Finite Group Databasebeta

← #11889170

Subgroups — #11889170

Order 1152.

1206 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596277C211yesmaximal, characteristic
2#10596112C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic, complemented
4#10592914C211yesmaximal, characteristic, complemented
5#10592872C211yesmaximal, characteristic, complemented
6#10592870C211yesmaximal, characteristic, complemented
7#10592865C211yesmaximal, characteristic, complemented
8#10592863C211yesmaximal, characteristic, complemented
9#10592751C211yesmaximal, characteristic, complemented
10#10592483C211yesmaximal, characteristic, complemented
11#10592471C211yesmaximal, characteristic, complemented
12#10592464C211yesmaximal, characteristic, complemented
13#10592460C211yesmaximal, characteristic, complemented
14#10592427C211yesmaximal, characteristic, complemented
15#10592422C211yesmaximal, characteristic, complemented
16#80162—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C2×#3830C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22#64162—21no—
23C2×#3757—21no—
24#64155C2211yescharacteristic, complemented
25Q8×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3756C2211yescharacteristic, complemented
27#64148—21no—
28#64147C2211yescharacteristic
29#64145C2211yescharacteristic
30#64144—21no—
31D4×C3⋊Dic3C2211yescharacteristic
32C4×#638C2211yescharacteristic
33#64135C2211yescharacteristic
34#64133C2211yescharacteristic
35C2×#3748C2211yescharacteristic
36C2×C8×C3⋊D3C2211yescharacteristic, complemented
37#64107—21no—
38#64101C2211yescharacteristic, complemented
39#64097C2211yescharacteristic, complemented
40#64096—21no—
41#64094—21no—
42#64088—21no—
43C32×#102C2211yescharacteristic
44C32×#102C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63659C2211yescharacteristic
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic
51#63647C2211yescharacteristic, complemented
52#63645C2211yescharacteristic, complemented
53#63644C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56#63642C2211yescharacteristic, complemented
57#63641C2211yescharacteristic, complemented
58#63637C2211yescharacteristic, complemented
59#63635C2211yescharacteristic, complemented
60#5806—34no—
61#5641—34no—
62C3×#450D314yescomplemented
63#5215—34no—
64#5173—34no—
65#5171—34no—
66#5166—34no—
67#5164—34no—
68#5052—34no—
69#4784—34no—
70#4772—34no—
71#4765—34no—
72#4761—34no—
73#4728—34no—
74#4723—34no—
75C24×C32—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4—22no—
78C2×C32×D4—21no—
79C2×C32×D4—41no—
80C2×C32×D4C2311yescharacteristic
81C2×C32×D4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638—21no—
85C2×#638D411yescharacteristic
86C22×C3⋊Dic3—21no—
87C22×C3⋊Dic3—21no—
88#3830—22no—
89#3830—41no—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634—21no—
92C2×#634C2311yescharacteristic
93C32×SD16—22no—
94C32×SD16—41no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4—21no—
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100#3757—21no—
101#3757—21no—
102#3757—21no—
103#3757—21no—
104#3757—21no—
105#3757—21no—
106#3757D411yescharacteristic
107#3756—41no—
108#3752—21no—
109#3752—21no—
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117#3750—21no—
118#3750D411yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3C2311yescharacteristic
123#3748—41no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C8×C3⋊D3—41no—
127#3311—91noSylow
128C22×C3×D4C2×D314yes—
129C2×#237—34no—
130C2×C3×SD16C2×D314yes—
131C2×C3×SD16C2×D314yes—
132C3×C22⋊Q8C2×D314yes—
133#953—64no—
134C2×#217—64no—
135#946—34no—
136Q8×Dic3—34no—
137C2×#216—34no—
138#939—64no—
139#938—34no—
140#936—34no—
141#935—64no—
142D4×Dic3—34no—
143C4×#67—34no—
144#926—34no—
145#924—34no—
146C2×#208—34no—
147C2×D3×C8—34no—
148#898—64no—
149#892—34no—
150#888—34no—
151#887—64no—
152#885—64no—
153#879—64no—
154C3×#102C2×D314yes—
155C3×#102C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157#835—34no—
158#832—34no—
159#832—34no—
160#832—34no—
161#832—34no—
162(C2×D3)⋊C8—34no—
163#818—34no—
164#817—34no—
165#816—34no—
166#816—34no—
167#815—34no—
168Dic3⋊C8—34no—
169#810—34no—
170#808—34no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—42no—
174C23×C32—42no—
175C23×C32—81no—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3C2×D411yescharacteristic
178C32×Q8—21no—
179C32×Q8—21no—
180C32×D4—21no—
181C32×D4—21no—
182C32×D4—21no—
183C32×D4—42no—
184C32×D4#4112yes—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191#638—41no—
192#638—42no—
193#638—81no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—42no—
199C2×C3⋊Dic3—81no—
200C2×C3⋊Dic3C2×D411yescharacteristic
201C2×C3⋊Dic3C2×D411yescharacteristic
202C2×C3⋊Dic3C2×D411yescharacteristic
203C4×C3⋊D3—21no—
204C4×C3⋊D3—21no—
205#634—21no—
206#634—21no—
207#634—42no—
208C32×C8—21no—
209C32×C8—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#556—91no—
213#546—91no—
214#489—91no—
215#485—91no—
216#482—91no—
217#476—91no—
218#470—91no—
219#465—91no—
220#464—91no—
221#452—91no—
222#450C3⋊D311yescharacteristic, complemented
223#440—91no—
224#435—91no—
225#418—91no—
226#416—91no—
227C24×C3—24no—
228C2×C3×Q8C22×D314yes—
229C2×C3×D4—28no—
230C2×C3×D4—24no—
231C2×C3×D4—44no—
232C2×C3×D4C22×D314yes—
233C2×C3×D4C22×D314yes—
234C22×C3×C4C22×D314yes—
235C2×#67—34no—
236C2×#67—64no—
237C2×#67—64no—
238C22×Dic3—64no—
239C22×Dic3—64no—
240#237—68no—
241#237—124no—
242C2×C4×D3—34no—
243C2×Dic6—34no—
244C2×Dic6—64no—
245C3×SD16—28no—
246C3×SD16—44no—
247C2×C3×C8C22×D314yes—
248C2×C3×C8C22×D314yes—
249C3×C4⋊C4—24no—
250C3×C4⋊C4C22×D314yes—
251C3×C22⋊C4—24no—
252#217—34no—
253#217—64no—
254#217—64no—
255#217—64no—
256#217—64no—
257#217—64no—
258#217—64no—
259#216—124no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—34no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—64no—
267Dic3⋊C4—34no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271C4×Dic3—34no—
272C4×Dic3—64no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275#208—124no—
276C2×C3⋊C8—34no—
277C2×C3⋊C8—34no—
278D3×C8—124no—
279C22×C32—22no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—84no—
289C22×C32C22×D411yescharacteristic
290C2×C3⋊D3—21no—
291C2×C3⋊D3—21no—
292C2×C3⋊D3—21no—
293C32×C4—21no—
294C32×C4—41no—
295C32×C4—41no—
296C32×C4C2×#4111yescharacteristic
297C32×C4H(5,𝔽2)11yescharacteristic
298C3⋊Dic3—21no—
299C3⋊Dic3—21no—
300C3⋊Dic3—21no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3⋊Dic3—41no—
305C2×#41—91no—
306C22×D4C2×C3⋊D311yescharacteristic
307C2×Q16—91no—
308C2×SD16C2×C3⋊D311yescharacteristic
309C2×SD16C2×C3⋊D311yescharacteristic
310C2×M16—91no—
311C22×C8—91no—
312C4⋊Q8—91no—
313#126—181no—
314#126—181no—
315#124—91no—
316#124—181no—
317#123—181no—
318C22⋊Q8—91no—
319C22⋊Q8—91no—
320C22⋊Q8C2×C3⋊D311yescharacteristic
321#121—91no—
322#121—181no—
323#120—181no—
324C4×Q8—91no—
325C4×Q8—181no—
326C4×D4—91no—
327C4×D4—91no—
328#117—91no—
329#117—91no—
330C2×C22⋊C4—181no—
331#107—91no—
332#106—91no—
333#106—91no—
334C4⋊C8—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102C2×C3⋊D311yescharacteristic
344#102C2×C3⋊D311yescharacteristic
345C22⋊C8—91no—
346C22⋊C8C2×C3⋊D311yescharacteristic
347#97—91no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—48no—
351C23×C3—48no—
352C23×C3—84no—
353C23×C3D3×D414yes—
354C22×D3—34no—
355C3×Q8—24no—
356C3×Q8—24no—
357C3×D4—24no—
358C3×D4—24no—
359C3×D4—24no—
360C3×D4—48no—
361C3×D4#23718yes—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4D3×D414yes—
367C2×C3×C4C23×D314yes—
368#67—124no—
369#67—128no—
370#67—244no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—64no—
378C2×Dic3—128no—
379C2×Dic3—244no—
380C4×D3—64no—
381C4×D3—64no—
382Dic6—64no—
383Dic6—64no—
384Dic6—128no—
385C3×C8—24no—
386C3×C8—24no—
387C3⋊C8—64no—
388C3⋊C8—64no—
389C2×C32—41no—
390C2×C32—42no—
391C2×C32—81no—
392C2×C32#54611yescharacteristic
393C2×C32#57511yescharacteristic
394C2×C32#57711yescharacteristic
395C3⋊D3—41no—
396C24—21no—
397#41—182no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8—181no—
401C2×Q8C22×C3⋊D311yescharacteristic
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—41no—
405C2×D4—91no—
406C2×D4—181no—
407C2×D4—181no—
408C2×D4C22×C3⋊D311yescharacteristic
409C2×D4C22×C3⋊D311yescharacteristic
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×C3⋊D311yescharacteristic
414Q16—361no—
415SD16—22no—
416SD16—41no—
417M16—361no—
418C2×C8—91no—
419C2×C8—91no—
420C2×C8—361no—
421C2×C8C22×C3⋊D311yescharacteristic
422C2×C8C22×C3⋊D311yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4C22×C3⋊D311yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—91no—
435C22⋊C4—91no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4—181no—
444C42—91no—
445C42—181no—
446C42—181no—
447C42—181no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—28no—
451C22×C3—24no—
452C22×C3—44no—
453C22×C3—44no—
454C22×C3—44no—
455C22×C3—44no—
456C22×C3—44no—
457C22×C3—816no—
458C22×C3C2×D3×D414yes—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—64no—
462C3×C4—24no—
463C3×C4—44no—
464C3×C4—44no—
465C3×C4C2×#23714yes—
466C3×C4#100414yes—
467Dic3—64no—
468Dic3—64no—
469Dic3—64no—
470Dic3—124no—
471Dic3—124no—
472Dic3—124no—
473Dic3—124no—
474C32#331111yescharacteristic, complemented, Sylow
475C23—21no—
476C23—21no—
477C23—42no—
478C23—42no—
479C23—81no—
480C23—91no—
481C23D4×C3⋊D311yescharacteristic
482Q8—21no—
483Q8—21no—
484Q8—181no—
485Q8—181no—
486Q8—362no—
487D4—21no—
488D4—21no—
489D4—21no—
490D4—42no—
491D4—361no—
492D4—362no—
493D4—721no—
494D4#383012yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—362no—
509C2×C4—721no—
510C2×C4D4×C3⋊D311yescharacteristic
511C2×C4C23×C3⋊D311yescharacteristic
512C8—21no—
513C8—21no—
514C8—181no—
515C8—181no—
516C2×C3—44no—
517C2×C3—48no—
518C2×C3—84no—
519C2×C3#559114yes—
520C2×C3#576214yes—
521C2×C3#577314yes—
522D3—124no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—22no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—84no—
533C22—181no—
534C22—181no—
535C22—181no—
536C22C2×D4×C3⋊D311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—181no—
541C4—181no—
542C4—181no—
543C4—361no—
544C4—361no—
545C4—361no—
546C4—361no—
547C4C2×#383011yescharacteristic
548C4#6436111yescharacteristic
549C3#8016214yescomplemented
550C2—41no—
551C2—42no—
552C2—81no—
553C2—361no—
554C2#1059606211yescharacteristic
555C2#1059623311yescharacteristic
556C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radical#10596277C2
hypercenter#450C3⋊D3
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #10596112C2semidirect
3. C32×#450C2semidirect
4. #10592914C2semidirect
5. #10592872C2semidirect
6. #10592870C2semidirect
7. #10592865C2semidirect
8. #10592863C2semidirect
9. #10592751C2semidirect
10. #10592483C2semidirect
11. #10592471C2semidirect
12. #10592464C2semidirect
13. #10592460C2semidirect
14. #10592427C2semidirect
15. #10592422C2semidirect
24. #64155C22semidirect
25. Q8×C3⋊Dic3C22semidirect
26. C2×#3756C22semidirect
36. C2×C8×C3⋊D3C22semidirect
38. #64101C22semidirect
39. #64097C22semidirect
46. #63662C22semidirect
51. #63647C22semidirect
52. #63645C22semidirect
53. #63644C22semidirect
54. #63643C22semidirect
55. #63643C22semidirect
56. #63642C22semidirect
57. #63641C22semidirect
58. #63637C22semidirect
59. #63635C22semidirect
62. C3×#450D3semidirect
222. #450C3⋊D3semidirect
474. C32#3311semidirect
549. C3#80162semidirect

Maximal subgroups

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

subgroupindex
#105962772
#105961122
C32×#4502
#105929142
#105928722
#105928702
#105928652
#105928632
#105927512
#105924832
#105924712
#105924642
#105924602
#105924272
#105924222
#801623