Finite Group Databasebeta

← #11909964

Subgroups — #11909964

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×#550C211yesmaximal, characteristic, complemented
2#10589933C211yesmaximal, characteristic, complemented
3#10589933C211yesmaximal, characteristic, complemented
4#10589929C211yesmaximal, characteristic, complemented
5#41×Dic9C211yesmaximal, characteristic, complemented
6#10589821C213yesmaximal, complemented
7#10589815C213yesmaximal, complemented
8#10589720C213yesmaximal, complemented
9#10589718C213yesmaximal, complemented
10#10589705C213yesmaximal, complemented
11#10589702C213yesmaximal, complemented
12#10589674C211yesmaximal, characteristic, complemented
13#10589671C211yesmaximal, characteristic, complemented
14#10589643C213yesmaximal, complemented
15#10589640C213yesmaximal, complemented
16#86777—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×C9×#41C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic
20C9×#127C2213yes—
21C9×#121C2213yes—
22C9×#121C2213yes—
23C4×Q8×C9C2211yescharacteristic
24C4×D4×C9C2213yes—
25Q8×Dic9C2211yescharacteristic
26Q8×Dic9C2211yescharacteristic
27Q8×Dic9C2211yescharacteristic
28#63501C2216yes—
29#63501C2213yes—
30#63500C2213yes—
31#63500C2213yes—
32#63498C2213yes—
33#63498C2216yes—
34#63498C2213yes—
35#63497C2216yes—
36#63497C2213yes—
37#63497C2216yes—
38D4×Dic9C2216yes—
39D4×Dic9C2213yes—
40D4×Dic9C2213yes—
41D4×Dic9C2213yes—
42D4×Dic9C2213yes—
43C4×#611C2213yes—
44C4×#611C2213yes—
45#63488C2213yes—
46#63488C2213yes—
47C2×C4⋊Dic9C2213yes—
48#63486C2213yes—
49#63486C2213yes—
50C2×C4×Dic9C2213yes—
51#63460C2211yescharacteristic
52#63454C2213yes—
53#63452C2213yes—
54#63451C2213yes—
55#63450C2213yes—
56#63449C2213yes—
57#63448C2213yes—
58#63447C2213yes—
59#63441C2213yes—
60#63441C2216yes—
61#63440C2213yes—
62#63439C2216yes—
63#63434C2213yes—
64#63432C2213yes—
65C4×Dic18C2213yes—
66C4×Dic18C2213yes—
67C3×#550D311yescharacteristic
68#5831—31no—
69#5831—31no—
70#5827—31no—
71Dic3×#41—31no—
72#5719—33no—
73#5713—33no—
74#5618—33no—
75#5616—33no—
76#5603—33no—
77#5600—33no—
78#5572—31no—
79#5569—31no—
80#5541—33no—
81#5538—33no—
82C9×#41—24no—
83C9×#41—24no—
84C2×Q8×C9C2311yescharacteristic
85C2×D4×C9C2313yes—
86C2×D4×C9C2313yes—
87C2×D4×C9C2316yes—
88C2×D4×C9C2313yes—
89C22×C4×C9C2313yes—
90C22×C4×C9C2313yes—
91C2×#611C2313yes—
92C2×#611C2313yes—
93C22×Dic9C2313yes—
94C22×Dic9C2316yes—
95C22×Dic9C2313yes—
96Q8×D9—24no—
97C2×C4×D9C2313yes—
98C2×Dic18C2313yes—
99C2×Dic18C2313yes—
100C9×C4⋊C4C2311yescharacteristic
101C9×C4⋊C4C2313yes—
102C9×C22⋊C4C2313yes—
103C9×C22⋊C4C2313yes—
104C42×C9C2313yes—
105#3676C2313yes—
106#3676C2313yes—
107#3676C2316yes—
108#3676C2313yes—
109#3676C2313yes—
110#3676C2316yes—
111#3676C2316yes—
112(C2×D9)⋊C4C2311yescharacteristic
113(C2×D9)⋊C4C2311yescharacteristic
114(C2×D9)⋊C4C2311yescharacteristic
115(C2×D9)⋊C4C2313yes—
116C4⋊Dic9C2311yescharacteristic
117C4⋊Dic9C2313yes—
118C4⋊Dic9C2313yes—
119C4⋊Dic9C2313yes—
120C4⋊Dic9C2313yes—
121C4⋊Dic9C2313yes—
122Dic9⋊C4C2313yes—
123Dic9⋊C4C2313yes—
124Dic9⋊C4C2311yescharacteristic
125Dic9⋊C4C2313yes—
126Dic9⋊C4C2313yes—
127Dic9⋊C4C2313yes—
128Dic9⋊C4C2316yes—
129C4×Dic9C2313yes—
130C4×Dic9C2313yes—
131C4×Dic9C2313yes—
132C4×Dic9C2313yes—
133C4×Dic9C2316yes—
134C4×Dic9C2311yescharacteristic
135#3524—91noSylow
136C2×C3×#41C2×D311yescharacteristic
137C2×C3×#41C2×D311yescharacteristic
138C2×D3×Q8—31no—
139C3×#127C2×D313yes—
140C3×#121C2×D313yes—
141C3×#121C2×D313yes—
142C3×C4×Q8C2×D311yescharacteristic
143C3×C4×D4C2×D313yes—
144Q8×Dic3—31no—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147#939—33no—
148#939—36no—
149#938—33no—
150#938—33no—
151#936—33no—
152#936—33no—
153#936—36no—
154#935—33no—
155#935—36no—
156#935—36no—
157D4×Dic3—33no—
158D4×Dic3—33no—
159D4×Dic3—36no—
160D4×Dic3—33no—
161D4×Dic3—33no—
162C4×#67—33no—
163C4×#67—33no—
164#926—33no—
165#926—33no—
166C2×C4⋊Dic3—33no—
167#924—33no—
168#924—33no—
169C2×C4×Dic3—33no—
170#898—31no—
171#892—33no—
172#890—33no—
173#889—33no—
174#888—33no—
175#887—33no—
176#886—33no—
177#885—33no—
178#879—33no—
179#879—36no—
180#878—33no—
181#877—36no—
182#872—33no—
183#870—33no—
184C4×Dic6—33no—
185C4×Dic6—33no—
186C23×C9C2413yes—
187C23×C9C2413yes—
188C22×D9C2411yescharacteristic
189Q8×C9#4114yes—
190D4×C9—26no—
191D4×C9—26no—
192D4×C9—46no—
193D4×C9—43no—
194C2×C4×C9—26no—
195C2×C4×C9—26no—
196C2×C4×C9C2411yescharacteristic
197C2×C4×C9C2413yes—
198C2×C4×C9C2411yescharacteristic
199C2×C4×C9C2411yescharacteristic
200C2×C4×C9C2413yes—
201#611—43no—
202#611—43no—
203C2×Dic9—43no—
204C2×Dic9—43no—
205C2×Dic9—46no—
206C2×Dic9C2411yescharacteristic
207C2×Dic9C2413yes—
208C2×Dic9C2411yescharacteristic
209C2×Dic9C2411yescharacteristic
210C2×Dic9C2413yes—
211C2×Dic9C2413yes—
212C2×Dic9C2413yes—
213C4×D9—26no—
214Dic18—26no—
215Dic18—43no—
216#559—93no—
217#557—91no—
218#555—93no—
219#553—93no—
220#552—93no—
221#550D911yescharacteristic, complemented
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—
231C3×#41—24no—
232C3×#41—24no—
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×D4C22×D313yes—
235C2×C3×D4C22×D313yes—
236C2×C3×D4C22×D316yes—
237C2×C3×D4C22×D313yes—
238C22×C3×C4C22×D313yes—
239C22×C3×C4C22×D313yes—
240C2×#67—33no—
241C2×#67—33no—
242C22×Dic3—36no—
243C22×Dic3—33no—
244C22×Dic3—33no—
245D3×Q8—64no—
246C2×C4×D3—33no—
247C2×Dic6—33no—
248C2×Dic6—33no—
249C3×C4⋊C4C22×D313yes—
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C22⋊C4C22×D313yes—
252C3×C22⋊C4C22×D313yes—
253C3×C42C22×D313yes—
254#217—36no—
255#217—33no—
256#217—36no—
257#217—33no—
258#217—36no—
259#217—33no—
260#217—33no—
261(C2×D3)⋊C4—31no—
262(C2×D3)⋊C4—33no—
263(C2×D3)⋊C4—31no—
264(C2×D3)⋊C4—31no—
265C4⋊Dic3—33no—
266C4⋊Dic3—33no—
267C4⋊Dic3—33no—
268C4⋊Dic3—33no—
269C4⋊Dic3—31no—
270C4⋊Dic3—33no—
271Dic3⋊C4—31no—
272Dic3⋊C4—33no—
273Dic3⋊C4—33no—
274Dic3⋊C4—36no—
275Dic3⋊C4—33no—
276Dic3⋊C4—33no—
277Dic3⋊C4—33no—
278C4×Dic3—36no—
279C4×Dic3—33no—
280C4×Dic3—33no—
281C4×Dic3—33no—
282C4×Dic3—33no—
283C4×Dic3—31no—
284C22×C9—23no—
285C22×C9—23no—
286C22×C9—23no—
287C22×C9—23no—
288C22×C9—23no—
289C22×C9—23no—
290C22×C9C2511yescharacteristic
291C2×D9—21no—
292C2×D9—21no—
293C2×D9—21no—
294C4×C9—21no—
295C4×C9—21no—
296C4×C9—23no—
297C4×C9—21no—
298C4×C9C2×#4116yes—
299Dic9—23no—
300Dic9—21no—
301Dic9—23no—
302Dic9—21no—
303Dic9—23no—
304Dic9—21no—
305Dic9—23no—
306C2×#41C2×D911yescharacteristic
307C2×#41C2×D911yescharacteristic
308C22×Q8—91no—
309C4⋊Q8—93no—
310#127C2×D913yes—
311#126—91no—
312#126—93no—
313#126—96no—
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—93no—
331#121—96no—
332#121C2×D913yes—
333#121C2×D913yes—
334C4×Q8—91no—
335C4×Q8—91no—
336C4×Q8—91no—
337C4×Q8—93no—
338C4×Q8—93no—
339C4×Q8—93no—
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×D4C2×D913yes—
349#117—93no—
350#117—93no—
351#117—93no—
352#117—96no—
353#117—93no—
354C2×C4⋊C4—93no—
355C2×C42—93no—
356C23×C3C23×D313yes—
357C23×C3C23×D313yes—
358C22×D3—31no—
359C3×Q8#23714yes—
360C3×D4—26no—
361C3×D4—26no—
362C3×D4—43no—
363C3×D4—46no—
364C2×C3×C4—26no—
365C2×C3×C4—26no—
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D313yes—
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D313yes—
371#67—123no—
372#67—123no—
373C2×Dic3—31no—
374C2×Dic3—33no—
375C2×Dic3—31no—
376C2×Dic3—31no—
377C2×Dic3—33no—
378C2×Dic3—33no—
379C2×Dic3—33no—
380C2×Dic3—123no—
381C2×Dic3—126no—
382C2×Dic3—123no—
383C4×D3—66no—
384Dic6—66no—
385Dic6—123no—
386C2×C9—43no—
387C2×C9—43no—
388C2×C9C22×#4111yescharacteristic
389C2×C9#58511yescharacteristic
390C2×C9#58511yescharacteristic
391D9—41no—
392#41—24no—
393#41—24no—
394C2×Q8—93no—
395C2×Q8—93no—
396C2×Q8—184no—
397C2×Q8C22×D911yescharacteristic
398C2×D4—93no—
399C2×D4—93no—
400C2×D4C22×D913yes—
401C2×D4C22×D913yes—
402C2×D4C22×D916yes—
403C2×D4C22×D913yes—
404C22×C4—93no—
405C22×C4—93no—
406C22×C4—96no—
407C22×C4—93no—
408C22×C4C22×D913yes—
409C22×C4C22×D913yes—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—93no—
413C4⋊C4—91no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—93no—
417C4⋊C4—93no—
418C4⋊C4—96no—
419C4⋊C4—93no—
420C4⋊C4—93no—
421C4⋊C4—91no—
422C4⋊C4—93no—
423C4⋊C4C22×D913yes—
424C4⋊C4C22×D911yescharacteristic
425C22⋊C4—93no—
426C22⋊C4—96no—
427C22⋊C4—93no—
428C22⋊C4—96no—
429C22⋊C4—93no—
430C22⋊C4—96no—
431C22⋊C4—93no—
432C22⋊C4—91no—
433C22⋊C4—93no—
434C22⋊C4—91no—
435C22⋊C4—91no—
436C22⋊C4C22×D913yes—
437C22⋊C4C22×D913yes—
438C42—91no—
439C42—93no—
440C42—93no—
441C42—93no—
442C42—96no—
443C42—93no—
444C42C22×D913yes—
445C22×C3—23no—
446C22×C3—23no—
447C22×C3—23no—
448C22×C3—23no—
449C22×C3—23no—
450C22×C3—23no—
451C22×C3C24×D311yescharacteristic
452C2×D3—61no—
453C2×D3—61no—
454C2×D3—61no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—23no—
459C3×C4C2×#23716yes—
460Dic3—63no—
461Dic3—63no—
462Dic3—61no—
463Dic3—63no—
464Dic3—61no—
465Dic3—63no—
466Dic3—61no—
467C9#352411yescharacteristic, complemented, Sylow
468C23—91no—
469C23C23×D913yes—
470C23C23×D913yes—
471Q8—186no—
472Q8—363no—
473Q8#369914yes—
474D4—26no—
475D4—26no—
476D4—43no—
477D4—46no—
478D4—363no—
479D4—363no—
480C2×C4—26no—
481C2×C4—26no—
482C2×C4—91no—
483C2×C4—93no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—93no—
487C2×C4—93no—
488C2×C4—93no—
489C2×C4—186no—
490C2×C4—363no—
491C2×C4—366no—
492C2×C4—363no—
493C2×C4C23×D911yescharacteristic
494C2×C4C23×D913yes—
495C2×C4C23×D911yescharacteristic
496C2×C4C23×D911yescharacteristic
497C2×C4C23×D913yes—
498C2×C3—43no—
499C2×C3—43no—
500C2×C3C22×#23711yescharacteristic
501C2×C3#596411yescharacteristic
502C2×C3#596611yescharacteristic
503D3—121no—
504C22—23no—
505C22—23no—
506C22—23no—
507C22—23no—
508C22—23no—
509C22—23no—
510C22—181no—
511C22—181no—
512C22—181no—
513C22C24×D911yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—23no—
518C4—183no—
519C4—181no—
520C4—183no—
521C4—183no—
522C4—181no—
523C4—183no—
524C4—181no—
525C4C2×#369916yes—
526C3#8677711yescharacteristic
527C2—43no—
528C2—43no—
529C2—361no—
530C2C22×#369911yescharacteristic
531C2#1059313911yescharacteristic
532C2#1059314111yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#550C2
hypercenter#550D9
hypocenterC9#3524
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C9×#550C2semidirect
2. #10589933C2semidirect
3. #10589933C2semidirect
4. #10589929C2semidirect
5. #41×Dic9C2semidirect
6. #10589821C2semidirect
7. #10589815C2semidirect
8. #10589720C2semidirect
9. #10589718C2semidirect
10. #10589705C2semidirect
11. #10589702C2semidirect
12. #10589674C2semidirect
13. #10589671C2semidirect
14. #10589643C2semidirect
15. #10589640C2semidirect
221. #550D9semidirect
467. C9#3524semidirect

Maximal subgroups

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

subgroupindex
C9×#5502
#105899332
#105899292
#41×Dic92
#105898212
#105898152
#105897202
#105897182
#105897052
#105897022
#105896742
#105896712
#105896432
#105896402
#867773