Finite Group Databasebeta

← #11860912

Subgroups — #11860912

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63478C211yesmaximal, characteristic
2#10589676C211yesmaximal, characteristic, complemented
3#10589648C211yesmaximal, characteristic, complemented
4C4×C9×SD16C211yesmaximal, characteristic, complemented
5SD16×Dic9C211yesmaximal, characteristic, complemented
6#10588706C211yesmaximal, characteristic, complemented
7#10588697C211yesmaximal, characteristic, complemented
8D9×#106C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588483C211yesmaximal, characteristic, complemented
11#10588469C211yesmaximal, characteristic, complemented
12#10588465C211yesmaximal, characteristic, complemented
13#10588451C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15#10588371C211yesmaximal, characteristic, complemented
16#79650—31nomaximal
17C2×#3701C2211yescharacteristic
18C2×#3699C2211yescharacteristic
19C2×C9×SD16C2211yescharacteristic
20C4×Q8×C9C2211yescharacteristic
21C4×D4×C9C2211yescharacteristic
22Q8×Dic9C2211yescharacteristic
23C2×#3674C2211yescharacteristic
24D4×Dic9C2211yescharacteristic
25C2×#3673C2211yescharacteristic
26C4×#611—21no—
27C2×Dic9⋊C4—21no—
28#63478C418yescomplemented
29C2×#3664C2211yescharacteristic
30C2×#3663C2211yescharacteristic
31C2×C8×D9C2211yescharacteristic
32#63455—21no—
33#63455C2211yescharacteristic
34C4⋊C4×D9—21no—
35C4⋊C4×D9C2211yescharacteristic
36C4⋊C4×D9C2211yescharacteristic
37#63449C2211yescharacteristic
38#611⋊C4—21no—
39#63439—21no—
40C4×D36—21no—
41C4×D36C2211yescharacteristic
42#63434—21no—
43#63434C2211yescharacteristic
44C4×Dic18C2211yescharacteristic
45C9×#106C2211yescharacteristic
46C9×#103C2211yescharacteristic
47C9×#102C2211yescharacteristic
48C4×C8×C9C2211yescharacteristic
49#63395C2211yescharacteristic
50#63392C2211yescharacteristic
51#63380C2211yescharacteristic
52#63377C2211yescharacteristic
53#63376C2211yescharacteristic
54#63375C2211yescharacteristic
55C8×Dic9C2211yescharacteristic
56#63369C2211yescharacteristic
57#63368C2211yescharacteristic
58#63367C2211yescharacteristic
59#63367C2211yescharacteristic
60#63362C2211yescharacteristic
61C2×#916—31no—
62#5574—31no—
63#5546—31no—
64C3×C4×SD16D311yescharacteristic
65Dic3×SD16—31no—
66#5030—31no—
67#5014—31no—
68D3×#106—31no—
69#4852—31no—
70#4803—31no—
71#4789—31no—
72#4785—31no—
73#4771—31no—
74C4×#204—31no—
75#4689—31no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C2×#611—21no—
80C22×Dic9—21no—
81C22×Dic9—21no—
82#3701—22no—
83#3701C2×C414yescomplemented
84#3699—22no—
85#3699C2×C414yescomplemented
86C2×D36—21no—
87C2×D36C2311yescharacteristic
88C2×C4×D9—21no—
89C2×C4×D9—21no—
90C2×C4×D9—21no—
91C2×C4×D9—21no—
92C2×C4×D9—21no—
93C2×C4×D9C2311yescharacteristic
94C2×Dic18C2311yescharacteristic
95C9×SD16C2×C414yescomplemented
96C2×C8×C9C2311yescharacteristic
97C2×C8×C9C2311yescharacteristic
98C9×C4⋊C4—21no—
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C22⋊C4—21no—
102C42×C9—21no—
103C42×C9C2311yescharacteristic
104#3676—21no—
105#3674C2×C414yescomplemented
106#3673C2×C414yescomplemented
107(C2×D9)⋊C4—21no—
108(C2×D9)⋊C4—21no—
109(C2×D9)⋊C4D411yescharacteristic
110(C2×D9)⋊C4D411yescharacteristic
111C4⋊Dic9—21no—
112C4⋊Dic9C2311yescharacteristic
113C4⋊Dic9C2311yescharacteristic
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4D411yescharacteristic
119Dic9⋊C4D411yescharacteristic
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9—21no—
123C4×Dic9C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126#3664C2×C414yescomplemented
127#3663—22no—
128C8×D9C2×C414yescomplemented
129#2952—91noSylow
130C2×#239—31no—
131C2×#237—31no—
132C2×C3×SD16C2×D311yescharacteristic
133C3×C4×Q8C2×D311yescharacteristic
134C3×C4×D4C2×D311yescharacteristic
135Q8×Dic3—31no—
136C2×#216—31no—
137D4×Dic3—31no—
138C2×#213—31no—
139C4×#67—61no—
140C2×Dic3⋊C4—61no—
141#916—38no—
142C2×#204—31no—
143C2×ΓL(1,𝔽25)—31no—
144C2×D3×C8—31no—
145#893—31no—
146#893—61no—
147D3×C4⋊C4—31no—
148D3×C4⋊C4—31no—
149D3×C4⋊C4—61no—
150#887—31no—
151#67⋊C4—61no—
152#877—61no—
153C4×D12—31no—
154C4×D12—61no—
155#872—31no—
156#872—61no—
157C4×Dic6—31no—
158C3×#106C2×D311yescharacteristic
159C3×#103C2×D311yescharacteristic
160C3×#102C2×D311yescharacteristic
161C3×C4×C8C2×D311yescharacteristic
162#835—31no—
163#832—31no—
164#821—31no—
165#817—31no—
166#816—31no—
167#815—31no—
168C8×Dic3—31no—
169#810—31no—
170#809—31no—
171#808—31no—
172#808—31no—
173#803—31no—
174C23×C9—21no—
175C22×D9—21no—
176C22×D9C2×D411yescharacteristic
177Q8×C9—21no—
178Q8×C9C22×C412yes—
179D4×C9—21no—
180D4×C9C22×C412yes—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—81no—
185C2×C4×C9C2×D411yescharacteristic
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2411yescharacteristic
188#611—24no—
189C2×Dic9—21no—
190C2×Dic9—24no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9—81no—
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196C2×Dic9C2×D411yescharacteristic
197D36—24no—
198D36—21no—
199D36C22×C412yes—
200C4×D9—24no—
201C4×D9—81no—
202C4×D9—81no—
203C4×D9—81no—
204C4×D9—81no—
205C4×D9C22×C412yes—
206C4×D9#4112yes—
207Dic18—21no—
208Dic18C22×C412yes—
209C8×C9—21no—
210C8×C9C22×C412yes—
211C9⋊C8—21no—
212C9⋊C8C22×C412yes—
213C2×#135—91no—
214#520—91no—
215#520—91no—
216#442—91no—
217#442—91no—
218#441—91no—
219#441—91no—
220C4×SD16—91no—
221C4×SD16—91no—
222C4×SD16—91no—
223C4×SD16D911yescharacteristic, complemented
224C2×#106—91no—
225#417—91no—
226#417—91no—
227#405—91no—
228C2×C3×Q8C22×D311yescharacteristic
229C2×C3×D4C22×D311yescharacteristic
230C22×C3×C4—21no—
231C2×#67—61no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234#239—34no—
235#239—62no—
236#237—34no—
237#237—62no—
238C2×D12—31no—
239C2×D12—61no—
240C2×C4×D3—31no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—61no—
245C2×C4×D3—61no—
246C2×Dic6—31no—
247C3×SD16C4×D314yes—
248C2×C3×C8C22×D311yescharacteristic
249C2×C3×C8C22×D311yescharacteristic
250C3×C4⋊C4—21no—
251C3×C4⋊C4C22×D311yescharacteristic
252C3×C4⋊C4C22×D311yescharacteristic
253C3×C22⋊C4—21no—
254C3×C42—21no—
255C3×C42C22×D311yescharacteristic
256#217—61no—
257#216—34no—
258#213—34no—
259(C2×D3)⋊C4—31no—
260(C2×D3)⋊C4—31no—
261(C2×D3)⋊C4—61no—
262(C2×D3)⋊C4—61no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266Dic3⋊C4—31no—
267Dic3⋊C4—31no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272C4×Dic3—31no—
273C4×Dic3—61no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—31no—
278#204—34no—
279ΓL(1,𝔽25)—62no—
280D3×C8—34no—
281C22×C9—22no—
282C22×C9—41no—
283C22×C9—41no—
284C22×C9C22×D411yescharacteristic
285C2×D9—21no—
286C2×D9—21no—
287C2×D9—22no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9C4×D412yes—
291C4×C9—22no—
292C4×C9—21no—
293C4×C9—21no—
294C4×C9—41no—
295C4×C9—41no—
296C4×C9C23×C411yescharacteristic
297C4×C9C2×#4111yescharacteristic
298Dic9—22no—
299Dic9—21no—
300Dic9—21no—
301Dic9—41no—
302Dic9—41no—
303Dic9C4×D412yes—
304C2×#41—91no—
305C2×#41—91no—
306#135—98no—
307C2×Q16—91no—
308C2×SD16—91no—
309C2×SD16C2×D911yescharacteristic
310C2×D8—91no—
311C2×M16—91no—
312C22×C8—91no—
313C4×Q8—91no—
314C4×Q8—91no—
315C4×Q8—91no—
316C4×Q8C2×D911yescharacteristic
317C4×D4—91no—
318C4×D4—91no—
319C4×D4—91no—
320C4×D4—181no—
321C4×D4—181no—
322C4×D4—181no—
323C4×D4—181no—
324C4×D4C2×D911yescharacteristic
325#117—91no—
326#117—181no—
327#117—181no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4—91no—
330C2×C4⋊C4—181no—
331C2×C4⋊C4—181no—
332#106—91no—
333#106—91no—
334#106—91no—
335#106C2×D911yescharacteristic
336#103—91no—
337#103—91no—
338#103—91no—
339#103C2×D911yescharacteristic
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×D911yescharacteristic
344#97—91no—
345#97—91no—
346C4×C8—91no—
347C4×C8C2×D911yescharacteristic
348C23×C3—21no—
349C22×D3—31no—
350C22×D3—61no—
351C3×Q8—21no—
352C3×Q8C2×C4×D312yes—
353C3×D4—21no—
354C3×D4C2×C4×D312yes—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—81no—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362#67—64no—
363C2×Dic3—31no—
364C2×Dic3—31no—
365C2×Dic3—31no—
366C2×Dic3—64no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—241no—
371D12—32no—
372D12—64no—
373D12—61no—
374C4×D3—32no—
375C4×D3—32no—
376C4×D3—64no—
377C4×D3—241no—
378C4×D3—241no—
379C4×D3—241no—
380C4×D3—241no—
381Dic6—32no—
382Dic6—61no—
383C3×C8—21no—
384C3×C8C2×C4×D312yes—
385C3⋊C8—32no—
386C3⋊C8—61no—
387C2×C9—42no—
388C2×C9C2×C4×D411yescharacteristic
389C2×C9#57711yescharacteristic
390C2×C9#57711yescharacteristic
391D9—22no—
392D9—42no—
393#41—94no—
394#41—94no—
395#41—182no—
396#41—182no—
397C2×Q8—91no—
398C2×Q8C22×D911yescharacteristic
399C2×D4—91no—
400C2×D4—181no—
401C2×D4—181no—
402C2×D4C22×D911yescharacteristic
403C22×C4—21no—
404C22×C4—91no—
405C22×C4—181no—
406C22×C4—181no—
407C22×C4—181no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412Q16—94no—
413SD16—94no—
414SD16C4×D914yescomplemented
415D8—94no—
416M16—182no—
417C2×C8—91no—
418C2×C8—94no—
419C2×C8—91no—
420C2×C8C22×D911yescharacteristic
421C2×C8C22×D911yescharacteristic
422C4⋊C4—21no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4C22×D911yescharacteristic
433C4⋊C4C22×D911yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—91no—
436C22⋊C4—91no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C42—21no—
441C42—91no—
442C42—181no—
443C42—181no—
444C42—181no—
445C42C22×D911yescharacteristic
446C22×C3—22no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3C2×D3×D411yescharacteristic
450C2×D3—32no—
451C2×D3—61no—
452C2×D3—61no—
453C2×D3—62no—
454C2×D3—121no—
455C2×D3—121no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4C22×C4×D311yescharacteristic
462C3×C4D3×#4111yescharacteristic
463Dic3—32no—
464Dic3—61no—
465Dic3—61no—
466Dic3—62no—
467Dic3—121no—
468Dic3—121no—
469C9#295211yescharacteristic, complemented, Sylow
470C23—21no—
471C23—91no—
472C23—181no—
473Q8—21no—
474Q8—92no—
475Q8—181no—
476Q8C2×C4×D912yes—
477D4—21no—
478D4—92no—
479D4—184no—
480D4—184no—
481D4—181no—
482D4C2×C4×D912yes—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—81no—
487C2×C4—91no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—91no—
491C2×C4—91no—
492C2×C4—184no—
493C2×C4—184no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—721no—
498C2×C4—721no—
499C2×C4—721no—
500C2×C4—721no—
501C2×C4—721no—
502C2×C4D4×D911yescharacteristic
503C2×C4D4×D911yescharacteristic
504C2×C4C23×D911yescharacteristic
505C8—21no—
506C8—92no—
507C8—181no—
508C8C2×C4×D912yes—
509C2×C3—42no—
510C2×C3C4×D3×D411yescharacteristic
511C2×C3#576211yescharacteristic
512C2×C3#577011yescharacteristic
513D3—62no—
514D3—122no—
515C22—22no—
516C22—41no—
517C22—41no—
518C22—92no—
519C22—181no—
520C22—181no—
521C22—182no—
522C22—361no—
523C22—361no—
524C22C2×D4×D911yescharacteristic
525C4—21no—
526C4—21no—
527C4—22no—
528C4—41no—
529C4—41no—
530C4—92no—
531C4—181no—
532C4—181no—
533C4—182no—
534C4—361no—
535C4—361no—
536C4C22×C4×D911yescharacteristic
537C4#41×D911yescharacteristic
538C3#7965011yescharacteristic
539C2—42no—
540C2—182no—
541C2—362no—
542C2C4×D4×D911yescharacteristic
543C2#1058986411yescharacteristic
544C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radicalC2×#63478C2
cosocleC2×C4×C9C24
hypercenterC4×SD16D9
hypocenterC9#2952
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #10589676C2semidirect
3. #10589648C2semidirect
4. C4×C9×SD16C2semidirect
5. SD16×Dic9C2semidirect
6. #10588706C2semidirect
7. #10588697C2semidirect
8. D9×#106C2semidirect
9. #10588532C2semidirect
10. #10588483C2semidirect
11. #10588469C2semidirect
12. #10588465C2semidirect
13. #10588451C2semidirect
14. C4×#3664C2semidirect
15. #10588371C2semidirect
28. #63478C4semidirect
83. #3701C2×C4semidirect
85. #3699C2×C4semidirect
95. C9×SD16C2×C4semidirect
105. #3674C2×C4semidirect
106. #3673C2×C4semidirect
126. #3664C2×C4semidirect
128. C8×D9C2×C4semidirect
223. C4×SD16D9semidirect
414. SD16C4×D9semidirect
469. C9#2952semidirect

Maximal subgroups

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

subgroupindex
C2×#634782
#105896762
#105896482
C4×C9×SD162
SD16×Dic92
#105887062
#105886972
D9×#1062
#105885322
#105884832
#105884692
#105884652
#105884512
C4×#36642
#105883712
#796503