Finite Group Databasebeta

← #36369476

Subgroups — #36369476

Order 22144.

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

normal subgroups only

This group has 272 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
1C2×#19149739C212yesmaximal
2#26012372C214yesmaximal, complemented
3#26011964C211yesmaximal, characteristic
4C2×#14583835C2214yes—
5#19149739—22no—
6#19149739—22no—
7C22×C22⋊D173C2211yescharacteristic
8C4×C22⋊D173—22no—
9#19149639—22no—
10#19149635C2212yes—
11C2×C22⋊Dic173C411yescharacteristic
12C22⋊C4×D173C412yes—
13C2×C22⋊C4×C173C411yescharacteristic
14#14583835—24no—
15#14583835—24no—
16C2×#13063443—24no—
17C23×D173C2×C411yescharacteristic
18C2×C22⋊D173—24no—
19C2×C22⋊D173D412yes—
20C2×C22⋊D173D412yes—
21C22×Dic173—21no—
22C22×Dic173C2311yescharacteristic
23C2×C4×D173—22no—
24#14583805—22no—
25C22⋊Dic173—21no—
26C22⋊Dic173C2×C412yes—
27#14583803—22no—
28C4×Dic173—22no—
29C24×C173C2×C411yescharacteristic
30C22×C4×C173—21no—
31C22⋊C4×C173—21no—
32C22⋊C4×C173C2×C412yes—
33#13063443—44no—
34C22×D173—22no—
35C22×D173—81no—
36C22×D173C22⋊C412yes—
37C22⋊D173—24no—
38C22⋊D173—24no—
39C2×Dic173—22no—
40C2×Dic173—81no—
41C2×Dic173C2×D412yes—
42C2×Dic173#4114yes—
43C4×D173—82no—
44C23×C173—22no—
45C23×C173—81no—
46C23×C173C22⋊C411yescharacteristic
47C23×C173C22⋊C411yescharacteristic
48C23×C173C22×C411yescharacteristic
49C2×C4×C173—22no—
50C2×C4×C173—81no—
51C22×C173—21no—
52C22×C173—21no—
53C22×C173—41no—
54C22×C173—41no—
55C22×C173—41no—
56C22×C173—82no—
57C22×C173C2×C22⋊C411yescharacteristic
58C22×C173#11712yes—
59C2×D173—22no—
60C2×D173—42no—
61C2×D173—82no—
62C4×C173—42no—
63Dic173—42no—
64Dic173#12314yes—
65C2×C173—21no—
66C2×C173—22no—
67C2×C173—41no—
68C2×C173—41no—
69C2×C173#38111yescharacteristic
70D173—42no—
71C173#182911yescharacteristic, complemented, Sylow
72#1829—1731nomaximal, Sylow
73#518—1731no—
74C2×#100—1732no—
75#344—1734no—
76C22×D4—1731no—
77C2×M16—1734no—
78C4×D4—3462no—
79C4×D4—3462no—
80#117—1732no—
81C2×C22⋊C4—1731no—
82C2×C22⋊C4—1732no—
83C2×C22⋊C4#1062192411yescharacteristic
84#100—3462no—
85#100—3462no—
86C24—1731no—
87C24C2×#1062192411yescharacteristic
88C2×D4—3464no—
89C2×D4—1732no—
90C2×D4—1732no—
91C22×C4—21no—
92C22×C4—3462no—
93C22×C4—3461no—
94C22×C4—1731no—
95M16—3464no—
96M16—3464no—
97C2×C8—3464no—
98C4⋊C4—3462no—
99C22⋊C4—21no—
100C22⋊C4—3462no—
101C22⋊C4—3461no—
102C22⋊C4—1732no—
103C22⋊C4C2×#1062192412yes—
104C42—3462no—
105C23—22no—
106C23—81no—
107C23—3462no—
108C23—13841no—
109C23—1732no—
110C23C22⋊#1062192411yescharacteristic
111C23C22⋊#1062192411yescharacteristic
112C23C22×#1062192411yescharacteristic
113D4—3464no—
114D4—3464no—
115C2×C4—22no—
116C2×C4—81no—
117C2×C4—3462no—
118C2×C4—13842no—
119C2×C4—13841no—
120C2×C4—1732no—
121C2×C4—1734no—
122C8—6924no—
123C22—21no—
124C22—21no—
125C22—41no—
126C22—41no—
127C22—41no—
128C22—82no—
129C22—3462no—
130C22—13842no—
131C22—6922no—
132C22C2×C22⋊#1062192411yescharacteristic
133C22#1914975812yes—
134C4—42no—
135C4—1734no—
136C4—6922no—
137C2—21no—
138C2—22no—
139C2—41no—
140C2—41no—
141C2—6922no—
142C2#2601243411yescharacteristic
subgroupG/H
centerC2#26012434
commutatorC23×C173C22×C4
FrattiniC23C22×#10621924
FittingC2×C22⋊C4×C173C4
socleC2×C173#381
prime radicalC22×C22⋊D173C22
cosocleC22×Dic173C23
hypercenterC2×C22⋊C4#10621924
hypocenterC173#1829
LCSG ▷ C23×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #26012372C2semidirect
71. C173#1829semidirect

Maximal subgroups

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

subgroupindex
C2×#191497392
#260123722
#260119642
#1829173