Finite Group Databasebeta

← #11787444

Subgroups — #11787444

Order 1152.

905 conjugacy classes of subgroups.

The subgroup lattice has 605 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic
3C2×#63659C211yesmaximal, characteristic
4#10591220C211yesmaximal, characteristic, complemented
5C2×#63565C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72047—31nomaximal
9#71612—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3×Dic3—21no—
12C22×C3×Dic6C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#217—21no—
16C3×D4×Dic3—22no—
17C3×D4×Dic3—22no—
18C2×C3×#214—22no—
19C2×C3×#214—22no—
20C2×C3×#214C414yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24#63659—22no—
25#63579—21no—
26#63579—21no—
27#63565—22no—
28C22×C3×SD16—31no—
29C2×C3×C4×D4—31no—
30C2×D4×Dic3D311yescharacteristic
31C22×#214D311yescharacteristic
32#5229—31no—
33C2×#835—31no—
34C2×#832—31no—
35C2×#832—31no—
36C2×#832—61no—
37C2×#810—31no—
38#4929—31no—
39#4551—31no—
40#4550—31no—
41#4529—31no—
42#4524—31no—
43C24×C32—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4C2×C412yes—
48C2×C32×D4D412yes—
49C2×C32×D4D412yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—24no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—42no—
56C22×C3×Dic3—42no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2×C412yescomplemented
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×#217—24no—
71C3×#214—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yescomplemented
79#1877—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2×D311yescharacteristic
83C22×C3×D4C2×D311yescharacteristic
84C23×C3×C4—61no—
85C23×Dic3—21no—
86C22×Dic6C2×D311yescharacteristic
87C2×C3×SD16—34no—
88C2×C3×SD16—62no—
89C2×C3×SD16—62no—
90C22×C3×C8—31no—
91C3×C4×D4—62no—
92C3×C4×D4—62no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—31no—
96C2×#217—21no—
97D4×Dic3—22no—
98D4×Dic3—22no—
99C2×#214—22no—
100C2×#214—22no—
101C2×#214Dic314yescomplemented
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4×Dic3C2×D311yescharacteristic
107C22×C3⋊C8—31no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111#835—62no—
112#832—64no—
113#832—62no—
114#832—62no—
115C3⋊#95—61no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118C3⋊#95—61no—
119#810—62no—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—22no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C2×D411yescharacteristic
128C32×D4—22no—
129C32×D4—22no—
130C32×D4—22no—
131C32×D4C22⋊C414yes—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—48no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3SD1612yescomplemented
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—41no—
157C3×Dic6—41no—
158C3⋊(C3⋊C8)—41no—
159C3×C3⋊C8—22no—
160C22×SD16—31no—
161C2×C4×D4—31no—
162C2×#103—91no—
163C2×#102—91no—
164#391—91no—
165#340—91no—
166#336—91no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—41no—
170C2×C3×Q8—32no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4C4×D312yes—
189C2×C3×D4D1212yes—
190C2×C3×D4C2×Dic312yes—
191C2×C3×D4#6712yes—
192C2×C3×D4#6712yes—
193C2×C3×D4#6712yes—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—64no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C22×C3×C4—122no—
201C22×C3×C4—122no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—24no—
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—42no—
208C22×Dic3—42no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—121no—
212C22×Dic3#6711yescharacteristic
213C22×Dic3#6711yescharacteristic
214C2×Dic6—21no—
215C2×Dic6—21no—
216C2×Dic6—21no—
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6C2×Dic312yescomplemented
220C3×SD16—68no—
221C2×C3×C8—32no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—61no—
226C3×C22⋊C4—64no—
227C3×C42—61no—
228C3×C42—61no—
229#217—24no—
230#214—28no—
231C4⋊Dic3—21no—
232C4⋊Dic3—62no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—121no—
238C4⋊Dic3#6712yes—
239C4×Dic3—21no—
240C4×Dic3—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—121no—
251C2×C3⋊C8—121no—
252C2×C3⋊C8C2×Dic312yescomplemented
253C22×C32—24no—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32C4×D411yescharacteristic
261C22×C32#12011yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32C2×SD1611yescharacteristic
264C22×C32#13511yescharacteristic
265C22×C32AGL(1,ℤ/8)11yescharacteristic
266C22×C32#13711yescharacteristic
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12311yescharacteristic
271C3⋊Dic3—81no—
272C3×Dic3—22no—
273C3×Dic3—42no—
274C3×Dic3—42no—
275C3×Dic3—41no—
276C22×Q8—31no—
277C22×D4D3211yescharacteristic
278C23×C4—61no—
279C2×SD16—34no—
280C2×SD16—62no—
281C2×SD16—62no—
282C22×C8—31no—
283C22×C8—91no—
284C4×D4—62no—
285C4×D4—62no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—91no—
288C2×C22⋊C4—61no—
289C2×C42—31no—
290#103—182no—
291#102—182no—
292#95—181no—
293#95—181no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—41no—
312C23×C3—81no—
313C23×C3—81no—
314C23×C3—81no—
315C23×C3—81no—
316C23×C3D3×D411yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—121no—
321C3×Q8—121no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—24no—
329C3×D4—42no—
330C3×D4—42no—
331C3×D4—42no—
332C3×D4(C2×D3)⋊C414yes—
333C3×D4#21714yes—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—32no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—128no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4—121no—
352C2×C3×C4—121no—
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4#23511yescharacteristic
356C2×C3×C4#23511yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4#23711yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4C22×Dic311yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—48no—
373C2×Dic3—41no—
374C2×Dic3—41no—
375C2×Dic3—41no—
376C2×Dic3—41no—
377C2×Dic3—122no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3—241no—
385C2×Dic3—241no—
386C2×Dic3#21412yescomplemented
387Dic6—22no—
388Dic6—22no—
389Dic6—41no—
390Dic6—41no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8—122no—
394C3⋊C8—121no—
395C3⋊C8—121no—
396C2×C32—44no—
397C2×C32#38611yescharacteristic
398C2×C32C4×SD1611yescharacteristic
399C2×C32#44011yescharacteristic
400C2×C32#45011yescharacteristic
401C2×C32#45211yescharacteristic
402C2×C32#46111yescharacteristic
403C2×C32#46311yescharacteristic
404C24—21no—
405C2×Q8—32no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×Q8—61no—
409C2×Q8—61no—
410C2×Q8—61no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4D3×Dic312yes—
415C2×D4#62512yes—
416C2×D4#62612yes—
417C22×C4—31no—
418C22×C4—31no—
419C22×C4—64no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—122no—
423C22×C4—122no—
424C22×C4—181no—
425C22×C4C2×D3211yescharacteristic
426SD16—68no—
427C2×C8—32no—
428C2×C8—61no—
429C2×C8—61no—
430C2×C8—181no—
431C2×C8—181no—
432C2×C8—181no—
433C4⋊C4—32no—
434C4⋊C4—61no—
435C4⋊C4—181no—
436C4⋊C4—181no—
437C22⋊C4—64no—
438C42—61no—
439C42—61no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—44no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—82no—
463C22×C3—82no—
464C22×C3—82no—
465C22×C3—82no—
466C22×C3—82no—
467C22×C3—82no—
468C22×C3D3×SD1611yescharacteristic
469C22×C3#91411yescharacteristic
470C22×C3#91511yescharacteristic
471C22×C3#91611yescharacteristic
472C22×C3C4×#6711yescharacteristic
473C22×C3#93011yescharacteristic
474C22×C3#93211yescharacteristic
475C22×C3C2×#21411yescharacteristic
476C22×C3D4×Dic311yescharacteristic
477C22×C3#93711yescharacteristic
478C22×C3#93911yescharacteristic
479C22×C3#95011yescharacteristic
480C22×C3#95111yescharacteristic
481C22×C3#95311yescharacteristic
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—62no—
487C3×C4—122no—
488C3×C4—121no—
489C3×C4—122no—
490C3×C4C2×(C2×D3)⋊C411yescharacteristic
491C3×C4C4×#6711yescharacteristic
492C3×C4#92911yescharacteristic
493C3×C4#93011yescharacteristic
494C3×C4D4×Dic311yescharacteristic
495C3×C4#93511yescharacteristic
496C3×C4#93911yescharacteristic
497C3×C4C2×#21711yescharacteristic
498Dic3—22no—
499Dic3—42no—
500Dic3—42no—
501Dic3—41no—
502Dic3—242no—
503Dic3—241no—
504Dic3—241no—
505C32#187711yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—22no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23D3×#6711yescharacteristic
514Q8—62no—
515Q8—62no—
516Q8—121no—
517Q8—121no—
518D4—22no—
519D4—22no—
520D4—22no—
521D4(C2×D3)⋊Dic314yes—
522C2×C4—32no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—62no—
530C2×C4—128no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—121no—
535C2×C4—361no—
536C2×C4—361no—
537C2×C4—361no—
538C2×C4C2×D3×Dic311yescharacteristic
539C2×C4#380411yescharacteristic
540C2×C4#380411yescharacteristic
541C2×C4C2×#62511yescharacteristic
542C2×C4C2×#62611yescharacteristic
543C2×C4D3×#6711yescharacteristic
544C8—62no—
545C8—361no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—44no—
554C2×C3—44no—
555C2×C3—84no—
556C2×C3#501611yescharacteristic
557C2×C3C4×#21411yescharacteristic
558C2×C3#501811yescharacteristic
559C2×C3#501911yescharacteristic
560C2×C3Dic3×SD1611yescharacteristic
561C2×C3#516211yescharacteristic
562C2×C3#516411yescharacteristic
563C2×C3#516511yescharacteristic
564C2×C3#516911yescharacteristic
565C2×C3#517311yescharacteristic
566C2×C3#521311yescharacteristic
567C2×C3#521811yescharacteristic
568C2×C3#522011yescharacteristic
569C2×C3#523911yescharacteristic
570C22—24no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22D3×#21411yescharacteristic
578C22#6392911yescharacteristic
579C22#6393411yescharacteristic
580C22#6393511yescharacteristic
581C22Dic3×#6711yescharacteristic
582C22#6397611yescharacteristic
583C22#6397811yescharacteristic
584C4—62no—
585C4—122no—
586C4—122no—
587C4—121no—
588C4—721no—
589C4C2×(C2×D3)⋊Dic311yescharacteristic
590C4#6396111yescharacteristic
591C4Dic3×#6711yescharacteristic
592C4#6397811yescharacteristic
593C3—21no—
594C3#7161211yescharacteristic, complemented
595C3#7204711yescharacteristic, complemented
596C2—44no—
597C2Dic3×#21411yescharacteristic
598C2#1059144011yescharacteristic
599C2#1059145811yescharacteristic
600C2#1059146111yescharacteristic
601C2#1059147111yescharacteristic
602C2#1059148911yescharacteristic
603C2#1059171011yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1877
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591220C2semidirect
5. C2×#63565C2semidirect
6. #10589164C2semidirect
7. #10589155C2semidirect
20. C2×C3×#214C4semidirect
64. C2×C3×Dic6C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
101. C2×#214Dic3semidirect
153. C2×C3×Dic3SD16semidirect
219. C2×Dic6C2×Dic3semidirect
252. C2×C3⋊C8C2×Dic3semidirect
386. C2×Dic3#214semidirect
505. C32#1877semidirect
594. C3#71612semidirect
595. C3#72047semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C22×C3×#2142
C2×#636592
#105912202
C2×#635652
#105891642
#105891552
#720473
#716123