Finite Group Databasebeta

← C2×#10591457 #11863720

Subgroups — C2×#10591457 #11863720

Order 1152.

2069 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591457C218yesmaximal, direct product factor
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic, complemented
9C2×#5158—31nomaximal
10C2×#4781—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#638—21no—
13C23×C3⋊Dic3—21no—
14C2×#3830—24no—
15C2×#3830—22no—
16C2×#3830—24no—
17C2×#3830C2214yescomplemented
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×#626—21no—
22C2×C3×#213—24no—
23C2×C3×#213C2214yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×(C2×D3)⋊Dic3—21no—
28#63916—22no—
29#63916C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32C3×#832C2214yescomplemented
33#63567C2214yescomplemented
34#63557C2214yescomplemented
35C22×#237—31no—
36C22×#237—31no—
37C22×#237—61no—
38C22×C3×D8—31no—
39C2×#938—31no—
40C22×#214—31no—
41C22×#213D311yescharacteristic, complemented
42C22×#204—31no—
43C2×#895—31no—
44C2×C3×#102—31no—
45C2×#832D311yescharacteristic, complemented
46#5158—38no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—31no—
49C2×#816—31no—
50C2×#810—31no—
51#4781—38no—
52C24×C32—21no—
53C23×C3⋊D3D411yescharacteristic
54C23×C3×D3—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4D414yescomplemented
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×#638—28no—
61C2×#638—24no—
62C22×C3⋊Dic3—28no—
63C22×C3⋊Dic3—21no—
64C22×C3⋊Dic3—24no—
65C22×C3⋊Dic3D411yescharacteristic
66#3830—216no—
67#3830—28no—
68#3830—28no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3D412yes—
72C2×C4×C3⋊D3C2312yes—
73C2×#634—21no—
74C2×#634—22no—
75C2×#634D414yescomplemented
76C2×#634C2312yes—
77C22×C3×Dic3—21no—
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12—21no—
81C2×C3×D12C2312yes—
82C2×#626—24no—
83C2×#626—44no—
84C3×#213—28no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90C2×C3×C3⋊C8C2312yes—
91(C2×D3)⋊Dic3—24no—
92#3716—28no—
93C2×#449—91noSylow
94C22×C3×D4—21no—
95C22×C3×D4—31no—
96C22×C3×D4C2×D311yescharacteristic
97C22×C3×D4C2×D311yescharacteristic
98C22×#67—61no—
99C22×#67—61no—
100C22×#67—61no—
101C22×#67—62no—
102C23×Dic3—61no—
103C23×Dic3—61no—
104C23×Dic3—62no—
105C2×#237—34no—
106C2×#237—34no—
107C2×#237—64no—
108C2×#237—64no—
109C2×#237—64no—
110C2×#237—62no—
111C2×#237—62no—
112C2×#237—64no—
113C2×#237—68no—
114C2×#237—68no—
115C2×#237—64no—
116C2×#237—64no—
117C22×D12—61no—
118C22×D12C2×D311yescharacteristic
119C22×C4×D3—31no—
120C22×C4×D3—31no—
121C22×C4×D3—61no—
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—61no—
125C2×C3×D8—34no—
126C2×C3×D8—64no—
127C22×C3×C8—31no—
128C22×C3×C8—31no—
129C2×C3×C4⋊C4—31no—
130C2×#217—61no—
131#938—34no—
132#938—62no—
133C2×#214—34no—
134C2×#214—64no—
135C2×#213—24no—
136C2×#213C2×D314yescomplemented
137C2×(C2×D3)⋊C4—61no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140C22×C3⋊C8C2×D311yescharacteristic
141C2×#204—34no—
142C2×#204—64no—
143#895—34no—
144#895—62no—
145C3×#102—34no—
146#832C2×D314yescomplemented
147(C2×D3)⋊C8—34no—
148(C2×D3)⋊C8—34no—
149#816—34no—
150#810—34no—
151C23×C32—24no—
152C23×C32—22no—
153C23×C32—42no—
154C23×C32—42no—
155C23×C32C2×D411yescharacteristic
156C22×C3⋊D3—22no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3C2×D412yes—
160C22×C3×D3—22no—
161C22×C3×D3—42no—
162C22×C3×D3—42no—
163C22×C3×D3—42no—
164C32×D4—24no—
165C32×D4—22no—
166C32×D4C2×D414yescomplemented
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2411yescharacteristic
171#638—216no—
172C2×C3⋊Dic3—216no—
173C2×C3⋊Dic3—24no—
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3C2×D412yes—
177C4×C3⋊D3—24no—
178C4×C3⋊D3—22no—
179C4×C3⋊D3—22no—
180#634—24no—
181#634—22no—
182#634C2×D414yescomplemented
183C2×C3×Dic3—22no—
184C2×C3×Dic3—42no—
185C3×D12—22no—
186C3×D12—22no—
187C3×D12—42no—
188#626—48no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—22no—
191C22×#41—91no—
192C22×SD16—91no—
193C22×D8—31no—
194C2×#121—91no—
195#449—98no—
196C2×#103—91no—
197C2×#102—31no—
198C2×C22⋊C8—91no—
199C24×C3—22no—
200C24×C3—21no—
201C24×C3—21no—
202C24×C3—61no—
203C23×D3—21no—
204C23×D3—31no—
205C23×D3—31no—
206C23×D3—61no—
207C2×C3×D4—24no—
208C2×C3×D4—22no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—21no—
212C2×C3×D4—22no—
213C2×C3×D4—24no—
214C2×C3×D4—22no—
215C2×C3×D4—32no—
216C2×C3×D4—62no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C2×C3×D4D1214yescomplemented
220C2×C3×D4#6714yescomplemented
221C2×C3×D4C22×D312yes—
222C2×C3×D4C22×D312yes—
223C22×C3×C4—21no—
224C22×C3×C4—61no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—64no—
228C2×#67—64no—
229C2×#67—64no—
230C2×#67—68no—
231C2×#67—616no—
232C2×#67—68no—
233C2×#67—68no—
234C2×#67—124no—
235C22×Dic3—21no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—61no—
239C22×Dic3—64no—
240C22×Dic3—64no—
241C22×Dic3—62no—
242C22×Dic3—68no—
243C22×Dic3—616no—
244C22×Dic3—68no—
245C22×Dic3—68no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248#237—68no—
249#237—68no—
250#237—616no—
251#237—632no—
252#237—616no—
253#237—616no—
254#237—616no—
255#237—68no—
256#237—68no—
257C2×D12—22no—
258C2×D12—22no—
259C2×D12—21no—
260C2×D12—64no—
261C2×D12—124no—
262C2×D12C22×D312yes—
263C2×C4×D3—32no—
264C2×C4×D3—32no—
265C2×C4×D3—32no—
266C2×C4×D3—32no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—62no—
272C2×C4×D3—62no—
273C2×C4×D3—62no—
274C2×C4×D3—62no—
275C2×Dic6—34no—
276C2×Dic6—34no—
277C2×Dic6—32no—
278C2×Dic6—32no—
279C2×Dic6—64no—
280C2×Dic6—62no—
281C2×Dic6—64no—
282C2×Dic6—62no—
283C2×Dic6—62no—
284C2×Dic6—61no—
285C2×Dic6—61no—
286C2×Dic6—62no—
287C3×D8—68no—
288C2×C3×C8—32no—
289C2×C3×C8—32no—
290C2×C3×C8—62no—
291C2×C3×C8—62no—
292C3×C4⋊C4—32no—
293C3×C4⋊C4—61no—
294#217—64no—
295#214—68no—
296#213—28no—
297(C2×D3)⋊C4—64no—
298C4⋊Dic3—21no—
299C4⋊Dic3C22×D312yes—
300C2×C3⋊C8—22no—
301C2×C3⋊C8—22no—
302C2×C3⋊C8C22×D312yes—
303C2×C3⋊C8C22×D312yes—
304#204—68no—
305C22×C32—24no—
306C22×C32—42no—
307C22×C32—42no—
308C22×C32—48no—
309C22×C32#12012yes—
310C22×C32#13512yes—
311C22×C32AGL(1,ℤ/8)12yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—22no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—22no—
316C2×C3⋊D3—44no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C2×C3×D3—84no—
321C32×C4#12012yes—
322C32×C4C22×D411yescharacteristic
323C32×C4C22×D411yescharacteristic
324C3⋊Dic3—24no—
325C3⋊Dic3—22no—
326C3×Dic3—42no—
327C2×#41—94no—
328C2×#41—182no—
329C2×#41—184no—
330C2×#41—184no—
331C22×Q8—91no—
332C22×D4—31no—
333C22×D4—181no—
334C22×D4—181no—
335C22×D4D3211yescharacteristic
336C23×C4—91no—
337C23×C4—181no—
338C2×SD16—94no—
339C2×SD16—184no—
340C2×D8—34no—
341C2×D8—64no—
342C22×C8—31no—
343C22×C8—31no—
344#121—94no—
345#121—182no—
346C2×C4⋊C4—31no—
347C2×C22⋊C4—181no—
348#103—94no—
349#102—34no—
350C22⋊C8—94no—
351C23×C3—24no—
352C23×C3—28no—
353C23×C3—24no—
354C23×C3—24no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—21no—
358C23×C3—44no—
359C23×C3—44no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—62no—
365C23×C3—122no—
366C23×C3—122no—
367C23×C3—122no—
368C23×C3D3×D411yescharacteristic
369C23×C3D3×D411yescharacteristic
370C22×D3—22no—
371C22×D3—32no—
372C22×D3—32no—
373C22×D3—42no—
374C22×D3—42no—
375C22×D3—42no—
376C22×D3—62no—
377C22×D3—64no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—122no—
385C22×D3—122no—
386C3×D4—24no—
387C3×D4—28no—
388C3×D4—24no—
389C3×D4—24no—
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—24no—
393C3×D4—62no—
394C3×D4—62no—
395C3×D4—122no—
396C3×D4C2×D1214yescomplemented
397C3×D4C2×#6714yescomplemented
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—62no—
403C2×C3×C4—122no—
404C2×C3×C4C2×D1212yes—
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D412yes—
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D412yes—
409C2×C3×C4C2×#6712yes—
410C2×C3×C4C23×D311yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412#67—632no—
413#67—616no—
414#67—616no—
415#67—128no—
416C2×Dic3—22no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—42no—
420C2×Dic3—62no—
421C2×Dic3—64no—
422C2×Dic3—68no—
423C2×Dic3—64no—
424C2×Dic3—632no—
425C2×Dic3—616no—
426C2×Dic3—616no—
427C2×Dic3—64no—
428C2×Dic3—62no—
429C2×Dic3—64no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433D12—22no—
434D12—22no—
435D12—42no—
436D12—128no—
437C4×D3—64no—
438C4×D3—64no—
439C4×D3—68no—
440C4×D3—64no—
441C4×D3—64no—
442C4×D3—62no—
443C4×D3—62no—
444C4×D3—62no—
445C4×D3—62no—
446Dic6—34no—
447Dic6—34no—
448Dic6—64no—
449Dic6—64no—
450Dic6—68no—
451Dic6—64no—
452Dic6—64no—
453Dic6—62no—
454Dic6—62no—
455C3×C8—62no—
456C3×C8—62no—
457C3⋊C8—22no—
458C3⋊C8—22no—
459C2×C32—44no—
460C2×C32#44914yescomplemented
461C2×C32C2×#12011yescharacteristic
462C2×C32C2×#13511yescharacteristic
463C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
464C3⋊D3—42no—
465C3×D3—82no—
466C24—21no—
467C24—61no—
468C24—91no—
469#41—188no—
470#41—1816no—
471#41—188no—
472C2×Q8—92no—
473C2×Q8—94no—
474C2×Q8—182no—
475C2×Q8—181no—
476C2×D4—22no—
477C2×D4—21no—
478C2×D4—32no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—61no—
482C2×D4—184no—
483C2×D4—184no—
484C2×D4—188no—
485C2×D4—364no—
486C2×D4#62614yescomplemented
487C2×D4C2×D3212yes—
488C22×C4—61no—
489C22×C4—91no—
490C22×C4—92no—
491C22×C4—92no—
492C22×C4—184no—
493C22×C4—188no—
494C22×C4—181no—
495C22×C4—182no—
496C22×C4—182no—
497C22×C4C2×D3211yescharacteristic
498SD16—188no—
499D8—68no—
500C2×C8—32no—
501C2×C8—32no—
502C2×C8—62no—
503C2×C8—62no—
504C4⋊C4—32no—
505C4⋊C4—61no—
506C22⋊C4—184no—
507C22×C3—28no—
508C22×C3—24no—
509C22×C3—24no—
510C22×C3—21no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—44no—
515C22×C3—44no—
516C22×C3—416no—
517C22×C3—48no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—48no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—244no—
527C22×C3#88212yes—
528C22×C3#91112yes—
529C22×C3#91112yes—
530C22×C3#91212yes—
531C22×C3#91612yes—
532C22×C3#93712yes—
533C22×C3C2×D3×D411yescharacteristic
534C22×C3C2×D3×D411yescharacteristic
535C2×D3—42no—
536C2×D3—42no—
537C2×D3—42no—
538C2×D3—64no—
539C2×D3—62no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—84no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—128no—
549C2×D3—124no—
550C2×D3—124no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—22no—
554C3×C4—122no—
555C3×C4#88212yes—
556C3×C4#93712yes—
557C3×C4C22×D1211yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560C3×C4C22×#6711yescharacteristic
561Dic3—42no—
562Dic3—68no—
563Dic3—64no—
564Dic3—64no—
565Dic3—62no—
566Dic3—64no—
567Dic3—62no—
568C32C2×#44911yescharacteristic, complemented, Sylow
569C23—22no—
570C23—24no—
571C23—42no—
572C23—42no—
573C23—62no—
574C23—92no—
575C23—122no—
576C23—122no—
577C23—122no—
578C23—182no—
579C23—182no—
580C23—182no—
581C23#381111yescharacteristic
582Q8—94no—
583Q8—182no—
584Q8—184no—
585D4—22no—
586D4—24no—
587D4—62no—
588D4—62no—
589D4—122no—
590D4—1816no—
591D4—368no—
592D4C2×#62614yescomplemented
593C2×C4—62no—
594C2×C4—92no—
595C2×C4—122no—
596C2×C4—1816no—
597C2×C4—182no—
598C2×C4—182no—
599C2×C4—184no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—184no—
603C2×C4C2×#62612yes—
604C2×C4#381112yes—
605C2×C4#381111yescharacteristic
606C2×C4C22×D3211yescharacteristic
607C8—62no—
608C8—62no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—24no—
613C2×C3—48no—
614C2×C3—44no—
615C2×C3—44no—
616C2×C3—242no—
617C2×C3#478114yescomplemented
618C2×C3#515814yescomplemented
619C2×C3C2×#88211yescharacteristic
620C2×C3C2×#91111yescharacteristic
621C2×C3C2×#91111yescharacteristic
622C2×C3C2×#91211yescharacteristic
623C2×C3C2×#91611yescharacteristic
624C2×C3C2×#93711yescharacteristic
625D3—82no—
626D3—124no—
627D3—122no—
628D3—122no—
629C22—24no—
630C22—42no—
631C22—42no—
632C22—48no—
633C22—122no—
634C22—122no—
635C22—122no—
636C22—182no—
637C22—182no—
638C22—182no—
639C22—244no—
640C22—364no—
641C22#6392712yes—
642C22#6393612yes—
643C22#6398112yes—
644C22C2×#381111yescharacteristic
645C4—122no—
646C4—182no—
647C4—184no—
648C4#6398112yes—
649C4C22×#62611yescharacteristic
650C4C2×#381111yescharacteristic
651C3—21no—
652C3C2×#478111yescharacteristic, complemented
653C3C2×#515811yescharacteristic, complemented
654C2—44no—
655C2—242no—
656C2—362no—
657C2#1059145714yesdirect product factor
658C2C2×#6392711yescharacteristic
659C2C2×#6393611yescharacteristic
660C2C2×#6398111yescharacteristic
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×#3830C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63916C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#832C2semidirect
6. #10591457C2direct (N × H)
7. C2×#63567C2semidirect
8. C2×#63557C2semidirect
17. C2×#3830C22semidirect
23. C2×C3×#213C22semidirect
29. #63916C22semidirect
31. C2×#3716C22semidirect
32. C3×#832C22semidirect
33. #63567C22semidirect
34. #63557C22semidirect
41. C22×#213D3semidirect
45. C2×#832D3semidirect
57. C2×C32×D4D4semidirect
75. C2×#634D4semidirect
136. C2×#213C2×D3semidirect
146. #832C2×D3semidirect
166. C32×D4C2×D4semidirect
182. #634C2×D4semidirect
219. C2×C3×D4D12semidirect
220. C2×C3×D4#67semidirect
396. C3×D4C2×D12semidirect
397. C3×D4C2×#67semidirect
460. C2×C32#449semidirect
486. C2×D4#626semidirect
568. C32C2×#449semidirect
592. D4C2×#626semidirect
617. C2×C3#4781semidirect
618. C2×C3#5158semidirect
652. C3C2×#4781semidirect
653. C3C2×#5158semidirect
657. C2#10591457direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×C3×#2132
C2×#639162
C22×#37162
C2×C3×#8322
#105914572
C2×#635672
C2×#635572
C2×#51583
C2×#47813