Finite Group Databasebeta

← #11787592

Subgroups — #11787592

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic
4C3×#5221C211yesmaximal, characteristic
5C2×#63565C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72048—31nomaximal
9#69660—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#217—21no—
16C2×C3×#214—22no—
17C2×C3×#214—22no—
18C2×C3×#214C414yescomplemented
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×Dic32—21no—
24Dic3×Dic6—22no—
25Dic3×Dic6—22no—
26#63659—22no—
27#63565—22no—
28C22×C3×SD16—31no—
29C2×Q8×Dic3—31no—
30C22×#214D311yescharacteristic
31C2×C4×Dic6—31no—
32C3×#390—31no—
33C2×#835—31no—
34#5221D311yescharacteristic
35C2×#832—31no—
36C2×#832—31no—
37C2×#832—61no—
38C2×#810—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×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4C2×C412yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C412yes—
60C2×C3×Dic6D412yes—
61C2×C3×Dic6D412yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)D412yes—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#217—42no—
68C3×#217—42no—
69C3×#214—28no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C412yes—
77Dic3⋊Dic3—24no—
78Dic32—24no—
79#1880—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—21no—
82C22×C3×D4C2×D311yescharacteristic
83C22×C3×D4C2×D311yescharacteristic
84C22×Dic6C2×D311yescharacteristic
85C2×C3×SD16—34no—
86C2×C3×SD16—62no—
87C2×C3×SD16—62no—
88C22×C3×C8—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C42—31no—
93C2×#217—21no—
94C2×#217—21no—
95Q8×Dic3—62no—
96Q8×Dic3—62no—
97C2×#214—22no—
98C2×#214—22no—
99C2×#214Dic314yescomplemented
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3C2×D311yescharacteristic
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—61no—
112C22×C3⋊C8C2×D311yescharacteristic
113C4×Dic6—62no—
114C4×Dic6—62no—
115#835—62no—
116#832—62no—
117#832—62no—
118#832—64no—
119#810—62no—
120C23×C32—22no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32C2×D411yescharacteristic
128C32×D4—22no—
129C32×D4—22no—
130C32×D4—41no—
131C32×D4—41no—
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—22no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6C22⋊C414yescomplemented
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—22no—
159C22×SD16—31no—
160C2×C4×Q8—91no—
161C2×#103—91no—
162C2×#102—91no—
163#390—31no—
164#340—91no—
165#336—91no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—41no—
169C2×C3×Q8—32no—
170C2×C3×Q8—32no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—41no—
189C2×C3×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4C4×D312yes—
192C2×C3×D4C2×Dic312yes—
193C22×C3×C4—21no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—61no—
197C22×C3×C4—61no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×Dic3—21no—
201C22×Dic3—21no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3#6711yescharacteristic
206C22×Dic3#6711yescharacteristic
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6C2×Dic312yes—
211C2×Dic6#6712yes—
212C2×Dic6#6712yes—
213C3×SD16—68no—
214C2×C3×C8—32no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—122no—
220C3×C22⋊C4—122no—
221C3×C42—61no—
222C3×C42—61no—
223#217—42no—
224#217—42no—
225#214—28no—
226C4⋊Dic3—21no—
227C4⋊Dic3—21no—
228C4⋊Dic3—32no—
229C4⋊Dic3—32no—
230C4⋊Dic3—62no—
231C4⋊Dic3—64no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—121no—
235Dic3⋊C4—64no—
236C4×Dic3—21no—
237C4×Dic3—21no—
238C4×Dic3—64no—
239C4×Dic3—64no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—121no—
250C2×C3⋊C8—121no—
251C2×C3⋊C8C2×Dic312yes—
252C22×C32—42no—
253C22×C32—42no—
254C22×C32—42no—
255C22×C32—81no—
256C22×C32—81no—
257C22×C32—81no—
258C22×C32—81no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12011yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32C2×SD1611yescharacteristic
263C22×C32#13511yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C22×C32#13711yescharacteristic
266C32×C4C2×C22⋊C411yescharacteristic
267C32×C4C4×D411yescharacteristic
268C32×C4#12111yescharacteristic
269C32×C4#12311yescharacteristic
270C3⋊Dic3—42no—
271C3×Dic3—24no—
272C3×Dic3—22no—
273C3×Dic3—41no—
274C3×Dic3—81no—
275C22×Q8—31no—
276C22×D4D3211yescharacteristic
277C2×SD16—34no—
278C2×SD16—62no—
279C2×SD16—62no—
280C22×C8—31no—
281C22×C8—91no—
282C4×Q8—182no—
283C4×Q8—182no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—181no—
287C2×C22⋊C4—61no—
288C2×C22⋊C4—61no—
289C2×C42—31no—
290C2×C42—181no—
291#103—182no—
292#102—182no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—21no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3—42no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—81no—
312C23×C3—81no—
313C23×C3—81no—
314C23×C3—81no—
315C23×C3D3×D411yescharacteristic
316C23×C3C2×#6711yescharacteristic
317C3×Q8—34no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—62no—
321C3×D4—24no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—42no—
327C3×D4—42no—
328C3×D4—42no—
329C3×D4—41no—
330C3×D4—41no—
331C3×D4—41no—
332C3×D4—41no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—61no—
348C2×C3×C4—121no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4#23711yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4C22×Dic311yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×Dic3—22no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—121no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—241no—
382C2×Dic3—241no—
383C2×Dic3#21412yescomplemented
384Dic6—22no—
385Dic6—22no—
386Dic6—22no—
387Dic6#21714yescomplemented
388C3×C8—62no—
389C3⋊C8—22no—
390C3⋊C8—122no—
391C3⋊C8—121no—
392C3⋊C8—121no—
393C2×C32—82no—
394C2×C32#38611yescharacteristic
395C2×C32C4×SD1611yescharacteristic
396C2×C32#44011yescharacteristic
397C2×C32#44811yescharacteristic
398C2×C32#44911yescharacteristic
399C2×C32#46011yescharacteristic
400C2×C32#46411yescharacteristic
401C24—21no—
402C2×Q8—32no—
403C2×Q8—32no—
404C2×Q8—32no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4D3×Dic312yes—
414C22×C4—31no—
415C22×C4—31no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—181no—
419C22×C4C2×D3211yescharacteristic
420SD16—68no—
421C2×C8—32no—
422C2×C8—61no—
423C2×C8—61no—
424C2×C8—181no—
425C2×C8—181no—
426C2×C8—181no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—92no—
430C4⋊C4—184no—
431C4⋊C4—181no—
432C22⋊C4—122no—
433C22⋊C4—122no—
434C42—61no—
435C42—61no—
436C42—184no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—44no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—82no—
452C22×C3—82no—
453C22×C3—82no—
454C22×C3—82no—
455C22×C3—82no—
456C22×C3—82no—
457C22×C3—81no—
458C22×C3—81no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3—81no—
465C22×C3D3×SD1611yescharacteristic
466C22×C3#91411yescharacteristic
467C22×C3#91511yescharacteristic
468C22×C3#91611yescharacteristic
469C22×C3C4×#6711yescharacteristic
470C22×C3#93211yescharacteristic
471C22×C3C2×#21411yescharacteristic
472C22×C3D4×Dic311yescharacteristic
473C22×C3#93711yescharacteristic
474C22×C3#93711yescharacteristic
475C22×C3#93811yescharacteristic
476C22×C3#93911yescharacteristic
477C22×C3#95011yescharacteristic
478C22×C3#95111yescharacteristic
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—62no—
484C3×C4—64no—
485C3×C4—121no—
486C3×C4—241no—
487C3×C4D3×C22⋊C411yescharacteristic
488C3×C4#67⋊C411yescharacteristic
489C3×C4#88311yescharacteristic
490C3×C4#88411yescharacteristic
491C3×C4D4×Dic311yescharacteristic
492C3×C4#93511yescharacteristic
493C3×C4#93911yescharacteristic
494C3×C4C2×#21711yescharacteristic
495Dic3—24no—
496Dic3—22no—
497Dic3—41no—
498Dic3—81no—
499Dic3—122no—
500Dic3—122no—
501Dic3—242no—
502C32#188011yescharacteristic, complemented, Sylow
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23D3×#6711yescharacteristic
511Q8—34no—
512Q8—62no—
513Q8—62no—
514Q8—62no—
515D4—22no—
516D4—22no—
517D4—41no—
518D4—41no—
519C2×C4—32no—
520C2×C4—61no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—61no—
528C2×C4—121no—
529C2×C4—121no—
530C2×C4—121no—
531C2×C4—182no—
532C2×C4—361no—
533C2×C4—361no—
534C2×C4C2×D3×Dic311yescharacteristic
535C2×C4#380411yescharacteristic
536C2×C4#380511yescharacteristic
537C2×C4D3×#6711yescharacteristic
538C2×C4D3×#6711yescharacteristic
539C2×C4#381111yescharacteristic
540C8—62no—
541C8—361no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—84no—
550C2×C3—82no—
551C2×C3—82no—
552C2×C3#495611yescharacteristic
553C2×C3C4×#21411yescharacteristic
554C2×C3#501811yescharacteristic
555C2×C3#503711yescharacteristic
556C2×C3#504011yescharacteristic
557C2×C3#505411yescharacteristic
558C2×C3#507511yescharacteristic
559C2×C3Dic3×SD1611yescharacteristic
560C2×C3#516311yescharacteristic
561C2×C3#516411yescharacteristic
562C2×C3#516611yescharacteristic
563C2×C3#517011yescharacteristic
564C2×C3#517211yescharacteristic
565C2×C3#522011yescharacteristic
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22D3×#21411yescharacteristic
574C22#6392911yescharacteristic
575C22#6393411yescharacteristic
576C22#6393511yescharacteristic
577C22#6397011yescharacteristic
578C22Dic3×#6711yescharacteristic
579C22#6398311yescharacteristic
580C4—62no—
581C4—64no—
582C4—121no—
583C4—241no—
584C4—362no—
585C4D3×#21711yescharacteristic
586C4#6396911yescharacteristic
587C4#6397111yescharacteristic
588C4#67⋊Dic311yescharacteristic
589C3—21no—
590C3#6966011yescharacteristic, complemented
591C3#7204811yescharacteristic, complemented
592C2—82no—
593C2Dic3×#21411yescharacteristic
594C2#1059143811yescharacteristic
595C2#1059144011yescharacteristic
596C2#1059144211yescharacteristic
597C2#1059151711yescharacteristic
598C2#1059152111yescharacteristic
599C2#1059172111yescharacteristic
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#1880
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
2. C2×Dic3×Dic6C2semidirect
5. C2×#63565C2semidirect
6. #10589164C2semidirect
7. #10589155C2semidirect
18. C2×C3×#214C4semidirect
99. C2×#214Dic3semidirect
152. C2×C3×Dic3SD16semidirect
156. C3×Dic6C22⋊C4semidirect
383. C2×Dic3#214semidirect
387. Dic6#217semidirect
502. C32#1880semidirect
590. C3#69660semidirect
591. C3#72048semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2142
C2×Dic3×Dic62
C2×#636592
C3×#52212
C2×#635652
#105891642
#105891552
#720483
#696603