Finite Group Databasebeta

← #11787250

Subgroups — #11787250

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic
3C2×#63637C211yesmaximal, characteristic, complemented
4C2×#63567C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71559—31nomaximal
9#68878—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×C4×D3—21no—
12C22×C3×C4×D3C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×D3×C4⋊C4—22no—
20C3×D3×C4⋊C4—22no—
21C2×Dic3⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23#63857—22no—
24#63857C414yescomplemented
25#63637—22no—
26#63567—22no—
27(C2×D3)⋊(C3⋊C8)—22no—
28C22×C3×C4⋊C4—31no—
29C2×#924—31no—
30C2×#897—31no—
31C2×D3×C4⋊C4D311yescharacteristic
32C2×#830—31no—
33C2×(C2×D3)⋊C8—31no—
34C2×#816—31no—
35C2×#810—31no—
36C2×#810—31no—
37C2×#810—31no—
38C2×#810—61no—
39C3×#340—31no—
40#4529—31no—
41#4529—31no—
42#4529D311yescharacteristic, complemented
43C23×C3×D3D411yescharacteristic
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634C2×C412yescomplemented
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—24no—
61C2×C3×C4×D3—42no—
62C2×C3×C4×D3—42no—
63C2×C3×C4×D3C2×C412yes—
64C2×C3×C4×D3D412yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2×C412yescomplemented
73C3×C4⋊Dic3D412yes—
74C3×Dic3⋊C4—24no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78Dic3⋊Dic3—24no—
79(C2×D3)⋊Dic3—24no—
80#1872—91noSylow
81C23×C3×C4—31no—
82C23×C3×C4—61no—
83C22×C4×D3—21no—
84C22×C4×D3C2×D311yescharacteristic
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—61no—
88C22×C3×C8—31no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4—62no—
93C2×C3×C4⋊C4—61no—
94C2×C3×C4⋊C4—62no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×#217—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102#924—34no—
103#924—62no—
104C2×Dic3⋊C4—21no—
105C2×Dic3⋊C4—61no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#897—34no—
111#897—62no—
112D3×C4⋊C4—22no—
113D3×C4⋊C4—22no—
114#830—62no—
115(C2×D3)⋊C8—62no—
116#816—62no—
117#810—62no—
118#810—64no—
119#810—62no—
120#810—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3—21no—
126C22×C3×D3C22⋊C412yes—
127C22×C3×D3SD1612yes—
128C22×C3×D3Q1612yes—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3—41no—
141#634—22no—
142#634—22no—
143#634—41no—
144#634—41no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3C22⋊C412yes—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158C3×C4×D3—48no—
159C3⋊(C3⋊C8)—41no—
160C3×C3⋊C8—41no—
161C2×C22⋊Q8—91no—
162C22×C4⋊C4—31no—
163C2×#103—91no—
164C2×#103—91no—
165C2×C22⋊C8—91no—
166#340—31no—
167#340—91no—
168C24×C3—31no—
169C23×D3#6711yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—31no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—41no—
177C22×C3×C4—64no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—122no—
185C22×C3×C4—122no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3#6711yescharacteristic
194C2×C4×D3—21no—
195C2×C4×D3—21no—
196C2×C4×D3—21no—
197C2×C4×D3—21no—
198C2×C4×D3—24no—
199C2×C4×D3—42no—
200C2×C4×D3—42no—
201C2×C4×D3C4×D312yes—
202C2×C4×D3D1212yes—
203C2×Dic6—32no—
204C2×Dic6—32no—
205C2×Dic6—62no—
206C2×Dic6—62no—
207C2×Dic6—62no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—121no—
219C2×Dic6—121no—
220C2×Dic6—121no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—64no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4D1212yes—
234C3×C4⋊C4#6712yes—
235#217—64no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—21no—
238C4⋊Dic3—21no—
239C4⋊Dic3—64no—
240C4⋊Dic3C4×D312yescomplemented
241C4⋊Dic3#6712yes—
242Dic3⋊C4—24no—
243Dic3⋊C4—64no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—61no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—61no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—121no—
255C2×C3⋊C8—121no—
256C22×C32C2×C22⋊C411yescharacteristic
257C22×C32#12011yescharacteristic
258C22×C32#12311yescharacteristic
259C22×C32C2×SD1611yescharacteristic
260C22×C32C2×Q1611yescharacteristic
261C22×C32AGL(1,ℤ/8)11yescharacteristic
262C22×C32#13711yescharacteristic
263C2×C3×D3—22no—
264C2×C3×D3—22no—
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—22no—
268C2×C3×D3—22no—
269C2×C3×D3#10314yescomplemented
270C32×C4—42no—
271C32×C4C4×D411yescharacteristic
272C32×C4C4×D411yescharacteristic
273C32×C4#12111yescharacteristic
274C32×C4#12111yescharacteristic
275C3⋊Dic3—42no—
276C3×Dic3—22no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C22×Q8—91no—
280C23×C4—31no—
281C23×C4—61no—
282C22×C8—31no—
283C22×C8—91no—
284C22⋊Q8—94no—
285C22⋊Q8—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—62no—
289C2×C4⋊C4—61no—
290C2×C4⋊C4—62no—
291C2×C4⋊C4—181no—
292C2×C4⋊C4D3211yescharacteristic
293C2×C22⋊C4—181no—
294#103—182no—
295#103—182no—
296C22⋊C8—182no—
297C23×C3—21no—
298C23×C3—32no—
299C23×C3—32no—
300C23×C3—32no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—61no—
304C23×C3—61no—
305C23×C3D3×D411yescharacteristic
306C23×C3C2×#6711yescharacteristic
307C22×D3—21no—
308C22×D3—21no—
309C22×D3—21no—
310C22×D3—21no—
311C22×D3(C2×D3)⋊C412yes—
312C22×D3#21412yes—
313C22×D3#21612yes—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—32no—
323C2×C3×C4—42no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—41no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—81no—
337C2×C3×C4—81no—
338C2×C3×C4—128no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4#23511yescharacteristic
348C2×C3×C4#23511yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23911yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3(C2×D3)⋊C412yes—
373C4×D3—22no—
374C4×D3—22no—
375C4×D3—22no—
376C4×D3—22no—
377C4×D3—48no—
378Dic6—64no—
379Dic6—62no—
380Dic6—62no—
381Dic6—62no—
382Dic6—62no—
383Dic6—122no—
384Dic6—122no—
385Dic6—122no—
386Dic6—121no—
387Dic6—121no—
388Dic6—121no—
389Dic6—121no—
390C3×C8—121no—
391C3⋊C8—41no—
392C3⋊C8—122no—
393C3⋊C8—121no—
394C3⋊C8—121no—
395C2×C32#38611yescharacteristic
396C2×C32C2×#10311yescharacteristic
397C2×C32#41711yescharacteristic
398C2×C32#45011yescharacteristic
399C2×C32#45111yescharacteristic
400C2×C32#48311yescharacteristic
401C2×C32#48411yescharacteristic
402C3×D3—24no—
403C24—31no—
404C2×Q8—92no—
405C2×Q8—181no—
406C2×Q8—181no—
407C2×Q8—181no—
408C2×Q8—181no—
409C2×Q8—181no—
410C22×C4—21no—
411C22×C4—31no—
412C22×C4—32no—
413C22×C4—32no—
414C22×C4—64no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—122no—
422C22×C4—122no—
423C22×C4—181no—
424C22×C4C2×D3211yescharacteristic
425C2×C8—61no—
426C2×C8—61no—
427C2×C8—61no—
428C2×C8—181no—
429C2×C8—181no—
430C2×C8—181no—
431C4⋊C4—21no—
432C4⋊C4—32no—
433C4⋊C4—32no—
434C4⋊C4—64no—
435C4⋊C4—61no—
436C4⋊C4—61no—
437C4⋊C4—184no—
438C4⋊C4#62612yes—
439C22⋊C4—184no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—34no—
448C22×C3—62no—
449C22×C3—62no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—62no—
453C22×C3—62no—
454C22×C3D3×C22⋊C411yescharacteristic
455C22×C3#88211yescharacteristic
456C22×C3#89411yescharacteristic
457C22×C3#91111yescharacteristic
458C22×C3D3×SD1611yescharacteristic
459C22×C3#91511yescharacteristic
460C22×C3D3×Q1611yescharacteristic
461C22×C3C2×(C2×D3)⋊C411yescharacteristic
462C22×C3#92911yescharacteristic
463C22×C3#93211yescharacteristic
464C22×C3C2×#21411yescharacteristic
465C22×C3#94211yescharacteristic
466C22×C3C2×#21611yescharacteristic
467C22×C3#95311yescharacteristic
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—22no—
472C2×D3—22no—
473C2×D3—22no—
474C2×D3#81014yescomplemented
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—42no—
480C3×C4—42no—
481C3×C4—62no—
482C3×C4—82no—
483C3×C4—122no—
484C3×C4—122no—
485C3×C4C4×D1211yescharacteristic
486C3×C4#88411yescharacteristic
487C3×C4#89311yescharacteristic
488C3×C4#89511yescharacteristic
489C3×C4C4×#6711yescharacteristic
490C3×C4C4×#6711yescharacteristic
491C3×C4#93011yescharacteristic
492C3×C4#93011yescharacteristic
493Dic3—22no—
494Dic3—42no—
495Dic3—42no—
496Dic3—124no—
497Dic3—122no—
498Dic3—122no—
499C32#187211yescharacteristic, complemented, Sylow
500C23—32no—
501C23—32no—
502C23—32no—
503C23—61no—
504C23—61no—
505C23—61no—
506C23—61no—
507C23D3×#6711yescharacteristic
508Q8—182no—
509Q8—182no—
510Q8—361no—
511Q8—361no—
512C2×C4—22no—
513C2×C4—32no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—128no—
525C2×C4—121no—
526C2×C4—121no—
527C2×C4—121no—
528C2×C4—121no—
529C2×C4—182no—
530C2×C4—361no—
531C2×C4—361no—
532C2×C4#379811yescharacteristic
533C2×C4#379911yescharacteristic
534C2×C4C4×D3211yescharacteristic
535C2×C4D3×D1211yescharacteristic
536C2×C4C2×#62611yescharacteristic
537C2×C4D3×#6711yescharacteristic
538C8—121no—
539C8—361no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—64no—
548C2×C3#466511yescharacteristic
549C2×C3#477111yescharacteristic
550C2×C3#477611yescharacteristic
551C2×C3D3×#10311yescharacteristic
552C2×C3#480911yescharacteristic
553C2×C3#486211yescharacteristic
554C2×C3#488411yescharacteristic
555C2×C3#496611yescharacteristic
556C2×C3C2×#81011yescharacteristic
557C2×C3#497011yescharacteristic
558C2×C3#497111yescharacteristic
559C2×C3#521311yescharacteristic
560C2×C3#521811yescharacteristic
561C2×C3#522811yescharacteristic
562D3—24no—
563C22—34no—
564C22—62no—
565C22—62no—
566C22—62no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22#6385011yescharacteristic
571C22D3×(C2×D3)⋊C411yescharacteristic
572C22D3×#21411yescharacteristic
573C22#6393211yescharacteristic
574C22D3×#21611yescharacteristic
575C22#6394611yescharacteristic
576C22#6397711yescharacteristic
577C4—42no—
578C4—62no—
579C4—122no—
580C4—122no—
581C4—362no—
582C4C4×#62611yescharacteristic
583C4#6390411yescharacteristic
584C4#6390611yescharacteristic
585C4#6390911yescharacteristic
586C3—21no—
587C3#6887811yescharacteristic, complemented
588C3#7155911yescharacteristic, complemented
589C2—64no—
590C2#1059042611yescharacteristic
591C2#1059042711yescharacteristic
592C2D3×#81011yescharacteristic
593C2#1059060711yescharacteristic
594C2#1059138211yescharacteristic
595C2#1059145911yescharacteristic
596C2#1059159511yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1872
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63637C2semidirect
4. C2×#63567C2semidirect
6. C3×#4529C2semidirect
7. #10589163C2semidirect
24. #63857C4semidirect
42. #4529D3semidirect
52. C2×#634C2×C4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
240. C4⋊Dic3C4×D3semidirect
269. C2×C3×D3#103semidirect
474. C2×D3#810semidirect
499. C32#1872semidirect
587. C3#68878semidirect
588. C3#71559semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
C2×#638572
C2×#636372
C2×#635672
C2×(C2×D3)⋊(C3⋊C8)2
C3×#45292
#105891632
#715593
#688783