Finite Group Databasebeta

← #11872113

Subgroups — #11872113

Order 1152.

1218 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596053C211yesmaximal, characteristic, complemented
2#10596016C211yesmaximal, characteristic, complemented
3C32×#440C211yesmaximal, characteristic, complemented
4#10592868C211yesmaximal, characteristic, complemented
5#10592864C211yesmaximal, characteristic, complemented
6C4×#3755C211yesmaximal, characteristic, complemented
7C4×#3753C211yesmaximal, characteristic, complemented
8#10592589C211yesmaximal, characteristic, complemented
9#10592584C211yesmaximal, characteristic, complemented
10#10592518C211yesmaximal, characteristic, complemented
11#10592514C211yesmaximal, characteristic, complemented
12#10592472C211yesmaximal, characteristic
13#10592460C211yesmaximal, characteristic, complemented
14#10592410C211yesmaximal, characteristic, complemented
15#10592408C211yesmaximal, characteristic, complemented
16#79785—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C2×C32×SD16C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic, complemented
20C32×C4×D4C2211yescharacteristic
21#64156C2211yescharacteristic, complemented
22#64155C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C4×#638—21no—
27C2×#3752—21no—
28C2×#3745C2211yescharacteristic
29#64105—21no—
30#64104C2211yescharacteristic
31#64103—21no—
32#64102C2211yescharacteristic
33#64101C2211yescharacteristic
34#64097C2211yescharacteristic, complemented
35#64090—21no—
36C22⋊C4×C3⋊D3—21no—
37#64085—21no—
38#64084—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
41#64081C2211yescharacteristic
42C32×#107C2211yescharacteristic, complemented
43C32×#103C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#97C2211yescharacteristic, complemented
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic, complemented
50#63647C2211yescharacteristic
51#63647C2211yescharacteristic
52#63644C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic, complemented
57#63635C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
60#5582—34no—
61#5545—34no—
62C3×#440D314yescomplemented
63#5169—34no—
64#5165—34no—
65C4×#215—34no—
66C4×#213—34no—
67#4890—34no—
68#4885—34no—
69#4819—34no—
70#4815—34no—
71#4773—34no—
72#4761—34no—
73#4711—34no—
74#4709—34no—
75C23×C3⋊D3—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C2×#638—21no—
80C22×C3⋊Dic3—21no—
81D4×C3⋊D3—22no—
82D4×C3⋊D3—22no—
83C2×C4⋊(C3⋊D3)—21no—
84C2×C4⋊(C3⋊D3)C2311yescharacteristic
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3C2311yescharacteristic
90C2×#634—21no—
91C32×SD16—22no—
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C32×C22⋊C4—21no—
98C32×C42—21no—
99C32×C42C2311yescharacteristic
100#3757—21no—
101#3755—22no—
102#3753—22no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752D411yescharacteristic
112#3752D411yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750D411yescharacteristic
118#3750D411yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123#3745—22no—
124#3118—91noSylow
125C2×D3×D4—34no—
126C2×C3×SD16C2×D314yes—
127C3×C4×Q8C2×D314yescomplemented
128C3×C4×D4C2×D314yes—
129#947—34no—
130#946—34no—
131C2×#215—34no—
132D4×Dic3—34no—
133C2×#213—34no—
134C4×#67—64no—
135C2×(C2×D3)⋊C4—64no—
136C2×D24—34no—
137#896—64no—
138#895—34no—
139#894—64no—
140#893—34no—
141#892—34no—
142#888—34no—
143#67⋊C4—64no—
144D3×C22⋊C4—64no—
145#876—64no—
146#875—64no—
147C4×D12—34no—
148C4×D12—34no—
149#872—34no—
150C3×#107C2×D314yescomplemented
151C3×#103C2×D314yescomplemented
152C3×#102C2×D314yes—
153C3×#97C2×D314yescomplemented
154#835—34no—
155#832—34no—
156#821—34no—
157#821—34no—
158(C2×D3)⋊C8—34no—
159(C2×D3)⋊C8—34no—
160#817—34no—
161Dic3⋊C8—34no—
162Dic3⋊C8—34no—
163#809—34no—
164#809—34no—
165#808—34no—
166#807—34no—
167C4×C3⋊C8—34no—
168C23×C32—21no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3—24no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—81no—
173C22×C3⋊D3—81no—
174C22×C3⋊D3C2×D411yescharacteristic
175C32×Q8—21no—
176C32×Q8—21no—
177C32×D4—21no—
178C32×D4#4112yes—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—81no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—24no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—81no—
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)—21no—
196C4⋊(C3⋊D3)—81no—
197C4⋊(C3⋊D3)#4112yes—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—21no—
200C4×C3⋊D3—81no—
201C4×C3⋊D3—81no—
202C4×C3⋊D3—81no—
203#634—81no—
204C32×C8—21no—
205C32×C8—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208#542—91no—
209#518—91no—
210#485—91no—
211#482—91no—
212#476—91no—
213#474—91no—
214#463—91no—
215#463—91no—
216#450—91no—
217#447—91no—
218#442—91no—
219#440C3⋊D311yescharacteristic, complemented
220C4×SD16—91no—
221C4×D8—91no—
222#433—91no—
223C23×D3—64no—
224C2×C3×Q8C22×D314yes—
225C2×C3×D4C22×D314yes—
226C22×C3×C4—24no—
227C2×#67—64no—
228C22×Dic3—64no—
229D3×D4—68no—
230D3×D4—68no—
231C2×D12—34no—
232C2×D12—34no—
233C2×D12—64no—
234C2×C4×D3—34no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×Dic6—64no—
239C3×SD16—28no—
240C2×C3×C8C22×D314yes—
241C2×C3×C8C22×D314yes—
242C3×C4⋊C4—24no—
243C3×C4⋊C4C22×D314yes—
244C3×C4⋊C4C22×D314yes—
245C3×C22⋊C4—24no—
246C3×C42—24no—
247C3×C42C22×D314yes—
248#217—64no—
249#215—68no—
250#213—68no—
251(C2×D3)⋊C4—34no—
252(C2×D3)⋊C4—34no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261C4⋊Dic3—34no—
262C4⋊Dic3—34no—
263Dic3⋊C4—34no—
264Dic3⋊C4—34no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267C4×Dic3—34no—
268C4×Dic3—64no—
269C2×C3⋊C8—34no—
270C2×C3⋊C8—34no—
271D24—68no—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—21no—
277C2×C3⋊D3—22no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—21no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—84no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—41no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C2×#4111yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3⋊Dic3—21no—
294C3⋊Dic3—21no—
295C3⋊Dic3—21no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C22×D4—91no—
299C2×SD16—91no—
300C2×SD16C2×C3⋊D311yescharacteristic
301C2×D8—91no—
302C2×D8—91no—
303C4⋊Q8—91no—
304#126—181no—
305#124—91no—
306#124—181no—
307#123—181no—
308C22⋊Q8—91no—
309C22⋊Q8—181no—
310#121—91no—
311C4×Q8C2×C3⋊D311yescharacteristic, complemented
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—181no—
317C4×D4—181no—
318C4×D4C2×C3⋊D311yescharacteristic
319#117—91no—
320#117—91no—
321C2×C22⋊C4—181no—
322C2×C22⋊C4—181no—
323#107—91no—
324#107C2×C3⋊D311yescharacteristic, complemented
325#106—91no—
326#106—91no—
327C4⋊C8—91no—
328C4⋊C8—91no—
329#103—91no—
330#103C2×C3⋊D311yescharacteristic, complemented
331#102—91no—
332#102—91no—
333#102—91no—
334#102—91no—
335#102—91no—
336#102C2×C3⋊D311yescharacteristic
337C22⋊C8—91no—
338C22⋊C8—91no—
339#97C2×C3⋊D311yescharacteristic, complemented
340C4×C8—91no—
341C23×C3—24no—
342C22×D3—34no—
343C22×D3—64no—
344C22×D3—616no—
345C22×D3—64no—
346C22×D3—244no—
347C22×D3—244no—
348C3×Q8—24no—
349C3×Q8—24no—
350C3×D4—24no—
351C3×D4#23518yes—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—84no—
356C2×C3×C4D3×D414yes—
357C2×C3×C4D3×D414yes—
358C2×C3×C4C23×D314yes—
359#67—616no—
360C2×Dic3—34no—
361C2×Dic3—34no—
362C2×Dic3—34no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C2×Dic3—244no—
366D12—38no—
367D12—64no—
368D12—64no—
369D12—64no—
370D12—244no—
371C4×D3—64no—
372C4×D3—64no—
373C4×D3—244no—
374C4×D3—244no—
375C4×D3—244no—
376Dic6—244no—
377C3×C8—24no—
378C3×C8—24no—
379C3⋊C8—64no—
380C3⋊C8—64no—
381C2×C32—42no—
382C2×C32#52511yescharacteristic
383C2×C32#57611yescharacteristic
384C2×C32#57711yescharacteristic
385C3⋊D3—41no—
386C3⋊D3—42no—
387C3⋊D3—81no—
388C24—181no—
389C2×Q8—181no—
390C2×Q8C22×C3⋊D311yescharacteristic
391C2×D4—91no—
392C2×D4—91no—
393C2×D4—181no—
394C2×D4—181no—
395C2×D4—182no—
396C2×D4—182no—
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404SD16—22no—
405SD16—182no—
406D8—182no—
407D8—182no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8C22×C3⋊D311yescharacteristic
411C2×C8C22×C3⋊D311yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4C22×C3⋊D311yescharacteristic
420C4⋊C4C22×C3⋊D311yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—91no—
423C22⋊C4—91no—
424C22⋊C4—181no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C42—21no—
434C42—91no—
435C42—181no—
436C42C22×C3⋊D311yescharacteristic
437C22×C3—28no—
438C22×C3—44no—
439C22×C3—44no—
440C22×C3C2×D3×D414yes—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—68no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—2416no—
451C3×C4—24no—
452C3×C4—24no—
453C3×C4—44no—
454C3×C4—44no—
455C3×C4—44no—
456C3×C4C2×#23514yes—
457C3×C4D3×#4114yes—
458Dic3—64no—
459Dic3—64no—
460Dic3—64no—
461Dic3—124no—
462Dic3—124no—
463C32#311811yescharacteristic, complemented, Sylow
464C23—21no—
465C23—91no—
466C23—184no—
467C23—181no—
468C23—181no—
469C23—721no—
470C23—721no—
471Q8—21no—
472Q8—21no—
473Q8—721no—
474D4—21no—
475D4—92no—
476D4—184no—
477D4—181no—
478D4—181no—
479D4—181no—
480D4—721no—
481D4#382812yes—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—81no—
486C2×C4—91no—
487C2×C4—91no—
488C2×C4—91no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—721no—
494C2×C4—721no—
495C2×C4—721no—
496C2×C4—721no—
497C2×C4D4×C3⋊D311yescharacteristic
498C2×C4D4×C3⋊D311yescharacteristic
499C2×C4C23×C3⋊D311yescharacteristic
500C8—21no—
501C8—21no—
502C8—181no—
503C8—181no—
504C2×C3—48no—
505C2×C3#554714yes—
506C2×C3#577414yes—
507C2×C3#577814yes—
508D3—124no—
509D3—128no—
510D3—244no—
511C22—22no—
512C22—41no—
513C22—41no—
514C22—181no—
515C22—181no—
516C22—181no—
517C22—182no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22—361no—
522C22—361no—
523C22—724no—
524C22C2×D4×C3⋊D311yescharacteristic
525C4—21no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—181no—
531C4—181no—
532C4—181no—
533C4—361no—
534C4—361no—
535C4C2×#382811yescharacteristic
536C4#41×C3⋊D311yescharacteristic
537C3#7978514yescomplemented
538C2—42no—
539C2—361no—
540C2—362no—
541C2—721no—
542C2#1059601811yescharacteristic
543C2#1059624511yescharacteristic
544C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radical#10592472C2
hypercenter#440C3⋊D3
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10596053C2semidirect
2. #10596016C2semidirect
3. C32×#440C2semidirect
4. #10592868C2semidirect
5. #10592864C2semidirect
6. C4×#3755C2semidirect
7. C4×#3753C2semidirect
8. #10592589C2semidirect
9. #10592584C2semidirect
10. #10592518C2semidirect
11. #10592514C2semidirect
13. #10592460C2semidirect
14. #10592410C2semidirect
15. #10592408C2semidirect
19. C32×C4×Q8C22semidirect
21. #64156C22semidirect
34. #64097C22semidirect
40. C4×C4⋊(C3⋊D3)C22semidirect
42. C32×#107C22semidirect
43. C32×#103C22semidirect
45. C32×#97C22semidirect
46. #63662C22semidirect
49. #63648C22semidirect
52. #63644C22semidirect
53. #63641C22semidirect
54. #63641C22semidirect
56. #63636C22semidirect
57. #63635C22semidirect
58. #63634C22semidirect
59. C4×C3⋊(C3⋊C8)C22semidirect
62. C3×#440D3semidirect
127. C3×C4×Q8C2×D3semidirect
150. C3×#107C2×D3semidirect
151. C3×#103C2×D3semidirect
153. C3×#97C2×D3semidirect
219. #440C3⋊D3semidirect
311. C4×Q8C2×C3⋊D3semidirect
324. #107C2×C3⋊D3semidirect
330. #103C2×C3⋊D3semidirect
339. #97C2×C3⋊D3semidirect
463. C32#3118semidirect
537. C3#79785semidirect

Maximal subgroups

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

subgroupindex
#105960532
#105960162
C32×#4402
#105928682
#105928642
C4×#37552
C4×#37532
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#105925842
#105925182
#105925142
#105924722
#105924602
#105924102
#105924082
#797853