Finite Group Databasebeta

← #36368955

Subgroups — #36368955

Order 22144.

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

normal subgroups only

This group has 228 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#26012513C211yesmaximal, characteristic
2#26012427C211yesmaximal, characteristic
3#26012344C214yesmaximal
4#26012046C211yesmaximal, characteristic
5C2×C4×#10621924—21no—
6C4⋊#13063443—21no—
7#19149736C2212yes—
8#19149734—21no—
9(C2×#10621924)⋊C4—21no—
10(C2×#10621924)⋊C4C2212yes—
11#19149679C411yescharacteristic, complemented
12#19149670—21no—
13#19149659C2212yes—
14#19149655—21no—
15Q8×Dic173—21no—
16#19149644C412yescomplemented
17#19149637—21no—
18C42×D173C2211yescharacteristic
19C4⋊Q8×C173C411yescharacteristic, complemented
20C22×#10621924—22no—
21C2×#13063443—22no—
22C4×#10621924—24no—
23C2×Dic346C2×C412yes—
24C2×C4×D173D411yescharacteristic
25C2×C4×D173D411yescharacteristic
26C2×C4×D173C2311yescharacteristic
27C4⋊Dic173—22no—
28C4⋊Dic173—21no—
29C4⋊Dic173—21no—
30#14583805—22no—
31#14583803—22no—
32C4×Dic173—22no—
33C4×Dic173C2×C411yescharacteristic
34C4×Dic173D411yescharacteristic
35C4×Dic173D411yescharacteristic
36C2×Q8×C173—21no—
37C4⋊C4×C173—21no—
38C4⋊C4×C173C2×C412yes—
39C42×C173C2×C411yescharacteristic
40C2×#10621924—24no—
41C2×#10621924—42no—
42C2×#10621924—42no—
43#13063443—42no—
44C22×D173C2×D411yescharacteristic
45Dic346—42no—
46C2×Dic173—22no—
47C2×Dic173C22⋊C411yescharacteristic
48C2×Dic173C22⋊C411yescharacteristic
49C2×Dic173C2×D411yescharacteristic
50C4×D173—22no—
51C4×D173—22no—
52C4×D173—41no—
53Q8×C173—42no—
54C2×C4×C173—22no—
55C2×C4×C173C22⋊C411yescharacteristic
56C2×C4×C173C22⋊C411yescharacteristic
57C2×C4×C173C22×C411yescharacteristic
58C22×C173C2×C22⋊C411yescharacteristic
59C2×D173—21no—
60C2×D173—21no—
61C2×D173#13712yes—
62#10621924—44no—
63C4×C173—21no—
64C4×C173—21no—
65C4×C173—42no—
66C4×C173#10412yes—
67Dic173—21no—
68Dic173—21no—
69Dic173—21no—
70Dic173—42no—
71C2×C173#41011yescharacteristic
72C2×C173#41911yescharacteristic
73C2×C173C2×#10411yescharacteristic
74D173—22no—
75C173#150611yescharacteristic, complemented, Sylow
76#1506—1731nomaximal, Sylow
77#533—1731no—
78#432—1731no—
79#376—1731no—
80#328—1734no—
81C4⋊Q8—1731no—
82C4⋊Q8#1062192411yescharacteristic, complemented
83#125—3461no—
84C22⋊Q8—3461no—
85C22⋊Q8—1732no—
86C4×Q8—3461no—
87C4×Q8—1732no—
88#117—3461no—
89C2×C42—3461no—
90C2×C42—1731no—
91C4⋊C8—3461no—
92C22⋊C8—1732no—
93#97—3461no—
94#95—3461no—
95#95—1732no—
96C2×Q8—21no—
97C2×Q8—1732no—
98C22×C4—3462no—
99C22×C4—1731no—
100C22×C4—1731no—
101C22×C4—1731no—
102C2×C8—3462no—
103C4⋊C4—21no—
104C4⋊C4—3462no—
105C4⋊C4—3462no—
106C4⋊C4—3461no—
107C4⋊C4—3461no—
108C4⋊C4C2×#1062192412yes—
109C22⋊C4—3462no—
110C42—3462no—
111C42—3464no—
112C42—1731no—
113C42—1731no—
114C42—1731no—
115C42C2×#1062192411yescharacteristic
116C23—1731no—
117Q8—42no—
118Q8—6922no—
119C2×C4—22no—
120C2×C4—3462no—
121C2×C4—3462no—
122C2×C4—3464no—
123C2×C4—3462no—
124C2×C4—1731no—
125C2×C4—1731no—
126C2×C4—1731no—
127C2×C4—6921no—
128C2×C4—6922no—
129C2×C4—6922no—
130C2×C4C22⋊#1062192411yescharacteristic
131C2×C4C22⋊#1062192411yescharacteristic
132C2×C4C22×#1062192411yescharacteristic
133C8—6922no—
134C22—3461no—
135C22—3461no—
136C22—1732no—
137C22C2×C22⋊#1062192411yescharacteristic
138C4—21no—
139C4—21no—
140C4—42no—
141C4—3461no—
142C4—3461no—
143C4—3461no—
144C4—6924no—
145C4—6922no—
146C4#1914974312yes—
147C2—3462no—
148C2#2601247211yescharacteristic
149C2#2601248411yescharacteristic
150C2C2×#1914974311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC4⋊Q8×C173C4
socleC22×C173C2×C22⋊C4
prime radicalC22×D173C2×D4
cosocleC2×C4×D173C23
hypercenterC4⋊Q8#10621924
hypocenterC173#1506
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #19149679C4semidirect
16. #19149644C4semidirect
19. C4⋊Q8×C173C4semidirect
75. C173#1506semidirect
82. C4⋊Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125132
#260124272
#260123442
#260120462
#1506173