Finite Group Databasebeta

← C2×#10590943 #11863582

Subgroups — C2×#10590943 #11863582

Order 1152.

2093 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590943C218yesmaximal, direct product factor
9C2×#5169—31nomaximal
10C2×#4776—31nomaximal
11C23×D32—21no—
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic, complemented
16C22×#625—21no—
17C2×#3802—22no—
18C2×#3802—24no—
19C2×#3802—24no—
20C2×#3802C2214yes—
21C22×C32×C8C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
24C2×C3×#204—24no—
25C2×C3×#204C2214yescomplemented
26C2×Dic3⋊Dic3—21no—
27C2×#3722—21no—
28#63871—22no—
29#63871C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63647C2214yescomplemented
33C3×#821C2214yescomplemented
34#63562C2214yescomplemented
35C22×D3×D4—31no—
36C22×D3×D4—31no—
37C22×C3×SD16—31no—
38C2×#946—31no—
39C22×#215—31no—
40C22×#214—31no—
41C22×#204D311yescharacteristic, complemented
42C2×#897—31no—
43C2×C3×#102—31no—
44C2×#832—31no—
45#5169—38no—
46C2×#821D311yescharacteristic, complemented
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—31no—
49C2×(C2×D3)⋊C8—61no—
50C2×#809—31no—
51#4776—38no—
52C23×C3⋊D3D411yescharacteristic
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C22×D32—28no—
56C22×D32—24no—
57C22×D32—44no—
58C22×D32—44no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3D411yescharacteristic
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3D412yes—
64C2×C4×C3⋊D3C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12D414yes—
72C2×C3×D12D414yes—
73C2×C3×D12C2312yes—
74C2×C3×D12C2312yes—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6C2312yescomplemented
79C2×#625—28no—
80C2×#625—24no—
81#3802—216no—
82#3802—28no—
83#3802—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yescomplemented
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yescomplemented
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yescomplemented
90C3×#204—28no—
91Dic3⋊Dic3—24no—
92#3722—24no—
93#3715—28no—
94C2×#450—91noSylow
95C24×D3—61no—
96C24×D3—61no—
97C22×C3×Q8—31no—
98C22×C3×D4—31no—
99C22×C3×D4—31no—
100C22×#67—61no—
101C22×#67—61no—
102C2×D3×D4—34no—
103C2×D3×D4—34no—
104C2×D3×D4—62no—
105C2×D3×D4—62no—
106C2×D3×D4—64no—
107C2×D3×D4—64no—
108C2×D3×D4—64no—
109C2×D3×D4—64no—
110C22×D12C2×D311yescharacteristic
111C22×D12C2×D311yescharacteristic
112C22×C4×D3—31no—
113C22×C4×D3—31no—
114C22×C4×D3—61no—
115C22×Dic6C2×D311yescharacteristic, complemented
116C2×C3×SD16—34no—
117C2×C3×SD16—64no—
118C22×C3×C8—21no—
119C22×C3×C8C2×D311yescharacteristic, complemented
120C22×C3×C8C2×D311yescharacteristic, complemented
121C2×C3×C4⋊C4—31no—
122#946—34no—
123#946—62no—
124C2×#215—34no—
125C2×#215—64no—
126C2×#214—34no—
127C2×#214—64no—
128C2×(C2×D3)⋊C4—61no—
129C2×(C2×D3)⋊C4—61no—
130C2×C4⋊Dic3—61no—
131C2×C4⋊Dic3C2×D311yescharacteristic, complemented
132C2×Dic3⋊C4—61no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—61no—
136C2×#204—24no—
137C2×#204C2×D314yescomplemented
138#897—34no—
139#897—62no—
140C3×#102—34no—
141#832—34no—
142#821C2×D314yescomplemented
143(C2×D3)⋊C8—34no—
144(C2×D3)⋊C8—34no—
145(C2×D3)⋊C8—64no—
146#809—34no—
147C23×C32C2×D411yescharacteristic
148C22×C3⋊D3—22no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3SD1614yescomplemented
151C22×C3⋊D3C2×D412yes—
152C22×C3×D3—24no—
153C22×C3×D3—24no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—42no—
157C22×C3×D3—42no—
158C22×C3×D3—42no—
159C22×C3×D3—42no—
160C2×D32—216no—
161C2×D32—48no—
162C2×D32—432no—
163C2×D32—48no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3C2×D412yes—
170C4×C3⋊D3—24no—
171C4×C3⋊D3—22no—
172C4×C3⋊D3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C2×C3×Dic3—42no—
177C3×D12—24no—
178C3×D12—24no—
179C3×D12—22no—
180C3×D12—22no—
181C3×D12C2×D414yes—
182C3×D12C2×D414yes—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—42no—
186#625—216no—
187C32×C8—22no—
188C3⋊(C3⋊C8)—22no—
189C23×D4—91no—
190C22×SD16—31no—
191C22×SD16—91no—
192C2×C22⋊Q8—91no—
193#450—98no—
194C2×#102—31no—
195C2×#102—91no—
196C2×C22⋊C8—91no—
197C24×C3—61no—
198C24×C3—61no—
199C23×D3—21no—
200C23×D3—21no—
201C23×D3—31no—
202C23×D3—31no—
203C23×D3—61no—
204C23×D3—64no—
205C23×D3—64no—
206C23×D3—68no—
207C23×D3—68no—
208C23×D3—124no—
209C23×D3—124no—
210C23×D3—124no—
211C23×D3—124no—
212C2×C3×Q8—32no—
213C2×C3×Q8—61no—
214C2×C3×Q8—62no—
215C2×C3×Q8—62no—
216C2×C3×D4—34no—
217C2×C3×D4—34no—
218C2×C3×D4—32no—
219C2×C3×D4—32no—
220C2×C3×D4—62no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×C3×D4—62no—
224C22×C3×C4—21no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—64no—
230C2×#67—64no—
231C2×#67—68no—
232C2×#67—68no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—61no—
238D3×D4—68no—
239D3×D4—68no—
240D3×D4—616no—
241D3×D4—616no—
242D3×D4—68no—
243D3×D4—68no—
244C2×D12—22no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—22no—
248C2×D12D1214yes—
249C2×D12#6714yes—
250C2×D12C22×D312yes—
251C2×D12C22×D312yes—
252C2×C4×D3—32no—
253C2×C4×D3—32no—
254C2×C4×D3—32no—
255C2×C4×D3—32no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—62no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—122no—
263C2×C4×D3—122no—
264C2×Dic6—22no—
265C2×Dic6—22no—
266C2×Dic6—21no—
267C2×Dic6C22×D312yescomplemented
268C3×SD16—68no—
269C2×C3×C8—22no—
270C2×C3×C8—22no—
271C2×C3×C8—22no—
272C2×C3×C8—42no—
273C2×C3×C8C22×D312yescomplemented
274C2×C3×C8C22×D312yescomplemented
275C3×C4⋊C4—32no—
276C3×C4⋊C4—61no—
277#215—68no—
278#214—68no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281C4⋊Dic3—21no—
282C4⋊Dic3—64no—
283C4⋊Dic3C22×D312yescomplemented
284Dic3⋊C4—64no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—32no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8—122no—
291#204—28no—
292C22×C32#12012yes—
293C22×C32C2×SD1612yes—
294C22×C32AGL(1,ℤ/8)12yes—
295C22×C32C22×D411yescharacteristic
296C2×C3⋊D3—22no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—28no—
299C2×C3⋊D3C2×SD1614yescomplemented
300C2×C3×D3—24no—
301C2×C3×D3—24no—
302C2×C3×D3—42no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—48no—
307C2×C3×D3—48no—
308D32—432no—
309C32×C4#12012yes—
310C32×C4C22×D411yescharacteristic
311C32×C4C22×D411yescharacteristic
312C3⋊Dic3—22no—
313C3×Dic3—42no—
314C3×Dic3—42no—
315C25—181no—
316C22×Q8—31no—
317C22×D4—31no—
318C22×D4—31no—
319C22×D4—94no—
320C22×D4—182no—
321C22×D4—181no—
322C22×D4—184no—
323C22×D4—184no—
324C23×C4—91no—
325C2×SD16—34no—
326C2×SD16—64no—
327C2×SD16—94no—
328C2×SD16—184no—
329C22×C8—91no—
330C22×C8D3211yescharacteristic, complemented
331C22⋊Q8—94no—
332C22⋊Q8—182no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—181no—
335C2×C22⋊C4—181no—
336#102—34no—
337#102—94no—
338C22⋊C8—94no—
339C23×C3—21no—
340C23×C3—64no—
341C23×C3—64no—
342C23×C3—62no—
343C23×C3—62no—
344C23×C3—122no—
345C23×C3—122no—
346C23×C3—122no—
347C23×C3—122no—
348C23×C3D3×D411yescharacteristic
349C23×C3D3×D411yescharacteristic
350C22×D3—24no—
351C22×D3—24no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—34no—
355C22×D3—34no—
356C22×D3—32no—
357C22×D3—32no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—64no—
363C22×D3—62no—
364C22×D3—616no—
365C22×D3—616no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—122no—
371C22×D3—122no—
372C22×D3—128no—
373C22×D3—128no—
374C22×D3—1232no—
375C22×D3—128no—
376C22×D3—128no—
377C22×D3—1232no—
378C3×Q8—62no—
379C3×Q8—62no—
380C3×Q8—122no—
381C3×D4—34no—
382C3×D4—34no—
383C3×D4—64no—
384C3×D4—64no—
385C3×D4—62no—
386C3×D4—62no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—122no—
394C2×C3×C4—122no—
395C2×C3×C4C2×D1212yes—
396C2×C3×C4D3×D412yes—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D412yes—
400C2×C3×C4C2×#6712yes—
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—616no—
404#67—616no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—42no—
410C2×Dic3—42no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—122no—
415D12—24no—
416D12—24no—
417D12—22no—
418D12—22no—
419D12C2×D1214yes—
420D12C2×#6714yes—
421C4×D3—64no—
422C4×D3—64no—
423C4×D3—62no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—122no—
428C4×D3—122no—
429C4×D3—124no—
430Dic6—22no—
431Dic6—22no—
432Dic6—42no—
433C3×C8—22no—
434C3×C8—22no—
435C3×C8—42no—
436C3⋊C8—62no—
437C3⋊C8—62no—
438C3⋊C8—122no—
439C2×C32#45014yescomplemented
440C2×C32C2×#12011yescharacteristic
441C2×C32C22×SD1611yescharacteristic
442C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
443C3⋊D3—24no—
444C3×D3—44no—
445C3×D3—44no—
446C24—61no—
447C24—61no—
448C24—91no—
449C24—184no—
450C24—188no—
451C24—364no—
452C24—364no—
453C2×Q8—32no—
454C2×Q8—61no—
455C2×Q8—62no—
456C2×Q8—62no—
457C2×D4—32no—
458C2×D4—32no—
459C2×D4—34no—
460C2×D4—34no—
461C2×D4—62no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—62no—
465C2×D4—184no—
466C2×D4—188no—
467C2×D4—188no—
468C2×D4—1816no—
469C2×D4—188no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—91no—
473C22×C4—92no—
474C22×C4—92no—
475C22×C4—182no—
476C22×C4—182no—
477C22×C4C2×D3211yescharacteristic
478SD16—68no—
479SD16—188no—
480C2×C8—22no—
481C2×C8—92no—
482C2×C8—182no—
483C2×C8C2×D3212yescomplemented
484C4⋊C4—32no—
485C4⋊C4—61no—
486C4⋊C4—184no—
487C22⋊C4—184no—
488C22×C3—21no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—64no—
493C22×C3—64no—
494C22×C3—128no—
495C22×C3—122no—
496C22×C3—122no—
497C22×C3—122no—
498C22×C3—122no—
499C22×C3—128no—
500C22×C3#88212yes—
501C22×C3#91112yes—
502C22×C3D3×SD1612yes—
503C22×C3D3×SD1612yes—
504C22×C3#91412yes—
505C22×C3#93712yes—
506C22×C3C2×D3×D411yescharacteristic
507C22×C3C2×D3×D411yescharacteristic
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—34no—
511C2×D3—34no—
512C2×D3—48no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—42no—
516C2×D3—42no—
517C2×D3—48no—
518C2×D3—64no—
519C2×D3—68no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—68no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—128no—
528C2×D3—1232no—
529C2×D3—1232no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—22no—
533C3×C4—122no—
534C3×C4—122no—
535C3×C4#88212yes—
536C3×C4#93712yes—
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—42no—
542Dic3—42no—
543Dic3—62no—
544Dic3—62no—
545Dic3—122no—
546C32C2×#45011yescharacteristic, complemented, Sylow
547C23—62no—
548C23—62no—
549C23—64no—
550C23—64no—
551C23—92no—
552C23—94no—
553C23—122no—
554C23—122no—
555C23—122no—
556C23—122no—
557C23—1816no—
558C23—182no—
559C23—182no—
560C23—368no—
561C23—368no—
562C23—3632no—
563C23#380211yescharacteristic
564Q8—62no—
565Q8—62no—
566Q8—122no—
567D4—34no—
568D4—34no—
569D4—62no—
570D4—62no—
571D4—64no—
572D4—64no—
573D4—1816no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—92no—
577C2×C4—122no—
578C2×C4—122no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—184no—
583C2×C4D3×D1212yes—
584C2×C4#380211yescharacteristic
585C2×C4D3×#6712yes—
586C2×C4C22×D3211yescharacteristic
587C8—22no—
588C8—182no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—24no—
592C2×C3—21no—
593C2×C3—124no—
594C2×C3—124no—
595C2×C3#477614yescomplemented
596C2×C3#516914yescomplemented
597C2×C3C2×#88211yescharacteristic
598C2×C3C2×#91111yescharacteristic
599C2×C3C2×D3×SD1611yescharacteristic
600C2×C3C2×D3×SD1611yescharacteristic
601C2×C3C2×#91411yescharacteristic
602C2×C3C2×#93711yescharacteristic
603D3—44no—
604D3—44no—
605D3—64no—
606D3—64no—
607D3—124no—
608C22—64no—
609C22—64no—
610C22—94no—
611C22—122no—
612C22—122no—
613C22—122no—
614C22—122no—
615C22—128no—
616C22—128no—
617C22—182no—
618C22—188no—
619C22—182no—
620C22—3632no—
621C22#6379612yes—
622C22#6379812yes—
623C22#6392212yes—
624C22C2×#380211yescharacteristic
625C4—122no—
626C4—122no—
627C4—182no—
628C4#6392212yes—
629C4C2×D3×D1211yescharacteristic
630C4C2×D3×#6711yescharacteristic
631C3—21no—
632C3C2×#477611yescharacteristic, complemented
633C3C2×#516911yescharacteristic, complemented
634C2—124no—
635C2—124no—
636C2—184no—
637C2#1059094314yesdirect product factor
638C2C2×#6379611yescharacteristic
639C2C2×#6379811yescharacteristic
640C2C2×#6392211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3802C2
hypercenterC22×C8D32
hypocenterC32C2×#450
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. C22×C3×#204C2semidirect
3. C2×#63871C2semidirect
4. C22×#3715C2semidirect
5. C2×#63647C2semidirect
6. C2×C3×#821C2semidirect
7. C2×#63562C2semidirect
8. #10590943C2direct (N × H)
15. C22×C3×Dic6C22semidirect
21. C22×C32×C8C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
23. C2×C3×C4⋊Dic3C22semidirect
25. C2×C3×#204C22semidirect
29. #63871C22semidirect
31. C2×#3715C22semidirect
32. #63647C22semidirect
33. C3×#821C22semidirect
34. #63562C22semidirect
41. C22×#204D3semidirect
46. C2×#821D3semidirect
78. C2×C3×Dic6C23semidirect
85. C2×C32×C8C23semidirect
87. C2×C3⋊(C3⋊C8)C23semidirect
89. C3×C4⋊Dic3C23semidirect
115. C22×Dic6C2×D3semidirect
119. C22×C3×C8C2×D3semidirect
120. C22×C3×C8C2×D3semidirect
131. C2×C4⋊Dic3C2×D3semidirect
137. C2×#204C2×D3semidirect
142. #821C2×D3semidirect
150. C22×C3⋊D3SD16semidirect
267. C2×Dic6C22×D3semidirect
273. C2×C3×C8C22×D3semidirect
274. C2×C3×C8C22×D3semidirect
283. C4⋊Dic3C22×D3semidirect
299. C2×C3⋊D3C2×SD16semidirect
330. C22×C8D32semidirect
439. C2×C32#450semidirect
483. C2×C8C2×D32semidirect
546. C32C2×#450semidirect
595. C2×C3#4776semidirect
596. C2×C3#5169semidirect
632. C3C2×#4776semidirect
633. C3C2×#5169semidirect
637. C2#10590943direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×C3×#2042
C2×#638712
C22×#37152
C2×#636472
C2×C3×#8212
C2×#635622
#105909432
C2×#51693
C2×#47763