Finite Group Databasebeta

← #11777041

Subgroups — #11777041

Order 1152.

268 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 60 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#10593806C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4#10590173C211yesmaximal, characteristic, complemented
5#10590172C211yesmaximal, characteristic, complemented
6#10590171C211yesmaximal, characteristic, complemented
7#10590170C211yesmaximal, characteristic, complemented
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22⋊#622—21no—
10C22⋊#622—21no—
11#63777—21no—
12C4⋊#622C2211yescharacteristic
13C4⋊#622C2211yescharacteristic
14C4⋊#622C2211yescharacteristic
15C4⋊#622C2211yescharacteristic
16C4×#622—21no—
17C32×C22⋊C8C411yescharacteristic
18#63657C411yescharacteristic
19#63641C411yescharacteristic
20#63641C411yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22C8×C3⋊Dic3C2211yescharacteristic
23#4718—62no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3⋊Dic3Q811yescharacteristic
27C2×#622—21no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—21no—
31C2×C32×C8C2×C411yescharacteristic
32C2×C32×C8C2×C411yescharacteristic
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3Q811yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39#1572—91nomaximal, Sylow
40C2×C4×Dic3—62no—
41C3×C22⋊C8—22no—
42#830—62no—
43Dic3⋊C8—62no—
44Dic3⋊C8—62no—
45C8×Dic3—62no—
46C8×Dic3—62no—
47C23×C32C4⋊C411yescharacteristic
48C2×C32×C4—21no—
49C2×C32×C4—21no—
50C2×C32×C4C4⋊C411yescharacteristic
51C2×C32×C4C22×C411yescharacteristic
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—41no—
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C2×C3⋊Dic3C4⋊C411yescharacteristic
57C2×C3⋊Dic3C2×D411yescharacteristic
58C2×C3⋊Dic3C2×Q811yescharacteristic
59#622—41no—
60#622—41no—
61#622—41no—
62#622—41no—
63C32×C8—21no—
64C32×C8—21no—
65C3⋊(C3⋊C8)—21no—
66C3⋊(C3⋊C8)—21no—
67#432—91no—
68#431—91no—
69#431—91no—
70#335—91no—
71#335—91no—
72#334—91no—
73#334—91no—
74C22×C3×C4—22no—
75C22×Dic3—62no—
76C22×Dic3—62no—
77C2×C3×C8—22no—
78C2×C3×C8—22no—
79C4×Dic3—62no—
80C4×Dic3—62no—
81C4×Dic3—62no—
82C4×Dic3—62no—
83C2×C3⋊C8—62no—
84C2×C3⋊C8—62no—
85C22×C32—21no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32C2×C4⋊C411yescharacteristic
89C32×C4—21no—
90C32×C4#13111yescharacteristic
91C32×C4#13111yescharacteristic
92C3⋊Dic3—21no—
93C3⋊Dic3—21no—
94C3⋊Dic3—21no—
95C3⋊Dic3#13511yescharacteristic
96C3⋊Dic3#13511yescharacteristic
97C2×C42—91no—
98C4⋊C8—91no—
99C4⋊C8—91no—
100C4⋊C8—91no—
101C4⋊C8—91no—
102C4⋊C8—91no—
103C4⋊C8—91no—
104C22⋊C8—91no—
105C22⋊C8—181no—
106C22⋊C8—181no—
107C22⋊C8#15711yescharacteristic
108#97—181no—
109C4×C8—91no—
110C4×C8—91no—
111C4×C8—181no—
112C23×C3—22no—
113C2×C3×C4—22no—
114C2×C3×C4—22no—
115C2×C3×C4—42no—
116C2×C3×C4—42no—
117C2×Dic3—62no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C2×Dic3—64no—
122C2×Dic3—64no—
123C2×Dic3—124no—
124C3×C8—42no—
125C3×C8—42no—
126C3⋊C8—122no—
127C3⋊C8—122no—
128C2×C32—41no—
129C2×C32#42411yescharacteristic
130C2×C32#42711yescharacteristic
131C2×C32#43011yescharacteristic
132C22×C4—91no—
133C22×C4—91no—
134C22×C4C2×#15711yescharacteristic
135C2×C8—91no—
136C2×C8—91no—
137C2×C8—181no—
138C2×C8—181no—
139C2×C8—181no—
140C2×C8—181no—
141C2×C8C2×#15711yescharacteristic
142C2×C8C2×#15711yescharacteristic
143C42—91no—
144C42—91no—
145C42—91no—
146C42—91no—
147C22×C3—24no—
148C22×C3—22no—
149C22×C3—42no—
150C22×C3—42no—
151C3×C4—22no—
152C3×C4—22no—
153C3×C4—42no—
154Dic3—62no—
155Dic3—62no—
156Dic3—64no—
157Dic3—64no—
158Dic3—122no—
159C32#157211yescharacteristic, complemented, Sylow
160C23C4⋊#15711yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—181no—
168C2×C4—181no—
169C2×C4—361no—
170C2×C4C4⋊#15711yescharacteristic
171C2×C4C22×#15711yescharacteristic
172C8—21no—
173C8—21no—
174C8—181no—
175C8—181no—
176C8—361no—
177C8—361no—
178C8—361no—
179C8—361no—
180C2×C3—22no—
181C2×C3—22no—
182C2×C3—22no—
183C2×C3—44no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22C2×C4⋊#15711yescharacteristic
188C4—21no—
189C4—91no—
190C4—91no—
191C4—181no—
192C4—181no—
193C4—181no—
194C4#6428711yescharacteristic
195C4#6428711yescharacteristic
196C3—22no—
197C2—41no—
198C2#1059374311yescharacteristic
199C2#1059376811yescharacteristic
200C2#1059377611yescharacteristic
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊C8C4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22⋊C8#157
hypocenterC32#1572
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #10590173C2semidirect
5. #10590172C2semidirect
6. #10590171C2semidirect
7. #10590170C2semidirect
159. C32#1572semidirect

Maximal subgroups

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

subgroupindex
#105938062
#105937952
#105924172
#105901732
#105901722
#105901712
#105901702
#15729