Finite Group Databasebeta

← C2×#10590962 #11863727

Subgroups — C2×#10590962 #11863727

Order 1152.

1705 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic, complemented
2C22×C3×D24C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590962C218yesmaximal, direct product factor
9C2×#5158—31nomaximal
10C2×#4734—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#625—21no—
16C22×#625—21no—
17C22×D3×Dic3—21no—
18C2×#3795—24no—
19C2×#3795—24no—
20C2×#3795—22no—
21C2×#3795C2214yescomplemented
22C22×C32×C8C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×D24—24no—
26C2×C3×D24C2214yescomplemented
27C2×(C2×D3)⋊Dic3—21no—
28#63908—22no—
29#63908C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32#63643C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63563C2214yescomplemented
35C22×#237—31no—
36C22×#235—31no—
37C22×C3×D8—31no—
38C2×#938—31no—
39C22×#214—31no—
40C2×#930—31no—
41C22×D24D311yescharacteristic, complemented
42C22×#204—31no—
43C2×C3×C22⋊C8—31no—
44C2×#832—31no—
45#5158—38no—
46C2×#821—31no—
47C2×(C2×D3)⋊C8D311yescharacteristic, complemented
48C2×#816—31no—
49C2×#816—31no—
50C2×#816—61no—
51#4734—38no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3—21no—
58C2×#634—21no—
59C2×#634—22no—
60C2×#634D414yescomplemented
61C2×#634C2312yes—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12D414yescomplemented
69C2×C3×D12C2312yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D412yes—
74C2×C3×C4×D3C2312yes—
75C2×#625—28no—
76C2×#625—24no—
77C2×#625—24no—
78C2×#625—44no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—24no—
81#3795—216no—
82#3795—28no—
83#3795—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yes—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90C3×D24—28no—
91(C2×D3)⋊Dic3—24no—
92#3716—28no—
93C2×#449—91noSylow
94C22×C3×D4—31no—
95C22×C3×D4—31no—
96C23×C3×C4—31no—
97C22×#67—61no—
98C22×#67—61no—
99C22×#67—61no—
100C22×#67—61no—
101C23×Dic3—61no—
102C2×#237—34no—
103C2×#237—64no—
104C2×#237—64no—
105C2×#237—62no—
106C2×#235—34no—
107C2×#235—64no—
108C2×#235—62no—
109C2×#235—64no—
110C22×D12C2×D311yescharacteristic
111C22×D12C2×D311yescharacteristic
112C22×C4×D3—61no—
113C22×C4×D3C2×D311yescharacteristic
114C22×Dic6—31no—
115C22×Dic6—31no—
116C22×Dic6—61no—
117C2×C3×D8—34no—
118C2×C3×D8—64no—
119C22×C3×C8—21no—
120C22×C3×C8—31no—
121C22×C3×C8C2×D311yescharacteristic
122C22×C3×C8C2×D311yescharacteristic
123C2×#217—61no—
124#938—34no—
125#938—62no—
126C2×#214—34no—
127C2×#214—64no—
128#930—34no—
129#930—62no—
130C2×(C2×D3)⋊C4—61no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—61no—
134C22×C3⋊C8C2×D311yescharacteristic
135C2×D24—24no—
136C2×D24C2×D314yescomplemented
137C2×#204—34no—
138C2×#204—64no—
139C3×C22⋊C8—34no—
140#832—34no—
141#821—34no—
142(C2×D3)⋊C8C2×D314yescomplemented
143#816—34no—
144#816—34no—
145#816—64no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—42no—
154C22×C3×D3—42no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C22×C3×D3—42no—
158C22×C3×D3C2×D412yes—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2411yescharacteristic
163C2×C3⋊Dic3—24no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—42no—
167#634—24no—
168#634—22no—
169#634C2×D414yescomplemented
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D412yes—
172C3×D12—24no—
173C3×D12—22no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—42no—
177C3×D12C2×D414yescomplemented
178C3×C4×D3—24no—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181#625—216no—
182#625—48no—
183D3×Dic3—216no—
184C32×C8—22no—
185C3×C3⋊C8—22no—
186C22×#41—91no—
187C22×SD16—91no—
188C22×D8—31no—
189C2×#121—91no—
190#449—98no—
191C2×#103—91no—
192C2×#102—91no—
193C2×C22⋊C8—31no—
194C24×C3—31no—
195C24×C3—61no—
196C24×C3—61no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3D1211yescharacteristic
200C2×C3×D4—34no—
201C2×C3×D4—32no—
202C2×C3×D4—32no—
203C2×C3×D4—61no—
204C2×C3×D4—61no—
205C2×C3×D4—62no—
206C2×C3×D4—62no—
207C2×C3×D4—62no—
208C22×C3×C4—21no—
209C22×C3×C4—31no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4—62no—
213C22×C3×C4—62no—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C2×#67—64no—
217C2×#67—68no—
218C2×#67—68no—
219C2×#67—64no—
220C2×#67—64no—
221C2×#67—64no—
222C2×#67—124no—
223C2×#67—124no—
224C22×Dic3—68no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—64no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—121no—
231C22×Dic3—121no—
232C22×Dic3D1211yescharacteristic
233#237—68no—
234#237—68no—
235#237—616no—
236#235—68no—
237#235—616no—
238#235—68no—
239C2×D12—21no—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—21no—
244C2×D12#6714yescomplemented
245C2×D12C22×D312yes—
246C2×D12C22×D312yes—
247C2×C4×D3—22no—
248C2×C4×D3—22no—
249C2×C4×D3—64no—
250C2×C4×D3—68no—
251C2×C4×D3D1212yes—
252C2×C4×D3C22×D312yes—
253C2×Dic6—34no—
254C2×Dic6—34no—
255C2×Dic6—32no—
256C2×Dic6—32no—
257C2×Dic6—62no—
258C2×Dic6—64no—
259C2×Dic6—61no—
260C2×Dic6—61no—
261C2×Dic6—62no—
262C2×Dic6—62no—
263C2×Dic6—121no—
264C2×Dic6—122no—
265C3×D8—68no—
266C2×C3×C8—22no—
267C2×C3×C8—22no—
268C2×C3×C8—22no—
269C2×C3×C8—32no—
270C2×C3×C8—42no—
271C2×C3×C8—62no—
272C2×C3×C8C22×D312yes—
273C2×C3×C8C22×D312yes—
274#217—64no—
275#214—68no—
276(C2×D3)⋊C4—64no—
277C4⋊Dic3—32no—
278C4⋊Dic3—32no—
279C4⋊Dic3—62no—
280C4⋊Dic3—61no—
281C4⋊Dic3—61no—
282C4⋊Dic3—121no—
283C2×C3⋊C8—22no—
284C2×C3⋊C8C22×D312yes—
285D24—28no—
286#204—68no—
287C22×C32#12012yes—
288C22×C32#13512yes—
289C22×C32AGL(1,ℤ/8)12yes—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—24no—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—42no—
296C2×C3×D3—42no—
297C2×C3×D3—44no—
298C2×C3×D3—48no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C2×C3×D3—84no—
303C32×C4#12012yes—
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3⋊Dic3—24no—
307C3⋊Dic3—42no—
308C3×Dic3—22no—
309C2×#41—94no—
310C2×#41—182no—
311C2×#41—184no—
312C2×#41—184no—
313C22×Q8—91no—
314C22×D4—31no—
315C22×D4—31no—
316C22×D4—181no—
317C22×D4—181no—
318C23×C4—31no—
319C23×C4—181no—
320C2×SD16—94no—
321C2×SD16—184no—
322C2×D8—34no—
323C2×D8—64no—
324C22×C8—31no—
325C22×C8D3211yescharacteristic
326#121—94no—
327#121—182no—
328C2×C4⋊C4—91no—
329C2×C22⋊C4—181no—
330#103—94no—
331#102—94no—
332C22⋊C8—34no—
333C23×C3—21no—
334C23×C3—32no—
335C23×C3—64no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—62no—
340C23×C3—62no—
341C23×C3—122no—
342C23×C3—122no—
343C23×C3—122no—
344C23×C3—122no—
345C23×C3—122no—
346C23×C3C2×D1211yescharacteristic
347C23×C3D3×D411yescharacteristic
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—24no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3C2×D1212yes—
360C3×D4—34no—
361C3×D4—64no—
362C3×D4—62no—
363C3×D4—62no—
364C3×D4—62no—
365C3×D4—122no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—32no—
371C2×C3×C4—62no—
372C2×C3×C4—64no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4C2×D1211yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D412yes—
378C2×C3×C4D3×D412yes—
379C2×C3×C4D3×D412yes—
380C2×C3×C4C2×#6712yes—
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—616no—
384#67—616no—
385#67—128no—
386#67—128no—
387C2×Dic3—22no—
388C2×Dic3—616no—
389C2×Dic3—64no—
390C2×Dic3—64no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—124no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3—122no—
400C2×Dic3—242no—
401C2×Dic3C2×D1212yes—
402D12—24no—
403D12—22no—
404D12—22no—
405D12—22no—
406D12—42no—
407D12C2×#6714yescomplemented
408C4×D3—24no—
409C4×D3—22no—
410C4×D3—22no—
411C4×D3—616no—
412Dic6—34no—
413Dic6—34no—
414Dic6—64no—
415Dic6—64no—
416Dic6—64no—
417Dic6—62no—
418Dic6—62no—
419Dic6—122no—
420Dic6—124no—
421C3×C8—22no—
422C3×C8—22no—
423C3×C8—42no—
424C3×C8—62no—
425C3⋊C8—22no—
426C2×C32#44914yescomplemented
427C2×C32C2×#12011yescharacteristic
428C2×C32C2×#13511yescharacteristic
429C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
430C3×D3—42no—
431C3×D3—44no—
432C3×D3—82no—
433C24—31no—
434C24—61no—
435C24—61no—
436#41—188no—
437#41—188no—
438#41—1816no—
439C2×Q8—92no—
440C2×Q8—94no—
441C2×Q8—181no—
442C2×Q8—182no—
443C2×D4—32no—
444C2×D4—32no—
445C2×D4—34no—
446C2×D4—61no—
447C2×D4—61no—
448C2×D4—62no—
449C2×D4—62no—
450C2×D4—62no—
451C2×D4—184no—
452C2×D4—188no—
453C2×D4—184no—
454C2×D4—364no—
455C22×C4—31no—
456C22×C4—32no—
457C22×C4—32no—
458C22×C4—62no—
459C22×C4—62no—
460C22×C4—184no—
461C22×C4—188no—
462C22×C4—181no—
463C22×C4—181no—
464C22×C4C2×D3211yescharacteristic
465SD16—188no—
466D8—68no—
467C2×C8—22no—
468C2×C8—32no—
469C2×C8—62no—
470C2×C8C2×D3212yes—
471C4⋊C4—92no—
472C4⋊C4—181no—
473C22⋊C4—184no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—64no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—124no—
483C22×C3—122no—
484C22×C3—122no—
485C22×C3—128no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3—244no—
490C22×C3#88212yes—
491C22×C3#90412yes—
492C22×C3#90812yes—
493C22×C3#91112yes—
494C22×C3#91212yes—
495C22×C3#93712yes—
496C22×C3C22×D1211yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C2×D3—22no—
499C2×D3—22no—
500C2×D3—22no—
501C2×D3—24no—
502C2×D3—48no—
503C2×D3—42no—
504C2×D3—42no—
505C2×D3—44no—
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—84no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—62no—
514C3×C4#88212yes—
515C3×C4#93712yes—
516C3×C4C2×D3×D411yescharacteristic
517C3×C4C2×D3×D411yescharacteristic
518C3×C4C2×D3×D411yescharacteristic
519C3×C4C22×#6711yescharacteristic
520Dic3—22no—
521Dic3—64no—
522Dic3—64no—
523Dic3—124no—
524Dic3—122no—
525Dic3—122no—
526Dic3—242no—
527C32C2×#44911yescharacteristic, complemented, Sylow
528C23—32no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23—62no—
533C23—64no—
534C23—62no—
535C23—122no—
536C23—122no—
537C23—122no—
538C23—122no—
539C23—122no—
540C23D3×D1211yescharacteristic
541Q8—94no—
542Q8—182no—
543Q8—184no—
544D4—34no—
545D4—62no—
546D4—62no—
547D4—62no—
548D4—64no—
549D4—122no—
550D4—1816no—
551D4—368no—
552C2×C4—32no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—64no—
557C2×C4—1816no—
558C2×C4—182no—
559C2×C4—184no—
560C2×C4—182no—
561C2×C4—362no—
562C2×C4D3×D1211yescharacteristic
563C2×C4#380212yes—
564C2×C4D3×#6712yes—
565C2×C4C22×D3211yescharacteristic
566C8—22no—
567C8—62no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—24no—
571C2×C3—21no—
572C2×C3—124no—
573C2×C3—122no—
574C2×C3—242no—
575C2×C3#473414yescomplemented
576C2×C3#515814yescomplemented
577C2×C3C2×#88211yescharacteristic
578C2×C3C2×#90411yescharacteristic
579C2×C3C2×#90811yescharacteristic
580C2×C3C2×#91111yescharacteristic
581C2×C3C2×#91211yescharacteristic
582C2×C3C2×#93711yescharacteristic
583D3—42no—
584D3—44no—
585D3—82no—
586C22—62no—
587C22—62no—
588C22—62no—
589C22—64no—
590C22—122no—
591C22—122no—
592C22—124no—
593C22—128no—
594C22—122no—
595C22—122no—
596C22—122no—
597C22—244no—
598C22#6379512yes—
599C22#6380712yes—
600C22#6392212yes—
601C22C2×D3×D1211yescharacteristic
602C4—62no—
603C4—184no—
604C4—362no—
605C4#6392212yes—
606C4C2×#380211yescharacteristic
607C4C2×D3×#6711yescharacteristic
608C3—21no—
609C3C2×#473411yescharacteristic, complemented
610C3C2×#515811yescharacteristic, complemented
611C2—122no—
612C2—124no—
613C2—242no—
614C2#1059096214yesdirect product factor
615C2C2×#6379511yescharacteristic
616C2C2×#6380711yescharacteristic
617C2C2×#6392211yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32C2×#449
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
1. C22×#3795C2semidirect
2. C22×C3×D24C2semidirect
3. C2×#63908C2semidirect
4. C22×#3716C2semidirect
5. C2×#63643C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63563C2semidirect
8. #10590962C2direct (N × H)
21. C2×#3795C22semidirect
26. C2×C3×D24C22semidirect
29. #63908C22semidirect
31. C2×#3716C22semidirect
32. #63643C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63563C22semidirect
41. C22×D24D3semidirect
47. C2×(C2×D3)⋊C8D3semidirect
60. C2×#634D4semidirect
68. C2×C3×D12D4semidirect
136. C2×D24C2×D3semidirect
142. (C2×D3)⋊C8C2×D3semidirect
169. #634C2×D4semidirect
177. C3×D12C2×D4semidirect
244. C2×D12#67semidirect
407. D12C2×#67semidirect
426. C2×C32#449semidirect
527. C32C2×#449semidirect
575. C2×C3#4734semidirect
576. C2×C3#5158semidirect
609. C3C2×#4734semidirect
610. C3C2×#5158semidirect
614. C2#10590962direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C22×C3×D242
C2×#639082
C22×#37162
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×#635632
#105909622
C2×#51583
C2×#47343