Finite Group Databasebeta

← C2×#10595101 #11918761

Subgroups — C2×#10595101 #11918761

Order 1152.

3413 conjugacy classes of subgroups.

The subgroup lattice has 693 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3C2×C3×#932C212yesmaximal, complemented
4C2×#63936C214yesmaximal, complemented
5C2×#63931C212yesmaximal, complemented
6#10595101C2116yesmaximal, direct product factor
7C2×#63927C212yesmaximal, complemented
8C2×#63831C212yesmaximal, complemented
9C2×#63818C211yesmaximal, characteristic, complemented
10C2×#5773—32nomaximal
11C22×C32×D4C2211yescharacteristic, complemented
12C22×#638—21no—
13C23×C3⋊Dic3—21no—
14C2×#3830—21no—
15C2×#3830—21no—
16C2×#3830—24no—
17C2×#3830C2212yes—
18C2×#3830C2212yescomplemented
19C2×#3830C2218yescomplemented
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C2×C3×#235C2212yes—
23C2×#3811—21no—
24C2×#3805—21no—
25#64306—24no—
26#64306C2218yescomplemented
27C2×#3802C2211yescharacteristic, complemented
28C2×C4×D32—21no—
29C2×#3798—21no—
30C2×#3797C2211yescharacteristic, complemented
31C2×#3796C2212yescomplemented
32C2×C3×#214C2214yescomplemented
33C3×#932C22116yescomplemented
34C2×C3×#213C2214yescomplemented
35C2×C3×#208C2212yescomplemented
36#63936C22132yescomplemented
37#63931C22116yescomplemented
38#63927C22116yescomplemented
39C2×#3719C2214yescomplemented
40#63831C22116yescomplemented
41C2×#3716C2214yescomplemented
42C2×#3712C2212yescomplemented
43#63818C2218yescomplemented
44C2×#3710C2212yescomplemented
45C2×D3×#41—32no—
46C22×#237—32no—
47C22×#237—61no—
48C2×C3×AGL(1,ℤ/8)—32no—
49C2×#951—32no—
50C2×#932D312yescomplemented
51#5773—332no—
52C2×#916—34no—
53C2×#915—34no—
54C2×#912—34no—
55C2×#911—34no—
56C2×#909—32no—
57C2×D3×M16—32no—
58C24×C32—21no—
59C23×C3⋊D3D411yescharacteristic
60C22×D32—21no—
61C2×C32×D4—21no—
62C2×C32×D4—22no—
63C2×C32×D4C2312yes—
64C2×C32×D4C2314yescomplemented
65C22×C32×C4C2311yescharacteristic
66C2×#638—22no—
67C2×#638—22no—
68C2×#638—28no—
69C22×C3⋊Dic3—21no—
70C22×C3⋊Dic3—22no—
71C22×C3⋊Dic3—22no—
72C22×C3⋊Dic3—28no—
73C22×C3⋊Dic3D411yescharacteristic
74#3830—24no—
75#3830—24no—
76#3830—28no—
77#3830—28no—
78#3830C2318yes—
79#3830C2318yescomplemented
80C2×C4×C3⋊D3D411yescharacteristic
81C2×C4×C3⋊D3D411yescharacteristic
82C2×C4×C3⋊D3D414yes—
83C2×C4×C3⋊D3C2311yescharacteristic
84C2×C4×C3⋊D3C2311yescharacteristic
85C2×C4×C3⋊D3C2314yes—
86C2×#634—22no—
87C2×#634—21no—
88C2×#634C2312yes—
89C2×#634C2314yescomplemented
90C2×C3×#67—22no—
91C3×#235—24no—
92C3×#235C2318yes—
93C2×C3×D12C2312yes—
94C2×C3×C4×D3—22no—
95C2×C3×Dic6C2312yes—
96#3811—28no—
97C2×#627—21no—
98C2×#626—22no—
99C2×#625—21no—
100C2×#624—21no—
101#3805—28no—
102C2×D3×Dic3—22no—
103#3802—22no—
104#3802C2314yescomplemented
105C4×D32—28no—
106#3798—28no—
107#3797—22no—
108#3797C2314yescomplemented
109#3796—24no—
110#3796C2318yescomplemented
111C3×#214C23116yescomplemented
112C3×#213C23116yescomplemented
113C3×#208C2318yescomplemented
114C2×C3×C3⋊C8C2314yes—
115#3719C23116yescomplemented
116#3716C23116yescomplemented
117#3712C2318yescomplemented
118#3710C2318yescomplemented
119C2×#575—91noSylow
120C2×C3×#41—32no—
121C22×C3×D4—21no—
122C22×C3×D4C2×D312yescomplemented
123C22×#67—62no—
124C22×#67—62no—
125C23×Dic3—62no—
126C23×Dic3—62no—
127D3×#41—316no—
128D3×#41—68no—
129C2×#239—32no—
130C2×D3×Q8—32no—
131C2×#237—34no—
132C2×#237—34no—
133C2×#237—316no—
134C2×#237—32no—
135C2×#237—62no—
136C2×#237—62no—
137C2×#237—68no—
138C2×#237—62no—
139C2×#237—62no—
140C2×#237—68no—
141C2×#237—62no—
142C2×#237—62no—
143C2×#237—62no—
144C2×#237—68no—
145C2×D3×D4—32no—
146C2×D3×D4—62no—
147C2×#235—62no—
148C2×#235C2×D312yes—
149C22×C4×D3—32no—
150C22×C4×D3—61no—
151C22×C4×D3—62no—
152C22×Dic6—32no—
153C22×Dic6—61no—
154C3×AGL(1,ℤ/8)—316no—
155C2×C3×SD16—34no—
156C2×C3×D8—34no—
157C2×C3×M16—32no—
158#951—316no—
159C2×#216—34no—
160C2×#214—34no—
161C2×#214C2×D314yescomplemented
162#932C2×D3116yescomplemented
163C2×#213C2×D314yescomplemented
164C2×#208C2×D312yescomplemented
165#916—332no—
166#915—332no—
167#912—332no—
168#911—332no—
169#909—316no—
170D3×M16—316no—
171C2×Dic12—34no—
172C2×#204—34no—
173C2×ΓL(1,𝔽25)—34no—
174C2×D3×C8—34no—
175C23×C32—22no—
176C23×C32—24no—
177C23×C32—44no—
178C23×C32C2×D411yescharacteristic
179C22×C3⋊D3—42no—
180C22×C3⋊D3C2×D411yescharacteristic
181C22×C3⋊D3C2×D411yescharacteristic
182C22×C3⋊D3C2×D414yes—
183C22×C3×D3—22no—
184C2×D32—24no—
185C2×D32—44no—
186C32×D4—22no—
187C32×D4—24no—
188C32×D4C2414yes—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D412yes—
191C2×C32×C4C2411yescharacteristic
192C2×C32×C4C2412yes—
193#638—28no—
194#638—28no—
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—24no—
197C2×C3⋊Dic3—28no—
198C2×C3⋊Dic3—28no—
199C2×C3⋊Dic3C2×D411yescharacteristic
200C2×C3⋊Dic3C2×D414yes—
201C2×C3⋊Dic3C2×D411yescharacteristic
202C4×C3⋊D3C2×D412yes—
203C4×C3⋊D3C2×D412yes—
204C4×C3⋊D3C2×D414yes—
205C4×C3⋊D3C2×D414yes—
206C4×C3⋊D3C2412yes—
207C4×C3⋊D3C2412yes—
208#634—22no—
209#634—24no—
210#634C2414yes—
211C3×#67—28no—
212C2×C3×Dic3—22no—
213C3×D12—22no—
214C3×D12C2414yes—
215C3×C4×D3—28no—
216C3×Dic6—22no—
217C3×Dic6C2414yes—
218#627—24no—
219#626—28no—
220#625—24no—
221#624—24no—
222D3×Dic3—28no—
223C3×C3⋊C8C2418yes—
224C22×#41—91no—
225C22×#41—91no—
226#575—916no—
227C2×#137—92no—
228C2×#137—92no—
229C2×AGL(1,ℤ/8)—32no—
230C2×AGL(1,ℤ/8)—92no—
231C2×#135—94no—
232C22×M16—91no—
233C24×C3—22no—
234C24×C3—22no—
235C23×D3—32no—
236C23×D3—61no—
237C23×D3—62no—
238C3×#41—38no—
239C3×#41—64no—
240C2×C3×Q8—32no—
241C2×C3×D4—24no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—24no—
245C2×C3×D4—22no—
246C2×C3×D4—24no—
247C2×C3×D4—32no—
248C2×C3×D4—62no—
249C2×C3×D4C22×D314yes—
250C2×C3×D4C22×D318yescomplemented
251C22×C3×C4—21no—
252C22×C3×C4—62no—
253C22×C3×C4C22×D312yes—
254C2×#67—22no—
255C2×#67—62no—
256C2×#67—62no—
257C2×#67—64no—
258C2×#67—64no—
259C2×#67—616no—
260C2×#67—64no—
261C2×#67—616no—
262C2×#67—64no—
263C22×Dic3—32no—
264C22×Dic3—61no—
265C22×Dic3—62no—
266C22×Dic3—64no—
267C22×Dic3—64no—
268C22×Dic3—616no—
269C22×Dic3—62no—
270C22×Dic3—64no—
271C22×Dic3—616no—
272C22×Dic3—64no—
273C22×Dic3—62no—
274#239—38no—
275#239—64no—
276D3×Q8—38no—
277D3×Q8—64no—
278#237—316no—
279#237—316no—
280#237—38no—
281#237—68no—
282#237—68no—
283#237—64no—
284#237—616no—
285#237—616no—
286#237—68no—
287#237—68no—
288#237—616no—
289#237—68no—
290#237—616no—
291#237—68no—
292#237—616no—
293D3×D4—38no—
294D3×D4—64no—
295D3×D4—616no—
296#235—24no—
297#235—616no—
298#235C22×D318yes—
299C2×D12—62no—
300C2×D12C22×D312yes—
301C2×C4×D3—22no—
302C2×C4×D3—32no—
303C2×C4×D3—32no—
304C2×C4×D3—38no—
305C2×C4×D3—32no—
306C2×C4×D3—32no—
307C2×C4×D3—38no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3—64no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—64no—
314C2×C4×D3—616no—
315C2×C4×D3—62no—
316C2×C4×D3—62no—
317C2×Dic6—34no—
318C2×Dic6—38no—
319C2×Dic6—62no—
320C2×Dic6—64no—
321C2×Dic6—62no—
322C2×Dic6—64no—
323C2×Dic6—62no—
324C2×Dic6—62no—
325C2×Dic6—64no—
326C2×Dic6C22×D312yes—
327C3×SD16—316no—
328C3×D8—316no—
329C3×M16—38no—
330C2×C3×C8—34no—
331#216—316no—
332#214—316no—
333#214C22×D3116yescomplemented
334#213C22×D3116yescomplemented
335#208C22×D318yescomplemented
336C2×C3⋊C8C22×D314yes—
337Dic12—316no—
338#204—316no—
339ΓL(1,𝔽25)—316no—
340D3×C8—316no—
341C22×C32—22no—
342C22×C32—24no—
343C22×C32—48no—
344C22×C32—44no—
345C22×C32C22×D412yes—
346C22×C32C22×D411yescharacteristic
347C2×C3⋊D3—22no—
348C2×C3⋊D3—22no—
349C2×C3⋊D3—44no—
350C2×C3⋊D3C22×D412yes—
351C2×C3⋊D3C22×D412yes—
352C2×C3×D3—24no—
353C2×C3×D3—44no—
354D32—48no—
355C32×C4C22×D411yescharacteristic
356C32×C4C22×D412yes—
357C32×C4C2511yescharacteristic
358C3⋊Dic3—24no—
359C3⋊Dic3C22×D412yes—
360C3⋊Dic3C22×D412yes—
361C3×Dic3—24no—
362C2×#41—32no—
363C2×#41—92no—
364C2×#41—98no—
365C2×#41—92no—
366C2×#41—92no—
367C2×#41—98no—
368C2×#41—181no—
369C2×#41—181no—
370C2×#41—184no—
371C2×#41—181no—
372C2×#41—181no—
373C2×#41—184no—
374C22×Q8—91no—
375C22×Q8—91no—
376C22×D4—91no—
377C22×D4—181no—
378C22×D4—181no—
379C22×D4D3211yescharacteristic, complemented
380C23×C4—91no—
381C23×C4—181no—
382C23×C4—181no—
383#137—916no—
384#137—916no—
385AGL(1,ℤ/8)—316no—
386AGL(1,ℤ/8)—916no—
387#135—932no—
388C2×Q16—94no—
389C2×SD16—34no—
390C2×SD16—94no—
391C2×D8—34no—
392C2×M16—32no—
393C2×M16—92no—
394C2×M16—98no—
395C22×C8—92no—
396C23×C3—28no—
397C23×C3—24no—
398C23×C3—24no—
399C23×C3—28no—
400C23×C3—21no—
401C23×C3—48no—
402C23×C3—48no—
403C23×C3—62no—
404C23×C3D3×D412yes—
405C22×D3—22no—
406C22×D3—32no—
407C22×D3—32no—
408C22×D3—38no—
409C22×D3—61no—
410C22×D3—61no—
411C22×D3—64no—
412C22×D3—68no—
413C22×D3—128no—
414C22×D3—124no—
415C22×D3—124no—
416C3×Q8—34no—
417C3×Q8—62no—
418C3×D4—24no—
419C3×D4—28no—
420C3×D4—24no—
421C3×D4—28no—
422C3×D4—24no—
423C3×D4—34no—
424C3×D4—68no—
425C3×D4—62no—
426C3×D4C23×D318yes—
427C2×C3×C4—22no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—62no—
432C2×C3×C4—68no—
433C2×C3×C4D3×D412yes—
434C2×C3×C4D3×D414yes—
435C2×C3×C4C23×D312yes—
436C2×C3×C4C23×D314yes—
437#67—28no—
438#67—68no—
439#67—68no—
440#67—616no—
441#67—616no—
442#67—616no—
443#67—616no—
444C2×Dic3—22no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—38no—
448C2×Dic3—64no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—68no—
452C2×Dic3—616no—
453C2×Dic3—616no—
454C2×Dic3—68no—
455C2×Dic3—64no—
456C2×Dic3—616no—
457C2×Dic3—616no—
458C2×Dic3—68no—
459C2×Dic3—64no—
460D12—22no—
461D12—68no—
462D12C23×D314yes—
463C4×D3—28no—
464C4×D3—38no—
465C4×D3—38no—
466C4×D3—34no—
467C4×D3—34no—
468C4×D3—34no—
469C4×D3—34no—
470C4×D3—64no—
471C4×D3—62no—
472C4×D3—62no—
473C4×D3—64no—
474C4×D3—62no—
475C4×D3—62no—
476C4×D3—68no—
477C4×D3—68no—
478Dic6—22no—
479Dic6—38no—
480Dic6—64no—
481Dic6—68no—
482Dic6—64no—
483Dic6—68no—
484Dic6—64no—
485Dic6—68no—
486Dic6C23×D314yes—
487C3×C8—38no—
488C3⋊C8C23×D318yes—
489C2×C32—22no—
490C2×C32—44no—
491C2×C32#57512yescomplemented
492C2×C32C23×D411yescharacteristic
493C3⋊D3—22no—
494C3⋊D3—22no—
495C3×D3—44no—
496C24—21no—
497C24—91no—
498C24—181no—
499#41—38no—
500#41—64no—
501#41—98no—
502#41—98no—
503#41—98no—
504#41—188no—
505#41—188no—
506#41—184no—
507#41—184no—
508#41—188no—
509#41—188no—
510#41—184no—
511C2×Q8—32no—
512C2×Q8—94no—
513C2×Q8—92no—
514C2×Q8—94no—
515C2×Q8—181no—
516C2×Q8—182no—
517C2×Q8—182no—
518C2×Q8—181no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—32no—
522C2×D4—62no—
523C2×D4—94no—
524C2×D4—182no—
525C2×D4—182no—
526C2×D4—181no—
527C2×D4—188no—
528C2×D4—188no—
529C2×D4—182no—
530C2×D4—182no—
531C2×D4C2×D3212yes—
532C2×D4C2×D3214yescomplemented
533C22×C4—62no—
534C22×C4—91no—
535C22×C4—91no—
536C22×C4—91no—
537C22×C4—94no—
538C22×C4—91no—
539C22×C4—94no—
540C22×C4—91no—
541C22×C4—188no—
542C22×C4—181no—
543C22×C4—182no—
544C22×C4—188no—
545C22×C4—182no—
546C22×C4—182no—
547C22×C4—181no—
548C22×C4C2×D3211yescharacteristic
549Q16—916no—
550SD16—316no—
551SD16—916no—
552D8—316no—
553M16—38no—
554M16—98no—
555C2×C8—34no—
556C2×C8—98no—
557C22×C3—24no—
558C22×C3—24no—
559C22×C3—28no—
560C22×C3—28no—
561C22×C3—22no—
562C22×C3—21no—
563C22×C3—416no—
564C22×C3—416no—
565C22×C3—48no—
566C22×C3—48no—
567C22×C3—64no—
568C22×C3—124no—
569C22×C3C2×D3×D414yes—
570C22×C3C2×D3×D412yes—
571C2×D3—24no—
572C2×D3—34no—
573C2×D3—34no—
574C2×D3—44no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—64no—
578C2×D3—64no—
579C2×D3—122no—
580C2×D3—122no—
581C2×D3—1216no—
582C2×D3—128no—
583C2×D3—128no—
584C3×C4—22no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—64no—
588C3×C4C2×D3×D412yes—
589C3×C4C2×D3×D414yes—
590C3×C4C24×D312yes—
591Dic3—24no—
592Dic3—34no—
593Dic3—34no—
594Dic3—62no—
595Dic3—62no—
596Dic3—68no—
597Dic3—68no—
598C32C2×#57511yescharacteristic, complemented, Sylow
599C23—24no—
600C23—22no—
601C23—44no—
602C23—62no—
603C23—91no—
604C23—91no—
605C23—94no—
606C23—184no—
607C23—362no—
608C23—364no—
609C23#381111yescharacteristic
610Q8—34no—
611Q8—62no—
612Q8—94no—
613Q8—184no—
614Q8—184no—
615Q8—182no—
616D4—22no—
617D4—24no—
618D4—34no—
619D4—68no—
620D4—62no—
621D4—188no—
622D4—184no—
623D4—188no—
624D4—188no—
625D4C22×D3214yes—
626C2×C4—62no—
627C2×C4—68no—
628C2×C4—94no—
629C2×C4—91no—
630C2×C4—91no—
631C2×C4—94no—
632C2×C4—92no—
633C2×C4—92no—
634C2×C4—94no—
635C2×C4—92no—
636C2×C4—92no—
637C2×C4—184no—
638C2×C4—188no—
639C2×C4—188no—
640C2×C4—188no—
641C2×C4—184no—
642C2×C4—182no—
643C2×C4#381112yes—
644C2×C4#381111yescharacteristic
645C2×C4C22×D3212yes—
646C2×C4C22×D3211yescharacteristic
647C8—38no—
648C2×C3—24no—
649C2×C3—24no—
650C2×C3—22no—
651C2×C3—21no—
652C2×C3—48no—
653C2×C3—48no—
654C2×C3—124no—
655C2×C3#577314yescomplemented
656C2×C3C22×D3×D412yes—
657D3—44no—
658D3—64no—
659D3—64no—
660D3—122no—
661D3—122no—
662C22—22no—
663C22—24no—
664C22—48no—
665C22—44no—
666C22—64no—
667C22—92no—
668C22—92no—
669C22—124no—
670C22—182no—
671C22—182no—
672C22—364no—
673C22—368no—
674C22C2×#381112yes—
675C22C2×#381111yescharacteristic
676C4—64no—
677C4—92no—
678C4—92no—
679C4—184no—
680C4C2×#381112yes—
681C4C2×#381111yescharacteristic
682C4C23×D3211yescharacteristic
683C3—21no—
684C3C2×#577312yescomplemented
685C2—22no—
686C2—44no—
687C2—124no—
688C2—182no—
689C2—182no—
690C2#1059510112yesdirect product factor
691C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#575
LCSG ▷ 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×#3830C2semidirect
2. C2×#64306C2semidirect
3. C2×C3×#932C2semidirect
4. C2×#63936C2semidirect
5. C2×#63931C2semidirect
6. #10595101C2direct (N × H)
7. C2×#63927C2semidirect
8. C2×#63831C2semidirect
9. C2×#63818C2semidirect
11. C22×C32×D4C22semidirect
18. C2×#3830C22semidirect
19. C2×#3830C22semidirect
21. C22×#634C22semidirect
26. #64306C22semidirect
27. C2×#3802C22semidirect
30. C2×#3797C22semidirect
31. C2×#3796C22semidirect
32. C2×C3×#214C22semidirect
33. C3×#932C22semidirect
34. C2×C3×#213C22semidirect
35. C2×C3×#208C22semidirect
36. #63936C22semidirect
37. #63931C22semidirect
38. #63927C22semidirect
39. C2×#3719C22semidirect
40. #63831C22semidirect
41. C2×#3716C22semidirect
42. C2×#3712C22semidirect
43. #63818C22semidirect
44. C2×#3710C22semidirect
50. C2×#932D3semidirect
64. C2×C32×D4C23semidirect
79. #3830C23semidirect
89. C2×#634C23semidirect
104. #3802C23semidirect
108. #3797C23semidirect
110. #3796C23semidirect
111. C3×#214C23semidirect
112. C3×#213C23semidirect
113. C3×#208C23semidirect
115. #3719C23semidirect
116. #3716C23semidirect
117. #3712C23semidirect
118. #3710C23semidirect
122. C22×C3×D4C2×D3semidirect
161. C2×#214C2×D3semidirect
162. #932C2×D3semidirect
163. C2×#213C2×D3semidirect
164. C2×#208C2×D3semidirect
250. C2×C3×D4C22×D3semidirect
333. #214C22×D3semidirect
334. #213C22×D3semidirect
335. #208C22×D3semidirect
379. C22×D4D32semidirect
491. C2×C32#575semidirect
532. C2×D4C2×D32semidirect
598. C32C2×#575semidirect
655. C2×C3#5773semidirect
684. C3C2×#5773semidirect
690. C2#10595101direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C2×#643062
C2×C3×#9322
C2×#639362
C2×#639312
#105951012
C2×#639272
C2×#638312
C2×#638182
C2×#57733