Finite Group Databasebeta

← #11803866

Subgroups — #11803866

Order 1152.

1729 conjugacy classes of subgroups.

The subgroup lattice has 609 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2C2×#63952C212yesmaximal, complemented
3C3×#5220C212yesmaximal, complemented
4#10591722C212yesmaximal, complemented
5#10591711C212yesmaximal, complemented
6#10591704C212yesmaximal, complemented
7#10591380C212yesmaximal, complemented
8#10591360C211yesmaximal, characteristic, complemented
9#10591252C211yesmaximal, characteristic, complemented
10#74667—32nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#638C2212yes—
13C22×#638C2212yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C22×#624C2212yes—
17#64149C418yescomplemented
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#217C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×#3724C2212yes—
23C2×#3722C2212yes—
24C2×#3722C2212yes—
25C2×#3722C2212yes—
26C2×Dic32C2211yescharacteristic
27C2×Dic32C2211yescharacteristic
28#63952—28no—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2212yes—
32#63579C2211yescharacteristic
33#63579C2211yescharacteristic
34C2×#940—32no—
35C2×#940—61no—
36C2×C4×#67—32no—
37C2×#67⋊C4—32no—
38C3×#386—32no—
39#5220D312yescomplemented
40#5213—32no—
41#4958—32no—
42#4957—32no—
43#4957—32no—
44#4956—32no—
45#4956—32no—
46#4665—32no—
47#4665—32no—
48#4650—32no—
49#4648—32no—
50C24×C32C2312yes—
51C23×C3⋊D3C2312yes—
52C2×C32×D4—42no—
53C2×C32×D4C2×C414yescomplemented
54C22×C32×C4C2311yescharacteristic
55C2×#638—24no—
56C2×#638—24no—
57C2×#638—42no—
58C2×#638—42no—
59C2×#638C2×C418yescomplemented
60C2×#638C2×C418yescomplemented
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C4⋊(C3⋊D3)—42no—
64C2×C4⋊(C3⋊D3)C2×C414yescomplemented
65C22×C3×Dic3—24no—
66C22×C3×Dic3—42no—
67C22×C3×Dic3—42no—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×#624—24no—
73C2×#624—42no—
74C2×#624—42no—
75C4×C3⋊Dic3C2×C414yescomplemented
76C3×#217—24no—
77C3×#217—42no—
78C3×#217—42no—
79#3724—24no—
80#3722—24no—
81#3722—42no—
82#3722—42no—
83Dic32—22no—
84Dic32D414yescomplemented
85#2328—91noSylow
86C22×C3×D4—21no—
87C22×C3×D4C2×D312yes—
88C23×C3×C4—32no—
89C22×#67—32no—
90C22×#67—32no—
91C22×#67—32no—
92C22×#67—32no—
93C22×#67—62no—
94C22×#67—62no—
95C23×Dic3C2×D312yes—
96C22×D12—32no—
97C22×D12—61no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C2×C3×C22⋊C4—32no—
101C2×C3×C22⋊C4—32no—
102C2×C3×C22⋊C4—32no—
103C2×#217C2×D312yes—
104C2×#217C2×D312yes—
105C2×#217C2×D312yes—
106#940—316no—
107#940—68no—
108C4×#67—68no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—61no—
121#67⋊C4—68no—
122C3×#95—32no—
123C3×#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95C2×D312yes—
129C3⋊#95C2×D312yes—
130C23×C32—22no—
131C23×C32—22no—
132C23×C32—22no—
133C23×C32—22no—
134C23×C32—22no—
135C23×C32—22no—
136C23×C32C22×C414yes—
137C23×C32C2411yescharacteristic
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3C22×C414yes—
145C32×D4—44no—
146C2×C32×C4—22no—
147C2×C32×C4C22×C412yes—
148#638—216no—
149#638—48no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3C22×C412yes—
152C2×C3⋊Dic3C22×C412yes—
153C2×C3⋊Dic3C2×D412yes—
154C2×C3⋊Dic3#4112yes—
155C4⋊(C3⋊D3)—44no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—48no—
168C2×C3×Dic3C2×D414yes—
169#624—48no—
170C2×#127—91no—
171C2×C4×D4—92no—
172#390—92no—
173#386—32no—
174#386—92no—
175#386—92no—
176#386—92no—
177#382—91no—
178#376—91no—
179C24×C3—22no—
180C24×C3C22×D312yes—
181C24×C3C22×D312yes—
182C23×D3—32no—
183C23×D3—32no—
184C23×D3—62no—
185C2×C3×D4—24no—
186C2×C3×D4—42no—
187C2×C3×D4—42no—
188C2×C3×D4—44no—
189C2×C3×D4C4×D318yescomplemented
190C22×C3×C4—21no—
191C22×C3×C4—32no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—64no—
196C22×C3×C4—122no—
197C22×C3×C4—122no—
198C22×C3×C4C22×D312yes—
199C2×#67—38no—
200C2×#67—38no—
201C2×#67—38no—
202C2×#67—38no—
203C2×#67—68no—
204C2×#67—68no—
205C2×#67—64no—
206C2×#67—64no—
207C2×#67—64no—
208C2×#67—64no—
209C2×#67—124no—
210C2×#67—124no—
211C2×#67—122no—
212C2×#67—122no—
213C2×#67—122no—
214C2×#67—122no—
215C2×#67—124no—
216C2×#67—124no—
217C22×Dic3—24no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—42no—
221C22×Dic3—42no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C2×D12—38no—
229C2×D12—64no—
230C2×D12—122no—
231C2×D12—122no—
232C2×D12—124no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—122no—
236C2×C4×D3—122no—
237C2×C4×D3—122no—
238C2×C4×D3—122no—
239C3×C22⋊C4—64no—
240C3×C22⋊C4—122no—
241C3×C22⋊C4—122no—
242#217—24no—
243#217—42no—
244#217—42no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—122no—
248(C2×D3)⋊C4—122no—
249(C2×D3)⋊C4—122no—
250(C2×D3)⋊C4—122no—
251Dic3⋊C4—64no—
252Dic3⋊C4—64no—
253C4×Dic3—38no—
254C4×Dic3—38no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C22×C32—24no—
258C22×C32—24no—
259C22×C32—24no—
260C22×C32—42no—
261C22×C32—42no—
262C22×C32—42no—
263C22×C32—42no—
264C22×C32C23×C411yescharacteristic
265C22×C32C22×D411yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32H(5,𝔽2)12yes—
268C22×C32H(5,𝔽2)12yes—
269C2×C3⋊D3—24no—
270C2×C3⋊D3—24no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C32×C4—22no—
277C3⋊Dic3—22no—
278C3⋊Dic3C4×D414yes—
279C3×Dic3—24no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C3×Dic3—42no—
283C22×D4—92no—
284C22×D4—92no—
285C22×D4—91no—
286C22×D4D3211yescharacteristic
287C23×C4—32no—
288C23×C4—92no—
289#127—98no—
290C4×D4—188no—
291C2×C4⋊C4—92no—
292C2×C22⋊C4—32no—
293C2×C22⋊C4—32no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—92no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4—92no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301#95—32no—
302#95—32no—
303#95—92no—
304#95—91no—
305#95—91no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—21no—
319C23×C3—24no—
320C23×C3—42no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—42no—
326C23×C3C2×C4×D314yes—
327C23×C3C2×C4×D314yes—
328C23×C3C23×D312yes—
329C22×D3—34no—
330C22×D3—34no—
331C22×D3—64no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—122no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C3×D4—48no—
351C3×D4—48no—
352C2×C3×C4—24no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—34no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—128no—
369C2×C3×C4C2×C4×D314yes—
370#67—616no—
371#67—616no—
372#67—1216no—
373#67—128no—
374#67—128no—
375#67—1216no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—34no—
388C2×Dic3—34no—
389C2×Dic3—34no—
390C2×Dic3—34no—
391C2×Dic3—48no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—64no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3D3×D414yes—
400D12—128no—
401D12—128no—
402C4×D3—128no—
403C4×D3—128no—
404C2×C32—44no—
405C2×C32C2×C4×D411yescharacteristic
406C2×C32#51811yescharacteristic
407C2×C32#51811yescharacteristic
408C2×C32#53512yes—
409C2×C32#54012yes—
410C3⋊D3—44no—
411C24—92no—
412C24C2×D3212yes—
413C2×D4—42no—
414C2×D4—98no—
415C2×D4—98no—
416C2×D4—94no—
417C2×D4—184no—
418C2×D4—184no—
419C2×D4—362no—
420C2×D4—362no—
421C2×D4—362no—
422C2×D4#62414yescomplemented
423C22×C4—32no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—32no—
427C22×C4—64no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—122no—
431C22×C4—122no—
432C22×C4—184no—
433C22×C4—362no—
434C22×C4—362no—
435C22×C4C2×D3211yescharacteristic
436C4⋊C4—184no—
437C22⋊C4—64no—
438C22⋊C4—122no—
439C22⋊C4—122no—
440C22⋊C4—184no—
441C22⋊C4—362no—
442C22⋊C4—362no—
443C42—94no—
444C42—94no—
445C42—182no—
446C22×C3—24no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3—22no—
457C22×C3—44no—
458C22×C3—44no—
459C22×C3—44no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—82no—
469C22×C3—82no—
470C22×C3—82no—
471C22×C3—82no—
472C22×C3C22×C4×D312yes—
473C22×C3C2×D3×D412yes—
474C22×C3#100412yes—
475C22×C3#100412yes—
476C22×C3#100412yes—
477C22×C3D3×#4112yes—
478C22×C3#100912yes—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—64no—
484C2×D3—64no—
485C2×D3—124no—
486C2×D3—124no—
487C2×D3—124no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—242no—
497C2×D3—242no—
498C2×D3—242no—
499C2×D3—242no—
500C3×C4—24no—
501C3×C4—24no—
502C3×C4—64no—
503C3×C4—122no—
504C3×C4—122no—
505C3×C4—122no—
506Dic3—24no—
507Dic3—38no—
508Dic3—42no—
509Dic3—42no—
510Dic3—42no—
511Dic3—64no—
512Dic3—64no—
513Dic3—64no—
514C32#232811yescharacteristic, complemented, Sylow
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—94no—
522C23—182no—
523C23—182no—
524C23—182no—
525C23—182no—
526C23—182no—
527C23—182no—
528C23C2×#62414yes—
529C23C22×D3211yescharacteristic
530D4—44no—
531D4—1816no—
532D4—364no—
533D4—368no—
534C2×C4—22no—
535C2×C4—34no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—92no—
548C2×C4—92no—
549C2×C4—92no—
550C2×C4—92no—
551C2×C4—128no—
552C2×C4—182no—
553C2×C4—368no—
554C2×C4C2×#62412yes—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—22no—
558C2×C3—21no—
559C2×C3—22no—
560C2×C3—44no—
561C2×C3—44no—
562C2×C3—84no—
563C2×C3#548612yes—
564C2×C3C4×D3×D412yes—
565C2×C3#554512yes—
566C2×C3#559212yes—
567C2×C3#560712yes—
568C2×C3#561512yes—
569C2×C3#566312yes—
570D3—124no—
571D3—124no—
572D3—244no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—42no—
580C22—184no—
581C22—184no—
582C22—184no—
583C22—362no—
584C22—362no—
585C22—362no—
586C22—362no—
587C22D32×D411yescharacteristic
588C22#6431211yescharacteristic
589C22#6431412yes—
590C22C22×#62411yescharacteristic
591C22#6433012yes—
592C4—22no—
593C4—64no—
594C4—94no—
595C4—122no—
596C4—122no—
597C4—122no—
598C4—182no—
599C3—21no—
600C3#7466712yescomplemented
601C2—44no—
602C2—364no—
603C2D4×#62411yescharacteristic
604C2#1059522311yescharacteristic
605C2#1059525112yes—
606C2#1059528512yes—
607C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64149C2
hypercenterC22×D4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63952C2semidirect
3. C3×#5220C2semidirect
4. #10591722C2semidirect
5. #10591711C2semidirect
6. #10591704C2semidirect
7. #10591380C2semidirect
8. #10591360C2semidirect
9. #10591252C2semidirect
17. #64149C4semidirect
39. #5220D3semidirect
53. C2×C32×D4C2×C4semidirect
59. C2×#638C2×C4semidirect
60. C2×#638C2×C4semidirect
64. C2×C4⋊(C3⋊D3)C2×C4semidirect
75. C4×C3⋊Dic3C2×C4semidirect
84. Dic32D4semidirect
189. C2×C3×D4C4×D3semidirect
422. C2×D4#624semidirect
514. C32#2328semidirect
600. C3#74667semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×#639522
C3×#52202
#105917222
#105917112
#105917042
#105913802
#105913602
#105912522
#746673