Finite Group Databasebeta

← #37533822

Subgroups — #37533822

Order 23168.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic181C211yesmaximal, characteristic
2#26041263C211yesmaximal, characteristic
3#26041038C212yesmaximal, complemented
4#26041035C212yesmaximal, complemented
5#410×C181C211yesmaximal, characteristic
6C2×#15668433C2212yes—
7Q8×Dic181—21no—
8D4×Dic181—22no—
9D4×Dic181—21no—
10#19153775C412yescomplemented
11#19153775C2211yescharacteristic
12C2×C4×Dic181C412yescomplemented
13C2×C4×Dic181C2211yescharacteristic
14#19153735—21no—
15#19153733—21no—
16C2×#41×C181C2211yescharacteristic
17#117×C181C2212yes—
18#99×C181—22no—
19C22×Dic181—22no—
20C22×Dic181—21no—
21#15668433—22no—
22#15668433—22no—
23C2×#13089678—22no—
24C4⋊Dic181—22no—
25C4⋊Dic181—21no—
26C22⋊Dic181—22no—
27C22⋊Dic181—21no—
28C4×Dic181—22no—
29C4×Dic181—21no—
30C4×Dic181C2×C411yescharacteristic
31C4×Dic181C2×C412yes—
32C4×Dic181C2×C411yescharacteristic
33#41×C181—22no—
34#41×C181—22no—
35C2×Q8×C181D411yescharacteristic
36C2×D4×C181D412yes—
37C2×D4×C181D411yescharacteristic
38C22×C4×C181C2×C412yes—
39C22×C4×C181C2311yescharacteristic
40C4⋊C4×C181—22no—
41C22⋊C4×C181—22no—
42C42×C181—22no—
43C2×Dic181—21no—
44C2×Dic181—22no—
45C2×Dic181—21no—
46C2×Dic181—42no—
47C2×Dic181—44no—
48#13089678—42no—
49C23×C181C22⋊C412yes—
50C23×C181C2×D411yescharacteristic
51Q8×C181—22no—
52D4×C181—24no—
53D4×C181—22no—
54C2×C4×C181—22no—
55C2×C4×C181—22no—
56C2×C4×C181—42no—
57C2×C4×C181C22⋊C412yes—
58C2×C4×C181C22×C411yescharacteristic
59C2×C4×C181C2×D411yescharacteristic
60C2×C4×C181#4112yes—
61C2×C4×C181#4112yes—
62C22×C181—22no—
63C22×C181—41no—
64C22×C181—42no—
65C22×C181C2×C22⋊C411yescharacteristic
66C22×C181#12312yes—
67C4×C181—22no—
68C4×C181—82no—
69C4×C181#11711yescharacteristic
70C4×C181#11711yescharacteristic
71C4×C181#12312yes—
72Dic181—22no—
73Dic181—42no—
74Dic181—41no—
75C2×C181—21no—
76C2×C181—22no—
77C2×C181—42no—
78C2×C181#38111yescharacteristic
79C181#182711yescharacteristic, complemented, Sylow
80#1827—1811nomaximal, Sylow
81C4×#41—1811no—
82#413—1811no—
83#410D18111yescharacteristic
84#339—1812no—
85H(3,ℤ/4)—1812no—
86C2×#41C2×D18111yescharacteristic
87C2×M16—1812no—
88C4×Q8—3621no—
89C4×D4—3622no—
90C4×D4—3621no—
91#117—1812no—
92#117—1811no—
93#117C2×D18112yes—
94C2×C42—1812no—
95C2×C42—1811no—
96#101—3621no—
97#100—3621no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D72411yescharacteristic
102C2×D4C22⋊D18112yes—
103C2×D4D72411yescharacteristic
104C22×C4—3622no—
105C22×C4—3621no—
106C22×C4C4×D18112yes—
107C22×C4C22×D18111yescharacteristic
108M16—3622no—
109M16—3622no—
110C2×C8—3622no—
111C4⋊C4—22no—
112C4⋊C4—3622no—
113C4⋊C4—3621no—
114C22⋊C4—22no—
115C22⋊C4—3622no—
116C22⋊C4—3621no—
117C42—22no—
118C42—3622no—
119C42—3621no—
120C42—1811no—
121C42—1812no—
122C42—1811no—
123C23#1566842612yes—
124C23C2×C22⋊D18111yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—3621no—
132C2×C4—3622no—
133C2×C4—3621no—
134C2×C4—7242no—
135C2×C4—7244no—
136C2×C4#1566842612yes—
137C2×C4C2×C4×D18111yescharacteristic
138C2×C4C2×D72411yescharacteristic
139C2×C4#1566844812yes—
140C2×C4#1566844812yes—
141C8—7242no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×#1566842611yescharacteristic
146C22#1915379712yes—
147C4—22no—
148C4—82no—
149C4—3622no—
150C4—7242no—
151C4—7241no—
152C4#1915377211yescharacteristic
153C4#1915377211yescharacteristic
154C4#1915380012yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#2604114011yescharacteristic
subgroupG/H
centerC4#19153772
commutatorC2×C4×C181C22×C4
FrattiniC22×C4C22×D181
Fitting#410×C181C2
socleC2×C181#381
prime radicalC2×#41×C181C22
cosocleC22×C4×C181C23
hypercenter#410D181
hypocenterC181#1827
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #26041038C2semidirect
4. #26041035C2semidirect
10. #19153775C4semidirect
12. C2×C4×Dic181C4semidirect
79. C181#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1812
#260412632
#260410382
#260410352
#410×C1812
#1827181