Finite Group Databasebeta

← #11910006

Subgroups — #11910006

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×#557C211yesmaximal, characteristic, complemented
2#10589836C213yesmaximal, complemented
3#10589835C213yesmaximal, complemented
4#10589799C213yesmaximal, complemented
5#10589797C213yesmaximal, complemented
6#10589796C213yesmaximal, complemented
7#10589793C213yesmaximal, complemented
8#10589687C213yesmaximal, complemented
9#10589682C213yesmaximal, complemented
10#10589679C211yesmaximal, characteristic, complemented
11#10589678C211yesmaximal, characteristic, complemented
12#10589678C211yesmaximal, characteristic, complemented
13#10589676C211yesmaximal, characteristic, complemented
14C4×#3701C211yesmaximal, characteristic, complemented
15#10589674C211yesmaximal, characteristic, complemented
16#87026—31nomaximal
17C2×#3701C2211yescharacteristic
18C2×#3701C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic
20C9×C4⋊Q8C2213yes—
21C9×#125C2213yes—
22C9×#125C2213yes—
23C4×Q8×C9C2211yescharacteristic
24C4×Q8×C9C2211yescharacteristic
25C4×Q8×C9C2211yescharacteristic
26C4×Q8×C9C2213yes—
27#63509C2216yes—
28#63509C2213yes—
29#63508C2213yes—
30Q8×Dic9C2211yescharacteristic
31#63460C2213yes—
32#63460C2216yes—
33#63460C2211yescharacteristic
34#63459C2213yes—
35#63459C2213yes—
36#63457C2213yes—
37#63457C2216yes—
38#63457C2213yes—
39#63457C2213yes—
40#63457C2213yes—
41#63457C2213yes—
42#63456C2216yes—
43#63456C2216yes—
44#63456C2213yes—
45#63456C2213yes—
46#63455C2216yes—
47#63455C2213yes—
48#63455C2213yes—
49#63454C2216yes—
50#63454C2213yes—
51#63454C2213yes—
52C4⋊C4×D9C2213yes—
53#63452C2213yes—
54#63449C2213yes—
55#63437C2213yes—
56#63437C2213yes—
57#63436C2213yes—
58C4×D36C2213yes—
59C4×D36C2213yes—
60C4×D36C2213yes—
61C4×D36C2213yes—
62C4×D36C2213yes—
63#63434C2213yes—
64#63434C2213yes—
65C42×D9C2213yes—
66C4×Dic18C2213yes—
67C3×#557D311yescharacteristic
68#5734—33no—
69#5733—33no—
70#5697—33no—
71#5695—33no—
72#5694—33no—
73#5691—33no—
74#5585—33no—
75#5580—33no—
76#5577—31no—
77#5576—31no—
78#5576—31no—
79#5574—31no—
80C4×#239—31no—
81#5572—31no—
82C2×Q8×C9C2313yes—
83C2×Q8×C9C2311yescharacteristic
84#3701—24no—
85#3701—24no—
86Q8×D9—24no—
87C2×D36C2313yes—
88C2×D36C2313yes—
89C2×D36C2313yes—
90C2×D36C2316yes—
91C2×D36C2313yes—
92C2×D36C2313yes—
93C2×C4×D9C2313yes—
94C2×C4×D9C2313yes—
95C2×C4×D9C2313yes—
96C2×C4×D9C2313yes—
97C2×C4×D9C2313yes—
98C2×C4×D9C2316yes—
99C2×Dic18C2313yes—
100C9×C4⋊C4C2311yescharacteristic
101C9×C4⋊C4C2313yes—
102C9×C4⋊C4C2313yes—
103C9×C4⋊C4C2313yes—
104C9×C4⋊C4C2313yes—
105C9×C4⋊C4C2313yes—
106C9×C4⋊C4C2316yes—
107C42×C9C2313yes—
108C42×C9C2313yes—
109C42×C9C2313yes—
110(C2×D9)⋊C4C2313yes—
111(C2×D9)⋊C4C2313yes—
112(C2×D9)⋊C4C2313yes—
113(C2×D9)⋊C4C2311yescharacteristic
114(C2×D9)⋊C4C2313yes—
115(C2×D9)⋊C4C2313yes—
116(C2×D9)⋊C4C2316yes—
117(C2×D9)⋊C4C2316yes—
118(C2×D9)⋊C4C2311yescharacteristic
119(C2×D9)⋊C4C2313yes—
120(C2×D9)⋊C4C2311yescharacteristic
121(C2×D9)⋊C4C2313yes—
122(C2×D9)⋊C4C2316yes—
123C4⋊Dic9C2313yes—
124C4⋊Dic9C2313yes—
125C4⋊Dic9C2311yescharacteristic
126C4⋊Dic9C2313yes—
127Dic9⋊C4C2311yescharacteristic
128Dic9⋊C4C2313yes—
129Dic9⋊C4C2313yes—
130Dic9⋊C4C2313yes—
131C4×Dic9C2313yes—
132C4×Dic9C2316yes—
133C4×Dic9C2313yes—
134C4×Dic9C2311yescharacteristic
135#3524—91noSylow
136C2×#239—31no—
137C2×#239—31no—
138C2×D3×Q8—31no—
139C3×C4⋊Q8C2×D313yes—
140C3×#125C2×D313yes—
141C3×#125C2×D313yes—
142C3×C4×Q8C2×D311yescharacteristic
143C3×C4×Q8C2×D311yescharacteristic
144C3×C4×Q8C2×D311yescharacteristic
145C3×C4×Q8C2×D313yes—
146#947—36no—
147#947—33no—
148#946—33no—
149Q8×Dic3—31no—
150#898—33no—
151#898—36no—
152#898—31no—
153#897—33no—
154#897—33no—
155#895—33no—
156#895—36no—
157#895—33no—
158#895—33no—
159#895—33no—
160#895—33no—
161#894—36no—
162#894—36no—
163#894—33no—
164#894—33no—
165#893—36no—
166#893—33no—
167#893—33no—
168#892—36no—
169#892—33no—
170#892—33no—
171D3×C4⋊C4—33no—
172#890—33no—
173#887—33no—
174#875—33no—
175#875—33no—
176#874—33no—
177C4×D12—33no—
178C4×D12—33no—
179C4×D12—33no—
180C4×D12—33no—
181C4×D12—33no—
182#872—33no—
183#872—33no—
184C42×D3—33no—
185C4×Dic6—33no—
186C22×D9C2411yescharacteristic
187C22×D9C2413yes—
188C22×D9C2413yes—
189Q8×C9—43no—
190Q8×C9#4114yes—
191C2×C4×C9C2413yes—
192C2×C4×C9C2413yes—
193C2×C4×C9C2411yescharacteristic
194C2×C4×C9C2411yescharacteristic
195C2×C4×C9C2413yes—
196C2×C4×C9C2411yescharacteristic
197C2×C4×C9C2413yes—
198C2×Dic9C2411yescharacteristic
199C2×Dic9C2413yes—
200C2×Dic9C2411yescharacteristic
201C2×Dic9C2413yes—
202C2×Dic9C2411yescharacteristic
203D36—26no—
204D36—26no—
205D36—43no—
206D36—43no—
207D36—43no—
208D36—46no—
209C4×D9—26no—
210C4×D9—26no—
211C4×D9—26no—
212C4×D9—43no—
213C4×D9—46no—
214C4×D9—43no—
215Dic18—26no—
216#559—93no—
217#557D911yescharacteristic, complemented
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#520—91no—
229#519—91no—
230C4×#41—91no—
231C2×C3×Q8C22×D313yes—
232C2×C3×Q8C22×D311yescharacteristic
233#239—64no—
234#239—64no—
235D3×Q8—64no—
236C2×D12—33no—
237C2×D12—33no—
238C2×D12—33no—
239C2×D12—33no—
240C2×D12—33no—
241C2×D12—36no—
242C2×C4×D3—33no—
243C2×C4×D3—33no—
244C2×C4×D3—33no—
245C2×C4×D3—33no—
246C2×C4×D3—33no—
247C2×C4×D3—36no—
248C2×Dic6—33no—
249C3×C4⋊C4C22×D313yes—
250C3×C4⋊C4C22×D313yes—
251C3×C4⋊C4C22×D313yes—
252C3×C4⋊C4C22×D313yes—
253C3×C4⋊C4C22×D316yes—
254C3×C4⋊C4C22×D313yes—
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C42C22×D313yes—
257C3×C42C22×D313yes—
258C3×C42C22×D313yes—
259(C2×D3)⋊C4—31no—
260(C2×D3)⋊C4—33no—
261(C2×D3)⋊C4—33no—
262(C2×D3)⋊C4—33no—
263(C2×D3)⋊C4—31no—
264(C2×D3)⋊C4—31no—
265(C2×D3)⋊C4—33no—
266(C2×D3)⋊C4—33no—
267(C2×D3)⋊C4—33no—
268(C2×D3)⋊C4—36no—
269(C2×D3)⋊C4—33no—
270(C2×D3)⋊C4—36no—
271(C2×D3)⋊C4—36no—
272C4⋊Dic3—33no—
273C4⋊Dic3—31no—
274C4⋊Dic3—33no—
275C4⋊Dic3—33no—
276Dic3⋊C4—33no—
277Dic3⋊C4—31no—
278Dic3⋊C4—33no—
279Dic3⋊C4—33no—
280C4×Dic3—36no—
281C4×Dic3—31no—
282C4×Dic3—33no—
283C4×Dic3—33no—
284C22×C9C2511yescharacteristic
285C2×D9—21no—
286C2×D9—23no—
287C2×D9—23no—
288C2×D9—23no—
289C2×D9—23no—
290C2×D9—23no—
291C2×D9—21no—
292C2×D9—23no—
293C2×D9—21no—
294C4×C9—21no—
295C4×C9—23no—
296C4×C9—23no—
297C4×C9—21no—
298C4×C9—23no—
299C4×C9—21no—
300C4×C9C2×#4116yes—
301Dic9—23no—
302Dic9—21no—
303Dic9—21no—
304Dic9—21no—
305Dic9—23no—
306C2×#41—91no—
307C2×#41—91no—
308C22×Q8—91no—
309C4⋊Q8C2×D913yes—
310#127—93no—
311#126—91no—
312#126—93no—
313#126—96no—
314#125—93no—
315#125C2×D913yes—
316#125C2×D913yes—
317#124—93no—
318#124—96no—
319#124—93no—
320#124—93no—
321#123—96no—
322#123—93no—
323#123—93no—
324#123—96no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8—93no—
328#121—93no—
329#121—93no—
330#121—93no—
331#121—93no—
332#121—96no—
333#121—93no—
334C4×Q8—91no—
335C4×Q8—93no—
336C4×Q8—93no—
337C4×Q8C2×D911yescharacteristic
338C4×Q8C2×D911yescharacteristic
339C4×Q8C2×D911yescharacteristic
340C4×Q8C2×D913yes—
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—96no—
344C4×D4—93no—
345C4×D4—93no—
346C4×D4—93no—
347C4×D4—93no—
348C4×D4—93no—
349#117—93no—
350#117—93no—
351#117—96no—
352#117—93no—
353#117—93no—
354C2×C4⋊C4—93no—
355C2×C42—93no—
356C22×D3—31no—
357C22×D3—33no—
358C22×D3—33no—
359C3×Q8—43no—
360C3×Q8#23914yes—
361C2×C3×C4C23×D313yes—
362C2×C3×C4C23×D313yes—
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365C2×C3×C4C23×D313yes—
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D313yes—
368C2×Dic3—31no—
369C2×Dic3—33no—
370C2×Dic3—31no—
371C2×Dic3—33no—
372C2×Dic3—31no—
373D12—66no—
374D12—66no—
375D12—123no—
376D12—126no—
377D12—123no—
378D12—123no—
379C4×D3—66no—
380C4×D3—66no—
381C4×D3—66no—
382C4×D3—123no—
383C4×D3—123no—
384C4×D3—126no—
385Dic6—66no—
386C2×C9C22×#4111yescharacteristic
387C2×C9#58511yescharacteristic
388C2×C9#58511yescharacteristic
389D9—41no—
390D9—43no—
391D9—43no—
392#41—184no—
393#41—184no—
394C2×Q8—93no—
395C2×Q8—184no—
396C2×Q8C22×D913yes—
397C2×Q8C22×D911yescharacteristic
398C2×D4—93no—
399C2×D4—93no—
400C2×D4—93no—
401C2×D4—93no—
402C2×D4—96no—
403C2×D4—93no—
404C22×C4—93no—
405C22×C4—93no—
406C22×C4—93no—
407C22×C4—93no—
408C22×C4—93no—
409C22×C4—96no—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—91no—
413C4⋊C4—93no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—91no—
417C4⋊C4—93no—
418C4⋊C4C22×D913yes—
419C4⋊C4C22×D913yes—
420C4⋊C4C22×D913yes—
421C4⋊C4C22×D916yes—
422C4⋊C4C22×D913yes—
423C4⋊C4C22×D911yescharacteristic
424C4⋊C4C22×D913yes—
425C22⋊C4—91no—
426C22⋊C4—93no—
427C22⋊C4—93no—
428C22⋊C4—93no—
429C22⋊C4—96no—
430C22⋊C4—93no—
431C22⋊C4—96no—
432C22⋊C4—91no—
433C22⋊C4—93no—
434C22⋊C4—91no—
435C22⋊C4—93no—
436C22⋊C4—96no—
437C22⋊C4—93no—
438C42—91no—
439C42—93no—
440C42—93no—
441C42—96no—
442C42C22×D913yes—
443C42C22×D913yes—
444C42C22×D913yes—
445C22×C3C24×D311yescharacteristic
446C2×D3—61no—
447C2×D3—63no—
448C2×D3—63no—
449C2×D3—63no—
450C2×D3—61no—
451C2×D3—63no—
452C2×D3—63no—
453C2×D3—63no—
454C2×D3—61no—
455C3×C4—23no—
456C3×C4—23no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—23no—
460C3×C4—21no—
461C3×C4C2×#23916yes—
462Dic3—63no—
463Dic3—61no—
464Dic3—61no—
465Dic3—61no—
466Dic3—63no—
467C9#352411yescharacteristic, complemented, Sylow
468C23—91no—
469C23—93no—
470C23—93no—
471Q8—43no—
472Q8—186no—
473Q8#370114yes—
474D4—186no—
475D4—186no—
476D4—363no—
477D4—366no—
478D4—363no—
479D4—363no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—93no—
483C2×C4—93no—
484C2×C4—91no—
485C2×C4—186no—
486C2×C4—186no—
487C2×C4—186no—
488C2×C4—363no—
489C2×C4—363no—
490C2×C4—366no—
491C2×C4C23×D913yes—
492C2×C4C23×D911yescharacteristic
493C2×C4C23×D913yes—
494C2×C4C23×D911yescharacteristic
495C2×C4C23×D911yescharacteristic
496C2×C4C23×D913yes—
497C2×C4C23×D913yes—
498C2×C3C22×#23911yescharacteristic
499C2×C3#596411yescharacteristic
500C2×C3#596811yescharacteristic
501D3—121no—
502D3—123no—
503D3—123no—
504C22—181no—
505C22—183no—
506C22—183no—
507C22—183no—
508C22—181no—
509C22—183no—
510C22—183no—
511C22—183no—
512C22—181no—
513C22C24×D911yescharacteristic
514C4—23no—
515C4—23no—
516C4—21no—
517C4—21no—
518C4—23no—
519C4—21no—
520C4—181no—
521C4—181no—
522C4—183no—
523C4—181no—
524C4—183no—
525C4C2×#370116yes—
526C3#8702611yescharacteristic
527C2—361no—
528C2—363no—
529C2—363no—
530C2C22×#370111yescharacteristic
531C2#1059313911yescharacteristic
532C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#557C2
hypercenter#557D9
hypocenterC9#3524
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C9×#557C2semidirect
2. #10589836C2semidirect
3. #10589835C2semidirect
4. #10589799C2semidirect
5. #10589797C2semidirect
6. #10589796C2semidirect
7. #10589793C2semidirect
8. #10589687C2semidirect
9. #10589682C2semidirect
10. #10589679C2semidirect
11. #10589678C2semidirect
12. #10589678C2semidirect
13. #10589676C2semidirect
14. C4×#3701C2semidirect
15. #10589674C2semidirect
217. #557D9semidirect
467. C9#3524semidirect

Maximal subgroups

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

subgroupindex
C9×#5572
#105898362
#105898352
#105897992
#105897972
#105897962
#105897932
#105896872
#105896822
#105896792
#105896782
#105896762
C4×#37012
#105896742
#870263