Finite Group Databasebeta

← #11857964

Subgroups — #11857964

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
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3D3×#926C211yesmaximal, characteristic, complemented
4#10592819C211yesmaximal, characteristic, complemented
5C3×#5131C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic, complemented
8#10590954C214yesmaximal, complemented
9#10590670C214yesmaximal, complemented
10#83768—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—
23C2×C32×M16C2211yescharacteristic
24#64135C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×D3×M16—24no—
28C2×C3×ΓL(1,𝔽25)C2212yescomplemented
29C2×C3×D3×C8C2212yescomplemented
30D3×#217—21no—
31#63955—21no—
32D3×C4⋊Dic3C2212yescomplemented
33C4×D3×Dic3—21no—
34#63855—21no—
35#63841C2212yescomplemented
36#63643C2214yescomplemented
37C3×#821C2214yescomplemented
38#63567C2214yescomplemented
39#63563C2214yescomplemented
40C22×#237—31no—
41C22×#235—31no—
42C22×C3×M16—31no—
43C2×#926—31no—
44C2×D3×M16D311yescharacteristic, complemented
45D3×#117—31no—
46C3×#418—31no—
47#5215—31no—
48#5133—34no—
49#5131—31no—
50#5131D311yescharacteristic, complemented
51#5120—31no—
52#5120—31no—
53#5120—31no—
54#5120—61no—
55#5113—34no—
56#5004—31no—
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×D3C2×C414yes—
73C2×C3×C4×D3D411yescharacteristic
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D414yes—
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×C4×D3C2311yescharacteristic
78C2×#625—28no—
79C2×#625—22no—
80C2×#625—22no—
81C2×D3×Dic3—28no—
82C2×D3×Dic3—22no—
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×M16—22no—
92C2×C32×C8C2312yes—
93#3757—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95C4×C3⋊Dic3—21no—
96C3×#217—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101C3×ΓL(1,𝔽25)—24no—
102C3×D3×C8—24no—
103Dic3⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105Dic32—22no—
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—61no—
116C2×#237—61no—
117C2×#237—64no—
118C2×#235—38no—
119C2×#235—32no—
120C2×#235—32no—
121C2×#235—61no—
122C2×#235—61no—
123C2×#235—64no—
124C22×D12C2×D311yescharacteristic
125C22×C4×D3—61no—
126C22×C4×D3C2×D311yescharacteristic
127C22×Dic6—31no—
128C22×Dic6—31no—
129C22×Dic6—61no—
130C2×C3×M16—21no—
131C2×C3×M16—31no—
132C2×C3×M16—32no—
133C2×C3×M16—64no—
134C2×C3×M16C2×D311yescharacteristic
135C2×C3×M16C2×D311yescharacteristic
136C22×C3×C8—32no—
137C3×#117—31no—
138C2×#217—61no—
139#926—31no—
140#926—31no—
141#926—32no—
142#926—61no—
143#926—61no—
144#926—61no—
145#926C2×D311yescharacteristic
146C2×C4⋊Dic3—32no—
147C2×C4×Dic3—61no—
148C2×#208C2×D311yescharacteristic
149D3×M16—24no—
150C2×ΓL(1,𝔽25)C2×D312yescomplemented
151C2×D3×C8C2×D312yescomplemented
152#892—32no—
153D3×C4⋊C4—32no—
154D3×C22⋊C4—61no—
155#877—61no—
156#872—61no—
157C42×D3—61no—
158C3×#102—34no—
159#832—34no—
160#821—34no—
161#821C2×D314yescomplemented
162#816—34no—
163#816—34no—
164#816—34no—
165#816—64no—
166#810—34no—
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×C4C22×C412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—24no—
180C2×C3⋊Dic3—22no—
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×D3C22⋊C414yes—
193C3×C4×D3C22⋊C414yes—
194C3×C4×D3C22×C412yes—
195C3×C4×D3C22×C412yes—
196C3×C4×D3C2×D412yes—
197C3×C4×D3C2×D412yes—
198#625—28no—
199#625—28no—
200D3×Dic3—28no—
201D3×Dic3—28no—
202D3×Dic3—44no—
203C32×C8—22no—
204C3×C3⋊C8—22no—
205C22×#41—91no—
206C22×M16—31no—
207C2×#117—91no—
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×D3D1211yescharacteristic
218C2×C3×D4—34no—
219C2×C3×D4—32no—
220C2×C3×D4—61no—
221C2×C3×D4—62no—
222C22×C3×C4—21no—
223C22×C3×C4—31no—
224C22×C3×C4—34no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—34no—
228C22×C3×C4—31no—
229C22×C3×C4—31no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—68no—
233C2×#67—62no—
234C2×#67—62no—
235C2×#67—68no—
236C2×#67—62no—
237C2×#67—62no—
238C22×Dic3—62no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3—68no—
242C22×Dic3—62no—
243C22×Dic3—62no—
244C22×Dic3—121no—
245C22×Dic3D1211yescharacteristic
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—21no—
259C2×D12—22no—
260C2×D12C4×D314yescomplemented
261C2×D12C22×D312yes—
262C2×C4×D3—68no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3C4×D314yes—
267C2×C4×D3D1211yescharacteristic
268C2×C4×D3D1211yescharacteristic
269C2×C4×D3#6714yes—
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—61no—
279C2×Dic6—61no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—121no—
283C2×Dic6—122no—
284C3×M16—22no—
285C3×M16—22no—
286C3×M16—42no—
287C3×M16—64no—
288C3×M16—62no—
289C2×C3×C8—22no—
290C2×C3×C8—32no—
291C2×C3×C8—64no—
292C2×C3×C8C22×D312yes—
293C2×C3×C8C22×D312yes—
294C3×C4⋊C4—32no—
295C3×C22⋊C4—61no—
296C3×C42—61no—
297#217—21no—
298#217—62no—
299#217—61no—
300#217—61no—
301#217—121no—
302(C2×D3)⋊C4—62no—
303C4⋊Dic3—32no—
304C4⋊Dic3—32no—
305C4⋊Dic3—62no—
306C4⋊Dic3—62no—
307C4⋊Dic3C22×D312yes—
308Dic3⋊C4—62no—
309C4×Dic3—21no—
310C4×Dic3—62no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—62no—
314C4×Dic3—121no—
315#208—22no—
316C2×C3⋊C8C22×D312yes—
317ΓL(1,𝔽25)—24no—
318D3×C8—24no—
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×C4C2×C22⋊C412yes—
331C32×C4C23×C411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—24no—
334C3⋊Dic3—42no—
335C3×Dic3—42no—
336C3×Dic3C2×C22⋊C412yes—
337C3×Dic3C2×C22⋊C412yes—
338C2×#41—92no—
339C2×#41—92no—
340C2×#41—98no—
341C2×#41—181no—
342C2×#41—181no—
343C2×#41—184no—
344C22×Q8—91no—
345C22×D4—31no—
346C22×D4—181no—
347C23×C4—31no—
348C23×C4—181no—
349C2×M16—31no—
350C2×M16—32no—
351C2×M16—64no—
352C2×M16D3211yescharacteristic
353C22×C8—32no—
354#117—31no—
355#117—92no—
356#117—91no—
357#117—181no—
358#117—181no—
359C2×C4⋊C4—92no—
360C2×C22⋊C4—181no—
361C2×C42—181no—
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×C3C2×D1211yescharacteristic
375C23×C3D3×D411yescharacteristic
376C22×D3—24no—
377C22×D3—22no—
378C22×D3—42no—
379C22×D3—44no—
380C22×D3(C2×D3)⋊C414yes—
381C22×D3C2×D1211yescharacteristic
382C22×D3C2×D1211yescharacteristic
383C3×D4—34no—
384C3×D4—64no—
385C3×D4—62no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—34no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—34no—
394C2×C3×C4—34no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—62no—
400C2×C3×C4C2×C4×D312yes—
401C2×C3×C4C2×C4×D312yes—
402C2×C3×C4C2×D1211yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D412yes—
405C2×C3×C4C2×#6712yes—
406C2×C3×C4C23×D311yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408#67—68no—
409#67—68no—
410#67—68no—
411#67—68no—
412C2×Dic3—22no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—68no—
418C2×Dic3—68no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—122no—
422C2×Dic3—124no—
423C2×Dic3—122no—
424C2×Dic3—124no—
425C2×Dic3(C2×D3)⋊C414yes—
426C2×Dic3C2×D1211yescharacteristic
427C2×Dic3C2×D1211yescharacteristic
428D12—24no—
429D12—22no—
430D12C2×C4×D314yes—
431C4×D3—68no—
432C4×D3—68no—
433C4×D3—124no—
434C4×D3(C2×D3)⋊C414yes—
435C4×D3(C2×D3)⋊C414yes—
436C4×D3C2×C4×D312yes—
437C4×D3C2×C4×D312yes—
438C4×D3C2×#6712yes—
439C4×D3C2×#6712yes—
440Dic6—34no—
441Dic6—34no—
442Dic6—64no—
443Dic6—64no—
444Dic6—64no—
445Dic6—62no—
446Dic6—62no—
447Dic6—122no—
448Dic6—124no—
449C3×C8—22no—
450C3×C8—22no—
451C3×C8—42no—
452C3×C8—62no—
453C3⋊C8—22no—
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—181no—
471C2×Q8—182no—
472C2×D4—32no—
473C2×D4—34no—
474C2×D4—61no—
475C2×D4—62no—
476C2×D4—182no—
477C2×D4—182no—
478C2×D4—188no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—34no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—34no—
486C22×C4—182no—
487C22×C4—182no—
488C22×C4—188no—
489C22×C4—182no—
490C22×C4—181no—
491C22×C4C2×D3211yescharacteristic
492M16—22no—
493M16—64no—
494M16—62no—
495C2×C8—32no—
496C2×C8—64no—
497C2×C8C2×D3212yes—
498C4⋊C4—32no—
499C4⋊C4—92no—
500C4⋊C4—182no—
501C22⋊C4—61no—
502C22⋊C4—182no—
503C22⋊C4—181no—
504C42—61no—
505C42—182no—
506C42—181no—
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×C3C22×D1211yescharacteristic
523C22×C3C2×D3×D411yescharacteristic
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—122no—
538C3×C4D3×C22⋊C412yes—
539C3×C4C2×(C2×D3)⋊C412yes—
540C3×C4C22×C4×D311yescharacteristic
541C3×C4C22×C4×D311yescharacteristic
542C3×C4C2×D3×D411yescharacteristic
543C3×C4C22×#6711yescharacteristic
544Dic3—42no—
545Dic3—64no—
546Dic3—64no—
547Dic3—124no—
548Dic3—122no—
549Dic3—122no—
550Dic3—242no—
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×D1211yescharacteristic
562Q8—94no—
563Q8—182no—
564Q8—184no—
565D4—34no—
566D4—62no—
567D4—64no—
568D4—188no—
569D4—188no—
570C2×C4—31no—
571C2×C4—31no—
572C2×C4—34no—
573C2×C4—32no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—34no—
578C2×C4—34no—
579C2×C4—62no—
580C2×C4—188no—
581C2×C4—188no—
582C2×C4—182no—
583C2×C4—184no—
584C2×C4—182no—
585C2×C4—364no—
586C2×C4C4×D3212yes—
587C2×C4D3×D1211yescharacteristic
588C2×C4D3×#6712yes—
589C2×C4C22×D3211yescharacteristic
590C8—22no—
591C8—62no—
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#574812yes—
602C2×C3#577312yes—
603C2×C3C22×(C2×D3)⋊C411yescharacteristic
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×D1211yescharacteristic
618C4—32no—
619C4—32no—
620C4—122no—
621C4—184no—
622C4—362no—
623C4D3×(C2×D3)⋊C412yes—
624C4C2×C4×D3211yescharacteristic
625C4C2×D3×#6711yescharacteristic
626C3—21no—
627C3#7892411yescharacteristic, complemented
628C3#8376811yescharacteristic, complemented
629C2—22no—
630C2—62no—
631C2—62no—
632C2—124no—
633C2#1059471212yes—
634C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC22×#3795C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×M16C2semidirect
3. D3×#926C2semidirect
4. #10592819C2semidirect
5. C3×#5131C2semidirect
6. #10591107C2semidirect
7. #10591086C2semidirect
8. #10590954C2semidirect
9. #10590670C2semidirect
20. C2×#3795C4semidirect
28. C2×C3×ΓL(1,𝔽25)C22semidirect
29. C2×C3×D3×C8C22semidirect
32. D3×C4⋊Dic3C22semidirect
35. #63841C22semidirect
36. #63643C22semidirect
37. C3×#821C22semidirect
38. #63567C22semidirect
39. #63563C22semidirect
44. C2×D3×M16D3semidirect
50. #5131D3semidirect
65. C2×#634C2×C4semidirect
70. C2×C3×D12C2×C4semidirect
90. #3795C2×C4semidirect
150. C2×ΓL(1,𝔽25)C2×D3semidirect
151. C2×D3×C8C2×D3semidirect
161. #821C2×D3semidirect
260. C2×D12C4×D3semidirect
553. C32#2896semidirect
627. C3#78924semidirect
628. C3#83768semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C3×D3×M162
D3×#9262
#105928192
C3×#51312
#105911072
#105910862
#105909542
#105906702
#837683
#789243