Finite Group Databasebeta

← #37549883

Subgroups — #37549883

Order 23168.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D181⋊#108C211yesmaximal, characteristic
2#26042272C212yesmaximal
3D181⋊#101C212yesmaximal
4#26042242C211yesmaximal, characteristic
5C2×Q16×D181C211yesmaximal, characteristic
6D181⋊M16C2212yes—
7D181⋊M16C2211yescharacteristic
8#19153895C2211yescharacteristic
9#19153887—21no—
10#19153886—21no—
11#19153879—24no—
12#19153877—24no—
13#19153870—21no—
14C8×#10624382—21no—
15C2×Q8×D181C2212yes—
16C2×Dic724C411yescharacteristic, complemented
17C2×#15668439C412yescomplemented
18Q16×D181—21no—
19Q16×D181—21no—
20Q16×D181—21no—
21Q16×D181—21no—
22C2×C8×D181C2211yescharacteristic
23C2×Q16×C181C411yescharacteristic, complemented
24#15668459—22no—
25#15668459—21no—
26#15668458—22no—
27#15668458D412yes—
28D181⋊C8—21no—
29D181⋊C8—22no—
30C4⋊#10624382D412yes—
31C22⋊#10624382—21no—
32C4×#10624382—21no—
33C2×Dic362—22no—
34C2×Dic362C2×C412yes—
35Q8×D181—22no—
36Q8×D181—22no—
37Q8×D181—22no—
38Q8×D181—22no—
39C2×C4×D181—22no—
40C2×C4×D181C2311yescharacteristic
41Dic724—21no—
42Dic724—21no—
43#15668439—22no—
44#15668439—22no—
45C2×#13089678C2×C411yescharacteristic
46C8×D181D411yescharacteristic
47C8×D181D411yescharacteristic
48C8×D181D411yescharacteristic
49C8×D181D411yescharacteristic
50C2×Q8×C181C2×C412yes—
51Q16×C181—21no—
52Q16×C181—21no—
53C2×C8×C181C2×C411yescharacteristic
54C2×#10624382—22no—
55#13089685—22no—
56#13089685—42no—
57C22×D181#4111yescharacteristic
58Dic362—22no—
59Dic362—22no—
60Dic362—42no—
61Dic362—42no—
62C2×Dic181—22no—
63C2×Dic181C2×D411yescharacteristic
64C4×D181—42no—
65C4×D181—42no—
66C4×D181C2×D411yescharacteristic
67C4×D181C2×D411yescharacteristic
68C4×D181C2×D411yescharacteristic
69C4×D181#4111yescharacteristic
70#13089678C22⋊C411yescharacteristic
71#13089678C22⋊C411yescharacteristic
72Q8×C181—22no—
73Q8×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181C22×C411yescharacteristic
76C8×C181C22⋊C411yescharacteristic
77C8×C181C22⋊C411yescharacteristic
78C22×C181C4×D411yescharacteristic
79C2×D181—22no—
80C2×D181#12111yescharacteristic
81C2×D181#12411yescharacteristic
82#10624382—42no—
83C4×C181—42no—
84C4×C181C2×C22⋊C411yescharacteristic
85C4×C181C4×D411yescharacteristic
86Dic181—42no—
87Dic181#12111yescharacteristic
88Dic181#12711yescharacteristic
89C2×C181—21no—
90C2×C181#39011yescharacteristic
91D181—21no—
92D181#47312yes—
93C181#197911yescharacteristic, complemented, Sylow
94#1979—1811nomaximal, Sylow
95C22×Q16—1811no—
96C2×#108—1811no—
97#419—1812no—
98C2×#101—1812no—
99#405—1811no—
100C22×Q8—1812no—
101C2×Q16—3621no—
102C2×Q16—3621no—
103C2×Q16—3621no—
104C2×Q16—3621no—
105C2×Q16—1812no—
106C2×Q16—1811no—
107C2×Q16#1062438211yescharacteristic, complemented
108C2×M16—1812no—
109C2×M16—1811no—
110C22×C8—1811no—
111#117—1811no—
112#108—3621no—
113#108—3621no—
114#103—3624no—
115#101—3624no—
116#97—3621no—
117C4×C8—3621no—
118C2×Q8—3622no—
119C2×Q8—3622no—
120C2×Q8—3622no—
121C2×Q8—3622no—
122C2×Q8—3622no—
123C2×Q8—1812no—
124C2×Q8C2×#1062438212yes—
125C22×C4—3622no—
126C22×C4—1811no—
127Q16—21no—
128Q16—21no—
129Q16—3622no—
130Q16—3622no—
131Q16—3621no—
132Q16—3621no—
133M16—3621no—
134M16—3622no—
135M16—3622no—
136M16—1812no—
137C2×C8—3621no—
138C2×C8—3622no—
139C2×C8—1811no—
140C2×C8—1811no—
141C2×C8—1811no—
142C2×C8—1811no—
143C2×C8—1811no—
144C2×C8C2×#1062438211yescharacteristic
145C4⋊C4—1812no—
146C22⋊C4—3621no—
147C42—3621no—
148C23—1811no—
149Q8—22no—
150Q8—22no—
151Q8—3622no—
152Q8—3622no—
153Q8—7242no—
154Q8—7242no—
155C2×C4—22no—
156C2×C4—3622no—
157C2×C4—3622no—
158C2×C4—1811no—
159C2×C4—1811no—
160C2×C4—1811no—
161C2×C4—1811no—
162C2×C4—1811no—
163C2×C4—7242no—
164C2×C4—7242no—
165C2×C4C22×#1062438211yescharacteristic
166C8—3622no—
167C8—1811no—
168C8—1811no—
169C8—7242no—
170C8C22⋊#1062438211yescharacteristic
171C8C22⋊#1062438211yescharacteristic
172C22—3622no—
173C22—1811no—
174C22—1811no—
175C22D4×#1062438211yescharacteristic
176C4—42no—
177C4—1811no—
178C4—1811no—
179C4—7242no—
180C4—7242no—
181C4C2×C22⋊#1062438211yescharacteristic
182C4D4×#1062438211yescharacteristic
183C2—21no—
184C2—3621no—
185C2—1812no—
186C2#2604223111yescharacteristic
subgroupG/H
centerC2#26042231
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×Q16×C181C4
socleC2×C181#390
prime radicalC22×D181#41
cosocleC2×C4×D181C23
hypercenterC2×Q16#10624382
hypocenterC181#1979
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
16. C2×Dic724C4semidirect
17. C2×#15668439C4semidirect
23. C2×Q16×C181C4semidirect
93. C181#1979semidirect
107. C2×Q16#10624382semidirect

Maximal subgroups

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

subgroupindex
D181⋊#1082
#260422722
D181⋊#1012
#260422422
C2×Q16×D1812
#1979181