Finite Group Databasebeta

← C2×#10591433 #11865443

Subgroups — C2×#10591433 #11865443

Order 1152.

1545 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63898C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591433C218yesmaximal, direct product factor
7C2×#63572C211yesmaximal, characteristic, complemented
8C2×#63564C211yesmaximal, characteristic, complemented
9C2×#5150—31nomaximal
10C2×#4786—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#638—21no—
13C22×#638—21no—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3—21no—
17#64149—22no—
18#64149C2214yescomplemented
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#213—24no—
21C2×C3×#213C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63898—22no—
27#63898C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yescomplemented
30C3×#832C2214yescomplemented
31#63572C2214yescomplemented
32#63564C2214yescomplemented
33C22×C3×D8—31no—
34C2×#940—31no—
35C2×#940—31no—
36C2×#940—61no—
37C2×D4×Dic3—31no—
38C22×#213—31no—
39C22×#213D311yescharacteristic, complemented
40C22×D24—31no—
41C2×#893—31no—
42C2×C3×#102—31no—
43C2×#832D311yescharacteristic, complemented
44#5150—38no—
45C2×#821—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—31no—
48C2×#809—31no—
49#4786—38no—
50C24×C32—21no—
51C23×C3⋊D3—21no—
52C23×C3×D3—21no—
53C2×C32×D4—22no—
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C2×#638—24no—
59C2×#638—24no—
60C2×#638—44no—
61C2×#638—44no—
62C22×C3⋊Dic3D411yescharacteristic
63C22×C3⋊Dic3D411yescharacteristic
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C22×C3×Dic3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12D414yescomplemented
72C2×C3×D12C2312yes—
73C2×D3×Dic3—24no—
74C2×D3×Dic3—44no—
75C4×C3⋊Dic3D412yes—
76C4×C3⋊Dic3C2312yes—
77C3×#213—28no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8—22no—
82C2×C3×C3⋊C8C2312yes—
83C2×C3×C3⋊C8C2312yes—
84(C2×D3)⋊Dic3—24no—
85#3714—28no—
86C2×#459—91noSylow
87C22×C3×D4—21no—
88C22×C3×D4—31no—
89C22×C3×D4C2×D311yescharacteristic
90C22×C3×D4C2×D311yescharacteristic
91C22×#67—61no—
92C22×#67—61no—
93C22×#67—61no—
94C22×#67—61no—
95C22×#67—62no—
96C22×#67—62no—
97C23×Dic3—61no—
98C22×D12—31no—
99C22×D12—31no—
100C22×D12—61no—
101C22×D12C2×D311yescharacteristic
102C22×C4×D3—61no—
103C2×C3×D8—34no—
104C2×C3×D8—64no—
105C22×C3×C8—31no—
106C22×C3×C8—31no—
107C2×C3×C4⋊C4—31no—
108C2×#217—61no—
109#940—34no—
110#940—34no—
111#940—64no—
112#940—62no—
113#940—62no—
114#940—64no—
115D4×Dic3—34no—
116D4×Dic3—62no—
117C2×#213—24no—
118C2×#213—34no—
119C2×#213—64no—
120C2×#213C2×D314yescomplemented
121C2×(C2×D3)⋊C4—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×C4×Dic3—31no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127C22×C3⋊C8C2×D311yescharacteristic
128C2×D24—34no—
129C2×D24—64no—
130#893—34no—
131#893—62no—
132C3×#102—34no—
133#832C2×D314yescomplemented
134#821—34no—
135Dic3⋊C8—34no—
136Dic3⋊C8—34no—
137#809—34no—
138C23×C32—22no—
139C23×C32—42no—
140C23×C32—42no—
141C23×C32—42no—
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—42no—
145C22×C3⋊D3—42no—
146C22×C3⋊D3—42no—
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—42no—
150C22×C3×D3—42no—
151C32×D4—22no—
152C32×D4—22no—
153C32×D4—42no—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4#4112yes—
157C2×C32×C4C2411yescharacteristic
158#638—48no—
159#638—48no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3D814yescomplemented
162C2×C3⋊Dic3C2×D412yes—
163C2×C3⋊Dic3C2×D412yes—
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)—22no—
166C4⋊(C3⋊D3)—42no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—42no—
169C3×D12—24no—
170C3×D12—22no—
171C3×D12C2×D414yescomplemented
172D3×Dic3—48no—
173C3×C3⋊C8—22no—
174C3×C3⋊C8—22no—
175C22×D8—31no—
176C22×D8—91no—
177C2×#127—91no—
178C2×C4×D4—91no—
179#459—98no—
180C2×C4⋊C8—91no—
181C2×#102—31no—
182C2×#102—91no—
183C24×C3—22no—
184C24×C3—21no—
185C24×C3—21no—
186C24×C3—61no—
187C23×D3—21no—
188C23×D3—62no—
189C23×D3—61no—
190C23×D3—61no—
191C2×C3×D4—22no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—34no—
200C2×C3×D4—32no—
201C2×C3×D4—42no—
202C2×C3×D4—42no—
203C2×C3×D4—62no—
204C2×C3×D4—61no—
205C2×C3×D4C22×D312yes—
206C2×C3×D4C22×D312yes—
207C22×C3×C4—21no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—64no—
212C2×#67—64no—
213C2×#67—64no—
214C2×#67—64no—
215C2×#67—68no—
216C2×#67—68no—
217C2×#67—124no—
218C2×#67—124no—
219C2×#67—128no—
220C2×#67—128no—
221C2×#67—124no—
222C2×#67—124no—
223C22×Dic3—21no—
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—64no—
231C22×Dic3—124no—
232C2×D12—21no—
233C2×D12—22no—
234C2×D12—32no—
235C2×D12—32no—
236C2×D12—62no—
237C2×D12—62no—
238C2×D12—62no—
239C2×D12—62no—
240C2×D12—62no—
241C2×D12—62no—
242C2×D12—61no—
243C2×D12—61no—
244C2×D12—122no—
245C2×D12—122no—
246C2×D12#6714yescomplemented
247C2×D12C22×D312yes—
248C2×C4×D3—64no—
249C2×C4×D3—124no—
250C3×D8—68no—
251C2×C3×C8—32no—
252C2×C3×C8—32no—
253C2×C3×C8—62no—
254C2×C3×C8—62no—
255C3×C4⋊C4—32no—
256C3×C4⋊C4—61no—
257#217—64no—
258#213—28no—
259#213—68no—
260(C2×D3)⋊C4—64no—
261C4⋊Dic3—21no—
262C4⋊Dic3C22×D312yes—
263C4×Dic3—32no—
264C4×Dic3—32no—
265C4×Dic3—32no—
266C4×Dic3—32no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C2×C3⋊C8—22no—
270C2×C3⋊C8—22no—
271C2×C3⋊C8C22×D312yes—
272C2×C3⋊C8C22×D312yes—
273D24—68no—
274C22×C32—42no—
275C22×C32—42no—
276C22×C32—42no—
277C22×C32—84no—
278C22×C32#12112yes—
279C22×C32C2×D812yes—
280C22×C32AGL(1,ℤ/8)12yes—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C2×C3⋊D3—84no—
286C2×C3×D3—24no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—48no—
290C32×C4#12112yes—
291C32×C4C22×D411yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3C2×D814yescomplemented
295C3×Dic3—42no—
296C22×D4—31no—
297C22×D4—91no—
298C22×D4—181no—
299C22×D4—181no—
300C22×D4D3211yescharacteristic
301C23×C4—181no—
302C2×D8—34no—
303C2×D8—64no—
304C2×D8—94no—
305C2×D8—184no—
306C22×C8—31no—
307C22×C8—31no—
308#127—94no—
309#127—182no—
310C4×D4—94no—
311C4×D4—182no—
312C2×C4⋊C4—31no—
313C2×C22⋊C4—181no—
314C2×C42—91no—
315C4⋊C8—94no—
316#102—34no—
317#102—94no—
318C23×C3—24no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—21no—
322C23×C3—44no—
323C23×C3—44no—
324C23×C3—44no—
325C23×C3—42no—
326C23×C3—42no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—64no—
332C23×C3—62no—
333C23×C3—122no—
334C23×C3—122no—
335C23×C3D3×D411yescharacteristic
336C23×C3D3×D411yescharacteristic
337C22×D3—24no—
338C22×D3—22no—
339C22×D3—42no—
340C22×D3—42no—
341C22×D3—64no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—124no—
345C22×D3—124no—
346C22×D3—124no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—122no—
352C22×D3—122no—
353C3×D4—22no—
354C3×D4—22no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—34no—
358C3×D4—42no—
359C3×D4—42no—
360C3×D4—44no—
361C3×D4—42no—
362C3×D4—42no—
363C3×D4—64no—
364C3×D4—62no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—62no—
370C2×C3×C4—122no—
371C2×C3×C4#23512yes—
372C2×C3×C4D3×D412yes—
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4#23712yes—
376C2×C3×C4C2×#6712yes—
377C2×C3×C4C23×D311yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379#67—128no—
380#67—128no—
381#67—1216no—
382#67—1216no—
383#67—128no—
384#67—128no—
385C2×Dic3—22no—
386C2×Dic3—34no—
387C2×Dic3—34no—
388C2×Dic3—32no—
389C2×Dic3—32no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—42no—
393C2×Dic3—64no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—64no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—128no—
400D12—24no—
401D12—22no—
402D12—62no—
403D12—62no—
404D12—62no—
405D12—62no—
406D12—122no—
407D12—122no—
408D12—124no—
409D12—122no—
410D12—122no—
411D12C2×#6714yescomplemented
412C4×D3—128no—
413C3×C8—62no—
414C3×C8—62no—
415C3⋊C8—22no—
416C3⋊C8—22no—
417C2×C32—82no—
418C2×C32#45914yescomplemented
419C2×C32C2×#12111yescharacteristic
420C2×C32C22×D811yescharacteristic
421C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
422C3⋊D3—82no—
423C3×D3—44no—
424C24—21no—
425C24—61no—
426C24—181no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—32no—
431C2×D4—34no—
432C2×D4—62no—
433C2×D4—61no—
434C2×D4—92no—
435C2×D4—184no—
436C2×D4—184no—
437C2×D4—182no—
438C2×D4—182no—
439C2×D4—181no—
440C2×D4—364no—
441C2×D4—364no—
442C2×D4C2×D3212yes—
443C22×C4—61no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—184no—
447C22×C4—364no—
448C22×C4C2×D3211yescharacteristic
449D8—68no—
450D8—188no—
451C2×C8—32no—
452C2×C8—32no—
453C2×C8—62no—
454C2×C8—62no—
455C4⋊C4—32no—
456C4⋊C4—61no—
457C22⋊C4—184no—
458C42—92no—
459C42—92no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—44no—
465C22×C3—44no—
466C22×C3—44no—
467C22×C3—42no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—64no—
474C22×C3—88no—
475C22×C3—84no—
476C22×C3—84no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—128no—
480C22×C3#88412yes—
481C22×C3D3×D812yes—
482C22×C3D3×D812yes—
483C22×C3#91112yes—
484C22×C3#91412yes—
485C22×C3#93912yes—
486C22×C3C2×D3×D411yescharacteristic
487C22×C3C2×D3×D411yescharacteristic
488C2×D3—24no—
489C2×D3—48no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3—124no—
493C2×D3—124no—
494C2×D3—124no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—248no—
502C2×D3—244no—
503C2×D3—244no—
504C3×C4—21no—
505C3×C4—21no—
506C3×C4—22no—
507C3×C4—122no—
508C3×C4#88412yes—
509C3×C4#93912yes—
510C3×C4C2×#23511yescharacteristic
511C3×C4C2×D3×D411yescharacteristic
512C3×C4C2×#23711yescharacteristic
513C3×C4C22×#6711yescharacteristic
514Dic3—34no—
515Dic3—34no—
516Dic3—42no—
517Dic3—64no—
518Dic3—64no—
519Dic3—62no—
520Dic3—62no—
521C32C2×#45911yescharacteristic, complemented, Sylow
522C23—22no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—62no—
527C23—64no—
528C23—122no—
529C23—122no—
530C23—182no—
531C23—362no—
532C23—362no—
533C23—362no—
534C23#381111yescharacteristic
535D4—22no—
536D4—22no—
537D4—34no—
538D4—42no—
539D4—62no—
540D4—64no—
541D4—182no—
542D4—182no—
543D4—368no—
544D4—368no—
545D4—362no—
546C2×C4—62no—
547C2×C4—92no—
548C2×C4—94no—
549C2×C4—92no—
550C2×C4—122no—
551C2×C4—182no—
552C2×C4—368no—
553C2×C4#380412yes—
554C2×C4D3×#6712yes—
555C2×C4#381111yescharacteristic
556C2×C4C22×D3211yescharacteristic
557C8—62no—
558C8—62no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—24no—
563C2×C3—84no—
564C2×C3—82no—
565C2×C3—82no—
566C2×C3—124no—
567C2×C3#478614yescomplemented
568C2×C3#515014yescomplemented
569C2×C3C2×#88411yescharacteristic
570C2×C3C2×D3×D811yescharacteristic
571C2×C3C2×D3×D811yescharacteristic
572C2×C3C2×#91111yescharacteristic
573C2×C3C2×#91411yescharacteristic
574C2×C3C2×#93911yescharacteristic
575D3—44no—
576D3—244no—
577D3—242no—
578D3—242no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—64no—
583C22—84no—
584C22—122no—
585C22—122no—
586C22—128no—
587C22—362no—
588C22—362no—
589C22—362no—
590C22—724no—
591C22#6392612yes—
592C22#6393712yes—
593C22#6397112yes—
594C22C2×#381111yescharacteristic
595C4—94no—
596C4—122no—
597C4—182no—
598C4#6397112yes—
599C4C2×#380411yescharacteristic
600C4C2×D3×#6711yescharacteristic
601C3—21no—
602C3C2×#478611yescharacteristic, complemented
603C3C2×#515011yescharacteristic, complemented
604C2—82no—
605C2—124no—
606C2—722no—
607C2#1059143314yesdirect product factor
608C2C2×#6392611yescharacteristic
609C2C2×#6393711yescharacteristic
610C2C2×#6397111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#459
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. C2×#64149C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63898C2semidirect
4. C22×#3714C2semidirect
5. C2×C3×#832C2semidirect
6. #10591433C2direct (N × H)
7. C2×#63572C2semidirect
8. C2×#63564C2semidirect
18. #64149C22semidirect
21. C2×C3×#213C22semidirect
27. #63898C22semidirect
29. C2×#3714C22semidirect
30. C3×#832C22semidirect
31. #63572C22semidirect
32. #63564C22semidirect
39. C22×#213D3semidirect
43. C2×#832D3semidirect
71. C2×C3×D12D4semidirect
120. C2×#213C2×D3semidirect
133. #832C2×D3semidirect
161. C2×C3⋊Dic3D8semidirect
171. C3×D12C2×D4semidirect
246. C2×D12#67semidirect
294. C3⋊Dic3C2×D8semidirect
411. D12C2×#67semidirect
418. C2×C32#459semidirect
521. C32C2×#459semidirect
567. C2×C3#4786semidirect
568. C2×C3#5150semidirect
602. C3C2×#4786semidirect
603. C3C2×#5150semidirect
607. C2#10591433direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641492
C22×C3×#2132
C2×#638982
C22×#37142
C2×C3×#8322
#105914332
C2×#635722
C2×#635642
C2×#51503
C2×#47863