Finite Group Databasebeta

← #11870561

Subgroups — #11870561

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
1C4×C9×#41C211yesmaximal, characteristic, complemented
2#10589581C211yesmaximal, characteristic, complemented
3#10588919C211yesmaximal, characteristic
4#10588918C211yesmaximal, characteristic, complemented
5#10588711C211yesmaximal, characteristic, complemented
6C4×#3675C211yesmaximal, characteristic, complemented
7C4×#3674C211yesmaximal, characteristic, complemented
8#10588704C211yesmaximal, characteristic, complemented
9#10588699C211yesmaximal, characteristic, complemented
10C4×#3673C211yesmaximal, characteristic, complemented
11C4×#3672C211yesmaximal, characteristic, complemented
12#10588692C211yesmaximal, characteristic, complemented
13#10588684C211yesmaximal, characteristic, complemented
14#10588680C211yesmaximal, characteristic, complemented
15#10588605C211yesmaximal, characteristic, complemented
16#82528—31nomaximal
17C2×C9×#41C2211yescharacteristic
18C4×Q8×C9C2211yescharacteristic
19C4×Q8×C9C2211yescharacteristic
20C4×D4×C9—21no—
21C4×D4×C9—21no—
22C4×D4×C9C2211yescharacteristic
23C4×D4×C9C2211yescharacteristic
24C9×#117—21no—
25C9×#117C2211yescharacteristic
26C2×C42×C9—21no—
27C2×C42×C9C2211yescharacteristic
28C2×#3675C2211yescharacteristic
29C2×#3674C2211yescharacteristic
30C2×#3673C2211yescharacteristic
31C2×#3672C2211yescharacteristic
32#63492C2211yescharacteristic
33#63491—21no—
34C4×#611—21no—
35#63486C2211yescharacteristic
36#63438—21no—
37#63437C2211yescharacteristic
38C4×D36C2211yescharacteristic
39#63434—21no—
40#63432C2211yescharacteristic
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×C4×#41D311yescharacteristic
61#5479—31no—
62#5239—31no—
63#5238—31no—
64C4×#216—31no—
65#5028—31no—
66C4×#215—31no—
67#5022—31no—
68C4×#214—31no—
69#5016—31no—
70C4×#213—31no—
71#5009—31no—
72#5003—31no—
73#4996—31no—
74#4925—31no—
75C9×#41—22no—
76C9×#41—22no—
77C2×Q8×C9C2311yescharacteristic
78C2×D4×C9—21no—
79C2×D4×C9C2311yescharacteristic
80C22×C4×C9—21no—
81C22×C4×C9—21no—
82C22×C4×C9—21no—
83C22×C4×C9D411yescharacteristic
84C22×C4×C9D411yescharacteristic
85C22×C4×C9C2311yescharacteristic
86C2×#611—21no—
87C2×D36C2311yescharacteristic
88C2×C4×D9—21no—
89C2×Dic18C2311yescharacteristic
90C9×C4⋊C4—21no—
91C9×C4⋊C4—21no—
92C9×C4⋊C4C2311yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C22⋊C4—21no—
95C9×C22⋊C4—21no—
96C9×C22⋊C4—21no—
97C42×C9—21no—
98C42×C9—21no—
99C42×C9—21no—
100C42×C9D411yescharacteristic
101C42×C9D411yescharacteristic
102C42×C9C2311yescharacteristic
103C42×C9C2311yescharacteristic
104#3676—21no—
105#3675—22no—
106#3674—22no—
107#3673—22no—
108#3672—22no—
109(C2×D9)⋊C4—21no—
110(C2×D9)⋊C4—21no—
111(C2×D9)⋊C4—21no—
112(C2×D9)⋊C4—21no—
113C4⋊Dic9C2311yescharacteristic
114C4⋊Dic9C2311yescharacteristic
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119C4×Dic9—21no—
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3102—91noSylow
125C2×C3×#41C2×D311yescharacteristic
126C3×C4×Q8C2×D311yescharacteristic
127C3×C4×Q8C2×D311yescharacteristic
128C3×C4×D4—21no—
129C3×C4×D4—21no—
130C3×C4×D4C2×D311yescharacteristic
131C3×C4×D4C2×D311yescharacteristic
132C3×#117—21no—
133C3×#117C2×D311yescharacteristic
134C2×C3×C42—21no—
135C2×C3×C42C2×D311yescharacteristic
136C2×#216—31no—
137C2×#215—31no—
138C2×#214—31no—
139C2×#213—31no—
140#930—31no—
141#929—61no—
142C4×#67—61no—
143#924—31no—
144#876—61no—
145#875—31no—
146C4×D12—31no—
147#872—61no—
148#870—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#4112yes—
173D4×C9—24no—
174D4×C9—21no—
175D4×C9#4112yes—
176C2×C4×C9—24no—
177C2×C4×C9—21no—
178C2×C4×C9—22no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—41no—
184C2×C4×C9—42no—
185C2×C4×C9—42no—
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2×D411yescharacteristic
191C2×C4×C9C2411yescharacteristic
192#611—42no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196D36—21no—
197D36—21no—
198C4×D9—42no—
199Dic18—21no—
200Dic18—21no—
201C9⋊C8—21no—
202C9⋊C8—21no—
203C9⋊C8—21no—
204C9⋊C8—21no—
205#529—91no—
206C4×#41D911yescharacteristic, complemented
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—
220C3×#41—22no—
221C3×#41—22no—
222C2×C3×Q8C22×D311yescharacteristic
223C2×C3×D4—21no—
224C2×C3×D4C22×D311yescharacteristic
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4#6711yescharacteristic
229C22×C3×C4#6711yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—61no—
232C2×D12—31no—
233C2×C4×D3—61no—
234C2×Dic6—31no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—21no—
242C3×C42—21no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42#6711yescharacteristic
246C3×C42#6711yescharacteristic
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—61no—
250#216—62no—
251#215—62no—
252#214—62no—
253#213—62no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263Dic3⋊C4—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—22no—
271C22×C9—21no—
272C22×C9—21no—
273C22×C9—41no—
274C22×C9—41no—
275C22×C9C22×D411yescharacteristic
276C2×D9—41no—
277C2×D9—41no—
278C2×D9—41no—
279C4×C9—21no—
280C4×C9—22no—
281C4×C9—21no—
282C4×C9—21no—
283C4×C9—21no—
284C4×C9—41no—
285C4×C9—41no—
286C4×C9#13512yes—
287C4×C9C2×#4111yescharacteristic
288C4×C9C2×#4111yescharacteristic
289Dic9—41no—
290Dic9—41no—
291Dic9—41no—
292C2×#41C2×D911yescharacteristic
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#126—181no—
298#125—91no—
299#124—91no—
300#123—181no—
301C22⋊Q8—91no—
302#121—91no—
303C4×Q8—91no—
304C4×Q8C2×D911yescharacteristic
305C4×Q8C2×D911yescharacteristic
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4C2×D911yescharacteristic
311C4×D4C2×D911yescharacteristic
312#117—21no—
313#117—181no—
314#117C2×D911yescharacteristic
315C2×C42—21no—
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#23512yes—
340C3×D4—24no—
341C3×D4—21no—
342C3×D4#23512yes—
343C2×C3×C4—24no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—41no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359#67—122no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363D12—61no—
364D12—61no—
365C4×D3—122no—
366Dic6—61no—
367Dic6—61no—
368C3⋊C8—61no—
369C3⋊C8—61no—
370C3⋊C8—61no—
371C3⋊C8—61no—
372C2×C9—41no—
373C2×C9—42no—
374C2×C9#52511yescharacteristic
375C2×C9C2×#13511yescharacteristic
376C2×C9#57511yescharacteristic
377D9—81no—
378#41—22no—
379#41—22no—
380C2×Q8—91no—
381C2×Q8C22×D911yescharacteristic
382C2×D4—21no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4C22×D911yescharacteristic
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
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—91no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4C22×D911yescharacteristic
410C4⋊C4C22×D911yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—181no—
423C42#61111yescharacteristic
424C42#61111yescharacteristic
425C42C22×D911yescharacteristic
426C42C22×D911yescharacteristic
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3C22×#6711yescharacteristic
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4#95012yes—
445C3×C4C2×#23511yescharacteristic
446C3×C4C2×#23511yescharacteristic
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450C9#310211yescharacteristic, complemented, Sylow
451C23—21no—
452C23—181no—
453C23C2×#61111yescharacteristic
454Q8—21no—
455Q8—181no—
456Q8—181no—
457Q8#369712yes—
458D4—24no—
459D4—21no—
460D4—181no—
461D4—181no—
462D4—362no—
463D4#369712yes—
464C2×C4—24no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
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—42no—
490C2×C3#579111yescharacteristic
491C2×C3C2×#95011yescharacteristic
492C2×C3#582211yescharacteristic
493D3—241no—
494C22—21no—
495C22—22no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—41no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22C22×#61111yescharacteristic
504C4—21no—
505C4—22no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—361no—
512C4—361no—
513C4—361no—
514C4#6351312yes—
515C4C2×#369711yescharacteristic
516C4C2×#369711yescharacteristic
517C3#8252811yescharacteristic
518C2—41no—
519C2—42no—
520C2—721no—
521C2#1058989311yescharacteristic
522C2C2×#6351311yescharacteristic
523C2#1058992511yescharacteristic
subgroupG/H
centerC2×C4C2×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×#41C2
socleC22×C3C22×#67
prime radical#10588919C2
hypercenterC4×#41D9
hypocenterC9#3102
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C4×C9×#41C2semidirect
2. #10589581C2semidirect
4. #10588918C2semidirect
5. #10588711C2semidirect
6. C4×#3675C2semidirect
7. C4×#3674C2semidirect
8. #10588704C2semidirect
9. #10588699C2semidirect
10. C4×#3673C2semidirect
11. C4×#3672C2semidirect
12. #10588692C2semidirect
13. #10588684C2semidirect
14. #10588680C2semidirect
15. #10588605C2semidirect
206. C4×#41D9semidirect
450. C9#3102semidirect

Maximal subgroups

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

subgroupindex
C4×C9×#412
#105895812
#105889192
#105889182
#105887112
C4×#36752
C4×#36742
#105887042
#105886992
C4×#36732
C4×#36722
#105886922
#105886842
#105886802
#105886052
#825283