Finite Group Databasebeta

← C2×#10591508 #11867930

Subgroups — C2×#10591508 #11867930

Order 1152.

1145 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4C2×#63815C211yesmaximal, characteristic, complemented
5C2×C3×#833C211yesmaximal, characteristic, complemented
6#10591508C218yesmaximal, direct product factor
7C2×#63578C211yesmaximal, characteristic, complemented
8C2×#63559C211yesmaximal, characteristic, complemented
9C2×#5199—31nomaximal
10C2×#4749—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×#3753—21no—
15C2×#3753—22no—
16C2×#3753—21no—
17C2×#3753C2214yescomplemented
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C2×C3×#214—21no—
20C3×#932—22no—
21C3×#932C2214yescomplemented
22C2×C3×#213—21no—
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×#3717—21no—
27#63825—22no—
28#63825C2214yescomplemented
29C2×#3714—21no—
30C2×#3711—21no—
31#63815—22no—
32#63815C2214yescomplemented
33C2×D3×C3⋊C8—21no—
34C3×#833C2214yescomplemented
35#63578C2214yescomplemented
36#63559C2214yescomplemented
37C2×C3×AGL(1,ℤ/8)—31no—
38C2×#949—31no—
39C2×#948—31no—
40C2×#932D311yescharacteristic, complemented
41C22×#213—31no—
42C22×#213—31no—
43C22×#213—61no—
44C2×#908—31no—
45C2×#907—31no—
46C2×C3×#100—31no—
47C2×#833D311yescharacteristic, complemented
48#5199—38no—
49C2×#823—31no—
50C2×#823—31no—
51C2×#822—31no—
52C2×#822—31no—
53#4749—38no—
54C24×C32—21no—
55C23×C3⋊D3—21no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4—21no—
60C2×C32×D4—21no—
61C2×C32×D4C2312yes—
62C22×C32×C4C2311yescharacteristic
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)—21no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C3×#67—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235D412yes—
73C3×#235C2312yes—
74C2×C3×D12D411yescharacteristic
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77#3753—24no—
78#3753—24no—
79C2×C3⋊(C3⋊C8)D411yescharacteristic
80C2×C3⋊(C3⋊C8)D412yes—
81C2×C3⋊(C3⋊C8)D411yescharacteristic
82C2×C3⋊(C3⋊C8)C2312yes—
83C3×#214—24no—
84C3×#213—24no—
85C3×#208—21no—
86C3×#208—21no—
87C3×#208—21no—
88C3×#208C2312yes—
89C3×#208C2312yes—
90C3×#208C2312yes—
91C2×C3×C3⋊C8—21no—
92C2×C3×C3⋊C8—21no—
93C2×C3×C3⋊C8—21no—
94#3717—24no—
95#3714—24no—
96#3711—24no—
97D3×C3⋊C8—24no—
98C2×#472—91noSylow
99C2×C3×#41—31no—
100C22×C3×D4—21no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C2×#235C2×D311yescharacteristic
104C22×D12—31no—
105C22×D12—31no—
106C22×D12—61no—
107C3×AGL(1,ℤ/8)—34no—
108C3×AGL(1,ℤ/8)—62no—
109C2×C3×SD16—61no—
110C2×C3×D8—61no—
111C2×C3×M16—31no—
112C2×C3×M16—31no—
113C2×C3×M16—31no—
114#949—34no—
115#949—62no—
116#948—34no—
117#948—62no—
118C2×#215—61no—
119C2×#214—21no—
120#932—22no—
121#932C2×D314yescomplemented
122C2×#213—21no—
123C2×#213—34no—
124C2×#213—34no—
125C2×#213—64no—
126C2×#213—61no—
127C2×#213—61no—
128C2×#213—61no—
129C2×#213—62no—
130C2×#213—61no—
131C2×#213—61no—
132C2×#213—62no—
133C2×#213—62no—
134C2×#213—62no—
135C2×#213—64no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138C2×#208C2×D311yescharacteristic
139C2×#208C2×D311yescharacteristic
140C22×C3⋊C8—31no—
141C22×C3⋊C8—31no—
142C22×C3⋊C8—61no—
143C22×C3⋊C8—61no—
144#908—34no—
145#908—62no—
146#907—34no—
147#907—62no—
148C2×D24—61no—
149C2×#204—61no—
150C2×ΓL(1,𝔽25)—61no—
151C2×D3×C8—61no—
152C3×#100—34no—
153#833C2×D314yescomplemented
154#823—34no—
155#823—34no—
156#822—34no—
157#822—34no—
158C23×C32—22no—
159C23×C32—41no—
160C23×C32—41no—
161C23×C32—82no—
162C23×C32#4111yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3⋊D3—41no—
165C22×C3⋊D3—41no—
166C22×C3⋊D3—82no—
167C22×C3×D3—21no—
168C32×D4—22no—
169C32×D4—22no—
170C32×D4—41no—
171C32×D4—41no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4#4111yescharacteristic
177C2×C32×C4C2411yescharacteristic
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—41no—
181C4⋊(C3⋊D3)—41no—
182C3×#67—22no—
183C3×#67—22no—
184C2×C3×Dic3—21no—
185C3×D12—21no—
186C3×D12C2×D412yes—
187C3×C4×D3—22no—
188C3×C4×D3—22no—
189C3×Dic6—21no—
190C3×Dic6C2×D412yes—
191C3⋊(C3⋊C8)C2×D412yes—
192C3⋊(C3⋊C8)C2×D412yes—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—22no—
195C3×C3⋊C8—22no—
196C2×AGL(1,ℤ/8)—31no—
197C2×AGL(1,ℤ/8)—91no—
198C22×D8—91no—
199C2×#131—91no—
200#472—98no—
201C2×#108—91no—
202C2×#100—31no—
203C2×#100—91no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—41no—
207C23×D3—61no—
208C23×D3—61no—
209C23×D3—121no—
210C3×#41—32no—
211C3×#41—32no—
212C3×#41—61no—
213C3×#41—61no—
214C2×C3×Q8—31no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—31no—
229C2×C3×D4—41no—
230C2×C3×D4—41no—
231C2×C3×D4—41no—
232C2×C3×D4—61no—
233C2×C3×D4C22×D312yes—
234C2×C3×D4C22×D312yes—
235C22×C3×C4—21no—
236C22×C3×C4—61no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—21no—
240#235—21no—
241#235—21no—
242#235#6712yes—
243#235C22×D312yes—
244C2×D12—32no—
245C2×D12—32no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—61no—
250C2×D12—61no—
251C2×D12—61no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—121no—
260C2×D12—121no—
261C2×D12—121no—
262C2×D12#6711yescharacteristic
263C2×C4×D3—21no—
264C2×Dic6#6711yescharacteristic
265C3×SD16—64no—
266C3×D8—64no—
267C3×M16—32no—
268C3×M16—32no—
269C3×M16—32no—
270C3×M16—61no—
271C3×M16—61no—
272C3×M16—61no—
273C2×C3×C8—61no—
274C2×C3×C8—61no—
275C2×C3×C8—61no—
276#215—64no—
277#214—24no—
278#213—24no—
279#213—64no—
280#213—64no—
281#213—64no—
282#213—64no—
283#213—64no—
284#213—68no—
285#213—68no—
286#208—21no—
287#208—21no—
288#208—21no—
289#208—64no—
290#208C22×D312yes—
291#208C22×D312yes—
292#208C22×D312yes—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—31no—
297C2×C3⋊C8—31no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—31no—
300C2×C3⋊C8—31no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—62no—
307C2×C3⋊C8—62no—
308C2×C3⋊C8—64no—
309D24—64no—
310#204—64no—
311ΓL(1,𝔽25)—64no—
312D3×C8—64no—
313C22×C32—22no—
314C22×C32—42no—
315C22×C32—82no—
316C22×C32—82no—
317C22×C32—82no—
318C22×C32#12111yescharacteristic
319C22×C32#12111yescharacteristic
320C22×C32C2×#4111yescharacteristic
321C2×C3⋊D3—42no—
322C2×C3⋊D3—82no—
323C2×C3⋊D3—82no—
324C2×C3⋊D3—82no—
325C2×C3×D3—22no—
326C2×C3×D3—42no—
327C32×C4#12111yescharacteristic
328C32×C4#12111yescharacteristic
329C32×C4C22×D411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3×Dic3—22no—
332C2×#41—31no—
333C22×D4—91no—
334C22×D4D3211yescharacteristic
335AGL(1,ℤ/8)—34no—
336AGL(1,ℤ/8)—62no—
337AGL(1,ℤ/8)—94no—
338AGL(1,ℤ/8)—182no—
339C2×SD16—61no—
340C2×SD16—181no—
341C2×D8—61no—
342C2×D8—94no—
343C2×D8—181no—
344C2×D8—181no—
345C2×D8—181no—
346C2×D8—182no—
347#131—94no—
348#131—182no—
349C2×M16—31no—
350C2×M16—31no—
351C2×M16—31no—
352C2×M16—181no—
353C22×C8—91no—
354C22×C8—181no—
355#108—94no—
356#100—34no—
357#100—94no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—61no—
369C23×C3—82no—
370C23×C3—82no—
371C23×C3—84no—
372C23×C3#23511yescharacteristic
373C23×C3#23711yescharacteristic
374C22×D3—21no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—122no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—121no—
381C22×D3—121no—
382C22×D3—121no—
383C22×D3—121no—
384C22×D3—244no—
385C22×D3—242no—
386C22×D3—242no—
387C3×Q8—32no—
388C3×Q8—61no—
389C3×D4—24no—
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—22no—
394C3×D4—32no—
395C3×D4—42no—
396C3×D4—42no—
397C3×D4—42no—
398C3×D4—41no—
399C3×D4—41no—
400C3×D4—41no—
401C3×D4—41no—
402C3×D4—62no—
403C3×D4—62no—
404C3×D4—61no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4#23511yescharacteristic
415C2×C3×C4D3×D411yescharacteristic
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D411yescharacteristic
418C2×C3×C4D3×D411yescharacteristic
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4#23711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—22no—
427#67—22no—
428C2×Dic3—21no—
429D12—21no—
430D12—64no—
431D12—62no—
432D12—62no—
433D12—62no—
434D12—62no—
435D12—122no—
436D12—122no—
437D12—122no—
438D12—121no—
439D12—121no—
440D12—121no—
441D12—121no—
442D12C2×#6712yes—
443C4×D3—22no—
444C4×D3—22no—
445Dic6—21no—
446Dic6C2×#6712yes—
447C3×C8—62no—
448C3×C8—62no—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—22no—
452C3⋊C8—22no—
453C3⋊C8—32no—
454C3⋊C8—32no—
455C3⋊C8—32no—
456C3⋊C8—32no—
457C3⋊C8—62no—
458C3⋊C8—62no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—82no—
462C2×C32#47212yescomplemented
463C2×C32C2×#12111yescharacteristic
464C3⋊D3—82no—
465C3×D3—42no—
466C24—21no—
467C24—181no—
468#41—32no—
469#41—32no—
470#41—61no—
471#41—61no—
472C2×Q8—31no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—31no—
479C2×D4—61no—
480C2×D4—92no—
481C2×D4—181no—
482C2×D4—181no—
483C2×D4—181no—
484C2×D4—181no—
485C2×D4—181no—
486C2×D4C2×D3212yes—
487C22×C4—61no—
488C22×C4C2×D3211yescharacteristic
489SD16—64no—
490SD16—184no—
491D8—64no—
492D8—184no—
493D8—184no—
494D8—184no—
495M16—32no—
496M16—32no—
497M16—32no—
498M16—61no—
499M16—61no—
500M16—61no—
501M16—184no—
502C2×C8—61no—
503C2×C8—61no—
504C2×C8—61no—
505C2×C8—92no—
506C2×C8—91no—
507C2×C8—91no—
508C2×C8—92no—
509C2×C8—184no—
510C22×C3—24no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—62no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3—84no—
523C22×C3—84no—
524C22×C3—82no—
525C22×C3—82no—
526C22×C3—84no—
527C22×C3—82no—
528C22×C3—82no—
529C22×C3—122no—
530C22×C3#88411yescharacteristic
531C22×C3#88411yescharacteristic
532C22×C3#93911yescharacteristic
533C22×C3#93911yescharacteristic
534C22×C3C2×#23511yescharacteristic
535C22×C3C2×#23711yescharacteristic
536C2×D3—22no—
537C2×D3—42no—
538C2×D3—124no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—244no—
542C2×D3—244no—
543C2×D3—242no—
544C2×D3—242no—
545C2×D3—244no—
546C2×D3—242no—
547C2×D3—242no—
548C2×D3—242no—
549C2×D3—242no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—62no—
555C3×C4#88411yescharacteristic
556C3×C4#88411yescharacteristic
557C3×C4#93911yescharacteristic
558C3×C4#93911yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560C3×C4C2×D3×D411yescharacteristic
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C22×#6711yescharacteristic
563Dic3—22no—
564C32C2×#47211yescharacteristic, complemented, Sylow
565C23—22no—
566C23—41no—
567C23—41no—
568C23—61no—
569C23—82no—
570C23—182no—
571C23—361no—
572C23—361no—
573C23—722no—
574C23#380411yescharacteristic
575Q8—32no—
576Q8—61no—
577D4—22no—
578D4—22no—
579D4—32no—
580D4—41no—
581D4—41no—
582D4—62no—
583D4—62no—
584D4—61no—
585D4—182no—
586D4—182no—
587D4—361no—
588D4—361no—
589C2×C4—61no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4#380411yescharacteristic
593C2×C4D3×#6711yescharacteristic
594C2×C4D3×#6711yescharacteristic
595C2×C4#381111yescharacteristic
596C2×C4#381111yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—62no—
599C8—62no—
600C8—62no—
601C8—92no—
602C8—92no—
603C2×C3—22no—
604C2×C3—22no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3—84no—
612C2×C3—82no—
613C2×C3—82no—
614C2×C3—122no—
615C2×C3#474912yescomplemented
616C2×C3#519912yescomplemented
617C2×C3C2×#88411yescharacteristic
618C2×C3C2×#93911yescharacteristic
619D3—42no—
620D3—244no—
621D3—242no—
622D3—242no—
623C22—22no—
624C22—42no—
625C22—62no—
626C22—82no—
627C22—82no—
628C22—82no—
629C22—122no—
630C22—362no—
631C22—722no—
632C22—722no—
633C22—722no—
634C22#6397111yescharacteristic
635C22#6397111yescharacteristic
636C22C2×#380411yescharacteristic
637C4—62no—
638C4#6397111yescharacteristic
639C4#6397111yescharacteristic
640C4C2×D3×#6711yescharacteristic
641C4C2×#381111yescharacteristic
642C3—21no—
643C3C2×#474911yescharacteristic, complemented
644C3C2×#519911yescharacteristic, complemented
645C2—21no—
646C2—21no—
647C2—82no—
648C2—122no—
649C2—722no—
650C2#1059150812yesdirect product factor
651C2C2×#6397111yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32#121
hypercenterC22×D4D32
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3753C2semidirect
2. C2×C3×#932C2semidirect
3. C2×#63825C2semidirect
4. C2×#63815C2semidirect
5. C2×C3×#833C2semidirect
6. #10591508C2direct (N × H)
7. C2×#63578C2semidirect
8. C2×#63559C2semidirect
17. C2×#3753C22semidirect
21. C3×#932C22semidirect
28. #63825C22semidirect
32. #63815C22semidirect
34. C3×#833C22semidirect
35. #63578C22semidirect
36. #63559C22semidirect
40. C2×#932D3semidirect
47. C2×#833D3semidirect
121. #932C2×D3semidirect
153. #833C2×D3semidirect
462. C2×C32#472semidirect
564. C32C2×#472semidirect
615. C2×C3#4749semidirect
616. C2×C3#5199semidirect
643. C3C2×#4749semidirect
644. C3C2×#5199semidirect
650. C2#10591508direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37532
C2×C3×#9322
C2×#638252
C2×#638152
C2×C3×#8332
#105915082
C2×#635782
C2×#635592
C2×#51993
C2×#47493