Finite Group Databasebeta

← #11895618

Subgroups — #11895618

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2#10596056C211yesmaximal, characteristic
3C32×#475C211yesmaximal, characteristic, complemented
4#10592787C211yesmaximal, characteristic
5C4×#3756C211yesmaximal, characteristic, complemented
6#10592570C212yesmaximal, complemented
7#10592551C212yesmaximal, complemented
8#10592547C211yesmaximal, characteristic
9#10592529C211yesmaximal, characteristic, complemented
10#10592499C212yesmaximal, complemented
11#10592497C212yesmaximal, complemented
12#81041—34nomaximal
13C32×C4⋊Q8C2211yescharacteristic
14C32×C4×Q8C2211yescharacteristic
15#64156C2212yes—
16Q8×C3⋊Dic3—21no—
17#64153—21no—
18C2×#3756C2211yescharacteristic
19C2×#3744C2212yes—
20#64103—22no—
21#64102C2212yes—
22#64099C2212yes—
23#64098—22no—
24#64096C2212yes—
25#64084—21no—
26#64083C2211yescharacteristic
27C4×C4⋊(C3⋊D3)—21no—
28C4×#634C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C32×#106C2212yes—
31C32×C4⋊C8C2211yescharacteristic
32C32×#103C2212yes—
33#63662C2211yescharacteristic
34#63648C2212yes—
35#63641C2212yes—
36C8×C3⋊Dic3C2212yes—
37#63637C2211yescharacteristic
38#63636C2212yes—
39#63636C2212yes—
40#63634C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42#5721—34no—
43#5585—34no—
44C3×#475D314yescomplemented
45#5088—34no—
46C4×#216—34no—
47#4871—38no—
48#4852—38no—
49#4848—34no—
50#4830—34no—
51#4800—38no—
52#4798—38no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—22no—
59C2×#634D411yescharacteristic
60C2×#634C2311yescharacteristic
61C2×C32×C8C2312yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C32×C4⋊C4C2311yescharacteristic
66C32×C42—21no—
67C32×C42C2311yescharacteristic
68#3756—22no—
69#3752—22no—
70#3752—22no—
71#3752—22no—
72C4⋊(C3⋊Dic3)—22no—
73C4⋊(C3⋊Dic3)D411yescharacteristic
74C4⋊(C3⋊Dic3)C2311yescharacteristic
75#3750—21no—
76#3750—22no—
77#3750—22no—
78#3750D412yes—
79C4×C3⋊Dic3—21no—
80C4×C3⋊Dic3—22no—
81C4×C3⋊Dic3C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84#3744—24no—
85#3365—91noSylow
86C3×C4⋊Q8C2×D314yes—
87C3×C4×Q8C2×D314yes—
88#947—38no—
89Q8×Dic3—64no—
90#944—64no—
91C2×#216—34no—
92C2×#204—38no—
93#894—68no—
94#893—38no—
95#890—38no—
96#889—68no—
97#887—38no—
98#875—64no—
99#874—34no—
100C4×D12—64no—
101C4×Dic6—34no—
102C4×Dic6—34no—
103C3×#106C2×D318yes—
104C3×C4⋊C8C2×D314yes—
105C3×#103C2×D318yes—
106#835—34no—
107#821—38no—
108Dic3⋊C8—38no—
109C8×Dic3—38no—
110#810—34no—
111#809—38no—
112#809—38no—
113#807—34no—
114C4×C3⋊C8—34no—
115C22×C3⋊D3—22no—
116C32×Q8—21no—
117C32×Q8—21no—
118C32×Q8—42no—
119C2×C32×C4—22no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2411yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C2×D412yes—
128C2×C3⋊Dic3C2×D412yes—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—42no—
132C4⋊(C3⋊D3)—81no—
133C4×C3⋊D3—82no—
134#634—22no—
135#634—21no—
136#634#4112yes—
137C32×C8—22no—
138C3⋊(C3⋊C8)—21no—
139C3⋊(C3⋊C8)—21no—
140#559—91no—
141#557—91no—
142#488—92no—
143#486—91no—
144#478—92no—
145#475C3⋊D311yescharacteristic, complemented
146#464—92no—
147#460—91no—
148C8×Q8—91no—
149C4×Q16—91no—
150C4×SD16—92no—
151C2×C3×Q8—24no—
152C2×C3×Q8C22×D314yes—
153C2×D12—38no—
154C2×D12—64no—
155C2×D12—64no—
156C2×C4×D3—68no—
157C2×Dic6—34no—
158C2×Dic6—34no—
159C2×C3×C8C22×D318yes—
160C3×C4⋊C4—24no—
161C3×C4⋊C4—24no—
162C3×C4⋊C4C22×D314yes—
163C3×C4⋊C4C22×D318yes—
164C3×C42—24no—
165C3×C42C22×D314yes—
166#216—68no—
167(C2×D3)⋊C4—68no—
168(C2×D3)⋊C4—68no—
169(C2×D3)⋊C4—68no—
170C4⋊Dic3—34no—
171C4⋊Dic3—34no—
172C4⋊Dic3—68no—
173Dic3⋊C4—38no—
174Dic3⋊C4—68no—
175Dic3⋊C4—68no—
176Dic3⋊C4—64no—
177C4×Dic3—38no—
178C4×Dic3—68no—
179C4×Dic3—64no—
180C2×C3⋊C8—34no—
181C2×C3⋊C8—34no—
182#204—616no—
183C22×C32C22×D411yescharacteristic
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C2×C3⋊D3—42no—
187C32×C4—21no—
188C32×C4—41no—
189C32×C4—42no—
190C32×C4—41no—
191C32×C4#13512yes—
192C32×C4C2×#4111yescharacteristic
193C32×C42−1+411yescharacteristic
194C3⋊Dic3—22no—
195C3⋊Dic3—22no—
196C3⋊Dic3—22no—
197C3⋊Dic3—41no—
198C2×Q16—91no—
199C2×SD16—92no—
200C4⋊Q8—181no—
201C4⋊Q8C2×C3⋊D311yescharacteristic
202#127—91no—
203#125—92no—
204#125—182no—
205#124—92no—
206#124—181no—
207#123—182no—
208C4×Q8—91no—
209C4×Q8—92no—
210C4×Q8—91no—
211C4×Q8—181no—
212C4×Q8C2×C3⋊D311yescharacteristic
213C4×D4—92no—
214C4×D4—181no—
215#107—91no—
216#106C2×C3⋊D312yes—
217C4⋊C8—92no—
218C4⋊C8C2×C3⋊D311yescharacteristic
219#103—91no—
220#103—91no—
221#103C2×C3⋊D312yes—
222#102—92no—
223#102—92no—
224#102—92no—
225C4×C8—92no—
226C4×C8—91no—
227C22×D3—68no—
228C3×Q8—24no—
229C3×Q8—24no—
230C3×Q8—48no—
231C2×C3×C4—28no—
232C2×C3×C4—24no—
233C2×C3×C4—24no—
234C2×C3×C4D3×D414yes—
235C2×C3×C4D3×D414yes—
236C2×C3×C4C23×D314yes—
237C2×Dic3—38no—
238C2×Dic3—38no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241D12—68no—
242D12—68no—
243D12—128no—
244D12—244no—
245C4×D3—248no—
246Dic6—38no—
247Dic6—68no—
248Dic6—64no—
249C3×C8—28no—
250C3⋊C8—64no—
251C3⋊C8—64no—
252C2×C32#54811yescharacteristic
253C2×C32C2×#13511yescharacteristic
254C2×C32#57711yescharacteristic
255C3⋊D3—82no—
256C2×Q8—21no—
257C2×Q8—91no—
258C2×Q8—91no—
259C2×Q8C22×C3⋊D311yescharacteristic
260C2×D4—92no—
261C2×D4—181no—
262C2×D4—181no—
263C22×C4—182no—
264Q16—182no—
265SD16—184no—
266C2×C8—91no—
267C2×C8—91no—
268C2×C8C22×C3⋊D312yes—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—91no—
272C4⋊C4—92no—
273C4⋊C4—91no—
274C4⋊C4—182no—
275C4⋊C4—182no—
276C4⋊C4—182no—
277C4⋊C4—181no—
278C4⋊C4C22×C3⋊D312yes—
279C4⋊C4C22×C3⋊D311yescharacteristic
280C22⋊C4—182no—
281C22⋊C4—182no—
282C22⋊C4—182no—
283C42—21no—
284C42—92no—
285C42—182no—
286C42—181no—
287C42C22×C3⋊D311yescharacteristic
288C22×C3C2×D3×D414yes—
289C2×D3—128no—
290C2×D3—128no—
291C2×D3—128no—
292C3×C4—24no—
293C3×C4—44no—
294C3×C4—48no—
295C3×C4—44no—
296C3×C4#91618yes—
297C3×C4#100714yes—
298C3×C4D3×#4114yes—
299Dic3—68no—
300Dic3—68no—
301Dic3—68no—
302Dic3—124no—
303C32#336511yescharacteristic, complemented, Sylow
304C23—182no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—92no—
309Q8—181no—
310Q8—182no—
311D4—182no—
312D4—182no—
313D4—362no—
314D4—721no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—92no—
319C2×C4—92no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4—722no—
323C2×C4D4×C3⋊D311yescharacteristic
324C2×C4D4×C3⋊D311yescharacteristic
325C2×C4C23×C3⋊D311yescharacteristic
326C8—22no—
327C8—181no—
328C8—181no—
329C2×C3#563314yes—
330C2×C3C2×#91614yes—
331C2×C3#577814yes—
332D3—248no—
333C22—362no—
334C22—362no—
335C22—362no—
336C22C2×D4×C3⋊D311yescharacteristic
337C4—21no—
338C4—41no—
339C4—42no—
340C4—41no—
341C4—182no—
342C4—182no—
343C4—182no—
344C4—361no—
345C4#6412512yes—
346C4#6436411yescharacteristic
347C4#41×C3⋊D311yescharacteristic
348C3#8104114yescomplemented
349C2—722no—
350C2#1059610411yescharacteristic
351C2C2×#6412511yescharacteristic
352C2#1059624911yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#475C2
socleC22×C32C22×D4
prime radical#64083C22
hypercenter#475C3⋊D3
hypocenterC32#3365
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
1. #10596192C2semidirect
3. C32×#475C2semidirect
5. C4×#3756C2semidirect
6. #10592570C2semidirect
7. #10592551C2semidirect
9. #10592529C2semidirect
10. #10592499C2semidirect
11. #10592497C2semidirect
44. C3×#475D3semidirect
145. #475C3⋊D3semidirect
303. C32#3365semidirect
348. C3#81041semidirect

Maximal subgroups

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

subgroupindex
#105961922
#105960562
C32×#4752
#105927872
C4×#37562
#105925702
#105925512
#105925472
#105925292
#105924992
#105924972
#810413