Finite Group Databasebeta

← #11867130

Subgroups — #11867130

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#525C211yesmaximal, characteristic, complemented
2C2×#63512C211yesmaximal, characteristic, complemented
3C2×#63492C211yesmaximal, characteristic, complemented
4C22×#3667C211yesmaximal, characteristic, complemented
5#10588916C211yesmaximal, characteristic, complemented
6#10588732C212yesmaximal, complemented
7#10588731C212yesmaximal, complemented
8#10588722C212yesmaximal, complemented
9#10588721C212yesmaximal, complemented
10#10588682C211yesmaximal, characteristic, complemented
11#10588679C211yesmaximal, characteristic, complemented
12#82924—31nomaximal
13C2×C9×#41C2211yescharacteristic
14C23×C4×C9C2211yescharacteristic
15C22×#611—21no—
16C22×D36C2211yescharacteristic
17C9×#123—21no—
18C9×C22⋊Q8C2211yescharacteristic, complemented
19C9×C22⋊Q8C2211yescharacteristic, complemented
20C9×#121C2211yescharacteristic, complemented
21C9×#121C2211yescharacteristic, complemented
22C9×#120—21no—
23C4×D4×C9—21no—
24C4×D4×C9—21no—
25C9×#117C2211yescharacteristic
26#63512—24no—
27C2×#3675C2212yescomplemented
28C2×#3673C2212yescomplemented
29#63492—21no—
30#63492—21no—
31#63492C2212yes—
32#63492C2212yes—
33C2×(C2×D9)⋊C4—21no—
34C2×C4⋊Dic9C2211yescharacteristic
35C2×#3667—24no—
36C2×#3667C2211yescharacteristic
37C2×#3667C2211yescharacteristic
38C2×#3667C2212yescomplemented
39C22×C9⋊C8C2212yescomplemented
40#63395C2212yescomplemented
41#63392C2212yescomplemented
42#63369C2212yescomplemented
43#63369C2212yescomplemented
44#63367C2212yescomplemented
45#63366C2212yescomplemented
46C3×#525D311yescharacteristic
47C2×#949—31no—
48C2×#930—31no—
49C22×#208—31no—
50#5232—31no—
51#5049—32no—
52#5048—32no—
53#5039—32no—
54#5038—32no—
55#5001—31no—
56#4995—31no—
57C24×C9D411yescharacteristic
58C23×D9—21no—
59C9×#41—22no—
60C9×#41—22no—
61C2×Q8×C9C2311yescharacteristic
62C2×D4×C9—21no—
63C2×D4×C9—21no—
64C2×D4×C9—21no—
65C2×D4×C9C2311yescharacteristic
66C22×C4×C9—22no—
67C22×C4×C9—22no—
68C22×C4×C9—21no—
69C22×C4×C9D411yescharacteristic
70C22×C4×C9D411yescharacteristic
71C22×C4×C9D411yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C2×#611—22no—
76C2×#611—22no—
77C2×#611—44no—
78C22×Dic9—21no—
79C2×D36—22no—
80C2×D36—22no—
81C2×D36—21no—
82C2×D36C2312yes—
83C9×C4⋊C4—21no—
84C9×C4⋊C4—21no—
85C9×C4⋊C4C2311yescharacteristic
86C9×C4⋊C4C2311yescharacteristic
87C9×C22⋊C4—21no—
88C9×C22⋊C4—21no—
89C9×C22⋊C4—21no—
90C9×C22⋊C4—21no—
91C9×C22⋊C4—21no—
92C42×C9—21no—
93#3675—24no—
94#3673—24no—
95(C2×D9)⋊C4—22no—
96(C2×D9)⋊C4—22no—
97C4⋊Dic9—21no—
98C4⋊Dic9C2312yes—
99#3667—22no—
100#3667—24no—
101#3667D414yescomplemented
102C2×C9⋊C8—24no—
103C2×C9⋊C8C2312yes—
104C2×C9⋊C8C2312yes—
105#3055—91noSylow
106C2×C3×#41C2×D311yescharacteristic
107C23×C3×C4C2×D311yescharacteristic
108C22×#67—61no—
109C22×D12—31no—
110C3×#123—21no—
111C3×C22⋊Q8C2×D311yescharacteristic
112C3×C22⋊Q8C2×D311yescharacteristic
113C3×#121C2×D311yescharacteristic
114C3×#121C2×D311yescharacteristic
115C3×#120—21no—
116C3×C4×D4—21no—
117C3×C4×D4—21no—
118C3×#117C2×D311yescharacteristic
119#949—64no—
120C2×#215—32no—
121C2×#213—32no—
122#930—32no—
123#930—32no—
124#930—61no—
125#930—61no—
126C2×(C2×D3)⋊C4—61no—
127C2×C4⋊Dic3—31no—
128C2×#208—31no—
129C2×#208—31no—
130C2×#208—32no—
131C2×#208—64no—
132C22×C3⋊C8—32no—
133#835—32no—
134#832—32no—
135#809—32no—
136#809—32no—
137#808—32no—
138#807—32no—
139C23×C9—22no—
140C23×C9—22no—
141C23×C9—21no—
142C23×C9—41no—
143C23×C9C2×D411yescharacteristic
144C23×C9C2×D411yescharacteristic
145C23×C9C2×D411yescharacteristic
146C22×D9—22no—
147C22×D9—42no—
148C22×D9—42no—
149C22×D9—42no—
150Q8×C9—21no—
151Q8×C9—21no—
152D4×C9—21no—
153D4×C9—21no—
154D4×C9—42no—
155D4×C9—42no—
156D4×C9—42no—
157C2×C4×C9—22no—
158C2×C4×C9—22no—
159C2×C4×C9—22no—
160C2×C4×C9—21no—
161C2×C4×C9—21no—
162C2×C4×C9—21no—
163C2×C4×C9—21no—
164C2×C4×C9—21no—
165C2×C4×C9—21no—
166C2×C4×C9—21no—
167C2×C4×C9—42no—
168C2×C4×C9C2×D412yes—
169C2×C4×C9C2×D411yescharacteristic
170C2×C4×C9C2×D411yescharacteristic
171C2×C4×C9C2×D411yescharacteristic
172C2×C4×C9#4112yes—
173C2×C4×C9C2411yescharacteristic
174#611—44no—
175#611—44no—
176C2×Dic9—22no—
177C2×Dic9—42no—
178D36—22no—
179D36—22no—
180D36—42no—
181C9⋊C8—22no—
182C9⋊C8C2×D414yescomplemented
183C2×AGL(1,ℤ/8)—91no—
184C22×M16—91no—
185#525D911yescharacteristic, complemented
186C2×#121—91no—
187#469—92no—
188#468—92no—
189#466—92no—
190#465—92no—
191#428—91no—
192#418—91no—
193#417—91no—
194C24×C3#6711yescharacteristic
195C23×D3—61no—
196C3×#41—22no—
197C3×#41—22no—
198C2×C3×Q8C22×D311yescharacteristic
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4C22×D311yescharacteristic
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4#6711yescharacteristic
207C22×C3×C4#6711yescharacteristic
208C22×C3×C4#6711yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—62no—
213C2×#67—62no—
214C2×#67—124no—
215C22×Dic3—61no—
216C2×D12—32no—
217C2×D12—62no—
218C2×D12—62no—
219C2×D12—61no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—21no—
222C3×C4⋊C4C22×D311yescharacteristic
223C3×C4⋊C4C22×D311yescharacteristic
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4—21no—
227C3×C22⋊C4—21no—
228C3×C22⋊C4—21no—
229C3×C42—21no—
230#215—64no—
231#213—64no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—62no—
234C4⋊Dic3—32no—
235C4⋊Dic3—61no—
236#208—34no—
237#208—64no—
238#208—62no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—64no—
242C22×C9—21no—
243C22×C9—21no—
244C22×C9—21no—
245C22×C9—21no—
246C22×C9—21no—
247C22×C9—21no—
248C22×C9—21no—
249C22×C9—44no—
250C22×C9—41no—
251C22×C9—41no—
252C22×C9—41no—
253C22×C9#12112yes—
254C22×C9AGL(1,ℤ/8)12yescomplemented
255C22×C9C22×D411yescharacteristic
256C2×D9—42no—
257C2×D9—42no—
258C2×D9—42no—
259C2×D9—84no—
260C4×C9—21no—
261C4×C9—21no—
262C4×C9—41no—
263C4×C9—41no—
264C4×C9—41no—
265C4×C9#12112yes—
266C4×C9C22×D411yescharacteristic
267C4×C9C2×#4111yescharacteristic
268Dic9—42no—
269C2×#41C2×D911yescharacteristic
270C22×D4—91no—
271C22×D4—181no—
272C23×C4C2×D911yescharacteristic
273AGL(1,ℤ/8)—184no—
274C2×SD16—92no—
275C2×D8—92no—
276C2×M16—91no—
277C2×M16—91no—
278C2×M16—92no—
279C2×M16—184no—
280C22×C8—92no—
281#123—21no—
282C22⋊Q8C2×D911yescharacteristic, complemented
283C22⋊Q8C2×D911yescharacteristic, complemented
284#121—92no—
285#121—92no—
286#121—181no—
287#121—181no—
288#121C2×D911yescharacteristic, complemented
289#121C2×D911yescharacteristic, complemented
290#120—21no—
291C4×D4—21no—
292C4×D4—21no—
293#117C2×D911yescharacteristic
294C2×C4⋊C4—91no—
295C2×C22⋊C4—181no—
296#107—92no—
297#106—92no—
298#103—92no—
299#102—92no—
300#102—92no—
301#102—92no—
302C23×C3—22no—
303C23×C3—22no—
304C23×C3—21no—
305C23×C3—41no—
306C23×C3C2×#6711yescharacteristic
307C23×C3C2×#6711yescharacteristic
308C23×C3C2×#6711yescharacteristic
309C22×D3—62no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C3×Q8—21no—
314C3×Q8—21no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—42no—
318C3×D4—42no—
319C3×D4—42no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—42no—
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23712yes—
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337#67—124no—
338#67—124no—
339C2×Dic3—62no—
340C2×Dic3—122no—
341D12—62no—
342D12—62no—
343D12—122no—
344C3⋊C8—34no—
345C3⋊C8—62no—
346C2×C9—22no—
347C2×C9—22no—
348C2×C9—41no—
349C2×C9—81no—
350C2×C9C2×#12111yescharacteristic
351C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
352C2×C9#57511yescharacteristic
353D9—82no—
354C24—181no—
355C24#61111yescharacteristic
356#41—22no—
357#41—22no—
358C2×Q8C22×D911yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—92no—
363C2×D4—182no—
364C2×D4—182no—
365C2×D4—182no—
366C2×D4—182no—
367C2×D4—181no—
368C2×D4—364no—
369C2×D4C22×D911yescharacteristic
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—181no—
374C22×C4#61111yescharacteristic
375C22×C4#61111yescharacteristic
376C22×C4#61111yescharacteristic
377C22×C4C22×D911yescharacteristic
378C22×C4C22×D911yescharacteristic
379C22×C4C22×D911yescharacteristic
380SD16—184no—
381D8—184no—
382M16—94no—
383M16—184no—
384M16—182no—
385C2×C8—92no—
386C2×C8—92no—
387C2×C8—184no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—92no—
391C4⋊C4—181no—
392C4⋊C4C22×D911yescharacteristic
393C4⋊C4C22×D911yescharacteristic
394C22⋊C4—21no—
395C22⋊C4—21no—
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—182no—
400C22⋊C4—182no—
401C42—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—44no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3—41no—
413C22×C3#93912yes—
414C22×C3#94912yes—
415C22×C3C22×#6711yescharacteristic
416C2×D3—122no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—244no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4#93912yes—
426C3×C4C2×D3×D411yescharacteristic
427C3×C4C2×#23711yescharacteristic
428Dic3—122no—
429C9#305511yescharacteristic, complemented, Sylow
430C23—22no—
431C23—22no—
432C23—21no—
433C23—41no—
434C23—182no—
435C23—362no—
436C23—362no—
437C23—362no—
438C23C2×#61111yescharacteristic
439C23C2×#61111yescharacteristic
440C23C2×#61111yescharacteristic
441Q8—21no—
442Q8—21no—
443D4—21no—
444D4—21no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—182no—
449D4—182no—
450D4—364no—
451D4—364no—
452D4—362no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—182no—
465C2×C4—362no—
466C2×C4D4×D912yes—
467C2×C4#369912yes—
468C2×C4C2×#61111yescharacteristic
469C2×C4C2×#61111yescharacteristic
470C2×C4C2×#61111yescharacteristic
471C2×C4C23×D911yescharacteristic
472C8—94no—
473C8—182no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—41no—
477C2×C3—81no—
478C2×C3C2×#93911yescharacteristic
479C2×C3C2×#94911yescharacteristic
480C2×C3#582211yescharacteristic
481D3—242no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—44no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—362no—
494C22—362no—
495C22—362no—
496C22—724no—
497C22#6350112yes—
498C22#6351212yescomplemented
499C22C22×#61111yescharacteristic
500C4—21no—
501C4—21no—
502C4—41no—
503C4—41no—
504C4—41no—
505C4—362no—
506C4#6350112yes—
507C4C2×D4×D911yescharacteristic
508C4C2×#369911yescharacteristic
509C3#8292411yescharacteristic
510C2—22no—
511C2—22no—
512C2—41no—
513C2—81no—
514C2—722no—
515C2C2×#6350111yescharacteristic
516C2C2×#6351211yescharacteristic
517C2#1058992511yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#525C2
socleC22×C3C22×#67
hypercenter#525D9
hypocenterC9#3055
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C9×#525C2semidirect
2. C2×#63512C2semidirect
3. C2×#63492C2semidirect
4. C22×#3667C2semidirect
5. #10588916C2semidirect
6. #10588732C2semidirect
7. #10588731C2semidirect
8. #10588722C2semidirect
9. #10588721C2semidirect
10. #10588682C2semidirect
11. #10588679C2semidirect
18. C9×C22⋊Q8C22semidirect
19. C9×C22⋊Q8C22semidirect
20. C9×#121C22semidirect
21. C9×#121C22semidirect
27. C2×#3675C22semidirect
28. C2×#3673C22semidirect
38. C2×#3667C22semidirect
39. C22×C9⋊C8C22semidirect
40. #63395C22semidirect
41. #63392C22semidirect
42. #63369C22semidirect
43. #63369C22semidirect
44. #63367C22semidirect
45. #63366C22semidirect
101. #3667D4semidirect
182. C9⋊C8C2×D4semidirect
185. #525D9semidirect
254. C22×C9AGL(1,ℤ/8)semidirect
282. C22⋊Q8C2×D9semidirect
283. C22⋊Q8C2×D9semidirect
288. #121C2×D9semidirect
289. #121C2×D9semidirect
429. C9#3055semidirect
498. C22#63512semidirect

Maximal subgroups

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

subgroupindex
C9×#5252
C2×#635122
C2×#634922
C22×#36672
#105889162
#105887322
#105887312
#105887222
#105887212
#105886822
#105886792
#829243