Finite Group Databasebeta

← #36369862

Subgroups — #36369862

Order 22144.

262 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 54 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#26012477C212yesmaximal, complemented
2#26012399C214yesmaximal, complemented
3#26012058C211yesmaximal, characteristic
4D173⋊M16—22no—
5#19149740C2214yescomplemented
6#19149739—22no—
7C2×#14583826C2211yescharacteristic
8#19149675C412yes—
9#19149666C2212yes—
10#19149650—22no—
11#19149648—22no—
12#19149638C411yescharacteristic
13C22×D4×C173C411yescharacteristic
14#14583836—42no—
15#14583835—24no—
16D173⋊C8—42no—
17#14583826—42no—
18C2×Dic346C2311yescharacteristic
19C2×D692C2×C411yescharacteristic
20C2×C22⋊D173—24no—
21C2×C22⋊D173D412yes—
22C2×C4×D173D412yes—
23C4⋊Dic173—21no—
24C22⋊Dic173—24no—
25C22⋊Dic173—21no—
26C4×Dic173C2×C412yes—
27C24×C173—21no—
28C2×D4×C173—21no—
29C2×D4×C173—42no—
30C2×D4×C173C2×C412yes—
31C22×C4×C173C2×C411yescharacteristic
32#13063443—44no—
33C22×D173C22⋊C412yes—
34Dic346—41no—
35D692—41no—
36C22⋊D173—42no—
37C22⋊D173—84no—
38C2×Dic173—22no—
39C2×Dic173C2×D412yes—
40C4×D173—22no—
41C4×D173—22no—
42C23×C173—22no—
43C23×C173—42no—
44C23×C173—82no—
45C23×C173C22⋊C411yescharacteristic
46D4×C173—42no—
47D4×C173—42no—
48C2×C4×C173—22no—
49C2×C4×C173C22⋊C411yescharacteristic
50C2×C4×C173C22×C411yescharacteristic
51C22×C173—21no—
52C22×C173—41no—
53C22×C173—44no—
54C22×C173—42no—
55C22×C173—84no—
56C22×C173C2×C22⋊C411yescharacteristic
57C2×D173—22no—
58C2×D173—42no—
59C4×C173—21no—
60C4×C173#9912yes—
61Dic173—22no—
62Dic173—42no—
63C2×C173—21no—
64C2×C173—41no—
65C2×C173—82no—
66C2×C173C2×#9911yescharacteristic
67D173—42no—
68C173#213411yescharacteristic, complemented, Sylow
69#2134—1731nomaximal, Sylow
70#535—1731no—
71#413—1732no—
72#355—1734no—
73C2×#41—1731no—
74C22×D4#1062192411yescharacteristic
75C2×M16—3462no—
76#127—1732no—
77#124—1732no—
78#121—3462no—
79#120—3462no—
80#117—1731no—
81#101—1734no—
82#100—3462no—
83C24—21no—
84#41—6922no—
85C2×Q8—1731no—
86C2×D4—21no—
87C2×D4—42no—
88C2×D4—3464no—
89C2×D4—1732no—
90C2×D4—1731no—
91C2×D4C2×#1062192412yes—
92C22×C4—1732no—
93C22×C4C2×#1062192411yescharacteristic
94M16—3464no—
95M16—6922no—
96C2×C8—6922no—
97C4⋊C4—3461no—
98C22⋊C4—3461no—
99C22⋊C4—3464no—
100C42—1732no—
101C23—22no—
102C23—42no—
103C23—82no—
104C23—1732no—
105C23C22⋊#1062192411yescharacteristic
106Q8—6921no—
107D4—42no—
108D4—42no—
109D4—13844no—
110D4—6921no—
111D4—6922no—
112C2×C4—22no—
113C2×C4—3462no—
114C2×C4—3462no—
115C2×C4—3462no—
116C2×C4—1732no—
117C2×C4C22⋊#1062192411yescharacteristic
118C2×C4C22×#1062192411yescharacteristic
119C8—6924no—
120C22—21no—
121C22—41no—
122C22—44no—
123C22—42no—
124C22—84no—
125C22—3462no—
126C22—6922no—
127C22C2×C22⋊#1062192411yescharacteristic
128C4—21no—
129C4—3462no—
130C4—6922no—
131C4#1914973712yes—
132C2—21no—
133C2—41no—
134C2—82no—
135C2—6922no—
136C2C2×#1914973711yescharacteristic
subgroupG/H
centerC2C2×#19149737
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC22×D4×C173C4
socleC2×C173C2×#99
prime radical#26012058C2
cosocleC2×Dic346C23
hypercenterC22×D4#10621924
hypocenterC173#2134
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #26012477C2semidirect
2. #26012399C2semidirect
5. #19149740C22semidirect
68. C173#2134semidirect

Maximal subgroups

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

subgroupindex
#260124772
#260123992
#260120582
#2134173