Finite Group Databasebeta

← #37534862

Subgroups — #37534862

Order 23168.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19153816C211yesmaximal, characteristic
2C2×#19153740C212yesmaximal
3#26041041C212yesmaximal
4#26041034C211yesmaximal, characteristic
5#391×C181C211yesmaximal, characteristic
6C22×Dic362—21no—
7C22×#13089678C2212yes—
8#19153816—24no—
9C2×C4⋊Dic181—21no—
10C2×C4⋊Dic181C2212yes—
11#19153740—24no—
12C22×Q8×C181C2211yescharacteristic
13C2×C4⋊C4×C181C2211yescharacteristic
14C2×C42×C181C2211yescharacteristic
15#95×C181—21no—
16#95×C181—21no—
17C2×Dic362—24no—
18C2×Dic362—42no—
19C2×Dic362—42no—
20C22×Dic181—22no—
21C2×#13089678—22no—
22C2×#13089678—22no—
23C2×#13089678—22no—
24C4⋊Dic181—24no—
25C4⋊Dic181—22no—
26C4⋊Dic181D414yes—
27C2×Q8×C181—21no—
28C2×Q8×C181—22no—
29C2×Q8×C181—22no—
30C2×Q8×C181Q812yescomplemented
31C22×C4×C181—21no—
32C22×C4×C181—21no—
33C22×C4×C181D411yescharacteristic
34C22×C4×C181D411yescharacteristic
35C22×C4×C181C2311yescharacteristic
36C4⋊C4×C181—22no—
37C42×C181—22no—
38Dic362—48no—
39C2×Dic181—24no—
40C2×Dic181—42no—
41C2×Dic181—42no—
42#13089678—42no—
43C23×C181C2×D411yescharacteristic
44Q8×C181—24no—
45Q8×C181—42no—
46C2×C4×C181—21no—
47C2×C4×C181—21no—
48C2×C4×C181—21no—
49C2×C4×C181—21no—
50C2×C4×C181—22no—
51C2×C4×C181—41no—
52C2×C4×C181—41no—
53C2×C4×C181—41no—
54C2×C4×C181—41no—
55C2×C4×C181—41no—
56C2×C4×C181SD1612yes—
57C2×C4×C181Q1612yes—
58C2×C4×C181C2×D412yes—
59C2×C4×C181C2×Q811yescharacteristic
60C2×C4×C181#4112yes—
61C2×C4×C181#4111yescharacteristic
62C22×C181#12011yescharacteristic
63C22×C181C22⋊Q811yescharacteristic
64C22×C181#12411yescharacteristic
65C22×C181C2×SD1611yescharacteristic
66C22×C181C2×Q1611yescharacteristic
67C22×C181AGL(1,ℤ/8)11yescharacteristic
68C22×C181#13711yescharacteristic
69C4×C181—22no—
70C4×C181—22no—
71C4×C181—42no—
72C4×C181—81no—
73C4×C181C22⋊Q812yes—
74C4×C181#12412yes—
75Dic181—44no—
76C2×C181#39311yescharacteristic
77C2×C181#45011yescharacteristic
78C2×C181#45111yescharacteristic
79C2×C181#47511yescharacteristic
80C2×C181#47711yescharacteristic
81C2×C181#48711yescharacteristic
82C2×C181#48911yescharacteristic
83C181#202411yescharacteristic, complemented, Sylow
84#2024—1811nomaximal, Sylow
85C2×C4⋊Q8—1811no—
86C2×#103—1812no—
87#391D18111yescharacteristic
88#340—1812no—
89#336—1811no—
90C22×Q8—3621no—
91C22×Q8C2×D18111yescharacteristic
92C22×C8—1812no—
93C4⋊Q8—3624no—
94C2×C4⋊C4—3621no—
95C2×C4⋊C4—1812no—
96C2×C4⋊C4C2×D18111yescharacteristic
97C2×C42C2×D18111yescharacteristic
98#103—3624no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—3624no—
105C2×Q8—7242no—
106C2×Q8—7242no—
107C2×Q8Dic36212yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—3622no—
111C22×C4C22⋊D18111yescharacteristic
112C22×C4C22⋊D18111yescharacteristic
113C22×C4C22×D18111yescharacteristic
114C2×C8—3622no—
115C2×C8—3622no—
116C2×C8—3622no—
117C4⋊C4—22no—
118C4⋊C4—3624no—
119C4⋊C4—3622no—
120C4⋊C4—1814no—
121C42—22no—
122C23C2×C22⋊D18111yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—7248no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—3624no—
137C2×C4—7242no—
138C2×C4—7242no—
139C2×C4#1566843612yes—
140C2×C4#1566843912yes—
141C2×C4D4×D18112yes—
142C2×C4C2×Dic36211yescharacteristic
143C2×C4#1566844812yes—
144C2×C4#1566844911yescharacteristic
145C8—7242no—
146C22#1915378411yescharacteristic
147C22#1915379511yescharacteristic
148C22#1915380311yescharacteristic
149C22C2×#1566843611yescharacteristic
150C22C2×#1566843911yescharacteristic
151C22#1915384111yescharacteristic
152C22#1915384611yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—7244no—
158C4#1915379312yes—
159C4#1915380212yes—
160C2#2604119111yescharacteristic
161C2#2604142911yescharacteristic
162C2#2604143411yescharacteristic
163C2#2604156411yescharacteristic
164C2#2604157411yescharacteristic
165C2#2604162911yescharacteristic
166C2#2604163811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D181
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#391×C181C2
socle, prime radicalC23×C181C2×D4
hypercenter#391D181
hypocenterC181#2024
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C181Q8semidirect
83. C181#2024semidirect
107. C2×Q8Dic362semidirect

Maximal subgroups

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

subgroupindex
C2×#191538162
C2×#191537402
#260410412
#260410342
#391×C1812
#2024181