Finite Group Databasebeta

← #11787590

Subgroups — #11787590

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×C3×#835C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic
5C2×#63563C211yesmaximal, characteristic
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#72048—31nomaximal
9#70240—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12Q8×C3⋊Dic3—22no—
13Q8×C3⋊Dic3—22no—
14C2×C4⋊(C3⋊Dic3)—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×#215—22no—
19C2×C3×#215—22no—
20C2×C3×#215C414yescomplemented
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×(C2×D3)⋊Dic3—21no—
25C2×(C2×D3)⋊Dic3—21no—
26C3×#835—22no—
27#63563—22no—
28C22×C3×SD16—31no—
29C2×Q8×Dic3—31no—
30C2×Q8×Dic3—31no—
31C2×Q8×Dic3—61no—
32C22×#215D311yescharacteristic
33C2×C3×#103—31no—
34C2×#835D311yescharacteristic, complemented
35#5221—31no—
36C2×#832—31no—
37C2×#821—31no—
38#4988—31no—
39#4551—31no—
40#4550—31no—
41#4550—31no—
42#4529—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⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3×Dic3—21no—
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)—24no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)D412yes—
65C4×C3⋊Dic3—24no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C3×#215—28no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
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—
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—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—31no—
91C2×#217—61no—
92C2×#217—61no—
93Q8×Dic3—62no—
94Q8×Dic3—62no—
95Q8×Dic3—64no—
96Q8×Dic3—64no—
97Q8×Dic3—62no—
98Q8×Dic3—62no—
99C2×#215—22no—
100C2×#215—22no—
101C2×#215Dic314yescomplemented
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3—62no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×C4×Dic3—31no—
112C2×C4×Dic3—31no—
113C2×C4×Dic3—61no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3—62no—
117C22×C3⋊C8C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119C3×#103—62no—
120#835—22no—
121#832—62no—
122#821—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C32×Q8—22no—
132C32×Q8—22no—
133C32×Q8—22no—
134C32×Q8C22⋊C414yescomplemented
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
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
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—41no—
159C3×D12—41no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C22×SD16—31no—
163C2×C4×Q8—91no—
164C2×#103—31no—
165C2×#102—91no—
166#390—91no—
167#340—91no—
168#336—91no—
169C24×C3—61no—
170C23×D3—21no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8C4×D312yes—
184C2×C3×Q8D1212yes—
185C2×C3×Q8C2×Dic312yes—
186C2×C3×Q8#6712yes—
187C2×C3×Q8#6712yes—
188C2×C3×Q8#6712yes—
189C2×C3×D4—32no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—62no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12C2×Dic312yes—
218C3×SD16—68no—
219C2×C3×C8—32no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227#217—122no—
228#217—122no—
229#215—28no—
230(C2×D3)⋊C4—122no—
231(C2×D3)⋊C4—122no—
232C4⋊Dic3—21no—
233C4⋊Dic3—21no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—62no—
237C4⋊Dic3—68no—
238C4⋊Dic3—64no—
239C4⋊Dic3—64no—
240C4⋊Dic3—62no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4×Dic3—68no—
244C4×Dic3—64no—
245C4×Dic3—64no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248C4×Dic3—61no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8C2×Dic312yes—
258C22×C32C4×D411yescharacteristic
259C22×C32#12011yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32C2×SD1611yescharacteristic
262C22×C32#13511yescharacteristic
263C22×C32AGL(1,ℤ/8)11yescharacteristic
264C22×C32#13711yescharacteristic
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—81no—
269C2×C3×D3—81no—
270C2×C3×D3—81no—
271C2×C3×D3—81no—
272C32×C4—24no—
273C32×C4C2×C22⋊C411yescharacteristic
274C32×C4C4×D411yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12311yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—41no—
279C3⋊Dic3—42no—
280C3×Dic3—81no—
281C22×Q8D3211yescharacteristic
282C22×D4—31no—
283C2×SD16—34no—
284C2×SD16—62no—
285C2×SD16—62no—
286C22×C8—31no—
287C22×C8—31no—
288C4×Q8—182no—
289C4×Q8—182no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C22⋊C4—181no—
295C2×C42—91no—
296C2×C42—181no—
297#103—62no—
298#102—182no—
299C23×C3—21no—
300C23×C3—62no—
301C23×C3—121no—
302C23×C3—121no—
303C23×C3—121no—
304C23×C3—121no—
305C23×C3—121no—
306C23×C3—121no—
307C23×C3D3×D411yescharacteristic
308C23×C3D3×D411yescharacteristic
309C22×D3—22no—
310C22×D3—41no—
311C22×D3—41no—
312C22×D3—41no—
313C22×D3—41no—
314C22×D3—41no—
315C22×D3—41no—
316C3×Q8—24no—
317C3×Q8—24no—
318C3×Q8—24no—
319C3×Q8—22no—
320C3×Q8—22no—
321C3×Q8—22no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—24no—
326C3×Q8(C2×D3)⋊C414yescomplemented
327C3×Q8#21714yescomplemented
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—121no—
331C3×D4—121no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4—121no—
350C2×C3×C4C2×C4×D311yescharacteristic
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4#23711yescharacteristic
358C2×C3×C4C22×Dic311yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—64no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—62no—
383C2×Dic3—61no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—122no—
387C2×Dic3—122no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392D12—22no—
393D12—22no—
394D12—41no—
395D12—41no—
396C3×C8—62no—
397C3×C8—121no—
398C3⋊C8—22no—
399C3⋊C8—41no—
400C2×C32#38611yescharacteristic
401C2×C32C4×SD1611yescharacteristic
402C2×C32#44011yescharacteristic
403C2×C32#44811yescharacteristic
404C2×C32#44911yescharacteristic
405C2×C32#46011yescharacteristic
406C2×C32#46411yescharacteristic
407C3×D3—82no—
408C24—61no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8D3×Dic312yes—
413C2×Q8#62512yes—
414C2×Q8#62612yes—
415C2×D4—32no—
416C2×D4—61no—
417C2×D4—61no—
418C2×D4—61no—
419C2×D4—61no—
420C2×D4—61no—
421C22×C4—21no—
422C22×C4—61no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—181no—
426C22×C4C2×D3211yescharacteristic
427SD16—68no—
428C2×C8—32no—
429C2×C8—61no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C4⋊C4—61no—
435C4⋊C4—61no—
436C4⋊C4—92no—
437C4⋊C4—184no—
438C4⋊C4—181no—
439C22⋊C4—362no—
440C22⋊C4—362no—
441C42—184no—
442C42—181no—
443C42—181no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—122no—
452C22×C3—122no—
453C22×C3—122no—
454C22×C3—241no—
455C22×C3—241no—
456C22×C3—241no—
457C22×C3—241no—
458C22×C3#67⋊C411yescharacteristic
459C22×C3#88211yescharacteristic
460C22×C3D3×SD1611yescharacteristic
461C22×C3D3×SD1611yescharacteristic
462C22×C3#91411yescharacteristic
463C22×C3#91411yescharacteristic
464C22×C3#91511yescharacteristic
465C22×C3#91611yescharacteristic
466C22×C3#91811yescharacteristic
467C22×C3#91911yescharacteristic
468C22×C3D4×Dic311yescharacteristic
469C22×C3#93711yescharacteristic
470C22×C3#93911yescharacteristic
471C22×C3#93911yescharacteristic
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—81no—
476C2×D3—81no—
477C2×D3—81no—
478C2×D3—81no—
479C3×C4—28no—
480C3×C4—24no—
481C3×C4—24no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—241no—
487C3×C4#67⋊C411yescharacteristic
488C3×C4#88611yescharacteristic
489C3×C4C2×(C2×D3)⋊C411yescharacteristic
490C3×C4D4×Dic311yescharacteristic
491C3×C4#93511yescharacteristic
492C3×C4#93911yescharacteristic
493C3×C4#93911yescharacteristic
494C3×C4C2×#21711yescharacteristic
495Dic3—64no—
496Dic3—62no—
497Dic3—62no—
498Dic3—81no—
499Dic3—122no—
500Dic3—124no—
501Dic3—121no—
502Dic3—122no—
503Dic3—121no—
504Dic3—122no—
505C32#188011yescharacteristic, complemented, Sylow
506C23—62no—
507C23—121no—
508C23—121no—
509C23—121no—
510C23—121no—
511C23—121no—
512C23—121no—
513C23#381111yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—22no—
517Q8(C2×D3)⋊Dic314yescomplemented
518D4—62no—
519D4—62no—
520D4—121no—
521D4—121no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—92no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—182no—
534C2×C4—181no—
535C2×C4—361no—
536C2×C4—361no—
537C2×C4C2×D3×Dic311yescharacteristic
538C2×C4#380511yescharacteristic
539C2×C4#380511yescharacteristic
540C2×C4C2×#62511yescharacteristic
541C2×C4C2×#62611yescharacteristic
542C2×C4#381111yescharacteristic
543C8—62no—
544C8—121no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—242no—
553C2×C3#478811yescharacteristic
554C2×C3#480611yescharacteristic
555C2×C3#481011yescharacteristic
556C2×C3#481711yescharacteristic
557C2×C3#495811yescharacteristic
558C2×C3Dic3×SD1611yescharacteristic
559C2×C3#516311yescharacteristic
560C2×C3#516311yescharacteristic
561C2×C3#516411yescharacteristic
562C2×C3#516611yescharacteristic
563C2×C3#517011yescharacteristic
564C2×C3#517211yescharacteristic
565C2×C3#518511yescharacteristic
566C2×C3#522011yescharacteristic
567D3—82no—
568C22—122no—
569C22—122no—
570C22—122no—
571C22—241no—
572C22—241no—
573C22—241no—
574C22—241no—
575C22#6394011yescharacteristic
576C22#6394111yescharacteristic
577C22#6395011yescharacteristic
578C22#6395111yescharacteristic
579C22#67⋊Dic311yescharacteristic
580C22#6398011yescharacteristic
581C22#6398111yescharacteristic
582C4—24no—
583C4—182no—
584C4—241no—
585C4—361no—
586C4—362no—
587C4C2×(C2×D3)⋊Dic311yescharacteristic
588C4#6396211yescharacteristic
589C4#67⋊Dic311yescharacteristic
590C4#6398011yescharacteristic
591C3—21no—
592C3#7024011yescharacteristic, complemented
593C3#7204811yescharacteristic, complemented
594C2—242no—
595C2#1059157111yescharacteristic
596C2#1059157211yescharacteristic
597C2#1059159211yescharacteristic
598C2#1059159311yescharacteristic
599C2#1059161211yescharacteristic
600C2#1059162211yescharacteristic
601C2#1059171311yescharacteristic
subgroupG/H
centerC23#3811
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×Q8×C3⋊Dic3C2semidirect
3. C2×C3×#835C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
20. C2×C3×#215C4semidirect
34. C2×#835D3semidirect
101. C2×#215Dic3semidirect
134. C32×Q8C22⋊C4semidirect
152. C2×C3⋊Dic3SD16semidirect
326. C3×Q8(C2×D3)⋊C4semidirect
327. C3×Q8#217semidirect
505. C32#1880semidirect
517. Q8(C2×D3)⋊Dic3semidirect
592. C3#70240semidirect
593. C3#72048semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C22×C3×#2152
C2×C3×#8352
#105913232
C2×#635632
#105891642
#105891562
#720483
#702403