Finite Group Databasebeta

← #11864067

Subgroups — #11864067

Order 1152.

1665 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4C2×C3×#951C211yesmaximal, characteristic, complemented
5#10591657C214yesmaximal, complemented
6#10591521C214yesmaximal, complemented
7#10591099C211yesmaximal, characteristic, complemented
8#10591096C211yesmaximal, characteristic, complemented
9#10591069C211yesmaximal, characteristic, complemented
10#83980—31nomaximal
11#82928—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626—21no—
17C22×#624—21no—
18C2×#3799—24no—
19C2×#3799—22no—
20C2×#3799—24no—
21C2×#3799C2214yes—
22#64158—24no—
23C2×#3755C2212yescomplemented
24C2×#3753C2212yescomplemented
25C2×#3748C2211yescharacteristic
26C3×#951—24no—
27C3×#946C2212yescomplemented
28C2×C3×#216C2212yescomplemented
29C3×#938C2212yescomplemented
30C3×#937—21no—
31C3×#935—21no—
32C2×C3×#214C2212yescomplemented
33C3×C4×#67—22no—
34C3×#926C2211yescharacteristic
35C2×C3×#208C2211yescharacteristic
36#63565C2214yescomplemented
37#63564C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C22×#239—31no—
40C22×#235—31no—
41C2×C3×#137—31no—
42C3×#525—31no—
43#5828D311yescharacteristic, complemented
44C2×#951D311yescharacteristic, complemented
45C2×#949—31no—
46C2×#949—31no—
47C2×#949—61no—
48#5225—31no—
49#5207—31no—
50#5187—34no—
51#5172—34no—
52#5131—31no—
53#5126—31no—
54#5047—34no—
55#5037—34no—
56#5004—31no—
57#5001—31no—
58C23×C3⋊D3—21no—
59C23×C3×D3D411yescharacteristic
60C32×#41—22no—
61C32×#41—22no—
62C2×C32×Q8C2311yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2311yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)D414yescomplemented
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C3×#67—22no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3D411yescharacteristic
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D412yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×Dic6—21no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6D414yescomplemented
81C2×C3×Dic6C2312yes—
82C2×#626—28no—
83C2×#626—24no—
84C2×#624—28no—
85C2×#624—24no—
86#3799—216no—
87#3799—28no—
88#3799—28no—
89#3755—24no—
90#3753—24no—
91#3748—22no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×#217—22no—
95C3×#216—24no—
96C3×#214—24no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—22no—
100C3×C4×Dic3—21no—
101C3×#208—22no—
102C2×C3×C3⋊C8C2312yes—
103#3005—91noSylow
104C2×C3×#41—21no—
105C2×C3×#41C2×D311yescharacteristic
106C2×C3×#41C2×D311yescharacteristic
107C22×C3×Q8—31no—
108C23×C3×C4—31no—
109C22×#67—61no—
110C2×#239—34no—
111C2×#239—64no—
112C2×#239—64no—
113C2×#239—62no—
114C2×#235—34no—
115C2×#235—64no—
116C2×#235—62no—
117C2×#235—64no—
118C22×D12—31no—
119C22×D12—31no—
120C22×D12—61no—
121C22×D12—61no—
122C22×C4×D3—61no—
123C22×C4×D3—61no—
124C22×C4×D3C2×D311yescharacteristic
125C22×Dic6C2×D311yescharacteristic
126C3×#137—64no—
127C2×C3×Q16—32no—
128C2×C3×SD16—32no—
129C2×C3×M16—31no—
130C3×#123—61no—
131C3×C22⋊Q8—32no—
132C3×#121—32no—
133C3×#120—61no—
134C3×C4×D4—62no—
135C3×#117—31no—
136#951—24no—
137#949—64no—
138#949—64no—
139#949—68no—
140#946C2×D312yescomplemented
141C2×#216C2×D312yescomplemented
142C2×#215—32no—
143C2×#215—32no—
144C2×#215—62no—
145#938C2×D312yescomplemented
146#937—21no—
147#935—21no—
148C2×#214C2×D312yescomplemented
149C2×#213—32no—
150C2×#213—32no—
151C2×#213—62no—
152C4×#67—22no—
153#926C2×D311yescharacteristic
154C2×#208—31no—
155C2×#208—31no—
156C2×#208—61no—
157C2×#208C2×D311yescharacteristic
158#835—34no—
159#830—34no—
160#821—34no—
161(C2×D3)⋊C8—34no—
162#810—34no—
163#809—34no—
164C23×C32—21no—
165C23×C32C2×D411yescharacteristic
166C22×C3⋊D3—24no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3—44no—
169C22×C3×D3—22no—
170C22×C3×D3—42no—
171C22×C3×D3C2×D412yes—
172C32×Q8—21no—
173C32×Q8—21no—
174C32×D4—21no—
175C32×D4—21no—
176C32×D4—42no—
177C2×C32×C4—21no—
178C2×C32×C4—42no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2411yescharacteristic
183C4⋊(C3⋊D3)—24no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)C2×D414yes—
186C3×#67—44no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D412yes—
192C3×C4×D3—24no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—24no—
196C3×Dic6—22no—
197C3×Dic6C2×D414yes—
198#626—216no—
199#624—216no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C22×#41—91no—
203C2×#137—31no—
204C2×AGL(1,ℤ/8)—91no—
205#525—31no—
206#452—94no—
207#449—94no—
208#419—91no—
209#418—91no—
210#407—91no—
211C24×C3—31no—
212C23×D3—61no—
213C23×D3—61no—
214C23×D3—121no—
215C23×D3#6711yescharacteristic
216C3×#41—24no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—42no—
222C2×C3×Q8—21no—
223C2×C3×Q8—34no—
224C2×C3×Q8—32no—
225C2×C3×Q8—62no—
226C2×C3×Q8—61no—
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×Q8C22×D311yescharacteristic
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—41no—
233C2×C3×D4—62no—
234C2×C3×D4C22×D311yescharacteristic
235C2×C3×D4C22×D311yescharacteristic
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—41no—
243C22×C3×C4—61no—
244C22×C3×C4—62no—
245C22×C3×C4—62no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—22no—
249C2×#67—64no—
250C2×#67—68no—
251C22×Dic3—21no—
252C22×Dic3#6711yescharacteristic
253#239—68no—
254#239—68no—
255#239—616no—
256#235—68no—
257#235—616no—
258#235—68no—
259C2×D12—34no—
260C2×D12—34no—
261C2×D12—32no—
262C2×D12—32no—
263C2×D12—62no—
264C2×D12—64no—
265C2×D12—68no—
266C2×D12—64no—
267C2×D12—61no—
268C2×D12—62no—
269C2×D12—62no—
270C2×D12—61no—
271C2×D12—121no—
272C2×D12—122no—
273C2×C4×D3—22no—
274C2×C4×D3—22no—
275C2×C4×D3—64no—
276C2×C4×D3—68no—
277C2×C4×D3—68no—
278C2×C4×D3—64no—
279C2×C4×D3#6712yes—
280C2×C4×D3C22×D312yes—
281C2×Dic6—21no—
282C2×Dic6—22no—
283C2×Dic6#6714yescomplemented
284C2×Dic6C22×D312yes—
285C3×Q16—64no—
286C3×SD16—64no—
287C3×M16—62no—
288C2×C3×C8—32no—
289C3×C4⋊C4—32no—
290C3×C4⋊C4—62no—
291C3×C22⋊C4—62no—
292C3×C22⋊C4—62no—
293C3×C22⋊C4—61no—
294C3×C42—61no—
295#217—21no—
296#217—22no—
297#216—24no—
298#215—64no—
299#215—64no—
300#215—68no—
301#214—24no—
302#213—64no—
303#213—64no—
304#213—68no—
305(C2×D3)⋊C4—22no—
306C4⋊Dic3C22×D312yes—
307Dic3⋊C4—22no—
308C4×Dic3—21no—
309#208—22no—
310#208—64no—
311#208—62no—
312#208—62no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—32no—
315C2×C3⋊C8—62no—
316C2×C3⋊C8C22×D312yes—
317C22×C32—22no—
318C22×C32—41no—
319C22×C32—42no—
320C22×C32#12012yes—
321C22×C32C22×D411yescharacteristic
322C2×C3⋊D3—24no—
323C2×C3⋊D3—48no—
324C2×C3⋊D3—44no—
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—22no—
328C2×C3×D3—44no—
329C32×C4—41no—
330C32×C4#12012yes—
331C32×C4C22×D411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3×Dic3—22no—
334C3×Dic3—24no—
335C3×Dic3—42no—
336C2×#41—94no—
337C2×#41—182no—
338C2×#41—184no—
339C2×#41—184no—
340C2×#41D3211yescharacteristic
341C22×Q8—31no—
342C22×D4—91no—
343C22×D4—181no—
344C23×C4—31no—
345C23×C4—181no—
346#137—64no—
347AGL(1,ℤ/8)—184no—
348C2×Q16—32no—
349C2×SD16—32no—
350C2×SD16—92no—
351C2×D8—92no—
352C2×M16—31no—
353C2×M16—91no—
354#123—61no—
355C22⋊Q8—32no—
356#121—32no—
357#120—61no—
358C4×D4—62no—
359#117—31no—
360#103—94no—
361#102—94no—
362C22⋊C8—94no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—32no—
367C23×C3—41no—
368C23×C3—62no—
369C23×C3—122no—
370C23×C3D3×D411yescharacteristic
371C23×C3C2×#6711yescharacteristic
372C22×D3—22no—
373C22×D3—42no—
374C22×D3—64no—
375C22×D3—64no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—122no—
379C22×D3—124no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—244no—
383C22×D3C2×#6712yes—
384C3×Q8—22no—
385C3×Q8—21no—
386C3×Q8—21no—
387C3×Q8—21no—
388C3×Q8—21no—
389C3×Q8—34no—
390C3×Q8—41no—
391C3×Q8—64no—
392C3×Q8—62no—
393C3×D4—22no—
394C3×D4—21no—
395C3×D4—21no—
396C3×D4—21no—
397C3×D4—21no—
398C3×D4—41no—
399C3×D4—44no—
400C3×D4—42no—
401C3×D4—42no—
402C3×D4—124no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—32no—
410C2×C3×C4—41no—
411C2×C3×C4—44no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—62no—
415C2×C3×C4—64no—
416C2×C3×C4—62no—
417C2×C3×C4—64no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4D3×D412yes—
423C2×C3×C4D3×D412yes—
424C2×C3×C4D3×D412yes—
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6712yes—
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D311yescharacteristic
429#67—44no—
430#67—616no—
431C2×Dic3—24no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3C2×#6712yes—
436D12—34no—
437D12—34no—
438D12—64no—
439D12—616no—
440D12—64no—
441D12—64no—
442D12—62no—
443D12—62no—
444D12—122no—
445D12—124no—
446C4×D3—24no—
447C4×D3—22no—
448C4×D3—22no—
449C4×D3—616no—
450C4×D3—616no—
451Dic6—24no—
452Dic6—22no—
453Dic6C2×#6714yes—
454C3×C8—62no—
455C3⋊C8—22no—
456C3⋊C8—64no—
457C3⋊C8—62no—
458C3⋊C8—62no—
459C2×C32—22no—
460C2×C32—81no—
461C2×C32C2×#12011yescharacteristic
462C2×C32#57512yes—
463C3⋊D3—44no—
464C3×D3—42no—
465C24—31no—
466C24—181no—
467#41—22no—
468#41—22no—
469#41—188no—
470#41—188no—
471#41—1816no—
472C2×Q8—32no—
473C2×Q8—34no—
474C2×Q8—61no—
475C2×Q8—62no—
476C2×Q8C2×D3211yescharacteristic
477C2×D4—21no—
478C2×D4—62no—
479C2×D4—92no—
480C2×D4—94no—
481C2×D4—184no—
482C2×D4—188no—
483C2×D4—182no—
484C2×D4—181no—
485C2×D4C2×D3211yescharacteristic
486C22×C4—21no—
487C22×C4—31no—
488C22×C4—32no—
489C22×C4—32no—
490C22×C4—61no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—184no—
494C22×C4—188no—
495C22×C4C2×D3211yescharacteristic
496Q16—64no—
497SD16—64no—
498SD16—184no—
499D8—184no—
500M16—62no—
501M16—182no—
502C2×C8—32no—
503C2×C8—92no—
504C4⋊C4—32no—
505C4⋊C4—62no—
506C22⋊C4—62no—
507C22⋊C4—62no—
508C22⋊C4—61no—
509C42—61no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—42no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—82no—
524C22×C3—124no—
525C22×C3#93712yes—
526C22×C3#93712yes—
527C22×C3C2×D3×D411yescharacteristic
528C22×C3C22×#6711yescharacteristic
529C2×D3—22no—
530C2×D3—22no—
531C2×D3—22no—
532C2×D3—44no—
533C2×D3—64no—
534C2×D3—64no—
535C2×D3—124no—
536C2×D3—128no—
537C2×D3—128no—
538C2×D3—124no—
539C2×D3—124no—
540C2×D3—244no—
541C2×D3—248no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—22no—
545C3×C4—42no—
546C3×C4—41no—
547C3×C4—41no—
548C3×C4—62no—
549C3×C4—64no—
550C3×C4—122no—
551C3×C4#93712yes—
552C3×C4#93712yes—
553C3×C4C2×D3×D411yescharacteristic
554C3×C4C2×D3×D411yescharacteristic
555C3×C4C2×D3×D411yescharacteristic
556C3×C4C22×#6711yescharacteristic
557Dic3—24no—
558Dic3—22no—
559Dic3—42no—
560C32#300511yescharacteristic, complemented, Sylow
561C23—21no—
562C23—32no—
563C23—62no—
564C23—122no—
565C23—182no—
566C23—184no—
567C23—364no—
568C23D3×#6711yescharacteristic
569Q8—21no—
570Q8—21no—
571Q8—34no—
572Q8—62no—
573Q8—64no—
574D4—21no—
575D4—21no—
576D4—42no—
577D4—94no—
578D4—124no—
579D4—1816no—
580D4—182no—
581D4—184no—
582C2×C4—21no—
583C2×C4—32no—
584C2×C4—42no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—64no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—64no—
591C2×C4—62no—
592C2×C4—1816no—
593C2×C4D3×#6712yes—
594C2×C4D3×#6711yescharacteristic
595C2×C4#381112yes—
596C2×C4C22×D3211yescharacteristic
597C8—62no—
598C8—182no—
599C2×C3—22no—
600C2×C3—22no—
601C2×C3—22no—
602C2×C3—21no—
603C2×C3—42no—
604C2×C3—82no—
605C2×C3—81no—
606C2×C3—81no—
607C2×C3—122no—
608C2×C3#577712yes—
609C2×C3C2×#93711yescharacteristic
610C2×C3C2×#93711yescharacteristic
611C2×C3#582212yes—
612D3—42no—
613D3—124no—
614D3—124no—
615D3—244no—
616C22—22no—
617C22—42no—
618C22—41no—
619C22—62no—
620C22—62no—
621C22—62no—
622C22—124no—
623C22—184no—
624C22—368no—
625C22—364no—
626C22#6398312yes—
627C22C2×D3×#6711yescharacteristic
628C4—41no—
629C4—62no—
630C4—64no—
631C4—122no—
632C4#6398312yes—
633C4C2×D3×#6711yescharacteristic
634C4C2×#381111yescharacteristic
635C3—21no—
636C3#8292811yescharacteristic, complemented
637C3#8398011yescharacteristic, complemented
638C2—22no—
639C2—81no—
640C2—122no—
641C2—364no—
642C2#1059547012yes—
643C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C2×#64158C2semidirect
3. C3×#5828C2semidirect
4. C2×C3×#951C2semidirect
5. #10591657C2semidirect
6. #10591521C2semidirect
7. #10591099C2semidirect
8. #10591096C2semidirect
9. #10591069C2semidirect
23. C2×#3755C22semidirect
24. C2×#3753C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#216C22semidirect
29. C3×#938C22semidirect
32. C2×C3×#214C22semidirect
36. #63565C22semidirect
37. #63564C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
43. #5828D3semidirect
44. C2×#951D3semidirect
69. C2×C4⋊(C3⋊D3)D4semidirect
80. C2×C3×Dic6D4semidirect
140. #946C2×D3semidirect
141. C2×#216C2×D3semidirect
145. #938C2×D3semidirect
148. C2×#214C2×D3semidirect
283. C2×Dic6#67semidirect
560. C32#3005semidirect
636. C3#82928semidirect
637. C3#83980semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C2×#641582
C3×#58282
C2×C3×#9512
#105916572
#105915212
#105910992
#105910962
#105910692
#839803
#829283