Finite Group Databasebeta

← #11777708

Subgroups — #11777708

Order 1152.

498 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 137 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#10592537C211yesmaximal, characteristic
2#10592529C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic
4C32×#335C211yesmaximal, characteristic, complemented
5#10589350C211yesmaximal, characteristic, complemented
6#10589349C211yesmaximal, characteristic
7#10589320C211yesmaximal, characteristic, complemented
8#68562—34nomaximal
9C2×#3744C411yescharacteristic
10C2×#3743—21no—
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C32×C4⋊C8C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C4×C8C2211yescharacteristic
16#63648C411yescharacteristic
17#63647—21no—
18#63644C411yescharacteristic
19#63643C411yescharacteristic
20#63641—21no—
21C8×C3⋊Dic3—21no—
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#4838—34no—
25#4830—34no—
26C4×#204—34no—
27C3×#335D314yescomplemented
28#4484—34no—
29#4483—34no—
30#4454—34no—
31C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
32C2×C4×C3⋊D3—21no—
33C2×#634C2×C411yescharacteristic
34C2×C32×C8—21no—
35C2×C32×C8—21no—
36C2×C32×C8C2×C411yescharacteristic
37C2×C32×C8C2×C411yescharacteristic
38C32×C42C2311yescharacteristic
39#3752—21no—
40C4⋊(C3⋊Dic3)C2×C411yescharacteristic
41C4⋊(C3⋊Dic3)C2×C411yescharacteristic
42#3750—21no—
43C4×C3⋊Dic3—21no—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#3744—22no—
48#3743—42no—
49#1588—91noSylow
50C2×#204—34no—
51C2×ΓL(1,𝔽25)—64no—
52C4×D12—34no—
53C4×Dic6—34no—
54C3×C4⋊C8C2×D314yes—
55C3×C4⋊C8C2×D314yes—
56C3×C4×C8C2×D314yes—
57#821—34no—
58(C2×D3)⋊C8—64no—
59#817—34no—
60#816—34no—
61Dic3⋊C8—64no—
62C8×Dic3—64no—
63C4×C3⋊C8—34no—
64C4×C3⋊C8—34no—
65C22×C3⋊D3—21no—
66C2×C32×C4C22×C411yescharacteristic
67C2×C32×C4C2×D411yescharacteristic
68C2×C32×C4#4111yescharacteristic
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—21no—
72C4⋊(C3⋊D3)—21no—
73C4⋊(C3⋊D3)—21no—
74C4×C3⋊D3—41no—
75C4×C3⋊D3—41no—
76#634—21no—
77#634M1612yescomplemented
78C32×C8—21no—
79C32×C8—21no—
80C32×C8—41no—
81C32×C8—41no—
82C3⋊(C3⋊C8)—22no—
83C3⋊(C3⋊C8)—21no—
84C3⋊(C3⋊C8)—21no—
85C8×Q8—91no—
86C4×SD16—91no—
87#436—91no—
88#335C3⋊D311yescharacteristic, complemented
89Q8⋊C8—91no—
90D4⋊C8—91no—
91#322—91no—
92C2×D12—34no—
93C2×C4×D3—64no—
94C2×Dic6—34no—
95C2×C3×C8—24no—
96C2×C3×C8—24no—
97C2×C3×C8C4×D314yes—
98C2×C3×C8C4×D314yes—
99C3×C42C22×D314yes—
100(C2×D3)⋊C4—64no—
101C4⋊Dic3—34no—
102C4⋊Dic3—34no—
103Dic3⋊C4—64no—
104C4×Dic3—64no—
105C2×C3⋊C8—34no—
106C2×C3⋊C8—34no—
107C2×C3⋊C8—64no—
108#204—68no—
109ΓL(1,𝔽25)—128no—
110C22×C32C4×D411yescharacteristic
111C2×C3⋊D3—41no—
112C2×C3⋊D3—41no—
113C2×C3⋊D3—41no—
114C32×C4—21no—
115C32×C4C2×M1611yescharacteristic
116C32×C4#13111yescharacteristic
117C32×C4AGL(1,ℤ/8)11yescharacteristic
118C32×C4#13711yescharacteristic
119C3⋊Dic3—22no—
120C3⋊Dic3—41no—
121C3⋊Dic3—41no—
122C2×SD16—91no—
123C2×M16—181no—
124C4×Q8—91no—
125C4×D4—91no—
126#106—91no—
127C4⋊C8—181no—
128C4⋊C8C2×C3⋊D311yescharacteristic
129C4⋊C8C2×C3⋊D311yescharacteristic
130#103—91no—
131#102—91no—
132C22⋊C8—181no—
133C4×C8—91no—
134C4×C8—91no—
135C4×C8—181no—
136C4×C8C2×C3⋊D311yescharacteristic
137C22×D3—64no—
138C2×C3×C4C2×C4×D314yes—
139C2×C3×C4D3×D414yes—
140C2×C3×C4#23914yes—
141C2×Dic3—64no—
142C2×Dic3—64no—
143C2×Dic3—64no—
144D12—64no—
145D12—64no—
146C4×D3—124no—
147C4×D3—124no—
148Dic6—38no—
149Dic6—64no—
150C3×C8—24no—
151C3×C8—24no—
152C3×C8—44no—
153C3×C8—44no—
154C3⋊C8—68no—
155C3⋊C8—64no—
156C3⋊C8—64no—
157C2×C32#43511yescharacteristic
158C2×C32#44011yescharacteristic
159C2×C32#44311yescharacteristic
160C3⋊D3—81no—
161C2×Q8—91no—
162C2×D4—91no—
163C22×C4—181no—
164SD16—182no—
165M16—362no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—91no—
169C2×C8—91no—
170C2×C8—181no—
171C2×C8C4×C3⋊D311yescharacteristic
172C2×C8C4×C3⋊D311yescharacteristic
173C4⋊C4—91no—
174C4⋊C4—91no—
175C4⋊C4—181no—
176C22⋊C4—181no—
177C42—181no—
178C42C22×C3⋊D311yescharacteristic
179C22×C3#89314yes—
180C2×D3—124no—
181C2×D3—124no—
182C2×D3—124no—
183C3×C4—24no—
184C3×C4#90114yes—
185C3×C4D3×M1614yes—
186C3×C4#91114yes—
187C3×C4#91814yes—
188Dic3—68no—
189Dic3—124no—
190Dic3—124no—
191C32#158811yescharacteristic, complemented, Sylow
192C23—181no—
193Q8—92no—
194Q8—181no—
195D4—181no—
196D4—181no—
197C2×C4—181no—
198C2×C4—181no—
199C2×C4—181no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4C2×C4×C3⋊D311yescharacteristic
203C2×C4D4×C3⋊D311yescharacteristic
204C2×C4#383211yescharacteristic
205C8—21no—
206C8—21no—
207C8—41no—
208C8—41no—
209C8—182no—
210C8—181no—
211C8—181no—
212C2×C3#483614yes—
213C2×C3#488914yes—
214C2×C3#489514yes—
215D3—244no—
216C22—361no—
217C22—361no—
218C22—361no—
219C22#6410211yescharacteristic
220C4—21no—
221C4—182no—
222C4—361no—
223C4—361no—
224C4#6411011yescharacteristic
225C4M16×C3⋊D311yescharacteristic
226C4#6412011yescharacteristic
227C4#6412711yescharacteristic
228C3#6856214yescomplemented
229C2—721no—
230C2#1059253511yescharacteristic
231C2#1059258811yescharacteristic
232C2#1059259411yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC42C22×C3⋊D3
FittingC32×#335C2
socleC22×C32C4×D4
prime radicalC2×C4⋊(C3⋊D3)C2×C4
cosocleC32×C42C23
hypercenter#335C3⋊D3
hypocenterC32#1588
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
2. #10592529C2semidirect
4. C32×#335C2semidirect
5. #10589350C2semidirect
7. #10589320C2semidirect
27. C3×#335D3semidirect
77. #634M16semidirect
88. #335C3⋊D3semidirect
191. C32#1588semidirect
228. C3#68562semidirect

Maximal subgroups

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

subgroupindex
#105925372
#105925292
C4×#37442
C32×#3352
#105893502
#105893492
#105893202
#685623