Finite Group Databasebeta

← #11785205

Subgroups — #11785205

Order 1152.

924 conjugacy classes of subgroups.

The subgroup lattice has 285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic
2C2×#63662C212yesmaximal
3#10592634C211yesmaximal, characteristic
4C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
5#10589395C212yesmaximal
6#71626—34nomaximal
7C22×C32×Q8C2211yescharacteristic
8C32×C4×Q8—22no—
9C32×C4×Q8C414yescomplemented
10C2×C32×C4⋊C4—21no—
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C42—21no—
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)—21no—
15C2×C4⋊(C3⋊Dic3)—21no—
16C2×C4⋊(C3⋊Dic3)C2212yes—
17C22×C3⋊(C3⋊C8)C2212yes—
18#63662—24no—
19C4⋊(C3⋊(C3⋊C8))—22no—
20C2×C3×C4×Q8D314yes—
21C2×#835—38no—
22#4935—34no—
23C2×C4⋊(C3⋊C8)—34no—
24#4529—38no—
25C2×C32×Q8—21no—
26C2×C32×Q8—21no—
27C2×C32×Q8—21no—
28C2×C32×Q8C2×C412yes—
29C2×C32×Q8D412yes—
30C2×C32×Q8Q812yes—
31C22×C32×C4—21no—
32C22×C32×C4—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—22no—
37C32×C4⋊C4—24no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4C2×C412yes—
40C32×C42—24no—
41C32×C42C2×C412yes—
42C32×C42D412yes—
43C4⋊(C3⋊Dic3)—22no—
44C4⋊(C3⋊Dic3)—22no—
45C4⋊(C3⋊Dic3)—42no—
46C4⋊(C3⋊Dic3)—42no—
47C2×C3⋊(C3⋊C8)—22no—
48C2×C3⋊(C3⋊C8)—22no—
49C2×C3⋊(C3⋊C8)—22no—
50#1803—91noSylow
51C22×C3×Q8C2×D314yes—
52C3×C4×Q8—28no—
53C3×C4×Q8Dic3116yescomplemented
54C2×C3×C4⋊C4—24no—
55C2×C3×C4⋊C4C2×D314yes—
56C2×C3×C42—24no—
57C2×C3×C42C2×D314yes—
58C2×C4⋊Dic3—38no—
59C2×C4⋊Dic3—64no—
60C2×C4⋊Dic3—64no—
61C22×C3⋊C8—38no—
62#835—616no—
63C4⋊(C3⋊C8)—68no—
64C23×C32C2×D411yescharacteristic
65C32×Q8—22no—
66C32×Q8—22no—
67C32×Q8—22no—
68C32×Q8C4⋊C414yescomplemented
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—21no—
73C2×C32×C4—21no—
74C2×C32×C4—22no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4C22⋊C412yes—
78C2×C32×C4C22⋊C412yes—
79C2×C32×C4SD1612yes—
80C2×C32×C4Q1612yes—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×Q811yescharacteristic
85C2×C32×C4#4111yescharacteristic
86C2×C32×C4#4111yescharacteristic
87C2×C3⋊Dic3—42no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3—42no—
90C3⋊(C3⋊C8)—42no—
91C2×C4×Q8C3⋊D311yescharacteristic
92C2×C4⋊C8—91no—
93C2×#103—92no—
94#384—91no—
95#340—92no—
96C2×C3×Q8—24no—
97C2×C3×Q8—24no—
98C2×C3×Q8—24no—
99C2×C3×Q8Dic618yes—
100C2×C3×Q8D1218yes—
101C2×C3×Q8C2×Dic318yes—
102C22×C3×C4—24no—
103C22×C3×C4—24no—
104C22×C3×C4#6714yes—
105C22×C3×C4#6714yes—
106C22×C3×C4C22×D314yes—
107C22×Dic3—68no—
108C3×C4⋊C4—216no—
109C3×C4⋊C4—24no—
110C3×C4⋊C4C2×Dic318yes—
111C3×C42—216no—
112C3×C42C2×Dic318yes—
113C3×C42#6718yes—
114C4⋊Dic3—68no—
115C4⋊Dic3—68no—
116C4⋊Dic3—128no—
117C4⋊Dic3—128no—
118C2×C3⋊C8—68no—
119C2×C3⋊C8—68no—
120C2×C3⋊C8—68no—
121C22×C32C2×C22⋊C411yescharacteristic
122C22×C32#12111yescharacteristic
123C22×C32C22⋊Q811yescharacteristic
124C22×C32C2×SD1611yescharacteristic
125C22×C32C2×Q1611yescharacteristic
126C22×C32AGL(1,ℤ/8)11yescharacteristic
127C22×C32#13711yescharacteristic
128C32×C4—24no—
129C32×C4—22no—
130C32×C4—42no—
131C32×C4#10314yescomplemented
132C32×C4C2×C4⋊C411yescharacteristic
133C32×C4#11711yescharacteristic
134C32×C4#12111yescharacteristic
135C32×C4C22⋊Q811yescharacteristic
136C3⋊Dic3—82no—
137C22×Q8C2×C3⋊D311yescharacteristic
138C22×C8—92no—
139C4×Q8—22no—
140C4×Q8C3⋊Dic314yescomplemented
141C2×C4⋊C4—21no—
142C2×C4⋊C4—92no—
143C2×C4⋊C4—181no—
144C2×C4⋊C4—181no—
145C2×C4⋊C4C2×C3⋊D311yescharacteristic
146C2×C42—21no—
147C2×C42C2×C3⋊D311yescharacteristic
148C4⋊C8—182no—
149#103—184no—
150C23×C3C2×#6714yes—
151C3×Q8—28no—
152C3×Q8—28no—
153C3×Q8—28no—
154C3×Q8C4⋊Dic3116yescomplemented
155C2×C3×C4—28no—
156C2×C3×C4—28no—
157C2×C3×C4—24no—
158C2×C3×C4—24no—
159C2×C3×C4—28no—
160C2×C3×C4—28no—
161C2×C3×C4—44no—
162C2×C3×C4—44no—
163C2×C3×C4#21518yes—
164C2×C3×C4#21618yes—
165C2×C3×C4#21718yes—
166C2×C3×C4#21718yes—
167C2×C3×C4C2×Dic614yes—
168C2×C3×C4C2×D1214yes—
169C2×C3×C4#23514yes—
170C2×C3×C4#23514yes—
171C2×C3×C4C22×Dic314yes—
172C2×C3×C4C2×#6714yes—
173C2×Dic3—128no—
174C2×Dic3—128no—
175C2×Dic3—128no—
176C3⋊C8—128no—
177C2×C32#38011yescharacteristic
178C2×C32C2×#10311yescharacteristic
179C2×C32#41711yescharacteristic
180C2×C32#46011yescharacteristic
181C2×C32#46211yescharacteristic
182C2×C32#47511yescharacteristic
183C2×C32#47711yescharacteristic
184C2×Q8—21no—
185C2×Q8—21no—
186C2×Q8—21no—
187C2×Q8#63412yes—
188C2×Q8C4⋊(C3⋊D3)12yes—
189C2×Q8C2×C3⋊Dic312yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—182no—
193C22×C4#63811yescharacteristic
194C22×C4#63811yescharacteristic
195C22×C4C22×C3⋊D311yescharacteristic
196C2×C8—182no—
197C2×C8—182no—
198C2×C8—182no—
199C4⋊C4—24no—
200C4⋊C4—21no—
201C4⋊C4—182no—
202C4⋊C4—182no—
203C4⋊C4—362no—
204C4⋊C4—362no—
205C4⋊C4C2×C3⋊Dic312yes—
206C42—24no—
207C42C2×C3⋊Dic312yes—
208C42#63812yes—
209C22×C3#92414yes—
210C22×C3#93014yes—
211C22×C3C2×#21514yes—
212C22×C3C2×#21614yes—
213C22×C3#94914yes—
214C22×C3#95114yes—
215C22×C3C2×#21714yes—
216C3×C4—216no—
217C3×C4—28no—
218C3×C4—48no—
219C3×C4#835116yescomplemented
220C3×C4#92414yes—
221C3×C4C2×C4⋊Dic314yes—
222C3×C4#92614yes—
223C3×C4#93014yes—
224Dic3—248no—
225C32#180311yescharacteristic, complemented, Sylow
226C23C2×#63811yescharacteristic
227Q8—22no—
228Q8—22no—
229Q8—22no—
230Q8C4⋊(C3⋊Dic3)14yescomplemented
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—362no—
240C2×C4—362no—
241C2×C4—362no—
242C2×C4#375512yes—
243C2×C4#375612yes—
244C2×C4#375712yes—
245C2×C4#375712yes—
246C2×C4C2×#63411yescharacteristic
247C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
248C2×C4#382811yescharacteristic
249C2×C4#382811yescharacteristic
250C2×C4C22×C3⋊Dic311yescharacteristic
251C2×C4C2×#63811yescharacteristic
252C8—362no—
253C2×C3#502014yes—
254C2×C3#502114yes—
255C2×C3#502714yes—
256C2×C3#503114yes—
257C2×C3#521214yes—
258C2×C3C2×#83514yes—
259C2×C3#523214yes—
260C22#6413311yescharacteristic
261C22#6413911yescharacteristic
262C22C2×#375511yescharacteristic
263C22C2×#375611yescharacteristic
264C22#6415811yescharacteristic
265C22#6416011yescharacteristic
266C22C2×#375711yescharacteristic
267C4—24no—
268C4—22no—
269C4—42no—
270C4—722no—
271C4#6366214yescomplemented
272C4#6413311yescharacteristic
273C4C2×C4⋊(C3⋊Dic3)11yescharacteristic
274C4#6413511yescharacteristic
275C4#6413911yescharacteristic
276C3#7162614yescomplemented
277C2#1059271911yescharacteristic
278C2#1059272011yescharacteristic
279C2#1059272611yescharacteristic
280C2#1059273011yescharacteristic
281C2#1059291111yescharacteristic
282C2C2×#6366211yescharacteristic
283C2#1059293111yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C4×Q8C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4×Q8C3⋊D3
hypocenterC32#1803
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
9. C32×C4×Q8C4semidirect
53. C3×C4×Q8Dic3semidirect
68. C32×Q8C4⋊C4semidirect
131. C32×C4#103semidirect
140. C4×Q8C3⋊Dic3semidirect
154. C3×Q8C4⋊Dic3semidirect
219. C3×C4#835semidirect
225. C32#1803semidirect
230. Q8C4⋊(C3⋊Dic3)semidirect
271. C4#63662semidirect
276. C3#71626semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C2×#636622
#105926342
C2×C4⋊(C3⋊(C3⋊C8))2
#105893952
#716263