Finite Group Databasebeta

← #11909973

Subgroups — #11909973

Order 1152.

1545 conjugacy classes of subgroups.

The subgroup lattice has 534 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
5C4×#3701C211yesmaximal, characteristic, complemented
6#10589674C211yesmaximal, characteristic, complemented
7#10589672C211yesmaximal, characteristic, complemented
8#10589665C213yesmaximal, complemented
9#10589664C213yesmaximal, complemented
10#10589661C213yesmaximal, complemented
11#10589659C213yesmaximal, complemented
12#10589636C213yesmaximal, complemented
13#10589630C213yesmaximal, complemented
14#10589616C213yesmaximal, complemented
15#10589615C213yesmaximal, complemented
16#85898—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×#3701C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic
21C4×Q8×C9C2211yescharacteristic
22C4×D4×C9C2213yes—
23C4×D4×C9C2213yes—
24C9×#117C2213yes—
25C2×C9×C4⋊C4C2213yes—
26Q8×Dic9C2211yescharacteristic
27Q8×Dic9C2211yescharacteristic
28#63502C2213yes—
29#63500C2213yes—
30#63500C2213yes—
31#63498C2213yes—
32#63492C2213yes—
33#63492C2216yes—
34#63491C2216yes—
35C4×#611C2213yes—
36C4×#611C2213yes—
37C4×#611C2216yes—
38#63488C2216yes—
39#63486C2213yes—
40#63460C2216yes—
41#63460C2211yescharacteristic
42#63459C2213yes—
43#63458C2213yes—
44#63457C2213yes—
45#63456C2213yes—
46#63455C2213yes—
47#63454C2213yes—
48#63454C2213yes—
49#63452C2213yes—
50#63452C2213yes—
51#63451C2213yes—
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—
71C4×#239—31no—
72#5572—31no—
73#5570—31no—
74#5563—33no—
75#5562—33no—
76#5559—33no—
77#5557—33no—
78#5534—33no—
79#5528—33no—
80#5514—33no—
81#5513—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—
92C2×D36C2313yes—
93C2×D36C2313yes—
94C2×C4×D9C2313yes—
95C2×C4×D9C2313yes—
96C2×C4×D9C2313yes—
97C2×C4×D9C2313yes—
98C2×Dic18C2313yes—
99C2×Dic18C2313yes—
100C9×C4⋊C4C2313yes—
101C9×C4⋊C4C2313yes—
102C9×C4⋊C4C2313yes—
103C9×C4⋊C4C2311yescharacteristic
104C9×C22⋊C4C2313yes—
105C9×C22⋊C4C2313yes—
106C42×C9C2313yes—
107C42×C9C2313yes—
108#3676C2313yes—
109#3676C2316yes—
110#3676C2313yes—
111(C2×D9)⋊C4C2311yescharacteristic
112(C2×D9)⋊C4C2316yes—
113(C2×D9)⋊C4C2313yes—
114(C2×D9)⋊C4C2316yes—
115(C2×D9)⋊C4C2313yes—
116(C2×D9)⋊C4C2311yescharacteristic
117(C2×D9)⋊C4C2311yescharacteristic
118(C2×D9)⋊C4C2313yes—
119C4⋊Dic9C2313yes—
120C4⋊Dic9C2316yes—
121C4⋊Dic9C2313yes—
122C4⋊Dic9C2313yes—
123C4⋊Dic9C2311yescharacteristic
124Dic9⋊C4C2311yescharacteristic
125Dic9⋊C4C2313yes—
126Dic9⋊C4C2313yes—
127Dic9⋊C4C2313yes—
128Dic9⋊C4C2313yes—
129Dic9⋊C4C2313yes—
130C4×Dic9C2313yes—
131C4×Dic9C2316yes—
132C4×Dic9C2313yes—
133C4×Dic9C2313yes—
134C4×Dic9C2311yescharacteristic
135#3524—91noSylow
136C2×C3×#41C2×D311yescharacteristic
137C2×#239—31no—
138C2×D3×Q8—31no—
139C3×C4×Q8C2×D311yescharacteristic
140C3×C4×Q8C2×D311yescharacteristic
141C3×C4×D4C2×D313yes—
142C3×C4×D4C2×D313yes—
143C3×#117C2×D313yes—
144C2×C3×C4⋊C4C2×D313yes—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147#940—33no—
148#938—33no—
149#938—33no—
150#936—33no—
151#930—33no—
152#930—36no—
153#929—36no—
154C4×#67—33no—
155C4×#67—33no—
156C4×#67—36no—
157#926—36no—
158#924—33no—
159#898—36no—
160#898—31no—
161#897—33no—
162#896—33no—
163#895—33no—
164#894—33no—
165#893—33no—
166#892—33no—
167#892—33no—
168#890—33no—
169#890—33no—
170#889—33no—
171#887—33no—
172#885—33no—
173#885—36no—
174#884—33no—
175#883—33no—
176#883—36no—
177#879—33no—
178#875—33no—
179C4×D12—33no—
180C4×D12—33no—
181#872—33no—
182C42×D3—33no—
183#869—33no—
184C4×Dic6—33no—
185C4×Dic6—33no—
186C23×C9C2413yes—
187C22×D9C2411yescharacteristic
188C22×D9C2413yes—
189Q8×C9#4114yes—
190D4×C9—26no—
191C2×C4×C9—26no—
192C2×C4×C9—46no—
193C2×C4×C9C2413yes—
194C2×C4×C9C2411yescharacteristic
195C2×C4×C9C2411yescharacteristic
196C2×C4×C9C2413yes—
197C2×C4×C9C2411yescharacteristic
198C2×C4×C9C2413yes—
199#611—43no—
200#611—46no—
201#611—43no—
202C2×Dic9C2411yescharacteristic
203C2×Dic9C2411yescharacteristic
204C2×Dic9C2411yescharacteristic
205C2×Dic9C2413yes—
206C2×Dic9C2413yes—
207C2×Dic9C2413yes—
208D36—26no—
209D36—43no—
210C4×D9—26no—
211C4×D9—26no—
212C4×D9—43no—
213C4×D9—43no—
214Dic18—26no—
215Dic18—43no—
216#559—93no—
217#557—91no—
218#555—93no—
219#553—93no—
220#552—93no—
221#550—91no—
222#548—91no—
223#548—91no—
224#542—93no—
225#540—93no—
226#529—93no—
227#529—93no—
228#520D911yescharacteristic, complemented
229#519—91no—
230C4×#41—91no—
231C3×#41—24no—
232C2×C3×Q8C22×D311yescharacteristic
233C2×C3×D4C22×D313yes—
234C22×C3×C4C22×D313yes—
235C22×C3×C4C22×D316yes—
236C2×#67—33no—
237C2×#67—36no—
238C2×#67—33no—
239#239—64no—
240D3×Q8—64no—
241C2×D12—33no—
242C2×D12—33no—
243C2×C4×D3—33no—
244C2×C4×D3—33no—
245C2×C4×D3—33no—
246C2×C4×D3—33no—
247C2×Dic6—33no—
248C2×Dic6—33no—
249C3×C4⋊C4C22×D313yes—
250C3×C4⋊C4C22×D313yes—
251C3×C4⋊C4C22×D313yes—
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C22⋊C4C22×D313yes—
254C3×C22⋊C4C22×D313yes—
255C3×C42C22×D313yes—
256C3×C42C22×D313yes—
257#217—33no—
258#217—33no—
259#217—36no—
260(C2×D3)⋊C4—31no—
261(C2×D3)⋊C4—33no—
262(C2×D3)⋊C4—31no—
263(C2×D3)⋊C4—33no—
264(C2×D3)⋊C4—36no—
265(C2×D3)⋊C4—36no—
266(C2×D3)⋊C4—31no—
267(C2×D3)⋊C4—33no—
268C4⋊Dic3—31no—
269C4⋊Dic3—33no—
270C4⋊Dic3—33no—
271C4⋊Dic3—36no—
272C4⋊Dic3—33no—
273Dic3⋊C4—33no—
274Dic3⋊C4—33no—
275Dic3⋊C4—33no—
276Dic3⋊C4—33no—
277Dic3⋊C4—31no—
278Dic3⋊C4—33no—
279C4×Dic3—33no—
280C4×Dic3—33no—
281C4×Dic3—36no—
282C4×Dic3—31no—
283C4×Dic3—33no—
284C22×C9—23no—
285C22×C9—23no—
286C22×C9—23no—
287C22×C9C2511yescharacteristic
288C2×D9—21no—
289C2×D9—23no—
290C2×D9—23no—
291C2×D9—23no—
292C2×D9—21no—
293C2×D9—21no—
294C4×C9—21no—
295C4×C9—21no—
296C4×C9—21no—
297C4×C9—23no—
298C4×C9—23no—
299C4×C9C2×#4116yes—
300Dic9—23no—
301Dic9—21no—
302Dic9—23no—
303Dic9—23no—
304Dic9—21no—
305Dic9—21no—
306C2×#41—91no—
307C2×#41C2×D911yescharacteristic
308C22×Q8—91no—
309C4⋊Q8—93no—
310#127—93no—
311#126—91no—
312#126—96no—
313#126—93no—
314#125—93no—
315#125—93no—
316#125—93no—
317#124—93no—
318#124—93no—
319#124—96no—
320#124—93no—
321#123—96no—
322#123—93no—
323#123—96no—
324#123—93no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328#121—93no—
329#121—93no—
330#121—96no—
331#121—93no—
332#121—93no—
333#121—93no—
334C4×Q8—91no—
335C4×Q8—91no—
336C4×Q8—93no—
337C4×Q8—93no—
338C4×Q8—93no—
339C4×Q8C2×D911yescharacteristic
340C4×Q8C2×D911yescharacteristic
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—96no—
344C4×D4—93no—
345C4×D4—93no—
346C4×D4—93no—
347C4×D4C2×D913yes—
348C4×D4C2×D913yes—
349#117—96no—
350#117—93no—
351#117—93no—
352#117—93no—
353#117C2×D913yes—
354C2×C4⋊C4C2×D913yes—
355C2×C42—93no—
356C23×C3C23×D313yes—
357C22×D3—31no—
358C22×D3—33no—
359C3×Q8#23514yes—
360C3×D4—26no—
361C2×C3×C4—26no—
362C2×C3×C4—46no—
363C2×C3×C4C23×D313yes—
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D313yes—
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D313yes—
369#67—123no—
370#67—123no—
371#67—126no—
372C2×Dic3—31no—
373C2×Dic3—31no—
374C2×Dic3—31no—
375C2×Dic3—33no—
376C2×Dic3—33no—
377C2×Dic3—33no—
378D12—66no—
379D12—123no—
380C4×D3—66no—
381C4×D3—66no—
382C4×D3—123no—
383C4×D3—123no—
384Dic6—66no—
385Dic6—123no—
386C2×C9—43no—
387C2×C9C22×#4111yescharacteristic
388C2×C9#58511yescharacteristic
389C2×C9#58511yescharacteristic
390D9—41no—
391D9—43no—
392#41—24no—
393#41—184no—
394C2×Q8—93no—
395C2×Q8—93no—
396C2×Q8—184no—
397C2×Q8C22×D911yescharacteristic
398C2×D4—93no—
399C2×D4—96no—
400C2×D4—93no—
401C2×D4—93no—
402C2×D4—93no—
403C2×D4C22×D913yes—
404C22×C4—93no—
405C22×C4—93no—
406C22×C4—93no—
407C22×C4—93no—
408C22×C4C22×D913yes—
409C22×C4C22×D916yes—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—93no—
413C4⋊C4—93no—
414C4⋊C4—93no—
415C4⋊C4—96no—
416C4⋊C4—91no—
417C4⋊C4—93no—
418C4⋊C4—93no—
419C4⋊C4—91no—
420C4⋊C4—93no—
421C4⋊C4C22×D913yes—
422C4⋊C4C22×D913yes—
423C4⋊C4C22×D913yes—
424C4⋊C4C22×D911yescharacteristic
425C22⋊C4—93no—
426C22⋊C4—96no—
427C22⋊C4—93no—
428C22⋊C4—91no—
429C22⋊C4—93no—
430C22⋊C4—96no—
431C22⋊C4—91no—
432C22⋊C4—91no—
433C22⋊C4—93no—
434C22⋊C4—96no—
435C22⋊C4—93no—
436C22⋊C4C22×D913yes—
437C22⋊C4C22×D913yes—
438C42—91no—
439C42—93no—
440C42—93no—
441C42—96no—
442C42—93no—
443C42C22×D913yes—
444C42C22×D913yes—
445C22×C3—23no—
446C22×C3—23no—
447C22×C3—23no—
448C22×C3C24×D311yescharacteristic
449C2×D3—61no—
450C2×D3—63no—
451C2×D3—63no—
452C2×D3—61no—
453C2×D3—63no—
454C2×D3—61no—
455C3×C4—21no—
456C3×C4—23no—
457C3×C4—23no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4C2×#23516yes—
461Dic3—63no—
462Dic3—61no—
463Dic3—61no—
464Dic3—61no—
465Dic3—63no—
466Dic3—63no—
467C9#352411yescharacteristic, complemented, Sylow
468C23—91no—
469C23—93no—
470C23C23×D913yes—
471Q8—186no—
472Q8—363no—
473Q8#369714yes—
474D4—26no—
475D4—186no—
476D4—363no—
477D4—363no—
478D4—363no—
479D4—366no—
480C2×C4—26no—
481C2×C4—46no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—93no—
485C2×C4—91no—
486C2×C4—93no—
487C2×C4—93no—
488C2×C4—186no—
489C2×C4—186no—
490C2×C4—363no—
491C2×C4—363no—
492C2×C4C23×D913yes—
493C2×C4C23×D911yescharacteristic
494C2×C4C23×D911yescharacteristic
495C2×C4C23×D913yes—
496C2×C4C23×D911yescharacteristic
497C2×C4C23×D913yes—
498C2×C3—43no—
499C2×C3C22×#23511yescharacteristic
500C2×C3#596611yescharacteristic
501C2×C3#596811yescharacteristic
502D3—121no—
503D3—123no—
504C22—23no—
505C22—23no—
506C22—23no—
507C22—181no—
508C22—183no—
509C22—183no—
510C22—181no—
511C22—183no—
512C22—181no—
513C22C24×D911yescharacteristic
514C4—21no—
515C4—23no—
516C4—23no—
517C4—21no—
518C4—21no—
519C4—181no—
520C4—183no—
521C4—181no—
522C4—181no—
523C4—183no—
524C4—183no—
525C4C2×#369716yes—
526C3#8589811yescharacteristic
527C2—43no—
528C2—361no—
529C2—363no—
530C2C22×#369711yescharacteristic
531C2#1059314111yescharacteristic
532C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#520C2
hypercenter#520D9
hypocenterC9#3524
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. C4×#3701C2semidirect
6. #10589674C2semidirect
7. #10589672C2semidirect
8. #10589665C2semidirect
9. #10589664C2semidirect
10. #10589661C2semidirect
11. #10589659C2semidirect
12. #10589636C2semidirect
13. #10589630C2semidirect
14. #10589616C2semidirect
15. #10589615C2semidirect
228. #520D9semidirect
467. C9#3524semidirect

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
C4×#37012
#105896742
#105896722
#105896652
#105896642
#105896612
#105896592
#105896362
#105896302
#105896162
#105896152
#858983