Finite Group Databasebeta

← #11885796

Subgroups — #11885796

Order 1152.

1578 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64128C211yesmaximal, characteristic, complemented
2C22×#3745C211yesmaximal, characteristic, complemented
3#10596101C212yesmaximal, complemented
4C32×#467C211yesmaximal, characteristic, complemented
5#10592890C211yesmaximal, characteristic, complemented
6C8×#638C211yesmaximal, characteristic, complemented
7#10592745C212yesmaximal, complemented
8#10592582C211yesmaximal, characteristic, complemented
9#10592571C211yesmaximal, characteristic, complemented
10#10592518C212yesmaximal, complemented
11#10592509C212yesmaximal, complemented
12#80773—34nomaximal
13C2×#3832C2212yescomplemented
14C22×C4⋊(C3⋊D3)C2212yes—
15C2×C32×Q16C2211yescharacteristic, complemented
16C22×C32×C8C2211yescharacteristic
17C32×C22⋊Q8C2212yes—
18#64156C2212yescomplemented
19C2×#3755C2212yescomplemented
20C2×#3755C2212yescomplemented
21C4×#638C2211yescharacteristic
22#64128—24no—
23C2×#3745—24no—
24C2×#3745C2212yes—
25C2×#3745C2211yescharacteristic
26C2×#3745C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28#64104—22no—
29#64104C2212yescomplemented
30#64103—22no—
31#64102C2212yescomplemented
32#64091—22no—
33C22⋊C4×C3⋊D3—22no—
34C32×#107C2211yescharacteristic, complemented
35C32×#103C2212yescomplemented
36#63657C2211yescharacteristic
37#63647C2211yescharacteristic, complemented
38#63641C2211yescharacteristic, complemented
39C8×C3⋊Dic3C2211yescharacteristic, complemented
40#63636C2212yescomplemented
41#63636C2212yescomplemented
42C2×#919—34no—
43C22×D24—34no—
44#5630—38no—
45C3×#467D314yescomplemented
46#5191—34no—
47C8×#67—34no—
48#5046—38no—
49#4883—34no—
50#4872—34no—
51#4819—38no—
52#4810—38no—
53C23×C3⋊D3—22no—
54C2×C32×Q8C2312yes—
55C22×C32×C4C2311yescharacteristic
56C2×#638D411yescharacteristic
57#3832—24no—
58#3832—42no—
59C2×C4⋊(C3⋊D3)—24no—
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—42no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3C2311yescharacteristic
69C32×Q16—22no—
70C2×C32×C8—22no—
71C2×C32×C8C2311yescharacteristic
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4—22no—
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—22no—
76#3757D411yescharacteristic
77#3755—24no—
78#3755—42no—
79#3752—22no—
80#3752—22no—
81#3752—22no—
82#3752—22no—
83#3752D411yescharacteristic
84#3750D411yescharacteristic
85C4×C3⋊Dic3C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3745—24no—
89#3745—22no—
90#3745D414yescomplemented
91C8×C3⋊D3—22no—
92#3280—91noSylow
93C2×#239—38no—
94C22×D12—38no—
95C2×C3×Q16C2×D314yescomplemented
96C22×C3×C8C2×D314yes—
97C3×C22⋊Q8C2×D318yes—
98#947—38no—
99C2×#215—38no—
100C2×#215—38no—
101C4×#67—34no—
102#919—616no—
103C2×D24—34no—
104C2×D24—34no—
105C2×D24—38no—
106C2×D24—616no—
107C2×D3×C8—34no—
108#895—38no—
109#895—68no—
110#894—68no—
111#893—38no—
112#882—68no—
113D3×C22⋊C4—68no—
114C3×#107C2×D314yescomplemented
115C3×#103C2×D318yescomplemented
116#830—34no—
117(C2×D3)⋊C8—34no—
118Dic3⋊C8—34no—
119C8×Dic3—34no—
120#809—38no—
121#809—38no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—44no—
126C22×C3⋊D3—44no—
127C22×C3⋊D3—82no—
128C22×C3⋊D3C2×D411yescharacteristic
129C32×Q8—22no—
130C32×Q8—22no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137#638—22no—
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—44no—
145C4⋊(C3⋊D3)—44no—
146C4⋊(C3⋊D3)—82no—
147C4⋊(C3⋊D3)C2×D414yes—
148C4×C3⋊D3—21no—
149C4×C3⋊D3—21no—
150C4×C3⋊D3—44no—
151C4×C3⋊D3—82no—
152C32×C8—21no—
153C32×C8C2×D412yes—
154C3⋊(C3⋊C8)—21no—
155C3⋊(C3⋊C8)—21no—
156C2×#135—91no—
157C22×D8—91no—
158#546—92no—
159#495—91no—
160#467C3⋊D311yescharacteristic, complemented
161#466—91no—
162#463—92no—
163#450—92no—
164#449—92no—
165C4×D8—91no—
166C8×D4—91no—
167C23×D3—68no—
168C2×C3×Q8C22×D318yes—
169C22×C3×C4C22×D314yes—
170C2×#67—34no—
171#239—616no—
172#239—128no—
173C2×D12—38no—
174C2×D12—38no—
175C2×D12—616no—
176C2×D12—68no—
177C2×D12—68no—
178C2×D12—68no—
179C2×D12—128no—
180C2×C4×D3—34no—
181C2×C4×D3—68no—
182C2×C4×D3—68no—
183C3×Q16—28no—
184C2×C3×C8—28no—
185C2×C3×C8C22×D314yes—
186C2×C3×C8C22×D314yes—
187C3×C4⋊C4—28no—
188C3×C4⋊C4C22×D318yes—
189C3×C22⋊C4—28no—
190#217—34no—
191#215—616no—
192#215—128no—
193(C2×D3)⋊C4—34no—
194(C2×D3)⋊C4—68no—
195(C2×D3)⋊C4—68no—
196(C2×D3)⋊C4—68no—
197(C2×D3)⋊C4—68no—
198Dic3⋊C4—34no—
199C4×Dic3—34no—
200C2×C3⋊C8—34no—
201C2×C3⋊C8—34no—
202D24—316no—
203D24—616no—
204D24—68no—
205D3×C8—68no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#13512yescomplemented
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—21no—
211C2×C3⋊D3—24no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3—21no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—42no—
216C2×C3⋊D3—42no—
217C2×C3⋊D3—42no—
218C2×C3⋊D3—42no—
219C2×C3⋊D3—88no—
220C32×C4—21no—
221C32×C4—42no—
222C32×C4—42no—
223C32×C4C22×D411yescharacteristic
224C32×C4H(5,𝔽2)11yescharacteristic
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—21no—
228C2×#41—92no—
229C22×D4—92no—
230#135—184no—
231C2×Q16C2×C3⋊D311yescharacteristic, complemented
232C2×SD16—92no—
233C2×SD16—92no—
234C2×D8—91no—
235C2×D8—92no—
236C2×D8—91no—
237C2×D8—184no—
238C22×C8—91no—
239C22×C8C2×C3⋊D311yescharacteristic
240#124—92no—
241#123—182no—
242C22⋊Q8C2×C3⋊D312yes—
243#121—92no—
244#121—182no—
245#120—182no—
246C4×D4—91no—
247C4×D4—92no—
248C2×C22⋊C4—182no—
249#107C2×C3⋊D311yescharacteristic, complemented
250C4⋊C8—91no—
251#103C2×C3⋊D312yescomplemented
252#102—92no—
253#102—92no—
254C22⋊C8—91no—
255C22⋊C8—91no—
256C4×C8—91no—
257C23×C3D3×D414yes—
258C22×D3—34no—
259C22×D3—68no—
260C22×D3—68no—
261C22×D3—1216no—
262C22×D3—1216no—
263C22×D3—248no—
264C3×Q8—28no—
265C3×Q8—28no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4D3×D414yes—
271C2×C3×C4C23×D314yes—
272#67—68no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276D12—316no—
277D12—68no—
278D12—68no—
279D12—68no—
280D12—1216no—
281D12—1216no—
282D12—248no—
283C4×D3—64no—
284C4×D3—64no—
285C4×D3—1216no—
286C4×D3—248no—
287C3×C8—24no—
288C3×C8D3×D418yes—
289C3⋊C8—64no—
290C3⋊C8—64no—
291C2×C32—22no—
292C2×C32D4211yescharacteristic
293C2×C32C2×#13511yescharacteristic
294C2×C32#57611yescharacteristic
295C3⋊D3—41no—
296C3⋊D3—44no—
297C3⋊D3—82no—
298C24—182no—
299#41—184no—
300#41—362no—
301C2×Q8C22×C3⋊D312yes—
302C2×D4—91no—
303C2×D4—92no—
304C2×D4—92no—
305C2×D4—184no—
306C2×D4—182no—
307C2×D4—182no—
308C2×D4—182no—
309C2×D4—362no—
310C22×C4—91no—
311C22×C4—182no—
312C22×C4—182no—
313C22×C4C22×C3⋊D311yescharacteristic
314Q16—22no—
315SD16—184no—
316SD16—362no—
317D8—94no—
318D8—184no—
319D8—182no—
320C2×C8—22no—
321C2×C8—91no—
322C2×C8—91no—
323C2×C8—182no—
324C2×C8C22×C3⋊D311yescharacteristic
325C2×C8C22×C3⋊D311yescharacteristic
326C4⋊C4—22no—
327C4⋊C4—91no—
328C4⋊C4C22×C3⋊D312yes—
329C22⋊C4—22no—
330C22⋊C4—91no—
331C22⋊C4—91no—
332C22⋊C4—182no—
333C22⋊C4—182no—
334C22⋊C4—182no—
335C22⋊C4—182no—
336C42—91no—
337C22×C3—24no—
338C22×C3—24no—
339C22×C3#91918yescomplemented
340C22×C3C2×D3×D414yes—
341C2×D3—64no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—616no—
345C2×D3—128no—
346C2×D3—128no—
347C2×D3—128no—
348C2×D3—128no—
349C2×D3—128no—
350C2×D3—2432no—
351C3×C4—24no—
352C3×C4—48no—
353C3×C4—48no—
354C3×C4C2×D3×D414yes—
355C3×C4#100914yes—
356Dic3—64no—
357Dic3—64no—
358Dic3—64no—
359C32#328011yescharacteristic, complemented, Sylow
360C23—91no—
361C23—182no—
362C23—182no—
363C23—364no—
364C23—364no—
365C23—722no—
366C23D4×C3⋊D311yescharacteristic
367Q8—22no—
368Q8—22no—
369D4—94no—
370D4—182no—
371D4—182no—
372D4—182no—
373D4—182no—
374D4—364no—
375D4—364no—
376D4—722no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—91no—
382C2×C4—91no—
383C2×C4—91no—
384C2×C4—181no—
385C2×C4—181no—
386C2×C4—364no—
387C2×C4—722no—
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4C23×C3⋊D311yescharacteristic
390C8—21no—
391C8—181no—
392C8—181no—
393C8D4×C3⋊D312yes—
394C2×C3—28no—
395C2×C3#560914yes—
396C2×C3C2×#91914yes—
397C2×C3#576914yes—
398D3—124no—
399D3—1216no—
400D3—248no—
401C22—21no—
402C22—21no—
403C22—181no—
404C22—181no—
405C22—181no—
406C22—184no—
407C22—362no—
408C22—362no—
409C22—362no—
410C22—362no—
411C22—362no—
412C22—728no—
413C22#6412812yescomplemented
414C22C2×D4×C3⋊D311yescharacteristic
415C4—21no—
416C4—42no—
417C4—42no—
418C4—181no—
419C4—181no—
420C4—181no—
421C4C2×D4×C3⋊D311yescharacteristic
422C4#6436611yescharacteristic
423C3#8077314yescomplemented
424C2—22no—
425C2—361no—
426C2—364no—
427C2—722no—
428C2#1059608011yescharacteristic
429C2C2×#6412811yescharacteristic
430C2#1059624011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#467C2
socleC22×C32C22×D4
hypercenter#467C3⋊D3
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#64128C2semidirect
2. C22×#3745C2semidirect
3. #10596101C2semidirect
4. C32×#467C2semidirect
5. #10592890C2semidirect
6. C8×#638C2semidirect
7. #10592745C2semidirect
8. #10592582C2semidirect
9. #10592571C2semidirect
10. #10592518C2semidirect
11. #10592509C2semidirect
13. C2×#3832C22semidirect
15. C2×C32×Q16C22semidirect
18. #64156C22semidirect
19. C2×#3755C22semidirect
20. C2×#3755C22semidirect
27. C2×C8×C3⋊D3C22semidirect
29. #64104C22semidirect
31. #64102C22semidirect
34. C32×#107C22semidirect
35. C32×#103C22semidirect
37. #63647C22semidirect
38. #63641C22semidirect
39. C8×C3⋊Dic3C22semidirect
40. #63636C22semidirect
41. #63636C22semidirect
45. C3×#467D3semidirect
90. #3745D4semidirect
95. C2×C3×Q16C2×D3semidirect
114. C3×#107C2×D3semidirect
115. C3×#103C2×D3semidirect
160. #467C3⋊D3semidirect
208. C22×C32#135semidirect
231. C2×Q16C2×C3⋊D3semidirect
249. #107C2×C3⋊D3semidirect
251. #103C2×C3⋊D3semidirect
339. C22×C3#919semidirect
359. C32#3280semidirect
413. C22#64128semidirect
423. C3#80773semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
C22×#37452
#105961012
C32×#4672
#105928902
C8×#6382
#105927452
#105925822
#105925712
#105925182
#105925092
#807733