Finite Group Databasebeta

← #11872790

Subgroups — #11872790

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#10589685C211yesmaximal, characteristic, complemented
2#10589647C211yesmaximal, characteristic
3C4×C9×SD16C211yesmaximal, characteristic, complemented
4#10588849C211yesmaximal, characteristic
5#10588842C211yesmaximal, characteristic, complemented
6#10588709C211yesmaximal, characteristic, complemented
7#10588694C211yesmaximal, characteristic, complemented
8#10588551C211yesmaximal, characteristic, complemented
9#10588548C211yesmaximal, characteristic, complemented
10#10588498C211yesmaximal, characteristic, complemented
11#10588495C211yesmaximal, characteristic, complemented
12#10588456C211yesmaximal, characteristic
13#10588443C211yesmaximal, characteristic, complemented
14C4×#3664C211yesmaximal, characteristic, complemented
15#10588372C211yesmaximal, characteristic, complemented
16#79659—31nomaximal
17C2×D4×D9C2211yescharacteristic
18C2×C9×SD16C2211yescharacteristic
19C4×Q8×C9C2211yescharacteristic, complemented
20C4×D4×C9C2211yescharacteristic
21#63508C2211yescharacteristic
22#63506C2211yescharacteristic, complemented
23C2×#3675C2211yescharacteristic
24D4×Dic9C2211yescharacteristic
25C2×#3672C2211yescharacteristic
26C4×#611—21no—
27C2×(C2×D9)⋊C4—21no—
28C2×#3664C2211yescharacteristic
29#63460—21no—
30#63459C2211yescharacteristic
31#63455C2211yescharacteristic
32#63454C2211yescharacteristic
33#63452C2211yescharacteristic, complemented
34#63451—21no—
35#611⋊C4—21no—
36C22⋊C4×D9—21no—
37#63438—21no—
38C4×D36C2211yescharacteristic
39#63434C2211yescharacteristic
40#63432—21no—
41C4×Dic18C2211yescharacteristic, complemented
42C9×#106C2211yescharacteristic, complemented
43C9×#103C2211yescharacteristic, complemented
44C9×#102C2211yescharacteristic
45C4×C8×C9C2211yescharacteristic, complemented
46#63395C2211yescharacteristic, complemented
47#63392C2211yescharacteristic
48#63380C2211yescharacteristic
49(C2×D9)⋊C8C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic
51#63377C2211yescharacteristic, complemented
52#63376C2211yescharacteristic, complemented
53Dic9⋊C8C2211yescharacteristic, complemented
54Dic9⋊C8C2211yescharacteristic, complemented
55#63369C2211yescharacteristic
56#63368C2211yescharacteristic, complemented
57#63366C2211yescharacteristic, complemented
58#63366C2211yescharacteristic, complemented
59#63362C2211yescharacteristic, complemented
60#5583—31no—
61#5545—31no—
62C3×C4×SD16D311yescharacteristic
63#5169—31no—
64#5162—31no—
65#5026—31no—
66#5018—31no—
67#4871—31no—
68#4868—31no—
69#4818—31no—
70#4815—31no—
71#4776—31no—
72#4763—31no—
73C4×#204—31no—
74#4690—31no—
75C23×D9—21no—
76C2×Q8×C9C2311yescharacteristic
77C2×D4×C9C2311yescharacteristic
78C22×C4×C9—21no—
79C2×#611—21no—
80C22×Dic9—21no—
81D4×D9—22no—
82D4×D9—22no—
83C2×D36C2311yescharacteristic
84C2×C4×D9—21no—
85C2×C4×D9—21no—
86C2×C4×D9C2311yescharacteristic
87C2×Dic18C2311yescharacteristic
88C9×SD16—22no—
89C2×C8×C9C2311yescharacteristic
90C2×C8×C9C2311yescharacteristic
91C9×C4⋊C4—21no—
92C9×C4⋊C4C2311yescharacteristic
93C9×C4⋊C4C2311yescharacteristic
94C9×C22⋊C4—21no—
95C42×C9—21no—
96C42×C9C2311yescharacteristic
97#3676—21no—
98#3675—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⋊Dic9C2311yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4D411yescharacteristic
117Dic9⋊C4D411yescharacteristic
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C2×C9⋊C8C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123#3664—22no—
124#3123—91noSylow
125C2×D3×D4—31no—
126C2×C3×SD16C2×D311yescharacteristic
127C3×C4×Q8C2×D311yescharacteristic
128C3×C4×D4C2×D311yescharacteristic
129#946—31no—
130#944—31no—
131C2×#215—31no—
132D4×Dic3—31no—
133C2×#214—31no—
134C4×#67—61no—
135C2×(C2×D3)⋊C4—61no—
136C2×#204—31no—
137#898—61no—
138#897—31no—
139#893—31no—
140#892—31no—
141#890—31no—
142#889—61no—
143#67⋊C4—61no—
144D3×C22⋊C4—61no—
145#876—61no—
146C4×D12—31no—
147#872—31no—
148#870—61no—
149C4×Dic6—31no—
150C3×#106C2×D311yescharacteristic
151C3×#103C2×D311yescharacteristic
152C3×#102C2×D311yescharacteristic
153C3×C4×C8C2×D311yescharacteristic
154#835—31no—
155#832—31no—
156#821—31no—
157(C2×D3)⋊C8—31no—
158(C2×D3)⋊C8—31no—
159#817—31no—
160#816—31no—
161Dic3⋊C8—31no—
162Dic3⋊C8—31no—
163#810—31no—
164#809—31no—
165#807—31no—
166#807—31no—
167#803—31no—
168C23×C9—21no—
169C22×D9—21no—
170C22×D9—24no—
171C22×D9—81no—
172C22×D9—81no—
173C22×D9C2×D411yescharacteristic
174Q8×C9—21no—
175Q8×C9—21no—
176D4×C9—21no—
177D4×C9#4112yes—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—81no—
182C2×C4×C9C2×D411yescharacteristic
183C2×C4×C9C2×D411yescharacteristic
184C2×C4×C9C2411yescharacteristic
185#611—24no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—81no—
190C2×Dic9C2×D411yescharacteristic
191C2×Dic9C2×D411yescharacteristic
192C2×Dic9C2×D411yescharacteristic
193D36—21no—
194D36#4112yes—
195C4×D9—21no—
196C4×D9—21no—
197C4×D9—81no—
198C4×D9—81no—
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#478—91no—
211#461—91no—
212#461—91no—
213#450—91no—
214#450—91no—
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16D911yescharacteristic, complemented
219#433—91no—
220C23×D3—61no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×D4C22×D311yescharacteristic
223C22×C3×C4—21no—
224C2×#67—61no—
225C22×Dic3—61no—
226D3×D4—62no—
227D3×D4—62no—
228C2×D12—31no—
229C2×C4×D3—31no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×Dic6—31no—
233C3×SD16—22no—
234C2×C3×C8C22×D311yescharacteristic
235C2×C3×C8C22×D311yescharacteristic
236C3×C4⋊C4—21no—
237C3×C4⋊C4C22×D311yescharacteristic
238C3×C4⋊C4C22×D311yescharacteristic
239C3×C22⋊C4—21no—
240C3×C42—21no—
241C3×C42C22×D311yescharacteristic
242#217—61no—
243#215—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—31no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256Dic3⋊C4—31no—
257Dic3⋊C4—31no—
258Dic3⋊C4—61no—
259Dic3⋊C4—61no—
260Dic3⋊C4—61no—
261Dic3⋊C4—61no—
262Dic3⋊C4—61no—
263C4×Dic3—31no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C2×C3⋊C8—31no—
267C2×C3⋊C8—31no—
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×SD16C2×D911yescharacteristic
298C4⋊Q8—91no—
299#126—181no—
300#126—181no—
301#125—91no—
302#125—181no—
303#125—181no—
304C22⋊Q8—91no—
305C22⋊Q8—91no—
306C4×Q8—91no—
307C4×Q8C2×D911yescharacteristic, complemented
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#107—91no—
320#106—91no—
321#106C2×D911yescharacteristic, complemented
322C4⋊C8—91no—
323C4⋊C8—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#103C2×D911yescharacteristic, complemented
328#102—91no—
329#102—91no—
330#102—91no—
331#102C2×D911yescharacteristic
332C22⋊C8—91no—
333C22⋊C8—91no—
334#97—91no—
335C4×C8C2×D911yescharacteristic, complemented
336C23×C3—21no—
337C22×D3—31no—
338C22×D3—61no—
339C22×D3—64no—
340C22×D3—241no—
341C22×D3—241no—
342C3×Q8—21no—
343C3×Q8—21no—
344C3×D4—21no—
345C3×D4#23512yes—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—81no—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353#67—64no—
354C2×Dic3—31no—
355C2×Dic3—31no—
356C2×Dic3—31no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—241no—
361D12—32no—
362D12—61no—
363C4×D3—61no—
364C4×D3—61no—
365C4×D3—241no—
366C4×D3—241no—
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×Q8C22×D911yescharacteristic
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—22no—
393SD16—182no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×D911yescharacteristic
399C2×C8C22×D911yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—91no—
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⋊C4—181no—
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—21no—
424C42—91no—
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×#23511yescharacteristic
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—21no—
460Q8—21no—
461Q8—181no—
462Q8—181no—
463D4—21no—
464D4—92no—
465D4—184no—
466D4—181no—
467D4#369712yes—
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#554711yescharacteristic
492C2×C3#576211yescharacteristic
493C2×C3#577011yescharacteristic
494D3—121no—
495D3—122no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—181no—
500C22—181no—
501C22—181no—
502C22—182no—
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×#369711yescharacteristic
519C4#41×D911yescharacteristic
520C3#7965911yescharacteristic
521C2—42no—
522C2—361no—
523C2—362no—
524C2#1058964911yescharacteristic
525C2#1058986411yescharacteristic
526C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radicalC2×D4×D9C22
hypercenterC4×SD16D9
hypocenterC9#3123
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10589685C2semidirect
3. C4×C9×SD16C2semidirect
5. #10588842C2semidirect
6. #10588709C2semidirect
7. #10588694C2semidirect
8. #10588551C2semidirect
9. #10588548C2semidirect
10. #10588498C2semidirect
11. #10588495C2semidirect
13. #10588443C2semidirect
14. C4×#3664C2semidirect
15. #10588372C2semidirect
19. C4×Q8×C9C22semidirect
22. #63506C22semidirect
33. #63452C22semidirect
41. C4×Dic18C22semidirect
42. C9×#106C22semidirect
43. C9×#103C22semidirect
45. C4×C8×C9C22semidirect
46. #63395C22semidirect
51. #63377C22semidirect
52. #63376C22semidirect
53. Dic9⋊C8C22semidirect
54. Dic9⋊C8C22semidirect
56. #63368C22semidirect
57. #63366C22semidirect
58. #63366C22semidirect
59. #63362C22semidirect
218. C4×SD16D9semidirect
307. C4×Q8C2×D9semidirect
321. #106C2×D9semidirect
327. #103C2×D9semidirect
335. 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
#105896852
#105896472
C4×C9×SD162
#105888492
#105888422
#105887092
#105886942
#105885512
#105885482
#105884982
#105884952
#105884562
#105884432
C4×#36642
#105883722
#796593