Finite Group Databasebeta

← #11870543

Subgroups — #11870543

Order 1152.

594 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#529C211yesmaximal, characteristic, complemented
2C4×#3697C211yesmaximal, characteristic, complemented
3#10588747C211yesmaximal, characteristic, complemented
4#10588745C211yesmaximal, characteristic, complemented
5#10588738C211yesmaximal, characteristic, complemented
6#10588736C211yesmaximal, characteristic, complemented
7#10588730C211yesmaximal, characteristic, complemented
8#10588725C211yesmaximal, characteristic, complemented
9#10588720C211yesmaximal, characteristic
10#10588715C211yesmaximal, characteristic, complemented
11C4×#3675C211yesmaximal, characteristic, complemented
12C4×#3674C211yesmaximal, characteristic, complemented
13C4×#3673C211yesmaximal, characteristic, complemented
14C4×#3672C211yesmaximal, characteristic, complemented
15#10588605C211yesmaximal, characteristic, complemented
16#83140—31nomaximal
17C2×#3697C2211yescharacteristic
18C9×#126—21no—
19C9×#125C2211yescharacteristic
20C9×#124C2211yescharacteristic
21C9×#123—21no—
22C9×C22⋊Q8C2211yescharacteristic
23C9×#121C2211yescharacteristic
24C4×Q8×C9C2211yescharacteristic
25C4×D4×C9—21no—
26C4×D4×C9C2211yescharacteristic
27C9×#117—21no—
28C2×C42×C9C2211yescharacteristic
29C2×#3675C2211yescharacteristic
30C2×#3674C2211yescharacteristic
31C2×#3673C2211yescharacteristic
32C2×#3672C2211yescharacteristic
33C4×#611—21no—
34C4×#611—21no—
35#63488C2211yescharacteristic
36C4×D36C2211yescharacteristic
37C4×D36C2211yescharacteristic
38#63434—21no—
39C42×D9—21no—
40C4×Dic18C2211yescharacteristic
41C4×Dic18C2211yescharacteristic
42#63395C2211yescharacteristic
43#63395C2211yescharacteristic
44#63392C2211yescharacteristic
45#63392C2211yescharacteristic
46#63389C2211yescharacteristic
47#63389C2211yescharacteristic
48#63369C2211yescharacteristic
49#63369C2211yescharacteristic
50#63368C2211yescharacteristic
51#63368C2211yescharacteristic
52#63367C2211yescharacteristic
53#63367C2211yescharacteristic
54#63366C2211yescharacteristic
55#63366C2211yescharacteristic
56C4⋊(C9⋊C8)C2211yescharacteristic
57C4⋊(C9⋊C8)C2211yescharacteristic
58C4×C9⋊C8C2211yescharacteristic
59C4×C9⋊C8C2211yescharacteristic
60C3×#529D311yescharacteristic
61C4×#235—31no—
62#5066—31no—
63#5063—31no—
64#5057—31no—
65#5054—31no—
66#5047—31no—
67#5045—31no—
68#5037—31no—
69#5035—31no—
70C4×#216—31no—
71C4×#215—31no—
72C4×#214—31no—
73C4×#213—31no—
74#4925—31no—
75C2×Q8×C9C2311yescharacteristic
76C2×D4×C9—21no—
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C22×C4×C9D411yescharacteristic
80C22×C4×C9D411yescharacteristic
81C22×C4×C9C2311yescharacteristic
82C2×#611—21no—
83#3697—22no—
84#3697—22no—
85C2×D36C2311yescharacteristic
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×Dic18C2311yescharacteristic
90C9×C4⋊C4—21no—
91C9×C4⋊C4—21no—
92C9×C4⋊C4—21no—
93C9×C4⋊C4—21no—
94C9×C4⋊C4C2311yescharacteristic
95C9×C4⋊C4C2311yescharacteristic
96C9×C22⋊C4—21no—
97C9×C22⋊C4—21no—
98C9×C22⋊C4—21no—
99C9×C22⋊C4—21no—
100C9×C22⋊C4—21no—
101C42×C9—21no—
102C42×C9D411yescharacteristic
103C42×C9D411yescharacteristic
104C42×C9C2311yescharacteristic
105C42×C9C2311yescharacteristic
106#3676—21no—
107#3675—22no—
108#3674—22no—
109#3673—22no—
110#3672—22no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3102—91noSylow
125C2×#235—31no—
126C3×#126—21no—
127C3×#125C2×D311yescharacteristic
128C3×#124C2×D311yescharacteristic
129C3×#123—21no—
130C3×C22⋊Q8C2×D311yescharacteristic
131C3×#121C2×D311yescharacteristic
132C3×C4×Q8C2×D311yescharacteristic
133C3×C4×D4—21no—
134C3×C4×D4C2×D311yescharacteristic
135C3×#117—21no—
136C2×C3×C42C2×D311yescharacteristic
137C2×#216—31no—
138C2×#215—31no—
139C2×#214—31no—
140C2×#213—31no—
141C4×#67—61no—
142C4×#67—61no—
143#926—31no—
144C4×D12—31no—
145C4×D12—31no—
146#872—61no—
147C42×D3—61no—
148C4×Dic6—31no—
149C4×Dic6—31no—
150#835—31no—
151#835—31no—
152#832—31no—
153#832—31no—
154#830—31no—
155#830—31no—
156#810—31no—
157#810—31no—
158#809—31no—
159#809—31no—
160#808—31no—
161#808—31no—
162#807—31no—
163#807—31no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—31no—
166C4×C3⋊C8—31no—
167C4×C3⋊C8—31no—
168C23×C9—21no—
169C23×C9C2×D411yescharacteristic
170C22×D9—21no—
171Q8×C9—21no—
172Q8×C9—21no—
173D4×C9—21no—
174D4×C9—21no—
175D4×C9—42no—
176C2×C4×C9—22no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—41no—
183C2×C4×C9—42no—
184C2×C4×C9C2×D411yescharacteristic
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2411yescharacteristic
190#611—24no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—21no—
194D36—21no—
195D36#4112yes—
196C4×D9—24no—
197C4×D9—42no—
198C4×D9—42no—
199Dic18—21no—
200Dic18#4112yes—
201C9⋊C8—21no—
202C9⋊C8—21no—
203C9⋊C8—21no—
204C9⋊C8—21no—
205#529D911yescharacteristic, complemented
206C4×#41—91no—
207#485—91no—
208#482—91no—
209#479—91no—
210#478—91no—
211#464—91no—
212#463—91no—
213#452—91no—
214#449—91no—
215C4×Q16—91no—
216C4×SD16—91no—
217C4×SD16—91no—
218C4×D8—91no—
219#431—91no—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×D4—21no—
222C2×C3×D4C22×D311yescharacteristic
223C22×C3×C4—21no—
224C22×C3×C4#6711yescharacteristic
225C22×C3×C4#6711yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—61no—
228#235—62no—
229#235—62no—
230C2×D12—31no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×Dic6—31no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C4⋊C4C22×D311yescharacteristic
241C3×C22⋊C4—21no—
242C3×C22⋊C4—21no—
243C3×C22⋊C4—21no—
244C3×C22⋊C4—21no—
245C3×C22⋊C4—21no—
246C3×C42—21no—
247C3×C42#6711yescharacteristic
248C3×C42#6711yescharacteristic
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D311yescharacteristic
251#217—61no—
252#216—62no—
253#215—62no—
254#214—62no—
255#213—62no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C22×C9—21no—
270C22×C9—21no—
271C22×C9—21no—
272C22×C9—41no—
273C22×C9—41no—
274C22×C9—41no—
275C22×C9C22×D411yescharacteristic
276C2×D9—22no—
277C2×D9—41no—
278C2×D9—41no—
279C4×C9—21no—
280C4×C9—21no—
281C4×C9—21no—
282C4×C9—21no—
283C4×C9—41no—
284C4×C9—41no—
285C4×C9—41no—
286C4×C9#13512yes—
287C4×C9C2×#4111yescharacteristic
288C4×C9C2×#4111yescharacteristic
289Dic9—22no—
290Dic9—41no—
291Dic9—41no—
292C2×#41—91no—
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#126—21no—
298#125C2×D911yescharacteristic
299#124C2×D911yescharacteristic
300#123—21no—
301C22⋊Q8C2×D911yescharacteristic
302#121C2×D911yescharacteristic
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8C2×D911yescharacteristic
306C4×D4—21no—
307C4×D4—91no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4—181no—
311C4×D4C2×D911yescharacteristic
312#117—21no—
313#117—91no—
314#117—181no—
315C2×C42—181no—
316C2×C42C2×D911yescharacteristic
317#107—91no—
318#107—91no—
319#106—91no—
320#106—91no—
321C4⋊C8—91no—
322C4⋊C8—91no—
323#103—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331C22⋊C8—91no—
332C22⋊C8—91no—
333C4×C8—91no—
334C4×C8—91no—
335C23×C3—21no—
336C23×C3C2×#6711yescharacteristic
337C22×D3—61no—
338C3×Q8—21no—
339C3×Q8—21no—
340C3×D4—21no—
341C3×D4—21no—
342C3×D4—42no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4C2×#6711yescharacteristic
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357#67—64no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361D12—32no—
362D12—61no—
363C4×D3—64no—
364C4×D3—122no—
365C4×D3—122no—
366Dic6—32no—
367Dic6—61no—
368C3⋊C8—61no—
369C3⋊C8—61no—
370C3⋊C8—61no—
371C3⋊C8—61no—
372C2×C9—41no—
373C2×C9—81no—
374C2×C9#52511yescharacteristic
375C2×C9C2×#13511yescharacteristic
376C2×C9#57511yescharacteristic
377D9—42no—
378#41—182no—
379#41—182no—
380C2×Q8—91no—
381C2×Q8C22×D911yescharacteristic
382C2×D4—21no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4C22×D911yescharacteristic
386C22×C4—21no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4#61111yescharacteristic
391C22×C4#61111yescharacteristic
392C22×C4C22×D911yescharacteristic
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8—91no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—91no—
406C4⋊C4—91no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4C22×D911yescharacteristic
410C4⋊C4C22×D911yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—21no—
420C42—181no—
421C42—181no—
422C42—181no—
423C42#61111yescharacteristic
424C42#61111yescharacteristic
425C42C22×D911yescharacteristic
426C42C22×D911yescharacteristic
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3C22×#6711yescharacteristic
434C2×D3—62no—
435C2×D3—121no—
436C2×D3—121no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4#95012yes—
445C3×C4D3×#4111yescharacteristic
446C3×C4D3×#4111yescharacteristic
447Dic3—62no—
448Dic3—121no—
449Dic3—121no—
450C9#310211yescharacteristic, complemented, Sylow
451C23—21no—
452C23—181no—
453C23C2×#61111yescharacteristic
454Q8—21no—
455Q8—21no—
456Q8—92no—
457Q8—181no—
458D4—21no—
459D4—21no—
460D4—42no—
461D4—92no—
462D4—184no—
463D4—181no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—184no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—362no—
477C2×C4—362no—
478C2×C4C2×#61111yescharacteristic
479C2×C4C2×#61111yescharacteristic
480C2×C4C2×#61111yescharacteristic
481C2×C4C2×#61111yescharacteristic
482C2×C4C2×#61111yescharacteristic
483C2×C4C23×D911yescharacteristic
484C8—181no—
485C8—181no—
486C8—181no—
487C8—181no—
488C2×C3—41no—
489C2×C3—81no—
490C2×C3C2×#95011yescharacteristic
491C2×C3#582211yescharacteristic
492C2×C3#582811yescharacteristic
493D3—122no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—182no—
501C22—361no—
502C22—361no—
503C22C22×#61111yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—182no—
512C4—361no—
513C4—361no—
514C4#6351312yes—
515C4#41×D911yescharacteristic
516C4#41×D911yescharacteristic
517C3#8314011yescharacteristic
518C2—41no—
519C2—81no—
520C2—362no—
521C2C2×#6351311yescharacteristic
522C2#1058992511yescharacteristic
523C2#1058993011yescharacteristic
subgroupG/H
centerC2×C4C2×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#529C2
socleC22×C3C22×#67
prime radical#10588720C2
hypercenter#529D9
hypocenterC9#3102
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C9×#529C2semidirect
2. C4×#3697C2semidirect
3. #10588747C2semidirect
4. #10588745C2semidirect
5. #10588738C2semidirect
6. #10588736C2semidirect
7. #10588730C2semidirect
8. #10588725C2semidirect
10. #10588715C2semidirect
11. C4×#3675C2semidirect
12. C4×#3674C2semidirect
13. C4×#3673C2semidirect
14. C4×#3672C2semidirect
15. #10588605C2semidirect
205. #529D9semidirect
450. C9#3102semidirect

Maximal subgroups

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

subgroupindex
C9×#5292
C4×#36972
#105887472
#105887452
#105887382
#105887362
#105887302
#105887252
#105887202
#105887152
C4×#36752
C4×#36742
C4×#36732
C4×#36722
#105886052
#831403