Finite Group Databasebeta

← #11864069

Subgroups — #11864069

Order 1152.

1645 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic, complemented
2C2×#64160C211yesmaximal, characteristic, complemented
3C3×#5828C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5#10591655C214yesmaximal, complemented
6#10591519C214yesmaximal, complemented
7#10591107C211yesmaximal, characteristic, complemented
8#10591085C211yesmaximal, characteristic, complemented
9#10591069C211yesmaximal, characteristic, complemented
10#83945—31nomaximal
11#82928—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#625—21no—
17C22×D3×Dic3—21no—
18C2×#3795—24no—
19C2×#3795—24no—
20C2×#3795—22no—
21C2×#3795C2214yes—
22#64160—24no—
23C2×#3756C2212yescomplemented
24C2×#3754C2212yescomplemented
25C2×#3748C2211yescharacteristic
26C3×#949—24no—
27C3×#946C2212yescomplemented
28C2×C3×#215C2212yescomplemented
29C3×#938C2212yescomplemented
30C3×#937—21no—
31C3×#935—21no—
32C2×C3×#213C2212yescomplemented
33C3×C4×#67—22no—
34C3×#926C2211yescharacteristic
35C2×C3×#208C2211yescharacteristic
36#63567C2214yescomplemented
37#63562C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C22×#237—31no—
40C22×#235—31no—
41C2×C3×AGL(1,ℤ/8)—31no—
42C3×#525—31no—
43#5828D311yescharacteristic, complemented
44C2×#951—31no—
45C2×#951—31no—
46C2×#951—61no—
47C2×#949D311yescharacteristic, complemented
48#5215—31no—
49#5207—31no—
50#5173—34no—
51#5158—34no—
52#5126—31no—
53#5120—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
67C22×C3⋊Dic3—21no—
68C2×#634—21no—
69C2×#634—22no—
70C2×#634D414yescomplemented
71C2×#634C2312yes—
72C2×C3×#67—22no—
73C22×C3×Dic3D411yescharacteristic
74C2×C3×D12—21no—
75C2×C3×D12—22no—
76C2×C3×D12D414yescomplemented
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3D412yes—
81C2×C3×C4×D3C2312yes—
82C2×#625—28no—
83C2×#625—24no—
84C2×D3×Dic3—28no—
85C2×D3×Dic3—24no—
86#3795—216no—
87#3795—28no—
88#3795—28no—
89#3756—24no—
90#3754—24no—
91#3748—22no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×#217—22no—
95C3×#215—24no—
96C3×#213—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×D4—31no—
108C23×C3×C4—31no—
109C22×#67—61no—
110C22×#67—61no—
111C23×Dic3—61no—
112C2×#237—34no—
113C2×#237—64no—
114C2×#237—64no—
115C2×#237—62no—
116C2×#235—34no—
117C2×#235—64no—
118C2×#235—62no—
119C2×#235—64no—
120C22×D12C2×D311yescharacteristic
121C22×C4×D3—61no—
122C22×C4×D3C2×D311yescharacteristic
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—61no—
126C3×AGL(1,ℤ/8)—64no—
127C2×C3×SD16—32no—
128C2×C3×D8—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—64no—
137#951—64no—
138#951—68no—
139#949—24no—
140#946C2×D312yescomplemented
141C2×#216—32no—
142C2×#216—32no—
143C2×#216—62no—
144C2×#215C2×D312yescomplemented
145#938C2×D312yescomplemented
146#937—21no—
147#935—21no—
148C2×#214—32no—
149C2×#214—32no—
150C2×#214—62no—
151C2×#213C2×D312yescomplemented
152C4×#67—22no—
153#926C2×D311yescharacteristic
154C2×#208—31no—
155C2×#208—31no—
156C2×#208—61no—
157C2×#208C2×D311yescharacteristic
158#832—34no—
159#830—34no—
160(C2×D3)⋊C8—34no—
161#816—34no—
162#810—34no—
163#809—34no—
164C23×C32—21no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3—24no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—42no—
170C22×C3×D3—44no—
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
183C2×C3⋊Dic3—24no—
184C2×C3⋊Dic3—22no—
185#634—24no—
186#634—22no—
187#634C2×D414yes—
188C3×#67—44no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D412yes—
192C3×D12—24no—
193C3×D12—22no—
194C3×D12C2×D414yes—
195C3×C4×D3—24no—
196C3×C4×D3—22no—
197C3×C4×D3—22no—
198#625—216no—
199D3×Dic3—216no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C22×#41—91no—
203C2×#137—91no—
204C2×AGL(1,ℤ/8)—31no—
205#525—31no—
206#452—94no—
207#449—94no—
208#419—91no—
209#418—91no—
210#407—91no—
211C24×C3—31no—
212C24×C3—61no—
213C23×D3—21no—
214C23×D3#6711yescharacteristic
215C3×#41—24no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—42no—
221C2×C3×Q8—21no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×Q8C22×D311yescharacteristic
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—34no—
228C2×C3×D4—32no—
229C2×C3×D4—41no—
230C2×C3×D4—62no—
231C2×C3×D4—62no—
232C2×C3×D4—61no—
233C2×C3×D4C22×D311yescharacteristic
234C2×C3×D4C22×D311yescharacteristic
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—41no—
242C22×C3×C4—62no—
243C22×C3×C4—62no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—22no—
247C2×#67—64no—
248C2×#67—68no—
249C2×#67—68no—
250C2×#67—64no—
251C22×Dic3—68no—
252C22×Dic3—61no—
253C22×Dic3—61no—
254C22×Dic3—64no—
255C22×Dic3—121no—
256C22×Dic3#6711yescharacteristic
257#237—68no—
258#237—68no—
259#237—616no—
260#235—68no—
261#235—616no—
262#235—68no—
263C2×D12—21no—
264C2×D12—22no—
265C2×D12#6714yescomplemented
266C2×D12C22×D312yes—
267C2×C4×D3—22no—
268C2×C4×D3—22no—
269C2×C4×D3—64no—
270C2×C4×D3—68no—
271C2×C4×D3#6712yes—
272C2×C4×D3C22×D312yes—
273C2×Dic6—34no—
274C2×Dic6—34no—
275C2×Dic6—32no—
276C2×Dic6—32no—
277C2×Dic6—62no—
278C2×Dic6—64no—
279C2×Dic6—61no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—61no—
283C2×Dic6—121no—
284C2×Dic6—122no—
285C3×SD16—64no—
286C3×D8—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—64no—
298#216—64no—
299#216—68no—
300#215—24no—
301#214—64no—
302#214—64no—
303#214—68no—
304#213—24no—
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—22no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—44no—
327C2×C3×D3—48no—
328C2×C3×D3—44no—
329C32×C4—41no—
330C32×C4#12012yes—
331C32×C4C22×D411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—24no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—94no—
337C2×#41—182no—
338C2×#41—184no—
339C2×#41—184no—
340C2×#41D3211yescharacteristic
341C22×Q8—91no—
342C22×D4—31no—
343C22×D4—181no—
344C23×C4—31no—
345C23×C4—181no—
346#137—184no—
347AGL(1,ℤ/8)—64no—
348C2×Q16—92no—
349C2×SD16—32no—
350C2×SD16—92no—
351C2×D8—32no—
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—64no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—122no—
372C23×C3—124no—
373C23×C3D3×D411yescharacteristic
374C23×C3C2×#6711yescharacteristic
375C22×D3—22no—
376C22×D3—24no—
377C22×D3—22no—
378C22×D3—42no—
379C22×D3—44no—
380C22×D3C2×#6712yes—
381C3×Q8—22no—
382C3×Q8—21no—
383C3×Q8—21no—
384C3×Q8—21no—
385C3×Q8—21no—
386C3×Q8—41no—
387C3×D4—22no—
388C3×D4—21no—
389C3×D4—21no—
390C3×D4—21no—
391C3×D4—21no—
392C3×D4—34no—
393C3×D4—41no—
394C3×D4—44no—
395C3×D4—42no—
396C3×D4—42no—
397C3×D4—64no—
398C3×D4—62no—
399C3×D4—124no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—32no—
407C2×C3×C4—41no—
408C2×C3×C4—44no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—62no—
412C2×C3×C4—64no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D412yes—
418C2×C3×C4D3×D412yes—
419C2×C3×C4D3×D412yes—
420C2×C3×C4C2×#6711yescharacteristic
421C2×C3×C4C2×#6712yes—
422C2×C3×C4C23×D311yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424#67—44no—
425#67—616no—
426#67—616no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—616no—
430C2×Dic3—64no—
431C2×Dic3—64no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435C2×Dic3—124no—
436C2×Dic3C2×#6712yes—
437D12—24no—
438D12—22no—
439D12C2×#6714yes—
440C4×D3—24no—
441C4×D3—22no—
442C4×D3—22no—
443C4×D3—616no—
444Dic6—34no—
445Dic6—34no—
446Dic6—64no—
447Dic6—64no—
448Dic6—64no—
449Dic6—62no—
450Dic6—62no—
451Dic6—122no—
452Dic6—124no—
453C3×C8—62no—
454C3⋊C8—22no—
455C3⋊C8—64no—
456C3⋊C8—62no—
457C3⋊C8—62no—
458C2×C32—22no—
459C2×C32—81no—
460C2×C32C2×#12011yescharacteristic
461C2×C32#57512yes—
462C3×D3—42no—
463C3×D3—44no—
464C24—31no—
465C24—61no—
466#41—22no—
467#41—22no—
468#41—188no—
469#41—188no—
470#41—1816no—
471C2×Q8—92no—
472C2×Q8—94no—
473C2×Q8—181no—
474C2×Q8—182no—
475C2×Q8C2×D3211yescharacteristic
476C2×D4—21no—
477C2×D4—32no—
478C2×D4—34no—
479C2×D4—62no—
480C2×D4—61no—
481C2×D4—62no—
482C2×D4—184no—
483C2×D4—188no—
484C2×D4C2×D3211yescharacteristic
485C22×C4—21no—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—184no—
492C22×C4—188no—
493C22×C4—181no—
494C22×C4C2×D3211yescharacteristic
495Q16—184no—
496SD16—64no—
497SD16—184no—
498D8—64no—
499M16—62no—
500M16—182no—
501C2×C8—32no—
502C2×C8—92no—
503C4⋊C4—32no—
504C4⋊C4—62no—
505C22⋊C4—62no—
506C22⋊C4—62no—
507C22⋊C4—61no—
508C42—61no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—22no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—42no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3—64no—
522C22×C3—62no—
523C22×C3—82no—
524C22×C3—124no—
525C22×C3—128no—
526C22×C3—124no—
527C22×C3#93712yes—
528C22×C3#93712yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C2×D3—22no—
532C2×D3—24no—
533C2×D3—22no—
534C2×D3—22no—
535C2×D3—48no—
536C2×D3—44no—
537C2×D3—44no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—62no—
545C3×C4—122no—
546C3×C4#93712yes—
547C3×C4#93712yes—
548C3×C4C2×D3×D411yescharacteristic
549C3×C4C2×D3×D411yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C22×#6711yescharacteristic
552Dic3—22no—
553Dic3—42no—
554Dic3—64no—
555Dic3—64no—
556Dic3—124no—
557C32#300511yescharacteristic, complemented, Sylow
558C23—21no—
559C23—32no—
560C23—62no—
561C23—62no—
562C23—64no—
563C23—122no—
564C23—124no—
565C23D3×#6711yescharacteristic
566Q8—21no—
567Q8—21no—
568Q8—94no—
569Q8—182no—
570Q8—184no—
571D4—21no—
572D4—21no—
573D4—34no—
574D4—42no—
575D4—62no—
576D4—64no—
577D4—124no—
578D4—1816no—
579C2×C4—21no—
580C2×C4—32no—
581C2×C4—42no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—64no—
586C2×C4—62no—
587C2×C4—1816no—
588C2×C4—182no—
589C2×C4—184no—
590C2×C4D3×#6712yes—
591C2×C4D3×#6711yescharacteristic
592C2×C4#381112yes—
593C2×C4C22×D3211yescharacteristic
594C8—62no—
595C8—182no—
596C2×C3—22no—
597C2×C3—22no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—42no—
601C2×C3—82no—
602C2×C3—81no—
603C2×C3—81no—
604C2×C3—122no—
605C2×C3—124no—
606C2×C3#577312yes—
607C2×C3C2×#93711yescharacteristic
608C2×C3C2×#93711yescharacteristic
609C2×C3#582212yes—
610D3—44no—
611D3—42no—
612C22—22no—
613C22—42no—
614C22—41no—
615C22—62no—
616C22—62no—
617C22—62no—
618C22—64no—
619C22—124no—
620C22—128no—
621C22—124no—
622C22#6398312yes—
623C22C2×D3×#6711yescharacteristic
624C4—41no—
625C4—62no—
626C4—122no—
627C4—184no—
628C4#6398312yes—
629C4C2×D3×#6711yescharacteristic
630C4C2×#381111yescharacteristic
631C3—21no—
632C3#8292811yescharacteristic, complemented
633C3#8394511yescharacteristic, complemented
634C2—22no—
635C2—81no—
636C2—122no—
637C2—124no—
638C2#1059546912yes—
639C2C2×#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×#3795C2semidirect
2. C2×#64160C2semidirect
3. C3×#5828C2semidirect
4. C2×C3×#949C2semidirect
5. #10591655C2semidirect
6. #10591519C2semidirect
7. #10591107C2semidirect
8. #10591085C2semidirect
9. #10591069C2semidirect
23. C2×#3756C22semidirect
24. C2×#3754C22semidirect
27. C3×#946C22semidirect
28. C2×C3×#215C22semidirect
29. C3×#938C22semidirect
32. C2×C3×#213C22semidirect
36. #63567C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
43. #5828D3semidirect
47. C2×#949D3semidirect
70. C2×#634D4semidirect
76. C2×C3×D12D4semidirect
140. #946C2×D3semidirect
144. C2×#215C2×D3semidirect
145. #938C2×D3semidirect
151. C2×#213C2×D3semidirect
265. C2×D12#67semidirect
557. C32#3005semidirect
632. C3#82928semidirect
633. C3#83945semidirect

Maximal subgroups

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

subgroupindex
C22×#37952
C2×#641602
C3×#58282
C2×C3×#9492
#105916552
#105915192
#105911072
#105910852
#105910692
#839453
#829283