Finite Group Databasebeta

← #11787249

Subgroups — #11787249

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C2×#63856C211yesmaximal, characteristic
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70268—31nomaximal
9#69930—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3724—21no—
19C2×Dic3⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21D3×C4⋊Dic3—22no—
22D3×C4⋊Dic3—22no—
23#63856—22no—
24#63856C414yescomplemented
25C3×(C2×D3)⋊C8—22no—
26C3×#816—22no—
27#63566—22no—
28C2×#946—31no—
29C22×C4⋊Dic3—31no—
30C2×#924—31no—
31C2×D3×C4⋊C4—31no—
32C2×C3×#103—31no—
33C2×C3×C22⋊C8—31no—
34C2×#835—31no—
35C2×(C2×D3)⋊C8D311yescharacteristic
36C2×#816—31no—
37C2×#816D311yescharacteristic, complemented
38#4551—31no—
39#4551—31no—
40#4551—31no—
41#4551—61no—
42#4529—31no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3C2×C412yes—
55C2×C3×C4×D3D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yescomplemented
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2×C412yescomplemented
71C4⋊(C3⋊Dic3)D412yes—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77#3724—24no—
78Dic3⋊Dic3—24no—
79(C2×D3)⋊Dic3—24no—
80#1872—91noSylow
81C22×C3×Q8—31no—
82C23×C3×C4—31no—
83C23×Dic3—61no—
84C22×C4×D3—61no—
85C22×C4×D3C2×D311yescharacteristic
86C22×Dic6C2×D311yescharacteristic
87C22×C3×C8—21no—
88C22×C3×C8—31no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91C2×C3×C4⋊C4—31no—
92C2×#217—61no—
93#946—34no—
94#946—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3—62no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3—62no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106#924—34no—
107#924—62no—
108C2×Dic3⋊C4—61no—
109C2×Dic3⋊C4—61no—
110C2×Dic3⋊C4—61no—
111C22×C3⋊C8C2×D311yescharacteristic
112D3×C4⋊C4—62no—
113D3×C4⋊C4—62no—
114C3×#103—62no—
115C3×C22⋊C8—62no—
116#835—62no—
117(C2×D3)⋊C8—22no—
118#816—22no—
119#816—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3C22⋊C412yes—
126C22×C3×D3SD1612yes—
127C22×C3×D3Q1612yes—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3C22⋊C412yes—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157D3×Dic3—48no—
158C32×C8—41no—
159C3×C3⋊C8—41no—
160C2×C22⋊Q8—91no—
161C22×C4⋊C4—91no—
162C2×#103—31no—
163C2×#103—91no—
164C2×C22⋊C8—31no—
165#340—91no—
166#340—91no—
167C24×C3—31no—
168C23×D3D1211yescharacteristic
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C22×C3×C4—21no—
176C22×C3×C4—31no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—64no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—121no—
195C22×Dic3—121no—
196C22×Dic3—122no—
197C22×Dic3—122no—
198C22×Dic3D1211yescharacteristic
199C2×C4×D3—21no—
200C2×C4×D3—21no—
201C2×C4×D3—21no—
202C2×C4×D3—21no—
203C2×C4×D3—64no—
204C2×C4×D3—122no—
205C2×C4×D3—122no—
206C2×C4×D3C4×D312yes—
207C2×C4×D3#6712yes—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6C4×D312yescomplemented
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—41no—
222C2×C3×C8—41no—
223C2×C3×C8—61no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—61no—
228#217—64no—
229(C2×D3)⋊C4—64no—
230C4⋊Dic3—21no—
231C4⋊Dic3—32no—
232C4⋊Dic3—32no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—62no—
236C4⋊Dic3—62no—
237C4⋊Dic3—64no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—121no—
243C4⋊Dic3—121no—
244C4⋊Dic3#6712yes—
245Dic3⋊C4—64no—
246Dic3⋊C4—64no—
247Dic3⋊C4—64no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C22×C32C2×C22⋊C411yescharacteristic
252C22×C32#12011yescharacteristic
253C22×C32#12311yescharacteristic
254C22×C32C2×SD1611yescharacteristic
255C22×C32C2×Q1611yescharacteristic
256C22×C32AGL(1,ℤ/8)11yescharacteristic
257C22×C32#13711yescharacteristic
258C2×C3×D3—22no—
259C2×C3×D3—22no—
260C2×C3×D3—22no—
261C2×C3×D3—22no—
262C2×C3×D3—22no—
263C2×C3×D3—22no—
264C2×C3×D3#10314yescomplemented
265C32×C4C4×D411yescharacteristic
266C32×C4C4×D411yescharacteristic
267C32×C4#12111yescharacteristic
268C32×C4#12111yescharacteristic
269C3⋊Dic3—42no—
270C3⋊Dic3—42no—
271C3×Dic3—22no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×Q8—31no—
275C23×C4—31no—
276C23×C4—181no—
277C22×C8—31no—
278C22×C8D3211yescharacteristic
279C22⋊Q8—94no—
280C22⋊Q8—182no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—182no—
285C2×C4⋊C4—182no—
286C2×C4⋊C4—181no—
287C2×C4⋊C4—181no—
288C2×C22⋊C4—181no—
289#103—62no—
290#103—182no—
291C22⋊C8—62no—
292C23×C3—21no—
293C23×C3—32no—
294C23×C3—32no—
295C23×C3—32no—
296C23×C3—61no—
297C23×C3—61no—
298C23×C3—61no—
299C23×C3—61no—
300C23×C3C2×D1211yescharacteristic
301C23×C3D3×D411yescharacteristic
302C22×D3—21no—
303C22×D3—21no—
304C22×D3—21no—
305C22×D3—21no—
306C22×D3#20412yes—
307C22×D3Dic1212yes—
308C22×D3(C2×D3)⋊C412yes—
309C3×Q8—62no—
310C3×Q8—62no—
311C3×Q8—121no—
312C3×Q8—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—32no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—121no—
331C2×C3×C4—121no—
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—128no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—241no—
368C2×Dic3—241no—
369C2×Dic3—241no—
370C2×Dic3—241no—
371C2×Dic3(C2×D3)⋊C412yes—
372C4×D3—22no—
373C4×D3—22no—
374C4×D3—22no—
375C4×D3—22no—
376C4×D3—128no—
377Dic6—22no—
378Dic6—22no—
379Dic6—41no—
380Dic6—41no—
381C3×C8—42no—
382C3×C8—41no—
383C3×C8—41no—
384C3×C8—121no—
385C3⋊C8—41no—
386C2×C32#38611yescharacteristic
387C2×C32C2×#10311yescharacteristic
388C2×C32#41711yescharacteristic
389C2×C32#45011yescharacteristic
390C2×C32#45111yescharacteristic
391C2×C32#48311yescharacteristic
392C2×C32#48411yescharacteristic
393C3×D3—24no—
394C24—31no—
395C2×Q8—32no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×Q8—61no—
401C22×C4—31no—
402C22×C4—32no—
403C22×C4—32no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—184no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—362no—
414C22×C4—362no—
415C22×C4C2×D3211yescharacteristic
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—61no—
420C2×C8—61no—
421C2×C8—61no—
422C4⋊C4—32no—
423C4⋊C4—61no—
424C4⋊C4—92no—
425C4⋊C4—92no—
426C4⋊C4—184no—
427C4⋊C4—184no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C22⋊C4—184no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—34no—
439C22×C3—62no—
440C22×C3—62no—
441C22×C3—62no—
442C22×C3—62no—
443C22×C3—62no—
444C22×C3—62no—
445C22×C3D3×C22⋊C411yescharacteristic
446C22×C3#88211yescharacteristic
447C22×C3#88311yescharacteristic
448C22×C3#88611yescharacteristic
449C22×C3C2×#20411yescharacteristic
450C22×C3C2×Dic1211yescharacteristic
451C22×C3#90811yescharacteristic
452C22×C3#90911yescharacteristic
453C22×C3D3×SD1611yescharacteristic
454C22×C3#91411yescharacteristic
455C22×C3D3×Q1611yescharacteristic
456C22×C3#91811yescharacteristic
457C22×C3C2×(C2×D3)⋊C411yescharacteristic
458C22×C3#93711yescharacteristic
459C2×D3—22no—
460C2×D3—22no—
461C2×D3—22no—
462C2×D3—22no—
463C2×D3—22no—
464C2×D3—22no—
465C2×D3#81614yescomplemented
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—62no—
471C3×C4—122no—
472C3×C4—122no—
473C3×C4#67⋊C411yescharacteristic
474C3×C4#67⋊C411yescharacteristic
475C3×C4#67⋊C411yescharacteristic
476C3×C4#88411yescharacteristic
477C3×C4C4×#6711yescharacteristic
478C3×C4#93811yescharacteristic
479C3×C4#93911yescharacteristic
480C3×C4#93911yescharacteristic
481Dic3—22no—
482Dic3—42no—
483Dic3—42no—
484Dic3—122no—
485Dic3—122no—
486Dic3—122no—
487Dic3—122no—
488Dic3—242no—
489Dic3—242no—
490C32#187211yescharacteristic, complemented, Sylow
491C23—32no—
492C23—32no—
493C23—32no—
494C23—61no—
495C23—61no—
496C23—61no—
497C23—61no—
498C23D3×D1211yescharacteristic
499Q8—62no—
500Q8—62no—
501Q8—121no—
502Q8—121no—
503C2×C4—32no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—121no—
515C2×C4—121no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—368no—
519C2×C4—361no—
520C2×C4—361no—
521C2×C4—361no—
522C2×C4—361no—
523C2×C4#379511yescharacteristic
524C2×C4C4×D3211yescharacteristic
525C2×C4#380211yescharacteristic
526C2×C4#380511yescharacteristic
527C2×C4D3×#6711yescharacteristic
528C2×C4D3×#6711yescharacteristic
529C8—41no—
530C8—121no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—64no—
539C2×C3#472111yescharacteristic
540C2×C3#472211yescharacteristic
541C2×C3#473111yescharacteristic
542C2×C3#473911yescharacteristic
543C2×C3D3×#10311yescharacteristic
544C2×C3#480311yescharacteristic
545C2×C3#480511yescharacteristic
546C2×C3#481111yescharacteristic
547C2×C3#495611yescharacteristic
548C2×C3#495811yescharacteristic
549C2×C3C2×#81611yescharacteristic
550C2×C3#513311yescharacteristic
551C2×C3#516911yescharacteristic
552C2×C3#518611yescharacteristic
553D3—24no—
554C22—34no—
555C22—62no—
556C22—62no—
557C22—62no—
558C22—62no—
559C22—62no—
560C22—62no—
561C22D3×#20411yescharacteristic
562C22#6379411yescharacteristic
563C22D3×Dic1211yescharacteristic
564C22#6380111yescharacteristic
565C22#6389111yescharacteristic
566C22D3×(C2×D3)⋊C411yescharacteristic
567C22#6392211yescharacteristic
568C4—62no—
569C4—122no—
570C4—122no—
571C4—362no—
572C4—362no—
573C4#6387911yescharacteristic
574C4#6388511yescharacteristic
575C4#6390211yescharacteristic
576C4#6397011yescharacteristic
577C3—21no—
578C3#6993011yescharacteristic, complemented
579C3#7026811yescharacteristic, complemented
580C2—64no—
581C2D3×#81611yescharacteristic
582C2#1059067111yescharacteristic
583C2#1059067511yescharacteristic
584C2#1059068211yescharacteristic
585C2#1059094211yescharacteristic
586C2#1059094911yescharacteristic
587C2#1059136311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1872
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#816C2semidirect
5. C2×#63566C2semidirect
6. #10589417C2semidirect
7. #10589164C2semidirect
24. #63856C4semidirect
37. C2×#816D3semidirect
61. C2×C3×Dic6C2×C4semidirect
70. C4⋊(C3⋊Dic3)C2×C4semidirect
213. C2×Dic6C4×D3semidirect
264. C2×C3×D3#103semidirect
465. C2×D3#816semidirect
490. C32#1872semidirect
578. C3#69930semidirect
579. C3#70268semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×#638562
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×#635662
#105894172
#105891642
#702683
#699303