Finite Group Databasebeta

← #11856268

Subgroups — #11856268

Order 1152.

2457 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#624C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×#63981C211yesmaximal, characteristic
4C2×#63961C211yesmaximal, characteristic, complemented
5#10592654C211yesmaximal, characteristic, complemented
6C3×#4943C211yesmaximal, characteristic, complemented
7#10591696C211yesmaximal, characteristic, complemented
8#10591378C214yesmaximal, complemented
9#10591275C214yesmaximal, complemented
10#82912—31nomaximal
11#74146—31nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C22×C3×#67C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C22×#626C2212yes—
17C22×#624—24no—
18C22×#624—24no—
19C22×#624—24no—
20C22×#624C2214yes—
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×#3752C2214yes—
24C2×C3×#217C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2212yescomplemented
26C2×C3×C4⋊Dic3C2212yescomplemented
27C3×#886—24no—
28#63981—24no—
29C2×#3724C2212yescomplemented
30C2×#3722C2212yes—
31#63961—24no—
32C2×(C2×D3)⋊Dic3C2212yescomplemented
33C3×C3⋊#95C2214yescomplemented
34#63579C2214yescomplemented
35C23×C4×D3—31no—
36C23×C4×D3—31no—
37C2×C3×#123—31no—
38C2×#937—31no—
39C2×#935—31no—
40C2×#929—31no—
41C2×#886D311yescharacteristic, complemented
42C2×#882—31no—
43C3×#381—31no—
44#5211—31no—
45#4989—34no—
46#4956—34no—
47#4955—31no—
48#4955—31no—
49#4955—61no—
50#4943—31no—
51#4943D311yescharacteristic, complemented
52#4668—34no—
53#4665—34no—
54C24×C32C2311yescharacteristic
55C23×C3⋊D3—22no—
56C23×C3⋊D3—22no—
57C23×C3⋊D3—28no—
58C23×C3⋊D3D414yes—
59C23×C3⋊D3C2312yes—
60C23×C3×D3C2311yescharacteristic
61C22×C32×C4C2312yes—
62C22×C3⋊Dic3C2312yes—
63C2×C3×#67—22no—
64C2×C3×#67—22no—
65C2×C3×#67—22no—
66C22×C3×Dic3—22no—
67C22×C3×Dic3—22no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—22no—
70C22×C3×Dic3D414yescomplemented
71C22×C3×Dic3D414yescomplemented
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×#626—24no—
77C2×#626—28no—
78C2×#624—232no—
79C2×#624—28no—
80C2×#624—28no—
81C2×#624—28no—
82C32×C22⋊C4—22no—
83#3757—22no—
84#3752—28no—
85C3×#217—22no—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—24no—
88#3724—24no—
89#3722—24no—
90(C2×D3)⋊Dic3—24no—
91#2849—91noSylow
92C24×D3—31no—
93C24×D3—31no—
94C24×D3—61no—
95C22×C3×D4—31no—
96C23×C3×C4—31no—
97C23×C3×C4—31no—
98C22×#67—32no—
99C22×#67C2×D311yescharacteristic
100C23×Dic3C2×D311yescharacteristic
101C23×Dic3C2×D311yescharacteristic
102C22×D12—32no—
103C22×C4×D3—34no—
104C22×C4×D3—34no—
105C22×C4×D3—64no—
106C22×C4×D3—64no—
107C22×C4×D3—64no—
108C22×C4×D3—64no—
109C22×C4×D3—64no—
110C22×C4×D3—64no—
111C3×#123—64no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4—32no—
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C22⋊C4C2×D311yescharacteristic
118C2×#217—31no—
119C2×#217—31no—
120C2×#217—32no—
121C2×#217—61no—
122C2×#217C2×D311yescharacteristic
123#937—64no—
124#935—64no—
125#929—64no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—34no—
128C2×(C2×D3)⋊C4—34no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—64no—
132C2×(C2×D3)⋊C4C2×D312yescomplemented
133C2×C4⋊Dic3C2×D312yescomplemented
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136#886—24no—
137#882—64no—
138C3×#95—34no—
139C3⋊#95—34no—
140C3⋊#95—34no—
141C3⋊#95C2×D314yescomplemented
142C23×C32—24no—
143C23×C32C2×D412yes—
144C23×C32C2×D412yes—
145C23×C32C2×D412yes—
146C23×C32C2411yescharacteristic
147C22×C3⋊D3—216no—
148C22×C3⋊D3—216no—
149C22×C3⋊D3—28no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—24no—
153C22×C3⋊D3—216no—
154C22×C3⋊D3C2×D414yes—
155C22×C3⋊D3#4118yes—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3—24no—
160C2×C32×C4—22no—
161C2×C32×C4—24no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—24no—
164C3×#67—44no—
165C2×C3×Dic3—28no—
166C2×C3×Dic3—28no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—24no—
176C2×C3×Dic3C2×D414yes—
177C2×C3×Dic3C2×D414yes—
178#626—48no—
179#624—232no—
180C24×C4—91no—
181C2×#123—31no—
182C2×#123—91no—
183C2×#120—91no—
184#386—94no—
185#385—94no—
186#381—31no—
187#381—91no—
188#379—91no—
189C24×C3—21no—
190C24×C3—31no—
191C24×C3C22×D311yescharacteristic
192C24×C3C22×D311yescharacteristic
193C23×D3—32no—
194C23×D3—32no—
195C23×D3—34no—
196C23×D3—34no—
197C23×D3—62no—
198C23×D3—64no—
199C23×D3—68no—
200C23×D3—68no—
201C23×D3—62no—
202C23×D3—62no—
203C23×D3—62no—
204C23×D3—62no—
205C23×D3—128no—
206C23×D3—122no—
207C23×D3—122no—
208C23×D3C22×D311yescharacteristic
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C22×C3×C4—22no—
213C22×C3×C4—34no—
214C22×C3×C4—34no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—31no—
219C22×C3×C4—62no—
220C22×C3×C4—62no—
221C22×C3×C4—62no—
222C22×C3×C4—62no—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C2×#67—22no—
226C2×#67—22no—
227C2×#67—22no—
228C2×#67—64no—
229C2×#67—68no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—62no—
237C22×Dic3D1214yescomplemented
238C22×Dic3#6714yescomplemented
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D311yescharacteristic
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C2×D12—64no—
244C2×D12—68no—
245C2×C4×D3—68no—
246C2×C4×D3—68no—
247C2×C4×D3—68no—
248C2×C4×D3—68no—
249C2×C4×D3—632no—
250C2×C4×D3—632no—
251C2×C4×D3—68no—
252C2×C4×D3—68no—
253C3×C4⋊C4—64no—
254C3×C22⋊C4—22no—
255C3×C22⋊C4—22no—
256C3×C22⋊C4—42no—
257C3×C22⋊C4—64no—
258C3×C22⋊C4—62no—
259#217—22no—
260#217—62no—
261#217—62no—
262#217—64no—
263#217—122no—
264(C2×D3)⋊C4—24no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—68no—
268(C2×D3)⋊C4—68no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—128no—
271C4⋊Dic3—24no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C22×C32—24no—
275C22×C32—24no—
276C22×C32—24no—
277C22×C32#12014yes—
278C22×C32C22×D411yescharacteristic
279C22×C32C22×D411yescharacteristic
280C22×C32C22×D411yescharacteristic
281C22×C32C2×#4114yes—
282C2×C3⋊D3—232no—
283C2×C3⋊D3—24no—
284C2×C3⋊D3—24no—
285C2×C3⋊D3—28no—
286C2×C3⋊D3—28no—
287C2×C3⋊D3#12318yescomplemented
288C2×C3×D3—41no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C32×C4—42no—
293C3⋊Dic3—42no—
294C3×Dic3—24no—
295C3×Dic3—24no—
296C3×Dic3—41no—
297C3×Dic3—42no—
298C25—91no—
299C22×D4—31no—
300C22×D4—92no—
301C23×C4—31no—
302C23×C4—31no—
303C23×C4—94no—
304C23×C4—184no—
305C23×C4—184no—
306C23×C4—184no—
307#123—64no—
308#123—184no—
309#120—184no—
310C2×C4⋊C4—32no—
311C2×C4⋊C4—92no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—32no—
314C2×C22⋊C4—92no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—94no—
318C2×C22⋊C4D3211yescharacteristic
319#95—34no—
320#95—94no—
321C23×C3—24no—
322C23×C3—24no—
323C23×C3—21no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—44no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3—64no—
332C23×C3C2×D1212yes—
333C23×C3D3×D412yes—
334C23×C3D3×D412yes—
335C23×C3D3×D412yes—
336C23×C3D3×D412yes—
337C23×C3C2×#6712yes—
338C23×C3C23×D311yescharacteristic
339C23×C3C23×D311yescharacteristic
340C22×D3—21no—
341C22×D3—21no—
342C22×D3—24no—
343C22×D3—21no—
344C22×D3—34no—
345C22×D3—34no—
346C22×D3—38no—
347C22×D3—38no—
348C22×D3—64no—
349C22×D3—68no—
350C22×D3—616no—
351C22×D3—616no—
352C22×D3—616no—
353C22×D3—616no—
354C22×D3—616no—
355C22×D3—616no—
356C22×D3—68no—
357C22×D3—68no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—64no—
362C22×D3—64no—
363C22×D3—62no—
364C22×D3—1216no—
365C22×D3—122no—
366C22×D3—124no—
367C22×D3—122no—
368C22×D3—128no—
369C22×D3—1216no—
370C22×D3—1216no—
371C3×D4—124no—
372C2×C3×C4—22no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—22no—
376C2×C3×C4—34no—
377C2×C3×C4—34no—
378C2×C3×C4—44no—
379C2×C3×C4—42no—
380C2×C3×C4—68no—
381C2×C3×C4—68no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—62no—
389C2×C3×C4—61no—
390C2×C3×C4—64no—
391#67—44no—
392#67—128no—
393C2×Dic3—28no—
394C2×Dic3—28no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—24no—
403C2×Dic3—21no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—124no—
409C2×Dic3—122no—
410C2×Dic3C2×D1214yes—
411C2×Dic3C2×#6714yes—
412D12—128no—
413C4×D3—632no—
414C4×D3—632no—
415C2×C32—24no—
416C2×C32C2×#12011yescharacteristic
417C2×C32C2×#12312yes—
418C2×C32#52512yes—
419C2×C32#52512yes—
420C3⋊D3—28no—
421C3×D3—81no—
422C24—31no—
423C24—92no—
424C24—94no—
425C24—188no—
426C24—182no—
427C24—182no—
428C24C2×D3211yescharacteristic
429C2×D4—62no—
430C2×D4—62no—
431C2×D4—62no—
432C2×D4—184no—
433C2×D4—188no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—34no—
437C22×C4—34no—
438C22×C4—32no—
439C22×C4—31no—
440C22×C4—62no—
441C22×C4—62no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—92no—
445C22×C4—188no—
446C22×C4—188no—
447C22×C4—188no—
448C22×C4—1832no—
449C22×C4C2×D3212yes—
450C4⋊C4—64no—
451C4⋊C4—184no—
452C22⋊C4—22no—
453C22⋊C4—64no—
454C22⋊C4—62no—
455C22⋊C4—188no—
456C22⋊C4—184no—
457C22⋊C4—184no—
458C22⋊C4—182no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—24no—
462C22×C3—24no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—24no—
468C22×C3—21no—
469C22×C3—24no—
470C22×C3—44no—
471C22×C3—44no—
472C22×C3—44no—
473C22×C3—122no—
474C22×C3—122no—
475C22×C3—121no—
476C22×C3—122no—
477C22×C3#88214yes—
478C22×C3#93714yes—
479C22×C3C22×D1211yescharacteristic
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×D3×D411yescharacteristic
483C22×C3C2×D3×D411yescharacteristic
484C22×C3D3×#4114yes—
485C22×C3D3×#4114yes—
486C22×C3C22×#6711yescharacteristic
487C2×D3—38no—
488C2×D3—38no—
489C2×D3—42no—
490C2×D3—42no—
491C2×D3—41no—
492C2×D3—42no—
493C2×D3—68no—
494C2×D3—632no—
495C2×D3—632no—
496C2×D3—64no—
497C2×D3—64no—
498C2×D3—68no—
499C2×D3—68no—
500C2×D3—64no—
501C2×D3—68no—
502C2×D3—64no—
503C2×D3—68no—
504C2×D3—128no—
505C2×D3—128no—
506C2×D3—124no—
507C2×D3—124no—
508C2×D3—1232no—
509C3×C4—42no—
510C3×C4—42no—
511C3×C4—64no—
512C3×C4—64no—
513C3×C4—82no—
514C3×C4—122no—
515C3×C4—121no—
516Dic3—24no—
517Dic3—24no—
518Dic3—42no—
519Dic3—41no—
520Dic3—122no—
521Dic3—122no—
522Dic3—242no—
523C32#284911yescharacteristic, complemented, Sylow
524C23—24no—
525C23—61no—
526C23—61no—
527C23—64no—
528C23—61no—
529C23—94no—
530C23—98no—
531C23—1816no—
532C23—1816no—
533C23—1816no—
534C23—182no—
535C23—184no—
536C23—182no—
537C23—188no—
538C23D3×D1212yes—
539C23#380212yes—
540C23D3×#6712yes—
541C23C22×D3211yescharacteristic
542D4—124no—
543D4—368no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—34no—
547C2×C4—34no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—68no—
553C2×C4—68no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—64no—
558C2×C4—61no—
559C2×C4—1832no—
560C2×C4—182no—
561C2×C4—184no—
562C2×C3—24no—
563C2×C3—24no—
564C2×C3—22no—
565C2×C3—22no—
566C2×C3—21no—
567C2×C3—22no—
568C2×C3—44no—
569C2×C3—241no—
570C2×C3C2×#88211yescharacteristic
571C2×C3#552412yes—
572C2×C3D3×#12312yes—
573C2×C3D3×#12312yes—
574C2×C3#565612yes—
575C2×C3#565612yes—
576C2×C3C2×#93711yescharacteristic
577C2×C3#582812yes—
578D3—68no—
579D3—68no—
580D3—81no—
581D3—128no—
582C22—24no—
583C22—24no—
584C22—24no—
585C22—98no—
586C22—122no—
587C22—122no—
588C22—121no—
589C22—122no—
590C22—1832no—
591C22—188no—
592C22—188no—
593C22—184no—
594C22—184no—
595C22#6392214yes—
596C22C2×D3×D1211yescharacteristic
597C22C2×#380211yescharacteristic
598C22#6431214yes—
599C22C2×D3×#6711yescharacteristic
600C4—42no—
601C4—64no—
602C4—64no—
603C4—121no—
604C4—122no—
605C4—362no—
606C3—21no—
607C3#7414611yescharacteristic, complemented
608C3#8291211yescharacteristic, complemented
609C2—24no—
610C2—188no—
611C2—241no—
612C2#1059407912yes—
613C2#1059429512yes—
614C2C2×#6392211yescharacteristic
615C2#1059515912yes—
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63981C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×#624C2semidirect
2. C2×C3×#886C2semidirect
4. C2×#63961C2semidirect
5. #10592654C2semidirect
6. C3×#4943C2semidirect
7. #10591696C2semidirect
8. #10591378C2semidirect
9. #10591275C2semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
29. C2×#3724C22semidirect
32. C2×(C2×D3)⋊Dic3C22semidirect
33. C3×C3⋊#95C22semidirect
34. #63579C22semidirect
41. C2×#886D3semidirect
51. #4943D3semidirect
70. C22×C3×Dic3D4semidirect
71. C22×C3×Dic3D4semidirect
132. C2×(C2×D3)⋊C4C2×D3semidirect
133. C2×C4⋊Dic3C2×D3semidirect
141. C3⋊#95C2×D3semidirect
237. C22×Dic3D12semidirect
238. C22×Dic3#67semidirect
287. C2×C3⋊D3#123semidirect
523. C32#2849semidirect
607. C3#74146semidirect
608. C3#82912semidirect

Maximal subgroups

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

subgroupindex
C23×#6242
C2×C3×#8862
C2×#639812
C2×#639612
#105926542
C3×#49432
#105916962
#105913782
#105912752
#829123
#741463