Finite Group Databasebeta

← #11791861

Subgroups — #11791861

Order 1152.

780 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
1C2×#64097C211yesmaximal, characteristic
2#10592817C211yesmaximal, characteristic
3M16×C3⋊Dic3C211yesmaximal, characteristic
4C32×#343C211yesmaximal, characteristic
5#10589420C211yesmaximal, characteristic
6#10589420C211yesmaximal, characteristic
7#10589396C211yesmaximal, characteristic
8#68974—34nomaximal
9C22×#634C412yes—
10C2×C32×M16C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3750C412yes—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18#64097—21no—
19#64097—21no—
20#64097—21no—
21#64097—21no—
22#63642—21no—
23#63641—21no—
24#63641—21no—
25C8×C3⋊Dic3—21no—
26C2×#888—34no—
27#5118—34no—
28Dic3×M16—34no—
29C3×#343D314yes—
30#4554—34no—
31#4554—34no—
32#4530—34no—
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C22×C3⋊Dic3C2×C412yes—
38C2×#634—22no—
39C2×#634—22no—
40C2×#634—44no—
41C32×M16—21no—
42C32×M16—21no—
43C32×M16—21no—
44C32×M16Q812yescomplemented
45C2×C32×C8—21no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51#3750—22no—
52#3750—22no—
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C4×C3⋊Dic3D411yescharacteristic
57#3748—21no—
58#3748—21no—
59#3748—21no—
60#3748Q812yescomplemented
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63#1997—91noSylow
64C22×Dic6—38no—
65C2×C3×M16C2×D314yes—
66C2×C3×M16C2×D314yes—
67C2×C3×C4⋊C4C2×D314yes—
68C2×C4⋊Dic3—34no—
69C2×Dic3⋊C4—38no—
70C2×C4×Dic3—34no—
71C2×#208—34no—
72C2×#208—34no—
73#888—64no—
74#888—64no—
75#888—64no—
76#888—64no—
77#815—64no—
78Dic3⋊C8—64no—
79Dic3⋊C8—64no—
80C8×Dic3—64no—
81C23×C32C22×C411yescharacteristic
82C2×C32×C4—22no—
83C2×C32×C4—42no—
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×Q811yescharacteristic
87C2×C32×C4C2×Q811yescharacteristic
88C2×C32×C4#4111yescharacteristic
89C2×C32×C4#4111yescharacteristic
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—22no—
92C2×C3⋊Dic3—22no—
93C2×C3⋊Dic3—42no—
94C2×C3⋊Dic3C22⋊C411yescharacteristic
95C2×C3⋊Dic3C22⋊C411yescharacteristic
96C2×C3⋊Dic3C22⋊C411yescharacteristic
97C2×C3⋊Dic3C22⋊C411yescharacteristic
98#634—44no—
99#634—44no—
100C32×C8—22no—
101C32×C8—41no—
102C3⋊(C3⋊C8)—22no—
103C3⋊(C3⋊C8)—41no—
104C2×C4⋊Q8—91no—
105#423—91no—
106C4×M16—91no—
107#343—91no—
108#343—91no—
109#343—91no—
110#343C3⋊D311yescharacteristic
111C22×C3×C4C4×D318yes—
112C22×C3×C4C22×D314yes—
113C22×Dic3—34no—
114C22×Dic3—34no—
115C22×Dic3—38no—
116C2×Dic6—68no—
117C2×Dic6—68no—
118C2×Dic6—1216no—
119C3×M16—24no—
120C3×M16—24no—
121C3×M16—24no—
122C3×M16Dic618yescomplemented
123C2×C3×C8—24no—
124C2×C3×C8—24no—
125C3×C4⋊C4—24no—
126C3×C4⋊C4—24no—
127C4⋊Dic3—64no—
128C4⋊Dic3—64no—
129Dic3⋊C4—68no—
130Dic3⋊C4—68no—
131C4×Dic3—34no—
132C4×Dic3—34no—
133C4×Dic3—34no—
134C4×Dic3—34no—
135#208—38no—
136#208—64no—
137#208—64no—
138#208—64no—
139C2×C3⋊C8—64no—
140C2×C3⋊C8—64no—
141C22×C32—21no—
142C22×C32—21no—
143C22×C32C2×C22⋊C411yescharacteristic
144C22×C32C4×Q811yescharacteristic
145C22×C32C4×Q811yescharacteristic
146C32×C4—42no—
147C32×C4C22⋊Q811yescharacteristic
148C32×C4C22⋊Q811yescharacteristic
149C32×C4#12411yescharacteristic
150C32×C4C4⋊Q811yescharacteristic
151C3⋊Dic3—21no—
152C3⋊Dic3—21no—
153C3⋊Dic3—42no—
154C3⋊Dic3#10012yes—
155C3⋊Dic3#10112yes—
156C22×Q8—92no—
157C2×M16—91no—
158C2×M16—91no—
159C2×M16C2×C3⋊D311yescharacteristic
160C2×M16C2×C3⋊D311yescharacteristic
161C4⋊Q8—181no—
162C4⋊Q8—181no—
163C4⋊Q8—181no—
164C4⋊Q8—181no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4C2×C3⋊D311yescharacteristic
168C2×C42—91no—
169C4⋊C8—181no—
170C4⋊C8—181no—
171#97—181no—
172C4×C8—181no—
173C23×C3C2×C4×D314yes—
174C2×C3×C4—28no—
175C2×C3×C4—48no—
176C2×C3×C4C2×Dic614yes—
177C2×C3×C4#23514yes—
178C2×C3×C4D3×D414yes—
179C2×C3×C4D3×D414yes—
180C2×C3×C4#23714yes—
181C2×C3×C4D3×Q814yes—
182C2×Dic3—34no—
183C2×Dic3—34no—
184C2×Dic3—34no—
185C2×Dic3—34no—
186C2×Dic3—68no—
187C2×Dic3—68no—
188C2×Dic3—68no—
189C2×Dic3—128no—
190Dic6—1216no—
191Dic6—1216no—
192C3×C8—28no—
193C3×C8—44no—
194C3⋊C8—68no—
195C3⋊C8—124no—
196C2×C32—21no—
197C2×C32—21no—
198C2×C32#39111yescharacteristic
199C2×C32C2×#10011yescharacteristic
200C2×C32C2×#10111yescharacteristic
201C2×Q8—182no—
202C2×Q8—182no—
203C2×Q8—364no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—92no—
207C22×C4C4×C3⋊D312yes—
208C22×C4C22×C3⋊D311yescharacteristic
209M16—21no—
210M16—21no—
211M16—21no—
212M16—92no—
213M16—181no—
214M16—181no—
215M16—181no—
216M16#63412yescomplemented
217C2×C8—21no—
218C2×C8—21no—
219C2×C8—181no—
220C2×C8—181no—
221C4⋊C4—21no—
222C4⋊C4—21no—
223C4⋊C4—182no—
224C4⋊C4—182no—
225C4⋊C4—181no—
226C4⋊C4—181no—
227C42—91no—
228C42—91no—
229C42—91no—
230C42—91no—
231C22×C3—24no—
232C22×C3—24no—
233C22×C3C4×Dic614yes—
234C22×C3D3×C22⋊C414yes—
235C22×C3#88714yes—
236C3×C4—48no—
237C3×C4#87814yes—
238C3×C4#88514yes—
239C3×C4#88814yes—
240C3×C4#89614yes—
241Dic3—38no—
242Dic3—38no—
243Dic3—64no—
244Dic3—64no—
245Dic3—128no—
246C32#199711yescharacteristic, complemented, Sylow
247C23C2×C4×C3⋊D311yescharacteristic
248Q8—364no—
249Q8—364no—
250C2×C4—22no—
251C2×C4—42no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—91no—
255C2×C4—91no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—182no—
259C2×C4—362no—
260C2×C4C2×#63411yescharacteristic
261C2×C4#382811yescharacteristic
262C2×C4D4×C3⋊D311yescharacteristic
263C2×C4D4×C3⋊D311yescharacteristic
264C2×C4#383011yescharacteristic
265C2×C4Q8×C3⋊D311yescharacteristic
266C8—22no—
267C8—41no—
268C8—182no—
269C8—361no—
270C2×C3—24no—
271C2×C3—24no—
272C2×C3#464614yes—
273C2×C3D3×#10014yes—
274C2×C3D3×#10114yes—
275C22—21no—
276C22—21no—
277C22C4×#63411yescharacteristic
278C22C22⋊C4×C3⋊D311yescharacteristic
279C22#6409611yescharacteristic
280C4—42no—
281C4—92no—
282C4—92no—
283C4—181no—
284C4—181no—
285C4—362no—
286C4#6408711yescharacteristic
287C4#6409411yescharacteristic
288C4#6409711yescharacteristic
289C4#6410511yescharacteristic
290C3#6897414yescomplemented
291C2—21no—
292C2—21no—
293C2#1059234511yescharacteristic
294C2C3⋊D3×#10011yescharacteristic
295C2C3⋊D3×#10111yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#343C2
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenter#343C3⋊D3
hypocenterC32#1997
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
44. C32×M16Q8semidirect
60. #3748Q8semidirect
122. C3×M16Dic6semidirect
216. M16#634semidirect
246. C32#1997semidirect
290. C3#68974semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
#105928172
M16×C3⋊Dic32
C32×#3432
#105894202
#105893962
#689743