Finite Group Databasebeta

← C2×#10591182 #11863723

Subgroups — C2×#10591182 #11863723

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×#3828C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×C3×#830C211yesmaximal, characteristic, complemented
6#10591182C218yesmaximal, direct product factor
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63564C211yesmaximal, characteristic, complemented
9C2×#5037—31nomaximal
10C2×#4734—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C2×#3828—22no—
14C2×#3828—24no—
15C2×#3828—24no—
16C2×#3828C2214yescomplemented
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3—21no—
19C22×#634C2211yescharacteristic
20C22×C3×#67—21no—
21C22×C3×D12C2211yescharacteristic
22C3×#930—22no—
23C3×#930C2214yescomplemented
24C2×C3×(C2×D3)⋊C4—21no—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3716—24no—
29C2×#3716C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yescomplemented
32C3×#830C2214yescomplemented
33#63567C2214yescomplemented
34#63564C2214yescomplemented
35C22×#235—31no—
36C22×#235—31no—
37C22×#235—61no—
38C2×C3×#121—31no—
39C22×#214—31no—
40C22×#213—31no—
41C2×#930D311yescharacteristic, complemented
42C22×D24—31no—
43C22×#204—31no—
44C2×C3×C22⋊C8—31no—
45C2×#830D311yescharacteristic, complemented
46C2×#821—31no—
47C2×#816—31no—
48#5037—38no—
49C2×#810—31no—
50C2×#809—31no—
51#4734—38no—
52C24×C32D411yescharacteristic
53C23×C3⋊D3—21no—
54C23×C3×D3—21no—
55C22×C32×C4—22no—
56C22×C32×C4—22no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4D412yes—
59C22×C32×C4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×#638—28no—
62C2×#638—24no—
63C22×C3⋊Dic3—21no—
64#3828—216no—
65#3828—28no—
66#3828—28no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)D414yescomplemented
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C4×C3⋊D3—28no—
72C2×C4×C3⋊D3—24no—
73C2×#634—21no—
74C2×#634—22no—
75C2×#634D414yescomplemented
76C2×#634C2312yes—
77C2×C3×#67—24no—
78C2×C3×#67—44no—
79C22×C3×Dic3—21no—
80C2×C3×D12—22no—
81C2×C3×D12—22no—
82C2×C3×D12—21no—
83C2×C3×D12C2312yes—
84C3×(C2×D3)⋊C4—24no—
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#3716—28no—
92#3714—28no—
93C2×#449—91noSylow
94C22×C3×D4—31no—
95C22×C3×D4—61no—
96C23×C3×C4—21no—
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C2×D311yescharacteristic
99C22×#67—21no—
100C22×#67—62no—
101C22×#67—61no—
102C22×#67—61no—
103C2×#235—34no—
104C2×#235—34no—
105C2×#235—64no—
106C2×#235—64no—
107C2×#235—64no—
108C2×#235—64no—
109C2×#235—64no—
110C2×#235—68no—
111C2×#235—68no—
112C2×#235—64no—
113C2×#235—62no—
114C2×#235—62no—
115C22×D12—31no—
116C22×D12—31no—
117C22×D12—61no—
118C22×D12C2×D311yescharacteristic
119C22×C4×D3—62no—
120C22×C4×D3—61no—
121C22×C4×D3—61no—
122C22×Dic6—31no—
123C22×Dic6—31no—
124C22×Dic6—61no—
125C22×C3×C8—31no—
126C22×C3×C8—31no—
127C3×#121—34no—
128C3×#121—62no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C22⋊C4—61no—
131C2×#214—34no—
132C2×#214—64no—
133C2×#213—34no—
134C2×#213—64no—
135#930—22no—
136#930C2×D314yescomplemented
137C2×(C2×D3)⋊C4—21no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140C22×C3⋊C8C2×D311yescharacteristic
141C2×D24—34no—
142C2×D24—64no—
143C2×#204—34no—
144C2×#204—64no—
145C3×C22⋊C8—34no—
146#830C2×D314yescomplemented
147#821—34no—
148#816—34no—
149#810—34no—
150#809—34no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—22no—
154C23×C32C2×D412yes—
155C23×C32C2×D411yescharacteristic
156C22×C3⋊D3—24no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—42no—
159C22×C3⋊D3—42no—
160C22×C3×D3—22no—
161C22×C3×D3—42no—
162C22×C3×D3—42no—
163C22×C3×D3—42no—
164C2×C32×C4—22no—
165C2×C32×C4—24no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2411yescharacteristic
173#638—216no—
174C2×C3⋊Dic3—24no—
175C2×C3⋊Dic3—22no—
176C4⋊(C3⋊D3)—24no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)C2×D414yescomplemented
179C4×C3⋊D3—216no—
180#634—24no—
181#634—22no—
182#634C2×D414yescomplemented
183C3×#67—48no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—42no—
186C3×D12—22no—
187C3×D12—22no—
188C3×D12—42no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—22no—
191C22×#41—91no—
192C22×SD16—91no—
193C22×D8—91no—
194C2×#121—31no—
195#449—98no—
196C2×#103—91no—
197C2×#102—91no—
198C2×C22⋊C8—31no—
199C24×C3—21no—
200C24×C3—61no—
201C24×C3D1211yescharacteristic
202C24×C3#6711yescharacteristic
203C23×D3—21no—
204C23×D3—62no—
205C23×D3—61no—
206C23×D3—61no—
207C2×C3×D4—32no—
208C2×C3×D4—64no—
209C2×C3×D4—61no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—124no—
213C22×C3×C4—24no—
214C22×C3×C4—24no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—61no—
224C22×C3×C4D1211yescharacteristic
225C22×C3×C4D1212yes—
226C22×C3×C4#6711yescharacteristic
227C22×C3×C4#6712yes—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D312yes—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—24no—
233C2×#67—44no—
234C2×#67—616no—
235C2×#67—68no—
236C2×#67—68no—
237C2×#67—68no—
238C2×#67—64no—
239C2×#67—64no—
240C22×Dic3—21no—
241C22×Dic3—62no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244#235—68no—
245#235—68no—
246#235—68no—
247#235—68no—
248#235—616no—
249#235—616no—
250#235—632no—
251#235—616no—
252#235—616no—
253C2×D12—22no—
254C2×D12—22no—
255C2×D12—21no—
256C2×D12—34no—
257C2×D12—34no—
258C2×D12—32no—
259C2×D12—32no—
260C2×D12—64no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—64no—
264C2×D12—61no—
265C2×D12—62no—
266C2×D12—62no—
267C2×D12—61no—
268C2×D12C22×D312yes—
269C2×C4×D3—616no—
270C2×C4×D3—68no—
271C2×C4×D3—68no—
272C2×C4×D3—68no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×Dic6—34no—
276C2×Dic6—34no—
277C2×Dic6—32no—
278C2×Dic6—32no—
279C2×Dic6—64no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—64no—
283C2×Dic6—61no—
284C2×Dic6—62no—
285C2×Dic6—62no—
286C2×Dic6—61no—
287C2×C3×C8—32no—
288C2×C3×C8—32no—
289C2×C3×C8—62no—
290C2×C3×C8—62no—
291C3×C4⋊C4—32no—
292C3×C4⋊C4—61no—
293C3×C22⋊C4—64no—
294#214—68no—
295#213—68no—
296(C2×D3)⋊C4—24no—
297C4⋊Dic3—21no—
298C4⋊Dic3C22×D312yes—
299C2×C3⋊C8—22no—
300C2×C3⋊C8—22no—
301C2×C3⋊C8C22×D312yes—
302C2×C3⋊C8C22×D312yes—
303D24—68no—
304#204—68no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—22no—
308C22×C32—44no—
309C22×C32#12012yes—
310C22×C32#13512yes—
311C22×C32AGL(1,ℤ/8)12yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—24no—
314C2×C3⋊D3—42no—
315C2×C3⋊D3—42no—
316C2×C3⋊D3—48no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C2×C3×D3—84no—
321C32×C4—22no—
322C32×C4#12012yes—
323C32×C4C22×D411yescharacteristic
324C32×C4C22×D411yescharacteristic
325C3⋊Dic3—24no—
326C3×Dic3—42no—
327C2×#41—94no—
328C2×#41—184no—
329C2×#41—184no—
330C2×#41—182no—
331C22×Q8—91no—
332C22×D4—31no—
333C22×D4—61no—
334C22×D4—91no—
335C22×D4—181no—
336C23×C4—181no—
337C23×C4D3211yescharacteristic
338C2×SD16—94no—
339C2×SD16—184no—
340C2×D8—94no—
341C2×D8—184no—
342C22×C8—31no—
343C22×C8—31no—
344#121—34no—
345#121—62no—
346C2×C4⋊C4—31no—
347C2×C22⋊C4—61no—
348#103—94no—
349#102—94no—
350C22⋊C8—34no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—62no—
363C23×C3—122no—
364C23×C3—122no—
365C23×C3—122no—
366C23×C3C2×D1212yes—
367C23×C3C2×D1211yescharacteristic
368C23×C3C2×#6712yes—
369C23×C3C2×#6711yescharacteristic
370C22×D3—22no—
371C22×D3—42no—
372C22×D3—42no—
373C22×D3—42no—
374C22×D3—64no—
375C22×D3—68no—
376C22×D3—64no—
377C22×D3—64no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—124no—
381C22×D3—124no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—128no—
389C3×D4—122no—
390C2×C3×C4—24no—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—28no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—62no—
408C2×C3×C4—122no—
409C2×C3×C4C2×D1212yes—
410C2×C3×C4C2×D1211yescharacteristic
411C2×C3×C4D3×D412yes—
412C2×C3×C4D3×D412yes—
413C2×C3×C4D3×D412yes—
414C2×C3×C4D3×D412yes—
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—48no—
420#67—632no—
421#67—616no—
422#67—616no—
423C2×Dic3—22no—
424C2×Dic3—42no—
425C2×Dic3—64no—
426C2×Dic3—68no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431D12—22no—
432D12—22no—
433D12—34no—
434D12—34no—
435D12—42no—
436D12—64no—
437D12—64no—
438D12—68no—
439D12—64no—
440D12—64no—
441D12—62no—
442D12—62no—
443C4×D3—632no—
444C4×D3—616no—
445C4×D3—616no—
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—42no—
460C2×C32#44914yescomplemented
461C2×C32C2×#12011yescharacteristic
462C2×C32C2×#13511yescharacteristic
463C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
464C3⋊D3—44no—
465C3×D3—82no—
466C24—61no—
467C24—181no—
468C24#62611yescharacteristic
469#41—188no—
470#41—188no—
471#41—1816no—
472C2×Q8—92no—
473C2×Q8—94no—
474C2×Q8—181no—
475C2×Q8—182no—
476C2×D4—32no—
477C2×D4—64no—
478C2×D4—61no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—92no—
482C2×D4—94no—
483C2×D4—124no—
484C2×D4—188no—
485C2×D4—184no—
486C2×D4—181no—
487C2×D4—182no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—61no—
491C22×C4—188no—
492C22×C4—181no—
493C22×C4—184no—
494C22×C4#62612yes—
495C22×C4#62611yescharacteristic
496C22×C4C2×D3212yes—
497C22×C4C2×D3211yescharacteristic
498SD16—188no—
499D8—188no—
500C2×C8—32no—
501C2×C8—32no—
502C2×C8—62no—
503C2×C8—62no—
504C4⋊C4—32no—
505C4⋊C4—61no—
506C22⋊C4—64no—
507C22×C3—24no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—48no—
521C22×C3—44no—
522C22×C3—44no—
523C22×C3—122no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—244no—
527C22×C3#88212yes—
528C22×C3#90412yes—
529C22×C3#90812yes—
530C22×C3#93212yes—
531C22×C3#93712yes—
532C22×C3#95012yes—
533C22×C3C22×D1211yescharacteristic
534C22×C3C22×#6711yescharacteristic
535C2×D3—42no—
536C2×D3—42no—
537C2×D3—42no—
538C2×D3—68no—
539C2×D3—64no—
540C2×D3—64no—
541C2×D3—84no—
542C2×D3—1216no—
543C2×D3—124no—
544C2×D3—124no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—128no—
548C2×D3—122no—
549C2×D3—128no—
550C2×D3—122no—
551C3×C4—24no—
552C3×C4—22no—
553C3×C4—22no—
554C3×C4—21no—
555C3×C4—21no—
556C3×C4—22no—
557C3×C4—122no—
558C3×C4#88212yes—
559C3×C4#93712yes—
560C3×C4C2×D3×D411yescharacteristic
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C2×D3×D411yescharacteristic
563C3×C4C2×D3×D411yescharacteristic
564Dic3—42no—
565Dic3—68no—
566Dic3—64no—
567Dic3—64no—
568C32C2×#44911yescharacteristic, complemented, Sylow
569C23—22no—
570C23—22no—
571C23—22no—
572C23—62no—
573C23—122no—
574C23—122no—
575C23—122no—
576C23—182no—
577C23—184no—
578C23—362no—
579C23—362no—
580C23C2×#62612yes—
581C23C2×#62611yescharacteristic
582Q8—94no—
583Q8—182no—
584Q8—184no—
585D4—62no—
586D4—62no—
587D4—94no—
588D4—128no—
589D4—122no—
590D4—1816no—
591D4—182no—
592D4—184no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—62no—
598C2×C4—122no—
599C2×C4—1816no—
600C2×C4—182no—
601C2×C4—184no—
602C2×C4C2×#62612yes—
603C2×C4C2×#62611yescharacteristic
604C2×C4#381112yes—
605C2×C4#381112yes—
606C2×C4C22×D3211yescharacteristic
607C8—62no—
608C8—62no—
609C2×C3—21no—
610C2×C3—24no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—44no—
614C2×C3—42no—
615C2×C3—42no—
616C2×C3—242no—
617C2×C3#473414yescomplemented
618C2×C3#503714yescomplemented
619C2×C3C2×#88211yescharacteristic
620C2×C3C2×#90411yescharacteristic
621C2×C3C2×#90811yescharacteristic
622C2×C3C2×#93211yescharacteristic
623C2×C3C2×#93711yescharacteristic
624C2×C3C2×#95011yescharacteristic
625D3—82no—
626D3—128no—
627D3—124no—
628D3—124no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—44no—
633C22—122no—
634C22—122no—
635C22—122no—
636C22—184no—
637C22—244no—
638C22—368no—
639C22—362no—
640C22—362no—
641C22#6382912yes—
642C22#6383012yes—
643C22#6398112yes—
644C22C22×#62611yescharacteristic
645C4—22no—
646C4—122no—
647C4—184no—
648C4#6398112yes—
649C4C2×#381111yescharacteristic
650C4C2×#381111yescharacteristic
651C3—21no—
652C3C2×#473411yescharacteristic, complemented
653C3C2×#503711yescharacteristic, complemented
654C2—42no—
655C2—242no—
656C2—364no—
657C2#1059118214yesdirect product factor
658C2C2×#6382911yescharacteristic
659C2C2×#6383011yescharacteristic
660C2C2×#6398111yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
hypercenterC23×C4D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C2×C3×#930C2semidirect
3. C22×#3716C2semidirect
4. C22×#3714C2semidirect
5. C2×C3×#830C2semidirect
6. #10591182C2direct (N × H)
7. C2×#63567C2semidirect
8. C2×#63564C2semidirect
16. C2×#3828C22semidirect
23. C3×#930C22semidirect
29. C2×#3716C22semidirect
31. C2×#3714C22semidirect
32. C3×#830C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
41. C2×#930D3semidirect
45. C2×#830D3semidirect
69. C2×C4⋊(C3⋊D3)D4semidirect
75. C2×#634D4semidirect
136. #930C2×D3semidirect
146. #830C2×D3semidirect
178. C4⋊(C3⋊D3)C2×D4semidirect
182. #634C2×D4semidirect
460. C2×C32#449semidirect
568. C32C2×#449semidirect
617. C2×C3#4734semidirect
618. C2×C3#5037semidirect
652. C3C2×#4734semidirect
653. C3C2×#5037semidirect
657. C2#10591182direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9302
C22×#37162
C22×#37142
C2×C3×#8302
#105911822
C2×#635672
C2×#635642
C2×#50373
C2×#47343