Finite Group Databasebeta

← #11885802

Subgroups — #11885802

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
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596147C212yesmaximal, complemented
4C32×#495C211yesmaximal, characteristic, complemented
5#10592887C211yesmaximal, characteristic, complemented
6#10592871C212yesmaximal, complemented
7#10592868C212yesmaximal, complemented
8#10592856C211yesmaximal, characteristic, complemented
9#10592756C212yesmaximal, complemented
10C4×#3745C211yesmaximal, characteristic, complemented
11C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
12#81831—34nomaximal
13C2×#3832C2212yescomplemented
14C2×D4×C3⋊D3C2212yes—
15C2×C32×Q16C2211yescharacteristic, complemented
16C2×C32×SD16C2212yescomplemented
17C2×C32×D8C2211yescharacteristic
18C32×#124C2212yescomplemented
19#64155C2212yes—
20C2×#3755C2212yescomplemented
21#64147C2212yescomplemented
22C2×#3753C2212yes—
23#64128—24no—
24D8×C3⋊D3—24no—
25C2×#3745C2211yescharacteristic
26C2×C8×C3⋊D3C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28#64093—22no—
29#64092—22no—
30#64091—22no—
31C22⋊C4×C3⋊D3—22no—
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33C4×C4⋊(C3⋊D3)C2212yescomplemented
34C32×C4×C8C2211yescharacteristic, complemented
35#63662C2212yescomplemented
36#63659C2212yescomplemented
37#63648C2212yescomplemented
38#63647C2211yescharacteristic
39#63647C2211yescharacteristic, complemented
40#63645C2211yescharacteristic, complemented
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
42C2×#919—34no—
43C2×D3×D8—34no—
44#5676—38no—
45C3×#495D314yescomplemented
46#5188—34no—
47#5172—38no—
48#5169—38no—
49#5157—34no—
50#5057—38no—
51C4×D24—34no—
52C8×D12—34no—
53C23×C3⋊D3—22no—
54C2×C32×Q8C2312yes—
55C2×C32×D4C2312yes—
56C2×#638—22no—
57C2×#638—22no—
58#3832—24no—
59#3832—42no—
60D4×C3⋊D3—24no—
61D4×C3⋊D3—42no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)D411yescharacteristic
64C2×C4⋊(C3⋊D3)C2312yes—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C32×Q16—22no—
70C32×SD16—42no—
71C32×D8—22no—
72C2×C32×C8C2311yescharacteristic
73C2×C32×C8C2311yescharacteristic
74C32×C22⋊C4—22no—
75C32×C22⋊C4—22no—
76C32×C42C2311yescharacteristic
77#3757—22no—
78#3755—24no—
79#3753—24no—
80#3752—22no—
81#3752—22no—
82#3752D411yescharacteristic
83#3752D411yescharacteristic
84C4⋊(C3⋊Dic3)D411yescharacteristic
85C4⋊(C3⋊Dic3)C2312yes—
86#3750—22no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89#3745D414yescomplemented
90C8×C3⋊D3—22no—
91C8×C3⋊D3—22no—
92#3280—91noSylow
93C2×#239—38no—
94C2×D3×D4—38no—
95C2×C3×Q16C2×D314yescomplemented
96C2×C3×SD16C2×D318yescomplemented
97C2×C3×D8C2×D314yes—
98C3×#124C2×D318yescomplemented
99#946—38no—
100C2×#215—38no—
101#938—38no—
102C2×#213—38no—
103#919—616no—
104D3×D8—616no—
105C2×D24—34no—
106C2×D3×C8—34no—
107C2×D3×C8—34no—
108#884—68no—
109#883—68no—
110#882—68no—
111D3×C22⋊C4—68no—
112C4×D12—34no—
113C4×D12—38no—
114C3×C4×C8C2×D314yescomplemented
115#835—38no—
116#832—38no—
117#821—38no—
118(C2×D3)⋊C8—34no—
119(C2×D3)⋊C8—34no—
120#818—34no—
121C4⋊(C3⋊C8)—34no—
122C23×C32—22no—
123C22×C3⋊D3—22no—
124C22×C3⋊D3—44no—
125C22×C3⋊D3—44no—
126C22×C3⋊D3—82no—
127C22×C3⋊D3C2×D411yescharacteristic
128C22×C3⋊D3C2×D411yescharacteristic
129C32×Q8—22no—
130C32×Q8—22no—
131C32×D4—22no—
132C32×D4—22no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137#638—44no—
138#638—82no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—44no—
145C4⋊(C3⋊D3)C2×D414yes—
146C4×C3⋊D3—21no—
147C4×C3⋊D3—21no—
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#495C3⋊D311yescharacteristic, complemented
160#467—91no—
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—
169C2×C3×D4C22×D318yes—
170C2×#67—68no—
171C2×#67—68no—
172#239—616no—
173#239—128no—
174D3×D4—616no—
175D3×D4—128no—
176C2×D12—38no—
177C2×D12—34no—
178C2×D12—68no—
179C2×C4×D3—34no—
180C2×C4×D3—34no—
181C2×C4×D3—68no—
182C2×C4×D3—68no—
183C3×Q16—28no—
184C3×SD16—48no—
185C3×D8—28no—
186C2×C3×C8C22×D314yes—
187C2×C3×C8C22×D314yes—
188C3×C22⋊C4—28no—
189C3×C22⋊C4—28no—
190C3×C42C22×D314yes—
191#217—68no—
192#215—616no—
193#213—616no—
194(C2×D3)⋊C4—34no—
195(C2×D3)⋊C4—34no—
196(C2×D3)⋊C4—68no—
197(C2×D3)⋊C4—68no—
198C4⋊Dic3—34no—
199C4⋊Dic3—38no—
200Dic3⋊C4—68no—
201C2×C3⋊C8—34no—
202C2×C3⋊C8—34no—
203D24—316no—
204D3×C8—68no—
205D3×C8—68no—
206C22×C32—42no—
207C22×C32—42no—
208C22×C32—42no—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—21no—
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3—24no—
214C2×C3⋊D3—21no—
215C2×C3⋊D3—21no—
216C2×C3⋊D3—42no—
217C2×C3⋊D3—42no—
218C2×C3⋊D3—88no—
219C2×C3⋊D3#13512yescomplemented
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—42no—
223C32×C4C22×D411yescharacteristic
224C32×C4H(5,𝔽2)11yescharacteristic
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—42no—
228C2×#41—92no—
229C22×D4—92no—
230#135—184no—
231C2×Q16C2×C3⋊D311yescharacteristic, complemented
232C2×SD16—92no—
233C2×SD16C2×C3⋊D312yescomplemented
234C2×D8—92no—
235C2×D8—91no—
236C2×D8—184no—
237C2×D8C2×C3⋊D311yescharacteristic
238C22×C8—91no—
239C22×C8—91no—
240#124C2×C3⋊D312yescomplemented
241#123—182no—
242C22⋊Q8—92no—
243#121—92no—
244#121—182no—
245#120—182no—
246C4×D4—91no—
247C4×D4—92no—
248C2×C22⋊C4—182no—
249#107—91no—
250C4⋊C8—91no—
251#103—92no—
252#102—92no—
253#102—92no—
254C22⋊C8—91no—
255C22⋊C8—91no—
256C4×C8C2×C3⋊D311yescharacteristic, complemented
257C23×C3—28no—
258C22×D3—34no—
259C22×D3—34no—
260C22×D3—68no—
261C22×D3—1216no—
262C22×D3—1216no—
263C22×D3—248no—
264C3×Q8—28no—
265C3×Q8—28no—
266C3×D4—28no—
267C3×D4—28no—
268C2×C3×C4—28no—
269C2×C3×C4D3×D414yes—
270C2×C3×C4D3×D414yes—
271C2×C3×C4C23×D314yes—
272#67—1216no—
273#67—248no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—68no—
277D12—316no—
278D12—68no—
279D12—68no—
280D12—1216no—
281C4×D3—64no—
282C4×D3—64no—
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—82no—
292C2×C32D4211yescharacteristic
293C2×C32C2×#13511yescharacteristic
294C2×C32#57611yescharacteristic
295C3⋊D3—22no—
296C3⋊D3—41no—
297C3⋊D3—44no—
298C24—182no—
299#41—184no—
300#41—362no—
301C2×Q8C22×C3⋊D312yes—
302C2×D4—92no—
303C2×D4—91no—
304C2×D4—182no—
305C2×D4—182no—
306C2×D4—184no—
307C2×D4—182no—
308C2×D4—362no—
309C2×D4C22×C3⋊D312yes—
310C22×C4—91no—
311C22×C4—91no—
312C22×C4—182no—
313C22×C4—182no—
314Q16—22no—
315SD16—42no—
316SD16—184no—
317D8—22no—
318D8—94no—
319D8—184no—
320C2×C8—91no—
321C2×C8—91no—
322C2×C8—182no—
323C2×C8—182no—
324C2×C8C22×C3⋊D311yescharacteristic
325C2×C8C22×C3⋊D311yescharacteristic
326C4⋊C4—91no—
327C4⋊C4—92no—
328C4⋊C4—182no—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—91no—
332C22⋊C4—91no—
333C22⋊C4—182no—
334C22⋊C4—182no—
335C22⋊C4—182no—
336C42C22×C3⋊D311yescharacteristic
337C22×C3—48no—
338C22×C3—48no—
339C22×C3—48no—
340C22×C3C2×D3×D414yes—
341C2×D3—38no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—616no—
346C2×D3—64no—
347C2×D3—64no—
348C2×D3—128no—
349C2×D3—128no—
350C2×D3—2432no—
351C3×C4—24no—
352C3×C4—24no—
353C3×C4—48no—
354C3×C4C2×D3×D414yes—
355C3×C4#100414yes—
356Dic3—64no—
357Dic3—64no—
358Dic3—128no—
359C32#328011yescharacteristic, complemented, Sylow
360C23—22no—
361C23—91no—
362C23—91no—
363C23—182no—
364C23—364no—
365C23—364no—
366C23—722no—
367Q8—22no—
368Q8—22no—
369D4—22no—
370D4—22no—
371D4—94no—
372D4—182no—
373D4—182no—
374D4—364no—
375D4—364no—
376D4—722no—
377C2×C4—22no—
378C2×C4—91no—
379C2×C4—91no—
380C2×C4—181no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—182no—
385C2×C4—364no—
386C2×C4—722no—
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4C23×C3⋊D311yescharacteristic
390C8—21no—
391C8—181no—
392C8—181no—
393C8D4×C3⋊D312yes—
394C2×C3—88no—
395C2×C3#571714yes—
396C2×C3D3×#13514yes—
397C2×C3#576914yes—
398D3—68no—
399D3—124no—
400D3—1216no—
401C22—42no—
402C22—42no—
403C22—42no—
404C22—92no—
405C22—181no—
406C22—181no—
407C22—181no—
408C22—184no—
409C22—181no—
410C22—181no—
411C22—362no—
412C22—362no—
413C22—728no—
414C22C2×D4×C3⋊D311yescharacteristic
415C4—21no—
416C4—21no—
417C4—42no—
418C4—181no—
419C4—181no—
420C4—362no—
421C4C2×D4×C3⋊D311yescharacteristic
422C4#6436111yescharacteristic
423C3#8183114yescomplemented
424C2—82no—
425C2—182no—
426C2—361no—
427C2—364no—
428C2#1059618811yescharacteristic
429C2C3⋊D3×#13511yescharacteristic
430C2#1059624011yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#495C2
socleC22×C32C22×D4
hypercenter#495C3⋊D3
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#64128C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. #10596147C2semidirect
4. C32×#495C2semidirect
5. #10592887C2semidirect
6. #10592871C2semidirect
7. #10592868C2semidirect
8. #10592856C2semidirect
9. #10592756C2semidirect
10. C4×#3745C2semidirect
11. C8×C4⋊(C3⋊D3)C2semidirect
13. C2×#3832C22semidirect
15. C2×C32×Q16C22semidirect
16. C2×C32×SD16C22semidirect
18. C32×#124C22semidirect
20. C2×#3755C22semidirect
21. #64147C22semidirect
27. C2×C8×C3⋊D3C22semidirect
33. C4×C4⋊(C3⋊D3)C22semidirect
34. C32×C4×C8C22semidirect
35. #63662C22semidirect
36. #63659C22semidirect
37. #63648C22semidirect
39. #63647C22semidirect
40. #63645C22semidirect
41. C4⋊(C3⋊(C3⋊C8))C22semidirect
45. C3×#495D3semidirect
89. #3745D4semidirect
95. C2×C3×Q16C2×D3semidirect
96. C2×C3×SD16C2×D3semidirect
98. C3×#124C2×D3semidirect
114. C3×C4×C8C2×D3semidirect
159. #495C3⋊D3semidirect
219. C2×C3⋊D3#135semidirect
231. C2×Q16C2×C3⋊D3semidirect
233. C2×SD16C2×C3⋊D3semidirect
240. #124C2×C3⋊D3semidirect
256. C4×C8C2×C3⋊D3semidirect
359. C32#3280semidirect
423. C3#81831semidirect

Maximal subgroups

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

subgroupindex
C2×#641282
C2×D8×C3⋊D32
#105961472
C32×#4952
#105928872
#105928712
#105928682
#105928562
#105927562
C4×#37452
C8×C4⋊(C3⋊D3)2
#818313