Finite Group Databasebeta

← #11790087

Subgroups — #11790087

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 297 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#389C211yesmaximal, characteristic
2C2×#63635C211yesmaximal, characteristic
3C2×#63635C211yesmaximal, characteristic
4#10592627C211yesmaximal, characteristic
5C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic
8#69618—34nomaximal
9C2×C32×C4⋊C4—21no—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×#3750—21no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C32×#95—21no—
19#63658—21no—
20#63635—22no—
21#63635C414yescomplemented
22C4×C3⋊(C3⋊C8)—22no—
23C3×#389D314yes—
24C2×#808—34no—
25C2×#808—34no—
26#4928—34no—
27C2×C4×C3⋊C8—34no—
28#4529—34no—
29#4529—34no—
30C22×C32×C4—21no—
31C22×C32×C4—21no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—42no—
41C32×C4⋊C4C2×C412yes—
42C32×C42—21no—
43C32×C42—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)C2×C412yes—
48#3750—42no—
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)C2×C412yes—
52C2×C3⋊(C3⋊C8)D412yes—
53C2×C3⋊(C3⋊C8)Q812yes—
54C2×C3⋊(C3⋊C8)Q812yes—
55#1941—91noSylow
56C2×C3×C4⋊C4—24no—
57C2×C3×C4⋊C4C2×D314yes—
58C2×C3×C4⋊C4C2×D314yes—
59C2×C3×C42C2×D314yes—
60C2×C4⋊Dic3—34no—
61C2×C4⋊Dic3—34no—
62C2×Dic3⋊C4—64no—
63C22×C3⋊C8—34no—
64C22×C3⋊C8—34no—
65C3×#95—24no—
66C3⋊#95—64no—
67#808—316no—
68#808—68no—
69C4×C3⋊C8—68no—
70C23×C32C2×D411yescharacteristic
71C2×C32×C4—21no—
72C2×C32×C4—21no—
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4—22no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4—41no—
79C2×C32×C4—41no—
80C2×C32×C4—41no—
81C2×C32×C4SD1612yes—
82C2×C32×C4SD1612yes—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×Q811yescharacteristic
86C2×C32×C4C2×Q811yescharacteristic
87C2×C32×C4#4111yescharacteristic
88C2×C32×C4#4111yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3—41no—
92C2×C3⋊Dic3—41no—
93C2×C3⋊Dic3—41no—
94C2×C3⋊Dic3—41no—
95C3⋊(C3⋊C8)—22no—
96C3⋊(C3⋊C8)C4⋊C414yescomplemented
97C2×#106—91no—
98C2×#106—91no—
99C2×C4×C8—91no—
100#389—91no—
101#389C3⋊D311yescharacteristic
102#340—91no—
103#340—91no—
104C22×C3×C4—24no—
105C22×C3×C4—24no—
106C22×C3×C4#6714yes—
107C22×C3×C4#6714yes—
108C22×C3×C4C22×D314yes—
109C22×Dic3—64no—
110C22×Dic3—64no—
111C3×C4⋊C4—24no—
112C3×C4⋊C4—24no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—48no—
115C3×C4⋊C4C4×D318yes—
116C3×C42—24no—
117C3×C42—24no—
118C4⋊Dic3—38no—
119C4⋊Dic3—64no—
120C4⋊Dic3—64no—
121C4⋊Dic3—64no—
122Dic3⋊C4—128no—
123C2×C3⋊C8—38no—
124C2×C3⋊C8—38no—
125C2×C3⋊C8—38no—
126C2×C3⋊C8—38no—
127C2×C3⋊C8—64no—
128C2×C3⋊C8—64no—
129C22×C32C4×D411yescharacteristic
130C22×C32#12111yescharacteristic
131C22×C32C4⋊Q811yescharacteristic
132C22×C32C2×SD1611yescharacteristic
133C22×C32C2×SD1611yescharacteristic
134C22×C32#13511yescharacteristic
135C22×C32#13511yescharacteristic
136C32×C4—22no—
137C32×C4—22no—
138C32×C4—42no—
139C32×C4—81no—
140C32×C4C2×C4⋊C411yescharacteristic
141C32×C4C4×Q811yescharacteristic
142C32×C4C22⋊Q811yescharacteristic
143C32×C4#12511yescharacteristic
144C3⋊Dic3—42no—
145C3⋊Dic3—81no—
146C22×C8—91no—
147C22×C8—91no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—91no—
150C2×C4⋊C4—91no—
151C2×C4⋊C4—181no—
152C2×C4⋊C4C2×C3⋊D311yescharacteristic
153C2×C4⋊C4C2×C3⋊D311yescharacteristic
154C2×C42C2×C3⋊D311yescharacteristic
155#106—94no—
156#106—182no—
157C4×C8—182no—
158#95—21no—
159#95—181no—
160C23×C3C2×#6714yes—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—24no—
164C2×C3×C4—24no—
165C2×C3×C4—28no—
166C2×C3×C4—44no—
167C2×C3×C4—44no—
168C2×C3×C4—44no—
169C2×C3×C4—44no—
170C2×C3×C4—44no—
171C2×C3×C4#21418yes—
172C2×C3×C4#21518yes—
173C2×C3×C4C2×C4×D314yes—
174C2×C3×C4#23514yes—
175C2×C3×C4D3×D414yes—
176C2×C3×C4#23714yes—
177C2×C3×C4D3×Q814yes—
178C2×C3×C4D3×Q814yes—
179C2×Dic3—68no—
180C2×Dic3—124no—
181C2×Dic3—124no—
182C2×Dic3—124no—
183C2×Dic3—124no—
184C2×Dic3—124no—
185C3⋊C8—316no—
186C3⋊C8—68no—
187C2×C32#38911yescharacteristic
188C2×C32C4×SD1611yescharacteristic
189C2×C32C4×SD1611yescharacteristic
190C2×C32#46511yescharacteristic
191C2×C32#46511yescharacteristic
192C2×C32#49811yescharacteristic
193C2×C32#49911yescharacteristic
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—181no—
197C22×C4—181no—
198C22×C4#63811yescharacteristic
199C22×C4#63811yescharacteristic
200C22×C4C22×C3⋊D311yescharacteristic
201C2×C8—92no—
202C2×C8—92no—
203C2×C8—92no—
204C2×C8—92no—
205C2×C8—181no—
206C2×C8—181no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—42no—
211C4⋊C4—92no—
212C4⋊C4—181no—
213C4⋊C4—181no—
214C4⋊C4—181no—
215C4⋊C4—362no—
216C4⋊C4C4×C3⋊D312yes—
217C42—21no—
218C42—21no—
219C22×C3C4×#6714yes—
220C22×C3C2×#21414yes—
221C22×C3#93914yes—
222C22×C3C2×#21514yes—
223C22×C3#94414yes—
224C22×C3#95014yes—
225C22×C3#95014yes—
226C3×C4—28no—
227C3×C4—28no—
228C3×C4—48no—
229C3×C4—84no—
230C3×C4#88714yes—
231C3×C4#88914yes—
232C3×C4D3×C4⋊C414yes—
233C3×C4#89614yes—
234Dic3—128no—
235Dic3—244no—
236C32#194111yescharacteristic, complemented, Sylow
237C23C2×#63811yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—182no—
249C2×C4—361no—
250C2×C4—361no—
251C2×C4—361no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4#375412yes—
255C2×C4#375512yes—
256C2×C4C2×C4×C3⋊D311yescharacteristic
257C2×C4#382811yescharacteristic
258C2×C4D4×C3⋊D311yescharacteristic
259C2×C4#383011yescharacteristic
260C2×C4Q8×C3⋊D311yescharacteristic
261C2×C4Q8×C3⋊D311yescharacteristic
262C8—94no—
263C8—182no—
264C2×C3#497614yes—
265C2×C3C4×#21414yes—
266C2×C3C4×#21514yes—
267C2×C3#504114yes—
268C2×C3#504814yes—
269C2×C3#506514yes—
270C2×C3#508014yes—
271C22C4×#63811yescharacteristic
272C22C2×#375411yescharacteristic
273C22#6414811yescharacteristic
274C22C2×#375511yescharacteristic
275C22#6415311yescharacteristic
276C22#6415911yescharacteristic
277C22#6415911yescharacteristic
278C4—22no—
279C4—22no—
280C4—42no—
281C4—81no—
282C4—362no—
283C4—721no—
284C4#6409611yescharacteristic
285C4#6409811yescharacteristic
286C4C4⋊C4×C3⋊D311yescharacteristic
287C4#6410511yescharacteristic
288C3#6961814yescomplemented
289C2#1059267511yescharacteristic
290C2C4×#375411yescharacteristic
291C2C4×#375511yescharacteristic
292C2#1059274011yescharacteristic
293C2#1059274711yescharacteristic
294C2#1059276411yescharacteristic
295C2#1059277911yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#389C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenter#389C3⋊D3
hypocenterC32#1941
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
21. #63635C4semidirect
96. C3⋊(C3⋊C8)C4⋊C4semidirect
236. C32#1941semidirect
288. C3#69618semidirect

Maximal subgroups

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

subgroupindex
C32×#3892
C2×#636352
#105926272
C2×C4×C3⋊(C3⋊C8)2
#105893952
#696183