Finite Group Databasebeta

← #11780832

Subgroups — #11780832

Order 1152.

516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#10592775C211yesmaximal, characteristic
2#10592774C211yesmaximal, characteristic
3#10592550C211yesmaximal, characteristic, complemented
4#10592529C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic
6#10589348C211yesmaximal, characteristic, complemented
7#10589346C211yesmaximal, characteristic, complemented
8#68408—34nomaximal
9C32×#127C2211yescharacteristic
10C2×#3754—21no—
11C2×#3754—21no—
12C2×#3754—21no—
13#64078C2211yescharacteristic
14C4×#634C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17#63659—21no—
18#63644—21no—
19#63643—21no—
20#63641—21no—
21C8×C3⋊Dic3—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5076—34no—
25#5075—34no—
26#4851—34no—
27#4830—34no—
28C3×#331D314yes—
29#4482—34no—
30#4480—34no—
31C2×C32×D4—21no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×#634—21no—
35C2×#634D411yescharacteristic
36C2×C32×C8—21no—
37C2×C32×C8—21no—
38C32×C42C2311yescharacteristic
39#3754—42no—
40#3754—42no—
41#3754—42no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)D411yescharacteristic
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50#1666—91noSylow
51C3×#127C2×D314yes—
52C2×#214—64no—
53C2×#214—64no—
54C2×#214—64no—
55#869—34no—
56C4×Dic6—34no—
57C3×C4⋊C8C2×D314yes—
58C3×C4⋊C8C2×D314yes—
59#832—64no—
60#817—64no—
61#816—64no—
62Dic3⋊C8—64no—
63C8×Dic3—64no—
64C4⋊(C3⋊C8)—34no—
65C4×C3⋊C8—34no—
66C23×C32—41no—
67C32×D4—41no—
68C32×D4—41no—
69C32×D4—41no—
70C32×D4—41no—
71C32×D4—81no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78#634—21no—
79#634—41no—
80#634—41no—
81#634SD1612yescomplemented
82C32×C8—41no—
83C32×C8—41no—
84C3⋊(C3⋊C8)—21no—
85C3⋊(C3⋊C8)—41no—
86C3⋊(C3⋊C8)SD1612yescomplemented
87#492—91no—
88#475—91no—
89#460—91no—
90C8×Q8—91no—
91#334—91no—
92#332—91no—
93#331C3⋊D311yescharacteristic
94C2×C3×D4—24no—
95C2×C3×D4—24no—
96C2×C3×D4—24no—
97C2×Dic6—34no—
98C2×Dic6—64no—
99C2×C3×C8—24no—
100C2×C3×C8—24no—
101C3×C42C22×D314yes—
102#214—128no—
103#214—128no—
104#214—128no—
105C4⋊Dic3—34no—
106C4⋊Dic3—64no—
107C4⋊Dic3—64no—
108Dic3⋊C4—64no—
109C4×Dic3—64no—
110C2×C3⋊C8—34no—
111C2×C3⋊C8—34no—
112C2×C3⋊C8—64no—
113C22×C32—81no—
114C22×C32—81no—
115C22×C32—81no—
116C22×C32#12111yescharacteristic
117C32×C4—21no—
118C32×C4C2×SD1611yescharacteristic
119C32×C4C2×SD1611yescharacteristic
120C32×C4#13511yescharacteristic
121C32×C4AGL(1,ℤ/8)11yescharacteristic
122C3⋊Dic3—22no—
123C3⋊Dic3—41no—
124C3⋊Dic3—81no—
125C2×SD16—181no—
126C2×SD16—181no—
127C2×SD16—181no—
128C4⋊Q8—91no—
129#127C2×C3⋊D311yescharacteristic
130C4×Q8—91no—
131#106—181no—
132C4⋊C8—91no—
133C4⋊C8—181no—
134C4⋊C8C2×C3⋊D311yescharacteristic
135C4⋊C8C2×C3⋊D311yescharacteristic
136#103—181no—
137#102—181no—
138C4×C8—91no—
139C4×C8—181no—
140C23×C3—44no—
141C3×D4—44no—
142C3×D4—44no—
143C3×D4—44no—
144C3×D4—44no—
145C3×D4—84no—
146C2×C3×C4#23514yes—
147C2×C3×C4D3×D414yes—
148C2×C3×C4D3×D414yes—
149C2×Dic3—64no—
150C2×Dic3—64no—
151C2×Dic3—124no—
152Dic6—38no—
153Dic6—64no—
154Dic6—124no—
155Dic6—124no—
156C3×C8—44no—
157C3×C8—44no—
158C3⋊C8—38no—
159C3⋊C8—64no—
160C3⋊C8—124no—
161C2×C32—161no—
162C2×C32#46011yescharacteristic
163C2×C32#46511yescharacteristic
164C2×C32#47111yescharacteristic
165C2×Q8—91no—
166C2×Q8—181no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170SD16—362no—
171SD16—362no—
172SD16—362no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—91no—
176C2×C8—91no—
177C2×C8—181no—
178C4⋊C4—91no—
179C4⋊C4—181no—
180C4⋊C4—181no—
181C4⋊C4—181no—
182C42—181no—
183C42C22×C3⋊D311yescharacteristic
184C22×C3—84no—
185C22×C3—84no—
186C22×C3—84no—
187C22×C3#88414yes—
188C3×C4—24no—
189C3×C4#91114yes—
190C3×C4#91214yes—
191C3×C4D3×SD1614yes—
192C3×C4D3×SD1614yes—
193Dic3—68no—
194Dic3—124no—
195Dic3—244no—
196C32#166611yescharacteristic, complemented, Sylow
197C23—41no—
198Q8—92no—
199Q8—181no—
200Q8—361no—
201Q8—361no—
202D4—41no—
203D4—41no—
204D4—41no—
205D4—41no—
206D4—81no—
207C2×C4—181no—
208C2×C4—181no—
209C2×C4—361no—
210C2×C4#382811yescharacteristic
211C2×C4D4×C3⋊D311yescharacteristic
212C2×C4D4×C3⋊D311yescharacteristic
213C8—41no—
214C8—41no—
215C8—92no—
216C8—181no—
217C8—361no—
218C2×C3—164no—
219C2×C3#474814yes—
220C2×C3#476214yes—
221C2×C3#477814yes—
222C22—81no—
223C22—81no—
224C22—81no—
225C22#6409311yescharacteristic
226C4—21no—
227C4—182no—
228C4—361no—
229C4—721no—
230C4#6412011yescharacteristic
231C4#6412111yescharacteristic
232C4SD16×C3⋊D311yescharacteristic
233C4SD16×C3⋊D311yescharacteristic
234C3#6840814yescomplemented
235C2—161no—
236C2#1059244711yescharacteristic
237C2#1059246111yescharacteristic
238C2#1059247711yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#331C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenter#331C3⋊D3
hypocenterC32#1666
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #10592550C2semidirect
4. #10592529C2semidirect
6. #10589348C2semidirect
7. #10589346C2semidirect
81. #634SD16semidirect
86. C3⋊(C3⋊C8)SD16semidirect
196. C32#1666semidirect
234. C3#68408semidirect

Maximal subgroups

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

subgroupindex
#105927752
#105927742
#105925502
#105925292
C32×#3312
#105893482
#105893462
#684083