Finite Group Databasebeta

← #11864068

Subgroups — #11864068

Order 1152.

1681 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic, complemented
2#10596299C211yesmaximal, characteristic, complemented
3C2×C3×#951C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5#10591656C214yesmaximal, complemented
6#10591520C214yesmaximal, complemented
7#10591100C211yesmaximal, characteristic, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591074C211yesmaximal, characteristic, complemented
10#83980—31nomaximal
11#83945—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626—21no—
17C22×D3×Dic3—21no—
18C2×#3796—22no—
19C2×#3796—24no—
20C2×#3796—24no—
21C2×#3796C2214yes—
22#64155C2212yescomplemented
23#64147C2212yescomplemented
24#64146—21no—
25#64144—21no—
26C4×#638—22no—
27#64135C2211yescharacteristic
28C3×#951—24no—
29C3×#949—24no—
30C2×C3×#216C2212yescomplemented
31C2×C3×#215C2212yescomplemented
32C2×C3×#214C2212yescomplemented
33C2×C3×#213C2212yescomplemented
34C2×C3×#208C2211yescharacteristic
35C2×C3×#208C2211yescharacteristic
36#63566C2214yescomplemented
37#63563C2214yescomplemented
38#63557C2214yescomplemented
39C22×#239—31no—
40C22×#237—31no—
41C2×C3×#137—31no—
42C2×C3×AGL(1,ℤ/8)—31no—
43#5828—31no—
44#5828—31no—
45#5828—61no—
46C2×#951D311yescharacteristic, complemented
47C2×#949D311yescharacteristic, complemented
48#5225—31no—
49#5215—31no—
50#5187—34no—
51#5173—34no—
52#5172—34no—
53#5158—34no—
54#5131—31no—
55#5126—31no—
56#5126—31no—
57#5120—31no—
58C23×C3⋊D3D411yescharacteristic
59C23×C3×D3—21no—
60C32×#41—22no—
61C32×#41—22no—
62C2×C32×Q8C2311yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2311yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—22no—
68C22×C3⋊Dic3D411yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3D412yes—
72C2×C4×C3⋊D3C2312yes—
73C22×C3×Dic3—21no—
74C2×C3×D12—21no—
75C2×C3×D12—22no—
76C2×C3×D12D414yescomplemented
77C2×C3×D12C2312yes—
78C2×C3×Dic6—21no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6D414yescomplemented
81C2×C3×Dic6C2312yes—
82C2×#626—28no—
83C2×#626—24no—
84C2×D3×Dic3—28no—
85C2×D3×Dic3—24no—
86#3796—216no—
87#3796—28no—
88#3796—28no—
89#3757—21no—
90#3757—22no—
91#3752—22no—
92C4⋊(C3⋊Dic3)C2312yes—
93#3750—22no—
94C4×C3⋊Dic3—21no—
95C3×#216—24no—
96C3×#215—24no—
97C3×#214—24no—
98C3×#213—24no—
99C3×#208—22no—
100C3×#208—22no—
101C2×C3×C3⋊C8C2312yes—
102C2×C3×C3⋊C8C2312yes—
103#3005—91noSylow
104C2×C3×#41—21no—
105C2×C3×#41C2×D311yescharacteristic
106C2×C3×#41C2×D311yescharacteristic
107C22×C3×Q8—31no—
108C22×C3×D4—31no—
109C22×#67—61no—
110C23×Dic3—61no—
111C2×#239—34no—
112C2×#239—62no—
113C2×#239—64no—
114C2×#239—64no—
115C2×#237—34no—
116C2×#237—62no—
117C2×#237—64no—
118C2×#237—64no—
119C22×D12—61no—
120C22×D12C2×D311yescharacteristic
121C22×C4×D3—31no—
122C22×C4×D3—31no—
123C22×C4×D3—61no—
124C22×C4×D3—61no—
125C22×Dic6C2×D311yescharacteristic
126C3×#137—64no—
127C3×AGL(1,ℤ/8)—64no—
128C2×C3×Q16—32no—
129C2×C3×SD16—32no—
130C2×C3×SD16—32no—
131C2×C3×D8—32no—
132C2×C3×M16—31no—
133C2×C3×M16—31no—
134#951—24no—
135#949—24no—
136#946—32no—
137#946—32no—
138#946—62no—
139C2×#216C2×D312yescomplemented
140C2×#215C2×D312yescomplemented
141#938—32no—
142#938—32no—
143#938—62no—
144#937—61no—
145#937—61no—
146#937—62no—
147#935—61no—
148#935—61no—
149#935—62no—
150C2×#214C2×D312yescomplemented
151C2×#213C2×D312yescomplemented
152C4×#67—62no—
153C4×#67—62no—
154C4×#67—64no—
155#926—31no—
156#926—31no—
157#926—61no—
158C2×#208C2×D311yescharacteristic
159C2×#208C2×D311yescharacteristic
160#835—34no—
161#832—34no—
162#821—34no—
163(C2×D3)⋊C8—34no—
164(C2×D3)⋊C8—34no—
165#816—34no—
166C23×C32—21no—
167C23×C32C2×D411yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—42no—
170C22×C3⋊D3C2×D412yes—
171C22×C3×D3—24no—
172C22×C3×D3—22no—
173C22×C3×D3—44no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×D4—21no—
177C32×D4—21no—
178C32×D4—42no—
179C2×C32×C4—21no—
180C2×C32×C4—42no—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2411yescharacteristic
185#638—44no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3C2×D412yes—
189C4×C3⋊D3—24no—
190C4×C3⋊D3—22no—
191C4×C3⋊D3—22no—
192C2×C3×Dic3—24no—
193C2×C3×Dic3—22no—
194C3×D12—24no—
195C3×D12—22no—
196C3×D12C2×D414yes—
197C3×Dic6—24no—
198C3×Dic6—22no—
199C3×Dic6C2×D414yes—
200#626—216no—
201D3×Dic3—216no—
202C3×C3⋊C8—22no—
203C3×C3⋊C8—22no—
204C22×#41—91no—
205C2×#137—31no—
206C2×AGL(1,ℤ/8)—31no—
207#525—91no—
208#452—94no—
209#449—94no—
210#419—91no—
211#418—91no—
212#407—91no—
213C24×C3—61no—
214C23×D3—21no—
215C23×D3—31no—
216C23×D3—31no—
217C23×D3—61no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—22no—
222C3×#41—42no—
223C3×#41—42no—
224C2×C3×Q8—21no—
225C2×C3×Q8—34no—
226C2×C3×Q8—32no—
227C2×C3×Q8—61no—
228C2×C3×Q8—62no—
229C2×C3×Q8C22×D311yescharacteristic
230C2×C3×Q8C22×D311yescharacteristic
231C2×C3×D4—22no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—34no—
236C2×C3×D4—32no—
237C2×C3×D4—61no—
238C2×C3×D4—62no—
239C2×C3×D4C22×D311yescharacteristic
240C2×C3×D4C22×D311yescharacteristic
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—61no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—64no—
249C2×#67—68no—
250C2×#67—62no—
251C2×#67—62no—
252C2×#67—64no—
253C22×Dic3—21no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—61no—
257C22×Dic3—64no—
258C22×Dic3—68no—
259#239—68no—
260#239—616no—
261#239—68no—
262#237—68no—
263#237—616no—
264#237—68no—
265C2×D12—22no—
266C2×D12—21no—
267C2×D12—64no—
268C2×D12—68no—
269C2×D12#6714yescomplemented
270C2×D12C22×D312yes—
271C2×C4×D3—32no—
272C2×C4×D3—32no—
273C2×C4×D3—32no—
274C2×C4×D3—32no—
275C2×C4×D3—62no—
276C2×C4×D3—62no—
277C2×C4×D3—64no—
278C2×C4×D3—68no—
279C2×C4×D3—62no—
280C2×C4×D3—62no—
281C2×C4×D3—62no—
282C2×C4×D3—62no—
283C2×C4×D3—122no—
284C2×C4×D3—122no—
285C2×Dic6—22no—
286C2×Dic6—21no—
287C2×Dic6#6714yescomplemented
288C2×Dic6C22×D312yes—
289C3×Q16—64no—
290C3×SD16—64no—
291C3×SD16—64no—
292C3×D8—64no—
293C3×M16—62no—
294C3×M16—62no—
295C2×C3×C8—32no—
296C2×C3×C8—32no—
297#217—62no—
298#217—62no—
299#217—62no—
300#217—64no—
301#217—61no—
302#217—61no—
303#216—24no—
304#215—24no—
305#214—24no—
306#213—24no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—62no—
309(C2×D3)⋊C4—64no—
310C4⋊Dic3—32no—
311C4⋊Dic3—32no—
312C4⋊Dic3—62no—
313Dic3⋊C4—62no—
314Dic3⋊C4—62no—
315Dic3⋊C4—64no—
316C4×Dic3—62no—
317C4×Dic3—61no—
318C4×Dic3—61no—
319#208—22no—
320#208—22no—
321C2×C3⋊C8C22×D312yes—
322C2×C3⋊C8C22×D312yes—
323C22×C32—22no—
324C22×C32—41no—
325C22×C32—42no—
326C22×C32#12012yes—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—22no—
329C2×C3⋊D3—22no—
330C2×C3⋊D3—22no—
331C2×C3⋊D3—44no—
332C2×C3×D3—24no—
333C2×C3×D3—48no—
334C2×C3×D3—44no—
335C32×C4—41no—
336C32×C4#12012yes—
337C32×C4C22×D411yescharacteristic
338C32×C4C22×D411yescharacteristic
339C3⋊Dic3—22no—
340C3⋊Dic3—42no—
341C3×Dic3—24no—
342C2×#41—94no—
343C2×#41—182no—
344C2×#41—184no—
345C2×#41—184no—
346C2×#41D3211yescharacteristic
347C22×Q8—31no—
348C22×D4—31no—
349C22×D4—181no—
350C23×C4—91no—
351C23×C4—181no—
352#137—64no—
353AGL(1,ℤ/8)—64no—
354C2×Q16—32no—
355C2×SD16—32no—
356C2×SD16—32no—
357C2×D8—32no—
358C2×M16—31no—
359C2×M16—31no—
360#123—181no—
361C22⋊Q8—92no—
362#121—92no—
363#120—181no—
364C4×D4—182no—
365#117—91no—
366#103—94no—
367#102—94no—
368C22⋊C8—94no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—64no—
374C23×C3—62no—
375C23×C3—124no—
376C23×C3D3×D411yescharacteristic
377C23×C3D3×D411yescharacteristic
378C22×D3—24no—
379C22×D3—22no—
380C22×D3—32no—
381C22×D3—32no—
382C22×D3—44no—
383C22×D3—62no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—122no—
387C22×D3—122no—
388C22×D3—122no—
389C22×D3—124no—
390C3×Q8—21no—
391C3×Q8—21no—
392C3×Q8—21no—
393C3×Q8—21no—
394C3×Q8—34no—
395C3×Q8—41no—
396C3×Q8—41no—
397C3×Q8—64no—
398C3×Q8—62no—
399C3×D4—21no—
400C3×D4—21no—
401C3×D4—21no—
402C3×D4—21no—
403C3×D4—34no—
404C3×D4—41no—
405C3×D4—41no—
406C3×D4—44no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—64no—
410C3×D4—62no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—44no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—64no—
422C2×C3×C4—62no—
423C2×C3×C4D3×D412yes—
424C2×C3×C4D3×D412yes—
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4D3×D411yescharacteristic
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C2×#6712yes—
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—616no—
432#67—128no—
433#67—124no—
434#67—124no—
435C2×Dic3—24no—
436C2×Dic3—22no—
437C2×Dic3—32no—
438C2×Dic3—32no—
439C2×Dic3—62no—
440C2×Dic3—616no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—64no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—122no—
447D12—24no—
448D12—22no—
449D12—616no—
450D12C2×#6714yes—
451C4×D3—616no—
452C4×D3—64no—
453C4×D3—64no—
454C4×D3—62no—
455C4×D3—62no—
456C4×D3—62no—
457C4×D3—62no—
458C4×D3—122no—
459C4×D3—122no—
460C4×D3—124no—
461Dic6—24no—
462Dic6—22no—
463Dic6C2×#6714yes—
464C3×C8—62no—
465C3×C8—62no—
466C3⋊C8—22no—
467C3⋊C8—22no—
468C2×C32—22no—
469C2×C32—81no—
470C2×C32C2×#12011yescharacteristic
471C2×C32#57512yes—
472C3⋊D3—42no—
473C3×D3—44no—
474C24—61no—
475C24—91no—
476#41—22no—
477#41—22no—
478#41—188no—
479#41—188no—
480#41—1816no—
481C2×Q8—32no—
482C2×Q8—34no—
483C2×Q8—62no—
484C2×Q8—61no—
485C2×Q8C2×D3211yescharacteristic
486C2×D4—21no—
487C2×D4—32no—
488C2×D4—34no—
489C2×D4—62no—
490C2×D4—61no—
491C2×D4—184no—
492C2×D4—188no—
493C2×D4—182no—
494C2×D4C2×D3211yescharacteristic
495C22×C4—21no—
496C22×C4—61no—
497C22×C4—91no—
498C22×C4—92no—
499C22×C4—92no—
500C22×C4—184no—
501C22×C4—188no—
502C22×C4—182no—
503C22×C4—182no—
504C22×C4C2×D3211yescharacteristic
505Q16—64no—
506SD16—64no—
507SD16—64no—
508D8—64no—
509M16—62no—
510M16—62no—
511C2×C8—32no—
512C2×C8—32no—
513C4⋊C4—92no—
514C4⋊C4—182no—
515C22⋊C4—182no—
516C22⋊C4—182no—
517C22⋊C4—181no—
518C42—181no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—42no—
524C22×C3—44no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—64no—
531C22×C3—128no—
532C22×C3—124no—
533C22×C3#93712yes—
534C22×C3#93712yes—
535C22×C3C2×D3×D411yescharacteristic
536C22×C3C2×D3×D411yescharacteristic
537C2×D3—24no—
538C2×D3—48no—
539C2×D3—44no—
540C2×D3—64no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—122no—
548C2×D3—122no—
549C2×D3—124no—
550C2×D3—124no—
551C2×D3—128no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—22no—
555C3×C4—42no—
556C3×C4—41no—
557C3×C4—41no—
558C3×C4—64no—
559C3×C4#93712yes—
560C3×C4#93712yes—
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C2×D3×D411yescharacteristic
563C3×C4C22×#6711yescharacteristic
564C3×C4C22×#6711yescharacteristic
565Dic3—24no—
566Dic3—62no—
567Dic3—62no—
568Dic3—122no—
569Dic3—124no—
570Dic3—122no—
571Dic3—122no—
572C32#300511yescharacteristic, complemented, Sylow
573C23—21no—
574C23—62no—
575C23—64no—
576C23—92no—
577C23—124no—
578C23—182no—
579C23—362no—
580C23#381111yescharacteristic
581Q8—21no—
582Q8—21no—
583Q8—34no—
584Q8—62no—
585Q8—64no—
586D4—21no—
587D4—21no—
588D4—34no—
589D4—42no—
590D4—62no—
591D4—64no—
592D4—1816no—
593D4—364no—
594C2×C4—21no—
595C2×C4—42no—
596C2×C4—62no—
597C2×C4—64no—
598C2×C4—92no—
599C2×C4—1816no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—182no—
603C2×C4—184no—
604C2×C4—182no—
605C2×C4D3×#6712yes—
606C2×C4D3×#6712yes—
607C2×C4#381111yescharacteristic
608C2×C4C22×D3211yescharacteristic
609C8—62no—
610C8—62no—
611C2×C3—22no—
612C2×C3—22no—
613C2×C3—22no—
614C2×C3—21no—
615C2×C3—42no—
616C2×C3—82no—
617C2×C3—81no—
618C2×C3—81no—
619C2×C3—124no—
620C2×C3#577312yes—
621C2×C3#577712yes—
622C2×C3C2×#93711yescharacteristic
623C2×C3C2×#93711yescharacteristic
624D3—44no—
625D3—124no—
626D3—122no—
627D3—122no—
628C22—22no—
629C22—42no—
630C22—41no—
631C22—64no—
632C22—128no—
633C22—124no—
634C22—182no—
635C22—182no—
636C22—182no—
637C22—364no—
638C22#6398312yes—
639C22C2×#381111yescharacteristic
640C4—41no—
641C4—64no—
642C4—182no—
643C4—362no—
644C4#6398312yes—
645C4C2×D3×#6711yescharacteristic
646C4C2×D3×#6711yescharacteristic
647C3—21no—
648C3#8394511yescharacteristic, complemented
649C3#8398011yescharacteristic, complemented
650C2—22no—
651C2—81no—
652C2—124no—
653C2—362no—
654C2#1059547112yes—
655C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×#3811
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×#3796C2semidirect
2. #10596299C2semidirect
3. C2×C3×#951C2semidirect
4. C2×C3×#949C2semidirect
5. #10591656C2semidirect
6. #10591520C2semidirect
7. #10591100C2semidirect
8. #10591086C2semidirect
9. #10591074C2semidirect
22. #64155C22semidirect
23. #64147C22semidirect
30. C2×C3×#216C22semidirect
31. C2×C3×#215C22semidirect
32. C2×C3×#214C22semidirect
33. C2×C3×#213C22semidirect
36. #63566C22semidirect
37. #63563C22semidirect
38. #63557C22semidirect
46. C2×#951D3semidirect
47. C2×#949D3semidirect
76. C2×C3×D12D4semidirect
80. C2×C3×Dic6D4semidirect
139. C2×#216C2×D3semidirect
140. C2×#215C2×D3semidirect
150. C2×#214C2×D3semidirect
151. C2×#213C2×D3semidirect
269. C2×D12#67semidirect
287. C2×Dic6#67semidirect
572. C32#3005semidirect
648. C3#83945semidirect
649. C3#83980semidirect

Maximal subgroups

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

subgroupindex
C22×#37962
#105962992
C2×C3×#9512
C2×C3×#9492
#105916562
#105915202
#105911002
#105910862
#105910742
#839803
#839453