Finite Group Databasebeta

← #11801986

Subgroups — #11801986

Order 1152.

1836 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D9C211yesmaximal, characteristic, complemented
2C2×#63499C211yesmaximal, characteristic
3C2×D4×Dic9C211yesmaximal, characteristic, complemented
4C2×#611⋊C4C212yesmaximal, complemented
5C9×#386C211yesmaximal, characteristic, complemented
6#10588890C211yesmaximal, characteristic, complemented
7#10588636C212yesmaximal, complemented
8#10588635C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic9C211yesmaximal, characteristic, complemented
10#10588348C212yesmaximal, complemented
11#10588346C212yesmaximal, complemented
12#74659—31nomaximal
13C24×D9C2211yescharacteristic
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2211yescharacteristic
16C22×#611C2212yes—
17C23×Dic9C2211yescharacteristic
18C23×Dic9C2211yescharacteristic, complemented
19C22×C4×D9—24no—
20C22×C4×D9—28no—
21C22×C4×D9C2212yes—
22C22×C4×D9C2212yes—
23C2×C9×C22⋊C4C2211yescharacteristic
24C2×C9×C22⋊C4C2212yescomplemented
25C2×#3676C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×#3676C2211yescharacteristic, complemented
28#63499C418yescomplemented
29D4×Dic9—24no—
30C2×(C2×D9)⋊C4C2212yes—
31C2×(C2×D9)⋊C4C2212yes—
32C2×(C2×D9)⋊C4C2212yes—
33C2×C4⋊Dic9C2211yescharacteristic, complemented
34C2×Dic9⋊C4C2212yescomplemented
35C2×C4×Dic9C2212yescomplemented
36C2×C4×Dic9C2211yescharacteristic, complemented
37#611⋊C4—28no—
38C9×#95C2212yescomplemented
39C9⋊#95C2212yescomplemented
40C9⋊#95C2212yescomplemented
41C23×C4×D3—31no—
42C2×#937—31no—
43C2×D4×Dic3—31no—
44C2×#67⋊C4—32no—
45C3×#386D311yescharacteristic
46#5210—31no—
47#4956—32no—
48#4955—31no—
49Dic3×C22⋊C4—31no—
50#4668—32no—
51#4666—32no—
52C24×C9C2311yescharacteristic
53C24×C9C2311yescharacteristic
54C23×D9—22no—
55C23×D9—22no—
56C23×D9—24no—
57C23×D9—24no—
58C23×D9C2×C414yescomplemented
59C23×D9C2312yes—
60C2×D4×C9—22no—
61C2×D4×C9—22no—
62C2×D4×C9C2×C414yescomplemented
63C22×C4×C9—22no—
64C22×C4×C9—24no—
65C22×C4×C9C2312yes—
66C22×C4×C9C2311yescharacteristic
67C22×C4×C9C2312yes—
68C2×#611—24no—
69C2×#611—24no—
70C2×#611C2×C418yescomplemented
71C22×Dic9—24no—
72C22×Dic9—22no—
73C22×Dic9—24no—
74C22×Dic9D414yescomplemented
75C22×Dic9C2311yescharacteristic
76C22×Dic9C2311yescharacteristic
77C22×Dic9C2312yes—
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C2×C4×D9—232no—
81C2×C4×D9—24no—
82C2×C4×D9—24no—
83C2×C4×D9—24no—
84C2×C4×D9—24no—
85C2×C4×D9—24no—
86C2×C4×D9D418yescomplemented
87C9×C22⋊C4—22no—
88C9×C22⋊C4—24no—
89#3676—22no—
90#3676—22no—
91#3676C2×C414yescomplemented
92(C2×D9)⋊C4—24no—
93(C2×D9)⋊C4—24no—
94(C2×D9)⋊C4C2×C418yescomplemented
95C4⋊Dic9—22no—
96Dic9⋊C4—24no—
97C4×Dic9—22no—
98C4×Dic9—24no—
99C4×#120—91noSylow
100C24×D3—31no—
101C22×C3×D4C2×D311yescharacteristic
102C23×C3×C4C2×D311yescharacteristic
103C22×#67—32no—
104C23×Dic3—31no—
105C23×Dic3—31no—
106C22×C4×D3—32no—
107C22×C4×D3—32no—
108C22×C4×D3—68no—
109C22×C4×D3—64no—
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C2×D312yes—
112C2×#217—31no—
113C2×#217—31no—
114C2×#217—31no—
115#937—38no—
116D4×Dic3—64no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×C4⋊Dic3—31no—
121C2×Dic3⋊C4—32no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—32no—
124#67⋊C4—68no—
125C3×#95C2×D312yes—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C23×C9—22no—
129C23×C9—22no—
130C23×C9—21no—
131C23×C9—22no—
132C23×C9—22no—
133C23×C9—21no—
134C23×C9C22×C412yes—
135C23×C9C22×C412yescomplemented
136C23×C9C2×D412yes—
137C23×C9#4112yes—
138C23×C9C2411yescharacteristic
139C22×D9—28no—
140C22×D9—216no—
141C22×D9—28no—
142C22×D9—28no—
143C22×D9—22no—
144C22×D9—22no—
145C22×D9—22no—
146C22×D9—22no—
147C22×D9—216no—
148C22×D9C22×C414yes—
149C22×D9C2×D414yes—
150C22×D9#4114yes—
151D4×C9—28no—
152C2×C4×C9—28no—
153C2×C4×C9—21no—
154C2×C4×C9—22no—
155C2×C4×C9—22no—
156C2×C4×C9—21no—
157C2×C4×C9—22no—
158C2×C4×C9—22no—
159C2×C4×C9—22no—
160C2×C4×C9C22×C412yescomplemented
161C2×C4×C9C2×D414yes—
162#611—216no—
163C2×Dic9—22no—
164C2×Dic9—22no—
165C2×Dic9—22no—
166C2×Dic9—28no—
167C2×Dic9—21no—
168C2×Dic9—22no—
169C2×Dic9—21no—
170C2×Dic9—22no—
171C2×Dic9—44no—
172C2×Dic9C22×C414yescomplemented
173C2×Dic9C2×D412yes—
174C2×Dic9C2×D412yes—
175C2×Dic9C2×D414yes—
176C4×D9—216no—
177C4×D9—216no—
178C24×C4—91no—
179C2×#120—91no—
180C2×C4×D4—91no—
181C2×C4×D4—92no—
182#386—92no—
183#386D911yescharacteristic, complemented
184#385—91no—
185#385—92no—
186#379—91no—
187C4×C22⋊C4—91no—
188C4×C22⋊C4—92no—
189C24×C3C22×D311yescharacteristic
190C24×C3C22×D311yescharacteristic
191C23×D3—32no—
192C23×D3—34no—
193C23×D3—64no—
194C23×D3—64no—
195C23×D3—62no—
196C23×D3—62no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4C4×D314yes—
200C22×C3×C4—22no—
201C22×C3×C4—24no—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D312yes—
205C2×#67—38no—
206C2×#67—64no—
207C2×#67—64no—
208C22×Dic3—31no—
209C22×Dic3—34no—
210C22×Dic3—32no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—64no—
215C22×Dic3—64no—
216C22×Dic3—62no—
217C2×C4×D3—38no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—632no—
223C2×C4×D3—64no—
224C3×C22⋊C4—22no—
225C3×C22⋊C4—24no—
226#217—34no—
227#217—62no—
228#217—62no—
229(C2×D3)⋊C4—38no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232C4⋊Dic3—62no—
233Dic3⋊C4—64no—
234C4×Dic3—64no—
235C4×Dic3—62no—
236C22×C9—24no—
237C22×C9—22no—
238C22×C9—22no—
239C22×C9—24no—
240C22×C9—24no—
241C22×C9—22no—
242C22×C9—41no—
243C22×C9—41no—
244C22×C9—42no—
245C22×C9C4×D414yescomplemented
246C22×C9C23×C411yescharacteristic
247C22×C9C22×D412yes—
248C22×C9C22×D411yescharacteristic
249C22×C9C2×#4111yescharacteristic
250C22×C9C2×#4112yes—
251C2×D9—232no—
252C2×D9—24no—
253C2×D9—24no—
254C2×D9—24no—
255C2×D9—24no—
256C2×D9—24no—
257C2×D9—24no—
258C2×D9C4×D418yescomplemented
259C4×C9—22no—
260C4×C9—24no—
261C4×C9—42no—
262Dic9—24no—
263Dic9—22no—
264Dic9—41no—
265Dic9—41no—
266Dic9#12014yescomplemented
267C25—91no—
268C22×D4—92no—
269C22×D4C2×D911yescharacteristic
270C23×C4—91no—
271C23×C4—92no—
272C23×C4—91no—
273C23×C4—92no—
274C23×C4—184no—
275C23×C4—188no—
276C23×C4C2×D911yescharacteristic
277#120—98no—
278C4×D4—188no—
279C4×D4—184no—
280C2×C4⋊C4—92no—
281C2×C4⋊C4—91no—
282C2×C22⋊C4—91no—
283C2×C22⋊C4—92no—
284C2×C22⋊C4—91no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—92no—
287C2×C22⋊C4—92no—
288C2×C22⋊C4C2×D911yescharacteristic
289C2×C22⋊C4C2×D912yescomplemented
290C2×C42—92no—
291C2×C42—91no—
292#95—92no—
293#95—92no—
294#95C2×D912yescomplemented
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—22no—
299C23×C3—21no—
300C23×C3—22no—
301C23×C3C2×C4×D312yes—
302C23×C3C2×C4×D312yes—
303C23×C3D3×D412yes—
304C23×C3#23712yes—
305C23×C3C23×D311yescharacteristic
306C22×D3—34no—
307C22×D3—34no—
308C22×D3—34no—
309C22×D3—616no—
310C22×D3—68no—
311C22×D3—68no—
312C22×D3—616no—
313C22×D3—68no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—62no—
318C3×D4—28no—
319C2×C3×C4—28no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4C2×C4×D312yes—
328C2×C3×C4D3×D414yes—
329#67—616no—
330C2×Dic3—34no—
331C2×Dic3—32no—
332C2×Dic3—34no—
333C2×Dic3—32no—
334C2×Dic3—68no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—61no—
339C2×Dic3—62no—
340C2×Dic3—61no—
341C2×Dic3—62no—
342C2×Dic3—124no—
343C4×D3—616no—
344C4×D3—616no—
345C2×C9—24no—
346C2×C9—42no—
347C2×C9C2×C4×D411yescharacteristic
348C2×C9C2×C4×D412yes—
349C2×C9C2×#12011yescharacteristic
350C2×C9#52511yescharacteristic
351C2×C9#52512yes—
352D9—28no—
353C24—92no—
354C24—94no—
355C24—184no—
356C24—184no—
357C24—182no—
358C24—182no—
359C24C22×D911yescharacteristic
360C24C22×D911yescharacteristic
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—98no—
364C2×D4—184no—
365C2×D4—184no—
366C2×D4C4×D914yescomplemented
367C22×C4—22no—
368C22×C4—24no—
369C22×C4—91no—
370C22×C4—94no—
371C22×C4—92no—
372C22×C4—91no—
373C22×C4—98no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—184no—
377C22×C4—184no—
378C22×C4—184no—
379C22×C4—184no—
380C22×C4—1832no—
381C22×C4—184no—
382C22×C4—184no—
383C22×C4—182no—
384C22×C4—184no—
385C22×C4C22×D912yes—
386C22×C4C22×D911yescharacteristic
387C22×C4C22×D912yes—
388C4⋊C4—182no—
389C4⋊C4—184no—
390C22⋊C4—22no—
391C22⋊C4—24no—
392C22⋊C4—94no—
393C22⋊C4—98no—
394C22⋊C4—184no—
395C22⋊C4—184no—
396C22⋊C4—182no—
397C22⋊C4—182no—
398C42—182no—
399C42—184no—
400C22×C3—22no—
401C22×C3—24no—
402C22×C3—22no—
403C22×C3—24no—
404C22×C3—22no—
405C22×C3—24no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—42no—
409C22×C3#67⋊C414yes—
410C22×C3C22×C4×D311yescharacteristic
411C22×C3C2×D3×D411yescharacteristic
412C22×C3C2×D3×D412yes—
413C22×C3C2×#23711yescharacteristic
414C22×C3D3×#4112yes—
415C2×D3—38no—
416C2×D3—632no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—64no—
422C2×D3—64no—
423C3×C4—22no—
424C3×C4—24no—
425C3×C4—42no—
426Dic3—34no—
427Dic3—64no—
428Dic3—62no—
429Dic3—121no—
430Dic3—121no—
431C9C4×#12011yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—22no—
435C23—21no—
436C23—21no—
437C23—22no—
438C23—94no—
439C23—94no—
440C23—94no—
441C23—1816no—
442C23—188no—
443C23—1816no—
444C23—188no—
445C23—188no—
446C23—182no—
447C23—182no—
448C23—182no—
449C23—182no—
450C23C2×C4×D912yes—
451C23C2×C4×D912yescomplemented
452C23D4×D912yes—
453C23#369912yes—
454C23C23×D911yescharacteristic
455D4—28no—
456D4—1816no—
457C2×C4—28no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—94no—
466C2×C4—92no—
467C2×C4—94no—
468C2×C4—92no—
469C2×C4—1816no—
470C2×C4—1816no—
471C2×C4—188no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—182no—
477C2×C4—181no—
478C2×C4—182no—
479C2×C4—364no—
480C2×C4C2×C4×D912yescomplemented
481C2×C4D4×D914yes—
482C2×C3—24no—
483C2×C3—42no—
484C2×C3C2×#67⋊C411yescharacteristic
485C2×C3C4×D3×D412yes—
486C2×C3D3×#12011yescharacteristic
487C2×C3#560612yes—
488C2×C3#565611yescharacteristic
489D3—68no—
490C22—24no—
491C22—22no—
492C22—24no—
493C22—22no—
494C22—22no—
495C22—24no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—98no—
500C22—1832no—
501C22—184no—
502C22—184no—
503C22—184no—
504C22—184no—
505C22—184no—
506C22—184no—
507C22#611⋊C414yescomplemented
508C22C22×C4×D911yescharacteristic
509C22C2×D4×D912yes—
510C22C2×D4×D911yescharacteristic
511C22C2×#369911yescharacteristic
512C22#41×D912yes—
513C4—22no—
514C4—24no—
515C4—42no—
516C4—94no—
517C4—184no—
518C4—182no—
519C4—361no—
520C4—361no—
521C3#7465911yescharacteristic
522C2—24no—
523C2—42no—
524C2—188no—
525C2C2×#611⋊C411yescharacteristic
526C2C4×D4×D912yes—
527C2D9×#12011yescharacteristic
528C2#1058970812yes—
529C2#1058975811yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#386C2
prime radicalC2×#63499C2
cosocleC23×C9C24
hypercenter#386D9
hypocenterC9C4×#120
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C23×C4×D9C2semidirect
3. C2×D4×Dic9C2semidirect
4. C2×#611⋊C4C2semidirect
5. C9×#386C2semidirect
6. #10588890C2semidirect
7. #10588636C2semidirect
8. #10588635C2semidirect
9. C22⋊C4×Dic9C2semidirect
10. #10588348C2semidirect
11. #10588346C2semidirect
18. C23×Dic9C22semidirect
24. C2×C9×C22⋊C4C22semidirect
27. C2×#3676C22semidirect
28. #63499C4semidirect
33. C2×C4⋊Dic9C22semidirect
34. C2×Dic9⋊C4C22semidirect
35. C2×C4×Dic9C22semidirect
36. C2×C4×Dic9C22semidirect
38. C9×#95C22semidirect
39. C9⋊#95C22semidirect
40. C9⋊#95C22semidirect
58. C23×D9C2×C4semidirect
62. C2×D4×C9C2×C4semidirect
70. C2×#611C2×C4semidirect
74. C22×Dic9D4semidirect
86. C2×C4×D9D4semidirect
91. #3676C2×C4semidirect
94. (C2×D9)⋊C4C2×C4semidirect
135. C23×C9C22×C4semidirect
160. C2×C4×C9C22×C4semidirect
172. C2×Dic9C22×C4semidirect
183. #386D9semidirect
245. C22×C9C4×D4semidirect
258. C2×D9C4×D4semidirect
266. Dic9#120semidirect
289. C2×C22⋊C4C2×D9semidirect
294. #95C2×D9semidirect
366. C2×D4C4×D9semidirect
431. C9C4×#120semidirect
451. C23C2×C4×D9semidirect
480. C2×C4C2×C4×D9semidirect
507. C22#611⋊C4semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D92
C2×#634992
C2×D4×Dic92
C2×#611⋊C42
C9×#3862
#105888902
#105886362
#105886352
C22⋊C4×Dic92
#105883482
#105883462
#746593