Finite Group Databasebeta

← C2×#10590617 #11863729

Subgroups — C2×#10590617 #11863729

Order 1152.

1837 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic, complemented
2C2×#64104C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic, complemented
8#10590617C218yesmaximal, direct product factor
9C2×#4810—31nomaximal
10C2×#4781—31nomaximal
11C22×C4⋊(C3⋊D3)—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626—21no—
17C22×D3×Dic3—21no—
18C2×#3796—22no—
19C2×#3796—24no—
20C2×#3796—24no—
21C2×#3796C2214yescomplemented
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752—21no—
24#64104—22no—
25#64104C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yescomplemented
32C3×#810C2214yescomplemented
33C3×#809C2214yescomplemented
34#63557C2214yescomplemented
35C22×#239—31no—
36C22×#237—31no—
37C22×#215—31no—
38C22×#213—31no—
39C22×D24—31no—
40C22×#204—31no—
41C2×#895—31no—
42C2×#895—31no—
43C2×#895—61no—
44C2×C3×#103—31no—
45C2×C3×#102—31no—
46C2×(C2×D3)⋊C8—31no—
47C2×(C2×D3)⋊C8—31no—
48C2×#810D311yescharacteristic, complemented
49C2×#809D311yescharacteristic, complemented
50#4810—38no—
51#4781—38no—
52C23×C3⋊D3—21no—
53C23×C3⋊D3D411yescharacteristic
54C23×C3×D3—21no—
55C22×C32×C4—21no—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3D411yescharacteristic
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—24no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—44no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3D412yes—
67C2×C4×C3⋊D3C2312yes—
68C22×C3×Dic3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12D414yescomplemented
72C2×C3×D12C2312yes—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6D414yescomplemented
76C2×C3×Dic6C2312yes—
77C2×#626—28no—
78C2×#626—24no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—24no—
81#3796—216no—
82#3796—28no—
83#3796—28no—
84C32×C4⋊C4—21no—
85C32×C4⋊C4C2312yes—
86#3752—24no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90C2×C3×C3⋊C8C2312yes—
91#3717—28no—
92#3714—28no—
93C2×#449—91noSylow
94C22×C3×Q8—31no—
95C22×C3×D4—31no—
96C22×#67—61no—
97C23×Dic3—61no—
98C2×#239—34no—
99C2×#239—62no—
100C2×#239—64no—
101C2×#239—64no—
102C2×#237—34no—
103C2×#237—62no—
104C2×#237—64no—
105C2×#237—64no—
106C22×D12—31no—
107C22×D12—31no—
108C22×D12—61no—
109C22×D12—61no—
110C22×D12—61no—
111C22×D12—61no—
112C22×D12—62no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—61no—
117C22×C4×D3—61no—
118C22×Dic6C2×D311yescharacteristic
119C22×C3×C8—31no—
120C22×C3×C8—31no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C2×D311yescharacteristic
124C2×#215—34no—
125C2×#215—64no—
126C2×#213—34no—
127C2×#213—64no—
128C2×(C2×D3)⋊C4—61no—
129C2×(C2×D3)⋊C4—61no—
130C2×(C2×D3)⋊C4—62no—
131C22×C3⋊C8C2×D311yescharacteristic
132C22×C3⋊C8C2×D311yescharacteristic
133C2×D24—34no—
134C2×D24—64no—
135C2×#204—34no—
136C2×#204—64no—
137#895—34no—
138#895—34no—
139#895—64no—
140#895—62no—
141#895—62no—
142#895—64no—
143C3×#103—34no—
144C3×#102—34no—
145(C2×D3)⋊C8—34no—
146(C2×D3)⋊C8—34no—
147#810C2×D314yescomplemented
148#809C2×D314yescomplemented
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—42no—
155C22×C3⋊D3—42no—
156C22×C3⋊D3—42no—
157C22×C3⋊D3C2×D412yes—
158C22×C3×D3—24no—
159C22×C3×D3—22no—
160C22×C3×D3—42no—
161C22×C3×D3—42no—
162C2×C32×C4—22no—
163C2×C32×C4—42no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3C2×D412yes—
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—48no—
173C4⋊(C3⋊D3)—42no—
174C4×C3⋊D3—24no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—22no—
177C2×C3×Dic3—24no—
178C2×C3×Dic3—22no—
179C3×D12—24no—
180C3×D12—22no—
181C3×D12C2×D414yescomplemented
182C3×Dic6—24no—
183C3×Dic6—22no—
184C3×Dic6C2×D414yescomplemented
185#626—216no—
186D3×Dic3—216no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8—22no—
189C22×#41—91no—
190C22×SD16—91no—
191C22×D8—91no—
192C2×#121—91no—
193#449—98no—
194C2×#103—31no—
195C2×#102—31no—
196C2×C22⋊C8—91no—
197C24×C3—61no—
198C23×D3—21no—
199C23×D3—31no—
200C23×D3—31no—
201C23×D3—61no—
202C23×D3—62no—
203C23×D3—61no—
204C23×D3—61no—
205C2×C3×Q8—34no—
206C2×C3×Q8—32no—
207C2×C3×Q8—62no—
208C2×C3×Q8—61no—
209C2×C3×D4—34no—
210C2×C3×D4—32no—
211C2×C3×D4—62no—
212C2×C3×D4—61no—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—61no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—64no—
221C2×#67—68no—
222C22×Dic3—21no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—61no—
226C22×Dic3—64no—
227C22×Dic3—68no—
228#239—68no—
229#239—616no—
230#239—68no—
231#237—68no—
232#237—616no—
233#237—68no—
234C2×D12—22no—
235C2×D12—21no—
236C2×D12—32no—
237C2×D12—32no—
238C2×D12—62no—
239C2×D12—64no—
240C2×D12—68no—
241C2×D12—62no—
242C2×D12—62no—
243C2×D12—62no—
244C2×D12—62no—
245C2×D12—64no—
246C2×D12—64no—
247C2×D12—68no—
248C2×D12—62no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—122no—
252C2×D12—122no—
253C2×D12—128no—
254C2×D12—124no—
255C2×D12—124no—
256C2×D12D1214yescomplemented
257C2×D12C22×D312yes—
258C2×C4×D3—32no—
259C2×C4×D3—32no—
260C2×C4×D3—32no—
261C2×C4×D3—32no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—64no—
265C2×C4×D3—68no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—122no—
271C2×C4×D3—122no—
272C2×Dic6—22no—
273C2×Dic6—21no—
274C2×Dic6D1214yescomplemented
275C2×Dic6C22×D312yes—
276C2×C3×C8—32no—
277C2×C3×C8—32no—
278C2×C3×C8—62no—
279C2×C3×C8—62no—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—22no—
284C3×C4⋊C4C22×D312yes—
285C3×C4⋊C4C22×D312yes—
286#215—68no—
287#213—68no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—64no—
290(C2×D3)⋊C4—68no—
291C2×C3⋊C8—22no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8C22×D312yes—
294C2×C3⋊C8C22×D312yes—
295D24—68no—
296#204—68no—
297C22×C32#12012yes—
298C22×C32#13512yes—
299C22×C32AGL(1,ℤ/8)12yes—
300C22×C32C22×D411yescharacteristic
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3—22no—
304C2×C3⋊D3—44no—
305C2×C3⋊D3—42no—
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—84no—
309C2×C3×D3—24no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—48no—
313C32×C4—42no—
314C32×C4#12012yes—
315C32×C4C22×D411yescharacteristic
316C32×C4C22×D411yescharacteristic
317C3⋊Dic3—22no—
318C3×Dic3—24no—
319C2×#41—94no—
320C2×#41—182no—
321C2×#41—184no—
322C2×#41—184no—
323C22×Q8—31no—
324C22×D4—31no—
325C22×D4—91no—
326C22×D4—181no—
327C22×D4—181no—
328C23×C4—91no—
329C23×C4—181no—
330C2×SD16—94no—
331C2×SD16—184no—
332C2×D8—94no—
333C2×D8—184no—
334C22×C8—31no—
335C22×C8—31no—
336#121—94no—
337#121—182no—
338C2×C4⋊C4D3211yescharacteristic
339C2×C22⋊C4—181no—
340#103—34no—
341#102—34no—
342C22⋊C8—94no—
343C23×C3—21no—
344C23×C3—64no—
345C23×C3—62no—
346C23×C3—122no—
347C23×C3—122no—
348C23×C3D3×D411yescharacteristic
349C23×C3D3×D411yescharacteristic
350C22×D3—24no—
351C22×D3—22no—
352C22×D3—32no—
353C22×D3—32no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—62no—
357C22×D3—64no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—64no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—122no—
368C22×D3—122no—
369C22×D3—124no—
370C22×D3—124no—
371C22×D3—124no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—122no—
378C3×Q8—34no—
379C3×Q8—64no—
380C3×Q8—62no—
381C3×D4—34no—
382C3×D4—64no—
383C3×D4—62no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—44no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—64no—
395C2×C3×C4—62no—
396C2×C3×C4C2×D1212yes—
397C2×C3×C4C2×D1212yes—
398C2×C3×C4D3×D412yes—
399C2×C3×C4D3×D412yes—
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—616no—
405C2×Dic3—24no—
406C2×Dic3—22no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—62no—
410C2×Dic3—616no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—122no—
414D12—24no—
415D12—22no—
416D12—616no—
417D12—62no—
418D12—62no—
419D12—62no—
420D12—62no—
421D12—122no—
422D12—122no—
423D12—124no—
424D12—1216no—
425D12—128no—
426D12—128no—
427D12—122no—
428D12—122no—
429D12C2×D1214yescomplemented
430C4×D3—616no—
431C4×D3—64no—
432C4×D3—64no—
433C4×D3—62no—
434C4×D3—62no—
435C4×D3—62no—
436C4×D3—62no—
437C4×D3—122no—
438C4×D3—122no—
439C4×D3—124no—
440Dic6—24no—
441Dic6—22no—
442Dic6C2×D1214yescomplemented
443C3×C8—62no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—22no—
447C2×C32#44914yescomplemented
448C2×C32C2×#12011yescharacteristic
449C2×C32C2×#13511yescharacteristic
450C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
451C3⋊D3—42no—
452C3⋊D3—82no—
453C3×D3—44no—
454C24—61no—
455C24—91no—
456C24—181no—
457#41—188no—
458#41—188no—
459#41—1816no—
460C2×Q8—32no—
461C2×Q8—34no—
462C2×Q8—62no—
463C2×Q8—61no—
464C2×D4—32no—
465C2×D4—34no—
466C2×D4—62no—
467C2×D4—61no—
468C2×D4—92no—
469C2×D4—184no—
470C2×D4—184no—
471C2×D4—188no—
472C2×D4—182no—
473C2×D4—182no—
474C2×D4—181no—
475C2×D4—364no—
476C22×C4—21no—
477C22×C4—61no—
478C22×C4—91no—
479C22×C4—92no—
480C22×C4—92no—
481C22×C4—184no—
482C22×C4—188no—
483C22×C4—182no—
484C22×C4—182no—
485C22×C4C2×D3211yescharacteristic
486SD16—188no—
487D8—188no—
488C2×C8—32no—
489C2×C8—32no—
490C2×C8—62no—
491C2×C8—62no—
492C4⋊C4—21no—
493C4⋊C4C2×D3212yes—
494C22⋊C4—184no—
495C22×C3—21no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—64no—
500C22×C3—122no—
501C22×C3—122no—
502C22×C3—128no—
503C22×C3#88212yes—
504C22×C3#88212yes—
505C22×C3#91112yes—
506C22×C3#91412yes—
507C22×C3#91612yes—
508C22×C3#91912yes—
509C22×C3C2×D3×D411yescharacteristic
510C22×C3C2×D3×D411yescharacteristic
511C2×D3—24no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—48no—
515C2×D3—64no—
516C2×D3—62no—
517C2×D3—62no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—128no—
525C2×D3—124no—
526C2×D3—124no—
527C2×D3—124no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—248no—
537C2×D3—244no—
538C2×D3—244no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—22no—
542C3×C4—44no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—64no—
546C3×C4#88212yes—
547C3×C4#88212yes—
548C3×C4C22×D1211yescharacteristic
549C3×C4C22×D1211yescharacteristic
550C3×C4C2×D3×D411yescharacteristic
551C3×C4C2×D3×D411yescharacteristic
552Dic3—24no—
553Dic3—62no—
554Dic3—62no—
555Dic3—122no—
556C32C2×#44911yescharacteristic, complemented, Sylow
557C23—62no—
558C23—64no—
559C23—92no—
560C23—122no—
561C23—122no—
562C23—182no—
563C23—182no—
564C23—182no—
565C23—182no—
566C23—362no—
567C23—362no—
568C23—362no—
569C23#381111yescharacteristic
570Q8—34no—
571Q8—62no—
572Q8—64no—
573D4—34no—
574D4—62no—
575D4—64no—
576D4—1816no—
577D4—182no—
578D4—182no—
579D4—368no—
580D4—362no—
581C2×C4—22no—
582C2×C4—42no—
583C2×C4—62no—
584C2×C4—64no—
585C2×C4—92no—
586C2×C4—1816no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4—184no—
591C2×C4D3×D1212yes—
592C2×C4D3×D1212yes—
593C2×C4#381111yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—62no—
596C8—62no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—24no—
600C2×C3—21no—
601C2×C3—124no—
602C2×C3#478114yescomplemented
603C2×C3#481014yescomplemented
604C2×C3C2×#88211yescharacteristic
605C2×C3C2×#88211yescharacteristic
606C2×C3C2×#91111yescharacteristic
607C2×C3C2×#91411yescharacteristic
608C2×C3C2×#91611yescharacteristic
609C2×C3C2×#91911yescharacteristic
610D3—44no—
611D3—124no—
612D3—122no—
613D3—122no—
614D3—244no—
615D3—242no—
616D3—242no—
617C22—64no—
618C22—122no—
619C22—122no—
620C22—128no—
621C22—182no—
622C22—182no—
623C22—182no—
624C22—364no—
625C22—362no—
626C22—362no—
627C22—362no—
628C22—724no—
629C22#6392312yes—
630C22#6393712yes—
631C22#6395012yes—
632C22C2×#381111yescharacteristic
633C4—42no—
634C4—64no—
635C4—182no—
636C4#6392312yes—
637C4C2×D3×D1211yescharacteristic
638C4C2×D3×D1211yescharacteristic
639C3—21no—
640C3C2×#478111yescharacteristic, complemented
641C3C2×#481011yescharacteristic, complemented
642C2—124no—
643C2—362no—
644C2—722no—
645C2#1059061714yesdirect product factor
646C2C2×#6392311yescharacteristic
647C2C2×#6393711yescharacteristic
648C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#449
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
1. C22×#3796C2semidirect
2. C2×#64104C2semidirect
3. C22×#3717C2semidirect
4. C22×#3714C2semidirect
5. C2×C3×#810C2semidirect
6. C2×C3×#809C2semidirect
7. C2×#63557C2semidirect
8. #10590617C2direct (N × H)
21. C2×#3796C22semidirect
25. #64104C22semidirect
29. C2×#3717C22semidirect
31. C2×#3714C22semidirect
32. C3×#810C22semidirect
33. C3×#809C22semidirect
34. #63557C22semidirect
48. C2×#810D3semidirect
49. C2×#809D3semidirect
71. C2×C3×D12D4semidirect
75. C2×C3×Dic6D4semidirect
147. #810C2×D3semidirect
148. #809C2×D3semidirect
181. C3×D12C2×D4semidirect
184. C3×Dic6C2×D4semidirect
256. C2×D12D12semidirect
274. C2×Dic6D12semidirect
429. D12C2×D12semidirect
442. Dic6C2×D12semidirect
447. C2×C32#449semidirect
556. C32C2×#449semidirect
602. C2×C3#4781semidirect
603. C2×C3#4810semidirect
640. C3C2×#4781semidirect
641. C3C2×#4810semidirect
645. C2#10590617direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×#641042
C22×#37172
C22×#37142
C2×C3×#8102
C2×C3×#8092
C2×#635572
#105906172
C2×#48103
C2×#47813