Finite Group Databasebeta

← #11872805

Subgroups — #11872805

Order 1152.

591 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#10589800C211yesmaximal, characteristic, complemented
2#10589647C211yesmaximal, characteristic
3C9×#478C211yesmaximal, characteristic, complemented
4#10588747C211yesmaximal, characteristic, complemented
5#10588695C211yesmaximal, characteristic, complemented
6#10588569C211yesmaximal, characteristic, complemented
7#10588568C211yesmaximal, characteristic, complemented
8#10588548C211yesmaximal, characteristic, complemented
9#10588532C211yesmaximal, characteristic, complemented
10#10588525C211yesmaximal, characteristic, complemented
11#10588524C211yesmaximal, characteristic, complemented
12#10588456C211yesmaximal, characteristic
13#10588456C211yesmaximal, characteristic
14#10588438C211yesmaximal, characteristic, complemented
15#10588437C211yesmaximal, characteristic, complemented
16#81147—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C9×#125C2211yescharacteristic, complemented
19C4×D4×C9C2211yescharacteristic
20D4×Dic9C2211yescharacteristic
21C2×#3672C2211yescharacteristic
22C2×#3672C2211yescharacteristic
23C4×#611—21no—
24C2×(C2×D9)⋊C4—21no—
25C2×#3664C2211yescharacteristic
26C2×#3664C2211yescharacteristic
27#63460—21no—
28#63460—21no—
29#63459C2211yescharacteristic
30#63459C2211yescharacteristic
31#63455C2211yescharacteristic
32#63454C2211yescharacteristic
33#63452—21no—
34#63452—21no—
35#63449C2211yescharacteristic, complemented
36#63449C2211yescharacteristic, complemented
37#611⋊C4—21no—
38C22⋊C4×D9—21no—
39C4×D36C2211yescharacteristic
40#63434C2211yescharacteristic
41#63431C2211yescharacteristic, complemented
42C9×#107C2211yescharacteristic, complemented
43C9×#106C2211yescharacteristic, complemented
44C9×C4⋊C8C2211yescharacteristic, complemented
45C9×#102C2211yescharacteristic
46C9×#102C2211yescharacteristic
47(C2×D9)⋊C8C2211yescharacteristic
48(C2×D9)⋊C8C2211yescharacteristic
49#63376C2211yescharacteristic, complemented
50#63376C2211yescharacteristic, complemented
51#63375C2211yescharacteristic, complemented
52C8×Dic9C2211yescharacteristic, complemented
53#63369C2211yescharacteristic
54#63369C2211yescharacteristic
55#63368C2211yescharacteristic, complemented
56#63368C2211yescharacteristic, complemented
57#63367C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59C4⋊(C9⋊C8)C2211yescharacteristic, complemented
60#5698—31no—
61#5545—31no—
62C3×#478D311yescharacteristic
63#5066—31no—
64#5019—31no—
65#4889—31no—
66#4888—31no—
67#4868—31no—
68#4852—31no—
69#4841—31no—
70#4840—31no—
71#4776—31no—
72#4776—31no—
73#4758—31no—
74#4757—31no—
75C23×D9—21no—
76C2×D4×C9C2311yescharacteristic
77C22×C4×C9—21no—
78C2×#611—21no—
79C22×Dic9—21no—
80D4×D9—22no—
81D4×D9—22no—
82C2×D36C2311yescharacteristic
83C2×C4×D9—21no—
84C2×C4×D9—21no—
85C2×C4×D9C2311yescharacteristic
86C2×Dic18C2311yescharacteristic
87C2×Dic18C2311yescharacteristic
88C2×C8×C9C2311yescharacteristic
89C2×C8×C9C2311yescharacteristic
90C9×C4⋊C4—21no—
91C9×C4⋊C4—21no—
92C9×C4⋊C4C2311yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C4⋊C4C2311yescharacteristic
95C9×C22⋊C4—21no—
96C42×C9C2311yescharacteristic
97#3676—21no—
98#3672—22no—
99#3672—22no—
100(C2×D9)⋊C4—21no—
101(C2×D9)⋊C4—21no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4D411yescharacteristic
106(C2×D9)⋊C4D411yescharacteristic
107C4⋊Dic9—21no—
108C4⋊Dic9—21no—
109C4⋊Dic9—21no—
110C4⋊Dic9—21no—
111C4⋊Dic9C2311yescharacteristic
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4D411yescharacteristic
115Dic9⋊C4D411yescharacteristic
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9C2311yescharacteristic
120C2×C9⋊C8C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122#3664—22no—
123#3664—22no—
124#3123—91noSylow
125C2×D3×D4—31no—
126C3×#125C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128D4×Dic3—31no—
129C2×#214—31no—
130C2×#214—31no—
131C4×#67—61no—
132C2×(C2×D3)⋊C4—61no—
133C2×#204—31no—
134C2×#204—31no—
135#898—61no—
136#898—61no—
137#897—31no—
138#897—31no—
139#893—31no—
140#892—31no—
141#890—61no—
142#890—61no—
143#887—31no—
144#887—31no—
145#67⋊C4—61no—
146D3×C22⋊C4—61no—
147C4×D12—31no—
148#872—31no—
149#869—31no—
150C3×#107C2×D311yescharacteristic
151C3×#106C2×D311yescharacteristic
152C3×C4⋊C8C2×D311yescharacteristic
153C3×#102C2×D311yescharacteristic
154C3×#102C2×D311yescharacteristic
155(C2×D3)⋊C8—31no—
156(C2×D3)⋊C8—31no—
157#816—31no—
158#816—31no—
159#815—31no—
160C8×Dic3—31no—
161#810—31no—
162#810—31no—
163#809—31no—
164#809—31no—
165#808—31no—
166#807—31no—
167C4⋊(C3⋊C8)—31no—
168C23×C9—21no—
169C22×D9—21no—
170C22×D9—24no—
171C22×D9—81no—
172C22×D9—81no—
173C22×D9C2×D411yescharacteristic
174D4×C9—21no—
175D4×C9#4112yes—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—81no—
180C2×C4×C9C2×D411yescharacteristic
181C2×C4×C9C2×D411yescharacteristic
182C2×C4×C9C2411yescharacteristic
183#611—24no—
184C2×Dic9—21no—
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—81no—
188C2×Dic9C2×D411yescharacteristic
189C2×Dic9C2×D411yescharacteristic
190C2×Dic9C2×D411yescharacteristic
191D36—21no—
192D36#4112yes—
193C4×D9—21no—
194C4×D9—21no—
195C4×D9—81no—
196C4×D9—81no—
197Dic18—21no—
198Dic18—21no—
199Dic18—21no—
200Dic18—21no—
201C8×C9—21no—
202C8×C9—21no—
203C9⋊C8—21no—
204C9⋊C8—21no—
205#541—91no—
206#518—91no—
207#485—91no—
208#485—91no—
209#478—91no—
210#478D911yescharacteristic, complemented
211#461—91no—
212#461—91no—
213#450—91no—
214#450—91no—
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C23×D3—61no—
221C2×C3×D4C22×D311yescharacteristic
222C22×C3×C4—21no—
223C2×#67—61no—
224C22×Dic3—61no—
225D3×D4—62no—
226D3×D4—62no—
227C2×D12—31no—
228C2×C4×D3—31no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×Dic6—31no—
232C2×Dic6—31no—
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C4⋊C4C22×D311yescharacteristic
240C3×C22⋊C4—21no—
241C3×C42C22×D311yescharacteristic
242#217—61no—
243#214—62no—
244#214—62no—
245(C2×D3)⋊C4—31no—
246(C2×D3)⋊C4—31no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252C4⋊Dic3—31no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257Dic3⋊C4—31no—
258Dic3⋊C4—31no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261C4×Dic3—31no—
262C4×Dic3—61no—
263C4×Dic3—61no—
264C4×Dic3—61no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—31no—
267#204—62no—
268#204—62no—
269C22×C9—22no—
270C22×C9—41no—
271C22×C9—41no—
272C22×C9C22×D411yescharacteristic
273C2×D9—21no—
274C2×D9—22no—
275C2×D9—21no—
276C2×D9—21no—
277C2×D9—41no—
278C2×D9—41no—
279C2×D9—84no—
280C4×C9—21no—
281C4×C9—21no—
282C4×C9—41no—
283C4×C9—41no—
284C4×C9—41no—
285C4×C9C2×#4111yescharacteristic
286C4×C9C2×#4111yescharacteristic
287Dic9—21no—
288Dic9—21no—
289Dic9—21no—
290Dic9—41no—
291Dic9—41no—
292Dic9—41no—
293C22×D4—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16—91no—
297C2×SD16—91no—
298C4⋊Q8—91no—
299#126—181no—
300#126—181no—
301#125—181no—
302#125—181no—
303#125C2×D911yescharacteristic, complemented
304C22⋊Q8—91no—
305C22⋊Q8—91no—
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—181no—
312C4×D4—181no—
313C4×D4C2×D911yescharacteristic
314#117—91no—
315#117—91no—
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318#107—91no—
319#107C2×D911yescharacteristic, complemented
320#106—91no—
321#106C2×D911yescharacteristic, complemented
322C4⋊C8—91no—
323C4⋊C8C2×D911yescharacteristic, complemented
324#103—91no—
325#103—91no—
326#103—91no—
327#103—91no—
328#102—91no—
329#102—91no—
330#102C2×D911yescharacteristic
331#102C2×D911yescharacteristic
332C22⋊C8—91no—
333C22⋊C8—91no—
334#97—91no—
335C4×C8—91no—
336C23×C3—21no—
337C22×D3—31no—
338C22×D3—61no—
339C22×D3—64no—
340C22×D3—241no—
341C22×D3—241no—
342C3×D4—21no—
343C3×D4#23912yes—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—81no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351#67—64no—
352C2×Dic3—31no—
353C2×Dic3—31no—
354C2×Dic3—31no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—241no—
359D12—32no—
360D12—61no—
361C4×D3—61no—
362C4×D3—61no—
363C4×D3—241no—
364C4×D3—241no—
365Dic6—61no—
366Dic6—61no—
367Dic6—61no—
368Dic6—61no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—61no—
372C3⋊C8—61no—
373C2×C9—42no—
374C2×C9#52511yescharacteristic
375C2×C9#57711yescharacteristic
376C2×C9#57711yescharacteristic
377D9—41no—
378D9—42no—
379C24—181no—
380C2×Q8—91no—
381C2×Q8—91no—
382C2×D4—91no—
383C2×D4—181no—
384C2×D4—182no—
385C2×D4—182no—
386C2×D4C22×D911yescharacteristic
387C22×C4—21no—
388C22×C4—91no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392SD16—182no—
393SD16—182no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×D911yescharacteristic
399C2×C8C22×D911yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4C22×D911yescharacteristic
412C4⋊C4C22×D911yescharacteristic
413C4⋊C4C22×D911yescharacteristic
414C22⋊C4—21no—
415C22⋊C4—91no—
416C22⋊C4—91no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C42—91no—
424C42—181no—
425C42—181no—
426C42—181no—
427C42C22×D911yescharacteristic
428C22×C3—22no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3C2×D3×D411yescharacteristic
432C2×D3—61no—
433C2×D3—61no—
434C2×D3—61no—
435C2×D3—62no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—244no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4C2×#23911yescharacteristic
445C3×C4D3×#4111yescharacteristic
446Dic3—61no—
447Dic3—61no—
448Dic3—61no—
449Dic3—121no—
450Dic3—121no—
451Dic3—121no—
452C9#312311yescharacteristic, complemented, Sylow
453C23—21no—
454C23—91no—
455C23—184no—
456C23—181no—
457C23—721no—
458C23—721no—
459Q8—181no—
460Q8—181no—
461Q8—181no—
462Q8—181no—
463D4—21no—
464D4—92no—
465D4—184no—
466D4—181no—
467D4#370112yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—81no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4D4×D911yescharacteristic
484C2×C4D4×D911yescharacteristic
485C2×C4C23×D911yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—42no—
491C2×C3#562711yescharacteristic
492C2×C3#577011yescharacteristic
493C2×C3#577511yescharacteristic
494D3—121no—
495D3—122no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—181no—
500C22—182no—
501C22—181no—
502C22—181no—
503C22—361no—
504C22—361no—
505C22—724no—
506C22C2×D4×D911yescharacteristic
507C4—21no—
508C4—21no—
509C4—41no—
510C4—41no—
511C4—41no—
512C4—181no—
513C4—181no—
514C4—181no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×#370111yescharacteristic
519C4#41×D911yescharacteristic
520C3#8114711yescharacteristic
521C2—42no—
522C2—361no—
523C2—362no—
524C2#1058972911yescharacteristic
525C2#1058987211yescharacteristic
526C2#1058987711yescharacteristic
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#3123
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. #10589800C2semidirect
3. C9×#478C2semidirect
4. #10588747C2semidirect
5. #10588695C2semidirect
6. #10588569C2semidirect
7. #10588568C2semidirect
8. #10588548C2semidirect
9. #10588532C2semidirect
10. #10588525C2semidirect
11. #10588524C2semidirect
14. #10588438C2semidirect
15. #10588437C2semidirect
18. C9×#125C22semidirect
35. #63449C22semidirect
36. #63449C22semidirect
41. #63431C22semidirect
42. C9×#107C22semidirect
43. C9×#106C22semidirect
44. C9×C4⋊C8C22semidirect
49. #63376C22semidirect
50. #63376C22semidirect
51. #63375C22semidirect
52. C8×Dic9C22semidirect
55. #63368C22semidirect
56. #63368C22semidirect
57. #63367C22semidirect
58. #63366C22semidirect
59. C4⋊(C9⋊C8)C22semidirect
210. #478D9semidirect
303. #125C2×D9semidirect
319. #107C2×D9semidirect
321. #106C2×D9semidirect
323. C4⋊C8C2×D9semidirect
452. C9#3123semidirect

Maximal subgroups

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

subgroupindex
#105898002
#105896472
C9×#4782
#105887472
#105886952
#105885692
#105885682
#105885482
#105885322
#105885252
#105885242
#105884562
#105884382
#105884372
#811473