Finite Group Databasebeta

← #11870544

Subgroups — #11870544

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
1C32×#529C211yesmaximal, characteristic, complemented
2C4×#3828C211yesmaximal, characteristic, complemented
3#10592765C211yesmaximal, characteristic, complemented
4#10592762C211yesmaximal, characteristic, complemented
5#10592756C211yesmaximal, characteristic, complemented
6#10592753C211yesmaximal, characteristic, complemented
7#10592746C211yesmaximal, characteristic, complemented
8#10592744C211yesmaximal, characteristic, complemented
9#10592736C211yesmaximal, characteristic
10#10592734C211yesmaximal, characteristic, complemented
11C4×#3756C211yesmaximal, characteristic, complemented
12C4×#3755C211yesmaximal, characteristic, complemented
13C4×#3754C211yesmaximal, characteristic, complemented
14C4×#3753C211yesmaximal, characteristic, complemented
15#10592624C211yesmaximal, characteristic, complemented
16#83140—34nomaximal
17C2×#3828C2211yescharacteristic
18C32×#126—21no—
19C32×#125C2211yescharacteristic
20C32×#124C2211yescharacteristic
21C32×#123—21no—
22C32×C22⋊Q8C2211yescharacteristic
23C32×#121C2211yescharacteristic
24C32×C4×Q8C2211yescharacteristic
25C32×C4×D4—21no—
26C32×C4×D4C2211yescharacteristic
27C32×#117—21no—
28C2×C32×C42C2211yescharacteristic
29C2×#3756C2211yescharacteristic
30C2×#3755C2211yescharacteristic
31C2×#3754C2211yescharacteristic
32C2×#3753C2211yescharacteristic
33C4×#638—21no—
34C4×#638—21no—
35#64135C2211yescharacteristic
36C4×C4⋊(C3⋊D3)C2211yescharacteristic
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38#64081—21no—
39C42×C3⋊D3—21no—
40C4×#634C2211yescharacteristic
41C4×#634C2211yescharacteristic
42#63662C2211yescharacteristic
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63657C2211yescharacteristic
47#63657C2211yescharacteristic
48#63637C2211yescharacteristic
49#63637C2211yescharacteristic
50#63636C2211yescharacteristic
51#63636C2211yescharacteristic
52#63635C2211yescharacteristic
53#63635C2211yescharacteristic
54#63634C2211yescharacteristic
55#63634C2211yescharacteristic
56C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
57C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
58C4×C3⋊(C3⋊C8)C2211yescharacteristic
59C4×C3⋊(C3⋊C8)C2211yescharacteristic
60C3×#529D314yescomplemented
61C4×#235—34no—
62#5066—34no—
63#5063—34no—
64#5057—34no—
65#5054—34no—
66#5047—34no—
67#5045—34no—
68#5037—34no—
69#5035—34no—
70C4×#216—34no—
71C4×#215—34no—
72C4×#214—34no—
73C4×#213—34no—
74#4925—34no—
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4D411yescharacteristic
80C22×C32×C4D411yescharacteristic
81C22×C32×C4C2311yescharacteristic
82C2×#638—21no—
83#3828—22no—
84#3828—22no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×#634C2311yescharacteristic
90C32×C4⋊C4—21no—
91C32×C4⋊C4—21no—
92C32×C4⋊C4—21no—
93C32×C4⋊C4—21no—
94C32×C4⋊C4C2311yescharacteristic
95C32×C4⋊C4C2311yescharacteristic
96C32×C22⋊C4—21no—
97C32×C22⋊C4—21no—
98C32×C22⋊C4—21no—
99C32×C22⋊C4—21no—
100C32×C22⋊C4—21no—
101C32×C42—21no—
102C32×C42D411yescharacteristic
103C32×C42D411yescharacteristic
104C32×C42C2311yescharacteristic
105C32×C42C2311yescharacteristic
106#3757—21no—
107#3756—22no—
108#3755—22no—
109#3754—22no—
110#3753—22no—
111#3752—21no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124#3102—91noSylow
125C2×#235—34no—
126C3×#126—24no—
127C3×#125C2×D314yes—
128C3×#124C2×D314yes—
129C3×#123—24no—
130C3×C22⋊Q8C2×D314yes—
131C3×#121C2×D314yes—
132C3×C4×Q8C2×D314yes—
133C3×C4×D4—24no—
134C3×C4×D4C2×D314yes—
135C3×#117—24no—
136C2×C3×C42C2×D314yes—
137C2×#216—34no—
138C2×#215—34no—
139C2×#214—34no—
140C2×#213—34no—
141C4×#67—64no—
142C4×#67—64no—
143#926—34no—
144C4×D12—34no—
145C4×D12—34no—
146#872—64no—
147C42×D3—64no—
148C4×Dic6—34no—
149C4×Dic6—34no—
150#835—34no—
151#835—34no—
152#832—34no—
153#832—34no—
154#830—34no—
155#830—34no—
156#810—34no—
157#810—34no—
158#809—34no—
159#809—34no—
160#808—34no—
161#808—34no—
162#807—34no—
163#807—34no—
164C4⋊(C3⋊C8)—34no—
165C4⋊(C3⋊C8)—34no—
166C4×C3⋊C8—34no—
167C4×C3⋊C8—34no—
168C23×C32—21no—
169C23×C32C2×D411yescharacteristic
170C22×C3⋊D3—21no—
171C32×Q8—21no—
172C32×Q8—21no—
173C32×D4—21no—
174C32×D4—21no—
175C32×D4—42no—
176C2×C32×C4—22no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—41no—
183C2×C32×C4—42no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2411yescharacteristic
190#638—24no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)#4112yes—
196C4×C3⋊D3—24no—
197C4×C3⋊D3—42no—
198C4×C3⋊D3—42no—
199#634—21no—
200#634#4112yes—
201C3⋊(C3⋊C8)—21no—
202C3⋊(C3⋊C8)—21no—
203C3⋊(C3⋊C8)—21no—
204C3⋊(C3⋊C8)—21no—
205#529C3⋊D311yescharacteristic, complemented
206C4×#41—91no—
207#485—91no—
208#482—91no—
209#479—91no—
210#478—91no—
211#464—91no—
212#463—91no—
213#452—91no—
214#449—91no—
215C4×Q16—91no—
216C4×SD16—91no—
217C4×SD16—91no—
218C4×D8—91no—
219#431—91no—
220C2×C3×Q8C22×D314yes—
221C2×C3×D4—24no—
222C2×C3×D4C22×D314yes—
223C22×C3×C4—24no—
224C22×C3×C4#6714yes—
225C22×C3×C4#6714yes—
226C22×C3×C4C22×D314yes—
227C2×#67—64no—
228#235—68no—
229#235—68no—
230C2×D12—34no—
231C2×C4×D3—64no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×Dic6—34no—
235C3×C4⋊C4—24no—
236C3×C4⋊C4—24no—
237C3×C4⋊C4—24no—
238C3×C4⋊C4—24no—
239C3×C4⋊C4C22×D314yes—
240C3×C4⋊C4C22×D314yes—
241C3×C22⋊C4—24no—
242C3×C22⋊C4—24no—
243C3×C22⋊C4—24no—
244C3×C22⋊C4—24no—
245C3×C22⋊C4—24no—
246C3×C42—24no—
247C3×C42#6714yes—
248C3×C42#6714yes—
249C3×C42C22×D314yes—
250C3×C42C22×D314yes—
251#217—64no—
252#216—68no—
253#215—68no—
254#214—68no—
255#213—68no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—64no—
258C4⋊Dic3—34no—
259C4⋊Dic3—34no—
260Dic3⋊C4—64no—
261Dic3⋊C4—64no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3—64no—
265C2×C3⋊C8—34no—
266C2×C3⋊C8—34no—
267C2×C3⋊C8—34no—
268C2×C3⋊C8—34no—
269C22×C32—21no—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4—21no—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4—41no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4#13512yes—
287C32×C4C2×#4111yescharacteristic
288C32×C4C2×#4111yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C2×#41—91no—
293C2×Q16—91no—
294C2×SD16—91no—
295C2×SD16—91no—
296C2×D8—91no—
297#126—21no—
298#125C2×C3⋊D311yescharacteristic
299#124C2×C3⋊D311yescharacteristic
300#123—21no—
301C22⋊Q8C2×C3⋊D311yescharacteristic
302#121C2×C3⋊D311yescharacteristic
303C4×Q8—91no—
304C4×Q8—91no—
305C4×Q8C2×C3⋊D311yescharacteristic
306C4×D4—21no—
307C4×D4—91no—
308C4×D4—91no—
309C4×D4—181no—
310C4×D4—181no—
311C4×D4C2×C3⋊D311yescharacteristic
312#117—21no—
313#117—91no—
314#117—181no—
315C2×C42—181no—
316C2×C42C2×C3⋊D311yescharacteristic
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#103—91no—
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331C22⋊C8—91no—
332C22⋊C8—91no—
333C4×C8—91no—
334C4×C8—91no—
335C23×C3—24no—
336C23×C3C2×#6714yes—
337C22×D3—64no—
338C3×Q8—24no—
339C3×Q8—24no—
340C3×D4—24no—
341C3×D4—24no—
342C3×D4—48no—
343C2×C3×C4—28no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—44no—
350C2×C3×C4—48no—
351C2×C3×C4C2×#6714yes—
352C2×C3×C4C2×#6714yes—
353C2×C3×C4C2×#6714yes—
354C2×C3×C4C2×#6714yes—
355C2×C3×C4C2×#6714yes—
356C2×C3×C4C23×D314yes—
357#67—616no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361D12—38no—
362D12—64no—
363C4×D3—616no—
364C4×D3—128no—
365C4×D3—128no—
366Dic6—38no—
367Dic6—64no—
368C3⋊C8—64no—
369C3⋊C8—64no—
370C3⋊C8—64no—
371C3⋊C8—64no—
372C2×C32—41no—
373C2×C32—81no—
374C2×C32#52511yescharacteristic
375C2×C32C2×#13511yescharacteristic
376C2×C32#57511yescharacteristic
377C3⋊D3—42no—
378#41—182no—
379#41—182no—
380C2×Q8—91no—
381C2×Q8C22×C3⋊D311yescharacteristic
382C2×D4—21no—
383C2×D4—91no—
384C2×D4—181no—
385C2×D4C22×C3⋊D311yescharacteristic
386C22×C4—21no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4#63811yescharacteristic
391C22×C4#63811yescharacteristic
392C22×C4C22×C3⋊D311yescharacteristic
393Q16—182no—
394SD16—182no—
395SD16—182no—
396D8—182no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8—91no—
400C2×C8—91no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—91no—
406C4⋊C4—91no—
407C4⋊C4—181no—
408C4⋊C4—181no—
409C4⋊C4C22×C3⋊D311yescharacteristic
410C4⋊C4C22×C3⋊D311yescharacteristic
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—21no—
416C22⋊C4—181no—
417C22⋊C4—181no—
418C22⋊C4—181no—
419C42—21no—
420C42—181no—
421C42—181no—
422C42—181no—
423C42#63811yescharacteristic
424C42#63811yescharacteristic
425C42C22×C3⋊D311yescharacteristic
426C42C22×C3⋊D311yescharacteristic
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—44no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3C22×#6714yes—
434C2×D3—68no—
435C2×D3—124no—
436C2×D3—124no—
437C3×C4—24no—
438C3×C4—24no—
439C3×C4—24no—
440C3×C4—24no—
441C3×C4—44no—
442C3×C4—44no—
443C3×C4—44no—
444C3×C4#95018yes—
445C3×C4D3×#4114yes—
446C3×C4D3×#4114yes—
447Dic3—68no—
448Dic3—124no—
449Dic3—124no—
450C32#310211yescharacteristic, complemented, Sylow
451C23—21no—
452C23—181no—
453C23C2×#63811yescharacteristic
454Q8—21no—
455Q8—21no—
456Q8—92no—
457Q8—181no—
458D4—21no—
459D4—21no—
460D4—42no—
461D4—92no—
462D4—184no—
463D4—181no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—184no—
473C2×C4—181no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—362no—
477C2×C4—362no—
478C2×C4C2×#63811yescharacteristic
479C2×C4C2×#63811yescharacteristic
480C2×C4C2×#63811yescharacteristic
481C2×C4C2×#63811yescharacteristic
482C2×C4C2×#63811yescharacteristic
483C2×C4C23×C3⋊D311yescharacteristic
484C8—181no—
485C8—181no—
486C8—181no—
487C8—181no—
488C2×C3—44no—
489C2×C3—84no—
490C2×C3C2×#95014yes—
491C2×C3#582214yes—
492C2×C3#582814yes—
493D3—128no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—182no—
501C22—361no—
502C22—361no—
503C22C22×#63811yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—182no—
512C4—361no—
513C4—361no—
514C4#6415912yes—
515C4#41×C3⋊D311yescharacteristic
516C4#41×C3⋊D311yescharacteristic
517C3#8314014yescomplemented
518C2—41no—
519C2—81no—
520C2—362no—
521C2C2×#6415911yescharacteristic
522C2#1059629311yescharacteristic
523C2#1059629911yescharacteristic
subgroupG/H
centerC2×C4C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#529C2
socleC22×C32C22×D4
prime radical#10592736C2
hypercenter#529C3⋊D3
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C32×#529C2semidirect
2. C4×#3828C2semidirect
3. #10592765C2semidirect
4. #10592762C2semidirect
5. #10592756C2semidirect
6. #10592753C2semidirect
7. #10592746C2semidirect
8. #10592744C2semidirect
10. #10592734C2semidirect
11. C4×#3756C2semidirect
12. C4×#3755C2semidirect
13. C4×#3754C2semidirect
14. C4×#3753C2semidirect
15. #10592624C2semidirect
60. C3×#529D3semidirect
205. #529C3⋊D3semidirect
450. C32#3102semidirect
517. C3#83140semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
C4×#38282
#105927652
#105927622
#105927562
#105927532
#105927462
#105927442
#105927362
#105927342
C4×#37562
C4×#37552
C4×#37542
C4×#37532
#105926242
#831403