Finite Group Databasebeta

← #11801513

Subgroups — #11801513

Order 1152.

1521 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic, complemented
2C2×C4×#626C211yesmaximal, characteristic
3C2×C4×#624C211yesmaximal, characteristic, complemented
4C4×#3752C211yesmaximal, characteristic, complemented
5C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#10591374C212yesmaximal, complemented
7#10591285C212yesmaximal, complemented
8C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
9#10591275C212yesmaximal
10#10591254C212yesmaximal, complemented
11#10591222C211yesmaximal, characteristic, complemented
12#82268—31nomaximal
13#73754—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#626C2211yescharacteristic
17C22×#624C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#872—24no—
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×#3722C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×Dic32C2212yes—
33C4×#626C418yescomplemented
34C4×#624—24no—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×C4×#67—31no—
42C2×C4×D12—31no—
43C2×#872D311yescharacteristic, complemented
44C2×C42×D3—31no—
45C2×C42×D3—31no—
46C3×C4×C4⋊C4—31no—
47C4×#217—31no—
48#4990—32no—
49#4989—32no—
50#4989—32no—
51#4978—32no—
52#4956—32no—
53#4944—32no—
54C4×(C2×D3)⋊C4—31no—
55C4×(C2×D3)⋊C4—31no—
56C4×(C2×D3)⋊C4—31no—
57C4×(C2×D3)⋊C4—61no—
58#4932—31no—
59#4932—31no—
60C4×Dic3⋊C4D311yescharacteristic, complemented
61#4665—32no—
62#4654—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3C2×C414yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3C2×C414yescomplemented
80C2×#626—24no—
81C2×#626C2×C414yes—
82C2×#624—24no—
83C2×#624—24no—
84C2×#624—24no—
85C32×C42—22no—
86#3752—24no—
87C4×C3⋊Dic3—22no—
88C3×(C2×D3)⋊C4—24no—
89C3×Dic3⋊C4—24no—
90C3×Dic3⋊C4—24no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3C2×C414yescomplemented
93C3×C4×Dic3D414yescomplemented
94Dic3⋊Dic3C2×C414yescomplemented
95#3722C2×C414yes—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3C2×C414yescomplemented
98Dic32—24no—
99#2290—91noSylow
100C23×C3×C4—31no—
101C22×#67—31no—
102C22×D12—31no—
103C22×C4×D3—31no—
104C22×C4×D3—31no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3—61no—
108C22×C4×D3C2×D311yescharacteristic
109C3×#117—64no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C42—21no—
114C2×C3×C42—31no—
115C2×C3×C42—31no—
116C2×C3×C42—31no—
117C2×C3×C42C2×D311yescharacteristic
118C2×C3×C42C2×D311yescharacteristic
119C2×#217—31no—
120C2×#217—32no—
121C4×#67—38no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—62no—
129C2×(C2×D3)⋊C4C2×D312yes—
130C2×C4⋊Dic3—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4C2×D312yes—
133C2×Dic3⋊C4C2×D312yes—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—61no—
139C2×C4×Dic3C2×D311yescharacteristic
140C2×C4×Dic3C2×D311yescharacteristic
141C2×C4×Dic3C2×D311yescharacteristic
142C4×D12—38no—
143#872—24no—
144C42×D3—64no—
145C42×D3—64no—
146C3×#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—62no—
156C3⋊#95C2×D312yes—
157C23×C32C2411yescharacteristic
158C22×C3⋊D3—21no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3C22×C412yes—
162C22×C3⋊D3#4114yes—
163C22×C3×D3—21no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—21no—
167C22×C3×D3C22×C412yes—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4C22×C412yes—
172C2×C32×C4C2×D412yes—
173C2×C32×C4#4112yes—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3C22×C412yes—
180C4×C3⋊D3—28no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C22×C412yes—
191C2×C3×Dic3C22×C412yes—
192C2×C3×Dic3C2×D414yes—
193C2×C3×Dic3#4114yes—
194C3×C4×D3—28no—
195#626—28no—
196#624—216no—
197C2×C4×D4—91no—
198C2×#117—31no—
199C22×C42—91no—
200#388—92no—
201#387—92no—
202#386—92no—
203#385—92no—
204C4×C4⋊C4—31no—
205C4×C22⋊C4—91no—
206C4×C22⋊C4—91no—
207#376—91no—
208C24×C3—31no—
209C23×D3—31no—
210C23×D3—31no—
211C23×D3—61no—
212C23×D3C22×D311yescharacteristic
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—34no—
221C22×C3×C4—62no—
222C22×C3×C4—62no—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—34no—
228C2×#67—64no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—61no—
234C22×Dic3—62no—
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C2×D12—34no—
241C2×D12—64no—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—34no—
245C2×C4×D3—34no—
246C2×C4×D3—64no—
247C2×C4×D3—64no—
248C2×C4×D3—64no—
249C2×C4×D3—64no—
250C2×C4×D3—64no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—122no—
258C2×C4×D3—122no—
259C2×C4×D3C4×D314yescomplemented
260C3×C4⋊C4—64no—
261C3×C4⋊C4—64no—
262C3×C22⋊C4—64no—
263C3×C42—22no—
264C3×C42—22no—
265C3×C42—34no—
266C3×C42—34no—
267C3×C42—42no—
268C3×C42—62no—
269#217—34no—
270#217—64no—
271(C2×D3)⋊C4—24no—
272(C2×D3)⋊C4—34no—
273(C2×D3)⋊C4—34no—
274(C2×D3)⋊C4—34no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—68no—
278(C2×D3)⋊C4—64no—
279C4⋊Dic3—34no—
280Dic3⋊C4—24no—
281Dic3⋊C4—24no—
282Dic3⋊C4—34no—
283C4×Dic3—22no—
284C4×Dic3—64no—
285C4×Dic3—62no—
286C4×Dic3—62no—
287C4×Dic3—64no—
288C4×Dic3—122no—
289C4×Dic3C4×D314yescomplemented
290C4×Dic3#6714yescomplemented
291C22×C32C23×C411yescharacteristic
292C22×C32C22×D411yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32C2×#4112yes—
295C22×C32C2×#4112yes—
296C2×C3⋊D3—22no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—24no—
299C2×C3⋊D3—24no—
300C2×C3⋊D3#11714yescomplemented
301C2×C3×D3—22no—
302C2×C3×D3—22no—
303C2×C3×D3—22no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C32×C4—42no—
307C32×C4C4×D414yes—
308C3⋊Dic3—22no—
309C3⋊Dic3—42no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—24no—
314C3×Dic3—24no—
315C22×D4—91no—
316C23×C4—31no—
317C23×C4—92no—
318C23×C4—91no—
319C4×D4—98no—
320#117—64no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—91no—
324C2×C22⋊C4—32no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—91no—
327C2×C22⋊C4—92no—
328C2×C22⋊C4—92no—
329C2×C42—31no—
330C2×C42—31no—
331C2×C42—31no—
332C2×C42—92no—
333C2×C42—91no—
334C2×C42—184no—
335C2×C42D3211yescharacteristic
336#95—32no—
337#95—92no—
338#95—92no—
339#95—92no—
340#95—92no—
341C23×C3—21no—
342C23×C3—32no—
343C23×C3—62no—
344C23×C3—61no—
345C23×C3—61no—
346C23×C3—62no—
347C23×C3C23×D311yescharacteristic
348C23×C3C23×D311yescharacteristic
349C22×D3—21no—
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—21no—
353C22×D3—32no—
354C22×D3—32no—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—62no—
358C22×D3—64no—
359C22×D3—61no—
360C22×D3—62no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—62no—
364C22×D3—61no—
365C22×D3—121no—
366C22×D3—121no—
367C22×D3—122no—
368C22×D3C2×C4×D312yes—
369C2×C3×C4—24no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—32no—
380C2×C3×C4—32no—
381C2×C3×C4—32no—
382C2×C3×C4—34no—
383C2×C3×C4—34no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—62no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—68no—
395C2×C3×C4C2×C4×D312yes—
396C2×C3×C4C2×C4×D312yes—
397C2×C3×C4#23512yes—
398C2×C3×C4D3×D412yes—
399C2×C3×C4#23912yes—
400C2×C3×C4C2×#6712yes—
401#67—68no—
402C2×Dic3—22no—
403C2×Dic3—21no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—32no—
411C2×Dic3—32no—
412C2×Dic3—62no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—64no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—122no—
425C2×Dic3—121no—
426C2×Dic3—121no—
427C2×Dic3—122no—
428C2×Dic3C2×C4×D312yes—
429C2×Dic3C2×C4×D312yes—
430C2×Dic3C2×C4×D312yes—
431C2×Dic3#23514yes—
432C2×Dic3C2×#6714yes—
433D12—68no—
434C4×D3—28no—
435C4×D3—616no—
436C4×D3—616no—
437C4×D3—68no—
438C4×D3—68no—
439C4×D3—128no—
440C2×C32C2×#11711yescharacteristic
441C2×C32C2×C4×D411yescharacteristic
442C2×C32C4×#4111yescharacteristic
443C2×C32#52512yes—
444C2×C32#52912yes—
445C3⋊D3—24no—
446C3×D3—42no—
447C24—31no—
448C24—91no—
449C2×D4—94no—
450C2×D4—184no—
451C22×C4—31no—
452C22×C4—32no—
453C22×C4—32no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—34no—
457C22×C4—62no—
458C22×C4—62no—
459C22×C4—91no—
460C22×C4—94no—
461C22×C4—92no—
462C22×C4—184no—
463C22×C4—184no—
464C22×C4—184no—
465C22×C4—182no—
466C22×C4—182no—
467C22×C4C2×D3212yes—
468C22×C4C2×D3211yescharacteristic
469C4⋊C4—64no—
470C4⋊C4—64no—
471C4⋊C4—94no—
472C22⋊C4—64no—
473C22⋊C4—94no—
474C22⋊C4—94no—
475C22⋊C4—184no—
476C22⋊C4—184no—
477C42—22no—
478C42—34no—
479C42—34no—
480C42—62no—
481C42—184no—
482C42—182no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—62no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3C22×C4×D311yescharacteristic
494C22×C3C22×C4×D311yescharacteristic
495C22×C3C2×#23511yescharacteristic
496C22×C3C2×#23512yes—
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C2×#23911yescharacteristic
499C22×C3D3×#4112yes—
500C22×C3D3×#4112yes—
501C22×C3D3×#4112yes—
502C22×C3C22×#6711yescharacteristic
503C2×D3—22no—
504C2×D3—22no—
505C2×D3—22no—
506C2×D3—34no—
507C2×D3—34no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—64no—
511C2×D3—62no—
512C2×D3—62no—
513C2×D3—62no—
514C2×D3—64no—
515C2×D3—62no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—122no—
520C2×D3—124no—
521C2×D3—122no—
522C2×D3—124no—
523C3×C4—24no—
524C3×C4—44no—
525C3×C4—42no—
526C3×C4—42no—
527C3×C4—62no—
528C3×C4—62no—
529C3×C4—62no—
530C3×C4—64no—
531C3×C4—64no—
532C3×C4#89314yes—
533C3×C4C4×#6714yes—
534Dic3—22no—
535Dic3—22no—
536Dic3—22no—
537Dic3—24no—
538Dic3—24no—
539Dic3—62no—
540Dic3—62no—
541Dic3—122no—
542Dic3—124no—
543Dic3—122no—
544Dic3—122no—
545C32#229011yescharacteristic, complemented, Sylow
546C23—32no—
547C23—61no—
548C23—62no—
549C23—62no—
550C23—61no—
551C23—92no—
552C23—94no—
553C23—181no—
554C23—182no—
555C23—181no—
556C23C22×D3211yescharacteristic
557D4—188no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—32no—
562C2×C4—32no—
563C2×C4—32no—
564C2×C4—34no—
565C2×C4—34no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—61no—
574C2×C4—68no—
575C2×C4—92no—
576C2×C4—1816no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—188no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—182no—
583C2×C4#379912yes—
584C2×C4C4×D3212yes—
585C2×C4D3×#6712yes—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—22no—
591C2×C3—122no—
592C2×C3C4×#23511yescharacteristic
593C2×C3C2×#89311yescharacteristic
594C2×C3D3×#11711yescharacteristic
595C2×C3D3×#11711yescharacteristic
596C2×C3#552211yescharacteristic
597C2×C3#552812yes—
598C2×C3#554712yes—
599C2×C3#558012yes—
600C2×C3C2×C4×#6711yescharacteristic
601C2×C3#582812yes—
602D3—42no—
603D3—64no—
604D3—64no—
605D3—124no—
606C22—62no—
607C22—62no—
608C22—62no—
609C22—94no—
610C22—122no—
611C22—122no—
612C22—184no—
613C22—182no—
614C22—182no—
615C22—184no—
616C22C2×#379911yescharacteristic
617C22C2×C4×D3211yescharacteristic
618C22D3×#23512yes—
619C22#6430612yes—
620C22C2×D3×#6711yescharacteristic
621C4—42no—
622C4—62no—
623C4—62no—
624C4—62no—
625C4—64no—
626C4—64no—
627C4—182no—
628C4—362no—
629C4#6390414yes—
630C3—21no—
631C3#7375411yescharacteristic, complemented
632C3#8226811yescharacteristic, complemented
633C2—122no—
634C2—184no—
635C2#1059393412yes—
636C2#1059396511yescharacteristic
637C2#1059399211yescharacteristic
638C2C2×#6390411yescharacteristic
639C2#1059506012yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C42D32
hypocenterC32#2290
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#872C2semidirect
3. C2×C4×#624C2semidirect
4. C4×#3752C2semidirect
5. C3×C4×Dic3⋊C4C2semidirect
6. #10591374C2semidirect
7. #10591285C2semidirect
8. C4×(C2×D3)⋊Dic3C2semidirect
10. #10591254C2semidirect
11. #10591222C2semidirect
33. C4×#626C4semidirect
43. C2×#872D3semidirect
60. C4×Dic3⋊C4D3semidirect
79. C2×C3×C4×D3C2×C4semidirect
92. C3×C4×Dic3C2×C4semidirect
93. C3×C4×Dic3D4semidirect
94. Dic3⋊Dic3C2×C4semidirect
97. (C2×D3)⋊Dic3C2×C4semidirect
259. C2×C4×D3C4×D3semidirect
289. C4×Dic3C4×D3semidirect
290. C4×Dic3#67semidirect
300. C2×C3⋊D3#117semidirect
545. C32#2290semidirect
631. C3#73754semidirect
632. C3#82268semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×C4×#6262
C2×C4×#6242
C4×#37522
C3×C4×Dic3⋊C42
#105913742
#105912852
C4×(C2×D3)⋊Dic32
#105912752
#105912542
#105912222
#822683
#737543