Finite Group Databasebeta

← #11870408

Subgroups — #11870408

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596067C211yesmaximal, characteristic, complemented
2C2×#64102C211yesmaximal, characteristic, complemented
3C32×#480C211yesmaximal, characteristic, complemented
4#10592735C211yesmaximal, characteristic, complemented
5#10592666C211yesmaximal, characteristic, complemented
6#10592589C212yesmaximal, complemented
7#10592571C212yesmaximal, complemented
8#10592485C212yesmaximal, complemented
9#10592455C212yesmaximal, complemented
10#10592431C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#81268—34nomaximal
13C2×#3830—21no—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3—21no—
16C32×#121C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18#64149C2211yescharacteristic, complemented
19#64148—21no—
20D4×C3⋊Dic3C2211yescharacteristic, complemented
21C2×#3753C2212yes—
22#64139C2211yescharacteristic
23C2×#3752—21no—
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×#3745C2212yes—
26#64102—21no—
27#64102—21no—
28#64102C2212yes—
29#64102C2212yes—
30#64102C2211yescharacteristic, complemented
31#64097C2211yescharacteristic, complemented
32#64094—21no—
33#64090—21no—
34C32×#107C2212yescomplemented
35C32×#102C2212yescomplemented
36C32×C22⋊C8C2211yescharacteristic
37#63657C2211yescharacteristic
38#63648C2212yes—
39#63641C2212yescomplemented
40C8×C3⋊Dic3C2212yescomplemented
41#63636C2212yes—
42#63636C2212yescomplemented
43#63634C2212yescomplemented
44#5596—34no—
45C2×#893—34no—
46C3×#480D314yescomplemented
47#5036—34no—
48#4967—34no—
49#4890—38no—
50#4872—38no—
51#4786—38no—
52#4756—38no—
53#4732—34no—
54#4718—34no—
55C23×C3⋊D3—21no—
56C2×C32×D4—21no—
57C2×C32×D4C2311yescharacteristic
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61C2×#638—21no—
62C2×#638—21no—
63C22×C3⋊Dic3—21no—
64C22×C3⋊Dic3D411yescharacteristic
65C22×C3⋊Dic3D411yescharacteristic
66#3830—44no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—24no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—22no—
74C2×C4×C3⋊D3—44no—
75C2×#634—21no—
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C4⋊C4C2312yes—
80C32×C22⋊C4—21no—
81#3757—21no—
82#3753—24no—
83#3752—21no—
84#3752—21no—
85#3752—22no—
86#3752—22no—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—21no—
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C2×C3⋊(C3⋊C8)C2312yes—
94#3745—24no—
95#3100—91noSylow
96C2×#237—64no—
97C22×D12—34no—
98C22×C4×D3—64no—
99C3×#121C2×D314yes—
100C2×C3×C4⋊C4C2×D314yes—
101#940—34no—
102#939—64no—
103D4×Dic3—34no—
104C2×#213—38no—
105#930—34no—
106C2×(C2×D3)⋊C4—64no—
107C2×C4×Dic3—34no—
108C2×D24—38no—
109#893—34no—
110#893—38no—
111#893—38no—
112#893—64no—
113#893—64no—
114#888—34no—
115#885—64no—
116#67⋊C4—64no—
117C3×#107C2×D318yescomplemented
118C3×#102C2×D318yescomplemented
119C3×C22⋊C8C2×D314yes—
120#830—34no—
121#821—38no—
122Dic3⋊C8—38no—
123C8×Dic3—38no—
124#809—38no—
125#809—38no—
126#807—38no—
127C23×C32—21no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—24no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—42no—
133C22×C3⋊D3—42no—
134C32×D4—22no—
135C32×D4—42no—
136C2×C32×C4—22no—
137C2×C32×C4—21no—
138C2×C32×C4—22no—
139C2×C32×C4—42no—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2411yescharacteristic
142#638—42no—
143#638—42no—
144#638—42no—
145C2×C3⋊Dic3—21no—
146C2×C3⋊Dic3—41no—
147C2×C3⋊Dic3—42no—
148C2×C3⋊Dic3D814yescomplemented
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153C4⋊(C3⋊D3)—24no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)#4114yescomplemented
157C4×C3⋊D3—44no—
158C4×C3⋊D3—44no—
159C4×C3⋊D3—42no—
160#634—42no—
161C32×C8—22no—
162C3⋊(C3⋊C8)—22no—
163#532—91no—
164C2×C4×D4—91no—
165#480—91no—
166#480C3⋊D311yescharacteristic, complemented
167#474—92no—
168#459—92no—
169#447—91no—
170#447—91no—
171C4×D8—92no—
172C4×D8—92no—
173#431—91no—
174C23×D3—64no—
175C2×C3×D4—24no—
176C2×C3×D4C22×D314yes—
177C22×C3×C4—24no—
178C22×C3×C4C22×D314yes—
179C2×#67—64no—
180C2×#67—64no—
181C2×#67—64no—
182C22×Dic3—34no—
183C22×Dic3—34no—
184C22×Dic3—64no—
185#237—1216no—
186C2×D12—38no—
187C2×D12—34no—
188C2×D12—616no—
189C2×D12—64no—
190C2×C4×D3—64no—
191C2×C4×D3—68no—
192C2×C4×D3—68no—
193C2×C4×D3—1216no—
194C2×Dic6—64no—
195C2×C3×C8C22×D318yes—
196C3×C4⋊C4—24no—
197C3×C4⋊C4C22×D318yes—
198C3×C4⋊C4C22×D314yes—
199C3×C22⋊C4—24no—
200#217—64no—
201#213—616no—
202(C2×D3)⋊C4—64no—
203(C2×D3)⋊C4—68no—
204(C2×D3)⋊C4—68no—
205(C2×D3)⋊C4—64no—
206C4⋊Dic3—34no—
207Dic3⋊C4—64no—
208C4×Dic3—34no—
209C4×Dic3—34no—
210C4×Dic3—34no—
211C4×Dic3—34no—
212C2×C3⋊C8—38no—
213D24—616no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32C2×D812yes—
220C22×C32C22×D411yescharacteristic
221C2×C3⋊D3—24no—
222C2×C3⋊D3—48no—
223C2×C3⋊D3—42no—
224C2×C3⋊D3—42no—
225C2×C3⋊D3—41no—
226C2×C3⋊D3—41no—
227C2×C3⋊D3—41no—
228C32×C4—21no—
229C32×C4—41no—
230C32×C4—42no—
231C32×C4C2×#4112yes—
232C3⋊Dic3—21no—
233C3⋊Dic3—21no—
234C3⋊Dic3—41no—
235C3⋊Dic3C2×D812yes—
236C3⋊Dic3C2×D812yes—
237C2×#41—181no—
238C22×D4—91no—
239C23×C4—181no—
240C2×D8—92no—
241C2×D8—92no—
242C4⋊Q8—91no—
243#127—91no—
244#124—181no—
245#121—91no—
246#121—181no—
247#121C2×C3⋊D311yescharacteristic
248C4×D4—91no—
249C4×D4—92no—
250C4×D4—92no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254C4×D4—181no—
255C2×C4⋊C4C2×C3⋊D311yescharacteristic
256C2×C22⋊C4—181no—
257C2×C42—91no—
258#107—92no—
259#107C2×C3⋊D312yescomplemented
260C4⋊C8—92no—
261#102—92no—
262#102—92no—
263#102—92no—
264#102C2×C3⋊D312yescomplemented
265C22⋊C8—91no—
266C22⋊C8C2×C3⋊D311yescharacteristic
267C4×C8—92no—
268C23×C3—24no—
269C23×C3D3×D414yes—
270C22×D3—616no—
271C22×D3—68no—
272C22×D3—64no—
273C22×D3—128no—
274C22×D3—128no—
275C3×D4—28no—
276C3×D4—48no—
277C2×C3×C4—28no—
278C2×C3×C4—24no—
279C2×C3×C4—28no—
280C2×C3×C4—48no—
281C2×C3×C4D3×D414yes—
282C2×C3×C4C23×D314yes—
283#67—128no—
284#67—128no—
285#67—128no—
286C2×Dic3—316no—
287C2×Dic3—34no—
288C2×Dic3—34no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—64no—
292C2×Dic3—128no—
293C2×Dic3—124no—
294D12—316no—
295D12—616no—
296D12—68no—
297D12—68no—
298C4×D3—1216no—
299C4×D3—1216no—
300C4×D3—128no—
301Dic6—128no—
302C3×C8—28no—
303C3⋊C8—68no—
304C2×C32—22no—
305C2×C32—81no—
306C2×C32#52511yescharacteristic
307C2×C32C22×D811yescharacteristic
308C2×C32#57511yescharacteristic
309C3⋊D3—44no—
310C3⋊D3—81no—
311C24—181no—
312#41—364no—
313C2×Q8—181no—
314C2×D4—21no—
315C2×D4—92no—
316C2×D4—91no—
317C2×D4—184no—
318C2×D4—181no—
319C2×D4—181no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4C22×C3⋊D311yescharacteristic
323C22×C4—21no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—182no—
327C22×C4—182no—
328C22×C4—181no—
329C22×C4—181no—
330C22×C4—364no—
331C22×C4C22×C3⋊D311yescharacteristic
332D8—184no—
333D8—184no—
334C2×C8—92no—
335C2×C8C22×C3⋊D312yes—
336C4⋊C4—21no—
337C4⋊C4—91no—
338C4⋊C4—181no—
339C4⋊C4C22×C3⋊D311yescharacteristic
340C4⋊C4C22×C3⋊D312yes—
341C22⋊C4—21no—
342C22⋊C4—182no—
343C22⋊C4—182no—
344C22⋊C4—181no—
345C22⋊C4—181no—
346C22⋊C4—181no—
347C42—91no—
348C42—91no—
349C42—91no—
350C42—91no—
351C22×C3—24no—
352C22×C3—24no—
353C22×C3—44no—
354C22×C3—44no—
355C22×C3—44no—
356C22×C3D3×D818yes—
357C22×C3C2×D3×D414yes—
358C2×D3—616no—
359C2×D3—1232no—
360C2×D3—128no—
361C2×D3—128no—
362C2×D3—124no—
363C2×D3—124no—
364C2×D3—124no—
365C3×C4—24no—
366C3×C4—44no—
367C3×C4—48no—
368C3×C4D3×#4118yes—
369Dic3—38no—
370Dic3—38no—
371Dic3—64no—
372Dic3—64no—
373Dic3—124no—
374C32#310011yescharacteristic, complemented, Sylow
375C23—21no—
376C23—184no—
377C23—182no—
378C23—181no—
379C23—362no—
380C23—362no—
381C23D4×C3⋊D311yescharacteristic
382Q8—362no—
383D4—22no—
384D4—42no—
385D4—94no—
386D4—184no—
387D4—182no—
388D4—182no—
389D4—362no—
390D4—362no—
391D4—362no—
392C2×C4—22no—
393C2×C4—21no—
394C2×C4—22no—
395C2×C4—42no—
396C2×C4—91no—
397C2×C4—91no—
398C2×C4—94no—
399C2×C4—91no—
400C2×C4—91no—
401C2×C4—181no—
402C2×C4—364no—
403C2×C4—364no—
404C2×C4—362no—
405C2×C4—362no—
406C2×C4—361no—
407C2×C4D4×C3⋊D311yescharacteristic
408C2×C4C23×C3⋊D311yescharacteristic
409C8—22no—
410C8—182no—
411C2×C3—28no—
412C2×C3—84no—
413C2×C3#565614yes—
414C2×C3C2×D3×D814yes—
415C2×C3#577714yes—
416D3—1216no—
417D3—244no—
418C22—21no—
419C22—21no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—184no—
424C22—368no—
425C22—362no—
426C22—362no—
427C22—361no—
428C22—361no—
429C22—361no—
430C22D8×C3⋊D312yes—
431C22C2×D4×C3⋊D311yescharacteristic
432C4—21no—
433C4—42no—
434C4—41no—
435C4—92no—
436C4—92no—
437C4—181no—
438C4—181no—
439C4—361no—
440C4#41×C3⋊D312yes—
441C3#8126814yescomplemented
442C2—22no—
443C2—81no—
444C2—364no—
445C2—721no—
446C2#1059612711yescharacteristic
447C2C2×D8×C3⋊D311yescharacteristic
448C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#480C2
socleC22×C32C22×D4
hypercenter#480C3⋊D3
hypocenterC32#3100
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #10596067C2semidirect
2. C2×#64102C2semidirect
3. C32×#480C2semidirect
4. #10592735C2semidirect
5. #10592666C2semidirect
6. #10592589C2semidirect
7. #10592571C2semidirect
8. #10592485C2semidirect
9. #10592455C2semidirect
10. #10592431C2semidirect
11. #10592417C2semidirect
18. #64149C22semidirect
20. D4×C3⋊Dic3C22semidirect
30. #64102C22semidirect
31. #64097C22semidirect
34. C32×#107C22semidirect
35. C32×#102C22semidirect
39. #63641C22semidirect
40. C8×C3⋊Dic3C22semidirect
42. #63636C22semidirect
43. #63634C22semidirect
46. C3×#480D3semidirect
117. C3×#107C2×D3semidirect
118. C3×#102C2×D3semidirect
148. C2×C3⋊Dic3D8semidirect
156. C4⋊(C3⋊D3)#41semidirect
166. #480C3⋊D3semidirect
259. #107C2×C3⋊D3semidirect
264. #102C2×C3⋊D3semidirect
374. C32#3100semidirect
441. C3#81268semidirect

Maximal subgroups

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

subgroupindex
#105960672
C2×#641022
C32×#4802
#105927352
#105926662
#105925892
#105925712
#105924852
#105924552
#105924312
#105924172
#812683