Finite Group Databasebeta

← #11790605

Subgroups — #11790605

Order 1152.

996 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic
5C2×C8×C3⋊Dic3C211yesmaximal, characteristic
6#10592674C211yesmaximal, characteristic
7C2×#63637C211yesmaximal, characteristic
8#70225—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13#64153—22no—
14#64153C414yescomplemented
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—22no—
17C2×#3750—22no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C32×#103—22no—
21#63662—22no—
22#63643—22no—
23C8×C3⋊Dic3—22no—
24#63637—22no—
25C2×#944—34no—
26C2×C3×#103D314yes—
27C2×#835—34no—
28C2×#816—34no—
29C2×C8×Dic3—34no—
30#4975—34no—
31C2×#810—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—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57#3750—28no—
58#3750—44no—
59C4×C3⋊Dic3C2×C412yes—
60C4×C3⋊Dic3D412yes—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)D412yes—
64#1956—91noSylow
65C22×C3×Q8C2×D314yes—
66C22×Dic6—34no—
67C22×C3×C8C2×D314yes—
68C2×C3×C4⋊C4C2×D314yes—
69#944—316no—
70#944—68no—
71C2×C4⋊Dic3—34no—
72C2×Dic3⋊C4—68no—
73C2×Dic3⋊C4—68no—
74C2×C4×Dic3—34no—
75C22×C3⋊C8—34no—
76C3×#103—28no—
77#835—68no—
78#816—68no—
79C8×Dic3—68no—
80#810—68no—
81C23×C32C2×D411yescharacteristic
82C32×Q8—22no—
83C32×Q8—22no—
84C32×Q8—41no—
85C32×Q8—41no—
86C2×C32×C4—22no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—42no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4#4111yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—42no—
102C2×C3⋊Dic3C22⋊C414yes—
103C2×C3⋊Dic3SD1614yes—
104C2×C3⋊Dic3Q1614yes—
105#634—22no—
106#634—22no—
107#634—41no—
108#634—41no—
109C32×C8—22no—
110C3⋊(C3⋊C8)—22no—
111C2×C4⋊Q8—91no—
112C2×#103—91no—
113C2×#103—91no—
114C2×#103—91no—
115C2×#103C3⋊D311yescharacteristic
116C2×C4×C8—91no—
117#384—91no—
118C2×C3×Q8—24no—
119C2×C3×Q8—24no—
120C2×C3×Q8—24no—
121C2×C3×Q8—24no—
122C2×C3×Q8—24no—
123C2×C3×Q8C4×D318yes—
124C22×C3×C4—24no—
125C22×C3×C4—24no—
126C22×C3×C4C22×D314yes—
127C22×Dic3—38no—
128C22×Dic3—64no—
129C22×Dic3—64no—
130C2×Dic6—38no—
131C2×Dic6—64no—
132C2×Dic6—64no—
133C2×Dic6—64no—
134C2×Dic6—64no—
135C2×Dic6—64no—
136C2×C3×C8—24no—
137C2×C3×C8—24no—
138C2×C3×C8#6718yes—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—24no—
141C4⋊Dic3—64no—
142C4⋊Dic3—64no—
143Dic3⋊C4—632no—
144Dic3⋊C4—1216no—
145C4×Dic3—38no—
146C4×Dic3—38no—
147C2×C3⋊C8—38no—
148C2×C3⋊C8—64no—
149C2×C3⋊C8—64no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32#12411yescharacteristic
152C22×C32#12711yescharacteristic
153C22×C32C2×SD1612yes—
154C22×C32C2×Q1612yes—
155C32×C4—42no—
156C32×C4—81no—
157C32×C4C4×D411yescharacteristic
158C32×C4C4×D411yescharacteristic
159C32×C4#12111yescharacteristic
160C32×C4#12111yescharacteristic
161C3⋊Dic3—42no—
162C3⋊Dic3—81no—
163C3⋊Dic3#10318yescomplemented
164C22×Q8—91no—
165C22×Q8C2×C3⋊D311yescharacteristic
166C22×C8—91no—
167C22×C8C2×C3⋊D311yescharacteristic
168C4⋊Q8—94no—
169C4⋊Q8—182no—
170C2×C4⋊C4—91no—
171C2×C4⋊C4—182no—
172C2×C4⋊C4—182no—
173C2×C4⋊C4C2×C3⋊D311yescharacteristic
174C2×C42—91no—
175#103—22no—
176#103—182no—
177#103—182no—
178#103—182no—
179C4×C8—182no—
180C23×C3D3×D414yes—
181C3×Q8—28no—
182C3×Q8—28no—
183C3×Q8—44no—
184C3×Q8—44no—
185C2×C3×C4—28no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4—48no—
189C2×C3×C4—44no—
190C2×C3×C4C2×C4×D314yes—
191C2×C3×C4#23514yes—
192C2×C3×C4D3×D414yes—
193C2×C3×C4D3×D414yes—
194C2×C3×C4#23714yes—
195C2×C3×C4C2×#6714yes—
196C2×Dic3—316no—
197C2×Dic3—316no—
198C2×Dic3—316no—
199C2×Dic3—68no—
200C2×Dic3—124no—
201C2×Dic3—124no—
202C2×Dic3—128no—
203C2×Dic3—124no—
204Dic6—68no—
205Dic6—68no—
206Dic6—124no—
207Dic6—124no—
208C3×C8—28no—
209C3⋊C8—68no—
210C2×C32#39011yescharacteristic
211C2×C32C2×#10312yes—
212C2×C32#48712yes—
213C2×C32#49211yescharacteristic
214C2×C32#49411yescharacteristic
215C2×Q8—21no—
216C2×Q8—21no—
217C2×Q8—21no—
218C2×Q8—21no—
219C2×Q8—21no—
220C2×Q8—92no—
221C2×Q8—181no—
222C2×Q8—181no—
223C2×Q8—181no—
224C2×Q8—181no—
225C2×Q8—181no—
226C2×Q8C4×C3⋊D312yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—92no—
230C22×C4—181no—
231C22×C4—181no—
232C22×C4C22×C3⋊D311yescharacteristic
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—92no—
236C2×C8—181no—
237C2×C8—181no—
238C2×C8#63812yes—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—188no—
242C4⋊C4—181no—
243C4⋊C4—181no—
244C4⋊C4—364no—
245C42—92no—
246C42—92no—
247C22×C3D3×C22⋊C414yes—
248C22×C3#88514yes—
249C22×C3D3×SD1618yes—
250C22×C3D3×Q1618yes—
251C22×C3#94014yes—
252C3×C4—48no—
253C3×C4—84no—
254C3×C4#67⋊C414yes—
255C3×C4#88414yes—
256C3×C4C4×#6714yes—
257C3×C4#93914yes—
258Dic3—332no—
259Dic3—128no—
260Dic3—244no—
261C32#195611yescharacteristic, complemented, Sylow
262C23D4×C3⋊D311yescharacteristic
263Q8—22no—
264Q8—22no—
265Q8—41no—
266Q8—41no—
267Q8—182no—
268Q8—182no—
269Q8—361no—
270Q8—361no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—41no—
276C2×C4—94no—
277C2×C4—94no—
278C2×C4—94no—
279C2×C4—182no—
280C2×C4—361no—
281C2×C4—361no—
282C2×C4—362no—
283C2×C4—361no—
284C2×C4C2×C4×C3⋊D311yescharacteristic
285C2×C4#382811yescharacteristic
286C2×C4D4×C3⋊D311yescharacteristic
287C2×C4D4×C3⋊D311yescharacteristic
288C2×C4#383011yescharacteristic
289C2×C4C2×#63811yescharacteristic
290C8—22no—
291C8—182no—
292C2×C3#479218yes—
293C2×C3D3×#10318yes—
294C2×C3#495714yes—
295C2×C3#517514yes—
296C2×C3#518314yes—
297C22C22⋊C4×C3⋊D311yescharacteristic
298C22#6409411yescharacteristic
299C22SD16×C3⋊D312yes—
300C22Q16×C3⋊D312yes—
301C22#6414911yescharacteristic
302C4—42no—
303C4—81no—
304C4—98no—
305C4—362no—
306C4—721no—
307C4#6409011yescharacteristic
308C4#6409311yescharacteristic
309C4C4×#63811yescharacteristic
310C4#6414811yescharacteristic
311C3#7022514yescomplemented
312C2#1059249112yes—
313C2C3⋊D3×#10312yes—
314C2#1059265611yescharacteristic
315C2#1059287411yescharacteristic
316C2#1059288211yescharacteristic
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#1956
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
14. #64153C4semidirect
163. C3⋊Dic3#103semidirect
261. C32#1956semidirect
311. C3#70225semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C32×#1032
C2×#636622
C2×#636432
C2×C8×C3⋊Dic32
#105926742
C2×#636372
#702253