Finite Group Databasebeta

← #11864085

Subgroups — #11864085

Order 1152.

1611 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
1C22×#3799C211yesmaximal, characteristic, complemented
2C2×C3×#909C211yesmaximal, characteristic, complemented
3#10595022C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5#10592830C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10591100C211yesmaximal, characteristic, complemented
8#10590966C214yesmaximal, complemented
9#10590823C214yesmaximal, complemented
10#83980—31nomaximal
11#78638—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626—21no—
17C22×#624—21no—
18C2×#3799—24no—
19C2×#3799—22no—
20C2×#3799—24no—
21C2×#3799C2214yes—
22C2×C32×M16C2211yescharacteristic
23#64135C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C3×#909—24no—
26C2×C3×Dic12C2212yescomplemented
27C2×C3×#204C2212yescomplemented
28#63976—21no—
29#63961—21no—
30#63908C2212yescomplemented
31C4×#625—22no—
32#63856C2212yescomplemented
33C2×#3717C2212yescomplemented
34#63825—24no—
35C2×#3714C2212yescomplemented
36#63648C2214yescomplemented
37C3×(C2×D3)⋊C8C2214yescomplemented
38#63566C2214yescomplemented
39C22×#239—31no—
40C22×#235—31no—
41C2×C3×#137—31no—
42#5828—31no—
43C2×#949—31no—
44#5791—31no—
45C2×#909D311yescharacteristic, complemented
46C2×#908—31no—
47C3×#407—31no—
48#5225—31no—
49#5187—34no—
50#5172—34no—
51#5131—31no—
52#5131—31no—
53#5131—61no—
54#5126D311yescharacteristic, complemented
55#5120—31no—
56#4734—34no—
57#4733—34no—
58C23×C3⋊D3—21no—
59C23×C3×D3D411yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)D414yescomplemented
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C3×#67—21no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3D411yescharacteristic
68C3×#235—22no—
69C3×#235—22no—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D412yes—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6D414yescomplemented
79C2×C3×Dic6C2311yescharacteristic
80C2×C3×Dic6C2312yes—
81C2×#626—28no—
82C2×#626—24no—
83C2×#625—22no—
84C2×#624—28no—
85C2×#624—24no—
86#3799—216no—
87#3799—28no—
88#3799—28no—
89C32×M16—22no—
90C2×C32×C8C2312yes—
91#3757—21no—
92C4⋊(C3⋊Dic3)C2312yes—
93C4×C3⋊Dic3—21no—
94C3×#208—22no—
95C2×C3×C3⋊C8C2312yes—
96C3×Dic12—24no—
97C3×#204—24no—
98#3724—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101#3717—24no—
102#3714—24no—
103#3005—91noSylow
104C2×C3×#41—31no—
105C22×C3×Q8—31no—
106C23×C3×C4—31no—
107C22×#67—61no—
108C2×#239—34no—
109C2×#239—64no—
110C2×#239—64no—
111C2×#239—62no—
112C2×#235—34no—
113C2×#235—64no—
114C2×#235—62no—
115C2×#235—64no—
116C2×#235C2×D311yescharacteristic
117C22×D12—31no—
118C22×D12—31no—
119C22×D12—61no—
120C22×D12—61no—
121C22×C4×D3—61no—
122C22×C4×D3—61no—
123C22×C4×D3C2×D311yescharacteristic
124C22×Dic6C2×D311yescharacteristic
125C3×#137—64no—
126C2×C3×Q16—32no—
127C2×C3×SD16—32no—
128C2×C3×M16—21no—
129C2×C3×M16—31no—
130C2×C3×M16C2×D311yescharacteristic
131C2×C3×M16C2×D311yescharacteristic
132#953—61no—
133#949—64no—
134#946—32no—
135C2×#215—32no—
136#938—32no—
137#937—61no—
138#935—61no—
139C2×#213—32no—
140#930—32no—
141#929—61no—
142C4×#67—62no—
143C4×#67—62no—
144#926—31no—
145#926—31no—
146#926—61no—
147#924—32no—
148C2×#208C2×D311yescharacteristic
149#909—24no—
150#908—64no—
151C2×Dic12C2×D312yescomplemented
152C2×D24—32no—
153C2×#204—32no—
154C2×#204C2×D312yescomplemented
155C3×C22⋊C8—34no—
156#835—34no—
157#821—34no—
158#821—34no—
159#821—64no—
160(C2×D3)⋊C8C2×D314yescomplemented
161#816—34no—
162C23×C32C2×D411yescharacteristic
163C22×C3⋊D3—24no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—44no—
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C22×C3×D3—42no—
169C22×C3×D3C2×D412yes—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C4⋊(C3⋊D3)—24no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)C2×D414yes—
178C3×#67—42no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3C2×D412yes—
184C3×D12—21no—
185C3×D12—21no—
186C3×C4×D3—24no—
187C3×C4×D3—22no—
188C3×C4×D3—22no—
189C3×C4×D3—42no—
190C3×Dic6—24no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194C3×Dic6C2×D414yes—
195#626—216no—
196#625—44no—
197#624—216no—
198C32×C8—22no—
199C3×C3⋊C8—22no—
200C22×#41—91no—
201C2×#137—31no—
202C2×AGL(1,ℤ/8)—91no—
203#525—91no—
204#452—94no—
205#449—94no—
206#419—91no—
207#418—91no—
208#407—31no—
209C24×C3—31no—
210C23×D3—61no—
211C23×D3—61no—
212C23×D3—121no—
213C23×D3D1211yescharacteristic
214C3×#41—62no—
215C3×#41—62no—
216C2×C3×Q8—34no—
217C2×C3×Q8—32no—
218C2×C3×Q8—31no—
219C2×C3×Q8—61no—
220C2×C3×Q8—62no—
221C2×C3×D4—31no—
222C2×C3×D4—61no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—61no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—61no—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—21no—
234C2×#67—64no—
235C2×#67—68no—
236C2×#67—62no—
237C2×#67—62no—
238C22×Dic3—21no—
239C22×Dic3D1211yescharacteristic
240#239—68no—
241#239—68no—
242#239—616no—
243#235—22no—
244#235—22no—
245#235—68no—
246#235—616no—
247#235—68no—
248C2×D12—34no—
249C2×D12—34no—
250C2×D12—32no—
251C2×D12—32no—
252C2×D12—62no—
253C2×D12—64no—
254C2×D12—68no—
255C2×D12—64no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12—121no—
261C2×D12—122no—
262C2×D12C22×D311yescharacteristic
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—21no—
266C2×C4×D3—64no—
267C2×C4×D3—68no—
268C2×C4×D3—68no—
269C2×C4×D3—64no—
270C2×C4×D3D1212yes—
271C2×C4×D3C22×D312yes—
272C2×Dic6—21no—
273C2×Dic6—22no—
274C2×Dic6#6714yescomplemented
275C2×Dic6C22×D311yescharacteristic
276C2×Dic6C22×D312yes—
277C3×Q16—64no—
278C3×SD16—64no—
279C3×M16—22no—
280C3×M16—22no—
281C3×M16—42no—
282C3×M16—62no—
283C2×C3×C8—22no—
284C2×C3×C8—32no—
285C2×C3×C8C22×D312yes—
286C2×C3×C8C22×D312yes—
287#217—62no—
288#217—61no—
289#217—61no—
290#217—62no—
291#217—121no—
292#215—64no—
293#213—64no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296C4⋊Dic3—32no—
297C4⋊Dic3—32no—
298C4⋊Dic3—62no—
299Dic3⋊C4—62no—
300Dic3⋊C4—62no—
301C4×Dic3—61no—
302C4×Dic3—61no—
303C4×Dic3—121no—
304#208—22no—
305C2×C3⋊C8C22×D312yes—
306Dic12—24no—
307D24—64no—
308#204—24no—
309#204—64no—
310C22×C32—22no—
311C22×C32#12012yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—24no—
314C2×C3⋊D3—48no—
315C2×C3⋊D3—44no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—44no—
320C2×C3×D3—41no—
321C2×C3×D3—42no—
322C32×C4#12012yes—
323C32×C4C22×D411yescharacteristic
324C32×C4C22×D411yescharacteristic
325C3⋊Dic3—42no—
326C3×Dic3—22no—
327C3×Dic3—24no—
328C3×Dic3—41no—
329C2×#41—31no—
330C2×#41—94no—
331C2×#41—182no—
332C2×#41—184no—
333C2×#41—184no—
334C22×Q8—31no—
335C22×D4—91no—
336C22×D4—181no—
337C23×C4—31no—
338C23×C4—181no—
339#137—64no—
340AGL(1,ℤ/8)—184no—
341C2×Q16—32no—
342C2×SD16—32no—
343C2×SD16—92no—
344C2×D8—92no—
345C2×M16—31no—
346C2×M16D3211yescharacteristic
347#123—181no—
348C22⋊Q8—92no—
349#121—92no—
350#120—181no—
351C4×D4—182no—
352#117—91no—
353#103—94no—
354#102—94no—
355C22⋊C8—34no—
356C23×C3—21no—
357C23×C3—32no—
358C23×C3—62no—
359C23×C3—61no—
360C23×C3—122no—
361C23×C3C2×D1211yescharacteristic
362C23×C3D3×D411yescharacteristic
363C22×D3—22no—
364C22×D3—21no—
365C22×D3—42no—
366C22×D3—64no—
367C22×D3—64no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—122no—
371C22×D3—124no—
372C22×D3—124no—
373C22×D3—124no—
374C22×D3—244no—
375C22×D3C2×D1212yes—
376C3×Q8—34no—
377C3×Q8—64no—
378C3×Q8—62no—
379C3×Q8—61no—
380C3×Q8—61no—
381C3×D4—61no—
382C3×D4—61no—
383C3×D4—122no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—32no—
389C2×C3×C4—64no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—64no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—122no—
397C2×C3×C4C2×D1211yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D412yes—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6712yes—
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—42no—
406#67—616no—
407#67—124no—
408#67—124no—
409C2×Dic3—22no—
410C2×Dic3—24no—
411C2×Dic3—22no—
412C2×Dic3—21no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—122no—
416C2×Dic3C2×D1212yes—
417D12—21no—
418D12—21no—
419D12—34no—
420D12—34no—
421D12—64no—
422D12—616no—
423D12—64no—
424D12—64no—
425D12—62no—
426D12—62no—
427D12—122no—
428D12—124no—
429C4×D3—24no—
430C4×D3—22no—
431C4×D3—22no—
432C4×D3—42no—
433C4×D3—616no—
434C4×D3—616no—
435Dic6—24no—
436Dic6—22no—
437Dic6—21no—
438Dic6—21no—
439Dic6C2×#6714yes—
440C3×C8—22no—
441C3×C8—22no—
442C3×C8—42no—
443C3×C8—62no—
444C3⋊C8—22no—
445C2×C32—22no—
446C2×C32C2×#12011yescharacteristic
447C2×C32#57512yes—
448C3⋊D3—44no—
449C3×D3—42no—
450C3×D3—81no—
451C24—31no—
452C24—181no—
453#41—62no—
454#41—62no—
455#41—188no—
456#41—188no—
457#41—1816no—
458C2×Q8—32no—
459C2×Q8—31no—
460C2×Q8—34no—
461C2×Q8—61no—
462C2×Q8—62no—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4—92no—
466C2×D4—94no—
467C2×D4—184no—
468C2×D4—188no—
469C2×D4—182no—
470C2×D4—181no—
471C2×D4—182no—
472C22×C4—31no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—61no—
476C22×C4—62no—
477C22×C4—62no—
478C22×C4—61no—
479C22×C4—184no—
480C22×C4—188no—
481C22×C4C2×D3211yescharacteristic
482Q16—64no—
483SD16—64no—
484SD16—184no—
485D8—184no—
486M16—22no—
487M16—62no—
488C2×C8—32no—
489C2×C8C2×D3212yes—
490C4⋊C4—92no—
491C4⋊C4—182no—
492C22⋊C4—182no—
493C22⋊C4—182no—
494C22⋊C4—181no—
495C42—181no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—42no—
501C22×C3—62no—
502C22×C3—62no—
503C22×C3—62no—
504C22×C3—124no—
505C22×C3—121no—
506C22×C3—122no—
507C22×C3#88212yes—
508C22×C3#93712yes—
509C22×C3C22×D1211yescharacteristic
510C22×C3C2×D3×D411yescharacteristic
511C2×D3—22no—
512C2×D3—22no—
513C2×D3—22no—
514C2×D3—44no—
515C2×D3—42no—
516C2×D3—41no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—124no—
520C2×D3—128no—
521C2×D3—128no—
522C2×D3—124no—
523C2×D3—124no—
524C2×D3—244no—
525C2×D3—248no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—22no—
529C3×C4—64no—
530C3×C4—62no—
531C3×C4—121no—
532C3×C4#88212yes—
533C3×C4#93712yes—
534C3×C4C2×D3×D411yescharacteristic
535C3×C4C2×D3×D411yescharacteristic
536C3×C4C2×D3×D411yescharacteristic
537C3×C4C22×#6711yescharacteristic
538Dic3—22no—
539Dic3—24no—
540Dic3—41no—
541Dic3—122no—
542Dic3—122no—
543Dic3—242no—
544C32#300511yescharacteristic, complemented, Sylow
545C23—32no—
546C23—62no—
547C23—61no—
548C23—122no—
549C23—182no—
550C23—184no—
551C23—364no—
552C23D3×D1211yescharacteristic
553Q8—34no—
554Q8—62no—
555Q8—64no—
556Q8—61no—
557Q8—61no—
558D4—61no—
559D4—61no—
560D4—94no—
561D4—122no—
562D4—1816no—
563D4—182no—
564D4—184no—
565D4—364no—
566C2×C4—32no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—64no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—64no—
573C2×C4—61no—
574C2×C4—122no—
575C2×C4—1816no—
576C2×C4—182no—
577C2×C4D3×D1211yescharacteristic
578C2×C4#380212yes—
579C2×C4D3×#6712yes—
580C2×C4C22×D3211yescharacteristic
581C8—22no—
582C8—62no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—22no—
586C2×C3—21no—
587C2×C3—42no—
588C2×C3—122no—
589C2×C3—241no—
590C2×C3C2×#88211yescharacteristic
591C2×C3#574812yes—
592C2×C3#577712yes—
593C2×C3C2×#93711yescharacteristic
594D3—42no—
595D3—81no—
596D3—124no—
597D3—124no—
598D3—244no—
599C22—22no—
600C22—62no—
601C22—62no—
602C22—62no—
603C22—124no—
604C22—122no—
605C22—121no—
606C22—184no—
607C22—368no—
608C22—364no—
609C22#6392212yes—
610C22C2×D3×D1211yescharacteristic
611C4—62no—
612C4—64no—
613C4—121no—
614C4—362no—
615C4#6392212yes—
616C4C2×#380211yescharacteristic
617C4C2×D3×#6711yescharacteristic
618C3—21no—
619C3#7863811yescharacteristic, complemented
620C3#8398011yescharacteristic, complemented
621C2—22no—
622C2—122no—
623C2—241no—
624C2—364no—
625C2#1059471112yes—
626C2C2×#6392211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C2×C3×#909C2semidirect
3. #10595022C2semidirect
4. C2×#63825C2semidirect
5. #10592830C2semidirect
6. C3×#5126C2semidirect
7. #10591100C2semidirect
8. #10590966C2semidirect
9. #10590823C2semidirect
26. C2×C3×Dic12C22semidirect
27. C2×C3×#204C22semidirect
30. #63908C22semidirect
32. #63856C22semidirect
33. C2×#3717C22semidirect
35. C2×#3714C22semidirect
36. #63648C22semidirect
37. C3×(C2×D3)⋊C8C22semidirect
38. #63566C22semidirect
45. C2×#909D3semidirect
54. #5126D3semidirect
63. C2×C4⋊(C3⋊D3)D4semidirect
78. C2×C3×Dic6D4semidirect
151. C2×Dic12C2×D3semidirect
154. C2×#204C2×D3semidirect
160. (C2×D3)⋊C8C2×D3semidirect
274. C2×Dic6#67semidirect
544. C32#3005semidirect
619. C3#78638semidirect
620. 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×C3×#9092
#105950222
C2×#638252
#105928302
C3×#51262
#105911002
#105909662
#105908232
#839803
#786383