Finite Group Databasebeta

← #11902758

Subgroups — #11902758

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
1C2×#41×D9C211yesmaximal, characteristic, complemented
2C22×#3701C211yesmaximal, characteristic, complemented
3C9×#548C211yesmaximal, characteristic, complemented
4#10589936C211yesmaximal, characteristic, complemented
5Q8×#611C211yesmaximal, characteristic, complemented
6#10589778C213yesmaximal, complemented
7#10589770C213yesmaximal, complemented
8#10589733C213yesmaximal, complemented
9#10589729C213yesmaximal, complemented
10#10589711C213yesmaximal, complemented
11#10589708C213yesmaximal, complemented
12#10589678C211yesmaximal, characteristic, complemented
13C4×#3701C211yesmaximal, characteristic, complemented
14#10589652C213yesmaximal, complemented
15C4×D4×D9C213yesmaximal, complemented
16#86710—31nomaximal
17C2×C9×#41C2211yescharacteristic, complemented
18C22×Q8×C9C2211yescharacteristic, complemented
19#41×D9—28no—
20C2×#3701—28no—
21C2×#3701C2211yescharacteristic
22C2×#3701C2213yescomplemented
23C2×#3701C2213yescomplemented
24C2×#3701C2211yescharacteristic, complemented
25C2×Q8×D9C2211yescharacteristic, complemented
26C2×#3699C2213yescomplemented
27C2×D4×D9C2213yes—
28C2×D4×D9C2213yescomplemented
29C2×#3697C2213yescomplemented
30C22×D36C2213yescomplemented
31C22×C4×D9C2213yescomplemented
32C22×C4×D9C2213yescomplemented
33C9×#124C2213yescomplemented
34C9×C22⋊Q8C2213yescomplemented
35C9×#121C2213yescomplemented
36C4×Q8×C9C2211yescharacteristic, complemented
37C4×D4×C9C2213yescomplemented
38#63508C2213yescomplemented
39Q8×Dic9C2211yescharacteristic, complemented
40#63506C2213yescomplemented
41#63502C2213yescomplemented
42#63500C2213yescomplemented
43#63499C2216yescomplemented
44D4×Dic9C2213yescomplemented
45#63492C2213yescomplemented
46C4×#611C2213yes—
47C4×#611C2213yescomplemented
48#63486C2213yescomplemented
49#63459C2213yescomplemented
50#63457C2213yescomplemented
51#63456C2216yescomplemented
52#63455C2213yescomplemented
53#63455C2213yescomplemented
54#63454C2213yescomplemented
55C4⋊C4×D9C2213yescomplemented
56#63446C2216yescomplemented
57#63446C2216yescomplemented
58#63445C2216yescomplemented
59#63444C2216yescomplemented
60#611⋊C4C2211yescharacteristic
61#611⋊C4C2216yescomplemented
62#611⋊C4C2213yescomplemented
63C22⋊C4×D9C2213yescomplemented
64C22⋊C4×D9C2213yescomplemented
65#63437C2213yescomplemented
66C4×D36C2213yescomplemented
67C4×D36C2213yescomplemented
68C42×D9C2213yescomplemented
69C2×D3×#41—31no—
70C22×#239—31no—
71C3×#548D311yescharacteristic
72#5834—31no—
73Q8×#67—31no—
74#5676—33no—
75#5668—33no—
76#5631—33no—
77#5627—33no—
78#5609—33no—
79#5606—33no—
80#5576—31no—
81C4×#239—31no—
82#5550—33no—
83C4×D3×D4—33no—
84C23×D9C2313yes—
85C23×D9C2313yes—
86C9×#41—24no—
87C2×Q8×C9—24no—
88C2×Q8×C9C2313yes—
89C2×Q8×C9C2311yescharacteristic
90C2×D4×C9C2313yes—
91C2×D4×C9C2313yes—
92C22×C4×C9C2313yes—
93C22×C4×C9C2313yes—
94C2×#611C2313yes—
95C2×#611C2316yes—
96C2×#611C2316yes—
97C2×#611C2311yescharacteristic
98C22×Dic9C2311yescharacteristic
99C22×Dic9C2313yes—
100#3701—24no—
101#3701—212no—
102#3701—212no—
103#3701D418yescomplemented
104Q8×D9—24no—
105#3699—212no—
106D4×D9—212no—
107D4×D9—212no—
108#3697—212no—
109C2×D36—212no—
110C2×D36C2313yes—
111C2×D36C2313yes—
112C2×D36C2316yes—
113C2×D36C2313yes—
114C2×C4×D9—212no—
115C2×C4×D9—212no—
116C2×C4×D9C2313yes—
117C2×C4×D9C2313yes—
118C2×C4×D9C2313yes—
119C2×C4×D9C2313yes—
120C2×C4×D9C2313yes—
121C2×C4×D9C2311yescharacteristic
122C2×C4×D9C2313yes—
123C2×C4×D9C2313yes—
124C2×C4×D9C2313yes—
125C2×Dic18C2313yes—
126C9×C4⋊C4C2313yes—
127C9×C4⋊C4C2313yes—
128C9×C22⋊C4C2311yescharacteristic
129C9×C22⋊C4C2313yes—
130C9×C22⋊C4C2316yes—
131C42×C9C2313yes—
132#3676C2313yes—
133#3676C2313yes—
134(C2×D9)⋊C4C2313yes—
135(C2×D9)⋊C4C2313yes—
136(C2×D9)⋊C4C2316yes—
137(C2×D9)⋊C4C2316yes—
138(C2×D9)⋊C4C2311yescharacteristic
139(C2×D9)⋊C4C2313yes—
140C4⋊Dic9C2313yes—
141C4⋊Dic9C2313yes—
142Dic9⋊C4C2313yes—
143Dic9⋊C4C2311yescharacteristic
144Dic9⋊C4C2316yes—
145C4×Dic9C2313yes—
146C4×Dic9C2313yes—
147C4×Dic9C2311yescharacteristic
148D4×#41—91noSylow
149C2×C3×#41C2×D311yescharacteristic
150C22×C3×Q8C2×D311yescharacteristic
151D3×#41—68no—
152C2×#239—31no—
153C2×#239—33no—
154C2×#239—33no—
155C2×#239—31no—
156C2×#239—68no—
157C2×D3×Q8—31no—
158C2×#237—33no—
159C2×D3×D4—33no—
160C2×D3×D4—33no—
161C2×#235—33no—
162C22×D12—33no—
163C22×C4×D3—33no—
164C22×C4×D3—33no—
165C3×#124C2×D313yes—
166C3×C22⋊Q8C2×D313yes—
167C3×#121C2×D313yes—
168C3×C4×Q8C2×D311yescharacteristic
169C3×C4×D4C2×D313yes—
170#946—33no—
171Q8×Dic3—31no—
172#944—33no—
173#940—33no—
174#938—33no—
175#937—36no—
176D4×Dic3—33no—
177#930—33no—
178C4×#67—33no—
179C4×#67—33no—
180#924—33no—
181#897—33no—
182#895—33no—
183#894—36no—
184#893—33no—
185#893—33no—
186#892—33no—
187D3×C4⋊C4—33no—
188#884—36no—
189#884—36no—
190#883—36no—
191#882—36no—
192#67⋊C4—33no—
193#67⋊C4—36no—
194#67⋊C4—31no—
195D3×C22⋊C4—33no—
196D3×C22⋊C4—33no—
197#875—33no—
198C4×D12—33no—
199C4×D12—33no—
200C42×D3—33no—
201C23×C9C2413yes—
202C23×C9C2411yescharacteristic
203C22×D9—26no—
204C22×D9—26no—
205C22×D9—26no—
206C22×D9—26no—
207C22×D9—43no—
208C22×D9—43no—
209C22×D9C2413yes—
210C22×D9C2413yes—
211C22×D9C2411yescharacteristic
212Q8×C9—26no—
213Q8×C9C2×D414yescomplemented
214D4×C9—26no—
215D4×C9—26no—
216C2×C4×C9—26no—
217C2×C4×C9—26no—
218C2×C4×C9C2413yes—
219C2×C4×C9C2411yescharacteristic
220C2×C4×C9C2413yes—
221C2×C4×C9C2411yescharacteristic
222C2×C4×C9C2413yes—
223#611—212no—
224#611—26no—
225#611—46no—
226#611#4114yescomplemented
227C2×Dic9—22no—
228C2×Dic9—26no—
229C2×Dic9C2413yes—
230C2×Dic9C2413yes—
231C2×Dic9C2411yescharacteristic
232C2×Dic9C2411yescharacteristic
233C2×Dic9C2411yescharacteristic
234D36—212no—
235D36—26no—
236D36—26no—
237D36C2×D4112yescomplemented
238C4×D9—26no—
239C4×D9—26no—
240C4×D9—26no—
241C4×D9—26no—
242C4×D9—22no—
243C4×D9—26no—
244C4×D9—26no—
245C4×D9—43no—
246C4×D9C2×D4112yescomplemented
247Dic18—26no—
248C22×#41—91no—
249C22×#41—91no—
250#550—91no—
251D4×Q8—91no—
252#548—91no—
253#548D911yescharacteristic, complemented
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—
263C23×D3—33no—
264C23×D3—33no—
265C3×#41—24no—
266C2×C3×Q8—24no—
267C2×C3×Q8C22×D313yes—
268C2×C3×Q8C22×D311yescharacteristic
269C2×C3×D4C22×D313yes—
270C2×C3×D4C22×D313yes—
271C22×C3×C4C22×D313yes—
272C22×C3×C4C22×D313yes—
273C2×#67—31no—
274C2×#67—33no—
275C2×#67—36no—
276C2×#67—36no—
277C22×Dic3—33no—
278C22×Dic3—31no—
279#239—38no—
280#239—612no—
281#239—612no—
282#239—64no—
283D3×Q8—64no—
284#237—612no—
285D3×D4—612no—
286D3×D4—612no—
287#235—612no—
288C2×D12—33no—
289C2×D12—33no—
290C2×D12—33no—
291C2×D12—36no—
292C2×D12—612no—
293C2×C4×D3—33no—
294C2×C4×D3—33no—
295C2×C4×D3—33no—
296C2×C4×D3—33no—
297C2×C4×D3—33no—
298C2×C4×D3—33no—
299C2×C4×D3—33no—
300C2×C4×D3—31no—
301C2×C4×D3—33no—
302C2×C4×D3—612no—
303C2×C4×D3—612no—
304C2×Dic6—33no—
305C3×C4⋊C4C22×D313yes—
306C3×C4⋊C4C22×D313yes—
307C3×C22⋊C4C22×D311yescharacteristic
308C3×C22⋊C4C22×D313yes—
309C3×C22⋊C4C22×D316yes—
310C3×C42C22×D313yes—
311#217—33no—
312#217—33no—
313(C2×D3)⋊C4—31no—
314(C2×D3)⋊C4—33no—
315(C2×D3)⋊C4—36no—
316(C2×D3)⋊C4—36no—
317(C2×D3)⋊C4—33no—
318(C2×D3)⋊C4—33no—
319C4⋊Dic3—33no—
320C4⋊Dic3—33no—
321Dic3⋊C4—36no—
322Dic3⋊C4—33no—
323Dic3⋊C4—31no—
324C4×Dic3—31no—
325C4×Dic3—33no—
326C4×Dic3—33no—
327C22×C9—21no—
328C22×C9—21no—
329C22×C9—23no—
330C22×C9—23no—
331C22×C9—23no—
332C22×C9C2×#4112yescomplemented
333C22×C9C2511yescharacteristic
334C2×D9—21no—
335C2×D9—23no—
336C2×D9—23no—
337C2×D9—21no—
338C2×D9—23no—
339C2×D9—23no—
340C2×D9—23no—
341C2×D9—412no—
342C2×D9—412no—
343C2×D9C22×D416yes—
344C2×D9C2×#4112yescomplemented
345C4×C9—21no—
346C4×C9—23no—
347C4×C9—23no—
348C4×C9—21no—
349C4×C9C22×D416yes—
350Dic9—23no—
351Dic9—21no—
352Dic9—23no—
353Dic9C22×D412yes—
354Dic9C2×#4112yescomplemented
355C2×#41—91no—
356C2×#41—93no—
357C2×#41—93no—
358C2×#41—91no—
359C2×#41—93no—
360C2×#41—93no—
361C2×#41—188no—
362C2×#41—188no—
363C2×#41C2×D911yescharacteristic, complemented
364C22×Q8—91no—
365C22×Q8C2×D911yescharacteristic, complemented
366C22×D4—93no—
367C22×D4—93no—
368C22×D4—93no—
369C23×C4—93no—
370C23×C4—93no—
371C4⋊Q8—93no—
372#127—93no—
373#124—93no—
374#124C2×D913yescomplemented
375#123—96no—
376#123—96no—
377C22⋊Q8—93no—
378C22⋊Q8—93no—
379C22⋊Q8—93no—
380C22⋊Q8C2×D913yescomplemented
381#121—93no—
382#121—93no—
383#121—93no—
384#121—96no—
385#121—96no—
386#121C2×D913yescomplemented
387#120—96no—
388#120—96no—
389C4×Q8—91no—
390C4×Q8C2×D911yescharacteristic, complemented
391C4×D4—93no—
392C4×D4—93no—
393C4×D4—93no—
394C4×D4—93no—
395C4×D4—93no—
396C4×D4—91no—
397C4×D4—93no—
398C4×D4—96no—
399C4×D4—93no—
400C4×D4—93no—
401C4×D4C2×D913yescomplemented
402#117—93no—
403C2×C4⋊C4—93no—
404C2×C22⋊C4—93no—
405C2×C22⋊C4—93no—
406C2×C42—93no—
407C23×C3C23×D313yes—
408C23×C3C23×D311yescharacteristic
409C22×D3—31no—
410C22×D3—33no—
411C22×D3—33no—
412C22×D3—66no—
413C22×D3—66no—
414C22×D3—66no—
415C22×D3—66no—
416C22×D3—123no—
417C22×D3—123no—
418C3×Q8—26no—
419C3×Q8D3×D414yes—
420C3×D4—26no—
421C3×D4—26no—
422C2×C3×C4—26no—
423C2×C3×C4—26no—
424C2×C3×C4C23×D313yes—
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D313yes—
427C2×C3×C4C23×D311yescharacteristic
428C2×C3×C4C23×D313yes—
429#67—34no—
430#67—66no—
431#67—612no—
432#67—126no—
433C2×Dic3—31no—
434C2×Dic3—31no—
435C2×Dic3—33no—
436C2×Dic3—33no—
437C2×Dic3—31no—
438C2×Dic3—62no—
439C2×Dic3—66no—
440D12—312no—
441D12—612no—
442D12—66no—
443D12—66no—
444C4×D3—312no—
445C4×D3—62no—
446C4×D3—66no—
447C4×D3—66no—
448C4×D3—66no—
449C4×D3—66no—
450C4×D3—66no—
451C4×D3—66no—
452C4×D3—123no—
453Dic6—66no—
454C2×C9—22no—
455C2×C9—43no—
456C2×C9C23×D411yescharacteristic
457C2×C9C22×#4111yescharacteristic
458C2×C9#58511yescharacteristic
459D9—22no—
460D9—26no—
461D9—43no—
462C24—93no—
463C24—93no—
464#41—24no—
465#41—98no—
466#41—1812no—
467#41—1812no—
468#41—1812no—
469#41—1812no—
470#41—184no—
471C2×Q8—24no—
472C2×Q8—93no—
473C2×Q8—184no—
474C2×Q8C22×D913yes—
475C2×Q8C22×D911yescharacteristic
476C2×D4—91no—
477C2×D4—93no—
478C2×D4—96no—
479C2×D4—96no—
480C2×D4—93no—
481C2×D4—93no—
482C2×D4—96no—
483C2×D4—93no—
484C2×D4—1812no—
485C2×D4—1812no—
486C2×D4—1812no—
487C2×D4C22×D913yes—
488C2×D4C22×D913yes—
489C22×C4—93no—
490C22×C4—91no—
491C22×C4—93no—
492C22×C4—93no—
493C22×C4—93no—
494C22×C4—93no—
495C22×C4—91no—
496C22×C4—93no—
497C22×C4—93no—
498C22×C4—93no—
499C22×C4—93no—
500C22×C4—1812no—
501C22×C4—1812no—
502C22×C4C22×D913yes—
503C22×C4C22×D913yes—
504C4⋊C4—91no—
505C4⋊C4—93no—
506C4⋊C4—93no—
507C4⋊C4—93no—
508C4⋊C4—96no—
509C4⋊C4C22×D913yes—
510C4⋊C4C22×D913yes—
511C22⋊C4—93no—
512C22⋊C4—93no—
513C22⋊C4—91no—
514C22⋊C4—93no—
515C22⋊C4—93no—
516C22⋊C4—93no—
517C22⋊C4—96no—
518C22⋊C4—96no—
519C22⋊C4C22×D911yescharacteristic
520C22⋊C4C22×D913yes—
521C22⋊C4C22×D916yes—
522C42—91no—
523C42—93no—
524C42—93no—
525C42C22×D913yes—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—23no—
529C22×C3—23no—
530C22×C3—23no—
531C22×C3D3×#4112yes—
532C22×C3C24×D311yescharacteristic
533C2×D3—36no—
534C2×D3—32no—
535C2×D3—61no—
536C2×D3—63no—
537C2×D3—63no—
538C2×D3—61no—
539C2×D3—63no—
540C2×D3—63no—
541C2×D3—63no—
542C2×D3—1212no—
543C2×D3—1212no—
544C3×C4—21no—
545C3×C4—23no—
546C3×C4—23no—
547C3×C4—21no—
548C3×C4C2×D3×D416yes—
549Dic3—32no—
550Dic3—32no—
551Dic3—63no—
552Dic3—61no—
553Dic3—63no—
554C9D4×#4111yescharacteristic, complemented, Sylow
555C23—91no—
556C23—93no—
557C23—93no—
558C23—186no—
559C23—186no—
560C23—186no—
561C23—186no—
562C23—363no—
563C23—363no—
564C23C23×D913yes—
565C23C23×D911yescharacteristic
566Q8—26no—
567Q8—186no—
568Q8D4×D914yescomplemented
569D4—26no—
570D4—26no—
571D4—94no—
572D4—912no—
573D4—1812no—
574D4—186no—
575D4—186no—
576D4—1812no—
577D4—186no—
578D4—366no—
579C2×C4—26no—
580C2×C4—26no—
581C2×C4—91no—
582C2×C4—91no—
583C2×C4—912no—
584C2×C4—93no—
585C2×C4—91no—
586C2×C4—93no—
587C2×C4—182no—
588C2×C4—186no—
589C2×C4—186no—
590C2×C4—186no—
591C2×C4—186no—
592C2×C4—182no—
593C2×C4—186no—
594C2×C4—186no—
595C2×C4—186no—
596C2×C4—363no—
597C2×C4C23×D911yescharacteristic
598C2×C4C23×D913yes—
599C2×C4C23×D911yescharacteristic
600C2×C4C23×D913yes—
601C2×C4C23×D913yes—
602C2×C3—22no—
603C2×C3—43no—
604C2×C3C22×D3×D411yescharacteristic
605C2×C3C2×D3×#4111yescharacteristic
606C2×C3#596811yescharacteristic
607D3—62no—
608D3—66no—
609D3—123no—
610C22—21no—
611C22—21no—
612C22—23no—
613C22—23no—
614C22—23no—
615C22—96no—
616C22—92no—
617C22—181no—
618C22—183no—
619C22—183no—
620C22—181no—
621C22—183no—
622C22—183no—
623C22—183no—
624C22—3612no—
625C22—3612no—
626C22#41×D912yescomplemented
627C22C24×D911yescharacteristic
628C4—21no—
629C4—23no—
630C4—23no—
631C4—21no—
632C4—92no—
633C4—92no—
634C4—181no—
635C4—183no—
636C4—183no—
637C4C2×D4×D916yes—
638C3#8671011yescharacteristic
639C2—22no—
640C2—43no—
641C2—182no—
642C2—186no—
643C2—363no—
644C2C22×D4×D911yescharacteristic
645C2C2×#41×D911yescharacteristic
646C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#548C2
hypercenter#548D9
hypocenterC9D4×#41
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D9C2semidirect
2. C22×#3701C2semidirect
3. C9×#548C2semidirect
4. #10589936C2semidirect
5. Q8×#611C2semidirect
6. #10589778C2semidirect
7. #10589770C2semidirect
8. #10589733C2semidirect
9. #10589729C2semidirect
10. #10589711C2semidirect
11. #10589708C2semidirect
12. #10589678C2semidirect
13. C4×#3701C2semidirect
14. #10589652C2semidirect
15. C4×D4×D9C2semidirect
17. C2×C9×#41C22semidirect
18. C22×Q8×C9C22semidirect
22. C2×#3701C22semidirect
23. C2×#3701C22semidirect
24. C2×#3701C22semidirect
25. C2×Q8×D9C22semidirect
26. C2×#3699C22semidirect
28. C2×D4×D9C22semidirect
29. C2×#3697C22semidirect
30. C22×D36C22semidirect
31. C22×C4×D9C22semidirect
32. C22×C4×D9C22semidirect
33. C9×#124C22semidirect
34. C9×C22⋊Q8C22semidirect
35. C9×#121C22semidirect
36. C4×Q8×C9C22semidirect
37. C4×D4×C9C22semidirect
38. #63508C22semidirect
39. Q8×Dic9C22semidirect
40. #63506C22semidirect
41. #63502C22semidirect
42. #63500C22semidirect
43. #63499C22semidirect
44. D4×Dic9C22semidirect
45. #63492C22semidirect
47. C4×#611C22semidirect
48. #63486C22semidirect
49. #63459C22semidirect
50. #63457C22semidirect
51. #63456C22semidirect
52. #63455C22semidirect
53. #63455C22semidirect
54. #63454C22semidirect
55. C4⋊C4×D9C22semidirect
56. #63446C22semidirect
57. #63446C22semidirect
58. #63445C22semidirect
59. #63444C22semidirect
61. #611⋊C4C22semidirect
62. #611⋊C4C22semidirect
63. C22⋊C4×D9C22semidirect
64. C22⋊C4×D9C22semidirect
65. #63437C22semidirect
66. C4×D36C22semidirect
67. C4×D36C22semidirect
68. C42×D9C22semidirect
103. #3701D4semidirect
213. Q8×C9C2×D4semidirect
226. #611#41semidirect
237. D36C2×D4semidirect
246. C4×D9C2×D4semidirect
253. #548D9semidirect
332. C22×C9C2×#41semidirect
344. C2×D9C2×#41semidirect
354. Dic9C2×#41semidirect
363. C2×#41C2×D9semidirect
365. C22×Q8C2×D9semidirect
374. #124C2×D9semidirect
380. C22⋊Q8C2×D9semidirect
386. #121C2×D9semidirect
390. C4×Q8C2×D9semidirect
401. C4×D4C2×D9semidirect
554. C9D4×#41semidirect
568. Q8D4×D9semidirect
626. C22#41×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D92
C22×#37012
C9×#5482
#105899362
Q8×#6112
#105897782
#105897702
#105897332
#105897292
#105897112
#105897082
#105896782
C4×#37012
#105896522
C4×D4×D92
#867103