Finite Group Databasebeta

← C2×#10591520 #11863717

Subgroups — C2×#10591520 #11863717

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×#64147C211yesmaximal, characteristic, complemented
3C22×C3×#214C211yesmaximal, characteristic, complemented
4C22×C3×#213C211yesmaximal, characteristic, complemented
5#10591520C218yesmaximal, direct product factor
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic, complemented
9C2×#5172—31nomaximal
10C2×#5158—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#638—21no—
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×#3757—21no—
23#64147—22no—
24#64147C2214yescomplemented
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C3×#214—24no—
27C2×C3×#214C2214yescomplemented
28C2×C3×#213—24no—
29C2×C3×#213C2214yescomplemented
30C22×C3×C3⋊C8C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32#63566C2214yescomplemented
33#63563C2214yescomplemented
34#63557C2214yescomplemented
35C22×#239—31no—
36C22×#237—31no—
37C22×C3×SD16—31no—
38C22×C3×D8—31no—
39C2×#938—31no—
40C2×#938—31no—
41C2×#938—61no—
42C22×#214D311yescharacteristic, complemented
43C22×#213D311yescharacteristic, complemented
44C2×#835—31no—
45C2×#832—31no—
46#5172—38no—
47#5158—38no—
48C2×#821—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×(C2×D3)⋊C8—31no—
51C2×#816—31no—
52C24×C32—21no—
53C23×C3⋊D3D411yescharacteristic
54C23×C3×D3—21no—
55C2×C32×D4—22no—
56C2×C32×D4—22no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×#638—24no—
61C2×#638—44no—
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3D411yescharacteristic
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—
84#3757—24no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C3×#214—28no—
88C3×#213—28no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C2×#449—91noSylow
94C22×C3×Q8—31no—
95C22×C3×D4—21no—
96C22×C3×D4—31no—
97C22×C3×D4C2×D311yescharacteristic
98C22×C3×D4C2×D311yescharacteristic
99C22×#67—61no—
100C22×#67—61no—
101C22×#67—61no—
102C22×#67—62no—
103C23×Dic3—61no—
104C2×#239—34no—
105C2×#239—62no—
106C2×#239—64no—
107C2×#239—64no—
108C2×#237—34no—
109C2×#237—62no—
110C2×#237—64no—
111C2×#237—64no—
112C22×D12—61no—
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—31no—
115C22×C4×D3—31no—
116C22×C4×D3—61no—
117C22×C4×D3—61no—
118C22×Dic6C2×D311yescharacteristic
119C2×C3×SD16—34no—
120C2×C3×SD16—64no—
121C2×C3×D8—34no—
122C2×C3×D8—64no—
123C22×C3×C8—31no—
124C22×C3×C8—31no—
125C2×#217—61no—
126C2×#217—61no—
127C2×#217—62no—
128#938—34no—
129#938—34no—
130#938—64no—
131#938—62no—
132#938—62no—
133#938—64no—
134C2×#214—24no—
135C2×#214C2×D314yescomplemented
136C2×#213—24no—
137C2×#213C2×D314yescomplemented
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—61no—
141C22×C3⋊C8C2×D311yescharacteristic
142C22×C3⋊C8C2×D311yescharacteristic
143#835—34no—
144#832—34no—
145#821—34no—
146(C2×D3)⋊C8—34no—
147(C2×D3)⋊C8—34no—
148#816—34no—
149C23×C32—22no—
150C23×C32—42no—
151C23×C32—42no—
152C23×C32—42no—
153C23×C32C2×D411yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3C2×D412yes—
158C22×C3×D3—24no—
159C22×C3×D3—22no—
160C22×C3×D3—42no—
161C22×C3×D3—42no—
162C32×D4—22no—
163C32×D4—22no—
164C32×D4—42no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2411yescharacteristic
169#638—48no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—42no—
173C2×C3⋊Dic3C2×D412yes—
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—31no—
191C22×D8—31no—
192C2×#121—91no—
193#449—98no—
194C2×#103—91no—
195C2×#102—91no—
196C2×C22⋊C8—91no—
197C24×C3—22no—
198C24×C3—21no—
199C24×C3—21no—
200C24×C3—61no—
201C23×D3—21no—
202C23×D3—31no—
203C23×D3—31no—
204C23×D3—61no—
205C2×C3×Q8—34no—
206C2×C3×Q8—32no—
207C2×C3×Q8—61no—
208C2×C3×Q8—62no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—34no—
218C2×C3×D4—32no—
219C2×C3×D4—42no—
220C2×C3×D4—42no—
221C2×C3×D4—61no—
222C2×C3×D4—62no—
223C2×C3×D4C22×D312yes—
224C2×C3×D4C22×D312yes—
225C22×C3×C4—21no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—64no—
230C2×#67—68no—
231C2×#67—64no—
232C2×#67—64no—
233C2×#67—68no—
234C2×#67—128no—
235C2×#67—124no—
236C2×#67—124no—
237C22×Dic3—21no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—61no—
241C22×Dic3—64no—
242C22×Dic3—68no—
243C22×Dic3—62no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246#239—68no—
247#239—616no—
248#239—68no—
249#237—68no—
250#237—616no—
251#237—68no—
252C2×D12—22no—
253C2×D12—21no—
254C2×D12—64no—
255C2×D12—68no—
256C2×D12#6714yescomplemented
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×Dic6#6714yescomplemented
275C2×Dic6C22×D312yes—
276C3×SD16—68no—
277C3×D8—68no—
278C2×C3×C8—32no—
279C2×C3×C8—32no—
280C2×C3×C8—62no—
281C2×C3×C8—62no—
282#217—64no—
283#217—64no—
284#217—68no—
285#214—28no—
286#213—28no—
287C4⋊Dic3—32no—
288C4⋊Dic3—32no—
289C4⋊Dic3—62no—
290C4⋊Dic3—62no—
291C4⋊Dic3—61no—
292C4⋊Dic3—61no—
293C2×C3⋊C8—22no—
294C2×C3⋊C8—22no—
295C2×C3⋊C8C22×D312yes—
296C2×C3⋊C8C22×D312yes—
297C22×C32—42no—
298C22×C32—42no—
299C22×C32—42no—
300C22×C32—84no—
301C22×C32#12012yes—
302C22×C32#13512yes—
303C22×C32AGL(1,ℤ/8)12yes—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—22no—
306C2×C3⋊D3—22no—
307C2×C3⋊D3—22no—
308C2×C3⋊D3—44no—
309C2×C3×D3—24no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—48no—
313C32×C4#12012yes—
314C32×C4C22×D411yescharacteristic
315C32×C4C22×D411yescharacteristic
316C3⋊Dic3—22no—
317C3⋊Dic3—42no—
318C3×Dic3—24no—
319C2×#41—94no—
320C2×#41—182no—
321C2×#41—184no—
322C2×#41—184no—
323C22×Q8—31no—
324C22×D4—31no—
325C22×D4—181no—
326C22×D4—181no—
327C22×D4D3211yescharacteristic
328C23×C4—91no—
329C23×C4—181no—
330C2×SD16—34no—
331C2×SD16—64no—
332C2×D8—34no—
333C2×D8—64no—
334C22×C8—31no—
335C22×C8—31no—
336#121—94no—
337#121—182no—
338C2×C4⋊C4—91no—
339C2×C22⋊C4—181no—
340#103—94no—
341#102—94no—
342C22⋊C8—94no—
343C23×C3—24no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—21no—
347C23×C3—44no—
348C23×C3—44no—
349C23×C3—44no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—64no—
357C23×C3—62no—
358C23×C3—122no—
359C23×C3—122no—
360C23×C3D3×D411yescharacteristic
361C23×C3D3×D411yescharacteristic
362C22×D3—24no—
363C22×D3—22no—
364C22×D3—32no—
365C22×D3—32no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—62no—
369C22×D3—64no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—122no—
377C22×D3—122no—
378C3×Q8—34no—
379C3×Q8—64no—
380C3×Q8—62no—
381C3×D4—22no—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—34no—
386C3×D4—42no—
387C3×D4—42no—
388C3×D4—44no—
389C3×D4—42no—
390C3×D4—42no—
391C3×D4—64no—
392C3×D4—62no—
393C2×C3×C4—21no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—64no—
398C2×C3×C4—62no—
399C2×C3×C4D3×D412yes—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D411yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4C2×#6712yes—
404C2×C3×C4C2×#6712yes—
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—616no—
408#67—1216no—
409#67—128no—
410#67—128no—
411C2×Dic3—24no—
412C2×Dic3—22no—
413C2×Dic3—32no—
414C2×Dic3—32no—
415C2×Dic3—62no—
416C2×Dic3—616no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—64no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—122no—
423C2×Dic3—124no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426D12—24no—
427D12—22no—
428D12—616no—
429D12C2×#6714yescomplemented
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×#6714yescomplemented
443C3×C8—62no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—22no—
447C2×C32—82no—
448C2×C32#44914yescomplemented
449C2×C32C2×#12011yescharacteristic
450C2×C32C2×#13511yescharacteristic
451C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
452C3⋊D3—42no—
453C3×D3—44no—
454C24—21no—
455C24—61no—
456C24—91no—
457#41—188no—
458#41—188no—
459#41—1816no—
460C2×Q8—32no—
461C2×Q8—34no—
462C2×Q8—62no—
463C2×Q8—61no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—21no—
467C2×D4—32no—
468C2×D4—34no—
469C2×D4—62no—
470C2×D4—61no—
471C2×D4—184no—
472C2×D4—188no—
473C2×D4—184no—
474C2×D4—364no—
475C2×D4C2×D3212yes—
476C22×C4—61no—
477C22×C4—91no—
478C22×C4—92no—
479C22×C4—92no—
480C22×C4—184no—
481C22×C4—188no—
482C22×C4—182no—
483C22×C4—182no—
484C22×C4—181no—
485C22×C4C2×D3211yescharacteristic
486SD16—68no—
487D8—68no—
488C2×C8—32no—
489C2×C8—32no—
490C2×C8—62no—
491C2×C8—62no—
492C4⋊C4—92no—
493C4⋊C4—181no—
494C22⋊C4—184no—
495C22×C3—21no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—44no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—64no—
509C22×C3—88no—
510C22×C3—84no—
511C22×C3—84no—
512C22×C3—128no—
513C22×C3—122no—
514C22×C3—122no—
515C22×C3#91112yes—
516C22×C3#91212yes—
517C22×C3#91412yes—
518C22×C3#91612yes—
519C22×C3#93712yes—
520C22×C3#93712yes—
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C2×D3×D411yescharacteristic
523C2×D3—24no—
524C2×D3—48no—
525C2×D3—42no—
526C2×D3—42no—
527C2×D3—64no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—128no—
537C2×D3—124no—
538C2×D3—124no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—22no—
542C3×C4—64no—
543C3×C4#93712yes—
544C3×C4#93712yes—
545C3×C4C2×D3×D411yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547C3×C4C22×#6711yescharacteristic
548C3×C4C22×#6711yescharacteristic
549Dic3—24no—
550Dic3—62no—
551Dic3—62no—
552Dic3—122no—
553Dic3—124no—
554Dic3—122no—
555Dic3—122no—
556C32C2×#44911yescharacteristic, complemented, Sylow
557C23—22no—
558C23—42no—
559C23—42no—
560C23—42no—
561C23—62no—
562C23—64no—
563C23—92no—
564C23—122no—
565C23—122no—
566C23—182no—
567C23—182no—
568C23—182no—
569C23#381111yescharacteristic
570Q8—34no—
571Q8—62no—
572Q8—64no—
573D4—22no—
574D4—22no—
575D4—34no—
576D4—42no—
577D4—62no—
578D4—64no—
579D4—1816no—
580D4—368no—
581C2×C4—62no—
582C2×C4—64no—
583C2×C4—92no—
584C2×C4—1816no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—184no—
589C2×C4—182no—
590C2×C4—362no—
591C2×C4D3×#6712yes—
592C2×C4D3×#6712yes—
593C2×C4#381111yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—62no—
596C8—62no—
597C2×C3—24no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—84no—
602C2×C3—82no—
603C2×C3—82no—
604C2×C3—124no—
605C2×C3#515814yescomplemented
606C2×C3#517214yescomplemented
607C2×C3C2×#91111yescharacteristic
608C2×C3C2×#91211yescharacteristic
609C2×C3C2×#91411yescharacteristic
610C2×C3C2×#91611yescharacteristic
611C2×C3C2×#93711yescharacteristic
612C2×C3C2×#93711yescharacteristic
613D3—44no—
614D3—124no—
615D3—122no—
616D3—122no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—64no—
621C22—84no—
622C22—128no—
623C22—122no—
624C22—122no—
625C22—182no—
626C22—182no—
627C22—182no—
628C22—364no—
629C22#6393612yes—
630C22#6393712yes—
631C22#6398312yes—
632C22C2×#381111yescharacteristic
633C4—64no—
634C4—182no—
635C4—362no—
636C4#6398312yes—
637C4C2×D3×#6711yescharacteristic
638C4C2×D3×#6711yescharacteristic
639C3—21no—
640C3C2×#515811yescharacteristic, complemented
641C3C2×#517211yescharacteristic, complemented
642C2—82no—
643C2—124no—
644C2—362no—
645C2#1059152014yesdirect product factor
646C2C2×#6393611yescharacteristic
647C2C2×#6393711yescharacteristic
648C2C2×#6398311yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3796C2semidirect
2. C2×#64147C2semidirect
3. C22×C3×#214C2semidirect
4. C22×C3×#213C2semidirect
5. #10591520C2direct (N × H)
6. C2×#63566C2semidirect
7. C2×#63563C2semidirect
8. C2×#63557C2semidirect
21. C2×#3796C22semidirect
24. #64147C22semidirect
27. C2×C3×#214C22semidirect
29. C2×C3×#213C22semidirect
32. #63566C22semidirect
33. #63563C22semidirect
34. #63557C22semidirect
42. C22×#214D3semidirect
43. C22×#213D3semidirect
71. C2×C3×D12D4semidirect
75. C2×C3×Dic6D4semidirect
135. C2×#214C2×D3semidirect
137. C2×#213C2×D3semidirect
181. C3×D12C2×D4semidirect
184. C3×Dic6C2×D4semidirect
256. C2×D12#67semidirect
274. C2×Dic6#67semidirect
429. D12C2×#67semidirect
442. Dic6C2×#67semidirect
448. C2×C32#449semidirect
556. C32C2×#449semidirect
605. C2×C3#5158semidirect
606. C2×C3#5172semidirect
640. C3C2×#5158semidirect
641. C3C2×#5172semidirect
645. C2#10591520direct (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×#641472
C22×C3×#2142
C22×C3×#2132
#105915202
C2×#635662
C2×#635632
C2×#635572
C2×#51723
C2×#51583