Finite Group Databasebeta

← #11871317

Subgroups — #11871317

Order 1152.

1332 conjugacy classes of subgroups.

The subgroup lattice has 411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596093C211yesmaximal, characteristic, complemented
2C2×#64102C211yesmaximal, characteristic
3C32×#484C211yesmaximal, characteristic, complemented
4#10592745C211yesmaximal, characteristic
5#10592669C211yesmaximal, characteristic, complemented
6#10592589C212yesmaximal, complemented
7#10592588C212yesmaximal, complemented
8#10592517C212yesmaximal, complemented
9#10592516C212yesmaximal, complemented
10#10592430C211yesmaximal, characteristic
11#10592418C211yesmaximal, characteristic, complemented
12#81454—34nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C32×C22⋊Q8C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17Q8×C3⋊Dic3C2211yescharacteristic, complemented
18#64153C2211yescharacteristic, complemented
19C2×#3755C2212yes—
20C2×#3752—21no—
21#64133C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×#3744C2212yes—
24#64102—21no—
25#64102—21no—
26#64102C2212yes—
27#64102C2212yes—
28#64098—21no—
29#64097C2211yescharacteristic, complemented
30#64096—21no—
31#64096C2211yescharacteristic, complemented
32#64087—21no—
33#64086—21no—
34C32×#107C2212yescomplemented
35C32×#103C2212yescomplemented
36C32×C22⋊C8C2211yescharacteristic
37#63657C2211yescharacteristic
38#63648C2212yes—
39#63642C2212yescomplemented
40#63641C2212yescomplemented
41#63637C2212yescomplemented
42#63636C2212yes—
43#63634C2212yescomplemented
44#5622—34no—
45C2×#893—34no—
46C3×#484D314yescomplemented
47#5046—34no—
48#4970—34no—
49#4890—38no—
50#4889—38no—
51#4818—38no—
52#4817—38no—
53#4731—34no—
54#4719—34no—
55C23×C3⋊D3—21no—
56C2×C32×Q8C2311yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3D411yescharacteristic
60C22×C3⋊Dic3D411yescharacteristic
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)—24no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—44no—
67C2×#634—21no—
68C2×#634C2311yescharacteristic
69C2×C32×C8C2312yes—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2311yescharacteristic
73C32×C4⋊C4C2312yes—
74C32×C22⋊C4—21no—
75#3757—21no—
76#3755—24no—
77#3752—22no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82#3750—21no—
83#3750—21no—
84#3750—21no—
85#3750—21no—
86C4×C3⋊Dic3—21no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C4×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2312yes—
93#3744—24no—
94#3110—91noSylow
95C22×D12—34no—
96C22×C4×D3—64no—
97C3×C22⋊Q8C2×D314yes—
98C2×C3×C4⋊C4C2×D314yes—
99Q8×Dic3—34no—
100#944—34no—
101C2×#215—38no—
102C2×(C2×D3)⋊C4—64no—
103#924—34no—
104C2×C4×Dic3—34no—
105C2×#204—38no—
106#893—38no—
107#893—38no—
108#893—64no—
109#893—64no—
110#889—64no—
111#888—34no—
112#887—34no—
113#887—64no—
114#878—64no—
115#877—64no—
116C3×#107C2×D318yescomplemented
117C3×#103C2×D318yescomplemented
118C3×C22⋊C8C2×D314yes—
119#830—34no—
120#821—38no—
121#815—38no—
122Dic3⋊C8—38no—
123#810—38no—
124#809—38no—
125#807—38no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—24no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—42no—
130C22×C3⋊D3—42no—
131C32×Q8—22no—
132C2×C32×C4—22no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4—42no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C2×C3⋊Dic3C2×D411yescharacteristic
146C2×C3⋊Dic3C2×D411yescharacteristic
147C4⋊(C3⋊D3)—24no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)#4114yes—
150C4×C3⋊D3—44no—
151C4×C3⋊D3—44no—
152#634—22no—
153#634—42no—
154C32×C8—22no—
155C3⋊(C3⋊C8)—22no—
156#533—91no—
157C2×C4×D4—91no—
158#484—91no—
159#484C3⋊D311yescharacteristic, complemented
160#474—92no—
161#461—92no—
162#450—91no—
163#450—91no—
164#440—92no—
165#440—92no—
166#432—91no—
167C23×D3—64no—
168C2×C3×Q8C22×D314yes—
169C22×C3×C4—24no—
170C22×C3×C4C22×D314yes—
171C22×Dic3—34no—
172C22×Dic3—34no—
173C2×D12—38no—
174C2×D12—616no—
175C2×D12—64no—
176C2×C4×D3—68no—
177C2×C4×D3—68no—
178C2×C4×D3—1216no—
179C2×Dic6—34no—
180C2×Dic6—64no—
181C2×C3×C8C22×D318yes—
182C3×C4⋊C4—24no—
183C3×C4⋊C4—24no—
184C3×C4⋊C4C22×D318yes—
185C3×C4⋊C4C22×D314yes—
186C3×C22⋊C4—24no—
187#217—64no—
188#215—616no—
189(C2×D3)⋊C4—68no—
190(C2×D3)⋊C4—68no—
191C4⋊Dic3—34no—
192C4⋊Dic3—64no—
193Dic3⋊C4—64no—
194Dic3⋊C4—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198C4×Dic3—34no—
199C4×Dic3—34no—
200C4×Dic3—34no—
201C4×Dic3—34no—
202C4×Dic3—64no—
203C4×Dic3—64no—
204C2×C3⋊C8—38no—
205#204—616no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#13712yes—
209C22×C32C22×D411yescharacteristic
210C2×C3⋊D3—24no—
211C2×C3⋊D3—48no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3—42no—
214C32×C4—21no—
215C32×C4—41no—
216C32×C4—41no—
217C32×C4—42no—
218C32×C4C2×#4112yes—
219C3⋊Dic3—21no—
220C3⋊Dic3—21no—
221C3⋊Dic3—21no—
222C3⋊Dic3—41no—
223C3⋊Dic3—41no—
224C3⋊Dic3AGL(1,ℤ/8)12yes—
225C22×D4—91no—
226C23×C4—181no—
227C2×SD16—92no—
228C2×SD16—92no—
229C4⋊Q8—91no—
230C4⋊Q8—91no—
231#125—181no—
232C22⋊Q8—91no—
233C22⋊Q8—181no—
234C22⋊Q8C2×C3⋊D311yescharacteristic
235C4×Q8—91no—
236C4×Q8—91no—
237C4×Q8—181no—
238C4×D4—92no—
239C4×D4—92no—
240C4×D4—181no—
241C4×D4—181no—
242#117—181no—
243C2×C4⋊C4C2×C3⋊D311yescharacteristic
244C2×C22⋊C4—181no—
245C2×C42—91no—
246#107—92no—
247#107C2×C3⋊D312yescomplemented
248C4⋊C8—92no—
249#103—92no—
250#103C2×C3⋊D312yescomplemented
251#102—92no—
252#102—92no—
253C22⋊C8—91no—
254C22⋊C8C2×C3⋊D311yescharacteristic
255#97—92no—
256C23×C3D3×D414yes—
257C22×D3—616no—
258C22×D3—68no—
259C22×D3—128no—
260C22×D3—128no—
261C3×Q8—28no—
262C2×C3×C4—28no—
263C2×C3×C4—24no—
264C2×C3×C4—24no—
265C2×C3×C4—28no—
266C2×C3×C4—48no—
267C2×C3×C4D3×D414yes—
268C2×C3×C4C23×D314yes—
269C2×Dic3—34no—
270C2×Dic3—34no—
271C2×Dic3—34no—
272C2×Dic3—34no—
273C2×Dic3—68no—
274C2×Dic3—68no—
275C2×Dic3—64no—
276C2×Dic3—64no—
277D12—316no—
278D12—616no—
279D12—68no—
280C4×D3—1216no—
281C4×D3—1216no—
282Dic6—68no—
283Dic6—128no—
284C3×C8—28no—
285C3⋊C8—68no—
286C2×C32—22no—
287C2×C32#52511yescharacteristic
288C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
289C2×C32C2×#13711yescharacteristic
290C3⋊D3—44no—
291C24—181no—
292C2×Q8—91no—
293C2×Q8—181no—
294C2×Q8C22×C3⋊D311yescharacteristic
295C2×D4—92no—
296C2×D4—184no—
297C2×D4—181no—
298C22×C4—21no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—182no—
302C22×C4—182no—
303C22×C4—364no—
304C22×C4C22×C3⋊D311yescharacteristic
305SD16—184no—
306SD16—184no—
307C2×C8—92no—
308C2×C8C22×C3⋊D312yes—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—91no—
312C4⋊C4—181no—
313C4⋊C4—181no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4C22×C3⋊D311yescharacteristic
319C4⋊C4C22×C3⋊D312yes—
320C22⋊C4—21no—
321C22⋊C4—182no—
322C22⋊C4—182no—
323C22⋊C4—181no—
324C42—91no—
325C42—91no—
326C42—91no—
327C42—91no—
328C42—181no—
329C42—181no—
330C22×C3—24no—
331C22×C3—24no—
332C22×C3#91818yes—
333C22×C3C2×D3×D414yes—
334C2×D3—616no—
335C2×D3—1232no—
336C2×D3—128no—
337C2×D3—128no—
338C3×C4—24no—
339C3×C4—44no—
340C3×C4—44no—
341C3×C4—48no—
342C3×C4D3×#4118yes—
343Dic3—38no—
344Dic3—64no—
345Dic3—64no—
346Dic3—64no—
347Dic3—124no—
348Dic3—124no—
349C32#311011yescharacteristic, complemented, Sylow
350C23—184no—
351C23—182no—
352C23—362no—
353C23—362no—
354C23D4×C3⋊D311yescharacteristic
355Q8—22no—
356Q8—182no—
357Q8—362no—
358D4—94no—
359D4—184no—
360D4—182no—
361C2×C4—22no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—42no—
366C2×C4—91no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—364no—
375C2×C4—364no—
376C2×C4D4×C3⋊D311yescharacteristic
377C2×C4C23×C3⋊D311yescharacteristic
378C8—22no—
379C8—182no—
380C2×C3—28no—
381C2×C3#565614yes—
382C2×C3C2×#91814yes—
383C2×C3D3×AGL(1,ℤ/8)14yes—
384D3—1216no—
385C22—21no—
386C22—21no—
387C22—184no—
388C22—368no—
389C22—362no—
390C22—362no—
391C22#6412712yes—
392C22C2×D4×C3⋊D311yescharacteristic
393C4—21no—
394C4—41no—
395C4—42no—
396C4—41no—
397C4—92no—
398C4—181no—
399C4—181no—
400C4—181no—
401C4—361no—
402C4—361no—
403C4#41×C3⋊D312yes—
404C3#8145414yescomplemented
405C2—22no—
406C2—364no—
407C2#1059612711yescharacteristic
408C2C2×#6412711yescharacteristic
409C2C3⋊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 radicalC22×C4⋊(C3⋊D3)C22
hypercenter#484C3⋊D3
hypocenterC32#3110
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. #10596093C2semidirect
3. C32×#484C2semidirect
5. #10592669C2semidirect
6. #10592589C2semidirect
7. #10592588C2semidirect
8. #10592517C2semidirect
9. #10592516C2semidirect
11. #10592418C2semidirect
17. Q8×C3⋊Dic3C22semidirect
18. #64153C22semidirect
29. #64097C22semidirect
31. #64096C22semidirect
34. C32×#107C22semidirect
35. C32×#103C22semidirect
39. #63642C22semidirect
40. #63641C22semidirect
41. #63637C22semidirect
43. #63634C22semidirect
46. C3×#484D3semidirect
116. C3×#107C2×D3semidirect
117. C3×#103C2×D3semidirect
159. #484C3⋊D3semidirect
247. #107C2×C3⋊D3semidirect
250. #103C2×C3⋊D3semidirect
349. C32#3110semidirect
404. C3#81454semidirect

Maximal subgroups

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

subgroupindex
#105960932
C2×#641022
C32×#4842
#105927452
#105926692
#105925892
#105925882
#105925172
#105925162
#105924302
#105924182
#814543