Finite Group Databasebeta

← #11864445

Subgroups — #11864445

Order 1152.

1543 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C3×#5830C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592933C211yesmaximal, characteristic, complemented
6#10591171C214yesmaximal, complemented
7#10591161C214yesmaximal, complemented
8#10591099C211yesmaximal, characteristic, complemented
9#10591083C211yesmaximal, characteristic, complemented
10#84113—31nomaximal
11#83390—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C3×#1010—24no—
14C3×#1010—24no—
15C2×C3×D3×Q8—21no—
16C2×C3×#237—21no—
17C2×C3×#237—22no—
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2212yescomplemented
20C22×C3×D12C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2212yescomplemented
23C2×#3748C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#947—21no—
26C3×#940—21no—
27C3×#937—22no—
28C3×#930C2214yes—
29C3×#926C2211yescharacteristic
30C2×#3715—24no—
31C2×#3715C2214yes—
32C2×#3715C2212yes—
33#63823—24no—
34C2×#3713C2212yes—
35#63657C2214yescomplemented
36#63565C2212yescomplemented
37#63565C2214yescomplemented
38#63562C2212yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic, complemented
41C3×#535—31no—
42#5830D311yescharacteristic, complemented
43C2×#949—31no—
44C22×#215—31no—
45C22×#214—31no—
46C2×#932—31no—
47#5238—34no—
48#5234—31no—
49#5234—31no—
50#5234—61no—
51#5233—31no—
52#5227—34no—
53#5225—31no—
54#5040—34no—
55#5037—34no—
56#5004—31no—
57#5002—31no—
58C23×C3×D3—21no—
59C32×#41—22no—
60C32×#41—22no—
61C2×C32×Q8D411yescharacteristic
62C2×C32×D4D412yes—
63C2×C32×D4D411yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C2×C3×#67—21no—
67C2×C3×#67—22no—
68C2×C3×#67—24no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—22no—
71C3×D3×Q8—28no—
72C3×#237—216no—
73C3×#237—28no—
74C3×#235—22no—
75C3×#235—24no—
76C3×#235—24no—
77C3×#235D414yescomplemented
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12C2312yes—
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—22no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—24no—
89C2×C3×Dic6—24no—
90C2×C3×Dic6D414yescomplemented
91C2×C3×Dic6C2312yes—
92C2×C3×Dic6C2311yescharacteristic
93#3748—22no—
94C2×C3⋊(C3⋊C8)—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C2×C3⋊(C3⋊C8)C2312yes—
97C3×#217—21no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4⋊Dic3C2312yes—
100C3×C4×Dic3—21no—
101#3715—24no—
102#3715—28no—
103#3713—24no—
104#3010—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C22×C3×Q8—61no—
117C22×C3×D4—31no—
118#1010—24no—
119#1010—24no—
120C2×D3×Q8—21no—
121C2×#237—21no—
122C2×#237—22no—
123C2×#235C2×D311yescharacteristic
124C2×#235C2×D312yescomplemented
125C22×D12C2×D311yescharacteristic
126C22×Dic6C2×D311yescharacteristic
127C22×Dic6C2×D312yescomplemented
128C3×#127—61no—
129C3×#124—61no—
130C3×#121—34no—
131C3×#120—62no—
132C3×#117—31no—
133#949—64no—
134#947—21no—
135C2×#215—32no—
136C2×#215—34no—
137C2×#215—64no—
138#940—21no—
139#937—22no—
140C2×#214—32no—
141C2×#214—34no—
142C2×#214—64no—
143#932—64no—
144C2×#213—32no—
145C2×#213—32no—
146#930C2×D314yes—
147#926C2×D311yescharacteristic
148C2×#208—31no—
149C2×#208—31no—
150C2×#208—61no—
151C22×C3⋊C8—31no—
152C22×C3⋊C8—31no—
153C22×C3⋊C8—61no—
154#835—34no—
155#835—32no—
156#832—32no—
157#830—34no—
158#830—34no—
159#830—64no—
160#810—32no—
161#810—34no—
162#809—32no—
163C23×C32C2×D412yes—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—21no—
166C22×C3×D3—22no—
167C22×C3×D3—42no—
168C22×C3×D3—82no—
169C32×Q8—22no—
170C32×D4—24no—
171C32×D4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C3×#67—28no—
180C3×#67—24no—
181C3×#67—84no—
182C2×C3×Dic3—28no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C3×D12—21no—
188C3×D12—22no—
189C3×D12—22no—
190C3×D12—42no—
191C3×D12C2×D412yes—
192C3×C4×D3—28no—
193C3×C4×D3—24no—
194C3×Dic6—28no—
195C3×Dic6—24no—
196C3×Dic6—22no—
197C3×Dic6—21no—
198C3×Dic6C2×D412yes—
199C3×Dic6C2×D414yes—
200C3⋊(C3⋊C8)—22no—
201C3⋊(C3⋊C8)—22no—
202C2×2−1+4—31no—
203C2×AGL(1,ℤ/8)—91no—
204C22×SD16—91no—
205#535—31no—
206#449—94no—
207#448—94no—
208#419—91no—
209#416—91no—
210#408—91no—
211C24×C3—61no—
212C23×D3—21no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—22no—
216C3×#41—22no—
217C3×#41—34no—
218C3×#41—42no—
219C3×#41—42no—
220C3×#41—64no—
221C3×#41—64no—
222C3×#41—616no—
223C3×#41—68no—
224C3×#41—62no—
225C2×C3×Q8—21no—
226C2×C3×Q8—34no—
227C2×C3×Q8—32no—
228C2×C3×Q8—31no—
229C2×C3×Q8—64no—
230C2×C3×Q8—64no—
231C2×C3×Q8—68no—
232C2×C3×Q8—62no—
233C2×C3×Q8—62no—
234C2×C3×Q8—61no—
235C2×C3×Q8#6711yescharacteristic
236C2×C3×Q8#6711yescharacteristic
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—31no—
240C2×C3×D4—32no—
241C2×C3×D4—62no—
242C2×C3×D4—61no—
243C2×C3×D4—64no—
244C2×C3×D4—62no—
245C2×C3×D4—62no—
246C2×C3×D4—61no—
247C2×C3×D4#6712yes—
248C2×C3×D4#6711yescharacteristic
249C2×C3×D4#6712yes—
250C2×C3×D4#6711yescharacteristic
251C22×C3×C4—21no—
252C22×C3×C4—22no—
253C22×C3×C4—62no—
254C22×C3×C4—61no—
255C22×C3×C4—62no—
256C22×C3×C4—61no—
257C22×C3×C4C22×D312yes—
258C22×C3×C4C22×D312yes—
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C2×#67—21no—
262C2×#67—22no—
263C2×#67—24no—
264C22×Dic3—21no—
265C22×Dic3—22no—
266D3×Q8—28no—
267#237—216no—
268#237—28no—
269#235—22no—
270#235—24no—
271#235—24no—
272#235#6714yescomplemented
273C2×D12—22no—
274C2×D12—22no—
275C2×D12—21no—
276C2×D12C22×D312yes—
277C2×D12C22×D311yescharacteristic
278C2×C4×D3—21no—
279C2×C4×D3—22no—
280C2×Dic6—21no—
281C2×Dic6—22no—
282C2×Dic6—22no—
283C2×Dic6—24no—
284C2×Dic6—24no—
285C2×Dic6#6714yescomplemented
286C2×Dic6C22×D312yes—
287C2×Dic6C22×D311yescharacteristic
288C3×C4⋊C4—32no—
289C3×C22⋊C4—61no—
290C3×C22⋊C4—64no—
291C3×C42—61no—
292#217—21no—
293#215—68no—
294#215—64no—
295#214—64no—
296#214—68no—
297#213—64no—
298#213—64no—
299(C2×D3)⋊C4—24no—
300C4⋊Dic3C22×D312yes—
301C4×Dic3—21no—
302#208—62no—
303#208—62no—
304#208—122no—
305C2×C3⋊C8—32no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8—122no—
314C22×C32—22no—
315C22×C32—22no—
316C22×C32—24no—
317C22×C32#12012yes—
318C22×C32C22×D411yescharacteristic
319C2×C3×D3—22no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—44no—
323C2×C3×D3—84no—
324C32×C4—22no—
325C32×C4#12012yes—
326C32×C4C22×D411yescharacteristic
327C32×C4C22×D411yescharacteristic
328C3×Dic3—22no—
329C3×Dic3—24no—
330C3×Dic3—42no—
3312−1+4—64no—
3322−1+4—64no—
333C2×#41—31no—
334C2×#41—32no—
335C2×#41—62no—
336C2×#41—61no—
337C2×#41D3211yescharacteristic
338C22×Q8—31no—
339C22×Q8—32no—
340C22×Q8—61no—
341C22×D4—31no—
342AGL(1,ℤ/8)—184no—
343C2×SD16—94no—
344C2×SD16—92no—
345C2×SD16—184no—
346C2×D8—92no—
347C2×M16—91no—
348C22×C8—91no—
349#127—61no—
350#124—61no—
351#121—34no—
352#120—62no—
353#117—31no—
354#103—92no—
355#103—94no—
356#102—92no—
357C22⋊C8—94no—
358C23×C3—21no—
359C23×C3—22no—
360C23×C3—61no—
361C23×C3—62no—
362C23×C3—122no—
363C23×C3—242no—
364C23×C3C2×#6712yes—
365C23×C3C2×#6712yes—
366C23×C3C2×#6711yescharacteristic
367C23×C3C2×#6711yescharacteristic
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—42no—
371C22×D3—82no—
372C3×Q8—22no—
373C3×Q8—22no—
374C3×Q8—34no—
375C3×Q8—32no—
376C3×Q8—42no—
377C3×Q8—68no—
378C3×Q8—64no—
379C3×Q8—62no—
380C3×Q8—61no—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—32no—
386C3×D4—42no—
387C3×D4—44no—
388C3×D4—68no—
389C3×D4—64no—
390C3×D4—61no—
391C3×D4—62no—
392C3×D4—62no—
393C3×D4—122no—
394C3×D4—244no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—68no—
407C2×C3×C4—68no—
408C2×C3×C4—64no—
409C2×C3×C4—62no—
410C2×C3×C4—61no—
411C2×C3×C4—64no—
412C2×C3×C4—62no—
413C2×C3×C4D3×D412yes—
414C2×C3×C4D3×D412yes—
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C2×#6712yes—
420C2×C3×C4C2×#6712yes—
421C2×C3×C4C23×D311yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423#67—28no—
424#67—24no—
425#67—84no—
426C2×Dic3—28no—
427C2×Dic3—24no—
428C2×Dic3—22no—
429C2×Dic3—21no—
430C2×Dic3—22no—
431D12—22no—
432D12—22no—
433D12—21no—
434D12—42no—
435D12C2×#6712yes—
436C4×D3—28no—
437C4×D3—24no—
438Dic6—28no—
439Dic6—24no—
440Dic6—22no—
441Dic6—21no—
442Dic6C2×#6712yes—
443Dic6C2×#6714yes—
444C3⋊C8—62no—
445C3⋊C8—62no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8—122no—
449C3⋊C8—122no—
450C2×C32—22no—
451C2×C32—42no—
452C2×C32C2×#12011yescharacteristic
453C2×C32#57712yes—
454C3×D3—42no—
455C3×D3—82no—
456C24—61no—
457#41—22no—
458#41—22no—
459#41—34no—
460#41—64no—
461#41—64no—
462#41—616no—
463#41—68no—
464#41—62no—
465C2×Q8—32no—
466C2×Q8—31no—
467C2×Q8—34no—
468C2×Q8—64no—
469C2×Q8—64no—
470C2×Q8—68no—
471C2×Q8—62no—
472C2×Q8—61no—
473C2×Q8—62no—
474C2×Q8#62511yescharacteristic
475C2×D4—31no—
476C2×D4—32no—
477C2×D4—62no—
478C2×D4—61no—
479C2×D4—64no—
480C2×D4—61no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4#62512yes—
484C2×D4#62511yescharacteristic
485C22×C4—62no—
486C22×C4—61no—
487C22×C4—62no—
488C22×C4—61no—
489C22×C4C2×D3212yes—
490C22×C4C2×D3211yescharacteristic
491SD16—188no—
492SD16—184no—
493D8—184no—
494M16—182no—
495C2×C8—92no—
496C2×C8—92no—
497C2×C8—182no—
498C4⋊C4—32no—
499C22⋊C4—61no—
500C22⋊C4—64no—
501C42—61no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—24no—
506C22×C3—24no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—22no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—44no—
513C22×C3—62no—
514C22×C3—122no—
515C22×C3—124no—
516C22×C3—122no—
517C22×C3—244no—
518C22×C3#93712yes—
519C22×C3#95312yes—
520C22×C3C22×#6711yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—22no—
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—44no—
526C2×D3—84no—
527C3×C4—22no—
528C3×C4—22no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—42no—
533C3×C4—64no—
534C3×C4—62no—
535C3×C4—122no—
536C3×C4#93712yes—
537C3×C4#95312yes—
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C22×#6711yescharacteristic
541C3×C4C22×#6711yescharacteristic
542Dic3—22no—
543Dic3—24no—
544Dic3—42no—
545C32#301011yescharacteristic, complemented, Sylow
546C23—61no—
547C23—62no—
548C23—122no—
549C23—242no—
550C23C2×#62512yes—
551C23C2×#62511yescharacteristic
552Q8—22no—
553Q8—34no—
554Q8—32no—
555Q8—68no—
556Q8—62no—
557Q8—61no—
558Q8—64no—
559D4—24no—
560D4—22no—
561D4—32no—
562D4—68no—
563D4—64no—
564D4—61no—
565D4—62no—
566D4—62no—
567D4—122no—
568D4—244no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—68no—
572C2×C4—68no—
573C2×C4—62no—
574C2×C4—61no—
575C2×C4—64no—
576C2×C4—64no—
577C2×C4—62no—
578C2×C4C2×#62512yes—
579C2×C4C2×#62511yescharacteristic
580C2×C4D3×#6712yes—
581C2×C4D3×#6712yes—
582C2×C4C22×D3211yescharacteristic
583C8—182no—
584C8—182no—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—22no—
588C2×C3—21no—
589C2×C3—42no—
590C2×C3—42no—
591C2×C3—42no—
592C2×C3—82no—
593C2×C3—122no—
594C2×C3—242no—
595C2×C3C2×#93711yescharacteristic
596C2×C3#583612yes—
597C2×C3#583712yes—
598C2×C3C2×#95311yescharacteristic
599D3—42no—
600D3—82no—
601C22—22no—
602C22—24no—
603C22—22no—
604C22—62no—
605C22—122no—
606C22—124no—
607C22—122no—
608C22—244no—
609C22#6397612yes—
610C22C22×#62511yescharacteristic
611C4—22no—
612C4—64no—
613C4—62no—
614C4—122no—
615C4#6397612yes—
616C4C2×D3×#6711yescharacteristic
617C4C2×D3×#6711yescharacteristic
618C3—21no—
619C3#8339011yescharacteristic, complemented
620C3#8411311yescharacteristic, complemented
621C2—22no—
622C2—42no—
623C2—122no—
624C2—242no—
625C2#1059544612yes—
626C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3010
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C3×#5830C2semidirect
3. C22×#3715C2semidirect
4. C2×#63823C2semidirect
5. #10592933C2semidirect
6. #10591171C2semidirect
7. #10591161C2semidirect
8. #10591099C2semidirect
9. #10591083C2semidirect
19. C2×C3×#235C22semidirect
22. C22×C3×Dic6C22semidirect
35. #63657C22semidirect
36. #63565C22semidirect
37. #63565C22semidirect
38. #63562C22semidirect
40. C2×#1010D3semidirect
42. #5830D3semidirect
77. C3×#235D4semidirect
90. C2×C3×Dic6D4semidirect
124. C2×#235C2×D3semidirect
127. C22×Dic6C2×D3semidirect
272. #235#67semidirect
285. C2×Dic6#67semidirect
545. C32#3010semidirect
619. C3#83390semidirect
620. C3#84113semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C3×#58302
C22×#37152
C2×#638232
#105929332
#105911712
#105911612
#105910992
#105910832
#841133
#833903