Finite Group Databasebeta

← #11787594

Subgroups — #11787594

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3#10592920C211yesmaximal, characteristic
4C2×C3×#832C211yesmaximal, characteristic
5C2×#63566C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72048—31nomaximal
9#70213—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×#3757—21no—
13C2×#3757—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×#214—22no—
17C2×C3×#214—22no—
18C2×C3×#214C414yescomplemented
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×Dic32—21no—
24#63843—22no—
25#63843—22no—
26C3×#832—22no—
27#63566—22no—
28C22×C3×SD16—31no—
29C2×Q8×Dic3—31no—
30C22×#214D311yescharacteristic
31C2×#887—31no—
32C2×C3×#102—31no—
33C2×#835—31no—
34#5221—31no—
35#5221—31no—
36#5221—61no—
37C2×#832D311yescharacteristic
38C2×#816—31no—
39#4551—31no—
40#4550—31no—
41#4550—31no—
42#4529—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⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C412yes—
60C2×C3×Dic6D412yes—
61C2×C3×Dic6D412yes—
62#3757—42no—
63#3757—42no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C3×#214—28no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—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—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—31no—
91C2×#217—61no—
92C2×#217—61no—
93C2×#217—61no—
94C2×#217—61no—
95C2×#217—62no—
96C2×#217—62no—
97Q8×Dic3—62no—
98Q8×Dic3—62no—
99C2×#214—22no—
100C2×#214—22no—
101C2×#214Dic314yescomplemented
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×Dic3⋊C4—61no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3—61no—
113C22×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115#887—62no—
116#887—62no—
117C3×#102—62no—
118#835—62no—
119#832—22no—
120#816—62no—
121C23×C32—22no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32—41no—
125C23×C32—41no—
126C23×C32—41no—
127C23×C32—41no—
128C23×C32C2×D411yescharacteristic
129C32×D4—22no—
130C32×D4—22no—
131C32×D4—41no—
132C32×D4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3—41no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3SD1612yescomplemented
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6C22⋊C414yescomplemented
158C3×C3⋊C8—22no—
159C3×C3⋊C8—41no—
160C22×SD16—31no—
161C2×C4×Q8—91no—
162C2×#103—91no—
163C2×#102—31no—
164#390—91no—
165#340—91no—
166#336—91no—
167C24×C3—22no—
168C24×C3—21no—
169C24×C3—21no—
170C2×C3×Q8—32no—
171C2×C3×Q8—32no—
172C2×C3×Q8—32no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
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×D4—41no—
192C2×C3×D4C4×D312yes—
193C2×C3×D4C2×Dic312yes—
194C22×C3×C4—21no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—62no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6C2×Dic312yes—
214C2×Dic6#6712yes—
215C2×Dic6#6712yes—
216C3×SD16—68no—
217C2×C3×C8—32no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—61no—
225#217—122no—
226#217—122no—
227#217—124no—
228#217—124no—
229#217—122no—
230#217—122no—
231#214—28no—
232C4⋊Dic3—21no—
233C4⋊Dic3—64no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—121no—
239C4⋊Dic3—121no—
240C4⋊Dic3#6712yes—
241Dic3⋊C4—64no—
242C4×Dic3—64no—
243C4×Dic3—64no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3—121no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8C2×Dic312yes—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—81no—
260C22×C32—81no—
261C22×C32—81no—
262C22×C32—81no—
263C22×C32C4×D411yescharacteristic
264C22×C32#12011yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32C2×SD1611yescharacteristic
267C22×C32#13511yescharacteristic
268C22×C32AGL(1,ℤ/8)11yescharacteristic
269C22×C32#13711yescharacteristic
270C32×C4C2×C22⋊C411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12311yescharacteristic
274C3⋊Dic3—22no—
275C3⋊Dic3—41no—
276C3⋊Dic3—81no—
277C3×Dic3—24no—
278C3×Dic3—42no—
279C22×Q8—31no—
280C22×D4D3211yescharacteristic
281C2×SD16—34no—
282C2×SD16—62no—
283C2×SD16—62no—
284C22×C8—31no—
285C22×C8—31no—
286C4×Q8—182no—
287C4×Q8—182no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—91no—
290C2×C4⋊C4—181no—
291C2×C22⋊C4—181no—
292C2×C22⋊C4—181no—
293C2×C42—91no—
294C2×C42—181no—
295#103—182no—
296#102—62no—
297C23×C3—24no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—41no—
312C23×C3—41no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3D3×D411yescharacteristic
320C23×C3D3×D411yescharacteristic
321C3×Q8—34no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—62no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—42no—
330C3×D4—42no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—41no—
334C3×D4—41no—
335C3×D4—41no—
336C3×D4—41no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4C2×C4×D311yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4C22×Dic311yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3—62no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—121no—
382C2×Dic3—121no—
383C2×Dic3—121no—
384C2×Dic3—121no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394Dic6—22no—
395Dic6—22no—
396Dic6—22no—
397Dic6#21714yescomplemented
398C3×C8—62no—
399C3×C8—121no—
400C3⋊C8—22no—
401C3⋊C8—41no—
402C2×C32—82no—
403C2×C32#38611yescharacteristic
404C2×C32C4×SD1611yescharacteristic
405C2×C32#44011yescharacteristic
406C2×C32#44811yescharacteristic
407C2×C32#44911yescharacteristic
408C2×C32#46011yescharacteristic
409C2×C32#46411yescharacteristic
410C24—21no—
411C2×Q8—32no—
412C2×Q8—32no—
413C2×Q8—32no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×Q8—61no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4D3×Dic312yes—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—91no—
426C22×C4—91no—
427C22×C4—181no—
428C22×C4C2×D3211yescharacteristic
429SD16—68no—
430C2×C8—32no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—61no—
435C2×C8—61no—
436C4⋊C4—32no—
437C4⋊C4—61no—
438C4⋊C4—184no—
439C4⋊C4—181no—
440C4⋊C4—181no—
441C22⋊C4—362no—
442C22⋊C4—362no—
443C42—184no—
444C42—181no—
445C42—181no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—44no—
454C22×C3—44no—
455C22×C3—44no—
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—81no—
467C22×C3—81no—
468C22×C3—81no—
469C22×C3—81no—
470C22×C3—81no—
471C22×C3—81no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3#67⋊C411yescharacteristic
475C22×C3#88411yescharacteristic
476C22×C3#91111yescharacteristic
477C22×C3#91211yescharacteristic
478C22×C3D3×SD1611yescharacteristic
479C22×C3D3×SD1611yescharacteristic
480C22×C3#91411yescharacteristic
481C22×C3#91511yescharacteristic
482C22×C3#91511yescharacteristic
483C22×C3#91611yescharacteristic
484C22×C3D4×Dic311yescharacteristic
485C22×C3#93711yescharacteristic
486C22×C3#93711yescharacteristic
487C22×C3#93911yescharacteristic
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—64no—
493C3×C4—122no—
494C3×C4D3×C22⋊C411yescharacteristic
495C3×C4#88311yescharacteristic
496C3×C4C4×#6711yescharacteristic
497C3×C4D4×Dic311yescharacteristic
498C3×C4#93511yescharacteristic
499C3×C4#93811yescharacteristic
500C3×C4#93911yescharacteristic
501C3×C4C2×#21711yescharacteristic
502Dic3—24no—
503Dic3—42no—
504Dic3—62no—
505Dic3—62no—
506Dic3—122no—
507Dic3—122no—
508Dic3—121no—
509Dic3—121no—
510Dic3—242no—
511Dic3—241no—
512Dic3—241no—
513C32#188011yescharacteristic, complemented, Sylow
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23#381111yescharacteristic
522Q8—34no—
523Q8—62no—
524Q8—62no—
525Q8—62no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—92no—
535C2×C4—121no—
536C2×C4—121no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—361no—
543C2×C4—361no—
544C2×C4—361no—
545C2×C4C2×D3×Dic311yescharacteristic
546C2×C4#380411yescharacteristic
547C2×C4#380511yescharacteristic
548C2×C4D3×#6711yescharacteristic
549C2×C4D3×#6711yescharacteristic
550C2×C4D3×#6711yescharacteristic
551C8—62no—
552C8—121no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—84no—
561C2×C3—82no—
562C2×C3—82no—
563C2×C3#475711yescharacteristic
564C2×C3#475811yescharacteristic
565C2×C3#476211yescharacteristic
566C2×C3#476711yescharacteristic
567C2×C3#495611yescharacteristic
568C2×C3#515811yescharacteristic
569C2×C3Dic3×SD1611yescharacteristic
570C2×C3#516311yescharacteristic
571C2×C3#516411yescharacteristic
572C2×C3#516611yescharacteristic
573C2×C3#517011yescharacteristic
574C2×C3#517011yescharacteristic
575C2×C3#517211yescharacteristic
576C2×C3#522011yescharacteristic
577C22—42no—
578C22—42no—
579C22—42no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22#6393011yescharacteristic
585C22#6393111yescharacteristic
586C22#6393611yescharacteristic
587C22#6393711yescharacteristic
588C22#6397111yescharacteristic
589C22#67⋊Dic311yescharacteristic
590C22#6398311yescharacteristic
591C4—64no—
592C4—122no—
593C4—182no—
594C4—361no—
595C4—721no—
596C4D3×#21711yescharacteristic
597C4#6396911yescharacteristic
598C4#6397011yescharacteristic
599C4Dic3×#6711yescharacteristic
600C3—21no—
601C3#7021311yescharacteristic, complemented
602C3#7204811yescharacteristic, complemented
603C2—82no—
604C2#1059144311yescharacteristic
605C2#1059144411yescharacteristic
606C2#1059144511yescharacteristic
607C2#1059144611yescharacteristic
608C2#1059151811yescharacteristic
609C2#1059152011yescharacteristic
610C2#1059172111yescharacteristic
subgroupG/H
centerC23#3811
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×#63843C2semidirect
5. C2×#63566C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
18. C2×C3×#214C4semidirect
101. C2×#214Dic3semidirect
147. C2×C3⋊Dic3SD16semidirect
157. C3×Dic6C22⋊C4semidirect
397. Dic6#217semidirect
513. C32#1880semidirect
601. C3#70213semidirect
602. 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×#638432
#105929202
C2×C3×#8322
C2×#635662
#105891642
#105891562
#720483
#702133