Finite Group Databasebeta

← #11777110

Subgroups — #11777110

Order 1152.

276 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 62 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#10593805C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic
3#10592417C211yesmaximal, characteristic
4#10590173C211yesmaximal, characteristic, complemented
5#10590172C211yesmaximal, characteristic, complemented
6#10590171C211yesmaximal, characteristic, complemented
7#10590170C211yesmaximal, characteristic, complemented
8C2×#3792—21no—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C22⋊#622—21no—
11#63779—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
27#3792—42no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—21no—
31C2×#622—21no—
32C2×C32×C8C2×C411yescharacteristic
33C2×C32×C8C2×C411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3Q811yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
40#1574—91nomaximal, Sylow
41C2×C4×Dic3—62no—
42C3×C22⋊C8—22no—
43#830—62no—
44Dic3⋊C8—62no—
45Dic3⋊C8—62no—
46C8×Dic3—62no—
47C8×Dic3—62no—
48C23×C32C4⋊C411yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4C4⋊C411yescharacteristic
52C2×C32×C4C22×C411yescharacteristic
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3C4⋊C411yescharacteristic
57C2×C3⋊Dic3C4⋊C411yescharacteristic
58C2×C3⋊Dic3C2×D411yescharacteristic
59C2×C3⋊Dic3C2×Q811yescharacteristic
60#622—41no—
61#622—41no—
62#622—41no—
63#622—41no—
64C32×C8—21no—
65C32×C8—21no—
66C3⋊(C3⋊C8)—21no—
67C3⋊(C3⋊C8)—21no—
68#431—91no—
69#431—91no—
70#423—91no—
71#335—91no—
72#335—91no—
73#334—91no—
74#334—91no—
75C22×C3×C4—22no—
76C22×Dic3—62no—
77C22×Dic3—62no—
78C2×C3×C8—22no—
79C2×C3×C8—22no—
80C4×Dic3—62no—
81C4×Dic3—62no—
82C4×Dic3—62no—
83C4×Dic3—62no—
84C2×C3⋊C8—62no—
85C2×C3⋊C8—62no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32C2×C4⋊C411yescharacteristic
90C32×C4—21no—
91C32×C4#13111yescharacteristic
92C32×C4#13111yescharacteristic
93C3⋊Dic3—21no—
94C3⋊Dic3—21no—
95C3⋊Dic3#10812yes—
96C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
97C3⋊Dic3#13711yescharacteristic
98C2×M16—181no—
99C2×C42—91no—
100C4⋊C8—91no—
101C4⋊C8—91no—
102C4⋊C8—91no—
103C4⋊C8—91no—
104C4⋊C8—91no—
105C4⋊C8—91no—
106C4⋊C8—181no—
107C22⋊C8—91no—
108C22⋊C8—181no—
109C22⋊C8#15711yescharacteristic
110C4×C8—91no—
111C4×C8—91no—
112C4×C8—181no—
113C23×C3—22no—
114C2×C3×C4—22no—
115C2×C3×C4—22no—
116C2×C3×C4—42no—
117C2×C3×C4—42no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C2×Dic3—62no—
122C2×Dic3—68no—
123C2×Dic3—122no—
124C2×Dic3—122no—
125C3×C8—42no—
126C3×C8—42no—
127C3⋊C8—122no—
128C3⋊C8—122no—
129C2×C32—41no—
130C2×C32#42411yescharacteristic
131C2×C32#42811yescharacteristic
132C2×C32C2×#10811yescharacteristic
133C22×C4—91no—
134C22×C4—91no—
135C22×C4C2×#15711yescharacteristic
136M16—362no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—181no—
140C2×C8—181no—
141C2×C8—181no—
142C2×C8—181no—
143C2×C8C2×#15711yescharacteristic
144C2×C8C2×#15711yescharacteristic
145C42—91no—
146C42—91no—
147C42—91no—
148C42—91no—
149C22×C3—24no—
150C22×C3—22no—
151C22×C3—42no—
152C22×C3—42no—
153C3×C4—22no—
154C3×C4—22no—
155C3×C4—42no—
156Dic3—64no—
157Dic3—62no—
158Dic3—62no—
159Dic3—64no—
160Dic3—122no—
161C32#157411yescharacteristic, complemented, Sylow
162C23C4⋊#15711yescharacteristic
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—181no—
170C2×C4—182no—
171C2×C4—181no—
172C2×C4C4⋊#15711yescharacteristic
173C2×C4C22×#15711yescharacteristic
174C8—21no—
175C8—21no—
176C8—181no—
177C8—181no—
178C8—361no—
179C8—361no—
180C8—361no—
181C8—361no—
182C2×C3—22no—
183C2×C3—22no—
184C2×C3—22no—
185C2×C3—44no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22C2×C4⋊#15711yescharacteristic
190C4—21no—
191C4—92no—
192C4—91no—
193C4—91no—
194C4—181no—
195C4—181no—
196C4#6428711yescharacteristic
197C4#6428711yescharacteristic
198C3—22no—
199C2—41no—
200C2#1059374311yescharacteristic
201C2#1059377111yescharacteristic
202C2#1059377411yescharacteristic
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#1574
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
161. C32#1574semidirect

Maximal subgroups

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

subgroupindex
#105938052
#105937952
#105924172
#105901732
#105901722
#105901712
#105901702
#15749