yes—
543C3×C4C22×C4×D311yescharacteristic
544C3×C4C22×C4×D311yescharacteristic
545C3×C4C22×D1211yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547Dic3—42no—
548Dic3—64no—
549Dic3—64no—
550Dic3—124no—
551Dic3C2×(C2×D3)⋊C412yes—
552Dic3C2×(C2×D3)⋊C412yes—
553C32#289611yescharacteristic, complemented, Sylow
554C23—31no—
555C23—31no—
556C23—34no—
557C23—62no—
558C23—64no—
559C23—122no—
560C23—124no—
561C23D3×#6711yescharacteristic
562Q8—94no—
563Q8—182no—
564Q8—184no—
565D4—34no—
566D4—62no—
567D4—64no—
568D4—188no—
569D4—188no—
570C2×C4—22no—
571C2×C4—31no—
572C2×C4—31no—
573C2×C4—34no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—34no—
579C2×C4—34no—
580C2×C4—62no—
581C2×C4—124no—
582C2×C4—188no—
583C2×C4—188no—
584C2×C4—182no—
585C2×C4—184no—
586C2×C4C4×D3212yes—
587C2×C4D3×D1212yes—
588C2×C4D3×#6711yescharacteristic
589C2×C4C22×D3211yescharacteristic
590C8—62no—
591C8—182no—
592C2×C3—22no—
593C2×C3—22no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—42no—
597C2×C3—62no—
598C2×C3—62no—
599C2×C3—124no—
600C2×C3C2×D3×C22⋊C411yescharacteristic
601C2×C3#577312yes—
602C2×C3C22×(C2×D3)⋊C411yescharacteristic
603C2×C3#582212yes—
604D3—22no—
605D3—22no—
606D3—44no—
607C22—22no—
608C22—32no—
609C22—32no—
610C22—62no—
611C22—62no—
612C22—64no—
613C22—124no—
614C22—128no—
615C22—124no—
616C22D3×(C2×D3)⋊C412yes—
617C22C2×D3×#6711yescharacteristic
618C4—32no—
619C4—32no—
620C4—42no—
621C4—122no—
622C4—184no—
623C4D3×(C2×D3)⋊C412yes—
624C4C2×C4×D3211yescharacteristic
625C4C2×D3×D1211yescharacteristic
626C3—21no—
627C3#7892411yescharacteristic, complemented
628C3#8221311yescharacteristic, complemented
629C2—22no—
630C2—62no—
631C2—62no—
632C2—124no—
633C2C2×D3×(C2×D3)⋊C411yescharacteristic
634C2#1059546912yes—
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×#3795C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2896
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. C3×D3×#117C2semidirect
3. C2×D3×#208C2semidirect
4. #10592703C2semidirect
5. C3×#5001C2semidirect
6. #10591107C2semidirect
7. #10591085C2semidirect
8. #10590608C2semidirect
9. #10590607C2semidirect
20. C2×#3795C4semidirect
27. C3×#892C22semidirect
28. C3×D3×C4⋊C4C22semidirect
33. C2×#3711C22semidirect
35. C2×D3×C3⋊C8C22semidirect
36. #63637C22semidirect
37. C3×#809C22semidirect
38. #63567C22semidirect
39. #63562C22semidirect
45. D3×#117D3semidirect
55. #5001D3semidirect
65. C2×#634C2×C4semidirect
70. C2×C3×D12C2×C4semidirect
90. #3795C2×C4semidirect
152. #892C2×D3semidirect
153. D3×C4⋊C4C2×D3semidirect
166. #809C2×D3semidirect
260. C2×D12C4×D3semidirect
553. C32#2896semidirect
627. C3#78924semidirect
628. C3#82213semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C3×D3×#1172
C2×D3×#2082
#105927032
C3×#50012
#105911072
#105910852
#105906082
#105906072
#822133
#789243