Finite Group Databasebeta

← #11909729

Subgroups — #11909729

Order 1152.

1656 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#520C211yesmaximal, characteristic, complemented
2#10589936C211yesmaximal, characteristic, complemented
3#10589933C211yesmaximal, characteristic, complemented
4#10589678C211yesmaximal, characteristic, complemented
5#10589676C211yesmaximal, characteristic, complemented
6C4×Q8×D9C211yesmaximal, characteristic, complemented
7Q8×Dic18C211yesmaximal, characteristic, complemented
8#10589663C213yesmaximal, complemented
9#10589661C213yesmaximal, complemented
10#10589653C213yesmaximal, complemented
11#10589650C213yesmaximal, complemented
12#10589636C213yesmaximal, complemented
13#10589630C213yesmaximal, complemented
14#10589613C213yesmaximal, complemented
15#10589609C213yesmaximal, complemented
16#85908—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×#3701C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic
20C2×#3697C2216yes—
21C4×Q8×C9C2211yescharacteristic
22C4×Q8×C9C2211yescharacteristic
23C4×D4×C9C2213yes—
24C4×D4×C9C2213yes—
25C9×#117C2213yes—
26C2×C9×C4⋊C4C2213yes—
27Q8×Dic9C2211yescharacteristic
28Q8×Dic9C2211yescharacteristic
29#63502C2213yes—
30#63500C2213yes—
31#63500C2213yes—
32#63498C2213yes—
33#63492C2213yes—
34#63491C2216yes—
35C4×#611C2213yes—
36C4×#611C2213yes—
37C4×#611C2216yes—
38#63486C2213yes—
39#63486C2216yes—
40#63460C2213yes—
41#63459C2213yes—
42#63458C2216yes—
43#63458C2211yescharacteristic
44#63457C2213yes—
45#63456C2213yes—
46#63455C2213yes—
47C4⋊C4×D9C2213yes—
48C4⋊C4×D9C2213yes—
49#63451C2213yes—
50#63450C2213yes—
51#63450C2213yes—
52#63449C2213yes—
53#63447C2213yes—
54#63447C2216yes—
55#63446C2213yes—
56#63445C2213yes—
57#63445C2216yes—
58#63441C2213yes—
59#63437C2213yes—
60C4×D36C2213yes—
61C4×D36C2213yes—
62#63434C2213yes—
63C42×D9C2213yes—
64#63431C2213yes—
65C4×Dic18C2213yes—
66C4×Dic18C2213yes—
67C3×#520D311yescharacteristic
68#5834—31no—
69#5831—31no—
70#5576—31no—
71#5574—31no—
72C4×D3×Q8—31no—
73Q8×Dic6—31no—
74#5561—33no—
75#5559—33no—
76#5551—33no—
77#5548—33no—
78#5534—33no—
79#5528—33no—
80#5511—33no—
81#5507—33no—
82C9×#41—24no—
83C2×Q8×C9C2311yescharacteristic
84C2×D4×C9C2313yes—
85C22×C4×C9C2313yes—
86C22×C4×C9C2316yes—
87C2×#611C2313yes—
88C2×#611C2313yes—
89C2×#611C2316yes—
90#3701—24no—
91Q8×D9—24no—
92#3697—412no—
93C2×D36C2313yes—
94C2×D36C2313yes—
95C2×C4×D9C2313yes—
96C2×C4×D9C2313yes—
97C2×C4×D9C2311yescharacteristic
98C2×C4×D9C2313yes—
99C2×C4×D9C2316yes—
100C2×Dic18C2313yes—
101C2×Dic18C2311yescharacteristic
102C2×Dic18C2316yes—
103C9×C4⋊C4C2313yes—
104C9×C4⋊C4C2313yes—
105C9×C4⋊C4C2313yes—
106C9×C4⋊C4C2311yescharacteristic
107C9×C22⋊C4C2313yes—
108C9×C22⋊C4C2313yes—
109C42×C9C2313yes—
110C42×C9C2313yes—
111#3676C2313yes—
112#3676C2316yes—
113#3676C2313yes—
114(C2×D9)⋊C4C2311yescharacteristic
115(C2×D9)⋊C4C2316yes—
116(C2×D9)⋊C4C2313yes—
117(C2×D9)⋊C4C2313yes—
118(C2×D9)⋊C4C2313yes—
119(C2×D9)⋊C4C2311yescharacteristic
120(C2×D9)⋊C4C2313yes—
121C4⋊Dic9C2313yes—
122C4⋊Dic9C2313yes—
123C4⋊Dic9C2313yes—
124C4⋊Dic9C2313yes—
125Dic9⋊C4C2311yescharacteristic
126Dic9⋊C4C2313yes—
127Dic9⋊C4C2313yes—
128Dic9⋊C4C2313yes—
129Dic9⋊C4C2316yes—
130Dic9⋊C4C2311yescharacteristic
131Dic9⋊C4C2313yes—
132C4×Dic9C2313yes—
133C4×Dic9C2313yes—
134C4×Dic9C2313yes—
135C4×Dic9C2313yes—
136#3522—91noSylow
137C2×C3×#41C2×D311yescharacteristic
138C2×#239—31no—
139C2×D3×Q8—31no—
140C2×#235—36no—
141C3×C4×Q8C2×D311yescharacteristic
142C3×C4×Q8C2×D311yescharacteristic
143C3×C4×D4C2×D313yes—
144C3×C4×D4C2×D313yes—
145C3×#117C2×D313yes—
146C2×C3×C4⋊C4C2×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—36no—
158#924—33no—
159#924—36no—
160#898—33no—
161#897—33no—
162#896—36no—
163#896—31no—
164#895—33no—
165#894—33no—
166#893—33no—
167D3×C4⋊C4—33no—
168D3×C4⋊C4—33no—
169#889—33no—
170#888—33no—
171#888—33no—
172#887—33no—
173#885—33no—
174#885—36no—
175#884—33no—
176#883—33no—
177#883—36no—
178#879—33no—
179#875—33no—
180C4×D12—33no—
181C4×D12—33no—
182#872—33no—
183C42×D3—33no—
184#869—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—46no—
194C2×C4×C9C2411yescharacteristic
195C2×C4×C9C2413yes—
196C2×C4×C9C2411yescharacteristic
197C2×C4×C9C2413yes—
198C2×C4×C9C2411yescharacteristic
199C2×C4×C9C2413yes—
200#611—26no—
201#611—26no—
202#611—46no—
203C2×Dic9C2411yescharacteristic
204C2×Dic9C2413yes—
205C2×Dic9C2413yes—
206C2×Dic9C2413yes—
207C2×Dic9C2411yescharacteristic
208C2×Dic9C2411yescharacteristic
209D36—26no—
210D36—26no—
211C4×D9—26no—
212C4×D9—26no—
213C4×D9—26no—
214C4×D9—22no—
215C4×D9—46no—
216Dic18—26no—
217Dic18—22no—
218Dic18—46no—
219#559—93no—
220Q82—91no—
221#554—93no—
222#550—91no—
223#548—91no—
224#548—91no—
225#547—93no—
226#547—93no—
227#542—93no—
228#542—93no—
229#532—93no—
230#529—93no—
231#520—91no—
232#520D911yescharacteristic, complemented
233C2×C4×Q8—91no—
234C3×#41—24no—
235C2×C3×Q8C22×D311yescharacteristic
236C2×C3×D4C22×D313yes—
237C22×C3×C4C22×D313yes—
238C22×C3×C4C22×D316yes—
239C2×#67—33no—
240C2×#67—33no—
241C2×#67—36no—
242#239—64no—
243D3×Q8—64no—
244#235—1212no—
245C2×D12—33no—
246C2×D12—33no—
247C2×C4×D3—31no—
248C2×C4×D3—33no—
249C2×C4×D3—33no—
250C2×C4×D3—33no—
251C2×C4×D3—36no—
252C2×Dic6—31no—
253C2×Dic6—33no—
254C2×Dic6—36no—
255C3×C4⋊C4C22×D313yes—
256C3×C4⋊C4C22×D313yes—
257C3×C4⋊C4C22×D313yes—
258C3×C4⋊C4C22×D311yescharacteristic
259C3×C22⋊C4C22×D313yes—
260C3×C22⋊C4C22×D313yes—
261C3×C42C22×D313yes—
262C3×C42C22×D313yes—
263#217—33no—
264#217—33no—
265#217—36no—
266(C2×D3)⋊C4—33no—
267(C2×D3)⋊C4—33no—
268(C2×D3)⋊C4—31no—
269(C2×D3)⋊C4—33no—
270(C2×D3)⋊C4—36no—
271(C2×D3)⋊C4—31no—
272(C2×D3)⋊C4—33no—
273C4⋊Dic3—33no—
274C4⋊Dic3—33no—
275C4⋊Dic3—33no—
276C4⋊Dic3—33no—
277Dic3⋊C4—33no—
278Dic3⋊C4—36no—
279Dic3⋊C4—33no—
280Dic3⋊C4—31no—
281Dic3⋊C4—33no—
282Dic3⋊C4—31no—
283Dic3⋊C4—33no—
284C4×Dic3—33no—
285C4×Dic3—33no—
286C4×Dic3—33no—
287C4×Dic3—33no—
288C22×C9—23no—
289C22×C9—23no—
290C22×C9—23no—
291C22×C9C2511yescharacteristic
292C2×D9—21no—
293C2×D9—21no—
294C2×D9—23no—
295C2×D9—23no—
296C2×D9—23no—
297C2×D9H(5,𝔽2)12yes—
298C4×C9—21no—
299C4×C9—23no—
300C4×C9—23no—
301C4×C9—21no—
302C4×C9—21no—
303C4×C9C2×#4116yes—
304Dic9—23no—
305Dic9—21no—
306Dic9—23no—
307Dic9—23no—
308Dic9—21no—
309Dic92−1+412yes—
310C2×#41—91no—
311C2×#41—96no—
312C2×#41C2×D911yescharacteristic
313C22×Q8—91no—
314C4⋊Q8—93no—
315C4⋊Q8—93no—
316C4⋊Q8—93no—
317#127—93no—
318#126—93no—
319#126—93no—
320#125—93no—
321#124—93no—
322#124—93no—
323#124—96no—
324#124—93no—
325#123—96no—
326#123—93no—
327#123—93no—
328#123—96no—
329C22⋊Q8—96no—
330C22⋊Q8—93no—
331C22⋊Q8—91no—
332C22⋊Q8—96no—
333C22⋊Q8—93no—
334#121—93no—
335#121—93no—
336#121—93no—
337#121—93no—
338#121—93no—
339C4×Q8—91no—
340C4×Q8—91no—
341C4×Q8—93no—
342C4×Q8—93no—
343C4×Q8—93no—
344C4×Q8C2×D911yescharacteristic
345C4×Q8C2×D911yescharacteristic
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—96no—
349C4×D4—93no—
350C4×D4—93no—
351C4×D4—93no—
352C4×D4C2×D913yes—
353C4×D4C2×D913yes—
354#117—93no—
355#117C2×D913yes—
356C2×C4⋊C4—93no—
357C2×C4⋊C4—93no—
358C2×C4⋊C4C2×D913yes—
359C2×C42—93no—
360C23×C3C23×D313yes—
361C22×D3—31no—
362C22×D3—33no—
363C3×Q8#23514yes—
364C3×D4—26no—
365C2×C3×C4—26no—
366C2×C3×C4—46no—
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D313yes—
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D313yes—
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D313yes—
373#67—66no—
374#67—66no—
375#67—126no—
376C2×Dic3—31no—
377C2×Dic3—31no—
378C2×Dic3—33no—
379C2×Dic3—33no—
380C2×Dic3—33no—
381C2×Dic3—31no—
382D12—66no—
383D12—66no—
384C4×D3—62no—
385C4×D3—66no—
386C4×D3—66no—
387C4×D3—66no—
388C4×D3—126no—
389Dic6—62no—
390Dic6—66no—
391Dic6—126no—
392C2×C9—43no—
393C2×C9C22×#4111yescharacteristic
394C2×C9C2×H(5,𝔽2)11yescharacteristic
395C2×C9C2×2−1+411yescharacteristic
396D9—22no—
397D9—43no—
398#41—24no—
399#41—184no—
400#41—3612no—
401C2×Q8—91no—
402C2×Q8—93no—
403C2×Q8—96no—
404C2×Q8—184no—
405C2×Q8C22×D911yescharacteristic
406C2×D4—93no—
407C2×D4—93no—
408C2×D4—96no—
409C2×D4—93no—
410C2×D4—93no—
411C2×D4C22×D913yes—
412C22×C4—91no—
413C22×C4—93no—
414C22×C4—93no—
415C22×C4—93no—
416C22×C4—96no—
417C22×C4C22×D913yes—
418C22×C4C22×D916yes—
419C4⋊C4—93no—
420C4⋊C4—93no—
421C4⋊C4—93no—
422C4⋊C4—96no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—93no—
426C4⋊C4—93no—
427C4⋊C4—93no—
428C4⋊C4—93no—
429C4⋊C4—93no—
430C4⋊C4C22×D913yes—
431C4⋊C4C22×D913yes—
432C4⋊C4C22×D913yes—
433C4⋊C4C22×D911yescharacteristic
434C22⋊C4—93no—
435C22⋊C4—96no—
436C22⋊C4—93no—
437C22⋊C4—93no—
438C22⋊C4—93no—
439C22⋊C4—91no—
440C22⋊C4—91no—
441C22⋊C4—93no—
442C22⋊C4—96no—
443C22⋊C4—93no—
444C22⋊C4C22×D913yes—
445C22⋊C4C22×D913yes—
446C42—93no—
447C42—93no—
448C42—93no—
449C42—93no—
450C42C22×D913yes—
451C42C22×D913yes—
452C22×C3—23no—
453C22×C3—23no—
454C22×C3—23no—
455C22×C3C24×D311yescharacteristic
456C2×D3—32no—
457C2×D3—61no—
458C2×D3—61no—
459C2×D3—63no—
460C2×D3—63no—
461C2×D3—63no—
462C3×C4—21no—
463C3×C4—23no—
464C3×C4—23no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4C2×#23516yes—
468Dic3—32no—
469Dic3—63no—
470Dic3—61no—
471Dic3—63no—
472Dic3—63no—
473Dic3—61no—
474C9#352211yescharacteristic, complemented, Sylow
475C23—91no—
476C23—93no—
477C23C23×D913yes—
478Q8—182no—
479Q8—186no—
480Q8—366no—
481Q8#369714yescomplemented
482D4—26no—
483D4—186no—
484D4—186no—
485D4—186no—
486D4—186no—
487D4—366no—
488C2×C4—26no—
489C2×C4—46no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—93no—
493C2×C4—93no—
494C2×C4—93no—
495C2×C4—91no—
496C2×C4—182no—
497C2×C4—186no—
498C2×C4—186no—
499C2×C4—186no—
500C2×C4—366no—
501C2×C4C23×D911yescharacteristic
502C2×C4C23×D913yes—
503C2×C4C23×D911yescharacteristic
504C2×C4C23×D913yes—
505C2×C4C23×D911yescharacteristic
506C2×C4C23×D913yes—
507C2×C3—43no—
508C2×C3C22×#23511yescharacteristic
509C2×C3D3×H(5,𝔽2)11yescharacteristic
510C2×C3D3×2−1+411yescharacteristic
511D3—62no—
512D3—123no—
513C22—23no—
514C22—23no—
515C22—23no—
516C22—92no—
517C22—181no—
518C22—181no—
519C22—183no—
520C22—183no—
521C22—183no—
522C22C24×D911yescharacteristic
523C4—21no—
524C4—23no—
525C4—23no—
526C4—21no—
527C4—21no—
528C4—92no—
529C4—181no—
530C4—183no—
531C4—183no—
532C4—183no—
533C4—181no—
534C4C2×#369716yes—
535C3#8590811yescharacteristic
536C2—43no—
537C2—182no—
538C2—363no—
539C2C22×#369711yescharacteristic
540C2D9×H(5,𝔽2)11yescharacteristic
541C2D9×2−1+411yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#520C2
hypercenter#520D9
hypocenterC9#3522
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C9×#520C2semidirect
2. #10589936C2semidirect
3. #10589933C2semidirect
4. #10589678C2semidirect
5. #10589676C2semidirect
6. C4×Q8×D9C2semidirect
7. Q8×Dic18C2semidirect
8. #10589663C2semidirect
9. #10589661C2semidirect
10. #10589653C2semidirect
11. #10589650C2semidirect
12. #10589636C2semidirect
13. #10589630C2semidirect
14. #10589613C2semidirect
15. #10589609C2semidirect
190. Q8×C9#41semidirect
232. #520D9semidirect
474. C9#3522semidirect
481. Q8#3697semidirect

Maximal subgroups

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

subgroupindex
C9×#5202
#105899362
#105899332
#105896782
#105896762
C4×Q8×D92
Q8×Dic182
#105896632
#105896612
#105896532
#105896502
#105896362
#105896302
#105896132
#105896092
#859083