Finite Group Databasebeta

← #36368663

Subgroups — #36368663

Order 22144.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#26012477C211yesmaximal, characteristic
2#26012470C211yesmaximal, characteristic
3#26011457C211yesmaximal, characteristic
4D173⋊M16—21no—
5#19149758—21no—
6#19149740C412yescomplemented
7#19149739—21no—
8#19149738C412yes—
9#19149737—21no—
10C2×#14583826C2211yescharacteristic
11C2×#14583810C411yescharacteristic, complemented
12#19149591—21no—
13#19149591—21no—
14C22×C8×C173C411yescharacteristic, complemented
15#14583836—41no—
16#14583835—22no—
17D173⋊C8—41no—
18C4⋊#10621924—41no—
19C22⋊#10621924—22no—
20C4×#10621924—41no—
21#14583826—41no—
22#14583826—41no—
23C2×Dic346C2×C411yescharacteristic
24C2×D692C2×C411yescharacteristic
25C2×C22⋊D173D411yescharacteristic
26C2×C22⋊D173Q811yescharacteristic
27C2×C4×D173D411yescharacteristic
28C2×C4×D173D411yescharacteristic
29#14583810—41no—
30C2×#13063436—21no—
31C22×C4×C173C2×C411yescharacteristic
32C2×C8×C173—21no—
33C2×C8×C173—41no—
34C2×#10621924—42no—
35#13063443—42no—
36C22×D173C22⋊C411yescharacteristic
37C22×D173C4⋊C411yescharacteristic
38Dic346—41no—
39D692—41no—
40C22⋊D173—41no—
41C22⋊D173—41no—
42C2×Dic173C22⋊C411yescharacteristic
43C2×Dic173C4⋊C411yescharacteristic
44C4×D173—21no—
45C4×D173—21no—
46C4×D173—21no—
47C4×D173—21no—
48#13063436—41no—
49C23×C173C4⋊C411yescharacteristic
50C2×C4×C173—21no—
51C2×C4×C173—21no—
52C2×C4×C173C4211yescharacteristic
53C2×C4×C173C22⋊C411yescharacteristic
54C8×C173—41no—
55C22×C173—21no—
56C22×C173—41no—
57C22×C173#9511yescharacteristic
58C2×D173—21no—
59C2×D173—21no—
60C2×D173—41no—
61C2×D173—41no—
62#10621924—82no—
63C4×C173—21no—
64C4×C173#9911yescharacteristic
65C4×C173#9911yescharacteristic
66Dic173—21no—
67Dic173—21no—
68C2×C173—21no—
69C2×C173—41no—
70C2×C173#34211yescharacteristic
71D173—41no—
72D173—41no—
73C173#139511yescharacteristic, complemented, Sylow
74#1395—1731nomaximal, Sylow
75#413—1731no—
76#410—1731no—
77#408—1731no—
78C2×#41—1731no—
79C2×M16—3461no—
80C2×M16—1731no—
81C22×C8#1062192411yescharacteristic, complemented
82#117—3461no—
83#101—1732no—
84#100—3461no—
85#99—3461no—
86#99—1732no—
87C22⋊C8—3461no—
88C22⋊C8—3461no—
89#41—6921no—
90#41—6921no—
91C2×Q8—1731no—
92C2×D4—1731no—
93C2×D4—1731no—
94C2×D4—1731no—
95C22×C4—1731no—
96C22×C4—1731no—
97C22×C4C2×#1062192411yescharacteristic
98M16—3462no—
99M16—6921no—
100M16—6921no—
101C2×C8—21no—
102C2×C8—41no—
103C2×C8—3461no—
104C2×C8—6921no—
105C4⋊C4—6921no—
106C22⋊C4—3462no—
107C42—6921no—
108C23—1731no—
109C23—1731no—
110C23C4⋊#1062192411yescharacteristic
111Q8—6921no—
112D4—6921no—
113D4—6921no—
114D4—6921no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—3461no—
118C2×C4—3461no—
119C2×C4—3461no—
120C2×C4—3461no—
121C2×C4—1731no—
122C2×C4—1731no—
123C2×C4—6922no—
124C2×C4C4×#1062192411yescharacteristic
125C2×C4C22⋊#1062192411yescharacteristic
126C8—41no—
127C8—6922no—
128C8—6921no—
129C22—21no—
130C22—41no—
131C22—3461no—
132C22—3461no—
133C22—6921no—
134C22—6921no—
135C22(C2×#10621924)⋊C411yescharacteristic
136C4—21no—
137C4—3461no—
138C4—3461no—
139C4—13842no—
140C4#1914973711yescharacteristic
141C4#1914973811yescharacteristic
142C2—21no—
143C2—41no—
144C2—6921no—
145C2—6921no—
146C2#2601236911yescharacteristic
subgroupG/H
centerC4#19149738
commutatorC2×C4×C173C42
FrattiniC22×C4C2×#10621924
FittingC22×C8×C173C4
socleC2×C173#342
prime radical, cosocleC2×#14583826C22
hypercenterC22×C8#10621924
hypocenterC173#1395
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
6. #19149740C4semidirect
11. C2×#14583810C4semidirect
14. C22×C8×C173C4semidirect
73. C173#1395semidirect
81. C22×C8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260124772
#260124702
#260114572
#1395173