Finite Group Databasebeta

← #11870858

Subgroups — #11870858

Order 1152.

1362 conjugacy classes of subgroups.

The subgroup lattice has 423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596095C211yesmaximal, characteristic, complemented
2C2×#64102C211yesmaximal, characteristic, complemented
3C32×#484C211yesmaximal, characteristic, complemented
4#10592745C211yesmaximal, characteristic, complemented
5#10592667C211yesmaximal, characteristic, complemented
6#10592590C212yesmaximal, complemented
7#10592571C212yesmaximal, complemented
8#10592518C212yesmaximal, complemented
9#10592487C212yesmaximal, complemented
10#10592431C211yesmaximal, characteristic
11#10592417C211yesmaximal, characteristic, complemented
12#81453—34nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C32×C22⋊Q8C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17#64156C2211yescharacteristic, complemented
18Q8×C3⋊Dic3C2211yescharacteristic, complemented
19C2×#3755C2212yes—
20#64139C2211yescharacteristic
21C2×#3752—21no—
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×#3745C2212yes—
24#64107—21no—
25#64102—21no—
26#64102—21no—
27#64102C2212yes—
28#64102C2212yes—
29#64102C2211yescharacteristic, complemented
30#64101—21no—
31#64099C2211yescharacteristic, complemented
32#64095—21no—
33#64090—21no—
34C32×#107C2212yescomplemented
35C32×#103C2212yescomplemented
36C32×C22⋊C8C2211yescharacteristic
37#63657C2211yescharacteristic
38#63648C2212yes—
39#63641C2212yescomplemented
40C8×C3⋊Dic3C2212yescomplemented
41#63636C2212yes—
42#63636C2212yescomplemented
43#63635C2212yescomplemented
44#5624—34no—
45C2×#893—34no—
46C3×#484D314yescomplemented
47#5046—34no—
48#4968—34no—
49#4891—38no—
50#4872—38no—
51#4819—38no—
52#4788—38no—
53#4732—34no—
54#4718—34no—
55C23×C3⋊D3—21no—
56C2×C32×Q8C2311yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60C22×C3⋊Dic3D411yescharacteristic
61C22×C3⋊Dic3D411yescharacteristic
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)—24no—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—21no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—44no—
70C2×C32×C8C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4—21no—
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2312yes—
75C32×C22⋊C4—21no—
76#3755—24no—
77#3752—21no—
78#3752—21no—
79#3752—21no—
80#3752—21no—
81#3752—22no—
82#3752—22no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86#3750—21no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93#3745—24no—
94#3105—91noSylow
95C22×D12—34no—
96C22×C4×D3—64no—
97C3×C22⋊Q8C2×D314yes—
98C2×C3×C4⋊C4C2×D314yes—
99#947—34no—
100Q8×Dic3—34no—
101C2×#215—38no—
102#930—34no—
103C2×(C2×D3)⋊C4—64no—
104C2×C4×Dic3—34no—
105C2×D24—38no—
106#898—64no—
107#893—34no—
108#893—38no—
109#893—38no—
110#893—64no—
111#893—64no—
112#892—64no—
113#890—34no—
114#886—64no—
115#67⋊C4—64no—
116C3×#107C2×D318yescomplemented
117C3×#103C2×D318yescomplemented
118C3×C22⋊C8C2×D314yes—
119#830—34no—
120#821—38no—
121Dic3⋊C8—38no—
122C8×Dic3—38no—
123#809—38no—
124#809—38no—
125#808—38no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—24no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—42no—
131C22×C3⋊D3—42no—
132C32×Q8—22no—
133C2×C32×C4—22no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—22no—
137C2×C32×C4—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140#638—42no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)#4114yes—
152C4×C3⋊D3—44no—
153C4×C3⋊D3—42no—
154C4×C3⋊D3—44no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157#529—91no—
158C2×C4×D4—91no—
159#484C3⋊D311yescharacteristic, complemented
160#481—91no—
161#478—92no—
162#463—92no—
163#450—91no—
164#447—91no—
165C4×SD16—92no—
166C4×D8—92no—
167#431—91no—
168C23×D3—64no—
169C2×C3×Q8C22×D314yes—
170C22×C3×C4—24no—
171C22×C3×C4C22×D314yes—
172C2×#67—64no—
173C22×Dic3—34no—
174C22×Dic3—34no—
175C2×D12—38no—
176C2×D12—34no—
177C2×D12—616no—
178C2×D12—64no—
179C2×C4×D3—64no—
180C2×C4×D3—68no—
181C2×C4×D3—68no—
182C2×C4×D3—1216no—
183C2×C3×C8C22×D318yes—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—24no—
186C3×C4⋊C4C22×D318yes—
187C3×C4⋊C4C22×D314yes—
188C3×C22⋊C4—24no—
189#215—616no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193(C2×D3)⋊C4—68no—
194(C2×D3)⋊C4—68no—
195(C2×D3)⋊C4—64no—
196C4⋊Dic3—34no—
197C4⋊Dic3—64no—
198C4⋊Dic3—64no—
199Dic3⋊C4—64no—
200C4×Dic3—34no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—64no—
205C2×C3⋊C8—38no—
206D24—616no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32#13512yes—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—24no—
212C2×C3⋊D3—48no—
213C2×C3⋊D3—42no—
214C2×C3⋊D3—42no—
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—42no—
221C32×C4—41no—
222C32×C4C2×#4112yes—
223C3⋊Dic3—21no—
224C3⋊Dic3—21no—
225C3⋊Dic3—21no—
226C3⋊Dic3—41no—
227C3⋊Dic3AGL(1,ℤ/8)12yes—
228C22×D4—91no—
229C23×C4—181no—
230C2×SD16—92no—
231C2×D8—92no—
232#126—181no—
233#125—91no—
234#124—91no—
235#123—181no—
236C22⋊Q8C2×C3⋊D311yescharacteristic
237#121—91no—
238C4×Q8—91no—
239C4×D4—92no—
240C4×D4—92no—
241C4×D4—91no—
242C4×D4—181no—
243C4×D4—181no—
244C4×D4—181no—
245#117—181no—
246C2×C4⋊C4C2×C3⋊D311yescharacteristic
247C2×C22⋊C4—181no—
248C2×C42—91no—
249#107C2×C3⋊D312yescomplemented
250#106—92no—
251C4⋊C8—92no—
252#103C2×C3⋊D312yescomplemented
253#102—92no—
254#102—92no—
255#102—92no—
256C22⋊C8—91no—
257C22⋊C8C2×C3⋊D311yescharacteristic
258C4×C8—92no—
259C23×C3D3×D414yes—
260C22×D3—616no—
261C22×D3—68no—
262C22×D3—64no—
263C22×D3—128no—
264C22×D3—128no—
265C3×Q8—28no—
266C2×C3×C4—28no—
267C2×C3×C4—24no—
268C2×C3×C4—24no—
269C2×C3×C4—28no—
270C2×C3×C4—48no—
271C2×C3×C4D3×D414yes—
272C2×C3×C4C23×D314yes—
273#67—128no—
274C2×Dic3—34no—
275C2×Dic3—34no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—68no—
279C2×Dic3—68no—
280C2×Dic3—64no—
281D12—316no—
282D12—616no—
283D12—68no—
284D12—68no—
285C4×D3—128no—
286C4×D3—1216no—
287C4×D3—1216no—
288C3×C8—28no—
289C3⋊C8—68no—
290C2×C32—22no—
291C2×C32#52511yescharacteristic
292C2×C32C2×#13511yescharacteristic
293C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
294C3⋊D3—44no—
295C3⋊D3—81no—
296C24—181no—
297C2×Q8C22×C3⋊D311yescharacteristic
298C2×D4—92no—
299C2×D4—91no—
300C2×D4—184no—
301C2×D4—181no—
302C2×D4—181no—
303C22×C4—21no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—181no—
307C22×C4—182no—
308C22×C4—182no—
309C22×C4—364no—
310C22×C4C22×C3⋊D311yescharacteristic
311SD16—184no—
312D8—184no—
313C2×C8—92no—
314C2×C8C22×C3⋊D312yes—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—91no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4C22×C3⋊D311yescharacteristic
322C4⋊C4C22×C3⋊D312yes—
323C22⋊C4—21no—
324C22⋊C4—182no—
325C22⋊C4—182no—
326C22⋊C4—181no—
327C22⋊C4—181no—
328C22⋊C4—181no—
329C22⋊C4—181no—
330C42—91no—
331C42—91no—
332C42—91no—
333C42—91no—
334C42—181no—
335C22×C3—24no—
336C22×C3—24no—
337C22×C3#91918yes—
338C22×C3C2×D3×D414yes—
339C2×D3—616no—
340C2×D3—1232no—
341C2×D3—128no—
342C2×D3—128no—
343C2×D3—124no—
344C2×D3—124no—
345C2×D3—124no—
346C3×C4—24no—
347C3×C4—44no—
348C3×C4—48no—
349C3×C4—44no—
350C3×C4D3×#4118yes—
351Dic3—38no—
352Dic3—64no—
353Dic3—64no—
354Dic3—64no—
355Dic3—124no—
356C32#310511yescharacteristic, complemented, Sylow
357C23—184no—
358C23—182no—
359C23—181no—
360C23—362no—
361C23—362no—
362C23D4×C3⋊D311yescharacteristic
363Q8—22no—
364D4—94no—
365D4—184no—
366D4—182no—
367D4—182no—
368D4—362no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4—181no—
381C2×C4—364no—
382C2×C4—362no—
383C2×C4—364no—
384C2×C4D4×C3⋊D311yescharacteristic
385C2×C4C23×C3⋊D311yescharacteristic
386C8—22no—
387C8—182no—
388C2×C3—28no—
389C2×C3#565614yes—
390C2×C3C2×#91914yes—
391C2×C3D3×AGL(1,ℤ/8)14yes—
392D3—1216no—
393D3—244no—
394C22—21no—
395C22—21no—
396C22—184no—
397C22—368no—
398C22—362no—
399C22—362no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22#6412812yes—
404C22C2×D4×C3⋊D311yescharacteristic
405C4—21no—
406C4—41no—
407C4—42no—
408C4—41no—
409C4—92no—
410C4—181no—
411C4—181no—
412C4—181no—
413C4—361no—
414C4#41×C3⋊D312yes—
415C3#8145314yescomplemented
416C2—22no—
417C2—364no—
418C2—721no—
419C2#1059612711yescharacteristic
420C2C2×#6412811yescharacteristic
421C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#484C2
socleC22×C32C22×D4
prime radical#10592431C2
hypercenter#484C3⋊D3
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #10596095C2semidirect
2. C2×#64102C2semidirect
3. C32×#484C2semidirect
4. #10592745C2semidirect
5. #10592667C2semidirect
6. #10592590C2semidirect
7. #10592571C2semidirect
8. #10592518C2semidirect
9. #10592487C2semidirect
11. #10592417C2semidirect
17. #64156C22semidirect
18. Q8×C3⋊Dic3C22semidirect
29. #64102C22semidirect
31. #64099C22semidirect
34. C32×#107C22semidirect
35. C32×#103C22semidirect
39. #63641C22semidirect
40. C8×C3⋊Dic3C22semidirect
42. #63636C22semidirect
43. #63635C22semidirect
46. C3×#484D3semidirect
116. C3×#107C2×D3semidirect
117. C3×#103C2×D3semidirect
159. #484C3⋊D3semidirect
249. #107C2×C3⋊D3semidirect
252. #103C2×C3⋊D3semidirect
356. C32#3105semidirect
415. C3#81453semidirect

Maximal subgroups

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

subgroupindex
#105960952
C2×#641022
C32×#4842
#105927452
#105926672
#105925902
#105925712
#105925182
#105924872
#105924312
#105924172
#814533