Finite Group Databasebeta

← #11909976

Subgroups — #11909976

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×#548C211yesmaximal, characteristic, complemented
2#10589936C211yesmaximal, characteristic, complemented
3#10589929C211yesmaximal, characteristic, complemented
4#10589919C211yesmaximal, characteristic, complemented
5#10589914C211yesmaximal, characteristic, complemented
6#10589783C213yesmaximal, complemented
7#10589782C213yesmaximal, complemented
8#10589745C213yesmaximal, complemented
9#10589744C213yesmaximal, complemented
10#10589721C213yesmaximal, complemented
11#10589718C213yesmaximal, complemented
12C4×#3701C211yesmaximal, characteristic, complemented
13#10589671C211yesmaximal, characteristic, complemented
14#10589667C213yesmaximal, complemented
15#10589659C213yesmaximal, complemented
16#86724—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C22×Q8×C9C2211yescharacteristic
19C2×#3701C2211yescharacteristic
20C9×#124C2213yes—
21C9×C22⋊Q8C2213yes—
22C9×#121C2213yes—
23C4×Q8×C9C2211yescharacteristic
24C4×D4×C9C2213yes—
25#63509C2213yes—
26#63508C2213yes—
27Q8×Dic9C2213yes—
28Q8×Dic9C2213yes—
29Q8×Dic9C2211yescharacteristic
30Q8×Dic9C2211yescharacteristic
31Q8×Dic9C2211yescharacteristic
32#63502C2213yes—
33#63501C2216yes—
34#63500C2213yes—
35#63500C2213yes—
36#63498C2213yes—
37D4×Dic9C2213yes—
38D4×Dic9C2213yes—
39#63492C2213yes—
40#63492C2213yes—
41C4×#611C2213yes—
42C4×#611C2213yes—
43#63488C2213yes—
44#63488C2213yes—
45#63488C2213yes—
46C2×C4⋊Dic9C2213yes—
47#63460C2216yes—
48#63459C2213yes—
49#63455C2213yes—
50#63454C2213yes—
51#63452C2213yes—
52#63452C2213yes—
53#63450C2213yes—
54#63448C2216yes—
55#63447C2216yes—
56#63445C2216yes—
57#63445C2213yes—
58#63445C2213yes—
59#611⋊C4C2216yes—
60#63441C2213yes—
61#63441C2211yescharacteristic
62#63439C2216yes—
63C4×D36C2213yes—
64C42×D9C2213yes—
65#63432C2213yes—
66C4×Dic18C2213yes—
67C3×#548D311yescharacteristic
68#5834—31no—
69#5827—31no—
70#5817—31no—
71#5812—31no—
72#5681—33no—
73#5680—33no—
74#5643—33no—
75#5642—33no—
76#5619—33no—
77#5616—33no—
78C4×#239—31no—
79#5569—31no—
80#5565—33no—
81#5557—33no—
82C9×#41—24no—
83C2×Q8×C9—24no—
84C2×Q8×C9C2313yes—
85C2×Q8×C9C2311yescharacteristic
86C2×D4×C9C2313yes—
87C2×D4×C9C2313yes—
88C22×C4×C9C2313yes—
89C22×C4×C9C2313yes—
90C2×#611C2313yes—
91C2×#611C2313yes—
92C2×#611C2316yes—
93C22×Dic9C2316yes—
94#3701—24no—
95C2×D36C2313yes—
96C2×C4×D9C2313yes—
97C2×C4×D9C2313yes—
98C2×C4×D9C2313yes—
99C2×Dic18C2313yes—
100C9×C4⋊C4C2313yes—
101C9×C4⋊C4C2313yes—
102C9×C22⋊C4C2311yescharacteristic
103C9×C22⋊C4C2313yes—
104C9×C22⋊C4C2316yes—
105C42×C9C2313yes—
106#3676C2313yes—
107#3676C2311yescharacteristic
108#3676C2313yes—
109#3676C2313yes—
110#3676C2311yescharacteristic
111#3676C2313yes—
112(C2×D9)⋊C4C2313yes—
113(C2×D9)⋊C4C2313yes—
114(C2×D9)⋊C4C2316yes—
115(C2×D9)⋊C4C2316yes—
116C4⋊Dic9C2311yescharacteristic
117C4⋊Dic9C2313yes—
118C4⋊Dic9C2313yes—
119C4⋊Dic9C2313yes—
120C4⋊Dic9C2313yes—
121C4⋊Dic9C2313yes—
122C4⋊Dic9C2313yes—
123C4⋊Dic9C2313yes—
124Dic9⋊C4C2311yescharacteristic
125Dic9⋊C4C2313yes—
126Dic9⋊C4C2316yes—
127Dic9⋊C4C2311yescharacteristic
128Dic9⋊C4C2313yes—
129C4×Dic9C2313yes—
130C4×Dic9C2313yes—
131C4×Dic9C2313yes—
132C4×Dic9C2316yes—
133C4×Dic9C2313yes—
134C4×Dic9C2311yescharacteristic
135#3524—91noSylow
136C2×C3×#41C2×D311yescharacteristic
137C22×C3×Q8C2×D311yescharacteristic
138C2×#239—31no—
139C3×#124C2×D313yes—
140C3×C22⋊Q8C2×D313yes—
141C3×#121C2×D313yes—
142C3×C4×Q8C2×D311yescharacteristic
143C3×C4×D4C2×D313yes—
144#947—33no—
145#946—33no—
146Q8×Dic3—33no—
147Q8×Dic3—33no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151#940—33no—
152#939—36no—
153#938—33no—
154#938—33no—
155#936—33no—
156D4×Dic3—33no—
157D4×Dic3—33no—
158#930—33no—
159#930—33no—
160C4×#67—33no—
161C4×#67—33no—
162#926—33no—
163#926—33no—
164#926—33no—
165C2×C4⋊Dic3—33no—
166#898—36no—
167#897—33no—
168#893—33no—
169#892—33no—
170#890—33no—
171#890—33no—
172#888—33no—
173#886—36no—
174#885—36no—
175#883—36no—
176#883—33no—
177#883—33no—
178#67⋊C4—36no—
179#879—33no—
180#879—31no—
181#877—36no—
182C4×D12—33no—
183C42×D3—33no—
184#870—33no—
185C4×Dic6—33no—
186C23×C9C2411yescharacteristic
187C23×C9C2413yes—
188C22×D9C2413yes—
189Q8×C9—26no—
190Q8×C9#4114yes—
191D4×C9—26no—
192D4×C9—43no—
193C2×C4×C9—26no—
194C2×C4×C9—26no—
195C2×C4×C9C2413yes—
196C2×C4×C9C2411yescharacteristic
197C2×C4×C9C2413yes—
198C2×C4×C9C2411yescharacteristic
199C2×C4×C9C2413yes—
200#611—46no—
201#611—43no—
202#611—43no—
203C2×Dic9—46no—
204C2×Dic9C2411yescharacteristic
205C2×Dic9C2413yes—
206C2×Dic9C2411yescharacteristic
207C2×Dic9C2413yes—
208C2×Dic9C2411yescharacteristic
209C2×Dic9C2411yescharacteristic
210C2×Dic9C2413yes—
211D36—26no—
212C4×D9—26no—
213C4×D9—43no—
214C4×D9—43no—
215Dic18—43no—
216#559—93no—
217#557—91no—
218#555—93no—
219#553—93no—
220#552—93no—
221#550—91no—
222#548—91no—
223#548D911yescharacteristic, complemented
224#542—93no—
225#540—93no—
226#529—93no—
227#529—93no—
228#520—91no—
229#519—91no—
230C4×#41—91no—
231C3×#41—24no—
232C2×C3×Q8—24no—
233C2×C3×Q8C22×D313yes—
234C2×C3×Q8C22×D311yescharacteristic
235C2×C3×D4C22×D313yes—
236C2×C3×D4C22×D313yes—
237C22×C3×C4C22×D313yes—
238C22×C3×C4C22×D313yes—
239C2×#67—36no—
240C2×#67—33no—
241C2×#67—33no—
242C22×Dic3—36no—
243#239—64no—
244C2×D12—33no—
245C2×C4×D3—33no—
246C2×C4×D3—33no—
247C2×C4×D3—33no—
248C2×Dic6—33no—
249C3×C4⋊C4C22×D313yes—
250C3×C4⋊C4C22×D313yes—
251C3×C22⋊C4C22×D316yes—
252C3×C22⋊C4C22×D313yes—
253C3×C22⋊C4C22×D311yescharacteristic
254C3×C42C22×D313yes—
255#217—33no—
256#217—33no—
257#217—31no—
258#217—31no—
259#217—33no—
260#217—33no—
261(C2×D3)⋊C4—36no—
262(C2×D3)⋊C4—36no—
263(C2×D3)⋊C4—33no—
264(C2×D3)⋊C4—33no—
265C4⋊Dic3—33no—
266C4⋊Dic3—33no—
267C4⋊Dic3—33no—
268C4⋊Dic3—33no—
269C4⋊Dic3—33no—
270C4⋊Dic3—31no—
271C4⋊Dic3—33no—
272C4⋊Dic3—33no—
273Dic3⋊C4—31no—
274Dic3⋊C4—33no—
275Dic3⋊C4—36no—
276Dic3⋊C4—33no—
277Dic3⋊C4—31no—
278C4×Dic3—33no—
279C4×Dic3—33no—
280C4×Dic3—31no—
281C4×Dic3—33no—
282C4×Dic3—33no—
283C4×Dic3—36no—
284C22×C9—21no—
285C22×C9—23no—
286C22×C9—23no—
287C22×C9—21no—
288C22×C9—23no—
289C22×C9—21no—
290C22×C9C2511yescharacteristic
291C2×D9—23no—
292C2×D9—23no—
293C2×D9—23no—
294C4×C9—21no—
295C4×C9—23no—
296C4×C9—23no—
297C4×C9—21no—
298C4×C9C2×#4116yes—
299Dic9—21no—
300Dic9—21no—
301Dic9—23no—
302Dic9—21no—
303Dic9—23no—
304Dic9—23no—
305Dic9—21no—
306C2×#41—91no—
307C2×#41C2×D911yescharacteristic
308C22×Q8C2×D911yescharacteristic
309C4⋊Q8—93no—
310#127—93no—
311#126—96no—
312#126—91no—
313#126—93no—
314#125—93no—
315#125—93no—
316#125—93no—
317#124—93no—
318#124—93no—
319#124—96no—
320#124C2×D913yes—
321#123—96no—
322#123—93no—
323#123—93no—
324#123—96no—
325C22⋊Q8—93no—
326C22⋊Q8—93no—
327C22⋊Q8C2×D913yes—
328#121—93no—
329#121—93no—
330#121—96no—
331#121—93no—
332#121—93no—
333#121C2×D913yes—
334C4×Q8—91no—
335C4×Q8—93no—
336C4×Q8—91no—
337C4×Q8—93no—
338C4×Q8—91no—
339C4×Q8—93no—
340C4×Q8C2×D911yescharacteristic
341C4×D4—93no—
342C4×D4—93no—
343C4×D4—93no—
344C4×D4—93no—
345C4×D4—93no—
346C4×D4—96no—
347C4×D4—93no—
348C4×D4C2×D913yes—
349#117—93no—
350#117—93no—
351#117—93no—
352#117—93no—
353#117—96no—
354C2×C4⋊C4—93no—
355C2×C42—93no—
356C23×C3C23×D311yescharacteristic
357C23×C3C23×D313yes—
358C22×D3—33no—
359C3×Q8—26no—
360C3×Q8#23714yes—
361C3×D4—26no—
362C3×D4—43no—
363C2×C3×C4—26no—
364C2×C3×C4—26no—
365C2×C3×C4C23×D313yes—
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D313yes—
368C2×C3×C4C23×D311yescharacteristic
369C2×C3×C4C23×D313yes—
370#67—126no—
371#67—123no—
372#67—123no—
373C2×Dic3—31no—
374C2×Dic3—33no—
375C2×Dic3—31no—
376C2×Dic3—33no—
377C2×Dic3—31no—
378C2×Dic3—31no—
379C2×Dic3—33no—
380C2×Dic3—126no—
381D12—66no—
382C4×D3—66no—
383C4×D3—123no—
384C4×D3—123no—
385Dic6—123no—
386C2×C9—41no—
387C2×C9—43no—
388C2×C9C22×#4111yescharacteristic
389C2×C9#58511yescharacteristic
390C2×C9#58511yescharacteristic
391D9—43no—
392#41—24no—
393#41—184no—
394C2×Q8—24no—
395C2×Q8—93no—
396C2×Q8C22×D913yes—
397C2×Q8C22×D911yescharacteristic
398C2×D4—93no—
399C2×D4—96no—
400C2×D4—93no—
401C2×D4—93no—
402C2×D4C22×D913yes—
403C2×D4C22×D913yes—
404C22×C4—96no—
405C22×C4—93no—
406C22×C4—93no—
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—91no—
420C4⋊C4—93no—
421C4⋊C4—91no—
422C4⋊C4—93no—
423C4⋊C4C22×D913yes—
424C4⋊C4C22×D913yes—
425C22⋊C4—91no—
426C22⋊C4—93no—
427C22⋊C4—93no—
428C22⋊C4—93no—
429C22⋊C4—93no—
430C22⋊C4—91no—
431C22⋊C4—96no—
432C22⋊C4—93no—
433C22⋊C4—96no—
434C22⋊C4—93no—
435C22⋊C4C22×D916yes—
436C22⋊C4C22×D913yes—
437C22⋊C4C22×D911yescharacteristic
438C42—91no—
439C42—93no—
440C42—93no—
441C42—96no—
442C42—93no—
443C42—93no—
444C42C22×D913yes—
445C22×C3—21no—
446C22×C3—23no—
447C22×C3—23no—
448C22×C3—21no—
449C22×C3—23no—
450C22×C3—21no—
451C22×C3C24×D311yescharacteristic
452C2×D3—63no—
453C2×D3—63no—
454C2×D3—63no—
455C3×C4—21no—
456C3×C4—23no—
457C3×C4—23no—
458C3×C4—21no—
459C3×C4C2×#23716yes—
460Dic3—61no—
461Dic3—61no—
462Dic3—63no—
463Dic3—61no—
464Dic3—63no—
465Dic3—63no—
466Dic3—61no—
467C9#352411yescharacteristic, complemented, Sylow
468C23—93no—
469C23C23×D911yescharacteristic
470C23C23×D913yes—
471Q8—26no—
472Q8—363no—
473Q8#369914yes—
474D4—26no—
475D4—43no—
476D4—186no—
477D4—366no—
478D4—363no—
479D4—363no—
480C2×C4—26no—
481C2×C4—26no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—93no—
485C2×C4—91no—
486C2×C4—93no—
487C2×C4—91no—
488C2×C4—93no—
489C2×C4—186no—
490C2×C4—363no—
491C2×C4—363no—
492C2×C4—366no—
493C2×C4C23×D913yes—
494C2×C4C23×D911yescharacteristic
495C2×C4C23×D913yes—
496C2×C4C23×D911yescharacteristic
497C2×C4C23×D913yes—
498C2×C3—41no—
499C2×C3—43no—
500C2×C3C22×#23711yescharacteristic
501C2×C3#596411yescharacteristic
502C2×C3#596811yescharacteristic
503D3—123no—
504C22—21no—
505C22—23no—
506C22—21no—
507C22—23no—
508C22—23no—
509C22—21no—
510C22—183no—
511C22—183no—
512C22—183no—
513C22C24×D911yescharacteristic
514C4—21no—
515C4—23no—
516C4—23no—
517C4—21no—
518C4—181no—
519C4—181no—
520C4—183no—
521C4—181no—
522C4—183no—
523C4—183no—
524C4—181no—
525C4C2×#369916yes—
526C3#8672411yescharacteristic
527C2—41no—
528C2—43no—
529C2—363no—
530C2C22×#369911yescharacteristic
531C2#1059313911yescharacteristic
532C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#548C2
hypercenter#548D9
hypocenterC9#3524
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C9×#548C2semidirect
2. #10589936C2semidirect
3. #10589929C2semidirect
4. #10589919C2semidirect
5. #10589914C2semidirect
6. #10589783C2semidirect
7. #10589782C2semidirect
8. #10589745C2semidirect
9. #10589744C2semidirect
10. #10589721C2semidirect
11. #10589718C2semidirect
12. C4×#3701C2semidirect
13. #10589671C2semidirect
14. #10589667C2semidirect
15. #10589659C2semidirect
223. #548D9semidirect
467. C9#3524semidirect

Maximal subgroups

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

subgroupindex
C9×#5482
#105899362
#105899292
#105899192
#105899142
#105897832
#105897822
#105897452
#105897442
#105897212
#105897182
C4×#37012
#105896712
#105896672
#105896592
#867243