Finite Group Databasebeta

← #11872782

Subgroups — #11872782

Order 1152.

1182 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#10596269C211yesmaximal, characteristic
2#10596096C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic
4#10592917C211yesmaximal, characteristic
5#10592863C211yesmaximal, characteristic, complemented
6#10592861C211yesmaximal, characteristic, complemented
7#10592861C211yesmaximal, characteristic, complemented
8SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
9#10592744C211yesmaximal, characteristic, complemented
10#10592465C211yesmaximal, characteristic, complemented
11#10592462C211yesmaximal, characteristic, complemented
12#10592457C211yesmaximal, characteristic, complemented
13#10592456C211yesmaximal, characteristic, complemented
14#10592422C211yesmaximal, characteristic, complemented
15#10592419C211yesmaximal, characteristic, complemented
16#80137—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C2×C32×SD16C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3757—21no—
22C2×#3757—21no—
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24#64153C2211yescharacteristic, complemented
25D4×C3⋊Dic3—21no—
26D4×C3⋊Dic3—21no—
27D4×C3⋊Dic3C2211yescharacteristic
28D4×C3⋊Dic3C2211yescharacteristic
29D4×C3⋊Dic3C2211yescharacteristic
30D4×C3⋊Dic3C2211yescharacteristic
31C2×#3754C2211yescharacteristic
32C2×#3754C2211yescharacteristic
33#64135C2211yescharacteristic
34#64135C2211yescharacteristic
35#64133C2211yescharacteristic
36#64099—21no—
37#64099C2211yescharacteristic, complemented
38#64098—21no—
39#64096C2211yescharacteristic, complemented
40#64088—21no—
41#64088—21no—
42C32×#102C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic, complemented
46#63662C2211yescharacteristic, complemented
47#63659C2211yescharacteristic
48#63659C2211yescharacteristic
49#63657C2211yescharacteristic
50#63645C2211yescharacteristic, complemented
51#63644C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63642C2211yescharacteristic, complemented
55#63641C2211yescharacteristic, complemented
56#63641C2211yescharacteristic, complemented
57C8×C3⋊Dic3C2211yescharacteristic, complemented
58#63635C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#5798—34no—
61#5625—34no—
62C3×#450D314yes—
63#5218—34no—
64#5164—34no—
65#5162—34no—
66#5162—34no—
67Dic3×SD16—34no—
68#5045—34no—
69#4766—34no—
70#4763—34no—
71#4758—34no—
72#4757—34no—
73#4723—34no—
74#4720—34no—
75C24×C32—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4—22no—
78C2×C32×D4—22no—
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C2×C32×D4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C22×C3⋊Dic3—21no—
84C22×C3⋊Dic3—21no—
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3—21no—
87C2×#634C2311yescharacteristic
88C32×SD16—22no—
89C32×SD16—22no—
90C2×C32×C8C2311yescharacteristic
91C2×C32×C8C2311yescharacteristic
92C32×C4⋊C4—21no—
93C32×C4⋊C4C2311yescharacteristic
94C32×C22⋊C4—21no—
95#3757—21no—
96#3757—21no—
97#3757—21no—
98#3757—21no—
99#3757—21no—
100#3757—21no—
101#3757D411yescharacteristic
102#3757D411yescharacteristic
103#3754—22no—
104#3754—22no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)D411yescharacteristic
108C4⋊(C3⋊Dic3)D411yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3123—91noSylow
125C22×C3×D4C2×D314yes—
126C2×C3×SD16C2×D314yes—
127C2×C3×SD16C2×D314yes—
128C3×C22⋊Q8C2×D314yes—
129C2×#217—64no—
130C2×#217—64no—
131Q8×Dic3—34no—
132#944—34no—
133D4×Dic3—34no—
134D4×Dic3—34no—
135D4×Dic3—34no—
136D4×Dic3—34no—
137D4×Dic3—64no—
138D4×Dic3—64no—
139C2×#214—34no—
140C2×#214—34no—
141#926—34no—
142#926—34no—
143#924—34no—
144#890—34no—
145#890—64no—
146#889—64no—
147#887—34no—
148#879—64no—
149#879—64no—
150C3×#102C2×D314yes—
151C3×#102C2×D314yes—
152C3×C22⋊C8C2×D314yes—
153#835—34no—
154#835—34no—
155#832—34no—
156#832—34no—
157#830—34no—
158#818—34no—
159#817—34no—
160#816—34no—
161#816—34no—
162#815—34no—
163Dic3⋊C8—34no—
164Dic3⋊C8—34no—
165C8×Dic3—34no—
166#808—34no—
167#807—34no—
168C23×C32—24no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—81no—
172C23×C32—81no—
173C23×C32C2×D411yescharacteristic
174C32×Q8—21no—
175C32×Q8—21no—
176C32×D4—24no—
177C32×D4—21no—
178C32×D4—21no—
179C32×D4#4112yes—
180C32×D4#4112yes—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—81no—
192C2×C3⋊Dic3—81no—
193C2×C3⋊Dic3—81no—
194C2×C3⋊Dic3—81no—
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199#634—21no—
200#634—21no—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊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#450C3⋊D311yescharacteristic
215#440—91no—
216#440—91no—
217C4×SD16—91no—
218C4×SD16—91no—
219#433—91no—
220C24×C3—24no—
221C2×C3×Q8C22×D314yes—
222C2×C3×D4—28no—
223C2×C3×D4—28no—
224C2×C3×D4—24no—
225C2×C3×D4C22×D314yes—
226C2×C3×D4C22×D314yes—
227C22×C3×C4C22×D314yes—
228C22×Dic3—64no—
229C22×Dic3—64no—
230C22×Dic3—64no—
231C22×Dic3—64no—
232C2×Dic6—34no—
233C3×SD16—28no—
234C3×SD16—28no—
235C2×C3×C8C22×D314yes—
236C2×C3×C8C22×D314yes—
237C3×C4⋊C4—24no—
238C3×C4⋊C4C22×D314yes—
239C3×C22⋊C4—24no—
240#217—34no—
241#217—34no—
242#217—64no—
243#217—64no—
244#217—64no—
245#217—64no—
246#217—64no—
247#217—64no—
248#214—68no—
249#214—68no—
250C4⋊Dic3—34no—
251C4⋊Dic3—34no—
252C4⋊Dic3—34no—
253C4⋊Dic3—34no—
254C4⋊Dic3—34no—
255C4⋊Dic3—64no—
256C4⋊Dic3—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—64no—
259Dic3⋊C4—64no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262C4×Dic3—34no—
263C4×Dic3—34no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C4×Dic3—64no—
267C2×C3⋊C8—34no—
268C2×C3⋊C8—34no—
269C22×C32—21no—
270C22×C32—22no—
271C22×C32—22no—
272C22×C32—21no—
273C22×C32—21no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—84no—
279C22×C32C22×D411yescharacteristic
280C32×C4—21no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4C2×#4111yescharacteristic
284C32×C4C2×#4111yescharacteristic
285C3⋊Dic3—21no—
286C3⋊Dic3—21no—
287C3⋊Dic3—21no—
288C3⋊Dic3—21no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C22×D4C2×C3⋊D311yescharacteristic
294C2×SD16—91no—
295C2×SD16—91no—
296C2×SD16C2×C3⋊D311yescharacteristic
297C2×SD16C2×C3⋊D311yescharacteristic
298C4⋊Q8—91no—
299#126—181no—
300#126—181no—
301#125—91no—
302#125—181no—
303#125—181no—
304C22⋊Q8—91no—
305C22⋊Q8C2×C3⋊D311yescharacteristic
306C4×Q8—91no—
307C4×Q8—91no—
308C4×D4—91no—
309C4×D4—91no—
310C4×D4—91no—
311C4×D4—91no—
312C4×D4—181no—
313C4×D4—181no—
314#117—91no—
315#117—91no—
316C2×C22⋊C4—181no—
317C2×C22⋊C4—181no—
318#107—91no—
319#107—91no—
320#106—91no—
321#106—91no—
322C4⋊C8—91no—
323C4⋊C8—91no—
324#103—91no—
325#103—91no—
326#103—91no—
327#103—91no—
328#102—91no—
329#102—91no—
330#102C2×C3⋊D311yescharacteristic
331#102C2×C3⋊D311yescharacteristic
332C22⋊C8—91no—
333C22⋊C8C2×C3⋊D311yescharacteristic
334#97—91no—
335C4×C8—91no—
336C23×C3—216no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—84no—
340C23×C3—84no—
341C23×C3D3×D414yes—
342C3×Q8—24no—
343C3×Q8—24no—
344C3×D4—216no—
345C3×D4—24no—
346C3×D4—24no—
347C3×D4#23718yes—
348C3×D4#23718yes—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4D3×D414yes—
354C2×C3×C4C23×D314yes—
355C2×Dic3—34no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—244no—
364C2×Dic3—244no—
365C2×Dic3—244no—
366C2×Dic3—244no—
367Dic6—64no—
368Dic6—64no—
369C3×C8—24no—
370C3×C8—24no—
371C3⋊C8—64no—
372C3⋊C8—64no—
373C2×C32—41no—
374C2×C32—42no—
375C2×C32—42no—
376C2×C32#52511yescharacteristic
377C2×C32#57711yescharacteristic
378C2×C32#57711yescharacteristic
379C24—21no—
380C2×Q8—91no—
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4C22×C3⋊D311yescharacteristic
386C2×D4C22×C3⋊D311yescharacteristic
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4C22×C3⋊D311yescharacteristic
392SD16—22no—
393SD16—22no—
394SD16—182no—
395SD16—182no—
396C2×C8—91no—
397C2×C8—91no—
398C2×C8C22×C3⋊D311yescharacteristic
399C2×C8C22×C3⋊D311yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—91no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—91no—
405C4⋊C4—91no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4—181no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C4⋊C4—181no—
413C4⋊C4C22×C3⋊D311yescharacteristic
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—91no—
425C42—181no—
426C42—181no—
427C42—181no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3—28no—
432C22×C3—28no—
433C22×C3—44no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—44no—
437C22×C3—816no—
438C22×C3C2×D3×D414yes—
439C3×C4—24no—
440C3×C4—44no—
441C3×C4—44no—
442C3×C4C2×#23714yes—
443C3×C4C2×#23714yes—
444Dic3—64no—
445Dic3—64no—
446Dic3—64no—
447Dic3—64no—
448Dic3—124no—
449Dic3—124no—
450Dic3—124no—
451Dic3—124no—
452C32#312311yescharacteristic, complemented, Sylow
453C23—24no—
454C23—21no—
455C23—21no—
456C23—81no—
457C23—81no—
458C23D4×C3⋊D311yescharacteristic
459Q8—21no—
460Q8—21no—
461Q8—181no—
462Q8—181no—
463D4—24no—
464D4—21no—
465D4—21no—
466D4#383012yes—
467D4#383012yes—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—91no—
475C2×C4—91no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—721no—
481C2×C4—721no—
482C2×C4—721no—
483C2×C4—721no—
484C2×C4D4×C3⋊D311yescharacteristic
485C2×C4C23×C3⋊D311yescharacteristic
486C8—21no—
487C8—21no—
488C8—181no—
489C8—181no—
490C2×C3—44no—
491C2×C3—48no—
492C2×C3—48no—
493C2×C3#558614yes—
494C2×C3#576214yes—
495C2×C3#577514yes—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—22no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—84no—
506C22C2×D4×C3⋊D311yescharacteristic
507C4—21no—
508C4—41no—
509C4—41no—
510C4—181no—
511C4—181no—
512C4—181no—
513C4—181no—
514C4—361no—
515C4—361no—
516C4—361no—
517C4—361no—
518C4C2×#383011yescharacteristic
519C4C2×#383011yescharacteristic
520C3#8013714yescomplemented
521C2—41no—
522C2—42no—
523C2—42no—
524C2#1059605711yescharacteristic
525C2#1059623311yescharacteristic
526C2#1059624611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC22×C32×D4C22
hypercenter#450C3⋊D3
hypocenterC32#3123
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. #10596096C2semidirect
5. #10592863C2semidirect
6. #10592861C2semidirect
7. #10592861C2semidirect
8. SD16×C3⋊Dic3C2semidirect
9. #10592744C2semidirect
10. #10592465C2semidirect
11. #10592462C2semidirect
12. #10592457C2semidirect
13. #10592456C2semidirect
14. #10592422C2semidirect
15. #10592419C2semidirect
23. Q8×C3⋊Dic3C22semidirect
24. #64153C22semidirect
37. #64099C22semidirect
39. #64096C22semidirect
45. #63662C22semidirect
46. #63662C22semidirect
50. #63645C22semidirect
51. #63644C22semidirect
52. #63643C22semidirect
53. #63643C22semidirect
54. #63642C22semidirect
55. #63641C22semidirect
56. #63641C22semidirect
57. C8×C3⋊Dic3C22semidirect
58. #63635C22semidirect
59. #63634C22semidirect
452. C32#3123semidirect
520. C3#80137semidirect

Maximal subgroups

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

subgroupindex
#105962692
#105960962
C32×#4502
#105929172
#105928632
#105928612
SD16×C3⋊Dic32
#105927442
#105924652
#105924622
#105924572
#105924562
#105924222
#105924192
#801373