Finite Group Databasebeta

← #11791053

Subgroups — #11791053

Order 1152.

912 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic
3#10592928C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic
5C2×#63642C211yesmaximal, characteristic
6#10592672C211yesmaximal, characteristic
7C2×#63635C211yesmaximal, characteristic
8#70259—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3756—22no—
14C2×#3756—22no—
15C2×#3756C414yescomplemented
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C32×#103—22no—
20#63658—22no—
21#63658—22no—
22#63643—22no—
23#63642—22no—
24#63635—22no—
25C22×#216—34no—
26C2×C3×#103D314yes—
27#5229—34no—
28C2×#816—34no—
29C2×#815—34no—
30#4973—34no—
31C2×#808—34no—
32C2×C32×Q8—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8C2×C412yes—
38C22×C32×C4—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3⋊Dic3D412yes—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3756—28no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C2×C3⋊(C3⋊C8)D412yes—
62C2×C3⋊(C3⋊C8)D412yes—
63#1971—91noSylow
64C22×C3×Q8C2×D314yes—
65C22×Dic6—34no—
66C22×C3×C8C2×D314yes—
67C2×C3×C4⋊C4C2×D314yes—
68C2×#216—316no—
69C2×#216—68no—
70C2×#216—68no—
71C2×C4⋊Dic3—34no—
72C2×C4×Dic3—34no—
73C22×C3⋊C8—34no—
74C3×#103—28no—
75C3⋊#95—68no—
76C3⋊#95—68no—
77#816—68no—
78#815—68no—
79#808—68no—
80C23×C32C2×D411yescharacteristic
81C32×Q8—22no—
82C32×Q8—22no—
83C32×Q8—41no—
84C32×Q8—41no—
85C2×C32×C4—22no—
86C2×C32×C4—41no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—42no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4111yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—42no—
104#634—22no—
105#634—22no—
106#634—41no—
107#634—41no—
108C32×C8—22no—
109C3⋊(C3⋊C8)C22⋊C414yes—
110C22×Q16—91no—
111C2×#106—91no—
112C2×#103—91no—
113C2×#103C3⋊D311yescharacteristic
114C2×#97—91no—
115#391—91no—
116#391—91no—
117C2×C3×Q8—24no—
118C2×C3×Q8—24no—
119C2×C3×Q8—24no—
120C2×C3×Q8—24no—
121C2×C3×Q8—24no—
122C2×C3×Q8C4×D318yes—
123C22×C3×C4—24no—
124C22×C3×C4—24no—
125C22×C3×C4C22×D314yes—
126C22×Dic3—38no—
127C22×Dic3—64no—
128C22×Dic3—64no—
129C2×Dic6—38no—
130C2×Dic6—64no—
131C2×Dic6—64no—
132C2×Dic6—64no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×C3×C8—24no—
136C2×C3×C8—24no—
137C2×C3×C8#6718yes—
138C3×C4⋊C4—24no—
139C3×C4⋊C4—24no—
140#216—632no—
141C4⋊Dic3—64no—
142C4⋊Dic3—64no—
143C4×Dic3—64no—
144C4×Dic3—64no—
145C2×C3⋊C8—38no—
146C2×C3⋊C8—38no—
147C2×C3⋊C8—38no—
148C22×C32C4×D411yescharacteristic
149C22×C32#12111yescharacteristic
150C22×C32#12711yescharacteristic
151C22×C32#13712yes—
152C22×C32#13712yes—
153C32×C4—42no—
154C32×C4—81no—
155C32×C4C2×C22⋊C411yescharacteristic
156C32×C4C4×D411yescharacteristic
157C32×C4#12111yescharacteristic
158C32×C4#12411yescharacteristic
159C3⋊Dic3—42no—
160C3⋊Dic3—42no—
161C3⋊Dic3—81no—
162C22×Q8—91no—
163C22×Q8C2×C3⋊D311yescharacteristic
164C2×Q16—94no—
165C2×Q16—182no—
166C2×Q16—182no—
167C22×C8—91no—
168C22×C8C2×C3⋊D311yescharacteristic
169C2×C4⋊C4—91no—
170C2×C4⋊C4C2×C3⋊D311yescharacteristic
171C2×C42—91no—
172#106—182no—
173#103—22no—
174#103—182no—
175#97—182no—
176#95—182no—
177#95—182no—
178C23×C3D3×D414yes—
179C3×Q8—28no—
180C3×Q8—28no—
181C3×Q8—44no—
182C3×Q8—44no—
183C2×C3×C4—28no—
184C2×C3×C4—44no—
185C2×C3×C4—44no—
186C2×C3×C4—48no—
187C2×C3×C4—44no—
188C2×C3×C4C2×C4×D314yes—
189C2×C3×C4#23514yes—
190C2×C3×C4D3×D414yes—
191C2×C3×C4D3×D414yes—
192C2×C3×C4#23714yes—
193C2×C3×C4C2×#6714yes—
194C2×Dic3—68no—
195C2×Dic3—68no—
196C2×Dic3—68no—
197C2×Dic3—68no—
198C2×Dic3—124no—
199C2×Dic3—124no—
200C2×Dic3—128no—
201C2×Dic3—124no—
202Dic6—68no—
203Dic6—68no—
204Dic6—124no—
205Dic6—124no—
206C3×C8—28no—
207C3⋊C8—316no—
208C2×C32#39011yescharacteristic
209C2×C32#44112yes—
210C2×C32#47012yes—
211C2×C32#49711yescharacteristic
212C2×C32#49711yescharacteristic
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—21no—
218C2×Q8—92no—
219C2×Q8—181no—
220C2×Q8—181no—
221C2×Q8—181no—
222C2×Q8—181no—
223C2×Q8—181no—
224C2×Q8C4×C3⋊D312yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—92no—
228C22×C4—181no—
229C22×C4—181no—
230C22×C4C22×C3⋊D311yescharacteristic
231Q16—188no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—92no—
235C2×C8—92no—
236C2×C8—92no—
237C2×C8#63812yes—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—181no—
241C4⋊C4—181no—
242C42—181no—
243C42—181no—
244C22×C3#67⋊C414yes—
245C22×C3#88414yes—
246C22×C3#91518yes—
247C22×C3#91818yes—
248C22×C3#94014yes—
249C3×C4—48no—
250C3×C4—84no—
251C3×C4D3×C22⋊C414yes—
252C3×C4#88514yes—
253C3×C4C4×#6714yes—
254C3×C4#93914yes—
255Dic3—128no—
256Dic3—128no—
257Dic3—244no—
258C32#197111yescharacteristic, complemented, Sylow
259C23D4×C3⋊D311yescharacteristic
260Q8—22no—
261Q8—22no—
262Q8—41no—
263Q8—41no—
264Q8—182no—
265Q8—182no—
266Q8—361no—
267Q8—361no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—182no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—361no—
278C2×C4—361no—
279C2×C4—362no—
280C2×C4—361no—
281C2×C4C2×C4×C3⋊D311yescharacteristic
282C2×C4#382811yescharacteristic
283C2×C4D4×C3⋊D311yescharacteristic
284C2×C4D4×C3⋊D311yescharacteristic
285C2×C4#383011yescharacteristic
286C2×C4C2×#63811yescharacteristic
287C8—22no—
288C8—94no—
289C2×C3#478918yes—
290C2×C3#481618yes—
291C2×C3#495714yes—
292C2×C3#516714yes—
293C2×C3#519014yes—
294C22#6409011yescharacteristic
295C22#6409311yescharacteristic
296C22#6412412yes—
297C22#6412712yes—
298C22#6414911yescharacteristic
299C4—42no—
300C4—81no—
301C4—362no—
302C4—362no—
303C4—721no—
304C4C22⋊C4×C3⋊D311yescharacteristic
305C4#6409411yescharacteristic
306C4C4×#63811yescharacteristic
307C4#6414811yescharacteristic
308C3#7025914yescomplemented
309C2#1059248812yes—
310C2#1059251512yes—
311C2#1059265611yescharacteristic
312C2#1059286611yescharacteristic
313C2#1059288911yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1971
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
15. C2×#3756C4semidirect
258. C32#1971semidirect
308. C3#70259semidirect

Maximal subgroups

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

subgroupindex
C22×#37562
C2×C32×#1032
#105929282
C2×#636432
C2×#636422
#105926722
C2×#636352
#702593