Finite Group Databasebeta

← #41×#611 #11902746

Subgroups — #41×#611 #11902746

Order 1152.

2472 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×#41C211yesmaximal, characteristic, complemented
2C2×#41×D9C211yesmaximal, characteristic, complemented
3#10589936C211yesmaximal, characteristic, complemented
4#10589934C213yesmaximal, complemented
5#10589933C211yesmaximal, characteristic, complemented
6#10589931C213yesmaximal, complemented
7#10589930C213yesmaximal, complemented
8#41×Dic9C211yesmaximal, characteristic, complemented
9#10589926C213yesmaximal, complemented
10#10589919C211yesmaximal, characteristic, complemented
11Q8×#611C211yesmaximal, characteristic, complemented
12#10589908C213yesmaximal, complemented
13D4×#611C213yesmaximal, complemented
14#10589893C213yesmaximal, complemented
15C2×C4×#611C213yesmaximal, complemented
16#41×#67—31nomaximal
17C2×C9×#41—28no—
18C2×C9×#41C2211yescharacteristic
19C2×C9×#41C2213yescomplemented
20C2×C9×#41C2213yescomplemented
21C2×C9×#41C2211yescharacteristic, complemented
22C22×Q8×C9C2211yescharacteristic, complemented
23C22×D4×C9C2213yescomplemented
24C23×C4×C9C2213yescomplemented
25C22×#611C2213yes—
26#41×D9—28no—
27C2×#3701C2211yescharacteristic, complemented
28C2×Q8×D9C2211yescharacteristic, complemented
29C2×#3699C2213yescomplemented
30C2×D4×D9C2213yescomplemented
31C2×#3697C2213yescomplemented
32C22×C4×D9C2213yescomplemented
33#63515C2216yescomplemented
34C2×#3676C2213yescomplemented
35#63509C2213yescomplemented
36#63508C2213yescomplemented
37#63508C2213yescomplemented
38Q8×Dic9C2211yescharacteristic, complemented
39Q8×Dic9C2211yescharacteristic, complemented
40#63506C2213yescomplemented
41#63502C2213yescomplemented
42#63501C2216yescomplemented
43#63501C2216yescomplemented
44#63500C2213yescomplemented
45#63500C2213yescomplemented
46#63499C2216yescomplemented
47#63498C2213yescomplemented
48#63497C2216yescomplemented
49D4×Dic9C2213yescomplemented
50D4×Dic9C2213yescomplemented
51#63492C2213yescomplemented
52#63492C2213yescomplemented
53#63491C2216yescomplemented
54C4×#611C2211yescharacteristic
55C4×#611C2213yes—
56C4×#611C2213yescomplemented
57C4×#611C2213yescomplemented
58C4×#611C2213yescomplemented
59C4×#611C2213yescomplemented
60C4×#611C2213yescomplemented
61C4×#611C2213yescomplemented
62C4×#611C2216yescomplemented
63C2×(C2×D9)⋊C4C2213yescomplemented
64#63488C2213yescomplemented
65#63486C2213yescomplemented
66#63486C2213yescomplemented
67C2×Dic9⋊C4C2213yescomplemented
68C2×C4×Dic9C2213yescomplemented
69C22×C3×#41D311yescharacteristic
70C2×D3×#41—31no—
71#5834—31no—
72#5832—33no—
73#5831—31no—
74#5829—33no—
75#5828—33no—
76Dic3×#41—31no—
77#5824—33no—
78#5817—31no—
79Q8×#67—31no—
80#5806—33no—
81D4×#67—33no—
82#5791—33no—
83C2×C4×#67—33no—
84C24×C9C2313yes—
85C23×D9C2313yes—
86C9×#41—24no—
87C9×#41—212no—
88C9×#41—212no—
89C9×#41D418yescomplemented
90C2×Q8×C9—24no—
91C2×Q8×C9C2313yes—
92C2×Q8×C9C2311yescharacteristic
93C2×D4×C9—212no—
94C2×D4×C9C2316yes—
95C2×D4×C9C2313yes—
96C2×D4×C9C2313yes—
97C22×C4×C9—212no—
98C22×C4×C9C2313yes—
99C22×C4×C9C2311yescharacteristic
100C22×C4×C9C2313yes—
101C22×C4×C9C2313yes—
102C22×C4×C9C2313yes—
103C22×C4×C9C2313yes—
104C2×#611—212no—
105C2×#611C2313yes—
106C2×#611C2313yes—
107C2×#611C2313yes—
108C2×#611C2316yes—
109C2×#611C2316yes—
110C2×#611C2311yescharacteristic
111C22×Dic9C2313yes—
112C22×Dic9C2313yes—
113C22×Dic9C2313yes—
114#3701—24no—
115Q8×D9—24no—
116#3699—212no—
117D4×D9—212no—
118#3697—212no—
119C2×D36C2313yes—
120C2×C4×D9—212no—
121C2×C4×D9C2311yescharacteristic
122C2×C4×D9C2313yes—
123C2×C4×D9C2313yes—
124C2×C4×D9C2313yes—
125C2×Dic18C2313yes—
126#3676C2316yes—
127#3676C2311yescharacteristic
128#3676C2313yes—
129#3676C2313yes—
130#3676C2313yes—
131#3676C2316yes—
132(C2×D9)⋊C4C2311yescharacteristic
133(C2×D9)⋊C4C2313yes—
134(C2×D9)⋊C4C2313yes—
135(C2×D9)⋊C4C2313yes—
136(C2×D9)⋊C4C2316yes—
137C4⋊Dic9C2313yes—
138C4⋊Dic9C2313yes—
139Dic9⋊C4C2311yescharacteristic
140Dic9⋊C4C2313yes—
141Dic9⋊C4C2313yes—
142Dic9⋊C4C2313yes—
143Dic9⋊C4C2316yes—
144C4×Dic9C2313yes—
145C4×Dic9C2311yescharacteristic
146C4×Dic9C2313yes—
147C4×Dic9C2313yes—
148D4×#41—91noSylow
149C2×C3×#41—28no—
150C2×C3×#41C2×D311yescharacteristic
151C2×C3×#41C2×D313yes—
152C2×C3×#41C2×D313yes—
153C2×C3×#41C2×D311yescharacteristic
154C22×C3×Q8C2×D311yescharacteristic
155C22×C3×D4C2×D313yes—
156C23×C3×C4C2×D313yes—
157C22×#67—33no—
158D3×#41—68no—
159C2×#239—31no—
160C2×D3×Q8—31no—
161C2×#237—33no—
162C2×D3×D4—33no—
163C2×#235—33no—
164C22×C4×D3—33no—
165#953—36no—
166C2×#217—33no—
167#947—33no—
168#946—33no—
169#946—33no—
170Q8×Dic3—31no—
171Q8×Dic3—31no—
172#944—33no—
173#940—33no—
174#939—36no—
175#939—36no—
176#938—33no—
177#938—33no—
178#937—36no—
179#936—33no—
180#935—36no—
181D4×Dic3—33no—
182D4×Dic3—33no—
183#930—33no—
184#930—33no—
185#929—36no—
186C4×#67—31no—
187C4×#67—33no—
188C4×#67—33no—
189C4×#67—33no—
190C4×#67—33no—
191C4×#67—33no—
192C4×#67—33no—
193C4×#67—33no—
194C4×#67—36no—
195C2×(C2×D3)⋊C4—33no—
196#926—33no—
197#924—33no—
198#924—33no—
199C2×Dic3⋊C4—33no—
200C2×C4×Dic3—33no—
201C23×C9—26no—
202C23×C9—26no—
203C23×C9—43no—
204C23×C9C2413yes—
205C23×C9C2413yes—
206C23×C9C2411yescharacteristic
207C22×D9—26no—
208C22×D9—26no—
209C22×D9—43no—
210C22×D9C2413yes—
211C22×D9C2411yescharacteristic
212Q8×C9—26no—
213Q8×C9C2×D414yescomplemented
214D4×C9—212no—
215D4×C9—26no—
216D4×C9C2×D4112yescomplemented
217C2×C4×C9—26no—
218C2×C4×C9—22no—
219C2×C4×C9—26no—
220C2×C4×C9—26no—
221C2×C4×C9—26no—
222C2×C4×C9C2×D4112yescomplemented
223C2×C4×C9C2411yescharacteristic
224C2×C4×C9C2413yes—
225C2×C4×C9C2411yescharacteristic
226C2×C4×C9C2413yes—
227#611—212no—
228#611—26no—
229#611—26no—
230#611—26no—
231#611—46no—
232#611#4114yesdirect product factor
233C2×Dic9—26no—
234C2×Dic9—26no—
235C2×Dic9—43no—
236C2×Dic9C2411yescharacteristic
237C2×Dic9C2413yes—
238C2×Dic9C2413yes—
239C2×Dic9C2413yes—
240C2×Dic9C2411yescharacteristic
241C2×Dic9C2411yescharacteristic
242D36—26no—
243C4×D9—22no—
244C4×D9—26no—
245C4×D9—26no—
246C4×D9—26no—
247Dic18—26no—
248C22×#41—91no—
249C22×#41D911yescharacteristic, complemented
250#550—91no—
251D4×Q8—91no—
252#548—91no—
253#548—91no—
254#547—93no—
255#546—93no—
256#546—93no—
257D42—93no—
258#532—93no—
259#525—93no—
260#525—93no—
261C4×#41—91no—
262C2×C4×D4—93no—
263C24×C3C22×D313yes—
264C23×D3—33no—
265C3×#41—24no—
266C3×#41—212no—
267C3×#41—212no—
268C3×#41#6718yes—
269C2×C3×Q8—24no—
270C2×C3×Q8C22×D313yes—
271C2×C3×Q8C22×D311yescharacteristic
272C2×C3×D4—212no—
273C2×C3×D4C22×D316yes—
274C2×C3×D4C22×D313yes—
275C2×C3×D4C22×D313yes—
276C22×C3×C4—212no—
277C22×C3×C4C22×D313yes—
278C22×C3×C4C22×D313yes—
279C22×C3×C4C22×D313yes—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D313yes—
282C22×C3×C4C22×D313yes—
283C2×#67—31no—
284C2×#67—33no—
285C2×#67—33no—
286C2×#67—33no—
287C2×#67—36no—
288C2×#67—36no—
289C2×#67—612no—
290C22×Dic3—33no—
291C22×Dic3—33no—
292C22×Dic3—33no—
293#239—64no—
294D3×Q8—64no—
295#237—612no—
296D3×D4—612no—
297#235—612no—
298C2×D12—33no—
299C2×C4×D3—31no—
300C2×C4×D3—33no—
301C2×C4×D3—33no—
302C2×C4×D3—33no—
303C2×C4×D3—612no—
304C2×Dic6—33no—
305#217—33no—
306#217—36no—
307#217—36no—
308#217—31no—
309#217—33no—
310#217—33no—
311(C2×D3)⋊C4—31no—
312(C2×D3)⋊C4—33no—
313(C2×D3)⋊C4—33no—
314(C2×D3)⋊C4—33no—
315(C2×D3)⋊C4—36no—
316C4⋊Dic3—33no—
317C4⋊Dic3—33no—
318Dic3⋊C4—31no—
319Dic3⋊C4—33no—
320Dic3⋊C4—33no—
321Dic3⋊C4—33no—
322Dic3⋊C4—36no—
323C4×Dic3—31no—
324C4×Dic3—33no—
325C4×Dic3—33no—
326C4×Dic3—33no—
327C22×C9—21no—
328C22×C9—23no—
329C22×C9—23no—
330C22×C9—21no—
331C22×C9—23no—
332C22×C9—23no—
333C22×C9—23no—
334C22×C9—412no—
335C22×C9C22×D416yes—
336C22×C9C2×#4112yescomplemented
337C22×C9C2511yescharacteristic
338C2×D9—21no—
339C2×D9—21no—
340C2×D9—23no—
341C2×D9—23no—
342C2×D9—23no—
343C2×D9—412no—
344C2×D9C2×#4112yescomplemented
345C4×C9—21no—
346C4×C9—23no—
347C4×C9C22×D416yes—
348C4×C9C22×D412yes—
349Dic9—23no—
350Dic9—21no—
351Dic9—23no—
352Dic9—21no—
353Dic9—23no—
354Dic9C2×#4112yescomplemented
355C2×#41—28no—
356C2×#41—91no—
357C2×#41—93no—
358C2×#41—93no—
359C2×#41—188no—
360C2×#41C2×D911yescharacteristic
361C2×#41C2×D913yescomplemented
362C2×#41C2×D913yescomplemented
363C2×#41C2×D911yescharacteristic, complemented
364C22×Q8—91no—
365C22×Q8C2×D911yescharacteristic, complemented
366C22×D4—93no—
367C22×D4—93no—
368C22×D4C2×D913yescomplemented
369C23×C4—93no—
370C23×C4C2×D913yescomplemented
371C4⋊Q8—93no—
372#127—93no—
373#124—93no—
374#124—93no—
375#123—96no—
376#123—96no—
377C22⋊Q8—93no—
378C22⋊Q8—93no—
379C22⋊Q8—93no—
380C22⋊Q8—93no—
381#121—93no—
382#121—93no—
383#121—96no—
384#121—96no—
385#121—93no—
386#121—93no—
387#120—96no—
388#120—96no—
389C4×Q8—91no—
390C4×Q8—91no—
391C4×D4—93no—
392C4×D4—93no—
393C4×D4—91no—
394C4×D4—93no—
395C4×D4—93no—
396C4×D4—93no—
397C4×D4—93no—
398C4×D4—93no—
399C4×D4—93no—
400C4×D4—93no—
401C4×D4—96no—
402#117—93no—
403C2×C4⋊C4—93no—
404C2×C22⋊C4—93no—
405C2×C22⋊C4—93no—
406C2×C42—93no—
407C23×C3—26no—
408C23×C3—26no—
409C23×C3—43no—
410C23×C3C23×D313yes—
411C23×C3C23×D311yescharacteristic
412C23×C3C23×D313yes—
413C22×D3—31no—
414C22×D3—33no—
415C22×D3—66no—
416C22×D3—66no—
417C22×D3—123no—
418C3×Q8—26no—
419C3×Q8C2×#6714yes—
420C3×D4—212no—
421C3×D4—26no—
422C3×D4C2×#67112yes—
423C2×C3×C4—26no—
424C2×C3×C4—22no—
425C2×C3×C4—26no—
426C2×C3×C4—26no—
427C2×C3×C4—26no—
428C2×C3×C4C2×#67112yes—
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D313yes—
431C2×C3×C4C23×D313yes—
432C2×C3×C4C23×D311yescharacteristic
433#67—34no—
434#67—66no—
435#67—66no—
436#67—66no—
437#67—612no—
438#67—126no—
439C2×Dic3—31no—
440C2×Dic3—31no—
441C2×Dic3—33no—
442C2×Dic3—33no—
443C2×Dic3—33no—
444C2×Dic3—31no—
445C2×Dic3—66no—
446C2×Dic3—66no—
447C2×Dic3—123no—
448D12—66no—
449C4×D3—62no—
450C4×D3—66no—
451C4×D3—66no—
452C4×D3—66no—
453Dic6—66no—
454C2×C9—26no—
455C2×C9—22no—
456C2×C9—43no—
457C2×C9C23×D411yescharacteristic
458C2×C9C22×#4111yescharacteristic
459C2×C9#58511yescharacteristic
460D9—22no—
461D9—43no—
462C24—93no—
463C24C22×D913yes—
464#41—24no—
465#41—212no—
466#41—212no—
467#41—184no—
468#41—1812no—
469#41—1812no—
470#41#61118yesdirect product factor
471C2×Q8—24no—
472C2×Q8—93no—
473C2×Q8—184no—
474C2×Q8C22×D913yes—
475C2×Q8C22×D911yescharacteristic
476C2×D4—212no—
477C2×D4—91no—
478C2×D4—93no—
479C2×D4—93no—
480C2×D4—93no—
481C2×D4—96no—
482C2×D4—96no—
483C2×D4—93no—
484C2×D4—1812no—
485C2×D4—1812no—
486C2×D4C22×D916yes—
487C2×D4C22×D913yes—
488C2×D4C22×D913yes—
489C22×C4—212no—
490C22×C4—93no—
491C22×C4—93no—
492C22×C4—93no—
493C22×C4—93no—
494C22×C4—93no—
495C22×C4—91no—
496C22×C4—93no—
497C22×C4—1812no—
498C22×C4C22×D913yes—
499C22×C4C22×D913yes—
500C22×C4C22×D913yes—
501C22×C4C22×D911yescharacteristic
502C22×C4C22×D913yes—
503C22×C4C22×D913yes—
504C4⋊C4—91no—
505C4⋊C4—93no—
506C4⋊C4—93no—
507C4⋊C4—93no—
508C4⋊C4—93no—
509C4⋊C4—93no—
510C4⋊C4—96no—
511C22⋊C4—91no—
512C22⋊C4—93no—
513C22⋊C4—93no—
514C22⋊C4—93no—
515C22⋊C4—96no—
516C22⋊C4—96no—
517C22⋊C4—91no—
518C22⋊C4—93no—
519C22⋊C4—93no—
520C22⋊C4—93no—
521C22⋊C4—96no—
522C42—93no—
523C42—93no—
524C42—91no—
525C42—93no—
526C22×C3—23no—
527C22×C3—23no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—23no—
531C22×C3—23no—
532C22×C3—23no—
533C22×C3—412no—
534C22×C3D3×#4112yes—
535C22×C3C22×#6716yes—
536C22×C3C24×D311yescharacteristic
537C2×D3—32no—
538C2×D3—61no—
539C2×D3—61no—
540C2×D3—63no—
541C2×D3—63no—
542C2×D3—63no—
543C2×D3—1212no—
544C3×C4—21no—
545C3×C4—23no—
546C3×C4C22×#6716yes—
547C3×C4C22×#6712yes—
548Dic3—32no—
549Dic3—63no—
550Dic3—61no—
551Dic3—63no—
552Dic3—63no—
553Dic3—61no—
554C9D4×#4111yescharacteristic, complemented, Sylow
555C23—26no—
556C23—26no—
557C23—43no—
558C23—91no—
559C23—93no—
560C23—186no—
561C23—186no—
562C23—363no—
563C23C23×D913yes—
564C23C23×D911yescharacteristic
565C23C23×D913yes—
566Q8—26no—
567Q8—186no—
568Q8C2×#61114yescomplemented
569D4—212no—
570D4—26no—
571D4—94no—
572D4—186no—
573D4—186no—
574D4—186no—
575D4—1812no—
576D4—186no—
577D4—366no—
578D4C2×#611112yescomplemented
579C2×C4—26no—
580C2×C4—22no—
581C2×C4—26no—
582C2×C4—26no—
583C2×C4—26no—
584C2×C4—91no—
585C2×C4—91no—
586C2×C4—93no—
587C2×C4—93no—
588C2×C4—91no—
589C2×C4—93no—
590C2×C4—186no—
591C2×C4—186no—
592C2×C4—182no—
593C2×C4—186no—
594C2×C4—186no—
595C2×C4—186no—
596C2×C4—363no—
597C2×C4C2×#611112yescomplemented
598C2×C4C23×D911yescharacteristic
599C2×C4C23×D913yes—
600C2×C4C23×D913yes—
601C2×C4C23×D911yescharacteristic
602C2×C3—26no—
603C2×C3—22no—
604C2×C3—43no—
605C2×C3C2×D3×#4111yescharacteristic
606C2×C3#596411yescharacteristic
607C2×C3C23×#6711yescharacteristic
608D3—62no—
609D3—123no—
610C22—23no—
611C22—23no—
612C22—21no—
613C22—21no—
614C22—23no—
615C22—23no—
616C22—23no—
617C22—412no—
618C22—92no—
619C22—181no—
620C22—181no—
621C22—183no—
622C22—183no—
623C22—183no—
624C22—3612no—
625C22#41×D912yescomplemented
626C22C22×#61116yes—
627C22C24×D911yescharacteristic
628C4—21no—
629C4—23no—
630C4—92no—
631C4—183no—
632C4—181no—
633C4—183no—
634C4—181no—
635C4—183no—
636C4C22×#61112yes—
637C4C22×#61116yes—
638C3#41×#6711yescharacteristic
639C2—22no—
640C2—26no—
641C2—43no—
642C2—182no—
643C2—363no—
644C2C2×#41×D911yescharacteristic
645C2#1059313911yescharacteristic
646C2C23×#61111yescharacteristic
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC22×C9×#41C2
hypercenterC22×#41D9
hypocenterC9D4×#41
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C9×#41C2semidirect
2. C2×#41×D9C2semidirect
3. #10589936C2semidirect
4. #10589934C2semidirect
5. #10589933C2semidirect
6. #10589931C2semidirect
7. #10589930C2semidirect
8. #41×Dic9C2semidirect
9. #10589926C2semidirect
10. #10589919C2semidirect
11. Q8×#611C2semidirect
12. #10589908C2semidirect
13. D4×#611C2semidirect
14. #10589893C2semidirect
15. C2×C4×#611C2semidirect
19. C2×C9×#41C22semidirect
20. C2×C9×#41C22semidirect
21. C2×C9×#41C22semidirect
22. C22×Q8×C9C22semidirect
23. C22×D4×C9C22semidirect
24. C23×C4×C9C22semidirect
27. C2×#3701C22semidirect
28. C2×Q8×D9C22semidirect
29. C2×#3699C22semidirect
30. C2×D4×D9C22semidirect
31. C2×#3697C22semidirect
32. C22×C4×D9C22semidirect
33. #63515C22semidirect
34. C2×#3676C22semidirect
35. #63509C22semidirect
36. #63508C22semidirect
37. #63508C22semidirect
38. Q8×Dic9C22semidirect
39. Q8×Dic9C22semidirect
40. #63506C22semidirect
41. #63502C22semidirect
42. #63501C22semidirect
43. #63501C22semidirect
44. #63500C22semidirect
45. #63500C22semidirect
46. #63499C22semidirect
47. #63498C22semidirect
48. #63497C22semidirect
49. D4×Dic9C22semidirect
50. D4×Dic9C22semidirect
51. #63492C22semidirect
52. #63492C22semidirect
53. #63491C22semidirect
56. C4×#611C22semidirect
57. C4×#611C22semidirect
58. C4×#611C22semidirect
59. C4×#611C22semidirect
60. C4×#611C22semidirect
61. C4×#611C22semidirect
62. C4×#611C22semidirect
63. C2×(C2×D9)⋊C4C22semidirect
64. #63488C22semidirect
65. #63486C22semidirect
66. #63486C22semidirect
67. C2×Dic9⋊C4C22semidirect
68. C2×C4×Dic9C22semidirect
89. C9×#41D4semidirect
213. Q8×C9C2×D4semidirect
216. D4×C9C2×D4semidirect
222. C2×C4×C9C2×D4semidirect
232. #611#41direct (N × H)
249. C22×#41D9semidirect
336. C22×C9C2×#41semidirect
344. C2×D9C2×#41semidirect
354. Dic9C2×#41semidirect
361. C2×#41C2×D9semidirect
362. C2×#41C2×D9semidirect
363. C2×#41C2×D9semidirect
365. C22×Q8C2×D9semidirect
368. C22×D4C2×D9semidirect
370. C23×C4C2×D9semidirect
470. #41#611direct (N × H)
554. C9D4×#41semidirect
568. Q8C2×#611semidirect
578. D4C2×#611semidirect
597. C2×C4C2×#611semidirect
625. C22#41×D9semidirect

Maximal subgroups

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

subgroupindex
C22×C9×#412
C2×#41×D92
#105899362
#105899342
#105899332
#105899312
#105899302
#41×Dic92
#105899262
#105899192
Q8×#6112
#105899082
D4×#6112
#105898932
C2×C4×#6112
#41×#673