Finite Group Databasebeta

← #36369860

Subgroups — #36369860

Order 22144.

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

normal subgroups only

This group has 230 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
1C2×#19149740C212yesmaximal, complemented
2#26012402C212yesmaximal, complemented
3#26012400C212yesmaximal, complemented
4#26012067C211yesmaximal, characteristic
5C2×#14583835—22no—
6#19149740—22no—
7#19149740C2214yes—
8C2×#14583826C411yescharacteristic
9C22×Dic346C2211yescharacteristic
10#19149679C411yescharacteristic
11#19149679C2211yescharacteristic
12#19149667C411yescharacteristic
13#19149667C2211yescharacteristic
14#19149663—22no—
15#19149659—22no—
16#117×C173C411yescharacteristic
17#14583835—24no—
18#14583835—42no—
19C2×#13063443—42no—
20#14583826—42no—
21C2×Dic346—42no—
22C2×Dic346C2×C411yescharacteristic
23C2×Dic346C2×C411yescharacteristic
24C2×Dic346D412yes—
25C2×Dic346C2311yescharacteristic
26C2×D692C2×C411yescharacteristic
27C2×C22⋊D173—21no—
28C22×Dic173D412yes—
29C2×C4×D173—21no—
30C4⋊Dic173—22no—
31C4⋊Dic173—22no—
32#14583803—22no—
33#14583803—22no—
34C22×C4×C173C2×C411yescharacteristic
35C4⋊C4×C173—21no—
36C22⋊C4×C173—21no—
37C42×C173C2×C411yescharacteristic
38C42×C173C2×C411yescharacteristic
39#13063443—44no—
40C22×D173—21no—
41Dic346—41no—
42Dic346—42no—
43Dic346—41no—
44Dic346—41no—
45D692—41no—
46C22⋊D173—42no—
47C2×Dic173—22no—
48C2×Dic173—22no—
49C2×Dic173—21no—
50C2×Dic173C22⋊C412yes—
51C2×Dic173C2×D412yes—
52C4×D173—42no—
53C23×C173C22⋊C411yescharacteristic
54C2×C4×C173—22no—
55C2×C4×C173—21no—
56C2×C4×C173—21no—
57C2×C4×C173C22⋊C411yescharacteristic
58C2×C4×C173C22×C411yescharacteristic
59C22×C173—41no—
60C22×C173#9912yes—
61C22×C173C2×C22⋊C411yescharacteristic
62C2×D173—42no—
63C2×D173—41no—
64C4×C173—21no—
65C4×C173—21no—
66C4×C173—41no—
67C4×C173—41no—
68Dic173—22no—
69Dic173—22no—
70Dic173—41no—
71C2×C173—21no—
72C2×C173—22no—
73C2×C173C2×#9911yescharacteristic
74D173—81no—
75C173#213311yescharacteristic, complemented, Sylow
76#2133—1731nomaximal, Sylow
77#536—1731no—
78C2×#101—1732no—
79#356—1732no—
80#355—1732no—
81C2×#41—1731no—
82C22×Q8—1731no—
83C2×M16—3462no—
84C4⋊Q8—1731no—
85C4⋊Q8—1731no—
86#124—1731no—
87#124—1731no—
88#123—3462no—
89C22⋊Q8—3462no—
90#117#1062192411yescharacteristic
91#101—3462no—
92#101—1734no—
93#41—6922no—
94C2×Q8—1731no—
95C2×Q8—1732no—
96C2×Q8—1731no—
97C2×Q8—1731no—
98C2×Q8—6922no—
99C2×D4—3461no—
100C2×D4—1731no—
101C22×C4—3461no—
102C22×C4—1732no—
103C22×C4C2×#1062192411yescharacteristic
104M16—3464no—
105M16—6922no—
106C2×C8—6922no—
107C4⋊C4—21no—
108C4⋊C4—3462no—
109C4⋊C4—3462no—
110C22⋊C4—21no—
111C22⋊C4—3462no—
112C22⋊C4—3462no—
113C42C2×#1062192411yescharacteristic
114C42C2×#1062192411yescharacteristic
115C23—3461no—
116C23C22⋊#1062192411yescharacteristic
117Q8—6922no—
118Q8—6921no—
119Q8—6921no—
120Q8—6921no—
121D4—6921no—
122D4—6922no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—3462no—
127C2×C4—3462no—
128C2×C4—3461no—
129C2×C4—1732no—
130C2×C4—1732no—
131C2×C4—6922no—
132C2×C4C22⋊#1062192411yescharacteristic
133C2×C4C22×#1062192411yescharacteristic
134C8—6924no—
135C22—41no—
136C22—6922no—
137C22—6921no—
138C22#1914973812yes—
139C22C2×C22⋊#1062192411yescharacteristic
140C4—21no—
141C4—21no—
142C4—41no—
143C4—41no—
144C4—3462no—
145C4—3462no—
146C4—6921no—
147C2—21no—
148C2—22no—
149C2—13841no—
150C2C2×#1914973811yescharacteristic
subgroupG/H
centerC2C2×#19149738
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
Fitting#117×C173C4
socleC2×C173C2×#99
prime radicalC2×#14583826C4
cosocleC2×Dic346C23
hypercenter#117#10621924
hypocenterC173#2133
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#19149740C2semidirect
2. #26012402C2semidirect
3. #26012400C2semidirect
75. C173#2133semidirect

Maximal subgroups

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

subgroupindex
C2×#191497402
#260124022
#260124002
#260120672
#2133173