Finite Group Databasebeta

← #11808799

Subgroups — #11808799

Order 1152.

1255 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic, complemented
3#10592921C211yesmaximal, characteristic
4C3×#5222C211yesmaximal, characteristic
5#10591717C212yesmaximal, complemented
6Dic3×#217C212yesmaximal, complemented
7Dic3×#217C212yesmaximal, complemented
8#10591692C212yesmaximal, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591227C211yesmaximal, characteristic, complemented
11#10591225C211yesmaximal, characteristic, complemented
12#82348—31nomaximal
13#76893—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C22×#627C2211yescharacteristic
17C2×#3757C2212yes—
18C2×#3757C2212yes—
19C2×#3750C2211yescharacteristic
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C3×D4×Dic3—24no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×Dic32C2212yes—
29C2×Dic32C2211yescharacteristic
30C2×Dic32C2211yescharacteristic
31#63837—24no—
32#63658C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×D4—31no—
40C2×D4×Dic3D311yescharacteristic
41C2×#887—31no—
42C2×C4×Dic6—31no—
43C3×#394—31no—
44#5222—31no—
45#5222—31no—
46#5222—61no—
47#5222D311yescharacteristic
48C4×#217—32no—
49C4×#217—32no—
50#4986—31no—
51#4985—31no—
52#4985—31no—
53#4953—32no—
54#4952—32no—
55#4947—32no—
56#4947—32no—
57Dic3×C22⋊C4—32no—
58Dic3×C22⋊C4—32no—
59#4932—31no—
60#4659—31no—
61#4648—31no—
62C24×C32C2312yes—
63C2×C32×D4—24no—
64C2×C32×D4—22no—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3—24no—
70C22×C3×Dic3—24no—
71C22×C3×Dic3—24no—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C2×#627—22no—
79C2×#627—22no—
80C2×#627—22no—
81#3757—24no—
82#3757—24no—
83#3750—22no—
84C3×#217—24no—
85C3×#217—24no—
86C3×#217—24no—
87C3×C4⋊Dic3—22no—
88C3×Dic3⋊C4—22no—
89C3×C4×Dic3D414yes—
90Dic3⋊Dic3—22no—
91Dic32—22no—
92Dic32—22no—
93Dic32—24no—
94#2398—91noSylow
95C22×C3×D4—21no—
96C22×C3×D4C2×D311yescharacteristic
97C22×C3×D4C2×D311yescharacteristic
98C23×C3×C4—32no—
99C23×Dic3C2×D312yes—
100C22×Dic6—31no—
101C22×Dic6—31no—
102C3×C4×D4—64no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C42—31no—
109C2×#217—32no—
110C2×#217—32no—
111C2×#217—32no—
112C2×#217—32no—
113C2×#217—62no—
114C2×#217—62no—
115C2×#217C2×D312yes—
116C2×#217C2×D312yes—
117C2×#217C2×D312yes—
118D4×Dic3—24no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—61no—
125C2×Dic3⋊C4C2×D311yescharacteristic
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3C2×D311yescharacteristic
133#887—64no—
134C4×Dic6—64no—
135C3×#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—61no—
149C3⋊#95C2×D311yescharacteristic
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32—22no—
156C23×C32#4114yes—
157C23×C32C2411yescharacteristic
158C32×D4—28no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D412yes—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3#4112yes—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—48no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C2×C3×Dic3#4112yes—
185C2×C3×Dic3#4114yes—
186#627—28no—
187C2×C4×Q8—91no—
188C2×C4×D4—31no—
189#400—91no—
190#400—91no—
191#397—92no—
192#394—31no—
193#394—91no—
194#393—92no—
195C4×C22⋊C4—92no—
196C4×C22⋊C4—92no—
197#376—91no—
198C24×C3—22no—
199C24×C3C22×D312yes—
200C24×C3C22×D312yes—
201C2×C3×D4—24no—
202C2×C3×D4—24no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—42no—
206C2×C3×D4—44no—
207C22×C3×C4—21no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—32no—
213C22×C3×C4—31no—
214C22×C3×C4—64no—
215C22×C3×C4—64no—
216C22×C3×C4—64no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C22×Dic3—24no—
220C22×Dic3—24no—
221C22×Dic3—24no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—61no—
229C22×Dic3—62no—
230C22×Dic3—61no—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D311yescharacteristic
237C2×Dic6—62no—
238C2×Dic6—62no—
239C2×Dic6—62no—
240C2×Dic6—62no—
241C2×Dic6—62no—
242C2×Dic6—62no—
243C3×C4⋊C4—62no—
244C3×C4⋊C4—62no—
245C3×C22⋊C4—64no—
246C3×C22⋊C4—64no—
247C3×C22⋊C4—64no—
248C3×C42—34no—
249#217—24no—
250#217—24no—
251#217—24no—
252#217—64no—
253#217—64no—
254#217—64no—
255#217—64no—
256#217—124no—
257#217—124no—
258C4⋊Dic3—22no—
259C4⋊Dic3—62no—
260Dic3⋊C4—22no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—122no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3#6714yes—
272C22×C32—24no—
273C22×C32—24no—
274C22×C32—24no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32—42no—
279C22×C32C22×D411yescharacteristic
280C22×C32C2×#4112yes—
281C22×C32C2×#4111yescharacteristic
282C22×C32C2×#4112yes—
283C22×C32C2×#4111yescharacteristic
284C32×C4—22no—
285C3⋊Dic3—22no—
286C3⋊Dic3—41no—
287C3⋊Dic3—42no—
288C3×Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C3×Dic3#12414yes—
294C22×Q8—91no—
295C22×D4D3211yescharacteristic
296C23×C4—32no—
297C4×Q8—184no—
298C4×D4—64no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—91no—
303C2×C22⋊C4—32no—
304C2×C22⋊C4—32no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4—92no—
307C2×C22⋊C4—92no—
308C2×C42—31no—
309C2×C42—91no—
310C2×C42—91no—
311C2×C42—92no—
312#95—31no—
313#95—92no—
314#95—92no—
315#95—92no—
316#95—92no—
317#95—92no—
318#95—91no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—24no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3#23514yes—
340C23×C3#23714yes—
341C23×C3C23×D311yescharacteristic
342C23×C3C23×D311yescharacteristic
343C3×D4—28no—
344C3×D4—28no—
345C3×D4—48no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—32no—
350C2×C3×C4—34no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—42no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
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—61no—
366C2×C3×C4—128no—
367C2×C3×C4D3×D412yes—
368C2×C3×C4C2×#6712yes—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—32no—
382C2×Dic3—32no—
383C2×Dic3—48no—
384C2×Dic3—62no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—61no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—61no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3—122no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—122no—
406C2×Dic3#23712yes—
407C2×Dic3#23714yes—
408C2×Dic3C2×#6712yes—
409C2×Dic3C2×#6712yes—
410Dic6—68no—
411Dic6—68no—
412C2×C32—44no—
413C2×C32#52511yescharacteristic
414C2×C32#52511yescharacteristic
415C2×C32C2×#12411yescharacteristic
416C2×C32#52912yes—
417C2×C32#52912yes—
418C24C2×D3212yes—
419C2×Q8—182no—
420C2×Q8—182no—
421C2×Q8—182no—
422C2×D4—24no—
423C2×D4—22no—
424C22×C4—31no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—32no—
428C22×C4—32no—
429C22×C4—31no—
430C22×C4—64no—
431C22×C4—64no—
432C22×C4—64no—
433C22×C4—91no—
434C22×C4—92no—
435C22×C4—91no—
436C22×C4C2×D3211yescharacteristic
437C4⋊C4—62no—
438C4⋊C4—62no—
439C4⋊C4—182no—
440C4⋊C4—182no—
441C22⋊C4—64no—
442C22⋊C4—64no—
443C22⋊C4—64no—
444C22⋊C4—184no—
445C22⋊C4—184no—
446C42—34no—
447C42—182no—
448C42—182no—
449C42—184no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—24no—
454C22×C3—24no—
455C22×C3—24no—
456C22×C3—22no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—44no—
462C22×C3—44no—
463C22×C3—44no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—82no—
473C22×C3—82no—
474C22×C3—82no—
475C22×C3—82no—
476C22×C3C2×#23512yes—
477C22×C3C2×D3×D411yescharacteristic
478C22×C3C2×#23712yes—
479C22×C3C2×#23711yescharacteristic
480C22×C3C2×#23712yes—
481C22×C3D3×#4112yes—
482C22×C3D3×#4111yescharacteristic
483C22×C3D3×#4111yescharacteristic
484C22×C3D3×#4111yescharacteristic
485C22×C3C22×#6711yescharacteristic
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—34no—
489C3×C4—42no—
490C3×C4—62no—
491C3×C4—62no—
492C3×C4—122no—
493C3×C4—121no—
494C3×C4—122no—
495Dic3—22no—
496Dic3—22no—
497Dic3—42no—
498Dic3—41no—
499Dic3—42no—
500Dic3—62no—
501Dic3—62no—
502Dic3—122no—
503Dic3—122no—
504Dic3—121no—
505Dic3—122no—
506Dic3—121no—
507Dic3—242no—
508Dic3—241no—
509Dic3#93614yes—
510C32#239811yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23#380414yes—
518C23C22×D3211yescharacteristic
519Q8—188no—
520D4—28no—
521C2×C4—22no—
522C2×C4—34no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—61no—
537C2×C4—62no—
538C2×C4—92no—
539C2×C4—128no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4—182no—
545C2×C4—182no—
546C2×C4—181no—
547C2×C4D3×#6712yes—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—22no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—44no—
554C2×C3—44no—
555C2×C3—84no—
556C2×C3#553812yes—
557C2×C3#553812yes—
558C2×C3#558611yescharacteristic
559C2×C3#560012yes—
560C2×C3#560611yescharacteristic
561C2×C3#564912yes—
562C2×C3D3×#12411yescharacteristic
563C2×C3#579111yescharacteristic
564C2×C3C2×#93611yescharacteristic
565C2×C3#582811yescharacteristic
566C22—24no—
567C22—24no—
568C22—24no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22D3×#23712yes—
574C22D3×#23711yescharacteristic
575C22#6431211yescharacteristic
576C22C2×#380412yes—
577C22C2×D3×#6711yescharacteristic
578C4—22no—
579C4—34no—
580C4—62no—
581C4—62no—
582C4—122no—
583C4—122no—
584C4—121no—
585C4—182no—
586C4—362no—
587C4—361no—
588C3—21no—
589C3#7689311yescharacteristic, complemented
590C3#8234811yescharacteristic, complemented
591C2—44no—
592C2#1059511612yes—
593C2D3×#93611yescharacteristic
594C2#1059518712yes—
595C2#1059530111yescharacteristic
596C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
Fitting, prime radicalC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63837C2semidirect
5. #10591717C2semidirect
6. Dic3×#217C2semidirect
7. Dic3×#217C2semidirect
8. #10591692C2semidirect
9. #10591239C2semidirect
10. #10591227C2semidirect
11. #10591225C2semidirect
510. C32#2398semidirect
589. C3#76893semidirect
590. C3#82348semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×#638372
#105929212
C3×#52222
#105917172
Dic3×#2172
#105916922
#105912392
#105912272
#105912252
#823483
#768933