Finite Group Databasebeta

← #11870565

Subgroups — #11870565

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
2#10596095C211yesmaximal, characteristic, complemented
3C32×#452C211yesmaximal, characteristic, complemented
4#10592937C211yesmaximal, characteristic
5#10592884C211yesmaximal, characteristic, complemented
6Q16×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#10592864C211yesmaximal, characteristic, complemented
8SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
9#10592744C211yesmaximal, characteristic, complemented
10#10592498C211yesmaximal, characteristic, complemented
11#10592487C211yesmaximal, characteristic, complemented
12#10592465C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic, complemented
14#10592436C211yesmaximal, characteristic, complemented
15#10592417C211yesmaximal, characteristic, complemented
16#80212—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×Q16C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64156C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26D4×C3⋊Dic3—21no—
27D4×C3⋊Dic3—21no—
28D4×C3⋊Dic3C2211yescharacteristic
29D4×C3⋊Dic3C2211yescharacteristic
30C2×#3753C2211yescharacteristic
31#64139C2211yescharacteristic
32#64135—21no—
33#64135C2211yescharacteristic
34C2×C4×C3⋊Dic3—21no—
35C2×C4×C3⋊Dic3C2211yescharacteristic
36#64107—21no—
37#64102C2211yescharacteristic
38#64101—21no—
39#64099C2211yescharacteristic
40#64095—21no—
41#64090—21no—
42C32×#103C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63659C2211yescharacteristic
49#63657C2211yescharacteristic
50#63648C2211yescharacteristic
51#63648C2211yescharacteristic
52#63645C2211yescharacteristic
53#63644C2211yescharacteristic
54#63641C2211yescharacteristic
55#63641C2211yescharacteristic
56C8×C3⋊Dic3C2211yescharacteristic
57C8×C3⋊Dic3C2211yescharacteristic
58#63635C2211yescharacteristic
59#63634C2211yescharacteristic
60Dic3×#41—34no—
61#5624—34no—
62C3×#452D314yescomplemented
63#5238—34no—
64#5185—34no—
65Dic3×Q16—34no—
66#5165—34no—
67Dic3×SD16—34no—
68#5045—34no—
69#4799—34no—
70#4788—34no—
71#4766—34no—
72#4756—34no—
73#4737—34no—
74#4718—34no—
75C32×#41—22no—
76C32×#41—22no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×Q8C2311yescharacteristic
79C2×C32×D4—21no—
80C2×C32×D4C2311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C22×C3⋊Dic3—21no—
85C22×C3⋊Dic3—21no—
86C22×C3⋊Dic3D411yescharacteristic
87C22×C3⋊Dic3D411yescharacteristic
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3—21no—
90C32×Q16—22no—
91C32×SD16—22no—
92C2×C32×C8C2311yescharacteristic
93C2×C32×C8C2311yescharacteristic
94C32×C4⋊C4—21no—
95C32×C4⋊C4C2311yescharacteristic
96C32×C22⋊C4—21no—
97#3757—21no—
98#3757—21no—
99#3757—21no—
100#3755—22no—
101#3753—22no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105#3752—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3D411yescharacteristic
119C4×C3⋊Dic3D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C4×C3⋊Dic3C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3102—91noSylow
125C2×C3×#41C2×D314yes—
126C2×C3×Q16C2×D314yes—
127C2×C3×SD16C2×D314yes—
128C3×C22⋊Q8C2×D314yes—
129#947—34no—
130Q8×Dic3—34no—
131Q8×Dic3—34no—
132Q8×Dic3—34no—
133C2×#215—34no—
134D4×Dic3—34no—
135D4×Dic3—34no—
136D4×Dic3—64no—
137D4×Dic3—64no—
138C2×#213—34no—
139#930—34no—
140#926—34no—
141#926—64no—
142C2×C4×Dic3—34no—
143C2×C4×Dic3—64no—
144#898—64no—
145#893—34no—
146#892—64no—
147#890—34no—
148#886—64no—
149#67⋊C4—64no—
150C3×#103C2×D314yes—
151C3×#102C2×D314yes—
152C3×C22⋊C8C2×D314yes—
153#835—34no—
154#835—34no—
155#835—34no—
156#832—34no—
157#830—34no—
158#821—34no—
159#821—34no—
160#818—34no—
161#817—34no—
162Dic3⋊C8—34no—
163Dic3⋊C8—34no—
164C8×Dic3—34no—
165C8×Dic3—34no—
166#808—34no—
167#807—34no—
168C23×C32—21no—
169C23×C32C2×D411yescharacteristic
170C22×C3⋊D3—21no—
171C32×Q8—21no—
172C32×Q8—21no—
173C32×Q8—21no—
174C32×Q8#4112yes—
175C32×D4—24no—
176C32×D4—21no—
177C32×D4#4112yes—
178C2×C32×C4—24no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—42no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—41no—
192C2×C3⋊Dic3—42no—
193C2×C3⋊Dic3—42no—
194C2×C3⋊Dic3C2×D411yescharacteristic
195C2×C3⋊Dic3C2×D411yescharacteristic
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)—21no—
200C4×C3⋊D3—42no—
201C32×C8—21no—
202C32×C8—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#529—91no—
206C4×#41—91no—
207#485—91no—
208#482—91no—
209#479—91no—
210#478—91no—
211#464—91no—
212#463—91no—
213#452C3⋊D311yescharacteristic, complemented
214#449—91no—
215C4×Q16—91no—
216C4×SD16—91no—
217C4×SD16—91no—
218C4×D8—91no—
219#431—91no—
220C3×#41—28no—
221C3×#41—28no—
222C2×C3×Q8C22×D314yes—
223C2×C3×Q8C22×D314yes—
224C2×C3×D4—24no—
225C2×C3×D4C22×D314yes—
226C22×C3×C4—24no—
227C22×C3×C4C22×D314yes—
228C2×#67—64no—
229C22×Dic3—34no—
230C22×Dic3—34no—
231C22×Dic3—64no—
232C22×Dic3—64no—
233C2×D12—34no—
234C2×C4×D3—64no—
235C3×Q16—28no—
236C3×SD16—28no—
237C2×C3×C8C22×D314yes—
238C2×C3×C8C22×D314yes—
239C3×C4⋊C4—24no—
240C3×C4⋊C4C22×D314yes—
241C3×C22⋊C4—24no—
242#217—64no—
243#217—64no—
244#217—64no—
245#215—68no—
246#213—68no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251C4⋊Dic3—34no—
252C4⋊Dic3—34no—
253C4⋊Dic3—34no—
254C4⋊Dic3—64no—
255C4⋊Dic3—64no—
256C4⋊Dic3—64no—
257C4⋊Dic3—64no—
258Dic3⋊C4—64no—
259C4×Dic3—34no—
260C4×Dic3—34no—
261C4×Dic3—34no—
262C4×Dic3—34no—
263C4×Dic3—64no—
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—21no—
272C22×C32—21no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4—22no—
281C32×C4—41no—
282C32×C4—41no—
283C32×C4C2×#4111yescharacteristic
284C32×C4C2×#4111yescharacteristic
285C3⋊Dic3—21no—
286C3⋊Dic3—21no—
287C3⋊Dic3—21no—
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3#13512yes—
292C2×#41C2×C3⋊D311yescharacteristic
293C2×Q16C2×C3⋊D311yescharacteristic
294C2×SD16—91no—
295C2×SD16C2×C3⋊D311yescharacteristic
296C2×D8—91no—
297#126—181no—
298#125—91no—
299#124—91no—
300#123—181no—
301C22⋊Q8C2×C3⋊D311yescharacteristic
302#121—91no—
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8—91no—
306C4×D4—91no—
307C4×D4—91no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4—181no—
311C4×D4—181no—
312#117—91no—
313#117—181no—
314#117—181no—
315C2×C42—91no—
316C2×C42—181no—
317#107—91no—
318#107—91no—
319#106—91no—
320#106—91no—
321C4⋊C8—91no—
322C4⋊C8—91no—
323#103—91no—
324#103—91no—
325#103—91no—
326#103C2×C3⋊D311yescharacteristic
327#102—91no—
328#102—91no—
329#102—91no—
330#102C2×C3⋊D311yescharacteristic
331C22⋊C8—91no—
332C22⋊C8C2×C3⋊D311yescharacteristic
333C4×C8—91no—
334C4×C8—91no—
335C23×C3—24no—
336C23×C3D3×D414yes—
337C22×D3—64no—
338C3×Q8—24no—
339C3×Q8—24no—
340C3×Q8—24no—
341C3×Q8#23718yes—
342C3×D4—216no—
343C3×D4—24no—
344C3×D4#23718yes—
345C2×C3×C4—216no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4D3×D414yes—
352C2×C3×C4C23×D314yes—
353#67—128no—
354C2×Dic3—34no—
355C2×Dic3—34no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—68no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—128no—
363C2×Dic3—124no—
364C2×Dic3—128no—
365D12—64no—
366D12—64no—
367C4×D3—128no—
368C3×C8—24no—
369C3×C8—24no—
370C3⋊C8—64no—
371C3⋊C8—64no—
372C2×C32—41no—
373C2×C32—42no—
374C2×C32#52511yescharacteristic
375C2×C32C2×#13511yescharacteristic
376C2×C32#57511yescharacteristic
377C3⋊D3—81no—
378#41—22no—
379#41—22no—
380C2×Q8C22×C3⋊D311yescharacteristic
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—21no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4C22×C3⋊D311yescharacteristic
386C22×C4—21no—
387C22×C4—91no—
388C22×C4—91no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4C22×C3⋊D311yescharacteristic
393Q16—22no—
394SD16—22no—
395SD16—182no—
396D8—182no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8C22×C3⋊D311yescharacteristic
400C2×C8C22×C3⋊D311yescharacteristic
401C4⋊C4—21no—
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⋊C4C22×C3⋊D311yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—181no—
413C22⋊C4—181no—
414C22⋊C4—181no—
415C22⋊C4—181no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—91no—
420C42—91no—
421C42—91no—
422C42—91no—
423C42—181no—
424C42—181no—
425C42—181no—
426C42—181no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—28no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3C2×D3×D414yes—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—124no—
437C3×C4—24no—
438C3×C4—28no—
439C3×C4—44no—
440C3×C4—44no—
441C3×C4C2×#23714yes—
442C3×C4C2×#23714yes—
443Dic3—38no—
444Dic3—64no—
445Dic3—64no—
446Dic3—64no—
447Dic3—124no—
448Dic3—124no—
449Dic3—124no—
450C32#310211yescharacteristic, complemented, Sylow
451C23—21no—
452C23—181no—
453C23D4×C3⋊D311yescharacteristic
454Q8—21no—
455Q8—21no—
456Q8—21no—
457Q8#383012yes—
458D4—24no—
459D4—21no—
460D4—181no—
461D4—181no—
462D4—362no—
463D4#383012yes—
464C2×C4—24no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—91no—
471C2×C4—91no—
472C2×C4—91no—
473C2×C4—91no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—362no—
479C2×C4—362no—
480C2×C4—361no—
481C2×C4—362no—
482C2×C4D4×C3⋊D311yescharacteristic
483C2×C4C23×C3⋊D311yescharacteristic
484C8—21no—
485C8—21no—
486C8—181no—
487C8—181no—
488C2×C3—44no—
489C2×C3—48no—
490C2×C3#558614yes—
491C2×C3D3×#13514yes—
492C2×C3#577714yes—
493D3—244no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—22no—
498C22—41no—
499C22—41no—
500C22—361no—
501C22—361no—
502C22—361no—
503C22C2×D4×C3⋊D311yescharacteristic
504C4—21no—
505C4—22no—
506C4—41no—
507C4—41no—
508C4—92no—
509C4—181no—
510C4—181no—
511C4—181no—
512C4—361no—
513C4—361no—
514C4—361no—
515C4C2×#383011yescharacteristic
516C4C2×#383011yescharacteristic
517C3#8021214yescomplemented
518C2—41no—
519C2—42no—
520C2—721no—
521C2#1059605711yescharacteristic
522C2C3⋊D3×#13511yescharacteristic
523C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#452C2
socleC22×C32C22×D4
prime radical#10592937C2
hypercenter#452C3⋊D3
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #41×C3⋊Dic3C2semidirect
2. #10596095C2semidirect
3. C32×#452C2semidirect
5. #10592884C2semidirect
6. Q16×C3⋊Dic3C2semidirect
7. #10592864C2semidirect
8. SD16×C3⋊Dic3C2semidirect
9. #10592744C2semidirect
10. #10592498C2semidirect
11. #10592487C2semidirect
12. #10592465C2semidirect
13. #10592455C2semidirect
14. #10592436C2semidirect
15. #10592417C2semidirect
62. C3×#452D3semidirect
213. #452C3⋊D3semidirect
450. C32#3102semidirect
517. C3#80212semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
#105960952
C32×#4522
#105929372
#105928842
Q16×C3⋊Dic32
#105928642
SD16×C3⋊Dic32
#105927442
#105924982
#105924872
#105924652
#105924552
#105924362
#105924172
#802123