Finite Group Databasebeta

← #11789039

Subgroups — #11789039

Order 1152.

690 conjugacy classes of subgroups.

The subgroup lattice has 291 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C4×C4⋊C4C211yesmaximal, characteristic
2C2×#63634C211yesmaximal, characteristic
3#10592627C211yesmaximal, characteristic
4#10589395C211yesmaximal, characteristic
5#10589395C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic
7#10589390C211yesmaximal, characteristic
8#69458—34nomaximal
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C32×C42—21no—
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#63634C414yescomplemented
21C3×C4×C4⋊C4D314yes—
22C2×#807—34no—
23#4928—34no—
24#4529—34no—
25#4529—34no—
26#4529—34no—
27#4524—34no—
28C22×C32×C4—21no—
29C22×C32×C4—21no—
30C22×C32×C4D411yescharacteristic
31C22×C32×C4D411yescharacteristic
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3—21no—
34C22×C3⋊Dic3—21no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C412yes—
38C32×C4⋊C4Q812yes—
39C32×C42—21no—
40C32×C42—21no—
41C32×C42—42no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)C2×C412yes—
46#3750—42no—
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—21no—
49C2×C3⋊(C3⋊C8)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)C2×C412yes—
53#1918—91noSylow
54C2×C3×C4⋊C4C2×D314yes—
55C2×C3×C4⋊C4C2×D314yes—
56C2×C3×C42—24no—
57C2×C3×C42C2×D314yes—
58C2×C4⋊Dic3—34no—
59C2×C4⋊Dic3—34no—
60C2×Dic3⋊C4—64no—
61C22×C3⋊C8—34no—
62C22×C3⋊C8—34no—
63C3×#95—24no—
64C3⋊#95—64no—
65#807—316no—
66C23×C32C2×D411yescharacteristic
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4—22no—
70C2×C32×C4—22no—
71C2×C32×C4—21no—
72C2×C32×C4—21no—
73C2×C32×C4—21no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4—41no—
77C2×C32×C4—41no—
78C2×C32×C4D812yes—
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×Q811yescharacteristic
81C2×C32×C4#4111yescharacteristic
82C2×C32×C4#4111yescharacteristic
83C2×C32×C4#4111yescharacteristic
84C2×C32×C4#4111yescharacteristic
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—41no—
87C2×C3⋊Dic3—41no—
88C2×C3⋊Dic3—41no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91C3⋊(C3⋊C8)—22no—
92C3⋊(C3⋊C8)—41no—
93C2×#107—91no—
94#389—91no—
95C4×C4⋊C4C3⋊D311yescharacteristic
96#340—91no—
97#340—91no—
98#340—91no—
99#336—91no—
100C22×C3×C4—24no—
101C22×C3×C4—24no—
102C22×C3×C4#6714yes—
103C22×C3×C4#6714yes—
104C22×C3×C4C22×D314yes—
105C22×Dic3—64no—
106C22×Dic3—64no—
107C3×C4⋊C4—24no—
108C3×C4⋊C4—24no—
109C3×C4⋊C4Dic618yes—
110C3×C4⋊C4C4×D318yes—
111C3×C42—24no—
112C3×C42—24no—
113C3×C42—48no—
114C4⋊Dic3—38no—
115C4⋊Dic3—64no—
116C4⋊Dic3—64no—
117C4⋊Dic3—64no—
118Dic3⋊C4—128no—
119C2×C3⋊C8—38no—
120C2×C3⋊C8—64no—
121C2×C3⋊C8—64no—
122C2×C3⋊C8—64no—
123C2×C3⋊C8—64no—
124C2×C3⋊C8—64no—
125C22×C32C4×D411yescharacteristic
126C22×C32C22⋊Q811yescharacteristic
127C22×C32#12311yescharacteristic
128C22×C32C2×D811yescharacteristic
129C22×C32#13511yescharacteristic
130C22×C32#13711yescharacteristic
131C22×C32#13711yescharacteristic
132C32×C4—22no—
133C32×C4—42no—
134C32×C4—42no—
135C32×C4—41no—
136C32×C4#11711yescharacteristic
137C32×C4C4×Q811yescharacteristic
138C32×C4#12511yescharacteristic
139C32×C4#12611yescharacteristic
140C3⋊Dic3—42no—
141C3⋊Dic3—81no—
142C22×C8—91no—
143C22×C8—91no—
144C2×C4⋊C4—91no—
145C2×C4⋊C4—91no—
146C2×C4⋊C4—181no—
147C2×C4⋊C4C2×C3⋊D311yescharacteristic
148C2×C4⋊C4C2×C3⋊D311yescharacteristic
149C2×C42—21no—
150C2×C42C2×C3⋊D311yescharacteristic
151#107—94no—
152#95—21no—
153#95—181no—
154C23×C3C2×#6714yes—
155C2×C3×C4—24no—
156C2×C3×C4—24no—
157C2×C3×C4—28no—
158C2×C3×C4—28no—
159C2×C3×C4—24no—
160C2×C3×C4—24no—
161C2×C3×C4—24no—
162C2×C3×C4—44no—
163C2×C3×C4—44no—
164C2×C3×C4—44no—
165C2×C3×C4—44no—
166C2×C3×C4#21318yes—
167C2×C3×C4C2×Dic614yes—
168C2×C3×C4C2×C4×D314yes—
169C2×C3×C4#23514yes—
170C2×C3×C4#23514yes—
171C2×C3×C4#23514yes—
172C2×C3×C4#23514yes—
173C2×Dic3—68no—
174C2×Dic3—124no—
175C2×Dic3—124no—
176C2×Dic3—124no—
177C2×Dic3—124no—
178C2×Dic3—124no—
179C3⋊C8—68no—
180C3⋊C8—124no—
181C2×C32#38711yescharacteristic
182C2×C32C4×D811yescharacteristic
183C2×C32#44111yescharacteristic
184C2×C32#47411yescharacteristic
185C2×C32#47911yescharacteristic
186C2×C32#48011yescharacteristic
187C2×C32#48511yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—181no—
191C22×C4—181no—
192C22×C4#63811yescharacteristic
193C22×C4#63811yescharacteristic
194C22×C4C22×C3⋊D311yescharacteristic
195C2×C8—92no—
196C2×C8—181no—
197C2×C8—181no—
198C2×C8—181no—
199C2×C8—181no—
200C2×C8—181no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—92no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4—181no—
207C4⋊C4—362no—
208C4⋊C4#63412yes—
209C4⋊C4C4×C3⋊D312yes—
210C42—21no—
211C42—21no—
212C42—42no—
213C22×C3#92414yes—
214C22×C3C4×#6714yes—
215C22×C3#92914yes—
216C22×C3C2×#21314yes—
217C22×C3#94214yes—
218C22×C3#95014yes—
219C22×C3#95114yes—
220C3×C4—28no—
221C3×C4—44no—
222C3×C4—48no—
223C3×C4—48no—
224C3×C4C4×Dic614yes—
225C3×C4#87014yes—
226C3×C4#87214yes—
227C3×C4#87614yes—
228Dic3—128no—
229Dic3—244no—
230C32#191811yescharacteristic, complemented, Sylow
231C23C2×#63811yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—182no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4#375312yes—
250C2×C4C2×#63411yescharacteristic
251C2×C4C2×C4×C3⋊D311yescharacteristic
252C2×C4#382811yescharacteristic
253C2×C4#382811yescharacteristic
254C2×C4#382811yescharacteristic
255C2×C4#382811yescharacteristic
256C8—182no—
257C8—361no—
258C2×C3#493314yes—
259C2×C3#496714yes—
260C2×C3#499614yes—
261C2×C3#500714yes—
262C2×C3C4×#21314yes—
263C2×C3#502214yes—
264C2×C3#503014yes—
265C22#6413311yescharacteristic
266C22C4×#63811yescharacteristic
267C22#6413811yescharacteristic
268C22C2×#375311yescharacteristic
269C22#6415111yescharacteristic
270C22#6415911yescharacteristic
271C22#6416011yescharacteristic
272C4—22no—
273C4—41no—
274C4—42no—
275C4—42no—
276C4—362no—
277C4—721no—
278C4C4×#63411yescharacteristic
279C4#6407911yescharacteristic
280C4#6408111yescharacteristic
281C4#6408511yescharacteristic
282C3#6945814yescomplemented
283C2#1059263211yescharacteristic
284C2#1059266611yescharacteristic
285C2#1059269511yescharacteristic
286C2#1059270611yescharacteristic
287C2C4×#375311yescharacteristic
288C2#1059272111yescharacteristic
289C2#1059272911yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC4×C4⋊C4C3⋊D3
hypocenterC32#1918
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
20. #63634C4semidirect
230. C32#1918semidirect
282. C3#69458semidirect

Maximal subgroups

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

subgroupindex
C32×C4×C4⋊C42
C2×#636342
#105926272
#105893952
#105893902
#694583