Finite Group Databasebeta

← #37534785

Subgroups — #37534785

Order 23168.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#26041786C212yesmaximal, complemented
2#26041296C212yesmaximal, complemented
3#26041242C211yesmaximal, characteristic, complemented
4#26041036C211yesmaximal, characteristic, complemented
5#575×C181C211yesmaximal, characteristic, complemented
6C22×C4×D181C2211yescharacteristic
7C2×#15668433C2211yescharacteristic
8#19153797—22no—
9#19153792—22no—
10#19153787—22no—
11#19153784—22no—
12C4×C22⋊D181—24no—
13#19153775C2212yes—
14#19153743—24no—
15#19153728—22no—
16C2×#41×C181C2212yes—
17#137×C181—22no—
18AGL(1,ℤ/8)×C181—22no—
19#135×C181—22no—
20C2×M16×C181C2211yescharacteristic
21C23×D181D411yescharacteristic
22C2×C22⋊D181—24no—
23C22×Dic181D411yescharacteristic
24C2×C4×D181—21no—
25C2×C4×D181—22no—
26C2×C4×D181—22no—
27C2×C4×D181—21no—
28#15668433—22no—
29C2×#13089678—21no—
30C4⋊Dic181—22no—
31#15668428—24no—
32C22⋊Dic181—24no—
33C22⋊Dic181—22no—
34#15668426—24no—
35C4×Dic181D414yescomplemented
36#41×C181—22no—
37#41×C181—22no—
38#41×C181—22no—
39#41×C181—22no—
40C2×Q8×C181D412yescomplemented
41C2×D4×C181—22no—
42C2×D4×C181D412yescomplemented
43C22×C4×C181—22no—
44C22×C4×C181C2311yescharacteristic
45Q16×C181—22no—
46SD16×C181—24no—
47D8×C181—22no—
48M16×C181—22no—
49C2×C8×C181D412yescomplemented
50C22×D181—22no—
51C22×D181—21no—
52C22×D181—42no—
53C22⋊D181—48no—
54C2×Dic181—24no—
55C2×Dic181—22no—
56C2×Dic181—21no—
57C4×D181—41no—
58C4×D181—42no—
59C4×D181—41no—
60#13089678—41no—
61C23×C181—22no—
62C23×C181C2×D411yescharacteristic
63Q8×C181—22no—
64Q8×C181—22no—
65D4×C181—22no—
66D4×C181—22no—
67D4×C181—42no—
68D4×C181—42no—
69C2×C4×C181—22no—
70C2×C4×C181—42no—
71C2×C4×C181—42no—
72C2×C4×C181C2×D412yes—
73C2×C4×C181C2×D412yes—
74C2×C4×C181C2×D411yescharacteristic
75C2×C4×C181#4111yescharacteristic
76C8×C181—22no—
77C22×C181—41no—
78C22×C181—44no—
79C22×C181—42no—
80C22×C181#12012yes—
81C22×C181#12111yescharacteristic
82C2×D181—24no—
83C2×D181—22no—
84C2×D181—42no—
85C2×D181—41no—
86C2×D181—41no—
87C4×C181—42no—
88C4×C181#12011yescharacteristic
89C4×C181#12112yes—
90C4×C181#12711yescharacteristic
91Dic181—44no—
92Dic181—41no—
93C2×C181—22no—
94C2×C181—21no—
95C2×C181—82no—
96C2×C181#39211yescharacteristic
97D181—42no—
98C181#201011yescharacteristic, complemented, Sylow
99#2010—1811nomaximal, Sylow
100#575D18111yescharacteristic, complemented
101#525—1812no—
102#421—1812no—
103#407—1811no—
104H(3,ℤ/4)—1811no—
105C2×#41C2×D18112yes—
106C23×C4—1811no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1811no—
111C2×M16C2×D18111yescharacteristic
112#123—3622no—
113C22⋊Q8—3622no—
114#121—3622no—
115#120—3622no—
116C4×D4—3624no—
117#117—1812no—
118#104—3624no—
119C22⋊C8—3622no—
120C24—1811no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D18112yescomplemented
126C2×D4—22no—
127C2×D4—3624no—
128C2×D4C22⋊D18112yescomplemented
129C22×C4—22no—
130C22×C4—3622no—
131C22×C4—3621no—
132C22×C4—3622no—
133C22×C4—3621no—
134C22×C4—1811no—
135C22×C4C22×D18111yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—3622no—
141C2×C8—3621no—
142C2×C8C22⋊D18112yescomplemented
143C4⋊C4—3624no—
144C4⋊C4—3622no—
145C22⋊C4—3624no—
146C22⋊C4—3624no—
147C22⋊C4—3622no—
148C42—1814no—
149C23—22no—
150C23—3622no—
151C23—3621no—
152C23—7242no—
153C23D4×D18111yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—7248no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—3624no—
165C2×C4—3622no—
166C2×C4—3621no—
167C2×C4—7241no—
168C2×C4—7242no—
169C2×C4—7241no—
170C2×C4D4×D18112yes—
171C2×C4C2×C22⋊D18112yes—
172C2×C4C2×C22⋊D18111yescharacteristic
173C2×C4#1566844811yescharacteristic
174C8—22no—
175C8—7241no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—3624no—
180C22—3622no—
181C22—7242no—
182C22—7241no—
183C22—7241no—
184C22#1915378412yes—
185C22#1915378711yescharacteristic
186C4—42no—
187C4—7244no—
188C4—7241no—
189C4#1915378511yescharacteristic
190C4#1915378812yes—
191C4#1915381211yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—7242no—
196C2#2604118711yescharacteristic
subgroupG/H
centerC4#19153812
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#575×C181C2
socleC2×C181#392
hypercenter#575D181
hypocenterC181#2010
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #26041786C2semidirect
2. #26041296C2semidirect
3. #26041242C2semidirect
4. #26041036C2semidirect
5. #575×C181C2semidirect
35. C4×Dic181D4semidirect
40. C2×Q8×C181D4semidirect
42. C2×D4×C181D4semidirect
49. C2×C8×C181D4semidirect
98. C181#2010semidirect
100. #575D181semidirect
125. C2×Q8C22⋊D181semidirect
128. C2×D4C22⋊D181semidirect
142. C2×C8C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
#260417862
#260412962
#260412422
#260410362
#575×C1812
#2010181