Finite Group Databasebeta

← C2×#10591519 #11863718

Subgroups — C2×#10591519 #11863718

Order 1152.

1773 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic, complemented
2C22×#3754C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C22×C3×#213C211yesmaximal, characteristic, complemented
5#10591519C218yesmaximal, direct product factor
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5158—31nomaximal
10C2×#5037—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#625—21no—
17C22×D3×Dic3—21no—
18C2×#3795—24no—
19C2×#3795—24no—
20C2×#3795—22no—
21C2×#3795C2214yescomplemented
22C2×#3754—24no—
23C2×#3754C2214yescomplemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C2×C3×#217—21no—
26C3×#938—22no—
27C3×#938C2214yescomplemented
28C2×C3×#213—24no—
29C2×C3×#213C2214yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32#63567C2214yescomplemented
33#63562C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×#237—31no—
36C22×#235—31no—
37C22×C3×D8—31no—
38C2×C3×#121—31no—
39C2×#938D311yescharacteristic, complemented
40C22×#214—31no—
41C22×#214—31no—
42C22×#214—61no—
43C22×#213D311yescharacteristic, complemented
44C2×#832—31no—
45C2×#830—31no—
46#5158—38no—
47C2×(C2×D3)⋊C8—31no—
48C2×#816—31no—
49#5037—38no—
50C2×#810—31no—
51C2×#809—31no—
52C24×C32—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C2×C32×D4—22no—
56C2×C32×D4—22no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×#634—21no—
62C2×#634—22no—
63C2×#634D414yescomplemented
64C2×#634C2312yes—
65C2×C3×#67—24no—
66C2×C3×#67—44no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3D411yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12D414yescomplemented
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3D412yes—
76C2×C3×C4×D3C2312yes—
77C2×#625—28no—
78C2×#625—24no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—24no—
81#3795—216no—
82#3795—28no—
83#3795—28no—
84#3754—28no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—24no—
88C3×#213—28no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C2×C3×C3⋊C8—22no—
92C2×C3×C3⋊C8C2312yes—
93C2×#449—91noSylow
94C22×C3×D4—21no—
95C22×C3×D4—31no—
96C22×C3×D4—61no—
97C22×C3×D4C2×D311yescharacteristic
98C22×C3×D4C2×D311yescharacteristic
99C23×C3×C4—31no—
100C22×#67—21no—
101C22×#67—61no—
102C22×#67—61no—
103C23×Dic3—61no—
104C2×#237—34no—
105C2×#237—64no—
106C2×#237—64no—
107C2×#237—62no—
108C2×#235—34no—
109C2×#235—64no—
110C2×#235—62no—
111C2×#235—64no—
112C22×D12C2×D311yescharacteristic
113C22×C4×D3—61no—
114C22×C4×D3C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C2×C3×D8—34no—
119C2×C3×D8—64no—
120C22×C3×C8—31no—
121C3×#121—34no—
122C3×#121—62no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C22⋊C4—61no—
125C2×#217—21no—
126#938—22no—
127#938C2×D314yescomplemented
128C2×#214—34no—
129C2×#214—34no—
130C2×#214—64no—
131C2×#214—64no—
132C2×#214—64no—
133C2×#214—68no—
134C2×#213—24no—
135C2×#213C2×D314yescomplemented
136C2×C4⋊Dic3C2×D311yescharacteristic
137C22×C3⋊C8—31no—
138C22×C3⋊C8—31no—
139C22×C3⋊C8—61no—
140C22×C3⋊C8C2×D311yescharacteristic
141#832—34no—
142#830—34no—
143(C2×D3)⋊C8—34no—
144#816—34no—
145#810—34no—
146#809—34no—
147C23×C32—22no—
148C23×C32—42no—
149C23×C32—42no—
150C23×C32—42no—
151C23×C32C2×D411yescharacteristic
152C22×C3×D3—24no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—42no—
158C22×C3×D3—42no—
159C22×C3×D3C2×D412yes—
160C32×D4—22no—
161C32×D4—22no—
162C32×D4—42no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—24no—
168C2×C3⋊Dic3—22no—
169#634—24no—
170#634—22no—
171#634C2×D414yescomplemented
172C3×#67—48no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C2×C3×Dic3C2×D412yes—
177C3×D12—24no—
178C3×D12—22no—
179C3×D12C2×D414yescomplemented
180C3×C4×D3—24no—
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183#625—216no—
184D3×Dic3—216no—
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—22no—
187C22×#41—91no—
188C22×SD16—91no—
189C22×D8—31no—
190C2×#121—31no—
191#449—98no—
192C2×#103—91no—
193C2×#102—91no—
194C2×C22⋊C8—91no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—31no—
198C24×C3—41no—
199C24×C3—61no—
200C23×D3—21no—
201C23×D3#6711yescharacteristic
202C2×C3×D4—24no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—22no—
206C2×C3×D4—21no—
207C2×C3×D4—22no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—34no—
211C2×C3×D4—32no—
212C2×C3×D4—42no—
213C2×C3×D4—41no—
214C2×C3×D4—64no—
215C2×C3×D4—62no—
216C2×C3×D4—61no—
217C2×C3×D4—124no—
218C2×C3×D4C22×D312yes—
219C2×C3×D4C22×D312yes—
220C22×C3×C4—21no—
221C22×C3×C4—31no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—24no—
230C2×#67—44no—
231C2×#67—64no—
232C2×#67—68no—
233C2×#67—68no—
234C2×#67—64no—
235C22×Dic3—21no—
236C22×Dic3—68no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—64no—
240C22×Dic3—121no—
241C22×Dic3#6711yescharacteristic
242#237—68no—
243#237—68no—
244#237—616no—
245#235—68no—
246#235—616no—
247#235—68no—
248C2×D12—21no—
249C2×D12—22no—
250C2×D12#6714yescomplemented
251C2×D12C22×D312yes—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—64no—
255C2×C4×D3—68no—
256C2×C4×D3#6712yes—
257C2×C4×D3C22×D312yes—
258C2×Dic6—34no—
259C2×Dic6—34no—
260C2×Dic6—32no—
261C2×Dic6—32no—
262C2×Dic6—64no—
263C2×Dic6—62no—
264C2×Dic6—61no—
265C2×Dic6—62no—
266C2×Dic6—62no—
267C2×Dic6—61no—
268C2×Dic6—121no—
269C2×Dic6—122no—
270C3×D8—68no—
271C2×C3×C8—32no—
272C2×C3×C8—62no—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—61no—
275C3×C22⋊C4—64no—
276#217—24no—
277#214—68no—
278#214—68no—
279#214—616no—
280#213—28no—
281C4⋊Dic3—21no—
282C4⋊Dic3C22×D312yes—
283C2×C3⋊C8—22no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8—64no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8C22×D312yes—
291C22×C32—42no—
292C22×C32—42no—
293C22×C32—42no—
294C22×C32—84no—
295C22×C32#12012yes—
296C22×C32#13512yes—
297C22×C32AGL(1,ℤ/8)12yes—
298C22×C32C22×D411yescharacteristic
299C2×C3×D3—24no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—22no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3—44no—
306C2×C3×D3—48no—
307C32×C4#12012yes—
308C32×C4C22×D411yescharacteristic
309C32×C4C22×D411yescharacteristic
310C3⋊Dic3—24no—
311C3×Dic3—22no—
312C3×Dic3—42no—
313C2×#41—94no—
314C2×#41—182no—
315C2×#41—184no—
316C2×#41—184no—
317C22×Q8—91no—
318C22×D4—31no—
319C22×D4—61no—
320C22×D4—181no—
321C22×D4D3211yescharacteristic
322C23×C4—31no—
323C23×C4—181no—
324C2×SD16—94no—
325C2×SD16—184no—
326C2×D8—34no—
327C2×D8—64no—
328C22×C8—31no—
329C22×C8—91no—
330#121—34no—
331#121—62no—
332C2×C4⋊C4—31no—
333C2×C22⋊C4—61no—
334#103—94no—
335#102—94no—
336C22⋊C8—94no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—21no—
340C23×C3—32no—
341C23×C3—42no—
342C23×C3—44no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3—64no—
352C23×C3—62no—
353C23×C3—62no—
354C23×C3—82no—
355C23×C3—82no—
356C23×C3—122no—
357C23×C3—122no—
358C23×C3D3×D411yescharacteristic
359C23×C3C2×#6711yescharacteristic
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—24no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—42no—
366C22×D3—42no—
367C22×D3C2×#6712yes—
368C3×D4—24no—
369C3×D4—22no—
370C3×D4—22no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—34no—
374C3×D4—42no—
375C3×D4—44no—
376C3×D4—42no—
377C3×D4—42no—
378C3×D4—64no—
379C3×D4—62no—
380C3×D4—128no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—32no—
386C2×C3×C4—62no—
387C2×C3×C4—64no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—122no—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D412yes—
394C2×C3×C4D3×D412yes—
395C2×C3×C4D3×D412yes—
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C2×#6712yes—
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400#67—48no—
401#67—616no—
402#67—616no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—42no—
406C2×Dic3—616no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—122no—
412C2×Dic3—124no—
413C2×Dic3C2×#6712yes—
414D12—24no—
415D12—22no—
416D12C2×#6714yescomplemented
417C4×D3—24no—
418C4×D3—22no—
419C4×D3—22no—
420C4×D3—616no—
421Dic6—34no—
422Dic6—34no—
423Dic6—64no—
424Dic6—64no—
425Dic6—64no—
426Dic6—62no—
427Dic6—62no—
428Dic6—122no—
429Dic6—124no—
430C3×C8—62no—
431C3⋊C8—22no—
432C3⋊C8—64no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C2×C32—82no—
436C2×C32#44914yescomplemented
437C2×C32C2×#12011yescharacteristic
438C2×C32C2×#13511yescharacteristic
439C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
440C3×D3—42no—
441C3×D3—44no—
442C24—21no—
443C24—31no—
444C24—61no—
445#41—188no—
446#41—188no—
447#41—1816no—
448C2×Q8—92no—
449C2×Q8—94no—
450C2×Q8—181no—
451C2×Q8—182no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—32no—
456C2×D4—34no—
457C2×D4—64no—
458C2×D4—61no—
459C2×D4—62no—
460C2×D4—124no—
461C2×D4—184no—
462C2×D4—188no—
463C2×D4C2×D3212yes—
464C22×C4—31no—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—62no—
468C22×C4—62no—
469C22×C4—61no—
470C22×C4—184no—
471C22×C4—188no—
472C22×C4—181no—
473C22×C4C2×D3211yescharacteristic
474SD16—188no—
475D8—68no—
476C2×C8—32no—
477C2×C8—62no—
478C2×C8—92no—
479C2×C8—182no—
480C4⋊C4—32no—
481C4⋊C4—61no—
482C22⋊C4—64no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—44no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—62no—
495C22×C3—62no—
496C22×C3—64no—
497C22×C3—62no—
498C22×C3—82no—
499C22×C3—82no—
500C22×C3—88no—
501C22×C3—84no—
502C22×C3—84no—
503C22×C3—124no—
504C22×C3—122no—
505C22×C3—128no—
506C22×C3—122no—
507C22×C3#91112yes—
508C22×C3#91212yes—
509C22×C3#93212yes—
510C22×C3#93712yes—
511C22×C3#93712yes—
512C22×C3#95012yes—
513C22×C3C2×D3×D411yescharacteristic
514C22×C3C22×#6711yescharacteristic
515C2×D3—22no—
516C2×D3—22no—
517C2×D3—24no—
518C2×D3—22no—
519C2×D3—48no—
520C2×D3—42no—
521C2×D3—42no—
522C2×D3—44no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—22no—
526C3×C4—62no—
527C3×C4—122no—
528C3×C4#93712yes—
529C3×C4#93712yes—
530C3×C4C2×D3×D411yescharacteristic
531C3×C4C2×D3×D411yescharacteristic
532C3×C4C2×D3×D411yescharacteristic
533C3×C4C22×#6711yescharacteristic
534Dic3—22no—
535Dic3—42no—
536Dic3—64no—
537Dic3—64no—
538Dic3—124no—
539C32C2×#44911yescharacteristic, complemented, Sylow
540C23—22no—
541C23—32no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—62no—
546C23—62no—
547C23—62no—
548C23—62no—
549C23—64no—
550C23—122no—
551C23—122no—
552C23D3×#6711yescharacteristic
553Q8—94no—
554Q8—182no—
555Q8—184no—
556D4—22no—
557D4—22no—
558D4—34no—
559D4—42no—
560D4—62no—
561D4—64no—
562D4—128no—
563D4—1816no—
564C2×C4—32no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—64no—
569C2×C4—62no—
570C2×C4—122no—
571C2×C4—1816no—
572C2×C4—182no—
573C2×C4—184no—
574C2×C4D3×#6712yes—
575C2×C4D3×#6711yescharacteristic
576C2×C4#381112yes—
577C2×C4C22×D3211yescharacteristic
578C8—62no—
579C8—182no—
580C2×C3—24no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—84no—
585C2×C3—82no—
586C2×C3—82no—
587C2×C3—122no—
588C2×C3—124no—
589C2×C3#503714yescomplemented
590C2×C3#515814yescomplemented
591C2×C3C2×#91111yescharacteristic
592C2×C3C2×#91211yescharacteristic
593C2×C3C2×#93211yescharacteristic
594C2×C3C2×#93711yescharacteristic
595C2×C3C2×#93711yescharacteristic
596C2×C3C2×#95011yescharacteristic
597D3—44no—
598D3—42no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—62no—
603C22—62no—
604C22—62no—
605C22—64no—
606C22—84no—
607C22—124no—
608C22—128no—
609C22—122no—
610C22—122no—
611C22#6393212yes—
612C22#6393312yes—
613C22#6398312yes—
614C22C2×D3×#6711yescharacteristic
615C4—62no—
616C4—122no—
617C4—184no—
618C4#6398312yes—
619C4C2×D3×#6711yescharacteristic
620C4C2×#381111yescharacteristic
621C3—21no—
622C3C2×#503711yescharacteristic, complemented
623C3C2×#515811yescharacteristic, complemented
624C2—82no—
625C2—122no—
626C2—124no—
627C2#1059151914yesdirect product factor
628C2C2×#6393211yescharacteristic
629C2C2×#6393311yescharacteristic
630C2C2×#6398311yescharacteristic
subgroupG/H
centerC23D3×#67
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×#3795C2semidirect
2. C22×#3754C2semidirect
3. C2×C3×#938C2semidirect
4. C22×C3×#213C2semidirect
5. #10591519C2direct (N × H)
6. C2×#63567C2semidirect
7. C2×#63562C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
21. C2×#3795C22semidirect
23. C2×#3754C22semidirect
27. C3×#938C22semidirect
29. C2×C3×#213C22semidirect
32. #63567C22semidirect
33. #63562C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C2×#938D3semidirect
43. C22×#213D3semidirect
63. C2×#634D4semidirect
71. C2×C3×D12D4semidirect
127. #938C2×D3semidirect
135. C2×#213C2×D3semidirect
171. #634C2×D4semidirect
179. C3×D12C2×D4semidirect
250. C2×D12#67semidirect
416. D12C2×#67semidirect
436. C2×C32#449semidirect
539. C32C2×#449semidirect
589. C2×C3#5037semidirect
590. C2×C3#5158semidirect
622. C3C2×#5037semidirect
623. C3C2×#5158semidirect
627. C2#10591519direct (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×#37542
C2×C3×#9382
C22×C3×#2132
#105915192
C2×#635672
C2×#635622
C2×(C2×D3)⋊(C3⋊C8)2
C2×#51583
C2×#50373