Finite Group Databasebeta

← #37532895

Subgroups — #37532895

Order 23168.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#26041999C211yesmaximal, characteristic
2#26041630C211yesmaximal, characteristic, complemented
3#26041575C211yesmaximal, characteristic, complemented
4#26041569C211yesmaximal, characteristic
5#26041024C211yesmaximal, characteristic, complemented
6#26041011C211yesmaximal, characteristic, complemented
7D4⋊C8×C181C211yesmaximal, characteristic
8#19153816C2211yescharacteristic
9#19153816C2211yescharacteristic
10#19153809—22no—
11#19153803—21no—
12#19153795—21no—
13C4×Dic362C2211yescharacteristic
14#19153781—21no—
15#19153775—21no—
16#19153750—21no—
17#19153747—21no—
18C4⋊#13089678C2211yescharacteristic
19#19153741—21no—
20#19153741—22no—
21#19153737—21no—
22C4×D4×C181C2211yescharacteristic
23C4⋊C8×C181C2211yescharacteristic
24C4×C8×C181C2211yescharacteristic
25C2×Dic362—21no—
26C2×Dic362—21no—
27C2×Dic362D411yescharacteristic
28C2×#13089678—21no—
29C4⋊Dic181—21no—
30C4⋊Dic181—21no—
31C4⋊Dic181—21no—
32C4⋊Dic181D412yes—
33C4⋊Dic181D411yescharacteristic
34#15668428—22no—
35#15668428—21no—
36C22⋊Dic181—22no—
37C22⋊Dic181—22no—
38C4×Dic181—22no—
39C4×Dic181—21no—
40C2×D4×C181D411yescharacteristic
41C22×C4×C181—21no—
42C2×C8×C181—21no—
43C2×C8×C181—21no—
44C4⋊C4×C181D411yescharacteristic
45C22⋊C4×C181—21no—
46C42×C181C2311yescharacteristic
47Dic362—21no—
48Dic362—21no—
49Dic362—41no—
50Dic362—41no—
51Dic362—42no—
52C2×Dic181—21no—
53C2×Dic181—21no—
54C2×Dic181—22no—
55C2×Dic181—41no—
56#13089678—41no—
57C23×C181—21no—
58D4×C181—21no—
59D4×C181—21no—
60C2×C4×C181—21no—
61C2×C4×C181—41no—
62C2×C4×C181—41no—
63C2×C4×C181C2×D411yescharacteristic
64C2×C4×C181C2×D411yescharacteristic
65C2×C4×C181C2×D411yescharacteristic
66C8×C181—41no—
67C8×C181—41no—
68C22×C181—41no—
69C22×C181—41no—
70C22×C181—41no—
71C22×C181#12011yescharacteristic
72C4×C181—21no—
73C4×C181—41no—
74C4×C181#13511yescharacteristic
75C4×C181#13511yescharacteristic
76C4×C181#13711yescharacteristic
77C4×C181#13711yescharacteristic
78Dic181—41no—
79Dic181—42no—
80Dic181—41no—
81Dic181—81no—
82C2×C181—81no—
83C2×C181#45211yescharacteristic
84C2×C181#45211yescharacteristic
85C2×C181#45411yescharacteristic
86C181#163811yescharacteristic, complemented, Sylow
87#1638—1811nomaximal, Sylow
88#556—1811no—
89#487—1811no—
90#477—1811no—
91#476—1811no—
92#332—1811no—
93Q8⋊C8—1811no—
94D4⋊C8D18111yescharacteristic
95C4⋊Q8—1811no—
96C4⋊Q8—1811no—
97#126—3622no—
98#124—3621no—
99C22⋊Q8—3621no—
100C4×Q8—3621no—
101C4×Q8—1811no—
102C4×D4C2×D18111yescharacteristic
103#117—3621no—
104#107—3621no—
105#106—3621no—
106C4⋊C8—1811no—
107C4⋊C8C2×D18111yescharacteristic
108#103—3621no—
109#103—3622no—
110#102—3621no—
111C4×C8C2×D18111yescharacteristic
112C2×Q8—3621no—
113C2×Q8—3621no—
114C2×Q8—1811no—
115C2×D4D72411yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—3621no—
120C4⋊C4—3622no—
121C4⋊C4—3621no—
122C4⋊C4—3621no—
123C4⋊C4—3621no—
124C4⋊C4—3621no—
125C4⋊C4—1812no—
126C4⋊C4—1811no—
127C4⋊C4D72411yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—3622no—
130C22⋊C4—3622no—
131C42—3622no—
132C42—3621no—
133C42C22×D18111yescharacteristic
134C23—21no—
135Q8—3621no—
136Q8—3621no—
137Q8—7242no—
138Q8—7241no—
139Q8—7241no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—3621no—
146C2×C4—3621no—
147C2×C4—3622no—
148C2×C4—7241no—
149C2×C4D4×D18111yescharacteristic
150C2×C4D4×D18111yescharacteristic
151C2×C4C2×D72411yescharacteristic
152C8—41no—
153C8—41no—
154C8—7241no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1915378611yescharacteristic
159C4—21no—
160C4—41no—
161C4—14481no—
162C4—7241no—
163C4—7242no—
164C4—7241no—
165C4#1915383511yescharacteristic
166C4#1915383811yescharacteristic
167C4#1915384511yescharacteristic
168C4#1915384911yescharacteristic
169C2—81no—
170C2#2604144211yescharacteristic
171C2#2604144311yescharacteristic
172C2#2604145311yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
FittingD4⋊C8×C181C2
socleC22×C181#120
prime radicalC2×D4×C181D4
hypercenterD4⋊C8D181
hypocenterC181#1638
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #26041630C2semidirect
3. #26041575C2semidirect
5. #26041024C2semidirect
6. #26041011C2semidirect
86. C181#1638semidirect

Maximal subgroups

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

subgroupindex
#260419992
#260416302
#260415752
#260415692
#260410242
#260410112
D4⋊C8×C1812
#1638181