Finite Group Databasebeta

← #11909997

Subgroups — #11909997

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
1C4×C9×#41C211yesmaximal, characteristic, complemented
2#10589936C211yesmaximal, characteristic, complemented
3#10589933C211yesmaximal, characteristic, complemented
4#10589678C211yesmaximal, characteristic, complemented
5#10589676C211yesmaximal, characteristic, complemented
6#10589674C211yesmaximal, characteristic, complemented
7#10589671C211yesmaximal, characteristic, complemented
8#10589664C213yesmaximal, complemented
9#10589663C213yesmaximal, complemented
10#10589661C213yesmaximal, complemented
11#10589660C213yesmaximal, complemented
12#10589634C213yesmaximal, complemented
13#10589631C213yesmaximal, complemented
14#10589581C213yesmaximal, complemented
15#10589581C213yesmaximal, complemented
16#85855—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C2×#3701C2211yescharacteristic
19C2×Q8×D9C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic
21C4×Q8×C9C2211yescharacteristic
22C4×D4×C9C2213yes—
23C4×D4×C9C2213yes—
24C9×#117C2213yes—
25C2×C42×C9C2213yes—
26Q8×Dic9C2211yescharacteristic
27Q8×Dic9C2211yescharacteristic
28#63502C2213yes—
29#63500C2213yes—
30#63500C2213yes—
31#63498C2213yes—
32#63492C2213yes—
33#63492C2213yes—
34#63491C2213yes—
35#63491C2213yes—
36#63491C2216yes—
37C4×#611C2213yes—
38C4×#611C2213yes—
39C4×#611C2216yes—
40#63486C2213yes—
41#63486C2213yes—
42#63459C2213yes—
43#63457C2213yes—
44#63455C2213yes—
45#63454C2213yes—
46C4⋊C4×D9C2213yes—
47#63452C2213yes—
48#63450C2213yes—
49#63449C2213yes—
50#63447C2216yes—
51#63446C2216yes—
52#63445C2216yes—
53#63441C2216yes—
54#63438C2211yescharacteristic
55#63438C2213yes—
56#63437C2213yes—
57#63437C2213yes—
58C4×D36C2213yes—
59C4×D36C2213yes—
60#63434C2216yes—
61#63434C2213yes—
62#63434C2213yes—
63#63432C2213yes—
64#63432C2213yes—
65C4×Dic18C2213yes—
66C4×Dic18C2213yes—
67C3×C4×#41D311yescharacteristic
68#5834—31no—
69#5831—31no—
70#5576—31no—
71#5574—31no—
72#5572—31no—
73#5569—31no—
74#5562—33no—
75#5561—33no—
76#5559—33no—
77#5558—33no—
78#5532—33no—
79#5529—33no—
80#5479—33no—
81#5479—33no—
82C9×#41—24no—
83C2×Q8×C9C2311yescharacteristic
84C2×D4×C9C2313yes—
85C22×C4×C9C2313yes—
86C22×C4×C9C2313yes—
87C22×C4×C9C2313yes—
88C2×#611C2313yes—
89C2×#611C2316yes—
90C2×#611C2313yes—
91#3701—24no—
92Q8×D9—24no—
93C2×D36C2313yes—
94C2×D36C2313yes—
95C2×C4×D9C2313yes—
96C2×C4×D9C2313yes—
97C2×C4×D9C2316yes—
98C2×Dic18C2313yes—
99C2×Dic18C2313yes—
100C9×C4⋊C4C2313yes—
101C9×C4⋊C4C2313yes—
102C9×C22⋊C4C2316yes—
103C42×C9C2311yescharacteristic
104C42×C9C2313yes—
105C42×C9C2313yes—
106C42×C9C2313yes—
107#3676C2313yes—
108#3676C2316yes—
109#3676C2313yes—
110(C2×D9)⋊C4C2311yescharacteristic
111(C2×D9)⋊C4C2313yes—
112(C2×D9)⋊C4C2313yes—
113(C2×D9)⋊C4C2311yescharacteristic
114(C2×D9)⋊C4C2313yes—
115(C2×D9)⋊C4C2316yes—
116(C2×D9)⋊C4C2313yes—
117(C2×D9)⋊C4C2313yes—
118(C2×D9)⋊C4C2311yescharacteristic
119C4⋊Dic9C2313yes—
120C4⋊Dic9C2313yes—
121C4⋊Dic9C2313yes—
122C4⋊Dic9C2313yes—
123Dic9⋊C4C2311yescharacteristic
124Dic9⋊C4C2313yes—
125Dic9⋊C4C2313yes—
126Dic9⋊C4C2311yescharacteristic
127Dic9⋊C4C2313yes—
128Dic9⋊C4C2313yes—
129Dic9⋊C4C2316yes—
130Dic9⋊C4C2313yes—
131Dic9⋊C4C2311yescharacteristic
132C4×Dic9C2313yes—
133C4×Dic9C2313yes—
134C4×Dic9C2316yes—
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×C42C2×D313yes—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147#940—33no—
148#938—33no—
149#938—33no—
150#936—33no—
151#930—33no—
152#930—33no—
153#929—33no—
154#929—33no—
155#929—36no—
156C4×#67—33no—
157C4×#67—33no—
158C4×#67—36no—
159#924—33no—
160#924—33no—
161#897—33no—
162#895—33no—
163#893—33no—
164#892—33no—
165D3×C4⋊C4—33no—
166#890—33no—
167#888—33no—
168#887—33no—
169#885—36no—
170#884—36no—
171#883—36no—
172#879—36no—
173#876—31no—
174#876—33no—
175#875—33no—
176#875—33no—
177C4×D12—33no—
178C4×D12—33no—
179#872—36no—
180#872—33no—
181#872—33no—
182#870—33no—
183#870—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—43no—
193C2×C4×C9—43no—
194C2×C4×C9C2413yes—
195C2×C4×C9C2411yescharacteristic
196C2×C4×C9C2411yescharacteristic
197C2×C4×C9C2411yescharacteristic
198C2×C4×C9C2413yes—
199C2×C4×C9C2413yes—
200#611—46no—
201#611—43no—
202#611—43no—
203C2×Dic9C2411yescharacteristic
204C2×Dic9C2413yes—
205C2×Dic9C2411yescharacteristic
206C2×Dic9C2413yes—
207C2×Dic9C2413yes—
208C2×Dic9C2411yescharacteristic
209D36—26no—
210D36—43no—
211C4×D9—26no—
212C4×D9—26no—
213C4×D9—46no—
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#520—91no—
229#519—91no—
230C4×#41D911yescharacteristic, complemented
231C3×#41—24no—
232C2×C3×Q8C22×D311yescharacteristic
233C2×C3×D4C22×D313yes—
234C22×C3×C4C22×D313yes—
235C22×C3×C4C22×D313yes—
236C22×C3×C4C22×D313yes—
237C2×#67—33no—
238C2×#67—33no—
239C2×#67—36no—
240#239—64no—
241D3×Q8—64no—
242C2×D12—33no—
243C2×D12—33no—
244C2×C4×D3—33no—
245C2×C4×D3—33no—
246C2×C4×D3—36no—
247C2×Dic6—33no—
248C2×Dic6—33no—
249C3×C4⋊C4C22×D313yes—
250C3×C4⋊C4C22×D313yes—
251C3×C22⋊C4C22×D316yes—
252C3×C42C22×D313yes—
253C3×C42C22×D313yes—
254C3×C42C22×D313yes—
255C3×C42C22×D311yescharacteristic
256#217—33no—
257#217—36no—
258#217—33no—
259(C2×D3)⋊C4—31no—
260(C2×D3)⋊C4—33no—
261(C2×D3)⋊C4—33no—
262(C2×D3)⋊C4—36no—
263(C2×D3)⋊C4—33no—
264(C2×D3)⋊C4—33no—
265(C2×D3)⋊C4—31no—
266(C2×D3)⋊C4—33no—
267(C2×D3)⋊C4—31no—
268C4⋊Dic3—33no—
269C4⋊Dic3—33no—
270C4⋊Dic3—33no—
271C4⋊Dic3—33no—
272Dic3⋊C4—31no—
273Dic3⋊C4—33no—
274Dic3⋊C4—33no—
275Dic3⋊C4—31no—
276Dic3⋊C4—33no—
277Dic3⋊C4—33no—
278Dic3⋊C4—36no—
279Dic3⋊C4—33no—
280Dic3⋊C4—31no—
281C4×Dic3—36no—
282C4×Dic3—33no—
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—21no—
292C2×D9—23no—
293C2×D9—21no—
294C4×C9—21no—
295C4×C9—23no—
296C4×C9—23no—
297C4×C9—21no—
298C4×C9—21no—
299C4×C9C2×#4116yes—
300Dic9—23no—
301Dic9—21no—
302Dic9—21no—
303Dic9—23no—
304Dic9—23no—
305Dic9—21no—
306C2×#41—91no—
307C2×#41C2×D911yescharacteristic
308C22×Q8—91no—
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—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—93no—
333#121—96no—
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—93no—
350#117—93no—
351#117—93no—
352#117—96no—
353#117C2×D913yes—
354C2×C4⋊C4—93no—
355C2×C42C2×D913yes—
356C23×C3C23×D313yes—
357C22×D3—31no—
358C22×D3—33no—
359C3×Q8#23514yes—
360C3×D4—26no—
361C2×C3×C4—26no—
362C2×C3×C4—43no—
363C2×C3×C4—43no—
364C2×C3×C4C23×D313yes—
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D313yes—
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—33no—
378C2×Dic3—31no—
379D12—66no—
380D12—123no—
381C4×D3—66no—
382C4×D3—66no—
383C4×D3—126no—
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—96no—
407C22×C4C22×D913yes—
408C22×C4C22×D913yes—
409C22×C4C22×D913yes—
410C4⋊C4—93no—
411C4⋊C4—93no—
412C4⋊C4—91no—
413C4⋊C4—93no—
414C4⋊C4—93no—
415C4⋊C4—93no—
416C4⋊C4—93no—
417C4⋊C4—96no—
418C4⋊C4—91no—
419C4⋊C4—93no—
420C4⋊C4—93no—
421C4⋊C4—91no—
422C4⋊C4—93no—
423C4⋊C4C22×D913yes—
424C4⋊C4C22×D913yes—
425C22⋊C4—93no—
426C22⋊C4—96no—
427C22⋊C4—93no—
428C22⋊C4—91no—
429C22⋊C4—93no—
430C22⋊C4—93no—
431C22⋊C4—93no—
432C22⋊C4—93no—
433C22⋊C4—96no—
434C22⋊C4—91no—
435C22⋊C4—93no—
436C22⋊C4—91no—
437C22⋊C4C22×D916yes—
438C42—96no—
439C42—93no—
440C42—93no—
441C42C22×D911yescharacteristic
442C42C22×D913yes—
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—63no—
465Dic3—63no—
466Dic3—61no—
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—43no—
482C2×C4—43no—
483C2×C4—91no—
484C2×C4—93no—
485C2×C4—91no—
486C2×C4—93no—
487C2×C4—93no—
488C2×C4—91no—
489C2×C4—186no—
490C2×C4—186no—
491C2×C4—366no—
492C2×C4C23×D913yes—
493C2×C4C23×D911yescharacteristic
494C2×C4C23×D911yescharacteristic
495C2×C4C23×D911yescharacteristic
496C2×C4C23×D913yes—
497C2×C4C23×D913yes—
498C2×C3—43no—
499C2×C3C22×#23511yescharacteristic
500C2×C3#596411yescharacteristic
501C2×C3#596411yescharacteristic
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—21no—
516C4—21no—
517C4—23no—
518C4—23no—
519C4—181no—
520C4—183no—
521C4—183no—
522C4—181no—
523C4—183no—
524C4—181no—
525C4C2×#369716yes—
526C3#8585511yescharacteristic
527C2—43no—
528C2—361no—
529C2—363no—
530C2C22×#369711yescharacteristic
531C2#1059313911yescharacteristic
532C2#1059313911yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC4×C9×#41C2
hypercenterC4×#41D9
hypocenterC9#3524
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C9×#41C2semidirect
2. #10589936C2semidirect
3. #10589933C2semidirect
4. #10589678C2semidirect
5. #10589676C2semidirect
6. #10589674C2semidirect
7. #10589671C2semidirect
8. #10589664C2semidirect
9. #10589663C2semidirect
10. #10589661C2semidirect
11. #10589660C2semidirect
12. #10589634C2semidirect
13. #10589631C2semidirect
14. #10589581C2semidirect
15. #10589581C2semidirect
230. C4×#41D9semidirect
467. C9#3524semidirect

Maximal subgroups

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

subgroupindex
C4×C9×#412
#105899362
#105899332
#105896782
#105896762
#105896742
#105896712
#105896642
#105896632
#105896612
#105896602
#105896342
#105896312
#105895812
#858553