Finite Group Databasebeta

← #11868644

Subgroups — #11868644

Order 1152.

660 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589790C211yesmaximal, characteristic, complemented
2C4×D4×D9C211yesmaximal, characteristic
3C9×#478C211yesmaximal, characteristic, complemented
4#10588747C211yesmaximal, characteristic, complemented
5#10588692C211yesmaximal, characteristic, complemented
6#10588570C211yesmaximal, characteristic, complemented
7#10588561C211yesmaximal, characteristic, complemented
8#10588550C211yesmaximal, characteristic, complemented
9#10588541C211yesmaximal, characteristic, complemented
10#10588531C211yesmaximal, characteristic, complemented
11#10588521C211yesmaximal, characteristic, complemented
12#10588450C211yesmaximal, characteristic
13#10588450C211yesmaximal, characteristic
14#10588441C211yesmaximal, characteristic, complemented
15#10588439C211yesmaximal, characteristic, complemented
16#81166—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C22×C4×D9—21no—
19C9×#125C2211yescharacteristic, complemented
20C4×D4×C9C2211yescharacteristic
21D4×Dic9C2211yescharacteristic
22C4×#611—21no—
23C2×#3663C2211yescharacteristic
24C2×#3663C2211yescharacteristic
25#63458—21no—
26#63458—21no—
27#63455C2211yescharacteristic
28#63454C2211yescharacteristic
29#63454C2211yescharacteristic
30C4⋊C4×D9C2211yescharacteristic
31#63450C2211yescharacteristic, complemented
32#63450C2211yescharacteristic, complemented
33#63449—21no—
34#63449—21no—
35#611⋊C4—21no—
36C22⋊C4×D9—21no—
37C4×D36C2211yescharacteristic
38C42×D9C2211yescharacteristic
39#63432C2211yescharacteristic, complemented
40C9×#107C2211yescharacteristic, complemented
41C9×#106C2211yescharacteristic, complemented
42C9×C4⋊C8C2211yescharacteristic, complemented
43C9×#102C2211yescharacteristic
44C9×#102C2211yescharacteristic
45#63392C2211yescharacteristic
46#63392C2211yescharacteristic
47#63380C2211yescharacteristic
48#63380C2211yescharacteristic
49#63378C2211yescharacteristic, complemented
50#63377C2211yescharacteristic, complemented
51Dic9⋊C8C2211yescharacteristic, complemented
52Dic9⋊C8C2211yescharacteristic, complemented
53#63369C2211yescharacteristic
54#63369C2211yescharacteristic
55#63367C2211yescharacteristic, complemented
56#63367C2211yescharacteristic, complemented
57#63366C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4⋊(C9⋊C8)C2211yescharacteristic, complemented
60#5688—31no—
61C4×D3×D4—31no—
62C3×#478D311yescharacteristic
63#5066—31no—
64#5009—31no—
65#4890—31no—
66#4881—31no—
67#4870—31no—
68#4861—31no—
69#4847—31no—
70#4837—31no—
71#4770—31no—
72#4770—31no—
73#4761—31no—
74#4759—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C2×#611—21no—
79C22×Dic9—21no—
80D4×D9—22no—
81D4×D9Q814yescomplemented
82C2×D36C2311yescharacteristic
83C2×C4×D9—21no—
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9—44no—
87C2×C4×D9D411yescharacteristic
88C2×C4×D9D411yescharacteristic
89C2×C4×D9C2311yescharacteristic
90C2×Dic18—21no—
91C2×Dic18—21no—
92C2×C8×C9C2311yescharacteristic
93C2×C8×C9C2311yescharacteristic
94C9×C4⋊C4—21no—
95C9×C4⋊C4—21no—
96C9×C4⋊C4C2311yescharacteristic
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99C9×C22⋊C4—21no—
100C42×C9C2311yescharacteristic
101#3676—21no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106C4⋊Dic9C2311yescharacteristic
107C4⋊Dic9C2311yescharacteristic
108C4⋊Dic9C2311yescharacteristic
109Dic9⋊C4—21no—
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114C4×Dic9—21no—
115C4×Dic9—21no—
116C4×Dic9D411yescharacteristic
117C4×Dic9D411yescharacteristic
118C4×Dic9C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121#3663—22no—
122#3663—22no—
123#3077—91noSylow
124C2×D3×D4—31no—
125C22×C4×D3—61no—
126C3×#125C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128D4×Dic3—31no—
129C4×#67—61no—
130C2×ΓL(1,𝔽25)—31no—
131C2×ΓL(1,𝔽25)—31no—
132#896—61no—
133#896—61no—
134#893—31no—
135#892—31no—
136#892—31no—
137D3×C4⋊C4—31no—
138#888—31no—
139#888—31no—
140#887—61no—
141#887—61no—
142#67⋊C4—61no—
143D3×C22⋊C4—61no—
144C4×D12—31no—
145C42×D3—31no—
146#870—31no—
147C3×#107C2×D311yescharacteristic
148C3×#106C2×D311yescharacteristic
149C3×C4⋊C8C2×D311yescharacteristic
150C3×#102C2×D311yescharacteristic
151C3×#102C2×D311yescharacteristic
152#832—31no—
153#832—31no—
154#821—31no—
155#821—31no—
156#818—31no—
157#817—31no—
158Dic3⋊C8—31no—
159Dic3⋊C8—31no—
160#809—31no—
161#809—31no—
162#808—31no—
163#808—31no—
164#807—31no—
165#807—31no—
166C4⋊(C3⋊C8)—31no—
167C23×C9—21no—
168C22×D9—21no—
169C22×D9—24no—
170C22×D9—42no—
171C22×D9—42no—
172C22×D9C2×D411yescharacteristic
173D4×C9—21no—
174D4×C9C2×Q812yes—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—42no—
179C2×C4×C9C2×D411yescharacteristic
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2411yescharacteristic
182#611—24no—
183C2×Dic9—21no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—42no—
187C2×Dic9C2×D411yescharacteristic
188C2×Dic9C2×D411yescharacteristic
189C2×Dic9C2×D411yescharacteristic
190D36—21no—
191D36C2×Q812yes—
192C4×D9—22no—
193C4×D9—41no—
194C4×D9—42no—
195C4×D9—42no—
196C4×D9—42no—
197C4×D9C2×Q812yes—
198C4×D9#4112yes—
199Dic18—42no—
200Dic18—42no—
201C8×C9—21no—
202C8×C9—21no—
203C9⋊C8—21no—
204C9⋊C8—21no—
205#533—91no—
206C2×C4×D4—91no—
207#478—91no—
208#478—91no—
209#478—91no—
210#478D911yescharacteristic, complemented
211#476—91no—
212#476—91no—
213#474—91no—
214#474—91no—
215#428—91no—
216#428—91no—
217#423—91no—
218#418—91no—
219#418—91no—
220C23×D3—61no—
221C2×C3×D4C22×D311yescharacteristic
222C22×C3×C4—21no—
223C2×#67—61no—
224C22×Dic3—61no—
225D3×D4—34no—
226D3×D4—62no—
227C2×D12—31no—
228C2×C4×D3—31no—
229C2×C4×D3—31no—
230C2×C4×D3—31no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—124no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C22⋊C4—21no—
245C3×C42C22×D311yescharacteristic
246#217—61no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254Dic3⋊C4—61no—
255Dic3⋊C4—61no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—61no—
259C4×Dic3—31no—
260C4×Dic3—31no—
261C4×Dic3—31no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266ΓL(1,𝔽25)—62no—
267ΓL(1,𝔽25)—62no—
268C22×C9—22no—
269C22×C9—41no—
270C22×C9—41no—
271C22×C9C22×D411yescharacteristic
272C2×D9—21no—
273C2×D9—21no—
274C2×D9—22no—
275C2×D9—48no—
276C2×D9—41no—
277C2×D9—41no—
278C2×D9C22⋊Q812yes—
279C4×C9—21no—
280C4×C9—21no—
281C4×C9—41no—
282C4×C9—41no—
283C4×C9—41no—
284C4×C9C22×Q811yescharacteristic
285C4×C9C2×#4111yescharacteristic
286Dic9—21no—
287Dic9—41no—
288Dic9—41no—
289Dic9—41no—
290Dic9C22⋊Q812yes—
291Dic9AGL(1,ℤ/8)12yes—
292C22×D4—91no—
293C23×C4—181no—
294C2×M16—91no—
295C2×M16—91no—
296C4⋊Q8—91no—
297C4⋊Q8—91no—
298#125—91no—
299#125C2×D911yescharacteristic, complemented
300C22⋊Q8—181no—
301C22⋊Q8—181no—
302C4×Q8—181no—
303C4×Q8—181no—
304C4×D4—91no—
305C4×D4—91no—
306C4×D4—91no—
307C4×D4—181no—
308C4×D4—181no—
309C4×D4C2×D911yescharacteristic
310#117—91no—
311#117—91no—
312C2×C4⋊C4—91no—
313C2×C22⋊C4—181no—
314C2×C42—91no—
315#107—91no—
316#107—91no—
317#107—91no—
318#107C2×D911yescharacteristic, complemented
319#106—91no—
320#106—91no—
321#106—91no—
322#106C2×D911yescharacteristic, complemented
323C4⋊C8—91no—
324C4⋊C8—91no—
325C4⋊C8—91no—
326C4⋊C8C2×D911yescharacteristic, complemented
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331#102—91no—
332#102—91no—
333#102C2×D911yescharacteristic
334#102C2×D911yescharacteristic
335C23×C3—21no—
336C22×D3—31no—
337C22×D3—64no—
338C22×D3—61no—
339C22×D3—122no—
340C22×D3—122no—
341C3×D4—21no—
342C3×D4D3×Q812yes—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—42no—
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350#67—64no—
351C2×Dic3—31no—
352C2×Dic3—31no—
353C2×Dic3—31no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—122no—
358D12—32no—
359D12—61no—
360C4×D3—32no—
361C4×D3—32no—
362C4×D3—62no—
363C4×D3—122no—
364C4×D3—121no—
365C4×D3—122no—
366C4×D3—122no—
367Dic6—122no—
368Dic6—122no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C2×C9—42no—
374C2×C9C2×C22⋊Q811yescharacteristic
375C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C9#57511yescharacteristic
377D9—22no—
378D9—42no—
379C24—181no—
380C2×Q8—181no—
381C2×Q8—181no—
382C2×D4—94no—
383C2×D4—91no—
384C2×D4—182no—
385C2×D4—181no—
386C2×D4C22×D911yescharacteristic
387C22×C4—21no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—181no—
392C22×C4—181no—
393C22×C4—181no—
394C22×C4—181no—
395C22×C4—364no—
396M16—182no—
397M16—182no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8C22×D911yescharacteristic
401C2×C8C22×D911yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—91no—
405C4⋊C4—91no—
406C4⋊C4—91no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4C22×D911yescharacteristic
413C4⋊C4C22×D911yescharacteristic
414C4⋊C4C22×D911yescharacteristic
415C22⋊C4—21no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C42—91no—
422C42—91no—
423C42—91no—
424C42—181no—
425C42—181no—
426C42C22×D911yescharacteristic
427C22×C3—22no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3C2×D3×D411yescharacteristic
431C2×D3—32no—
432C2×D3—61no—
433C2×D3—61no—
434C2×D3—62no—
435C2×D3—128no—
436C2×D3—121no—
437C2×D3—121no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4C2×D3×Q811yescharacteristic
444C3×C4D3×#4111yescharacteristic
445Dic3—32no—
446Dic3—32no—
447Dic3—61no—
448Dic3—121no—
449Dic3—121no—
450Dic3—121no—
451C9#307711yescharacteristic, complemented, Sylow
452C23—21no—
453C23—91no—
454C23—184no—
455C23—181no—
456C23—362no—
457C23—362no—
458Q8—362no—
459Q8—362no—
460D4—21no—
461D4—92no—
462D4—184no—
463D4—181no—
464D4Q8×D912yes—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—91no—
470C2×C4—91no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—91no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—361no—
479C2×C4—362no—
480C2×C4—362no—
481C2×C4—362no—
482C2×C4—362no—
483C2×C4D4×D911yescharacteristic
484C2×C4D4×D911yescharacteristic
485C2×C4C23×D911yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—42no—
491C2×C3D3×C22⋊Q811yescharacteristic
492C2×C3#576811yescharacteristic
493C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
494D3—62no—
495D3—122no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—92no—
500C22—181no—
501C22—181no—
502C22—182no—
503C22—368no—
504C22—361no—
505C22—361no—
506C22C2×D4×D911yescharacteristic
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—92no—
513C4—92no—
514C4—181no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×Q8×D911yescharacteristic
519C4#41×D911yescharacteristic
520C3#8116611yescharacteristic
521C2—42no—
522C2—182no—
523C2—362no—
524C2D9×C22⋊Q811yescharacteristic
525C2#1058987011yescharacteristic
526C2D9×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#478C2
socleC22×C3C2×D3×D4
prime radicalC2×D4×D9C22
hypercenter#478D9
hypocenterC9#3077
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10589790C2semidirect
3. C9×#478C2semidirect
4. #10588747C2semidirect
5. #10588692C2semidirect
6. #10588570C2semidirect
7. #10588561C2semidirect
8. #10588550C2semidirect
9. #10588541C2semidirect
10. #10588531C2semidirect
11. #10588521C2semidirect
14. #10588441C2semidirect
15. #10588439C2semidirect
19. C9×#125C22semidirect
31. #63450C22semidirect
32. #63450C22semidirect
39. #63432C22semidirect
40. C9×#107C22semidirect
41. C9×#106C22semidirect
42. C9×C4⋊C8C22semidirect
49. #63378C22semidirect
50. #63377C22semidirect
51. Dic9⋊C8C22semidirect
52. Dic9⋊C8C22semidirect
55. #63367C22semidirect
56. #63367C22semidirect
57. #63366C22semidirect
58. #63366C22semidirect
59. C4⋊(C9⋊C8)C22semidirect
81. D4×D9Q8semidirect
210. #478D9semidirect
299. #125C2×D9semidirect
318. #107C2×D9semidirect
322. #106C2×D9semidirect
326. C4⋊C8C2×D9semidirect
451. C9#3077semidirect

Maximal subgroups

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

subgroupindex
#105897902
C4×D4×D92
C9×#4782
#105887472
#105886922
#105885702
#105885612
#105885502
#105885412
#105885312
#105885212
#105884502
#105884412
#105884392
#811663