Finite Group Databasebeta

← #11787589

Subgroups — #11787589

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic, complemented
4#10591318C211yesmaximal, characteristic
5C2×#63562C211yesmaximal, characteristic
6#10589164C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#72048—31nomaximal
9#71633—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×Q8×Dic3—22no—
15C3×Q8×Dic3—22no—
16C2×C3×#215—22no—
17C2×C3×#215—22no—
18C2×C3×#215C414yescomplemented
19C2×C3×C4⋊Dic3—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×(C2×D3)⋊Dic3—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63662—22no—
27#63562—22no—
28C22×C3×SD16—31no—
29C2×C3×C4×Q8—31no—
30C2×Q8×Dic3D311yescharacteristic, complemented
31C22×#215D311yescharacteristic
32C2×#835—31no—
33C2×#835—31no—
34C2×#835—61no—
35#5221—31no—
36C2×#832—31no—
37C2×#809—31no—
38#4939—31no—
39#4551—31no—
40#4550—31no—
41#4529—31no—
42#4524—31no—
43C23×C3×D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C2×C32×Q8D412yes—
49C2×C32×Q8D412yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#215—28no—
68C3×C4⋊Dic3—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3D412yes—
71C3×C4×Dic3—24no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C412yes—
77(C2×D3)⋊Dic3—42no—
78(C2×D3)⋊Dic3—42no—
79#1880—91noSylow
80C22×C3×Q8—21no—
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×D4—31no—
84C22×D12C2×D311yescharacteristic
85C2×C3×SD16—34no—
86C2×C3×SD16—62no—
87C2×C3×SD16—62no—
88C22×C3×C8—31no—
89C3×C4×Q8—62no—
90C3×C4×Q8—62no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—61no—
93C2×C3×C42—31no—
94C2×C3×C42—61no—
95C2×#217—61no—
96C2×#217—61no—
97Q8×Dic3—22no—
98Q8×Dic3—22no—
99C2×#215—22no—
100C2×#215—22no—
101C2×#215Dic314yescomplemented
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3—21no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×C4×Dic3—21no—
110C2×C4×Dic3C2×D311yescharacteristic
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114C22×C3⋊C8C2×D311yescharacteristic
115#835—64no—
116#835—62no—
117#835—62no—
118#832—62no—
119#809—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C32×Q8—22no—
129C32×Q8—22no—
130C32×Q8—22no—
131C32×Q8C22⋊C414yescomplemented
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×D12—22no—
154C3×D12—22no—
155C3×D12—41no—
156C3×D12—41no—
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—22no—
159C22×SD16—31no—
160C2×C4×Q8—31no—
161C2×#103—91no—
162C2×#102—91no—
163#390—91no—
164#340—91no—
165#336—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—21no—
169C2×C3×Q8—21no—
170C2×C3×Q8—21no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—41no—
178C2×C3×Q8—41no—
179C2×C3×Q8—41no—
180C2×C3×Q8C4×D312yes—
181C2×C3×Q8D1212yes—
182C2×C3×Q8C2×Dic312yes—
183C2×C3×Q8#6712yes—
184C2×C3×Q8#6712yes—
185C2×C3×Q8#6712yes—
186C2×C3×D4—32no—
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—41no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—121no—
205C22×Dic3#6711yescharacteristic
206C22×Dic3#6711yescharacteristic
207C2×D12—21no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12C2×Dic312yes—
213C3×SD16—68no—
214C2×C3×C8—32no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—64no—
219C3×C4⋊C4—61no—
220C3×C42—64no—
221C3×C42—61no—
222C3×C42—61no—
223#217—122no—
224#217—122no—
225#215—28no—
226(C2×D3)⋊C4—122no—
227(C2×D3)⋊C4—122no—
228C4⋊Dic3—24no—
229C4⋊Dic3—21no—
230C4⋊Dic3—62no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—121no—
236C4⋊Dic3#6712yes—
237C4×Dic3—24no—
238C4×Dic3—21no—
239C4×Dic3—21no—
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×C32C4×D411yescharacteristic
253C22×C32#12011yescharacteristic
254C22×C32#12111yescharacteristic
255C22×C32C2×SD1611yescharacteristic
256C22×C32#13511yescharacteristic
257C22×C32AGL(1,ℤ/8)11yescharacteristic
258C22×C32#13711yescharacteristic
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—81no—
263C2×C3×D3—81no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C32×C4—24no—
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12311yescharacteristic
271C3⋊Dic3—81no—
272C3×Dic3—22no—
273C3×Dic3—41no—
274C3×Dic3—42no—
275C22×Q8D3211yescharacteristic
276C22×D4—31no—
277C2×SD16—34no—
278C2×SD16—62no—
279C2×SD16—62no—
280C22×C8—31no—
281C22×C8—91no—
282C4×Q8—62no—
283C4×Q8—62no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—61no—
286C2×C4⋊C4—91no—
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289C2×C42—31no—
290C2×C42—61no—
291#103—182no—
292#102—182no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—121no—
298C23×C3—121no—
299C23×C3—121no—
300C23×C3—121no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—22no—
304C22×D3—41no—
305C22×D3—41no—
306C22×D3—41no—
307C22×D3—41no—
308C22×D3—41no—
309C22×D3—41no—
310C3×Q8—22no—
311C3×Q8—22no—
312C3×Q8—22no—
313C3×Q8—22no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—24no—
317C3×Q8—42no—
318C3×Q8—42no—
319C3×Q8—42no—
320C3×Q8(C2×D3)⋊C414yescomplemented
321C3×Q8#21714yescomplemented
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4—61no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—61no—
348C2×C3×C4—121no—
349C2×C3×C4—121no—
350C2×C3×C4C2×C4×D311yescharacteristic
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4#23511yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
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×C3×C4C2×#6711yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—22no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—122no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3—121no—
376C2×Dic3—121no—
377C2×Dic3—241no—
378C2×Dic3—241no—
379C2×Dic3#21512yescomplemented
380D12—22no—
381D12—22no—
382D12—41no—
383D12—41no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—122no—
387C3⋊C8—121no—
388C3⋊C8—121no—
389C2×C32#38611yescharacteristic
390C2×C32C4×SD1611yescharacteristic
391C2×C32#44011yescharacteristic
392C2×C32#44811yescharacteristic
393C2×C32#44911yescharacteristic
394C2×C32#46011yescharacteristic
395C2×C32#46411yescharacteristic
396C3×D3—82no—
397C24—61no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8D3×Dic312yes—
402C2×Q8#62512yes—
403C2×Q8#62612yes—
404C2×D4—32no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—61no—
409C2×D4—61no—
410C22×C4—21no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—61no—
414C22×C4—181no—
415C22×C4C2×D3211yescharacteristic
416SD16—68no—
417C2×C8—32no—
418C2×C8—61no—
419C2×C8—61no—
420C2×C8—181no—
421C2×C8—181no—
422C2×C8—181no—
423C4⋊C4—32no—
424C4⋊C4—64no—
425C4⋊C4—61no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C22⋊C4—362no—
429C22⋊C4—362no—
430C42—64no—
431C42—61no—
432C42—61no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—241no—
444C22×C3—241no—
445C22×C3—241no—
446C22×C3—241no—
447C22×C3D3×SD1611yescharacteristic
448C22×C3#91411yescharacteristic
449C22×C3#91511yescharacteristic
450C22×C3#91611yescharacteristic
451C22×C3C4×#6711yescharacteristic
452C22×C3#93011yescharacteristic
453C22×C3D4×Dic311yescharacteristic
454C22×C3#93711yescharacteristic
455C22×C3#93911yescharacteristic
456C22×C3C2×#21511yescharacteristic
457C22×C3#94211yescharacteristic
458C22×C3#94911yescharacteristic
459C22×C3#95011yescharacteristic
460C22×C3#95311yescharacteristic
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C2×D3—81no—
465C2×D3—81no—
466C2×D3—81no—
467C2×D3—81no—
468C3×C4—24no—
469C3×C4—24no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—44no—
475C3×C4—62no—
476C3×C4—121no—
477C3×C4—122no—
478C3×C4C2×(C2×D3)⋊C411yescharacteristic
479C3×C4C4×#6711yescharacteristic
480C3×C4#92911yescharacteristic
481C3×C4#93011yescharacteristic
482C3×C4D4×Dic311yescharacteristic
483C3×C4#93511yescharacteristic
484C3×C4#93911yescharacteristic
485C3×C4C2×#21711yescharacteristic
486Dic3—22no—
487Dic3—41no—
488Dic3—42no—
489Dic3—242no—
490Dic3—241no—
491Dic3—241no—
492C32#188011yescharacteristic, complemented, Sylow
493C23—62no—
494C23—121no—
495C23—121no—
496C23—121no—
497C23—121no—
498C23—121no—
499C23—121no—
500C23D3×#6711yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—22no—
504Q8(C2×D3)⋊Dic314yescomplemented
505D4—62no—
506D4—62no—
507D4—121no—
508D4—121no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—32no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—62no—
518C2×C4—61no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—361no—
522C2×C4—361no—
523C2×C4—361no—
524C2×C4C2×D3×Dic311yescharacteristic
525C2×C4#380411yescharacteristic
526C2×C4#380411yescharacteristic
527C2×C4C2×#62511yescharacteristic
528C2×C4C2×#62611yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C8—62no—
531C8—361no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—242no—
540C2×C3C4×#21511yescharacteristic
541C2×C3#502611yescharacteristic
542C2×C3#502711yescharacteristic
543C2×C3#502811yescharacteristic
544C2×C3Dic3×SD1611yescharacteristic
545C2×C3#516311yescharacteristic
546C2×C3#516411yescharacteristic
547C2×C3#516611yescharacteristic
548C2×C3#517011yescharacteristic
549C2×C3#517211yescharacteristic
550C2×C3#521311yescharacteristic
551C2×C3#522011yescharacteristic
552C2×C3#522711yescharacteristic
553C2×C3#523811yescharacteristic
554D3—82no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22—241no—
559C22—241no—
560C22—241no—
561C22—241no—
562C22D3×#21511yescharacteristic
563C22#6393911yescharacteristic
564C22#6394611yescharacteristic
565C22#6394711yescharacteristic
566C22Dic3×#6711yescharacteristic
567C22#6397611yescharacteristic
568C22#6397811yescharacteristic
569C4—24no—
570C4—62no—
571C4—121no—
572C4—122no—
573C4—721no—
574C4C2×(C2×D3)⋊Dic311yescharacteristic
575C4#6396111yescharacteristic
576C4Dic3×#6711yescharacteristic
577C4#6397811yescharacteristic
578C3—21no—
579C3#7163311yescharacteristic, complemented
580C3#7204811yescharacteristic, complemented
581C2—242no—
582C2Dic3×#21511yescharacteristic
583C2#1059156611yescharacteristic
584C2#1059158311yescharacteristic
585C2#1059158611yescharacteristic
586C2#1059160411yescharacteristic
587C2#1059161711yescharacteristic
588C2#1059171011yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
3. C2×#63662C2semidirect
6. #10589164C2semidirect
7. #10589155C2semidirect
18. C2×C3×#215C4semidirect
30. C2×Q8×Dic3D3semidirect
101. C2×#215Dic3semidirect
131. C32×Q8C22⋊C4semidirect
152. C2×C3×Dic3SD16semidirect
320. C3×Q8(C2×D3)⋊C4semidirect
321. C3×Q8#217semidirect
379. C2×Dic3#215semidirect
492. C32#1880semidirect
504. Q8(C2×D3)⋊Dic3semidirect
579. C3#71633semidirect
580. C3#72048semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C22×C3×#2152
C2×#636622
#105913182
C2×#635622
#105891642
#105891552
#720483
#716333