Finite Group Databasebeta

← #11794642

Subgroups — #11794642

Order 1152.

822 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#384C211yesmaximal, characteristic, complemented
2C2×#63636C212yesmaximal
3#10592638C211yesmaximal, characteristic
4#10589395C212yesmaximal, complemented
5#10589390C211yesmaximal, characteristic, complemented
6#69585—34nomaximal
7C22×C4⋊(C3⋊D3)C2211yescharacteristic
8C2×C32×C4⋊C4—21no—
9C2×C32×C4⋊C4—21no—
10C2×C32×C4⋊C4C2212yes—
11C2×C32×C42C2211yescharacteristic
12C2×#3752—21no—
13C2×#3752—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2212yes—
16#63636—24no—
17C3×#384D314yescomplemented
18C2×#809—38no—
19#4939—34no—
20#4529—38no—
21#4524—34no—
22C23×C3⋊D3—21no—
23C22×C32×C4—22no—
24C22×C32×C4D411yescharacteristic
25C22×C32×C4D411yescharacteristic
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3—21no—
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—22no—
30C2×C4⋊(C3⋊D3)—21no—
31C2×C4⋊(C3⋊D3)D412yes—
32C32×C4⋊C4—22no—
33C32×C4⋊C4—22no—
34C32×C4⋊C4—42no—
35C32×C4⋊C4—42no—
36C32×C42—22no—
37#3752—42no—
38#3752—42no—
39C4⋊(C3⋊Dic3)—22no—
40C2×C3⋊(C3⋊C8)—22no—
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)—22no—
43#2071—91noSylow
44C22×D12—34no—
45C2×C3×C4⋊C4—24no—
46C2×C3×C4⋊C4—24no—
47C2×C3×C4⋊C4C2×D318yes—
48C2×C3×C42C2×D314yes—
49C2×(C2×D3)⋊C4—64no—
50C2×(C2×D3)⋊C4—64no—
51C2×C4⋊Dic3—34no—
52C22×C3⋊C8—38no—
53#809—616no—
54C23×C32C2×D411yescharacteristic
55C22×C3⋊D3—22no—
56C22×C3⋊D3—41no—
57C22×C3⋊D3—41no—
58C22×C3⋊D3—41no—
59C22×C3⋊D3—41no—
60C22×C3⋊D3—41no—
61C22×C3⋊D3—41no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4—42no—
67C2×C32×C4—42no—
68C2×C32×C4—42no—
69C2×C32×C4D812yes—
70C2×C32×C4SD1612yes—
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4#4112yes—
73C2×C32×C4#4111yescharacteristic
74C2×C32×C4#4112yes—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3—41no—
77C2×C3⋊Dic3—41no—
78C4⋊(C3⋊D3)—24no—
79C4⋊(C3⋊D3)—42no—
80C3⋊(C3⋊C8)—42no—
81C2×#102—92no—
82#390—91no—
83#384C3⋊D311yescharacteristic, complemented
84#340—92no—
85#336—91no—
86C23×D3—64no—
87C22×C3×C4—28no—
88C22×C3×C4#6714yes—
89C22×C3×C4#6714yes—
90C22×C3×C4C22×D314yes—
91C22×Dic3—64no—
92C2×D12—38no—
93C2×D12—68no—
94C2×D12—68no—
95C2×D12—64no—
96C3×C4⋊C4—28no—
97C3×C4⋊C4—28no—
98C3×C4⋊C4—48no—
99C3×C4⋊C4—48no—
100C3×C42—28no—
101(C2×D3)⋊C4—128no—
102(C2×D3)⋊C4—128no—
103C4⋊Dic3—68no—
104C2×C3⋊C8—68no—
105C2×C3⋊C8—68no—
106C2×C3⋊C8—68no—
107C22×C32#12111yescharacteristic
108C22×C32#12311yescharacteristic
109C22×C32#12411yescharacteristic
110C22×C32C2×D811yescharacteristic
111C22×C32C2×SD1611yescharacteristic
112C22×C32AGL(1,ℤ/8)11yescharacteristic
113C22×C32#13711yescharacteristic
114C2×C3⋊D3—42no—
115C2×C3⋊D3—42no—
116C2×C3⋊D3—42no—
117C2×C3⋊D3—81no—
118C2×C3⋊D3—81no—
119C2×C3⋊D3—81no—
120C2×C3⋊D3—81no—
121C32×C4—22no—
122C32×C4—22no—
123C32×C4—82no—
124C32×C4#12312yes—
125C32×C4#12612yes—
126C3⋊Dic3—81no—
127C22×D4—91no—
128C22×C8—92no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4C2×C3⋊D312yes—
133C2×C22⋊C4—181no—
134C2×C22⋊C4—181no—
135C2×C42C2×C3⋊D311yescharacteristic
136#102—184no—
137C23×C3C2×#6714yes—
138C22×D3—68no—
139C22×D3—124no—
140C22×D3—124no—
141C22×D3—124no—
142C22×D3—124no—
143C22×D3—124no—
144C22×D3—124no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—48no—
150C2×C3×C4—48no—
151C2×C3×C4—48no—
152C2×C3×C4#21318yes—
153C2×C3×C4#21518yes—
154C2×C3×C4#23518yes—
155C2×C3×C4D3×D414yes—
156C2×C3×C4#23714yes—
157C2×C3×C4#23918yes—
158C2×Dic3—124no—
159C2×Dic3—124no—
160C2×Dic3—124no—
161D12—616no—
162D12—128no—
163C3⋊C8—128no—
164C2×C32#39711yescharacteristic
165C2×C32#45911yescharacteristic
166C2×C32#46111yescharacteristic
167C2×C32#48011yescharacteristic
168C2×C32#48111yescharacteristic
169C2×C32#48611yescharacteristic
170C2×C32#48911yescharacteristic
171C3⋊D3—82no—
172C24—181no—
173C2×D4—92no—
174C2×D4—182no—
175C2×D4—181no—
176C2×D4—182no—
177C22×C4—22no—
178C22×C4—181no—
179C22×C4#63811yescharacteristic
180C22×C4#63811yescharacteristic
181C22×C4C22×C3⋊D311yescharacteristic
182C2×C8—182no—
183C2×C8—182no—
184C2×C8—182no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—182no—
190C22⋊C4—362no—
191C22⋊C4—362no—
192C42—22no—
193C22×C3#92914yes—
194C22×C3C2×#21314yes—
195C22×C3#93214yes—
196C22×C3#93814yes—
197C22×C3C2×#21514yes—
198C22×C3#94214yes—
199C22×C3#94714yes—
200C2×D3—128no—
201C2×D3—128no—
202C2×D3—128no—
203C2×D3—244no—
204C2×D3—244no—
205C2×D3—244no—
206C2×D3—244no—
207C3×C4—28no—
208C3×C4—28no—
209C3×C4—88no—
210C3×C4#89418yes—
211C3×C4#89818yes—
212Dic3—244no—
213C32#207111yescharacteristic, complemented, Sylow
214C23—182no—
215C23—361no—
216C23—361no—
217C23—361no—
218C23—361no—
219C23—361no—
220C23—361no—
221C23C2×#63811yescharacteristic
222D4—184no—
223D4—362no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—361no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4#375312yes—
235C2×C4#375512yes—
236C2×C4#382812yes—
237C2×C4D4×C3⋊D311yescharacteristic
238C2×C4#383011yescharacteristic
239C2×C4#383212yes—
240C8—362no—
241C2×C3#496714yes—
242C2×C3#496814yes—
243C2×C3#499214yes—
244C2×C3#507214yes—
245C2×C3#508314yes—
246C2×C3#508814yes—
247C2×C3#508914yes—
248D3—248no—
249C22—362no—
250C22—362no—
251C22—362no—
252C22—721no—
253C22—721no—
254C22—721no—
255C22—721no—
256C22#6413811yescharacteristic
257C22C2×#375311yescharacteristic
258C22#6414111yescharacteristic
259C22#6414711yescharacteristic
260C22C2×#375511yescharacteristic
261C22#6415111yescharacteristic
262C22#6415611yescharacteristic
263C4—22no—
264C4—22no—
265C4—82no—
266C4—721no—
267C4#6410312yes—
268C4#6410712yes—
269C3#6958514yescomplemented
270C2—722no—
271C2#1059266611yescharacteristic
272C2#1059266711yescharacteristic
273C2#1059269111yescharacteristic
274C2#1059277111yescharacteristic
275C2#1059278211yescharacteristic
276C2#1059278711yescharacteristic
277C2#1059278811yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#384C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#384C3⋊D3
hypocenterC32#2071
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C32×#384C2semidirect
4. #10589395C2semidirect
5. #10589390C2semidirect
17. C3×#384D3semidirect
83. #384C3⋊D3semidirect
213. C32#2071semidirect
269. C3#69585semidirect

Maximal subgroups

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

subgroupindex
C32×#3842
C2×#636362
#105926382
#105893952
#105893902
#695853