Finite Group Databasebeta

← #11811928

Subgroups — #11811928

Order 1152.

1833 conjugacy classes of subgroups.

The subgroup lattice has 635 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C211yesmaximal, characteristic
2C2×#64105C211yesmaximal, characteristic, complemented
3C2×#63913C211yesmaximal, characteristic, complemented
4C2×#63840C211yesmaximal, characteristic, complemented
5C3×#4989C212yesmaximal, complemented
6#10591386C211yesmaximal, characteristic, complemented
7#10591312C212yesmaximal, complemented
8#10591291C212yesmaximal, complemented
9#10591278C212yesmaximal, complemented
10#10591260C211yesmaximal, characteristic, complemented
11#10591236C211yesmaximal, characteristic, complemented
12#74411—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×#627C2211yescharacteristic
17C22×#626C2212yes—
18C22×#625C2211yescharacteristic
19C2×#3798—24no—
20C2×#3798—24no—
21C2×#3798—24no—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27#64105—24no—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×#3722C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37#63913—24no—
38#63840—24no—
39C3×C3⋊#95C2212yes—
40C3×C3⋊#95C2212yes—
41#63579C2212yes—
42C22×#235—32no—
43C2×#896—32no—
44C2×#896—61no—
45C2×#888—32no—
46C2×#885—32no—
47C3×#385—32no—
48#5210—32no—
49#4991—32no—
50#4989D312yescomplemented
51#4961—32no—
52#4959—32no—
53#4957—32no—
54#4672—32no—
55#4668—32no—
56#4666—32no—
57#4646—32no—
58C23×C3⋊D3C2311yescharacteristic
59C23×C3×D3C2312yes—
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3D414yes—
69C2×#634—22no—
70C2×#634—22no—
71C2×#634—22no—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3—24no—
77C2×C3×C4×D3—24no—
78C2×#627—22no—
79C2×#627—22no—
80C2×#627D414yes—
81C2×#626—24no—
82C2×#626—24no—
83C2×#626—24no—
84C2×#625—22no—
85C2×#625—22no—
86C2×#625D414yes—
87#3798—232no—
88C32×C4⋊C4—22no—
89#3752—22no—
90#3752—22no—
91#3750—22no—
92#3750—22no—
93C3×(C2×D3)⋊C4—24no—
94C3×(C2×D3)⋊C4—24no—
95C3×Dic3⋊C4—24no—
96Dic3⋊Dic3—24no—
97#3722—24no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—24no—
100Dic32—22no—
101Dic32—22no—
102#2432—91noSylow
103C23×C3×C4—32no—
104C22×#67—32no—
105C22×#67—32no—
106C2×#235—68no—
107C2×#235—68no—
108C2×#235—68no—
109C22×D12—32no—
110C22×C4×D3—32no—
111C22×C4×D3—61no—
112C22×C4×D3C2×D312yes—
113C22×Dic6—32no—
114C22×Dic6—32no—
115C22×Dic6—61no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—32no—
118C2×C3×C4⋊C4C2×D312yes—
119C2×C3×C22⋊C4—32no—
120C2×C3×C22⋊C4—32no—
121C2×#217—32no—
122C2×#217—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—61no—
130C2×(C2×D3)⋊C4—61no—
131C2×(C2×D3)⋊C4C2×D312yes—
132C2×(C2×D3)⋊C4C2×D312yes—
133C2×C4⋊Dic3—32no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—61no—
138C2×Dic3⋊C4—61no—
139C2×Dic3⋊C4C2×D312yes—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—32no—
142#896—68no—
143#896—68no—
144#888—68no—
145#885—68no—
146C3×#95—32no—
147C3×#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95C2×D312yes—
151C3⋊#95C2×D312yes—
152C23×C32C2411yescharacteristic
153C22×C3⋊D3—22no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3C2×D412yes—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3C2×D414yes—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4C2×D412yes—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3⋊Dic3C2×D412yes—
180C2×C3⋊Dic3C2×D412yes—
181C4×C3⋊D3—28no—
182#634—44no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D414yes—
191C2×C3×Dic3#4114yescomplemented
192C3×C4×D3—216no—
193#627—28no—
194#626—216no—
195#625—28no—
196C22×#41—91no—
197C2×C4⋊Q8—91no—
198C2×#124—91no—
199C2×C22⋊Q8—91no—
200#394—92no—
201#394—92no—
202#391—91no—
203#390—91no—
204#385—32no—
205#385—92no—
206C4×C22⋊C4—91no—
207C24×C3—32no—
208C23×D3—32no—
209C23×D3—61no—
210C23×D3C22×D312yes—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—64no—
218C22×C3×C4—64no—
219C22×C3×C4—64no—
220C22×C3×C4C22×D312yes—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C2×#67—38no—
224C2×#67—64no—
225C2×#67—64no—
226C2×#67—64no—
227C2×#67—64no—
228C2×#67—64no—
229C22×Dic3—32no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D312yes—
238#235—664no—
239C2×D12—64no—
240C2×D12—64no—
241C2×D12—64no—
242C2×C4×D3—24no—
243C2×C4×D3—24no—
244C2×C4×D3—24no—
245C2×C4×D3—38no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—122no—
250C2×C4×D3—122no—
251C2×Dic6—38no—
252C2×Dic6—64no—
253C2×Dic6—64no—
254C2×Dic6—64no—
255C2×Dic6—64no—
256C2×Dic6—64no—
257C2×Dic6—64no—
258C2×Dic6—122no—
259C2×Dic6—122no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—24no—
262C3×C4⋊C4—64no—
263C3×C22⋊C4—64no—
264C3×C22⋊C4—64no—
265#217—64no—
266#217—64no—
267(C2×D3)⋊C4—24no—
268(C2×D3)⋊C4—24no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—64no—
274(C2×D3)⋊C4—64no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—64no—
277C4⋊Dic3—64no—
278Dic3⋊C4—24no—
279Dic3⋊C4—64no—
280Dic3⋊C4—64no—
281Dic3⋊C4—64no—
282Dic3⋊C4—64no—
283Dic3⋊C4—64no—
284C4×Dic3—64no—
285C4×Dic3—64no—
286C22×C32C22×D411yescharacteristic
287C22×C32C22×D411yescharacteristic
288C22×C32C22×D411yescharacteristic
289C22×C32C2×#4112yes—
290C22×C322−1+412yes—
291C2×C3⋊D3—22no—
292C2×C3⋊D3—22no—
293C2×C3⋊D3—22no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—42no—
296C2×C3×D3—24no—
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C2×C3×D3—42no—
303C32×C4—22no—
304C32×C4—41no—
305C32×C4—41no—
306C3⋊Dic3—41no—
307C3⋊Dic3—41no—
308C3⋊Dic3#12014yes—
309C3×Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—42no—
312C2×#41—184no—
313C2×#41—184no—
314C2×#41—184no—
315C22×Q8—91no—
316C22×Q8—91no—
317C22×D4—92no—
318C22×D4—91no—
319C23×C4—32no—
320C23×C4—91no—
321C4⋊Q8—184no—
322#124—184no—
323C22⋊Q8—184no—
324C2×C4⋊C4—32no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4D3211yescharacteristic
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—91no—
335C2×C22⋊C4—91no—
336C2×C42—91no—
337C2×C42—91no—
338#95—32no—
339#95—32no—
340#95—92no—
341C23×C3—21no—
342C23×C3—34no—
343C23×C3—62no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3C23×D312yes—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—34no—
357C22×D3—62no—
358C22×D3—64no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—121no—
366C22×D3—121no—
367C22×D3—122no—
368C22×D3D3×D414yes—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—34no—
381C2×C3×C4—34no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—42no—
387C2×C3×C4—616no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4D3×D414yes—
396#67—616no—
397#67—616no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—34no—
406C2×Dic3—34no—
407C2×Dic3—34no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—121no—
420C2×Dic3—121no—
421C2×Dic3—122no—
422C2×Dic3#23514yescomplemented
423C2×Dic3D3×D414yes—
424D12—616no—
425C4×D3—216no—
426C4×D3—616no—
427C4×D3—128no—
428Dic6—616no—
429Dic6—128no—
430Dic6—128no—
431C2×C32C2×#12011yescharacteristic
432C2×C32#53211yescharacteristic
433C2×C32#53611yescharacteristic
434C2×C32#54712yes—
435C2×C32#54812yes—
436C3⋊D3—42no—
437C3×D3—44no—
438C24—32no—
439C24—91no—
440#41—1832no—
441C2×Q8—94no—
442C2×Q8—182no—
443C2×Q8—182no—
444C2×Q8—182no—
445C2×Q8—182no—
446C2×Q8—182no—
447C2×D4—94no—
448C2×D4—184no—
449C2×D4—184no—
450C2×D4—184no—
451C2×D4—182no—
452C2×D4—182no—
453C22×C4—32no—
454C22×C4—32no—
455C22×C4—32no—
456C22×C4—64no—
457C22×C4—64no—
458C22×C4—64no—
459C22×C4—91no—
460C22×C4—94no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—182no—
464C22×C4—182no—
465C22×C4C2×D3211yescharacteristic
466C22×C4C2×D3211yescharacteristic
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—22no—
469C4⋊C4—64no—
470C4⋊C4—182no—
471C4⋊C4—184no—
472C4⋊C4—182no—
473C22⋊C4—64no—
474C22⋊C4—64no—
475C22⋊C4—182no—
476C22⋊C4—182no—
477C22⋊C4—184no—
478C22⋊C4—184no—
479C22⋊C4—184no—
480C42—182no—
481C42—182no—
482C22×C3—22no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—64no—
488C22×C3—64no—
489C22×C3—64no—
490C22×C3—122no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3C2×#23512yes—
495C22×C3C2×D3×D412yes—
496C22×C3C2×D3×D412yes—
497C22×C3C2×D3×D412yes—
498C22×C3#100712yes—
499C22×C3D3×#4112yes—
500C22×C3#101012yes—
501C2×D3—24no—
502C2×D3—24no—
503C2×D3—24no—
504C2×D3—42no—
505C2×D3—42no—
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—64no—
509C2×D3—64no—
510C2×D3—64no—
511C2×D3—64no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—124no—
515C2×D3—124no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—122no—
520C3×C4—24no—
521C3×C4—42no—
522C3×C4—42no—
523C3×C4—42no—
524C3×C4—42no—
525C3×C4—42no—
526C3×C4—64no—
527C3×C4—64no—
528C3×C4—122no—
529Dic3—24no—
530Dic3—24no—
531Dic3—38no—
532Dic3—42no—
533Dic3—64no—
534Dic3—122no—
535Dic3—122no—
536Dic3—122no—
537Dic3—122no—
538C32#243211yescharacteristic, complemented, Sylow
539C23—34no—
540C23—62no—
541C23—62no—
542C23—62no—
543C23—62no—
544C23—62no—
545C23—62no—
546C23—92no—
547C23—182no—
548C23—181no—
549C23—181no—
550C23—182no—
551C23C22×D3211yescharacteristic
552Q8—188no—
553Q8—364no—
554D4—1816no—
555D4—188no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—34no—
564C2×C4—34no—
565C2×C4—616no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—92no—
574C2×C4—92no—
575C2×C4—92no—
576C2×C4—188no—
577C2×C4—182no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4#381112yes—
583C2×C3—22no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—22no—
588C2×C3—124no—
589C2×C3#550712yes—
590C2×C3#554812yes—
591C2×C3#555212yes—
592C2×C3D3×#12012yes—
593C2×C3#562812yes—
594C2×C3#563312yes—
595C2×C3#565512yes—
596D3—44no—
597D3—124no—
598D3—124no—
599C22—64no—
600C22—64no—
601C22—64no—
602C22—122no—
603C22—122no—
604C22—122no—
605C22—122no—
606C22—182no—
607C22—182no—
608C22—182no—
609C22—362no—
610C22—362no—
611C22D3×#23512yes—
612C22D32×D411yescharacteristic
613C22D32×D411yescharacteristic
614C22#6431512yes—
615C22C2×#381111yescharacteristic
616C4—22no—
617C4—41no—
618C4—41no—
619C4—64no—
620C4—64no—
621C4—94no—
622C4—122no—
623C4—361no—
624C4—361no—
625C3—21no—
626C3#7441112yescomplemented
627C2—124no—
628C2—362no—
629C2#1059437512yes—
630C2#1059451312yes—
631C2#1059501711yescharacteristic
632C2#1059527811yescharacteristic
633C2#1059540511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#3798C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2432
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64105C2semidirect
3. C2×#63913C2semidirect
4. C2×#63840C2semidirect
5. C3×#4989C2semidirect
6. #10591386C2semidirect
7. #10591312C2semidirect
8. #10591291C2semidirect
9. #10591278C2semidirect
10. #10591260C2semidirect
11. #10591236C2semidirect
50. #4989D3semidirect
191. C2×C3×Dic3#41semidirect
422. C2×Dic3#235semidirect
538. C32#2432semidirect
626. C3#74411semidirect

Maximal subgroups

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

subgroupindex
C22×#37982
C2×#641052
C2×#639132
C2×#638402
C3×#49892
#105913862
#105913122
#105912912
#105912782
#105912602
#105912362
#744113