Finite Group Databasebeta

← C2×#10591681 #11867880

Subgroups — C2×#10591681 #11867880

Order 1152.

1069 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64157C211yesmaximal, characteristic, complemented
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#949C211yesmaximal, characteristic
4C22×#3715C211yesmaximal, characteristic, complemented
5#10591681C218yesmaximal, direct product factor
6C2×#63578C211yesmaximal, characteristic, complemented
7C2×#63560C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5203—31nomaximal
10C2×#5200—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14#64157—22no—
15#64157C2214yescomplemented
16C2×#3748—21no—
17C2×#3748C2211yescharacteristic
18C22×C3⋊(C3⋊C8)—21no—
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#951—22no—
21C3×#951C2214yescomplemented
22C3×#949—22no—
23C3×#949C2214yes—
24C2×C3×#216—21no—
25C2×C3×#215—21no—
26C2×C3×#214—21no—
27C2×C3×#213—21no—
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C2×#3715—21no—
31C2×#3715—21no—
32C2×#3715—22no—
33C2×#3715C2214yescomplemented
34#63578C2214yescomplemented
35#63560C2214yescomplemented
36#63558C2214yescomplemented
37C2×C3×#137—31no—
38C2×C3×AGL(1,ℤ/8)—31no—
39C2×#951D311yescharacteristic, complemented
40C2×#949D311yescharacteristic
41C2×#948—31no—
42C2×#948—31no—
43C2×#948—61no—
44C22×#215—31no—
45C22×#214—31no—
46C2×#836—31no—
47C2×#833—31no—
48#5203—38no—
49#5200—38no—
50C2×#824—31no—
51C2×#823—31no—
52C2×#822—31no—
53C2×#822—31no—
54C23×C3×D3—21no—
55C32×#41—21no—
56C32×#41—21no—
57C32×#41D412yes—
58C32×#41C2312yes—
59C2×C32×Q8D411yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4D411yescharacteristic
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C22×C3×Dic3—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2312yes—
77#3748—21no—
78#3748—24no—
79#3748C2312yes—
80C2×C3⋊(C3⋊C8)—21no—
81C2×C3⋊(C3⋊C8)—24no—
82C2×C3⋊(C3⋊C8)D411yescharacteristic
83C2×C3⋊(C3⋊C8)D411yescharacteristic
84C2×C3⋊(C3⋊C8)D412yes—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#216—24no—
87C3×#215—24no—
88C3×#214—24no—
89C3×#213—24no—
90C3×#208—21no—
91C3×#208—21no—
92C3×#208C2312yes—
93C3×#208C2312yes—
94C2×C3×C3⋊C8—21no—
95C2×C3×C3⋊C8—21no—
96#3715—24no—
97#3715—24no—
98C2×#471—91noSylow
99C2×C3×#41—21no—
100C2×C3×#41C2×D311yescharacteristic
101C2×C3×#41C2×D311yescharacteristic
102C22×C3×Q8—31no—
103C22×C3×D4—31no—
104C22×D12C2×D311yescharacteristic
105C22×Dic6C2×D311yescharacteristic
106C3×#137—34no—
107C3×#137—62no—
108C3×AGL(1,ℤ/8)—34no—
109C3×AGL(1,ℤ/8)—62no—
110C2×C3×Q16—61no—
111C2×C3×SD16—61no—
112C2×C3×SD16—61no—
113C2×C3×D8—61no—
114C2×C3×M16—31no—
115C2×C3×M16—31no—
116#951—22no—
117#951C2×D314yescomplemented
118#949—22no—
119#949C2×D314yes—
120#948—34no—
121#948—34no—
122#948—64no—
123#948—62no—
124#948—62no—
125#948—64no—
126C2×#216—21no—
127C2×#215—21no—
128C2×#215—34no—
129C2×#215—61no—
130C2×#215—61no—
131C2×#215—62no—
132C2×#214—21no—
133C2×#214—34no—
134C2×#214—61no—
135C2×#214—61no—
136C2×#214—62no—
137C2×#213—21no—
138C2×#208—31no—
139C2×#208—31no—
140C2×#208—61no—
141C2×#208—61no—
142C2×#208—61no—
143C2×#208—62no—
144C2×#208C2×D311yescharacteristic
145C2×#208C2×D311yescharacteristic
146C22×C3⋊C8—31no—
147C22×C3⋊C8—31no—
148C22×C3⋊C8—61no—
149C22×C3⋊C8—61no—
150C22×C3⋊C8—61no—
151C22×C3⋊C8—62no—
152#836—34no—
153#833—34no—
154#824—34no—
155#823—34no—
156#822—34no—
157#822—34no—
158C23×C32—21no—
159C23×C32#4111yescharacteristic
160C22×C3×D3—22no—
161C22×C3×D3—41no—
162C22×C3×D3—41no—
163C22×C3×D3—82no—
164C32×Q8—21no—
165C32×Q8C2×D412yes—
166C32×D4—22no—
167C32×D4—22no—
168C32×D4—21no—
169C32×D4C2×D412yes—
170C2×C32×C4—21no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4111yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3×Dic3—22no—
180C2×C3×Dic3—41no—
181C2×C3×Dic3—41no—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—41no—
185C3×D12—41no—
186C3×Dic6—22no—
187C3×Dic6—22no—
188C3×Dic6—41no—
189C3×Dic6—41no—
190C3⋊(C3⋊C8)—22no—
191C3⋊(C3⋊C8)C2×D412yes—
192C3⋊(C3⋊C8)C2×D412yes—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—22no—
195C2×#137—31no—
196C2×AGL(1,ℤ/8)—31no—
197C22×SD16—91no—
198C2×#131—91no—
199#471—98no—
200C2×#108—91no—
201C2×#101—91no—
202C2×#100—91no—
203C24×C3—61no—
204C23×D3—21no—
205C3×#41—22no—
206C3×#41—22no—
207C3×#41—21no—
208C3×#41—21no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—22no—
212C3×#41—22no—
213C3×#41#6712yes—
214C3×#41#6712yes—
215C3×#41C22×D312yes—
216C3×#41C22×D312yes—
217C2×C3×Q8—21no—
218C2×C3×Q8—32no—
219C2×C3×Q8—61no—
220C2×C3×Q8—61no—
221C2×C3×Q8—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8—61no—
224C2×C3×Q8#6711yescharacteristic
225C2×C3×Q8#6711yescharacteristic
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—32no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C2×C3×D4—61no—
236C2×C3×D4#6711yescharacteristic
237C2×C3×D4#6711yescharacteristic
238C22×C3×C4—22no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—61no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×Dic3—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12C22×D312yes—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6C22×D312yes—
258C3×Q16—64no—
259C3×SD16—64no—
260C3×SD16—64no—
261C3×D8—64no—
262C3×M16—32no—
263C3×M16—32no—
264C3×M16—61no—
265C3×M16—61no—
266C2×C3×C8—61no—
267C2×C3×C8—61no—
268#216—24no—
269#215—24no—
270#215—64no—
271#215—64no—
272#214—24no—
273#214—64no—
274#214—64no—
275#213—24no—
276#208—21no—
277#208—21no—
278#208—32no—
279#208—32no—
280#208—62no—
281#208—64no—
282#208—64no—
283#208—68no—
284#208—62no—
285#208—61no—
286#208—61no—
287#208C22×D312yes—
288#208C22×D312yes—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—32no—
296C2×C3⋊C8—32no—
297C2×C3⋊C8—32no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—61no—
300C2×C3⋊C8—61no—
301C2×C3⋊C8—62no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—64no—
304C2×C3⋊C8—64no—
305C2×C3⋊C8—62no—
306C2×C3⋊C8—68no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C22×C32—22no—
310C22×C32—22no—
311C22×C32—42no—
312C22×C32#12111yescharacteristic
313C22×C32#12111yescharacteristic
314C22×C32C2×#4111yescharacteristic
315C2×C3×D3—42no—
316C2×C3×D3—82no—
317C2×C3×D3—82no—
318C2×C3×D3—82no—
319C32×C4—22no—
320C32×C4#12111yescharacteristic
321C32×C4#12111yescharacteristic
322C32×C4C22×D411yescharacteristic
323C32×C4C22×D411yescharacteristic
324C3×Dic3—42no—
325C2×#41D3211yescharacteristic
326C22×Q8—31no—
327C22×D4—31no—
328#137—34no—
329#137—62no—
330AGL(1,ℤ/8)—34no—
331AGL(1,ℤ/8)—62no—
332C2×Q16—61no—
333C2×SD16—61no—
334C2×SD16—61no—
335C2×SD16—94no—
336C2×SD16—181no—
337C2×SD16—181no—
338C2×SD16—182no—
339C2×D8—61no—
340#131—94no—
341#131—182no—
342C2×M16—31no—
343C2×M16—31no—
344C2×M16—91no—
345C2×M16—181no—
346C22×C8—91no—
347C22×C8—181no—
348#108—94no—
349#101—94no—
350#100—94no—
351C23×C3—22no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—62no—
356C23×C3—121no—
357C23×C3—121no—
358C23×C3—242no—
359C23×C3#23711yescharacteristic
360C23×C3#23711yescharacteristic
361C22×D3—22no—
362C22×D3—41no—
363C22×D3—41no—
364C22×D3—82no—
365C3×Q8—22no—
366C3×Q8—21no—
367C3×Q8—21no—
368C3×Q8—22no—
369C3×Q8—62no—
370C3×Q8—62no—
371C3×Q8—121no—
372C3×Q8—121no—
373C3×Q8C2×#6712yes—
374C3×Q8C2×#6712yes—
375C3×D4—24no—
376C3×D4—24no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—22no—
380C3×D4—22no—
381C3×D4—22no—
382C3×D4—21no—
383C3×D4—21no—
384C3×D4—22no—
385C3×D4—62no—
386C3×D4—62no—
387C3×D4—121no—
388C3×D4—121no—
389C3×D4C2×#6712yes—
390C3×D4C2×#6712yes—
391C2×C3×C4—24no—
392C2×C3×C4—22no—
393C2×C3×C4—24no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—62no—
407C2×C3×C4—121no—
408C2×C3×C4—121no—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4#23711yescharacteristic
414C2×C3×C4#23711yescharacteristic
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421C2×Dic3—22no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424D12—22no—
425D12—22no—
426D12—41no—
427D12—41no—
428Dic6—22no—
429Dic6—22no—
430Dic6—41no—
431Dic6—41no—
432C3×C8—62no—
433C3×C8—62no—
434C3⋊C8—22no—
435C3⋊C8—22no—
436C3⋊C8—32no—
437C3⋊C8—32no—
438C3⋊C8—32no—
439C3⋊C8—32no—
440C3⋊C8—62no—
441C3⋊C8—62no—
442C3⋊C8—64no—
443C3⋊C8—62no—
444C3⋊C8—62no—
445C2×C32—21no—
446C2×C32—21no—
447C2×C32—42no—
448C2×C32#47112yescomplemented
449C2×C32C2×#12111yescharacteristic
450C3×D3—82no—
451C24—61no—
452#41—21no—
453#41—21no—
454#41#62512yes—
455#41C2×D3212yes—
456C2×Q8—32no—
457C2×Q8—61no—
458C2×Q8—61no—
459C2×Q8—61no—
460C2×Q8—61no—
461C2×Q8—61no—
462C2×Q8#62511yescharacteristic
463C2×D4—21no—
464C2×D4—32no—
465C2×D4—61no—
466C2×D4—61no—
467C2×D4—61no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4#62511yescharacteristic
471C22×C4—21no—
472C22×C4—61no—
473C22×C4C2×D3211yescharacteristic
474Q16—64no—
475SD16—64no—
476SD16—64no—
477SD16—184no—
478SD16—184no—
479D8—64no—
480M16—32no—
481M16—32no—
482M16—61no—
483M16—61no—
484M16—92no—
485M16—184no—
486M16—181no—
487C2×C8—61no—
488C2×C8—61no—
489C2×C8—92no—
490C2×C8—91no—
491C2×C8—91no—
492C2×C8—92no—
493C2×C8—184no—
494C2×C8—181no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—42no—
504C22×C3—44no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—122no—
508C22×C3—242no—
509C22×C3—242no—
510C22×C3—242no—
511C22×C3#93911yescharacteristic
512C22×C3#93911yescharacteristic
513C22×C3#93911yescharacteristic
514C22×C3#93911yescharacteristic
515C22×C3C2×#23711yescharacteristic
516C22×C3C2×#23711yescharacteristic
517C2×D3—42no—
518C2×D3—82no—
519C2×D3—82no—
520C2×D3—82no—
521C3×C4—24no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—122no—
529C3×C4#93911yescharacteristic
530C3×C4#93911yescharacteristic
531C3×C4#93911yescharacteristic
532C3×C4#93911yescharacteristic
533C3×C4C2×D3×D411yescharacteristic
534C3×C4C2×D3×D411yescharacteristic
535C3×C4C22×#6711yescharacteristic
536C3×C4C22×#6711yescharacteristic
537Dic3—42no—
538C32C2×#47111yescharacteristic, complemented, Sylow
539C23—21no—
540C23—62no—
541C23—121no—
542C23—121no—
543C23—242no—
544C23#380511yescharacteristic
545Q8—21no—
546Q8—62no—
547Q8—62no—
548Q8—121no—
549Q8—121no—
550Q8C2×#62512yes—
551D4—22no—
552D4—22no—
553D4—21no—
554D4—62no—
555D4—62no—
556D4—121no—
557D4—121no—
558D4C2×#62512yes—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—62no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4#380511yescharacteristic
566C2×C4C2×#62511yescharacteristic
567C2×C4C2×#62511yescharacteristic
568C2×C4#381111yescharacteristic
569C2×C4#381111yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—62no—
572C8—62no—
573C8—92no—
574C8—92no—
575C8—182no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—22no—
582C2×C3—41no—
583C2×C3—41no—
584C2×C3—44no—
585C2×C3—42no—
586C2×C3—42no—
587C2×C3—242no—
588C2×C3#520012yescomplemented
589C2×C3#520312yescomplemented
590C2×C3C2×#93911yescharacteristic
591C2×C3C2×#93911yescharacteristic
592D3—82no—
593C22—22no—
594C22—22no—
595C22—42no—
596C22—122no—
597C22—242no—
598C22—242no—
599C22—242no—
600C22#6398011yescharacteristic
601C22#6398011yescharacteristic
602C22C2×#380511yescharacteristic
603C4—22no—
604C4—122no—
605C4#6398011yescharacteristic
606C4#6398011yescharacteristic
607C4C22×#62511yescharacteristic
608C4C2×#381111yescharacteristic
609C3—21no—
610C3C2×#520011yescharacteristic, complemented
611C3C2×#520311yescharacteristic, complemented
612C2—21no—
613C2—21no—
614C2—42no—
615C2—242no—
616C2#1059168112yesdirect product factor
617C2C2×#6398011yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32#121
prime radicalC2×C3×#949C2
hypercenterC2×#41D32
hypocenterC32C2×#471
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64157C2semidirect
2. C2×C3×#951C2semidirect
4. C22×#3715C2semidirect
5. #10591681C2direct (N × H)
6. C2×#63578C2semidirect
7. C2×#63560C2semidirect
8. C2×#63558C2semidirect
15. #64157C22semidirect
21. C3×#951C22semidirect
33. C2×#3715C22semidirect
34. #63578C22semidirect
35. #63560C22semidirect
36. #63558C22semidirect
39. C2×#951D3semidirect
117. #951C2×D3semidirect
448. C2×C32#471semidirect
538. C32C2×#471semidirect
588. C2×C3#5200semidirect
589. C2×C3#5203semidirect
610. C3C2×#5200semidirect
611. C3C2×#5203semidirect
616. C2#10591681direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641572
C2×C3×#9512
C2×C3×#9492
C22×#37152
#105916812
C2×#635782
C2×#635602
C2×#635582
C2×#52033
C2×#52003