Finite Group Databasebeta

← #11873466

Subgroups — #11873466

Order 1152.

1200 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic
2#10595988C211yesmaximal, characteristic, complemented
3C32×#416C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5#10592812C211yesmaximal, characteristic, complemented
6C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
7#10592701C211yesmaximal, characteristic, complemented
8#10592499C212yesmaximal, complemented
9#10592491C212yesmaximal, complemented
10#10592467C212yesmaximal, complemented
11#10592459C212yesmaximal, complemented
12#78825—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×#3828C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C32×#117C2211yescharacteristic
17#64156C2211yescharacteristic
18#64153C2211yescharacteristic
19#64149C2211yescharacteristic
20#64148—22no—
21#64145C2211yescharacteristic
22C4×#638—22no—
23#64135C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26#64099C2212yes—
27#64097C2212yes—
28#64087—22no—
29C4×#634—22no—
30C32×#103C2212yes—
31C32×#102C2212yes—
32#63662C2212yes—
33#63659C2212yes—
34#63648C2212yes—
35#63643C2212yes—
36C8×C3⋊Dic3C2212yes—
37C8×C3⋊Dic3C2212yes—
38#63637C2212yes—
39#63636C2212yes—
40#5832—34no—
41#5517—34no—
42C3×#416D314yescomplemented
43#5233—34no—
44#5113—34no—
45C2×C8×Dic3—34no—
46#5002—34no—
47#4800—38no—
48#4792—38no—
49#4768—38no—
50#4760—38no—
51C32×#41—22no—
52C32×#41—22no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4C2311yescharacteristic
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×#638—21no—
59C2×#638—22no—
60C22×C3⋊Dic3D412yes—
61#3828—22no—
62#3828—22no—
63C2×C4⋊(C3⋊D3)C2311yescharacteristic
64C2×C4×C3⋊D3—21no—
65C2×#634—22no—
66C2×#634C2311yescharacteristic
67C2×C32×C8—22no—
68C2×C32×C8C2312yes—
69C32×C4⋊C4C2312yes—
70C32×C22⋊C4—21no—
71C32×C42—21no—
72#3757—21no—
73#3757—22no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)C2312yes—
77#3750—22no—
78#3750—22no—
79#3750—22no—
80C4×C3⋊Dic3—21no—
81C4×C3⋊Dic3D412yes—
82C4×C3⋊Dic3C2311yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86#3131—91noSylow
87C2×C3×#41C2×D314yes—
88C2×#235—34no—
89C22×C3×C8C2×D314yes—
90C3×#117C2×D314yes—
91#947—34no—
92#944—34no—
93#940—34no—
94#939—68no—
95#936—34no—
96C4×#67—68no—
97#926—34no—
98C2×C4×Dic3—34no—
99C22×C3⋊C8—34no—
100#890—38no—
101#888—38no—
102#878—68no—
103C4×Dic6—68no—
104C3×#103C2×D318yes—
105C3×#102C2×D318yes—
106#835—38no—
107#832—38no—
108#821—38no—
109#816—38no—
110C8×Dic3—38no—
111C8×Dic3—38no—
112#810—38no—
113#809—38no—
114C23×C32—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3⋊D3—21no—
117C32×Q8—21no—
118C32×Q8—21no—
119C32×D4—21no—
120C32×D4—21no—
121C32×D4—42no—
122C2×C32×C4—22no—
123C2×C32×C4—21no—
124C2×C32×C4—42no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4#4112yes—
127C2×C32×C4#4112yes—
128C2×C32×C4C2411yescharacteristic
129#638—42no—
130#638—44no—
131C2×C3⋊Dic3—24no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3C2×D412yes—
135C2×C3⋊Dic3C2×D412yes—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)—21no—
138C4×C3⋊D3—42no—
139#634—21no—
140#634—21no—
141#634—44no—
142C32×C8—22no—
143C3⋊(C3⋊C8)—22no—
144#533—91no—
145#532—91no—
146#488—92no—
147#488—92no—
148#487—92no—
149#486—92no—
150#416—91no—
151#416—91no—
152#416—91no—
153#416C3⋊D311yescharacteristic, complemented
154C2×C4×C8—91no—
155C3×#41—28no—
156C3×#41—28no—
157C2×C3×Q8C22×D314yes—
158C2×C3×D4—24no—
159C2×C3×D4C22×D314yes—
160C22×C3×C4—24no—
161C22×C3×C4C22×D314yes—
162C2×#67—68no—
163C2×#67—64no—
164C22×Dic3—38no—
165#235—68no—
166#235—68no—
167C2×D12—34no—
168C2×C4×D3—64no—
169C2×Dic6—34no—
170C2×Dic6—68no—
171C2×C3×C8—28no—
172C2×C3×C8C22×D318yes—
173C3×C4⋊C4C22×D318yes—
174C3×C22⋊C4—24no—
175C3×C42—24no—
176#217—68no—
177#217—64no—
178(C2×D3)⋊C4—68no—
179C4⋊Dic3—38no—
180C4⋊Dic3—68no—
181Dic3⋊C4—68no—
182Dic3⋊C4—68no—
183Dic3⋊C4—68no—
184C4×Dic3—38no—
185C4×Dic3—34no—
186C4×Dic3—34no—
187C4×Dic3—64no—
188C2×C3⋊C8—38no—
189C2×C3⋊C8—68no—
190C22×C32—22no—
191C22×C32—41no—
192C22×C32—42no—
193C22×C32#12412yes—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—41no—
196C2×C3⋊D3—42no—
197C32×C4—41no—
198C32×C4—42no—
199C32×C4#12412yes—
200C32×C4C2×#4111yescharacteristic
201C32×C4C2×#4111yescharacteristic
202C3⋊Dic3—22no—
203C3⋊Dic3—41no—
204C3⋊Dic3—42no—
205C3⋊Dic3#13514yes—
206C2×#41—91no—
207C2×#41C2×C3⋊D311yescharacteristic
208C22×C8—91no—
209C22×C8C2×C3⋊D311yescharacteristic
210C4⋊Q8—92no—
211C4⋊Q8—91no—
212#127—91no—
213#125—92no—
214#124—91no—
215#124—91no—
216C22⋊Q8—182no—
217#121—182no—
218C4×Q8—182no—
219C4×D4—182no—
220#117—91no—
221#117C2×C3⋊D311yescharacteristic
222C2×C42—91no—
223#103—92no—
224#103—92no—
225#103—92no—
226#103C2×C3⋊D312yes—
227#102—92no—
228#102—92no—
229#102—92no—
230#102C2×C3⋊D312yes—
231C4×C8—92no—
232C4×C8—92no—
233C23×C3—24no—
234C23×C3D3×D414yes—
235C22×D3—64no—
236C3×Q8—24no—
237C3×Q8—24no—
238C3×D4—24no—
239C3×D4—24no—
240C3×D4—48no—
241C2×C3×C4—28no—
242C2×C3×C4—24no—
243C2×C3×C4—48no—
244C2×C3×C4#23518yes—
245C2×C3×C4D3×D414yes—
246C2×C3×C4#23718yes—
247C2×C3×C4C23×D314yes—
248#67—1216no—
249#67—128no—
250C2×Dic3—38no—
251C2×Dic3—38no—
252C2×Dic3—616no—
253C2×Dic3—68no—
254C2×Dic3—64no—
255D12—64no—
256D12—64no—
257C4×D3—128no—
258Dic6—64no—
259Dic6—64no—
260Dic6—1216no—
261C3×C8—28no—
262C3⋊C8—68no—
263C2×C32—22no—
264C2×C32—81no—
265C2×C32C2×#12411yescharacteristic
266C2×C32C2×#13512yes—
267C3⋊D3—81no—
268#41—22no—
269#41—22no—
270#41—182no—
271#41—182no—
272C2×Q8—91no—
273C2×Q8—182no—
274C2×Q8C22×C3⋊D311yescharacteristic
275C2×D4—21no—
276C2×D4—91no—
277C2×D4—182no—
278C2×D4—181no—
279C2×D4C22×C3⋊D311yescharacteristic
280C22×C4—21no—
281C22×C4—92no—
282C22×C4—181no—
283C22×C4C22×C3⋊D311yescharacteristic
284C2×C8—22no—
285C2×C8—92no—
286C2×C8—182no—
287C2×C8C22×C3⋊D312yes—
288C4⋊C4—92no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—182no—
292C4⋊C4—182no—
293C4⋊C4C22×C3⋊D312yes—
294C22⋊C4—21no—
295C22⋊C4—182no—
296C22⋊C4—182no—
297C22⋊C4—181no—
298C42—21no—
299C42—91no—
300C42—91no—
301C42—92no—
302C42—181no—
303C22×C3—28no—
304C22×C3—44no—
305C22×C3—48no—
306C22×C3#88518yes—
307C22×C3C2×D3×D414yes—
308C2×D3—124no—
309C2×D3—128no—
310C3×C4—44no—
311C3×C4—48no—
312C3×C4#88518yes—
313C3×C4C2×#23514yes—
314C3×C4C2×#23714yes—
315Dic3—316no—
316Dic3—68no—
317Dic3—124no—
318Dic3—128no—
319C32#313111yescharacteristic, complemented, Sylow
320C23—21no—
321C23—181no—
322C23D4×C3⋊D311yescharacteristic
323Q8—21no—
324Q8—21no—
325Q8—181no—
326Q8—181no—
327Q8—364no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—181no—
332D4—181no—
333D4—364no—
334D4—362no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—92no—
339C2×C4—92no—
340C2×C4—184no—
341C2×C4—182no—
342C2×C4—181no—
343C2×C4—362no—
344C2×C4#382812yes—
345C2×C4D4×C3⋊D311yescharacteristic
346C2×C4#383012yes—
347C2×C4C23×C3⋊D311yescharacteristic
348C8—22no—
349C8—182no—
350C2×C3—28no—
351C2×C3—84no—
352C2×C3C2×#88514yes—
353C2×C3D3×#13518yes—
354D3—244no—
355C22—22no—
356C22—41no—
357C22—42no—
358C22—361no—
359C22—362no—
360C22#6409412yes—
361C22C2×D4×C3⋊D311yescharacteristic
362C4—41no—
363C4—42no—
364C4—94no—
365C4—182no—
366C4—361no—
367C4—362no—
368C4#6409412yes—
369C4C2×#382811yescharacteristic
370C4C2×#383011yescharacteristic
371C3#7882514yescomplemented
372C2—22no—
373C2—81no—
374C2—721no—
375C2C2×#6409411yescharacteristic
376C2C3⋊D3×#13512yes—
subgroupG/H
centerC2×C4D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#416C2
socleC22×C32C22×D4
prime radical#10596303C2
hypercenter#416C3⋊D3
hypocenterC32#3131
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #10595988C2semidirect
3. C32×#416C2semidirect
4. #10592932C2semidirect
5. #10592812C2semidirect
6. C2×C8×C3⋊Dic3C2semidirect
7. #10592701C2semidirect
8. #10592499C2semidirect
9. #10592491C2semidirect
10. #10592467C2semidirect
11. #10592459C2semidirect
42. C3×#416D3semidirect
153. #416C3⋊D3semidirect
319. C32#3131semidirect
371. C3#78825semidirect

Maximal subgroups

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

subgroupindex
#105963032
#105959882
C32×#4162
#105929322
#105928122
C2×C8×C3⋊Dic32
#105927012
#105924992
#105924912
#105924672
#105924592
#788253