Finite Group Databasebeta

← #11871320

Subgroups — #11871320

Order 1152.

1332 conjugacy classes of subgroups.

The subgroup lattice has 543 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic, complemented
2C4×D4×C3⋊D3C211yesmaximal, characteristic
3C32×#440C211yesmaximal, characteristic, complemented
4#10592868C211yesmaximal, characteristic
5#10592861C211yesmaximal, characteristic, complemented
6#10592725C211yesmaximal, characteristic, complemented
7#10592717C211yesmaximal, characteristic, complemented
8#10592589C211yesmaximal, characteristic, complemented
9#10592583C211yesmaximal, characteristic, complemented
10#10592517C211yesmaximal, characteristic, complemented
11#10592510C211yesmaximal, characteristic, complemented
12#10592475C211yesmaximal, characteristic
13#10592458C211yesmaximal, characteristic, complemented
14#10592409C211yesmaximal, characteristic, complemented
15#10592404C211yesmaximal, characteristic, complemented
16#79779—34nomaximal
17C2×D4×C3⋊D3C2211yescharacteristic
18C22×C4×C3⋊D3—21no—
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22#64155C2211yescharacteristic
23#64153C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic
26C2×#3754C2211yescharacteristic
27C4×#638—21no—
28C2×#3744C2211yescharacteristic
29#64106C2211yescharacteristic
30#64105—21no—
31#64102C2211yescharacteristic
32C4⋊C4×C3⋊D3C2211yescharacteristic
33#64098—21no—
34#64097C2211yescharacteristic, complemented
35#64090—21no—
36C22⋊C4×C3⋊D3—21no—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38#64081—21no—
39C42×C3⋊D3C2211yescharacteristic
40C4×#634—21no—
41C4×#634C2211yescharacteristic, complemented
42C32×#107C2211yescharacteristic, complemented
43C32×#103C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#97C2211yescharacteristic, complemented
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63648C2211yescharacteristic
49#63647C2211yescharacteristic
50#63647C2211yescharacteristic
51#63645C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63641C2211yescharacteristic, complemented
55#63637C2211yescharacteristic, complemented
56#63636C2211yescharacteristic
57#63634C2211yescharacteristic, complemented
58#63634C2211yescharacteristic, complemented
59#63630C2211yescharacteristic, complemented
60#5578—34no—
61C4×D3×D4—34no—
62C3×#440D314yescomplemented
63#5169—34no—
64#5162—34no—
65#5026—34no—
66#5018—34no—
67#4890—34no—
68#4884—34no—
69#4818—34no—
70#4811—34no—
71#4776—34no—
72#4759—34no—
73#4710—34no—
74#4705—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)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×C4×C3⋊D3—21no—
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—44no—
88C2×C4×C3⋊D3D411yescharacteristic
89C2×C4×C3⋊D3D411yescharacteristic
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634—21no—
92C2×#634C2311yescharacteristic
93C32×SD16—22no—
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C42—21no—
101C32×C42C2311yescharacteristic
102#3757—21no—
103#3755—22no—
104#3754—22no—
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3D411yescharacteristic
120C4×C3⋊Dic3D411yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3744—22no—
125#3110—91noSylow
126C2×D3×D4—34no—
127C22×C4×D3—64no—
128C2×C3×SD16C2×D314yes—
129C3×C4×Q8C2×D314yescomplemented
130C3×C4×D4C2×D314yes—
131#946—34no—
132#944—34no—
133C2×#215—34no—
134D4×Dic3—34no—
135C2×#214—34no—
136C4×#67—64no—
137C2×#204—34no—
138#897—34no—
139#896—64no—
140#893—34no—
141D3×C4⋊C4—34no—
142#889—64no—
143#888—34no—
144#67⋊C4—64no—
145D3×C22⋊C4—64no—
146C4×D12—34no—
147#872—64no—
148C42×D3—34no—
149C4×Dic6—34no—
150C4×Dic6—64no—
151C3×#107C2×D314yescomplemented
152C3×#103C2×D314yescomplemented
153C3×#102C2×D314yes—
154C3×#97C2×D314yescomplemented
155#835—34no—
156#832—34no—
157#821—34no—
158(C2×D3)⋊C8—34no—
159(C2×D3)⋊C8—34no—
160#818—34no—
161#816—34no—
162Dic3⋊C8—34no—
163Dic3⋊C8—34no—
164#810—34no—
165#809—34no—
166#807—34no—
167#807—34no—
168#803—34no—
169C23×C32—21no—
170C22×C3⋊D3—24no—
171C22×C3⋊D3—21no—
172C22×C3⋊D3—42no—
173C22×C3⋊D3—42no—
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—42no—
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—21no—
190C2×C3⋊Dic3—42no—
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C2×C3⋊Dic3C2×D411yescharacteristic
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)#4112yes—
196C4×C3⋊D3—22no—
197C4×C3⋊D3—21no—
198C4×C3⋊D3—21no—
199C4×C3⋊D3—22no—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—42no—
202C4×C3⋊D3—42no—
203#634—21no—
204#634—21no—
205#634—42no—
206C32×C8—21no—
207C32×C8—21no—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210#533—91no—
211C2×C4×D4—91no—
212#484—91no—
213#484—91no—
214#474—91no—
215#474—91no—
216#461—91no—
217#461—91no—
218#450—91no—
219#450—91no—
220#440—91no—
221#440—91no—
222#440—91no—
223#440C3⋊D311yescharacteristic, complemented
224#432—91no—
225C23×D3—64no—
226C2×C3×Q8C22×D314yes—
227C2×C3×D4C22×D314yes—
228C22×C3×C4—24no—
229C2×#67—64no—
230C22×Dic3—64no—
231D3×D4—68no—
232D3×D4—68no—
233C2×D12—34no—
234C2×C4×D3—34no—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—1216no—
241C2×Dic6—34no—
242C2×Dic6—64no—
243C3×SD16—28no—
244C2×C3×C8C22×D314yes—
245C2×C3×C8C22×D314yes—
246C3×C4⋊C4—24no—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C22⋊C4—24no—
250C3×C42—24no—
251C3×C42C22×D314yes—
252#217—64no—
253#215—68no—
254#214—68no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259C4⋊Dic3—34no—
260C4⋊Dic3—34no—
261C4⋊Dic3—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268C4×Dic3—34no—
269C4×Dic3—34no—
270C4×Dic3—34no—
271C4×Dic3—64no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274#204—68no—
275C22×C32—22no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—48no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3#13712yes—
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—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3⋊Dic3AGL(1,ℤ/8)12yes—
299C22×D4—91no—
300C23×C4—181no—
301C2×SD16—91no—
302C2×SD16—91no—
303C2×SD16—91no—
304C2×SD16C2×C3⋊D311yescharacteristic
305C4⋊Q8—91no—
306C4⋊Q8—91no—
307#125—181no—
308C22⋊Q8—91no—
309C22⋊Q8—91no—
310C22⋊Q8—181no—
311C4×Q8—91no—
312C4×Q8—181no—
313C4×Q8C2×C3⋊D311yescharacteristic, complemented
314C4×D4—91no—
315C4×D4—91no—
316C4×D4—91no—
317C4×D4—181no—
318C4×D4—181no—
319C4×D4C2×C3⋊D311yescharacteristic
320#117—181no—
321C2×C4⋊C4—91no—
322C2×C22⋊C4—181no—
323C2×C42—91no—
324#107—91no—
325#107—91no—
326#107—91no—
327#107C2×C3⋊D311yescharacteristic, complemented
328C4⋊C8—91no—
329C4⋊C8—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103C2×C3⋊D311yescharacteristic, complemented
334#102—91no—
335#102—91no—
336#102—91no—
337#102C2×C3⋊D311yescharacteristic
338C22⋊C8—91no—
339C22⋊C8—91no—
340#97—91no—
341#97C2×C3⋊D311yescharacteristic, complemented
342C23×C3—24no—
343C22×D3—34no—
344C22×D3—616no—
345C22×D3—64no—
346C22×D3—128no—
347C22×D3—128no—
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—48no—
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—64no—
366C2×Dic3—128no—
367D12—38no—
368D12—64no—
369C4×D3—68no—
370C4×D3—68no—
371C4×D3—64no—
372C4×D3—64no—
373C4×D3—128no—
374C4×D3—128no—
375C4×D3—128no—
376Dic6—64no—
377Dic6—64no—
378Dic6—128no—
379C3×C8—24no—
380C3×C8—24no—
381C3⋊C8—64no—
382C3⋊C8—64no—
383C2×C32—42no—
384C2×C32#52511yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C2×C32C2×#13711yescharacteristic
387C3⋊D3—22no—
388C3⋊D3—42no—
389C24—181no—
390C2×Q8—91no—
391C2×Q8—181no—
392C2×Q8C22×C3⋊D311yescharacteristic
393C2×D4—91no—
394C2×D4—181no—
395C2×D4—182no—
396C2×D4—182no—
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—181no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4—364no—
407SD16—22no—
408SD16—182no—
409SD16—182no—
410SD16—182no—
411C2×C8—91no—
412C2×C8—91no—
413C2×C8C22×C3⋊D311yescharacteristic
414C2×C8C22×C3⋊D311yescharacteristic
415C4⋊C4—21no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4C22×C3⋊D311yescharacteristic
426C4⋊C4C22×C3⋊D311yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C42—21no—
434C42—91no—
435C42—91no—
436C42—91no—
437C42—181no—
438C42C22×C3⋊D311yescharacteristic
439C22×C3—28no—
440C22×C3—44no—
441C22×C3—44no—
442C22×C3C2×D3×D414yes—
443C2×D3—38no—
444C2×D3—64no—
445C2×D3—64no—
446C2×D3—68no—
447C2×D3—1232no—
448C2×D3—124no—
449C2×D3—124no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—44no—
455C3×C4C2×#23514yes—
456C3×C4D3×#4114yes—
457Dic3—38no—
458Dic3—64no—
459Dic3—64no—
460Dic3—124no—
461Dic3—124no—
462Dic3—124no—
463C32#311011yescharacteristic, complemented, Sylow
464C23—21no—
465C23—91no—
466C23—184no—
467C23—181no—
468C23—362no—
469C23—362no—
470Q8—21no—
471Q8—21no—
472Q8—181no—
473Q8—181no—
474Q8—362no—
475D4—21no—
476D4—92no—
477D4—184no—
478D4—181no—
479D4#382812yes—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—42no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—91no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—362no—
495C2×C4—362no—
496C2×C4—362no—
497C2×C4—362no—
498C2×C4D4×C3⋊D311yescharacteristic
499C2×C4D4×C3⋊D311yescharacteristic
500C2×C4C23×C3⋊D311yescharacteristic
501C8—21no—
502C8—21no—
503C8—181no—
504C8—181no—
505C2×C3—48no—
506C2×C3#554714yes—
507C2×C3D3×AGL(1,ℤ/8)14yes—
508C2×C3D3×#13714yes—
509D3—68no—
510D3—128no—
511C22—22no—
512C22—41no—
513C22—41no—
514C22—92no—
515C22—181no—
516C22—181no—
517C22—182no—
518C22—368no—
519C22—361no—
520C22—361no—
521C22C2×D4×C3⋊D311yescharacteristic
522C4—21no—
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—92no—
528C4—181no—
529C4—181no—
530C4—361no—
531C4—361no—
532C4—361no—
533C4C2×#382811yescharacteristic
534C4#41×C3⋊D311yescharacteristic
535C3#7977914yescomplemented
536C2—42no—
537C2—182no—
538C2—362no—
539C2#1059601811yescharacteristic
540C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
541C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenter#440C3⋊D3
hypocenterC32#3110
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. #10596049C2semidirect
3. C32×#440C2semidirect
5. #10592861C2semidirect
6. #10592725C2semidirect
7. #10592717C2semidirect
8. #10592589C2semidirect
9. #10592583C2semidirect
10. #10592517C2semidirect
11. #10592510C2semidirect
13. #10592458C2semidirect
14. #10592409C2semidirect
15. #10592404C2semidirect
20. C32×C4×Q8C22semidirect
23. #64153C22semidirect
34. #64097C22semidirect
41. C4×#634C22semidirect
42. C32×#107C22semidirect
43. C32×#103C22semidirect
45. C32×#97C22semidirect
46. #63662C22semidirect
51. #63645C22semidirect
52. #63643C22semidirect
53. #63641C22semidirect
54. #63641C22semidirect
55. #63637C22semidirect
57. #63634C22semidirect
58. #63634C22semidirect
59. #63630C22semidirect
62. C3×#440D3semidirect
129. C3×C4×Q8C2×D3semidirect
151. C3×#107C2×D3semidirect
152. C3×#103C2×D3semidirect
154. C3×#97C2×D3semidirect
223. #440C3⋊D3semidirect
313. C4×Q8C2×C3⋊D3semidirect
327. #107C2×C3⋊D3semidirect
333. #103C2×C3⋊D3semidirect
341. #97C2×C3⋊D3semidirect
463. C32#3110semidirect
535. C3#79779semidirect

Maximal subgroups

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

subgroupindex
#105960492
C4×D4×C3⋊D32
C32×#4402
#105928682
#105928612
#105927252
#105927172
#105925892
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