Finite Group Databasebeta

← #11903873

Subgroups — #11903873

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
1C4×C9×#41C211yesmaximal, characteristic, complemented
2#10589936C211yesmaximal, characteristic, complemented
3#10589933C211yesmaximal, characteristic, complemented
4#10589678C211yesmaximal, characteristic, complemented
5C4×#3701C211yesmaximal, characteristic, complemented
6C4×Q8×D9C211yesmaximal, characteristic, complemented
7#10589671C211yesmaximal, characteristic, complemented
8#10589661C213yesmaximal, complemented
9#10589660C213yesmaximal, complemented
10#10589659C213yesmaximal, complemented
11#10589650C213yesmaximal, complemented
12#10589635C213yesmaximal, complemented
13#10589632C213yesmaximal, complemented
14#10589581C213yesmaximal, complemented
15C4×#3697C213yesmaximal, complemented
16#85842—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×#3701C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic
20C2×#3697C2213yes—
21C4×Q8×C9C2211yescharacteristic
22C4×Q8×C9C2211yescharacteristic
23C4×D4×C9C2213yes—
24C4×D4×C9C2213yes—
25C9×#117C2213yes—
26C2×C42×C9C2213yes—
27Q8×Dic9C2211yescharacteristic
28Q8×Dic9C2211yescharacteristic
29#63502C2213yes—
30#63500C2213yes—
31#63500C2213yes—
32#63498C2213yes—
33#63492C2213yes—
34#63491C2216yes—
35C4×#611C2213yes—
36C4×#611C2213yes—
37C4×#611C2213yes—
38C4×#611C2213yes—
39C4×#611C2216yes—
40#63488C2213yes—
41#63486C2213yes—
42#63459C2213yes—
43#63457C2213yes—
44#63455C2213yes—
45#63454C2213yes—
46C4⋊C4×D9C2213yes—
47#63452C2213yes—
48#63450C2213yes—
49#63449C2213yes—
50#63447C2216yes—
51#63446C2216yes—
52#63445C2216yes—
53#63441C2216yes—
54#63438C2216yes—
55#63437C2213yes—
56C4×D36C2213yes—
57C4×D36C2213yes—
58C4×D36C2213yes—
59#63434C2211yescharacteristic
60#63434C2213yes—
61C42×D9C2213yes—
62C42×D9C2213yes—
63#63432C2213yes—
64C4×Dic18C2213yes—
65C4×Dic18C2213yes—
66C4×Dic18C2213yes—
67C3×C4×#41D311yescharacteristic
68#5834—31no—
69#5831—31no—
70#5576—31no—
71C4×#239—31no—
72C4×D3×Q8—31no—
73#5569—31no—
74#5559—33no—
75#5558—33no—
76#5557—33no—
77#5548—33no—
78#5533—33no—
79#5530—33no—
80#5479—33no—
81C4×#235—33no—
82C9×#41—24no—
83C2×Q8×C9C2311yescharacteristic
84C2×D4×C9C2313yes—
85C22×C4×C9C2313yes—
86C22×C4×C9C2313yes—
87C22×C4×C9C2313yes—
88C2×#611C2313yes—
89C2×#611C2313yes—
90C2×#611C2316yes—
91#3701—24no—
92Q8×D9—24no—
93#3697—212no—
94C2×D36C2313yes—
95C2×D36C2313yes—
96C2×C4×D9C2313yes—
97C2×C4×D9C2313yes—
98C2×C4×D9C2313yes—
99C2×C4×D9C2313yes—
100C2×C4×D9C2313yes—
101C2×C4×D9C2311yescharacteristic
102C2×Dic18C2313yes—
103C2×Dic18C2313yes—
104C9×C4⋊C4C2313yes—
105C9×C4⋊C4C2313yes—
106C9×C22⋊C4C2316yes—
107C42×C9C2311yescharacteristic
108C42×C9C2313yes—
109C42×C9C2313yes—
110C42×C9C2313yes—
111#3676C2313yes—
112#3676C2313yes—
113#3676C2316yes—
114(C2×D9)⋊C4C2311yescharacteristic
115(C2×D9)⋊C4C2311yescharacteristic
116(C2×D9)⋊C4C2313yes—
117(C2×D9)⋊C4C2313yes—
118(C2×D9)⋊C4C2316yes—
119(C2×D9)⋊C4C2316yes—
120C4⋊Dic9C2313yes—
121C4⋊Dic9C2313yes—
122C4⋊Dic9C2313yes—
123C4⋊Dic9C2313yes—
124Dic9⋊C4C2311yescharacteristic
125Dic9⋊C4C2311yescharacteristic
126Dic9⋊C4C2313yes—
127Dic9⋊C4C2313yes—
128Dic9⋊C4C2316yes—
129Dic9⋊C4C2316yes—
130C4×Dic9C2311yescharacteristic
131C4×Dic9C2313yes—
132C4×Dic9C2313yes—
133C4×Dic9C2313yes—
134C4×Dic9C2313yes—
135C4×Dic9C2313yes—
136#3480—91noSylow
137C2×C3×#41C2×D311yescharacteristic
138C2×#239—31no—
139C2×D3×Q8—31no—
140C2×#235—33no—
141C3×C4×Q8C2×D311yescharacteristic
142C3×C4×Q8C2×D311yescharacteristic
143C3×C4×D4C2×D313yes—
144C3×C4×D4C2×D313yes—
145C3×#117C2×D313yes—
146C2×C3×C42C2×D313yes—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149#940—33no—
150#938—33no—
151#938—33no—
152#936—33no—
153#930—33no—
154#929—36no—
155C4×#67—33no—
156C4×#67—33no—
157C4×#67—33no—
158C4×#67—33no—
159C4×#67—36no—
160#926—33no—
161#924—33no—
162#897—33no—
163#895—33no—
164#893—33no—
165#892—33no—
166D3×C4⋊C4—33no—
167#890—33no—
168#888—33no—
169#887—33no—
170#885—36no—
171#884—36no—
172#883—36no—
173#879—36no—
174#876—36no—
175#875—33no—
176C4×D12—33no—
177C4×D12—33no—
178C4×D12—33no—
179#872—31no—
180#872—33no—
181C42×D3—33no—
182C42×D3—33no—
183#870—33no—
184C4×Dic6—33no—
185C4×Dic6—33no—
186C4×Dic6—33no—
187C23×C9C2413yes—
188C22×D9C2413yes—
189C22×D9C2411yescharacteristic
190Q8×C9#4114yescomplemented
191D4×C9—26no—
192C2×C4×C9—26no—
193C2×C4×C9—26no—
194C2×C4×C9—43no—
195C2×C4×C9C2413yes—
196C2×C4×C9C2411yescharacteristic
197C2×C4×C9C2411yescharacteristic
198C2×C4×C9C2413yes—
199C2×C4×C9C2411yescharacteristic
200C2×C4×C9C2413yes—
201#611—26no—
202#611—26no—
203#611—46no—
204C2×Dic9C2411yescharacteristic
205C2×Dic9C2411yescharacteristic
206C2×Dic9C2413yes—
207C2×Dic9C2413yes—
208C2×Dic9C2413yes—
209C2×Dic9C2411yescharacteristic
210D36—26no—
211D36—26no—
212C4×D9—26no—
213C4×D9—26no—
214C4×D9—26no—
215C4×D9—43no—
216C4×D9—43no—
217C4×D9#4114yescomplemented
218Dic18—26no—
219Dic18—26no—
220#559—93no—
221#557—91no—
222#556—93no—
223#553—93no—
224#553—93no—
225#550—91no—
226#548—91no—
227#548—91no—
228#532—93no—
229#529—93no—
230#529—93no—
231C4×#41—91no—
232C4×#41—93no—
233C4×#41D911yescharacteristic, complemented
234C2×C4×Q8—91no—
235C3×#41—24no—
236C2×C3×Q8C22×D311yescharacteristic
237C2×C3×D4C22×D313yes—
238C22×C3×C4C22×D313yes—
239C22×C3×C4C22×D313yes—
240C22×C3×C4C22×D313yes—
241C2×#67—33no—
242C2×#67—33no—
243C2×#67—36no—
244#239—64no—
245D3×Q8—64no—
246#235—612no—
247C2×D12—33no—
248C2×D12—33no—
249C2×C4×D3—31no—
250C2×C4×D3—33no—
251C2×C4×D3—33no—
252C2×C4×D3—33no—
253C2×C4×D3—33no—
254C2×C4×D3—33no—
255C2×Dic6—33no—
256C2×Dic6—33no—
257C3×C4⋊C4C22×D313yes—
258C3×C4⋊C4C22×D313yes—
259C3×C22⋊C4C22×D316yes—
260C3×C42C22×D313yes—
261C3×C42C22×D313yes—
262C3×C42C22×D313yes—
263C3×C42C22×D311yescharacteristic
264#217—33no—
265#217—36no—
266#217—33no—
267(C2×D3)⋊C4—31no—
268(C2×D3)⋊C4—31no—
269(C2×D3)⋊C4—33no—
270(C2×D3)⋊C4—33no—
271(C2×D3)⋊C4—36no—
272(C2×D3)⋊C4—36no—
273C4⋊Dic3—33no—
274C4⋊Dic3—33no—
275C4⋊Dic3—33no—
276C4⋊Dic3—33no—
277Dic3⋊C4—31no—
278Dic3⋊C4—31no—
279Dic3⋊C4—33no—
280Dic3⋊C4—33no—
281Dic3⋊C4—36no—
282Dic3⋊C4—36no—
283C4×Dic3—33no—
284C4×Dic3—33no—
285C4×Dic3—33no—
286C4×Dic3—33no—
287C4×Dic3—33no—
288C4×Dic3—31no—
289C22×C9—23no—
290C22×C9—23no—
291C22×C9—23no—
292C22×C9C2511yescharacteristic
293C2×D9—21no—
294C2×D9—21no—
295C2×D9—23no—
296C2×D9—23no—
297C2×D9—23no—
298C2×D9C2×#4112yes—
299C4×C9—23no—
300C4×C9—21no—
301C4×C9—23no—
302C4×C9—21no—
303C4×C9C2×#4116yes—
304C4×C9C2×#4112yes—
305Dic9—23no—
306Dic9—23no—
307Dic9—21no—
308Dic9—21no—
309Dic9—23no—
310Dic9C2×#4112yes—
311C2×#41—91no—
312C2×#41—93no—
313C2×#41C2×D911yescharacteristic
314C22×Q8—91no—
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#124—93no—
324#123—96no—
325#123—96no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328#121—93no—
329#121—93no—
330#121—93no—
331#121—93no—
332#121—96no—
333C4×Q8—91no—
334C4×Q8—91no—
335C4×Q8—93no—
336C4×Q8—93no—
337C4×Q8—93no—
338C4×Q8—93no—
339C4×Q8C2×D911yescharacteristic
340C4×Q8C2×D911yescharacteristic
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—93no—
344C4×D4—93no—
345C4×D4—96no—
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—93no—
349C4×D4—93no—
350C4×D4C2×D913yes—
351C4×D4C2×D913yes—
352#117—93no—
353#117—93no—
354#117—91no—
355#117—93no—
356#117C2×D913yes—
357C2×C4⋊C4—93no—
358C2×C42—93no—
359C2×C42—93no—
360C2×C42C2×D913yes—
361C23×C3C23×D313yes—
362C22×D3—31no—
363C22×D3—33no—
364C3×Q8#23514yes—
365C3×D4—26no—
366C2×C3×C4—26no—
367C2×C3×C4—26no—
368C2×C3×C4—43no—
369C2×C3×C4C23×D313yes—
370C2×C3×C4C23×D311yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D313yes—
373C2×C3×C4C23×D313yes—
374C2×C3×C4C23×D311yescharacteristic
375#67—66no—
376#67—66no—
377#67—126no—
378C2×Dic3—31no—
379C2×Dic3—31no—
380C2×Dic3—31no—
381C2×Dic3—33no—
382C2×Dic3—33no—
383C2×Dic3—33no—
384D12—66no—
385D12—66no—
386C4×D3—34no—
387C4×D3—66no—
388C4×D3—66no—
389C4×D3—66no—
390C4×D3—123no—
391C4×D3—123no—
392Dic6—66no—
393Dic6—66no—
394C2×C9—43no—
395C2×C9C22×#4111yescharacteristic
396C2×C9C22×#4111yescharacteristic
397C2×C9#58511yescharacteristic
398D9—22no—
399D9—43no—
400#41—24no—
401#41—1812no—
402#41—184no—
403C2×Q8—93no—
404C2×Q8—93no—
405C2×Q8—184no—
406C2×Q8C22×D911yescharacteristic
407C2×D4—93no—
408C2×D4—93no—
409C2×D4—96no—
410C2×D4—93no—
411C2×D4—93no—
412C2×D4C22×D913yes—
413C22×C4—91no—
414C22×C4—93no—
415C22×C4—93no—
416C22×C4—93no—
417C22×C4—93no—
418C22×C4—93no—
419C22×C4C22×D913yes—
420C22×C4C22×D913yes—
421C22×C4C22×D913yes—
422C4⋊C4—93no—
423C4⋊C4—96no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—93no—
427C4⋊C4—93no—
428C4⋊C4—93no—
429C4⋊C4—93no—
430C4⋊C4—93no—
431C4⋊C4—96no—
432C4⋊C4C22×D913yes—
433C4⋊C4C22×D913yes—
434C22⋊C4—93no—
435C22⋊C4—93no—
436C22⋊C4—96no—
437C22⋊C4—91no—
438C22⋊C4—91no—
439C22⋊C4—93no—
440C22⋊C4—96no—
441C22⋊C4—93no—
442C22⋊C4—96no—
443C22⋊C4C22×D916yes—
444C42—93no—
445C42—93no—
446C42—93no—
447C42—93no—
448C42—91no—
449C42—93no—
450C42C22×D913yes—
451C42C22×D913yes—
452C42C22×D913yes—
453C42C22×D911yescharacteristic
454C22×C3—23no—
455C22×C3—23no—
456C22×C3—23no—
457C22×C3C24×D311yescharacteristic
458C2×D3—32no—
459C2×D3—61no—
460C2×D3—61no—
461C2×D3—63no—
462C2×D3—63no—
463C2×D3—63no—
464C3×C4—21no—
465C3×C4—23no—
466C3×C4—23no—
467C3×C4—21no—
468C3×C4C2×#23516yes—
469C3×C4D3×#4112yes—
470Dic3—32no—
471Dic3—63no—
472Dic3—61no—
473Dic3—63no—
474Dic3—61no—
475Dic3—63no—
476C9#348011yescharacteristic, complemented, Sylow
477C23—91no—
478C23—93no—
479C23C23×D913yes—
480Q8—186no—
481Q8—186no—
482Q8#369714yescomplemented
483D4—26no—
484D4—186no—
485D4—186no—
486D4—186no—
487D4—186no—
488D4—366no—
489C2×C4—26no—
490C2×C4—26no—
491C2×C4—43no—
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×C4C23×D913yes—
505C2×C4C23×D911yescharacteristic
506C2×C4C23×D911yescharacteristic
507C2×C4C23×D913yes—
508C2×C4C23×D913yes—
509C2×C4C23×D911yescharacteristic
510C2×C3—43no—
511C2×C3C22×#23511yescharacteristic
512C2×C3C2×D3×#4111yescharacteristic
513C2×C3#596411yescharacteristic
514D3—62no—
515D3—123no—
516C22—23no—
517C22—23no—
518C22—23no—
519C22—92no—
520C22—181no—
521C22—181no—
522C22—183no—
523C22—183no—
524C22—183no—
525C22C24×D911yescharacteristic
526C4—21no—
527C4—23no—
528C4—21no—
529C4—23no—
530C4—92no—
531C4—181no—
532C4—183no—
533C4—183no—
534C4—181no—
535C4—183no—
536C4C2×#369716yes—
537C4#41×D912yes—
538C3#8584211yescharacteristic
539C2—43no—
540C2—182no—
541C2—363no—
542C2C22×#369711yescharacteristic
543C2C2×#41×D911yescharacteristic
544C2#1059313911yescharacteristic
subgroupG/H
centerC2×C4C23×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC4×C9×#41C2
hypercenterC4×#41D9
hypocenterC9#3480
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C9×#41C2semidirect
2. #10589936C2semidirect
3. #10589933C2semidirect
4. #10589678C2semidirect
5. C4×#3701C2semidirect
6. C4×Q8×D9C2semidirect
7. #10589671C2semidirect
8. #10589661C2semidirect
9. #10589660C2semidirect
10. #10589659C2semidirect
11. #10589650C2semidirect
12. #10589635C2semidirect
13. #10589632C2semidirect
14. #10589581C2semidirect
15. C4×#3697C2semidirect
190. Q8×C9#41semidirect
217. C4×D9#41semidirect
233. C4×#41D9semidirect
476. C9#3480semidirect
482. Q8#3697semidirect

Maximal subgroups

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

subgroupindex
C4×C9×#412
#105899362
#105899332
#105896782
C4×#37012
C4×Q8×D92
#105896712
#105896612
#105896602
#105896592
#105896502
#105896352
#105896322
#105895812
C4×#36972
#858423