Finite Group Databasebeta

← #11882230

Subgroups — #11882230

Order 1152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596196C211yesmaximal, characteristic
2#10596049C211yesmaximal, characteristic, complemented
3C32×#475C211yesmaximal, characteristic, complemented
4#10592793C211yesmaximal, characteristic, complemented
5#10592726C211yesmaximal, characteristic, complemented
6#10592569C212yesmaximal, complemented
7#10592563C212yesmaximal, complemented
8#10592547C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
10#10592517C212yesmaximal, complemented
11#10592506C212yesmaximal, complemented
12#81002—34nomaximal
13C2×#3832—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64156—21no—
17#64155C2211yescharacteristic
18#64153C2211yescharacteristic
19C2×#3755C2212yes—
20C2×#3744C2212yes—
21C2×C8×C3⋊D3C2212yes—
22#64106C2211yescharacteristic
23#64105—21no—
24#64104—21no—
25#64104C2212yes—
26#64102—21no—
27#64102C2212yes—
28#64098—21no—
29#64097C2211yescharacteristic
30#64083C2211yescharacteristic
31#64081—21no—
32C42×C3⋊D3C2211yescharacteristic
33C4×#634—21no—
34C4×#634C2211yescharacteristic
35C32×#106C2212yes—
36C32×C4⋊C8C2211yescharacteristic
37C32×#103C2212yes—
38#63648C2212yes—
39#63641C2212yes—
40#63637C2212yes—
41#63636C2212yes—
42#63635C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44#5725—34no—
45#5578—34no—
46C3×#475D314yescomplemented
47#5094—34no—
48#5027—34no—
49#4870—38no—
50#4864—38no—
51#4848—34no—
52D3×C4⋊C8—34no—
53#4818—38no—
54#4807—38no—
55C2×C32×Q8—21no—
56C2×C32×Q8C2311yescharacteristic
57#3832—44no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×#634—21no—
67C2×#634C2311yescharacteristic
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4C2311yescharacteristic
72C32×C4⋊C4C2312yes—
73C32×C42—21no—
74C32×C42C2311yescharacteristic
75#3755—42no—
76#3752—21no—
77#3752—21no—
78#3752—22no—
79#3752—22no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83#3750—21no—
84#3750—21no—
85#3750—21no—
86#3750—21no—
87C4×C3⋊Dic3—21no—
88C4×C3⋊Dic3D411yescharacteristic
89C4×C3⋊Dic3D411yescharacteristic
90C4×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊(C3⋊C8)C2312yes—
92#3744—42no—
93C8×C3⋊D3—42no—
94#3246—91noSylow
95C2×#239—64no—
96C3×C4⋊Q8C2×D314yes—
97C3×C4×Q8C2×D314yes—
98#947—64no—
99#946—34no—
100#944—34no—
101C2×#215—38no—
102C2×#204—38no—
103C2×D3×C8—38no—
104#897—34no—
105#896—64no—
106#895—38no—
107#895—64no—
108#893—38no—
109#893—64no—
110#889—64no—
111#888—34no—
112#874—34no—
113#872—64no—
114C42×D3—34no—
115C4×Dic6—34no—
116C4×Dic6—64no—
117C3×#106C2×D318yes—
118C3×C4⋊C8C2×D314yes—
119C3×#103C2×D318yes—
120#821—38no—
121Dic3⋊C8—38no—
122#810—38no—
123#809—38no—
124#808—38no—
125C4⋊(C3⋊C8)—34no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3C2×D411yescharacteristic
128C32×Q8—21no—
129C32×Q8—21no—
130C32×Q8—42no—
131C2×C32×C4—21no—
132C2×C32×C4—21no—
133C2×C32×C4—22no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—42no—
145C4⋊(C3⋊D3)—44no—
146C4⋊(C3⋊D3)—42no—
147C4×C3⋊D3—21no—
148C4×C3⋊D3—21no—
149C4×C3⋊D3—41no—
150C4×C3⋊D3—44no—
151C4×C3⋊D3SD1614yescomplemented
152#634—21no—
153#634—21no—
154#634—42no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157#533—91no—
158#532—91no—
159#476—92no—
160#475—91no—
161#475C3⋊D311yescharacteristic, complemented
162#465—92no—
163#465—92no—
164#461—92no—
165#460—91no—
166#460—91no—
167C2×C4⋊C8—91no—
168C2×C3×Q8—24no—
169C2×C3×Q8C22×D314yes—
170#239—1216no—
171C2×D12—38no—
172C2×D12—68no—
173C2×D12—64no—
174C2×D12—64no—
175C2×C4×D3—34no—
176C2×C4×D3—34no—
177C2×C4×D3—34no—
178C2×C4×D3—68no—
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×C42—24no—
187C3×C42C22×D314yes—
188#215—128no—
189(C2×D3)⋊C4—68no—
190(C2×D3)⋊C4—68no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193C4⋊Dic3—34no—
194C4⋊Dic3—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199Dic3⋊C4—64no—
200C4×Dic3—34no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—64no—
204C2×C3⋊C8—38no—
205#204—128no—
206D3×C8—128no—
207C22×C32C22×D411yescharacteristic
208C2×C3⋊D3—21no—
209C2×C3⋊D3—21no—
210C2×C3⋊D3—42no—
211C2×C3⋊D3—42no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3C2×SD1612yes—
214C32×C4—21no—
215C32×C4—41no—
216C32×C4—42no—
217C32×C4—41no—
218C32×C4C2×SD1612yes—
219C32×C4H(5,𝔽2)11yescharacteristic
220C32×C42−1+411yescharacteristic
221C3⋊Dic3—21no—
222C3⋊Dic3—21no—
223C3⋊Dic3—41no—
224C3⋊Dic3—41no—
225C3⋊Dic3C2×SD1612yes—
226C2×#41—181no—
227C2×SD16—92no—
228C2×SD16—92no—
229C22×C8—92no—
230C4⋊Q8—91no—
231C4⋊Q8—91no—
232C4⋊Q8C2×C3⋊D311yescharacteristic
233#127—91no—
234#125—181no—
235#124—181no—
236C22⋊Q8—91no—
237C22⋊Q8—91no—
238C22⋊Q8—181no—
239#121—92no—
240#121—181no—
241C4×Q8—91no—
242C4×Q8—181no—
243C4×Q8C2×C3⋊D311yescharacteristic
244C4×D4—92no—
245C4×D4—181no—
246#117—181no—
247C2×C42—91no—
248#106—92no—
249#106C2×C3⋊D312yes—
250C4⋊C8—92no—
251C4⋊C8—91no—
252C4⋊C8C2×C3⋊D311yescharacteristic
253#103—92no—
254#103C2×C3⋊D312yes—
255#102—92no—
256#102—92no—
257C22×D3—34no—
258C22×D3—68no—
259C3×Q8—24no—
260C3×Q8—24no—
261C3×Q8—48no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—28no—
265C2×C3×C4D3×D414yes—
266C2×C3×C4D3×D414yes—
267C2×C3×C4C23×D314yes—
268C2×Dic3—34no—
269C2×Dic3—34no—
270C2×Dic3—34no—
271C2×Dic3—64no—
272C2×Dic3—64no—
273D12—68no—
274D12—68no—
275D12—128no—
276D12—1216no—
277D12—128no—
278C4×D3—316no—
279C4×D3—64no—
280C4×D3—64no—
281C4×D3—1216no—
282C4×D3—124no—
283Dic6—64no—
284Dic6—64no—
285Dic6—128no—
286C3×C8—28no—
287C3⋊C8—68no—
288C2×C32#53711yescharacteristic
289C2×C32C22×SD1611yescharacteristic
290C2×C32#57511yescharacteristic
291C3⋊D3—22no—
292C3⋊D3—82no—
293#41—364no—
294C2×Q8—21no—
295C2×Q8—91no—
296C2×Q8—181no—
297C2×Q8C22×C3⋊D311yescharacteristic
298C2×D4—92no—
299C2×D4—182no—
300C2×D4—181no—
301C2×D4—181no—
302C22×C4—91no—
303C22×C4—91no—
304C22×C4—91no—
305C22×C4—182no—
306SD16—362no—
307SD16—362no—
308C2×C8—92no—
309C2×C8—362no—
310C2×C8C22×C3⋊D312yes—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—91no—
314C4⋊C4—181no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4C22×C3⋊D311yescharacteristic
321C4⋊C4C22×C3⋊D312yes—
322C22⋊C4—182no—
323C22⋊C4—182no—
324C22⋊C4—181no—
325C22⋊C4—181no—
326C42—21no—
327C42—91no—
328C42—91no—
329C42—91no—
330C42—181no—
331C42C22×C3⋊D311yescharacteristic
332C22×C3C2×D3×D414yes—
333C2×D3—38no—
334C2×D3—64no—
335C2×D3—64no—
336C2×D3—128no—
337C2×D3—128no—
338C2×D3—128no—
339C3×C4—24no—
340C3×C4—48no—
341C3×C4—44no—
342C3×C4—44no—
343C3×C4D3×SD1618yes—
344C3×C4#100714yes—
345C3×C4#100914yes—
346Dic3—38no—
347Dic3—64no—
348Dic3—64no—
349Dic3—124no—
350Dic3—124no—
351C32#324611yescharacteristic, complemented, Sylow
352C23—91no—
353C23—182no—
354Q8—21no—
355Q8—21no—
356Q8—42no—
357Q8—181no—
358Q8—181no—
359Q8—362no—
360D4—182no—
361D4—182no—
362D4—362no—
363D4—364no—
364D4—362no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—91no—
369C2×C4—94no—
370C2×C4—91no—
371C2×C4—91no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—181no—
375C2×C4—181no—
376C2×C4—361no—
377C2×C4—364no—
378C2×C4D4×C3⋊D311yescharacteristic
379C2×C4D4×C3⋊D311yescharacteristic
380C2×C4C23×C3⋊D311yescharacteristic
381C8—22no—
382C8—182no—
383C2×C3#562914yes—
384C2×C3C2×D3×SD1614yes—
385C2×C3#577714yes—
386D3—68no—
387D3—248no—
388C22—92no—
389C22—181no—
390C22—181no—
391C22—362no—
392C22—362no—
393C22—362no—
394C22C2×D4×C3⋊D311yescharacteristic
395C4—21no—
396C4—41no—
397C4—42no—
398C4—41no—
399C4—92no—
400C4—181no—
401C4—181no—
402C4—361no—
403C4—361no—
404C4SD16×C3⋊D312yes—
405C4#6436411yescharacteristic
406C4#6436611yescharacteristic
407C3#8100214yescomplemented
408C2—182no—
409C2—722no—
410C2#1059610011yescharacteristic
411C2C2×SD16×C3⋊D311yescharacteristic
412C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radical#10596196C2
hypercenter#475C3⋊D3
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #10596049C2semidirect
3. C32×#475C2semidirect
4. #10592793C2semidirect
5. #10592726C2semidirect
6. #10592569C2semidirect
7. #10592563C2semidirect
8. #10592547C2semidirect
9. C3⋊D3×C4⋊C8C2semidirect
10. #10592517C2semidirect
11. #10592506C2semidirect
46. C3×#475D3semidirect
151. C4×C3⋊D3SD16semidirect
161. #475C3⋊D3semidirect
351. C32#3246semidirect
407. C3#81002semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105960492
C32×#4752
#105927932
#105927262
#105925692
#105925632
#105925472
C3⋊D3×C4⋊C82
#105925172
#105925062
#810023