Finite Group Databasebeta

← #11919014

Subgroups — #11919014

Order 1152.

2234 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596695C212yesmaximal, complemented
2#10596647C211yesmaximal, characteristic, complemented
3#10596522C211yesmaximal, characteristic, complemented
4#10596521C212yesmaximal, complemented
5#10596520C211yesmaximal, characteristic, complemented
6#10596516C213yesmaximal, complemented
7#10596515C216yesmaximal, complemented
8#10596514C213yesmaximal, complemented
9#10596500C213yesmaximal, complemented
10#10596499C216yesmaximal, complemented
11C2×#64223C213yesmaximal, complemented
12#41×C3⋊D3C2211yescharacteristic
13C3×D3×#41—22no—
14#64320C2212yescomplemented
15#64316C2212yescomplemented
16#64315—22no—
17#64314—26no—
18#64313C2216yescomplemented
19#64309C2216yescomplemented
20#64306C2216yescomplemented
21D3×#235—26no—
22C2×#3798C2216yescomplemented
23#64289C2211yescharacteristic, complemented
24#64289C2211yescharacteristic, complemented
25#64287C2213yescomplemented
26#64287C2213yescomplemented
27#64283C2213yescomplemented
28C2×#3787C2213yescomplemented
29C2×#3776C2213yescomplemented
30#64239C22112yescomplemented
31C2×#3775C2216yescomplemented
32#64237C2216yescomplemented
33#64237C2216yescomplemented
34#64236C22112yescomplemented
35C2×#3774C2213yescomplemented
36#64228C2213yescomplemented
37#64227C2216yescomplemented
38#64226C2216yescomplemented
39#64226C2216yescomplemented
40#64225C2213yescomplemented
41#64224C2216yescomplemented
42#64224C2216yescomplemented
43#64223C2211yescharacteristic, complemented
44#64223C2216yescomplemented
45#64223C2213yescomplemented
46#64223C2213yescomplemented
47#64223C2216yescomplemented
48#64223C2213yescomplemented
49#64223C2216yescomplemented
50#5964—62no—
51C32×#41D411yescharacteristic
52#3832C2311yescharacteristic
53Q8×C3⋊D3D411yescharacteristic
54#3830C2313yes—
55D4×C3⋊D3D413yes—
56#3828D413yes—
57C2×C4×C3⋊D3C2313yes—
58C3×#239—22no—
59C3×D3×Q8—22no—
60C3×#237—26no—
61C3×D3×D4—26no—
62C3×#235—26no—
63C2×C3×C4×D3—26no—
64#3811—26no—
65D3×#67—212no—
66C2×#627C2316yes—
67C2×#626—26no—
68C2×#625C2316yes—
69#3805C23112yes—
70#3804—212no—
71#3802C2316yes—
72D3×D12—26no—
73C4×D32—26no—
74#3799—26no—
75#3798—26no—
76#3798—26no—
77#3798C2312yes—
78#3798C2316yes—
79#3798C2316yes—
80#3798C2316yes—
81#3797C2316yes—
82#3796—26no—
83#3795—26no—
84D3×Dic6—26no—
85#3792C2316yes—
86C2×#622C2313yes—
87C2×#622C2313yes—
88#3788C2313yes—
89#3788C2313yes—
90#3787C2311yescharacteristic
91#3787C2313yes—
92#3787C2313yes—
93#3787C2313yes—
94#3776C2311yescharacteristic
95#3776C2316yes—
96#3776C2313yes—
97#3776C2316yes—
98#3775C2312yes—
99#3775C2316yes—
100#3775C2316yes—
101#3775C2316yes—
102#3775C23112yes—
103#3774C2311yescharacteristic
104#3774C2316yes—
105#3774C2313yes—
106#3774C2316yes—
107#3584—91nomaximal, Sylow
108C2×C3×#41—62no—
109#1010—66no—
110#1010—62no—
111#1009—62no—
112#1009—66no—
113D3×#41—22no—
114D3×#41—66no—
115D3×#41—62no—
116D3×#41—66no—
117#1007—62no—
118#1007—62no—
119#1004—66no—
120#1004—66no—
121C2×#235—66no—
122C2×#235—66no—
123C22×C3⋊D3C2×D413yes—
124C22×C3×D3—26no—
125C2×D32—26no—
126C32×Q8C2×D411yescharacteristic
127C32×D4C2×D413yes—
128C2×C32×C4C2×D413yes—
129#638C2×D416yes—
130C2×C3⋊Dic3C2413yes—
131C4⋊(C3⋊D3)C2×D413yes—
132C4×C3⋊D3C2×D413yes—
133C4×C3⋊D3C2×D413yes—
134C4×C3⋊D3C2411yescharacteristic
135C4×C3⋊D3C2413yes—
136#634C2×D413yes—
137C3×#67—212no—
138C2×C3×Dic3—26no—
139C3×D12—26no—
140C3×C4×D3—26no—
141C3×C4×D3—26no—
142C3×C4×D3—22no—
143C3×C4×D3—26no—
144C3×Dic6—26no—
145#627—26no—
146#627C2416yes—
147#627C2412yes—
148#626—26no—
149#626—22no—
150#626—26no—
151#626—26no—
152#625—26no—
153#625C2412yes—
154#625C2416yes—
155#624—26no—
156D3×Dic3—212no—
157#622C2411yescharacteristic
158#622C2413yes—
159#622C2413yes—
160#622C2411yescharacteristic
161#585—92no—
162#578—93no—
163#578—91no—
164#577—96no—
165#577—92no—
166#576—93no—
167#576—91no—
168#575—96no—
169C2×#135—93no—
170C2×#135—93no—
171C2×#131—91no—
172C3×#41—22no—
173C3×#41—66no—
174C3×#41—66no—
175C3×#41—62no—
176C2×C3×Q8—62no—
177C2×C3×D4—66no—
178C22×C3×C4—66no—
179C2×#67—66no—
180C2×#67—66no—
181C2×#67—612no—
182#239—22no—
183#239—62no—
184#239—66no—
185#239—66no—
186D3×Q8—22no—
187D3×Q8—66no—
188D3×Q8—62no—
189D3×Q8—66no—
190#237—26no—
191#237—612no—
192#237—66no—
193#237—66no—
194#237—66no—
195#237—612no—
196D3×D4—26no—
197D3×D4—66no—
198D3×D4—66no—
199D3×D4—66no—
200D3×D4—612no—
201D3×D4—612no—
202#235—26no—
203#235—62no—
204#235—66no—
205#235—66no—
206#235—66no—
207#235—66no—
208#235—66no—
209#235—66no—
210#235—66no—
211#235—66no—
212#235—66no—
213#235—66no—
214#235—612no—
215C2×D12—66no—
216C2×D12—66no—
217C2×C4×D3—26no—
218C2×C4×D3—66no—
219C2×C4×D3—612no—
220C2×Dic6—66no—
221C2×Dic6—66no—
222C22×C32C22×D413yes—
223C2×C3⋊D3—43no—
224C2×C3⋊D3C22×D413yes—
225C2×C3⋊D3C22×D411yescharacteristic
226C2×C3×D3—26no—
227C2×C3×D3—22no—
228C2×C3×D3—86no—
229D32—86no—
230C32×C4C22×D413yes—
231C32×C4C22×D411yescharacteristic
232C3⋊Dic3C22×D413yes—
233C3⋊Dic3C2511yescharacteristic
234C3×Dic3—26no—
235C3×Dic3—22no—
2362−1+4—92no—
2372−1+4—96no—
2382−1+4—182no—
239H(5,𝔽2)—96no—
240H(5,𝔽2)—92no—
241H(5,𝔽2)—186no—
242C2×#41—62no—
243C2×#41—96no—
244C2×#41—91no—
245C2×#41—96no—
246C2×#41—186no—
247#137—96no—
248#137—96no—
249#137—912no—
250AGL(1,ℤ/8)—96no—
251AGL(1,ℤ/8)—96no—
252AGL(1,ℤ/8)—912no—
253#135—91no—
254#135—93no—
255#135—96no—
256#135—96no—
257#135—93no—
258#135—93no—
259#135—96no—
260#135—96no—
261#135—96no—
262C2×Q16—93no—
263C2×Q16—93no—
264C2×SD16—96no—
265C2×SD16—96no—
266C2×D8—93no—
267C2×D8—93no—
268#131—93no—
269#131—93no—
270#131—91no—
271#131—91no—
272C2×M16—93no—
273C22×C8—93no—
274C23×C3—66no—
275C22×D3—26no—
276C22×D3—66no—
277C22×D3—612no—
278C3×Q8—22no—
279C3×Q8—66no—
280C3×D4—26no—
281C3×D4—66no—
282C3×D4—612no—
283C2×C3×C4—26no—
284C2×C3×C4—66no—
285C2×C3×C4—66no—
286C2×C3×C4—62no—
287C2×C3×C4—66no—
288C2×C3×C4—66no—
289#67—212no—
290#67—62no—
291#67—66no—
292#67—612no—
293#67—66no—
294#67—62no—
295#67—66no—
296#67—66no—
297#67—66no—
298#67—66no—
299C2×Dic3—26no—
300C2×Dic3—66no—
301C2×Dic3—612no—
302D12—26no—
303D12—66no—
304D12—62no—
305D12—66no—
306D12—66no—
307D12—66no—
308C4×D3—22no—
309C4×D3—26no—
310C4×D3—26no—
311C4×D3—26no—
312C4×D3—66no—
313C4×D3—66no—
314C4×D3—62no—
315C4×D3—66no—
316C4×D3—612no—
317C4×D3—612no—
318Dic6—26no—
319Dic6—62no—
320Dic6—66no—
321Dic6—66no—
322Dic6—66no—
323Dic6—66no—
324C2×C32—23no—
325C2×C32C23×D411yescharacteristic
326C3⋊D3—23no—
327C3⋊D3—21no—
328C3×D3—46no—
329C3×D3—42no—
330#41—62no—
331#41—66no—
332#41—66no—
333#41—92no—
334#41—96no—
335#41—96no—
336#41—96no—
337#41—91no—
338#41—93no—
339#41—93no—
340#41—912no—
341#41—186no—
342#41—186no—
343#41—1812no—
344#41—186no—
345#41—186no—
346#41—186no—
347#41GO+(4,𝔽2)11yescharacteristic
348C2×Q8—62no—
349C2×Q8—96no—
350C2×Q8—91no—
351C2×Q8—96no—
352C2×Q8—186no—
353C2×D4—66no—
354C2×D4—96no—
355C2×D4—93no—
356C2×D4—96no—
357C2×D4—186no—
358C2×D4—186no—
359C2×D4—186no—
360C2×D4—1812no—
361C22×C4—66no—
362C22×C4—93no—
363C22×C4—186no—
364Q16—93no—
365Q16—91no—
366Q16—96no—
367Q16—96no—
368SD16—96no—
369SD16—92no—
370SD16—912no—
371SD16—96no—
372SD16—96no—
373D8—93no—
374D8—91no—
375D8—96no—
376D8—96no—
377M16—93no—
378M16—93no—
379M16—96no—
380C2×C8—91no—
381C2×C8—93no—
382C2×C8—93no—
383C2×C8—93no—
384C2×C8—93no—
385C2×C8—93no—
386C22×C3—26no—
387C22×C3—66no—
388C22×C3—62no—
389C22×C3—246no—
390C2×D3—22no—
391C2×D3—26no—
392C2×D3—62no—
393C2×D3—66no—
394C2×D3—86no—
395C2×D3—246no—
396C2×D3—2412no—
397C3×C4—26no—
398C3×C4—22no—
399C3×C4—62no—
400C3×C4—66no—
401Dic3—26no—
402Dic3—22no—
403Dic3—66no—
404Dic3—62no—
405C32#358411yescharacteristic, complemented, Sylow
406C23—66no—
407C23—93no—
408C23—186no—
409Q8—66no—
410Q8—92no—
411Q8—96no—
412Q8—93no—
413Q8—186no—
414Q8C2×GO+(4,𝔽2)11yescharacteristic
415D4—612no—
416D4—66no—
417D4—92no—
418D4—96no—
419D4—96no—
420D4—93no—
421D4—182no—
422D4—186no—
423D4—186no—
424D4—186no—
425D4—186no—
426D4C2×GO+(4,𝔽2)13yes—
427C2×C4—66no—
428C2×C4—66no—
429C2×C4—66no—
430C2×C4—62no—
431C2×C4—66no—
432C2×C4—93no—
433C2×C4—93no—
434C2×C4—93no—
435C2×C4—91no—
436C2×C4—93no—
437C2×C4—186no—
438C2×C4—1812no—
439C2×C4C2×GO+(4,𝔽2)13yes—
440C8—91no—
441C8—91no—
442C8—93no—
443C8—93no—
444C2×C3—22no—
445C2×C3—46no—
446C2×C3—126no—
447C2×C3—122no—
448D3—42no—
449D3—46no—
450D3—122no—
451D3—126no—
452C22—62no—
453C22—66no—
454C22—91no—
455C22—93no—
456C22—246no—
457C22—363no—
458C22—726no—
459C22C22×GO+(4,𝔽2)13yes—
460C4—62no—
461C4—66no—
462C4—91no—
463C4—93no—
464C4C22×GO+(4,𝔽2)13yes—
465C4C22×GO+(4,𝔽2)11yescharacteristic
466C3—22no—
467C2—23no—
468C2—122no—
469C2—126no—
470C2—181no—
471C2—183no—
472C2C23×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC4C22×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC32×#41D4
socleC2×C32C23×D4
hypercenter#41GO+(4,𝔽2)
hypocenterC32#3584
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ #41

Complements

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

NH ≅ G/Ntype
1. #10596695C2semidirect
2. #10596647C2semidirect
3. #10596522C2semidirect
4. #10596521C2semidirect
5. #10596520C2semidirect
6. #10596516C2semidirect
7. #10596515C2semidirect
8. #10596514C2semidirect
9. #10596500C2semidirect
10. #10596499C2semidirect
11. C2×#64223C2semidirect
14. #64320C22semidirect
15. #64316C22semidirect
18. #64313C22semidirect
19. #64309C22semidirect
20. #64306C22semidirect
22. C2×#3798C22semidirect
23. #64289C22semidirect
24. #64289C22semidirect
25. #64287C22semidirect
26. #64287C22semidirect
27. #64283C22semidirect
28. C2×#3787C22semidirect
29. C2×#3776C22semidirect
30. #64239C22semidirect
31. C2×#3775C22semidirect
32. #64237C22semidirect
33. #64237C22semidirect
34. #64236C22semidirect
35. C2×#3774C22semidirect
36. #64228C22semidirect
37. #64227C22semidirect
38. #64226C22semidirect
39. #64226C22semidirect
40. #64225C22semidirect
41. #64224C22semidirect
42. #64224C22semidirect
43. #64223C22semidirect
44. #64223C22semidirect
45. #64223C22semidirect
46. #64223C22semidirect
47. #64223C22semidirect
48. #64223C22semidirect
49. #64223C22semidirect
405. C32#3584semidirect

Maximal subgroups

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

subgroupindex
#105966952
#105966472
#105965222
#105965212
#105965202
#105965162
#105965152
#105965142
#105965002
#105964992
C2×#642232
#35849