Finite Group Databasebeta

← #11808754

Subgroups — #11808754

Order 1152.

1893 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C212yesmaximal, complemented
3C2×C4×#626C212yesmaximal, complemented
4C2×C4×#625C211yesmaximal, characteristic, complemented
5#10591724C212yesmaximal, complemented
6#10591723C211yesmaximal, characteristic, complemented
7#10591715C211yesmaximal, characteristic, complemented
8#10591393C211yesmaximal, characteristic, complemented
9#10591303C212yesmaximal, complemented
10#10591222C211yesmaximal, characteristic, complemented
11#10591203C211yesmaximal, characteristic, complemented
12#82347—32nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×#67C2212yes—
17C22×C3×C4×D3C2212yes—
18C22×#626C2212yes—
19C22×#625C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C4×#638—24no—
22C2×#3752C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2212yes—
26C3×C4×#67—28no—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×C4×Dic3C2212yes—
30C2×#3724C2211yescharacteristic
31C2×Dic3⋊Dic3C2212yes—
32C2×#3722C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C4×#626—28no—
36C4×#625—24no—
37#63579C2212yes—
38#63579C2211yescharacteristic
39#63579C2211yescharacteristic
40C2×C3×C4×D4—32no—
41C2×C4×#67—32no—
42C2×C4×#67—32no—
43C2×C4×#67—32no—
44C2×C4×#67—61no—
45C2×C4×#67D312yescomplemented
46C2×C4×D12—32no—
47#5223—32no—
48#5223—32no—
49#4993—32no—
50#4993—32no—
51#4960—32no—
52#4960—32no—
53#4949—32no—
54#4949—32no—
55#4932—32no—
56C24×C32C2311yescharacteristic
57C23×C3⋊D3C2311yescharacteristic
58C23×C3×D3C2312yes—
59C22×C32×C4—22no—
60C22×C32×C4—24no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C2×#638—22no—
64C2×#638—22no—
65C2×#638—22no—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—24no—
71C2×C3×#67—24no—
72C2×C3×#67—24no—
73C2×C3×#67—24no—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—24no—
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—24no—
80C2×#626—24no—
81C2×#626—24no—
82C2×#626—24no—
83C2×#625—24no—
84C2×#625—22no—
85#3757—22no—
86#3752—22no—
87#3750—22no—
88C4×C3⋊Dic3D414yescomplemented
89C3×#217—24no—
90C3×(C2×D3)⋊C4—24no—
91C3×Dic3⋊C4—24no—
92C3×C4×Dic3D418yescomplemented
93#3724—22no—
94Dic3⋊Dic3—24no—
95#3722—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—24no—
98#2397—91noSylow
99C22×C3×D4—32no—
100C23×C3×C4—21no—
101C23×C3×C4—32no—
102C23×C3×C4C2×D312yes—
103C22×#67—32no—
104C22×#67—32no—
105C22×#67—32no—
106C22×#67—61no—
107C22×#67C2×D312yes—
108C22×D12—32no—
109C22×C4×D3—32no—
110C22×C4×D3—61no—
111C22×C4×D3C2×D312yes—
112C3×C4×D4—68no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4—32no—
116C2×C3×C42—32no—
117C2×#217—32no—
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—61no—
121C2×#217C2×D312yes—
122C4×#67—28no—
123C4×#67—68no—
124C4×#67—68no—
125C4×#67—68no—
126C4×#67—68no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—61no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×C4⋊Dic3—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—61no—
139C2×Dic3⋊C4C2×D312yes—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—61no—
142C2×C4×Dic3C2×D312yes—
143C4×D12—68no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C23×C32—21no—
149C23×C32—21no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32#4112yes—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3#4112yes—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3#4114yes—
166C2×C32×C4—21no—
167C2×C32×C4—22no—
168C2×C32×C4—44no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D414yes—
171#638—28no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3C2×D412yes—
178C2×C3⋊Dic3C2×D412yes—
179C4×C3⋊D3—44no—
180C3×#67—216no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D414yes—
189C2×C3×Dic3C2×D414yes—
190C3×C4×D3—48no—
191#626—216no—
192#625—28no—
193C2×C4×D4—32no—
194C2×C4×D4—92no—
195C2×C4×D4—91no—
196C2×C4×D4—91no—
197#399—91no—
198#399—92no—
199#399—91no—
200#392—91no—
201#392—92no—
202#392—91no—
203#376—91no—
204C24×C3—21no—
205C24×C3—32no—
206C24×C3C22×D312yes—
207C23×D3—32no—
208C23×D3—61no—
209C23×D3C22×D312yes—
210C2×C3×D4—64no—
211C2×C3×D4—64no—
212C2×C3×D4—64no—
213C22×C3×C4—24no—
214C22×C3×C4—24no—
215C22×C3×C4—24no—
216C22×C3×C4—24no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—44no—
223C22×C3×C4—64no—
224C22×C3×C4—64no—
225C22×C3×C4—64no—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D312yes—
228C2×#67—24no—
229C2×#67—24no—
230C2×#67—24no—
231C2×#67—64no—
232C2×#67—64no—
233C2×#67—64no—
234C2×#67—64no—
235C2×#67—64no—
236C2×#67—64no—
237C2×#67—64no—
238C2×#67—64no—
239C2×#67—64no—
240C2×#67—64no—
241C2×#67—64no—
242C2×#67—64no—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C2×D12—64no—
253C2×D12—64no—
254C2×D12—64no—
255C2×C4×D3—24no—
256C2×C4×D3—24no—
257C2×C4×D3—24no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—124no—
263C3×C4⋊C4—64no—
264C3×C22⋊C4—64no—
265C3×C22⋊C4—64no—
266C3×C42—38no—
267#217—24no—
268#217—64no—
269#217—64no—
270#217—64no—
271#217—64no—
272(C2×D3)⋊C4—24no—
273(C2×D3)⋊C4—64no—
274(C2×D3)⋊C4—64no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—64no—
279C4⋊Dic3—64no—
280Dic3⋊C4—24no—
281Dic3⋊C4—64no—
282Dic3⋊C4—64no—
283Dic3⋊C4—64no—
284Dic3⋊C4—64no—
285C4×Dic3—38no—
286C4×Dic3—64no—
287C4×Dic3#6718yescomplemented
288C22×C32—22no—
289C22×C32—24no—
290C22×C32—41no—
291C22×C32—42no—
292C22×C32—41no—
293C22×C32C22×D411yescharacteristic
294C22×C32C22×D412yes—
295C22×C32C2×#4111yescharacteristic
296C22×C32C2×#4112yes—
297C22×C32C2×#4111yescharacteristic
298C2×C3⋊D3—22no—
299C2×C3⋊D3—24no—
300C2×C3⋊D3—42no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3×D3—24no—
304C2×C3×D3—24no—
305C2×C3×D3—24no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C2×C3×D3—42no—
309C2×C3×D3—42no—
310C32×C4—41no—
311C32×C4#12714yes—
312C3⋊Dic3—22no—
313C3⋊Dic3—22no—
314C3⋊Dic3—41no—
315C3×Dic3—24no—
316C3×Dic3—24no—
317C3×Dic3—42no—
318C22×D4—32no—
319C22×D4—92no—
320C22×D4—91no—
321C22×D4—91no—
322C23×C4—32no—
323C23×C4—91no—
324C23×C4D3211yescharacteristic
325C4×D4—68no—
326C4×D4—188no—
327C4×D4—184no—
328C4×D4—184no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—91no—
331C2×C4⋊C4—92no—
332C2×C4⋊C4—91no—
333C2×C22⋊C4—32no—
334C2×C22⋊C4—32no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4—91no—
340C2×C42—32no—
341C2×C42—91no—
342#95—91no—
343#95—92no—
344#95—91no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—21no—
354C23×C3—22no—
355C23×C3—34no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—62no—
359C23×C3—62no—
360C23×C3—62no—
361C23×C3—62no—
362C23×C3—62no—
363C23×C3—62no—
364C23×C3#23514yes—
365C23×C3C23×D312yes—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—34no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3#23514yes—
385C3×D4—616no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—24no—
391C2×C3×C4—22no—
392C2×C3×C4—34no—
393C2×C3×C4—34no—
394C2×C3×C4—42no—
395C2×C3×C4—48no—
396C2×C3×C4—48no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—128no—
405C2×C3×C4D3×D414yes—
406C2×C3×C4D3×D414yes—
407C2×C3×C4C2×#6714yes—
408#67—216no—
409#67—616no—
410#67—616no—
411#67—616no—
412#67—616no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—34no—
421C2×Dic3—34no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3C2×#6714yes—
437C2×Dic3C2×#6714yes—
438D12—616no—
439C4×D3—48no—
440C4×D3—128no—
441C4×D3—128no—
442C2×C32—42no—
443C2×C32#52512yes—
444C2×C32#52511yescharacteristic
445C2×C32#52511yescharacteristic
446C2×C32#52512yes—
447C2×C32C2×#12711yescharacteristic
448C3⋊D3—42no—
449C3×D3—44no—
450C24—32no—
451C24—91no—
452C24C2×D3211yescharacteristic
453C2×D4—64no—
454C2×D4—64no—
455C2×D4—64no—
456C2×D4—184no—
457C2×D4—184no—
458C2×D4—184no—
459C2×D4—182no—
460C2×D4—182no—
461C2×D4—182no—
462C2×D4—184no—
463C2×D4—182no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—64no—
470C22×C4—64no—
471C22×C4—64no—
472C22×C4—91no—
473C22×C4—91no—
474C22×C4—91no—
475C22×C4—184no—
476C22×C4—182no—
477C22×C4C2×D3211yescharacteristic
478C22×C4C2×D3211yescharacteristic
479C4⋊C4—64no—
480C4⋊C4—182no—
481C4⋊C4—184no—
482C4⋊C4—182no—
483C22⋊C4—64no—
484C22⋊C4—64no—
485C22⋊C4—182no—
486C22⋊C4—184no—
487C22⋊C4—184no—
488C22⋊C4—184no—
489C22⋊C4—182no—
490C42—38no—
491C42—94no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—24no—
495C22×C3—24no—
496C22×C3—21no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—44no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—44no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—64no—
510C22×C3—64no—
511C22×C3—64no—
512C22×C3—122no—
513C22×C3—122no—
514C22×C3—122no—
515C22×C3—122no—
516C22×C3C2×#23512yes—
517C22×C3C2×#23512yes—
518C22×C3C2×D3×D412yes—
519C22×C3C2×D3×D412yes—
520C22×C3D3×#4112yes—
521C22×C3D3×#4112yes—
522C22×C3C22×#6712yes—
523C2×D3—24no—
524C2×D3—24no—
525C2×D3—24no—
526C2×D3—42no—
527C2×D3—42no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—64no—
531C2×D3—64no—
532C2×D3—64no—
533C2×D3—64no—
534C2×D3—124no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—124no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C3×C4—24no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—64no—
546C3×C4—64no—
547C3×C4—122no—
548C3×C4#94018yes—
549Dic3—24no—
550Dic3—24no—
551Dic3—42no—
552Dic3—64no—
553Dic3—64no—
554Dic3—64no—
555Dic3—122no—
556Dic3—122no—
557Dic3—122no—
558C32#239711yescharacteristic, complemented, Sylow
559C23—22no—
560C23—21no—
561C23—22no—
562C23—21no—
563C23—34no—
564C23—62no—
565C23—62no—
566C23—62no—
567C23—62no—
568C23—62no—
569C23—62no—
570C23—92no—
571C23—181no—
572C23—182no—
573C23—182no—
574C23—181no—
575C23#379812yes—
576C23C22×D3211yescharacteristic
577D4—616no—
578D4—1816no—
579D4—188no—
580D4—188no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—34no—
584C2×C4—34no—
585C2×C4—44no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—92no—
594C2×C4—92no—
595C2×C4—128no—
596C2×C4—181no—
597C2×C4—182no—
598C2×C4—181no—
599C2×C4—182no—
600C2×C4—181no—
601C2×C4—364no—
602C2×C4D3×#6714yes—
603C2×C4#381112yes—
604C2×C3—21no—
605C2×C3—22no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—22no—
609C2×C3—44no—
610C2×C3—44no—
611C2×C3—124no—
612C2×C3#554712yes—
613C2×C3#554712yes—
614C2×C3#554712yes—
615C2×C3#554712yes—
616C2×C3#579112yes—
617C2×C3C2×#94012yes—
618C2×C3#582812yes—
619D3—44no—
620D3—124no—
621D3—124no—
622C22—24no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—42no—
627C22—64no—
628C22—64no—
629C22—64no—
630C22—122no—
631C22—122no—
632C22—122no—
633C22—122no—
634C22—182no—
635C22—184no—
636C22—361no—
637C22—362no—
638C22—361no—
639C22C2×#379811yescharacteristic
640C22D3×#23512yes—
641C22#6430611yescharacteristic
642C22C2×D3×#6712yes—
643C22C2×#381111yescharacteristic
644C4—41no—
645C4—64no—
646C4—64no—
647C4—122no—
648C4—182no—
649C4—182no—
650C4—361no—
651C4#6397914yes—
652C3—21no—
653C3#8234712yescomplemented
654C2—42no—
655C2—124no—
656C2—362no—
657C2#1059500212yes—
658C2#1059501611yescharacteristic
659C2#1059506012yes—
660C2#1059507611yescharacteristic
661C2C2×#6397911yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C4×#626C2semidirect
4. C2×C4×#625C2semidirect
5. #10591724C2semidirect
6. #10591723C2semidirect
7. #10591715C2semidirect
8. #10591393C2semidirect
9. #10591303C2semidirect
10. #10591222C2semidirect
11. #10591203C2semidirect
45. C2×C4×#67D3semidirect
88. C4×C3⋊Dic3D4semidirect
92. C3×C4×Dic3D4semidirect
287. C4×Dic3#67semidirect
558. C32#2397semidirect
653. C3#82347semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×C4×#672
C2×C4×#6262
C2×C4×#6252
#105917242
#105917232
#105917152
#105913932
#105913032
#105912222
#105912032
#823473