Finite Group Databasebeta

← #11903849

Subgroups — #11903849

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#548C211yesmaximal, characteristic, complemented
2#10589936C211yesmaximal, characteristic, complemented
3#41×Dic9C211yesmaximal, characteristic, complemented
4#10589919C211yesmaximal, characteristic, complemented
5C2×Q8×Dic9C211yesmaximal, characteristic, complemented
6#10589783C213yesmaximal, complemented
7#10589782C213yesmaximal, complemented
8#10589743C213yesmaximal, complemented
9#10589726C213yesmaximal, complemented
10#10589720C213yesmaximal, complemented
11#10589698C213yesmaximal, complemented
12C4×#3701C211yesmaximal, characteristic, complemented
13#10589671C211yesmaximal, characteristic, complemented
14#10589667C213yesmaximal, complemented
15C4×#3699C213yesmaximal, complemented
16#86711—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic
19C2×#3701C2211yescharacteristic
20C2×#3699C2213yes—
21C9×#124C2213yes—
22C9×C22⋊Q8C2213yes—
23C9×#121C2213yes—
24C4×Q8×C9C2211yescharacteristic
25C4×D4×C9C2213yes—
26#63509C2213yes—
27#63508C2213yes—
28Q8×Dic9C2213yes—
29Q8×Dic9C2213yes—
30Q8×Dic9C2211yescharacteristic
31Q8×Dic9C2211yescharacteristic
32Q8×Dic9C2211yescharacteristic
33#63502C2213yes—
34#63501C2216yes—
35#63500C2213yes—
36D4×Dic9C2213yes—
37D4×Dic9C2213yes—
38D4×Dic9C2213yes—
39#63492C2213yes—
40#63492C2213yes—
41C4×#611C2213yes—
42C4×#611C2213yes—
43#63488C2213yes—
44C2×C4⋊Dic9C2213yes—
45C2×C4×Dic9C2213yes—
46C2×C4×Dic9C2213yes—
47#63460C2216yes—
48#63455C2213yes—
49#63454C2213yes—
50#63454C2213yes—
51#63452C2213yes—
52#63450C2213yes—
53#63449C2213yes—
54#63448C2216yes—
55#63447C2216yes—
56#63445C2216yes—
57#611⋊C4C2216yes—
58#611⋊C4C2213yes—
59#611⋊C4C2213yes—
60#63441C2216yes—
61#63439C2213yes—
62#63439C2211yescharacteristic
63C4×D36C2213yes—
64C42×D9C2213yes—
65#63432C2213yes—
66C4×Dic18C2213yes—
67C3×#548D311yescharacteristic
68#5834—31no—
69Dic3×#41—31no—
70#5817—31no—
71C2×Q8×Dic3—31no—
72#5681—33no—
73#5680—33no—
74#5641—33no—
75#5624—33no—
76#5618—33no—
77#5596—33no—
78C4×#239—31no—
79#5569—31no—
80#5565—33no—
81C4×#237—33no—
82C9×#41—24no—
83C2×Q8×C9—24no—
84C2×Q8×C9C2313yes—
85C2×Q8×C9C2311yescharacteristic
86C2×D4×C9C2313yes—
87C2×D4×C9C2313yes—
88C22×C4×C9C2313yes—
89C22×C4×C9C2313yes—
90C2×#611C2313yes—
91C2×#611C2313yes—
92C2×#611C2316yes—
93C22×Dic9C2313yes—
94C22×Dic9C2313yes—
95C22×Dic9C2313yes—
96C22×Dic9C2311yescharacteristic
97#3701—24no—
98#3699—212no—
99C2×D36C2313yes—
100C2×C4×D9C2313yes—
101C2×C4×D9C2313yes—
102C2×C4×D9C2313yes—
103C2×Dic18C2313yes—
104C9×C4⋊C4C2313yes—
105C9×C4⋊C4C2313yes—
106C9×C22⋊C4C2311yescharacteristic
107C9×C22⋊C4C2313yes—
108C9×C22⋊C4C2316yes—
109C42×C9C2313yes—
110#3676C2316yes—
111#3676C2311yescharacteristic
112#3676C2313yes—
113(C2×D9)⋊C4C2313yes—
114(C2×D9)⋊C4C2313yes—
115(C2×D9)⋊C4C2316yes—
116(C2×D9)⋊C4C2316yes—
117C4⋊Dic9C2313yes—
118C4⋊Dic9C2313yes—
119C4⋊Dic9C2313yes—
120C4⋊Dic9C2313yes—
121C4⋊Dic9C2316yes—
122Dic9⋊C4C2311yescharacteristic
123Dic9⋊C4C2313yes—
124Dic9⋊C4C2316yes—
125Dic9⋊C4C2311yescharacteristic
126Dic9⋊C4C2313yes—
127C4×Dic9C2313yes—
128C4×Dic9C2313yes—
129C4×Dic9C2313yes—
130C4×Dic9C2313yes—
131C4×Dic9C2313yes—
132C4×Dic9C2313yes—
133C4×Dic9C2313yes—
134C4×Dic9C2311yescharacteristic
135C4×Dic9C2311yescharacteristic
136#3480—91noSylow
137C2×C3×#41C2×D311yescharacteristic
138C22×C3×Q8C2×D311yescharacteristic
139C2×#239—31no—
140C2×#237—33no—
141C3×#124C2×D313yes—
142C3×C22⋊Q8C2×D313yes—
143C3×#121C2×D313yes—
144C3×C4×Q8C2×D311yescharacteristic
145C3×C4×D4C2×D313yes—
146#947—33no—
147#946—33no—
148Q8×Dic3—33no—
149Q8×Dic3—33no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153#940—33no—
154#939—36no—
155#938—33no—
156D4×Dic3—33no—
157D4×Dic3—33no—
158D4×Dic3—33no—
159#930—33no—
160#930—33no—
161C4×#67—33no—
162C4×#67—33no—
163#926—33no—
164C2×C4⋊Dic3—33no—
165C2×C4×Dic3—33no—
166C2×C4×Dic3—33no—
167#898—36no—
168#893—33no—
169#892—33no—
170#892—33no—
171#890—33no—
172#888—33no—
173#887—33no—
174#886—36no—
175#885—36no—
176#883—36no—
177#67⋊C4—36no—
178#67⋊C4—33no—
179#67⋊C4—33no—
180#879—36no—
181#877—33no—
182#877—31no—
183C4×D12—33no—
184C42×D3—33no—
185#870—33no—
186C4×Dic6—33no—
187C23×C9C2413yes—
188C23×C9C2411yescharacteristic
189C22×D9C2413yes—
190Q8×C9—26no—
191Q8×C9#4114yescomplemented
192D4×C9—26no—
193D4×C9—26no—
194C2×C4×C9—26no—
195C2×C4×C9—26no—
196C2×C4×C9C2411yescharacteristic
197C2×C4×C9C2413yes—
198C2×C4×C9C2411yescharacteristic
199C2×C4×C9C2413yes—
200C2×C4×C9C2413yes—
201#611—26no—
202#611—26no—
203#611—46no—
204C2×Dic9—26no—
205C2×Dic9—43no—
206C2×Dic9—43no—
207C2×Dic9#4114yescomplemented
208C2×Dic9C2411yescharacteristic
209C2×Dic9C2411yescharacteristic
210C2×Dic9C2413yes—
211C2×Dic9C2413yes—
212C2×Dic9C2413yes—
213C2×Dic9C2411yescharacteristic
214C2×Dic9C2411yescharacteristic
215D36—26no—
216C4×D9—26no—
217C4×D9—26no—
218C4×D9—43no—
219Dic18—26no—
220#559—93no—
221#557—91no—
222#556—93no—
223#553—93no—
224#553—93no—
225#550—91no—
226#548—91no—
227#548D911yescharacteristic, complemented
228#532—93no—
229#529—93no—
230#529—93no—
231C4×#41—91no—
232C4×#41—91no—
233C4×#41—93no—
234C2×C4×Q8—91no—
235C3×#41—24no—
236C2×C3×Q8—24no—
237C2×C3×Q8C22×D313yes—
238C2×C3×Q8C22×D311yescharacteristic
239C2×C3×D4C22×D313yes—
240C2×C3×D4C22×D313yes—
241C22×C3×C4C22×D313yes—
242C22×C3×C4C22×D313yes—
243C2×#67—33no—
244C2×#67—33no—
245C2×#67—36no—
246C22×Dic3—31no—
247C22×Dic3—33no—
248C22×Dic3—33no—
249C22×Dic3—33no—
250#239—64no—
251#237—612no—
252C2×D12—33no—
253C2×C4×D3—33no—
254C2×C4×D3—33no—
255C2×C4×D3—33no—
256C2×Dic6—33no—
257C3×C4⋊C4C22×D313yes—
258C3×C4⋊C4C22×D313yes—
259C3×C22⋊C4C22×D311yescharacteristic
260C3×C22⋊C4C22×D313yes—
261C3×C22⋊C4C22×D316yes—
262C3×C42C22×D313yes—
263#217—33no—
264#217—31no—
265#217—36no—
266(C2×D3)⋊C4—36no—
267(C2×D3)⋊C4—36no—
268(C2×D3)⋊C4—33no—
269(C2×D3)⋊C4—33no—
270C4⋊Dic3—33no—
271C4⋊Dic3—33no—
272C4⋊Dic3—33no—
273C4⋊Dic3—33no—
274C4⋊Dic3—36no—
275Dic3⋊C4—31no—
276Dic3⋊C4—33no—
277Dic3⋊C4—36no—
278Dic3⋊C4—33no—
279Dic3⋊C4—31no—
280C4×Dic3—33no—
281C4×Dic3—33no—
282C4×Dic3—31no—
283C4×Dic3—33no—
284C4×Dic3—33no—
285C4×Dic3—33no—
286C4×Dic3—31no—
287C4×Dic3—33no—
288C4×Dic3—33no—
289C22×C9—21no—
290C22×C9—21no—
291C22×C9—23no—
292C22×C9—23no—
293C22×C9—23no—
294C22×C9C2×#4112yes—
295C22×C9C2511yescharacteristic
296C2×D9—23no—
297C2×D9—23no—
298C2×D9—23no—
299C4×C9—23no—
300C4×C9—21no—
301C4×C9—23no—
302C4×C9—21no—
303C4×C9C2×#4116yes—
304Dic9—23no—
305Dic9—21no—
306Dic9—23no—
307Dic9—21no—
308Dic9—23no—
309Dic9C2×#4112yes—
310Dic9C2×#4112yes—
311C2×#41—91no—
312C2×#41—93no—
313C2×#41C2×D911yescharacteristic
314C22×Q8C2×D911yescharacteristic
315C4⋊Q8—93no—
316#127—93no—
317#126—96no—
318#126—96no—
319#125—93no—
320#125—93no—
321#124—93no—
322#124—96no—
323#124C2×D913yes—
324#123—96no—
325#123—96no—
326C22⋊Q8—93no—
327C22⋊Q8C2×D913yes—
328#121—93no—
329#121—96no—
330#121—93no—
331#121—93no—
332#121C2×D913yes—
333C4×Q8—91no—
334C4×Q8—93no—
335C4×Q8—91no—
336C4×Q8—93no—
337C4×Q8—91no—
338C4×Q8—93no—
339C4×Q8—93no—
340C4×Q8C2×D911yescharacteristic
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—93no—
344C4×D4—93no—
345C4×D4—93no—
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—93no—
349C4×D4—96no—
350C4×D4—93no—
351C4×D4C2×D913yes—
352#117—93no—
353#117—93no—
354#117—93no—
355#117—91no—
356#117—93no—
357C2×C4⋊C4—93no—
358C2×C42—93no—
359C2×C42—93no—
360C2×C42—93no—
361C23×C3C23×D313yes—
362C23×C3C23×D311yescharacteristic
363C22×D3—33no—
364C3×Q8—26no—
365C3×Q8#23714yes—
366C3×D4—26no—
367C3×D4—26no—
368C2×C3×C4—26no—
369C2×C3×C4—26no—
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D313yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D313yes—
374C2×C3×C4C23×D313yes—
375#67—66no—
376#67—66no—
377#67—126no—
378C2×Dic3—34no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—31no—
382C2×Dic3—31no—
383C2×Dic3—33no—
384C2×Dic3—33no—
385C2×Dic3—33no—
386C2×Dic3—66no—
387C2×Dic3—123no—
388C2×Dic3—123no—
389D12—66no—
390C4×D3—66no—
391C4×D3—66no—
392C4×D3—123no—
393Dic6—66no—
394C2×C9—22no—
395C2×C9—43no—
396C2×C9C22×#4111yescharacteristic
397C2×C9C22×#4111yescharacteristic
398C2×C9#58511yescharacteristic
399D9—43no—
400#41—24no—
401#41—1812no—
402#41—184no—
403C2×Q8—24no—
404C2×Q8—93no—
405C2×Q8C22×D913yes—
406C2×Q8C22×D911yescharacteristic
407C2×D4—93no—
408C2×D4—93no—
409C2×D4—96no—
410C2×D4—93no—
411C2×D4C22×D913yes—
412C2×D4C22×D913yes—
413C22×C4—91no—
414C22×C4—93no—
415C22×C4—93no—
416C22×C4—93no—
417C22×C4—93no—
418C22×C4—93no—
419C22×C4—93no—
420C22×C4C22×D913yes—
421C22×C4C22×D913yes—
422C4⋊C4—93no—
423C4⋊C4—93no—
424C4⋊C4—96no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—93no—
428C4⋊C4—93no—
429C4⋊C4—93no—
430C4⋊C4—93no—
431C4⋊C4—96no—
432C4⋊C4C22×D913yes—
433C4⋊C4C22×D913yes—
434C22⋊C4—91no—
435C22⋊C4—93no—
436C22⋊C4—96no—
437C22⋊C4—93no—
438C22⋊C4—96no—
439C22⋊C4—93no—
440C22⋊C4—96no—
441C22⋊C4C22×D911yescharacteristic
442C22⋊C4C22×D913yes—
443C22⋊C4C22×D916yes—
444C42—91no—
445C42—91no—
446C42—93no—
447C42—93no—
448C42—93no—
449C42—93no—
450C42—93no—
451C42—93no—
452C42—93no—
453C42C22×D913yes—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—23no—
457C22×C3—23no—
458C22×C3—23no—
459C22×C3D3×#4112yes—
460C22×C3C24×D311yescharacteristic
461C2×D3—63no—
462C2×D3—63no—
463C2×D3—63no—
464C3×C4—21no—
465C3×C4—23no—
466C3×C4—23no—
467C3×C4—21no—
468C3×C4C2×#23716yes—
469Dic3—32no—
470Dic3—32no—
471Dic3—61no—
472Dic3—63no—
473Dic3—63no—
474Dic3—61no—
475Dic3—63no—
476C9#348011yescharacteristic, complemented, Sylow
477C23—93no—
478C23C23×D913yes—
479C23C23×D911yescharacteristic
480Q8—26no—
481Q8—186no—
482Q8#369914yescomplemented
483D4—26no—
484D4—26no—
485D4—186no—
486D4—186no—
487D4—186no—
488D4—366no—
489C2×C4—26no—
490C2×C4—26no—
491C2×C4—91no—
492C2×C4—91no—
493C2×C4—94no—
494C2×C4—91no—
495C2×C4—91no—
496C2×C4—93no—
497C2×C4—93no—
498C2×C4—93no—
499C2×C4—186no—
500C2×C4—186no—
501C2×C4—186no—
502C2×C4—363no—
503C2×C4—363no—
504C2×C4—363no—
505C2×C4C23×D911yescharacteristic
506C2×C4C23×D913yes—
507C2×C4C23×D911yescharacteristic
508C2×C4C23×D913yes—
509C2×C4C23×D913yes—
510C2×C3—22no—
511C2×C3—43no—
512C2×C3C22×#23711yescharacteristic
513C2×C3C2×D3×#4111yescharacteristic
514C2×C3#596811yescharacteristic
515D3—123no—
516C22—21no—
517C22—21no—
518C22—23no—
519C22—23no—
520C22—23no—
521C22—183no—
522C22—183no—
523C22—183no—
524C22#41×D912yes—
525C22C24×D911yescharacteristic
526C4—21no—
527C4—23no—
528C4—23no—
529C4—21no—
530C4—92no—
531C4—92no—
532C4—181no—
533C4—183no—
534C4—183no—
535C4—181no—
536C4—183no—
537C4C2×#369916yes—
538C3#8671111yescharacteristic
539C2—22no—
540C2—43no—
541C2—363no—
542C2C22×#369911yescharacteristic
543C2C2×#41×D911yescharacteristic
544C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#548C2
hypercenter#548D9
hypocenterC9#3480
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C9×#548C2semidirect
2. #10589936C2semidirect
3. #41×Dic9C2semidirect
4. #10589919C2semidirect
5. C2×Q8×Dic9C2semidirect
6. #10589783C2semidirect
7. #10589782C2semidirect
8. #10589743C2semidirect
9. #10589726C2semidirect
10. #10589720C2semidirect
11. #10589698C2semidirect
12. C4×#3701C2semidirect
13. #10589671C2semidirect
14. #10589667C2semidirect
15. C4×#3699C2semidirect
191. Q8×C9#41semidirect
207. C2×Dic9#41semidirect
227. #548D9semidirect
476. C9#3480semidirect
482. Q8#3699semidirect

Maximal subgroups

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

subgroupindex
C9×#5482
#105899362
#41×Dic92
#105899192
C2×Q8×Dic92
#105897832
#105897822
#105897432
#105897262
#105897202
#105896982
C4×#37012
#105896712
#105896672
C4×#36992
#867113