Finite Group Databasebeta

← #11784741

Subgroups — #11784741

Order 1152.

1265 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C2×#63643C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5#10591313C211yesmaximal, characteristic
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#70266—31nomaximal
9#69963—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#627—21no—
14C22×D3×Dic3—21no—
15C2×D3×Dic6—22no—
16C2×D3×Dic6—22no—
17C2×D3×Dic6—22no—
18C2×D3×Dic6—22no—
19C2×D3×Dic6—22no—
20C2×D3×Dic6C414yescomplemented
21C22×C32×C8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63643—22no—
27C3×(C2×D3)⋊C8—22no—
28C3×#816—22no—
29#63579—21no—
30#63567—22no—
31#63566—22no—
32C22×D3×Q8—31no—
33C23×Dic6—31no—
34C2×C3×#103—31no—
35C2×C3×C22⋊C8—31no—
36C2×#835—31no—
37#5212—31no—
38C2×(C2×D3)⋊C8D311yescharacteristic
39C2×#816—31no—
40C2×#816—31no—
41C2×#816—31no—
42C2×#816—31no—
43C2×#816—61no—
44C2×#816D311yescharacteristic, complemented
45#4987—31no—
46C2×#810—31no—
47C23×C3×D3D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3⋊Dic3—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634C2×C412yes—
55C2×#634D412yes—
56C2×#634D412yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3C2×C412yes—
65C2×C3×C4×D3D412yes—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6C2×C412yes—
70C2×C3×Dic6D412yes—
71C2×C3×Dic6D412yes—
72C2×#627—24no—
73C2×#627—24no—
74C2×#627—24no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—24no—
77C2×D3×Dic3—24no—
78D3×Dic6—28no—
79D3×Dic6—28no—
80D3×Dic6—28no—
81D3×Dic6—28no—
82C2×C32×C8—21no—
83C2×C32×C8—21no—
84C2×C32×C8—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8—21no—
91C2×C3×C3⋊C8—21no—
92(C2×D3)⋊Dic3—42no—
93#1787—91noSylow
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C23×Dic3—61no—
97C2×D3×Q8—34no—
98C2×D3×Q8—62no—
99C2×D3×Q8—62no—
100C2×D3×Q8—62no—
101C2×D3×Q8—62no—
102C2×D3×Q8—62no—
103C22×C4×D3—61no—
104C22×C4×D3C2×D311yescharacteristic
105C22×Dic6—31no—
106C22×Dic6—31no—
107C22×Dic6—34no—
108C22×Dic6—61no—
109C22×Dic6—62no—
110C22×Dic6—62no—
111C22×Dic6—62no—
112C22×Dic6—61no—
113C22×Dic6—61no—
114C22×Dic6—62no—
115C22×Dic6—62no—
116C22×Dic6C2×D311yescharacteristic
117C22×C3×C8—21no—
118C22×C3×C8—31no—
119C22×C3×C8C2×D311yescharacteristic
120C22×C3×C8C2×D311yescharacteristic
121C2×C3×C4⋊C4—31no—
122C2×#217—61no—
123C2×(C2×D3)⋊C4—61no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—61no—
127C2×C4⋊Dic3C2×D311yescharacteristic
128C22×C3⋊C8C2×D311yescharacteristic
129C3×#103—62no—
130C3×C22⋊C8—62no—
131#835—62no—
132C3⋊#95—61no—
133C3⋊#95—61no—
134(C2×D3)⋊C8—22no—
135#816—22no—
136#816—62no—
137#816—62no—
138#816—62no—
139#816—64no—
140#816—62no—
141#810—62no—
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—21no—
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3C22⋊C412yes—
148C22×C3×D3SD1612yes—
149C22×C3×D3Q1612yes—
150C2×C32×C4C22×C411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—41no—
160C2×C3⋊Dic3—41no—
161C2×C3⋊Dic3—41no—
162#634—22no—
163#634—22no—
164#634—22no—
165#634C22⋊C414yescomplemented
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C2×C3×Dic3—41no—
174C2×C3×Dic3C22⋊C412yes—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×C4×D3—22no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×Dic6—22no—
182C3×Dic6C22⋊C414yescomplemented
183#627—216no—
184D3×Dic3—216no—
185C32×C8—41no—
186C3×C3⋊C8—41no—
187C23×Q8—91no—
188C2×#103—31no—
189C2×#103—91no—
190C2×#103—91no—
191C2×#103—91no—
192C2×C22⋊C8—31no—
193#380—91no—
194C24×C3—31no—
195C23×D3D1211yescharacteristic
196C2×C3×Q8—32no—
197C2×C3×Q8—32no—
198C2×C3×Q8—32no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8—61no—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—61no—
207C22×C3×C4—61no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—64no—
217C22×Dic3—64no—
218C22×Dic3—64no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—121no—
224C22×Dic3—121no—
225C22×Dic3D1211yescharacteristic
226D3×Q8—68no—
227D3×Q8—68no—
228D3×Q8—68no—
229D3×Q8—68no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3C4×D312yes—
238C2×C4×D3#6712yes—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—32no—
243C2×Dic6—32no—
244C2×Dic6—32no—
245C2×Dic6—32no—
246C2×Dic6—32no—
247C2×Dic6—32no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—68no—
252C2×Dic6—68no—
253C2×Dic6—68no—
254C2×Dic6—64no—
255C2×Dic6—64no—
256C2×Dic6—64no—
257C2×Dic6—64no—
258C2×Dic6—64no—
259C2×Dic6—61no—
260C2×Dic6—61no—
261C2×Dic6—61no—
262C2×Dic6—61no—
263C2×Dic6—61no—
264C2×Dic6—61no—
265C2×Dic6—64no—
266C2×Dic6—68no—
267C2×Dic6—121no—
268C2×Dic6—121no—
269C2×Dic6—121no—
270C2×Dic6C4×D312yes—
271C2×Dic6D1212yes—
272C2×Dic6#6712yes—
273C2×C3×C8—22no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—41no—
281C2×C3×C8—41no—
282C2×C3×C8—61no—
283C2×C3×C8—61no—
284C2×C3×C8—61no—
285C3×C4⋊C4—61no—
286C3×C4⋊C4—61no—
287#217—122no—
288(C2×D3)⋊C4—122no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—62no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296C4⋊Dic3—121no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C22×C32C2×C22⋊C411yescharacteristic
301C22×C32#12011yescharacteristic
302C22×C32#12011yescharacteristic
303C22×C32C2×SD1611yescharacteristic
304C22×C32C2×Q1611yescharacteristic
305C22×C32#13711yescharacteristic
306C22×C32#13711yescharacteristic
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C2×C3×D3—22no—
311C2×C3×D3—22no—
312C2×C3×D3—22no—
313C2×C3×D3#10314yescomplemented
314C32×C4C2×C22⋊C411yescharacteristic
315C32×C4C2×C22⋊C411yescharacteristic
316C32×C4#12011yescharacteristic
317C32×C4#12011yescharacteristic
318C3⋊Dic3—24no—
319C3⋊Dic3—81no—
320C3×Dic3—24no—
321C3×Dic3—22no—
322C3×Dic3—81no—
323C22×Q8—31no—
324C22×Q8—94no—
325C22×Q8—91no—
326C22×Q8—181no—
327C22×Q8—182no—
328C22×Q8—182no—
329C22×Q8—182no—
330C22×Q8—182no—
331C22×Q8—182no—
332C23×C4—31no—
333C23×C4—181no—
334C22×C8—31no—
335C22×C8D3211yescharacteristic
336C2×C4⋊C4—31no—
337C2×C4⋊C4—91no—
338C2×C22⋊C4—181no—
339#103—62no—
340#103—182no—
341#103—182no—
342#103—182no—
343C22⋊C8—62no—
344#95—181no—
345C23×C3—21no—
346C23×C3—32no—
347C23×C3—32no—
348C23×C3—32no—
349C23×C3—61no—
350C23×C3—61no—
351C23×C3—61no—
352C23×C3—61no—
353C23×C3C2×D1211yescharacteristic
354C23×C3D3×D411yescharacteristic
355C22×D3—21no—
356C22×D3—21no—
357C22×D3—21no—
358C22×D3—21no—
359C22×D3#20412yes—
360C22×D3Dic1212yes—
361C22×D3(C2×D3)⋊C412yes—
362C3×Q8—34no—
363C3×Q8—62no—
364C3×Q8—62no—
365C3×Q8—62no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—32no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—121no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4C2×C4×D311yescharacteristic
386C2×C3×C4C2×C4×D311yescharacteristic
387C2×C3×C4C2×D1211yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D411yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—41no—
403C2×Dic3—41no—
404C2×Dic3—41no—
405C2×Dic3—616no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—121no—
417C2×Dic3—121no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—241no—
423C2×Dic3—241no—
424C2×Dic3(C2×D3)⋊C412yes—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—22no—
428C4×D3—22no—
429C4×D3—616no—
430Dic6—22no—
431Dic6—22no—
432Dic6—22no—
433Dic6—34no—
434Dic6—34no—
435Dic6—64no—
436Dic6—616no—
437Dic6—616no—
438Dic6—62no—
439Dic6—62no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6—62no—
444Dic6—122no—
445Dic6—122no—
446Dic6—122no—
447Dic6(C2×D3)⋊C414yescomplemented
448C3×C8—42no—
449C3×C8—41no—
450C3×C8—41no—
451C3×C8—121no—
452C3⋊C8—41no—
453C2×C32#37911yescharacteristic
454C2×C32C2×#10311yescharacteristic
455C2×C32#41911yescharacteristic
456C2×C32#44811yescharacteristic
457C2×C32#44811yescharacteristic
458C2×C32#45111yescharacteristic
459C2×C32#45111yescharacteristic
460C3×D3—24no—
461C24—31no—
462C2×Q8—32no—
463C2×Q8—32no—
464C2×Q8—32no—
465C2×Q8—61no—
466C2×Q8—61no—
467C2×Q8—61no—
468C2×Q8—92no—
469C2×Q8—92no—
470C2×Q8—92no—
471C2×Q8—184no—
472C2×Q8—184no—
473C2×Q8—184no—
474C2×Q8—188no—
475C2×Q8—188no—
476C2×Q8—188no—
477C2×Q8—188no—
478C2×Q8—181no—
479C2×Q8—181no—
480C2×Q8—181no—
481C22×C4—31no—
482C22×C4—32no—
483C22×C4—32no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—184no—
491C22×C4—184no—
492C22×C4—184no—
493C22×C4—181no—
494C22×C4—181no—
495C22×C4C2×D3211yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—61no—
500C2×C8—61no—
501C2×C8—61no—
502C4⋊C4—61no—
503C4⋊C4—61no—
504C4⋊C4—181no—
505C4⋊C4—181no—
506C22⋊C4—362no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—34no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—62no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3D3×C22⋊C411yescharacteristic
522C22×C3#88211yescharacteristic
523C22×C3#88211yescharacteristic
524C22×C3#88211yescharacteristic
525C22×C3C2×#20411yescharacteristic
526C22×C3C2×Dic1211yescharacteristic
527C22×C3#90911yescharacteristic
528C22×C3#90911yescharacteristic
529C22×C3D3×SD1611yescharacteristic
530C22×C3#91511yescharacteristic
531C22×C3D3×Q1611yescharacteristic
532C22×C3#91811yescharacteristic
533C22×C3C2×(C2×D3)⋊C411yescharacteristic
534C22×C3#93711yescharacteristic
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—22no—
539C2×D3—22no—
540C2×D3—22no—
541C2×D3#81614yescomplemented
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—62no—
547C3×C4—64no—
548C3×C4—241no—
549C3×C4D3×C22⋊C411yescharacteristic
550C3×C4D3×C22⋊C411yescharacteristic
551C3×C4D3×C22⋊C411yescharacteristic
552C3×C4#88211yescharacteristic
553C3×C4C2×(C2×D3)⋊C411yescharacteristic
554C3×C4#93711yescharacteristic
555C3×C4#93711yescharacteristic
556C3×C4#93711yescharacteristic
557Dic3—24no—
558Dic3—22no—
559Dic3—64no—
560Dic3—64no—
561Dic3—81no—
562Dic3—124no—
563Dic3—242no—
564Dic3—241no—
565Dic3—241no—
566C32#178711yescharacteristic, complemented, Sylow
567C23—32no—
568C23—32no—
569C23—32no—
570C23—61no—
571C23—61no—
572C23—61no—
573C23—61no—
574C23D3×D1211yescharacteristic
575Q8—34no—
576Q8—62no—
577Q8—62no—
578Q8—62no—
579Q8—94no—
580Q8—1816no—
581Q8—182no—
582Q8—182no—
583Q8—182no—
584C2×C4—32no—
585C2×C4—62no—
586C2×C4—61no—
587C2×C4—62no—
588C2×C4—61no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—121no—
595C2×C4—121no—
596C2×C4—121no—
597C2×C4—1816no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—182no—
601C2×C4—361no—
602C2×C4—361no—
603C2×C4—361no—
604C2×C4C4×D3211yescharacteristic
605C2×C4D3×D1211yescharacteristic
606C2×C4#380211yescharacteristic
607C2×C4D3×#6711yescharacteristic
608C2×C4D3×#6711yescharacteristic
609C2×C4#381111yescharacteristic
610C8—41no—
611C8—121no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—64no—
620C2×C3#473811yescharacteristic
621C2×C3#473811yescharacteristic
622C2×C3#473911yescharacteristic
623C2×C3#473911yescharacteristic
624C2×C3D3×#10311yescharacteristic
625C2×C3#480211yescharacteristic
626C2×C3#480611yescharacteristic
627C2×C3#480911yescharacteristic
628C2×C3#495511yescharacteristic
629C2×C3#495511yescharacteristic
630C2×C3C2×#81611yescharacteristic
631C2×C3#512011yescharacteristic
632C2×C3#517011yescharacteristic
633C2×C3#518611yescharacteristic
634D3—24no—
635C22—34no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—62no—
640C22—62no—
641C22—62no—
642C22D3×#20411yescharacteristic
643C22D3×Dic1211yescharacteristic
644C22#6380011yescharacteristic
645C22#6380111yescharacteristic
646C22D3×(C2×D3)⋊C411yescharacteristic
647C22#6392211yescharacteristic
648C22#6392311yescharacteristic
649C4—62no—
650C4—64no—
651C4—184no—
652C4—241no—
653C4—721no—
654C4D3×(C2×D3)⋊C411yescharacteristic
655C4#6392111yescharacteristic
656C4#6392211yescharacteristic
657C4#6398311yescharacteristic
658C3—21no—
659C3#6996311yescharacteristic, complemented
660C3#7026611yescharacteristic, complemented
661C2—64no—
662C2D3×#81611yescharacteristic
663C2#1059082211yescharacteristic
664C2#1059094811yescharacteristic
665C2#1059094911yescharacteristic
666C2#1059095111yescharacteristic
667C2#1059095211yescharacteristic
668C2#1059139911yescharacteristic
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#1787
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
2. C2×#63643C2semidirect
4. C2×C3×#816C2semidirect
6. C2×#63567C2semidirect
7. C2×#63566C2semidirect
20. C2×D3×Dic6C4semidirect
44. C2×#816D3semidirect
165. #634C22⋊C4semidirect
182. C3×Dic6C22⋊C4semidirect
313. C2×C3×D3#103semidirect
447. Dic6(C2×D3)⋊C4semidirect
541. C2×D3#816semidirect
566. C32#1787semidirect
659. C3#69963semidirect
660. C3#70266semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
#105913132
C2×#635672
C2×#635662
#702663
#699633