Finite Group Databasebeta

← #11885808

Subgroups — #11885808

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×#64121C211yesmaximal, characteristic, complemented
2C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
3#10596025C212yesmaximal, complemented
4C32×C4×D8C211yesmaximal, characteristic, complemented
5#10592715C212yesmaximal, complemented
6#10592586C211yesmaximal, characteristic, complemented
7#10592582C211yesmaximal, characteristic, complemented
8#10592480C212yesmaximal, complemented
9#10592475C212yesmaximal, complemented
10#10592395C211yesmaximal, characteristic, complemented
11C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
12#79606—34nomaximal
13C2×#3830C2212yescomplemented
14C2×D4×C3⋊D3C2212yes—
15C2×C32×D8C2211yescharacteristic
16C32×C4×D4C2212yescomplemented
17C2×#3754C2212yescomplemented
18C2×#3753C2212yes—
19#64139—22no—
20C2×#3752—22no—
21#64121—24no—
22D8×C3⋊D3—24no—
23C2×#3746C2211yescharacteristic, complemented
24C2×#3745C2211yescharacteristic
25C2×#3744C2212yescomplemented
26C2×C8×C3⋊D3C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic, complemented
28#64106C2212yes—
29#64104C2212yescomplemented
30#64095—22no—
31#64091—22no—
32#64084C2212yescomplemented
33C4×C4⋊(C3⋊D3)C2211yescharacteristic
34C32×#107C2211yescharacteristic, complemented
35C32×#102C2212yescomplemented
36C32×C4×C8C2211yescharacteristic, complemented
37#63647C2211yescharacteristic
38#63647C2211yescharacteristic, complemented
39#63637C2212yescomplemented
40#63636C2212yescomplemented
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
42C2×#912—34no—
43C2×D3×D8—34no—
44#5554—38no—
45C3×C4×D8D314yescomplemented
46#5016—38no—
47#4887—34no—
48#4883—34no—
49#4781—38no—
50#4776—38no—
51#4696—34no—
52C8×D12—34no—
53C23×C3⋊D3—22no—
54C2×C32×D4C2312yes—
55C22×C32×C4—22no—
56C2×#638—22no—
57C2×#638—22no—
58C22×C3⋊Dic3—22no—
59#3830—24no—
60#3830—42no—
61D4×C3⋊D3—24no—
62D4×C3⋊D3—42no—
63C2×C4⋊(C3⋊D3)—22no—
64C2×C4⋊(C3⋊D3)D411yescharacteristic
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C4×C3⋊D3C2311yescharacteristic
68C2×#634C2312yes—
69C32×D8D414yescomplemented
70C2×C32×C8C2311yescharacteristic
71C2×C32×C8C2311yescharacteristic
72C32×C4⋊C4C2312yes—
73C32×C22⋊C4—22no—
74C32×C42C2311yescharacteristic
75#3754—24no—
76#3753—24no—
77#3752—22no—
78#3752—22no—
79#3752—22no—
80#3752—22no—
81#3752D411yescharacteristic
82#3752D411yescharacteristic
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)D411yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87#3746—22no—
88#3745—22no—
89#3744—42no—
90C8×C3⋊D3—22no—
91C8×C3⋊D3—22no—
92#3280—91noSylow
93C2×#237—38no—
94C2×D3×D4—38no—
95C2×C3×D8C2×D314yes—
96C3×C4×D4C2×D318yescomplemented
97C2×#214—38no—
98C2×#213—38no—
99#930—68no—
100C2×(C2×D3)⋊C4—68no—
101#912—616no—
102D3×D8—616no—
103C2×Dic12—34no—
104C2×D24—34no—
105C2×#204—38no—
106C2×D3×C8—34no—
107C2×D3×C8—34no—
108#897—38no—
109#895—38no—
110#886—68no—
111#882—68no—
112#875—38no—
113C4×D12—34no—
114C3×#107C2×D314yescomplemented
115C3×#102C2×D318yescomplemented
116C3×C4×C8C2×D314yescomplemented
117(C2×D3)⋊C8—34no—
118(C2×D3)⋊C8—34no—
119#810—38no—
120#809—38no—
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×D4—22no—
130C32×D4C2×D414yes—
131C2×C32×C4—22no—
132C2×C32×C4—82no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2411yescharacteristic
136#638—44no—
137#638—44no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—44no—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—82no—
146C4×C3⋊D3—21no—
147C4×C3⋊D3—21no—
148C4×C3⋊D3—21no—
149C4×C3⋊D3—21no—
150#634—22no—
151#634—22no—
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#467—91no—
161#466—91no—
162#463—92no—
163#450—92no—
164#449—92no—
165C4×D8C3⋊D311yescharacteristic, complemented
166C8×D4—91no—
167C23×D3—68no—
168C2×C3×D4C22×D318yes—
169C22×C3×C4—28no—
170C2×#67—68no—
171C2×#67—68no—
172C22×Dic3—68no—
173#237—616no—
174#237—128no—
175D3×D4—616no—
176D3×D4—128no—
177C2×D12—34no—
178C2×D12—38no—
179C2×D12—68no—
180C2×C4×D3—34no—
181C2×C4×D3—34no—
182C2×Dic6—38no—
183C3×D8D12116yescomplemented
184C2×C3×C8C22×D314yes—
185C2×C3×C8C22×D314yes—
186C3×C4⋊C4C22×D318yes—
187C3×C22⋊C4—28no—
188C3×C42C22×D314yes—
189#214—616no—
190#213—616no—
191(C2×D3)⋊C4—34no—
192(C2×D3)⋊C4—34no—
193(C2×D3)⋊C4—68no—
194(C2×D3)⋊C4—68no—
195(C2×D3)⋊C4—68no—
196(C2×D3)⋊C4—68no—
197C4⋊Dic3—34no—
198C4⋊Dic3—68no—
199C2×C3⋊C8—34no—
200C2×C3⋊C8—34no—
201Dic12—68no—
202D24—68no—
203#204—128no—
204D3×C8—68no—
205D3×C8—68no—
206C22×C32—24no—
207C22×C32—42no—
208C22×C32—42no—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—21no—
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3—21no—
214C2×C3⋊D3—21no—
215C2×C3⋊D3—42no—
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×Q16—91no—
232C2×SD16—92no—
233C2×SD16—92no—
234C2×D8—92no—
235C2×D8—91no—
236C2×D8—184no—
237C2×D8C2×C3⋊D311yescharacteristic
238C22×C8—91no—
239C22×C8—91no—
240#124—92no—
241#123—182no—
242C22⋊Q8—92no—
243#121—92no—
244#121—182no—
245#120—182no—
246C4×D4—91no—
247C4×D4C2×C3⋊D312yescomplemented
248C2×C22⋊C4—182no—
249#107C2×C3⋊D311yescharacteristic, complemented
250C4⋊C8—91no—
251#103—92no—
252#102—92no—
253#102C2×C3⋊D312yescomplemented
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×D4—28no—
265C3×D4C2×D12116yes—
266C2×C3×C4—28no—
267C2×C3×C4—88no—
268C2×C3×C4D3×D414yes—
269C2×C3×C4D3×D414yes—
270C2×C3×C4C23×D314yes—
271#67—1216no—
272#67—1216no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—68no—
276C2×Dic3—1216no—
277D12—68no—
278D12—68no—
279D12—68no—
280D12—248no—
281C4×D3—64no—
282C4×D3—64no—
283C4×D3—64no—
284C4×D3—64no—
285Dic6—68no—
286Dic6—68no—
287C3×C8—24no—
288C3×C8C2×D1218yes—
289C3⋊C8—64no—
290C3⋊C8—64no—
291C2×C32—44no—
292C2×C32D4211yescharacteristic
293C2×C32C2×#13511yescharacteristic
294C2×C32#57611yescharacteristic
295C3⋊D3—22no—
296C3⋊D3—41no—
297C3⋊D3—82no—
298C24—182no—
299#41—184no—
300#41—362no—
301C2×Q8—92no—
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—22no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—182no—
314Q16—182no—
315SD16—184no—
316SD16—362no—
317D8—184no—
318D8—182no—
319D8C4⋊(C3⋊D3)14yescomplemented
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—182no—
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—
336C42C22×C3⋊D311yescharacteristic
337C22×C3—216no—
338C22×C3—48no—
339C22×C3—48no—
340C22×C3C2×D3×D414yes—
341C2×D3—38no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—64no—
347C2×D3—128no—
348C2×D3—128no—
349C2×D3—128no—
350C2×D3—2432no—
351C3×C4—24no—
352C3×C4—24no—
353C3×C4—48no—
354C3×C4C22×D1214yes—
355C3×C4#100914yes—
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—182no—
368Q8—182no—
369D4—22no—
370D4—182no—
371D4—182no—
372D4—182no—
373D4—364no—
374D4—364no—
375D4—722no—
376D4C2×C4⋊(C3⋊D3)14yes—
377C2×C4—22no—
378C2×C4—82no—
379C2×C4—91no—
380C2×C4—91no—
381C2×C4—181no—
382C2×C4—181no—
383C2×C4—181no—
384C2×C4—181no—
385C2×C4—182no—
386C2×C4—364no—
387C2×C4D4×C3⋊D311yescharacteristic
388C2×C4D4×C3⋊D311yescharacteristic
389C2×C4C23×C3⋊D311yescharacteristic
390C8—21no—
391C8—181no—
392C8—181no—
393C8C2×C4⋊(C3⋊D3)12yes—
394C2×C3—416no—
395C2×C3D4×D1214yes—
396C2×C3#575714yes—
397C2×C3D3×#13514yes—
398D3—68no—
399D3—124no—
400D3—248no—
401C22—24no—
402C22—42no—
403C22—42no—
404C22—92no—
405C22—181no—
406C22—181no—
407C22—181no—
408C22—181no—
409C22—181no—
410C22—362no—
411C22—362no—
412C22—362no—
413C22—728no—
414C22C2×D4×C3⋊D311yescharacteristic
415C4—21no—
416C4—21no—
417C4—42no—
418C4—181no—
419C4—181no—
420C4—362no—
421C4C22×C4⋊(C3⋊D3)11yescharacteristic
422C4#6436611yescharacteristic
423C3#7960614yescomplemented
424C2—44no—
425C2—182no—
426C2—361no—
427C2—722no—
428C2D4×C4⋊(C3⋊D3)11yescharacteristic
429C2#1059622811yescharacteristic
430C2C3⋊D3×#13511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
hypercenterC4×D8C3⋊D3
hypocenterC32#3280
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64121C2semidirect
2. C2×D8×C3⋊D3C2semidirect
3. #10596025C2semidirect
4. C32×C4×D8C2semidirect
5. #10592715C2semidirect
6. #10592586C2semidirect
7. #10592582C2semidirect
8. #10592480C2semidirect
9. #10592475C2semidirect
10. #10592395C2semidirect
11. C8×C4⋊(C3⋊D3)C2semidirect
13. C2×#3830C22semidirect
16. C32×C4×D4C22semidirect
17. C2×#3754C22semidirect
23. C2×#3746C22semidirect
25. C2×#3744C22semidirect
27. C2×C8×C3⋊D3C22semidirect
29. #64104C22semidirect
32. #64084C22semidirect
34. C32×#107C22semidirect
35. C32×#102C22semidirect
36. C32×C4×C8C22semidirect
38. #63647C22semidirect
39. #63637C22semidirect
40. #63636C22semidirect
41. C4⋊(C3⋊(C3⋊C8))C22semidirect
45. C3×C4×D8D3semidirect
69. C32×D8D4semidirect
96. C3×C4×D4C2×D3semidirect
114. C3×#107C2×D3semidirect
115. C3×#102C2×D3semidirect
116. C3×C4×C8C2×D3semidirect
165. C4×D8C3⋊D3semidirect
183. C3×D8D12semidirect
219. C2×C3⋊D3#135semidirect
247. C4×D4C2×C3⋊D3semidirect
249. #107C2×C3⋊D3semidirect
253. #102C2×C3⋊D3semidirect
256. C4×C8C2×C3⋊D3semidirect
319. D8C4⋊(C3⋊D3)semidirect
359. C32#3280semidirect
423. C3#79606semidirect

Maximal subgroups

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

subgroupindex
C2×#641212
C2×D8×C3⋊D32
#105960252
C32×C4×D82
#105927152
#105925862
#105925822
#105924802
#105924752
#105923952
C8×C4⋊(C3⋊D3)2
#796063