Finite Group Databasebeta

← #37549898

Subgroups — #37549898

Order 23168.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#15668459C211yesmaximal, characteristic
2C4×C4⋊#10624382C211yesmaximal, characteristic
3#26042149C212yesmaximal
4#26042149C212yesmaximal
5#26041835C211yesmaximal, characteristic
6C2×#15668459C2212yes—
7C2×C4⋊#10624382—21no—
8C2×C4×#10624382C2212yes—
9#19153871—21no—
10C4×#13089685—21no—
11(C2×#10624382)⋊C4—21no—
12#19153815C411yescharacteristic, complemented
13#19153815C411yescharacteristic, complemented
14#19153808C411yescharacteristic, complemented
15#19153794—21no—
16#19153794—21no—
17#19153781—21no—
18#19153781—21no—
19#19153774C2211yescharacteristic
20#19153774C2211yescharacteristic
21C42×D181C2211yescharacteristic
22#125×C181C411yescharacteristic, complemented
23C22×#10624382—22no—
24#15668459—22no—
25#15668459Q814yescomplemented
26C2×#13089685—22no—
27C4⋊#10624382—24no—
28C4×#10624382—24no—
29C2×Dic362—21no—
30C2×Dic362—21no—
31C2×C4×D181D411yescharacteristic
32C2×C4×D181D411yescharacteristic
33C2×C4×D181C2311yescharacteristic
34C4⋊Dic181C2×C411yescharacteristic
35C4⋊Dic181C2×C411yescharacteristic
36#15668428—21no—
37#15668428—21no—
38#15668428—21no—
39#15668428—21no—
40#15668426—21no—
41#15668426—21no—
42C4×Dic181—21no—
43C4×Dic181—21no—
44C4×Dic181C2×C411yescharacteristic
45C4×Dic181D411yescharacteristic
46C4×Dic181D411yescharacteristic
47C4⋊C4×C181—21no—
48C4⋊C4×C181—21no—
49C4⋊C4×C181C2×C411yescharacteristic
50C4⋊C4×C181C2×C411yescharacteristic
51C42×C181C2×C411yescharacteristic
52C2×#10624382—24no—
53C2×#10624382—42no—
54C2×#10624382—42no—
55#13089685—24no—
56C22×D181C2×D411yescharacteristic
57Dic362—42no—
58Dic362—42no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181C22⋊C411yescharacteristic
62C2×Dic181C22⋊C411yescharacteristic
63C2×Dic181C2×D411yescharacteristic
64C4×D181—22no—
65C4×D181—41no—
66C4×D181C2×Q812yes—
67C4×D181#4112yes—
68C2×C4×C181—21no—
69C2×C4×C181—21no—
70C2×C4×C181C22⋊C411yescharacteristic
71C2×C4×C181C22⋊C411yescharacteristic
72C2×C4×C181C22×C411yescharacteristic
73C22×C181C2×C22⋊C411yescharacteristic
74C2×D181—21no—
75C2×D181—21no—
76C2×D181#12411yescharacteristic
77C2×D181C4⋊Q811yescharacteristic
78#10624382—44no—
79C4×C181—21no—
80C4×C181—21no—
81C4×C181—41no—
82C4×C181—41no—
83C4×C181C4×Q812yes—
84Dic181—21no—
85Dic181—41no—
86Dic181—41no—
87Dic181#10412yes—
88Dic181C22⋊Q812yes—
89C2×C181#39111yescharacteristic
90C2×C181C2×#10411yescharacteristic
91C2×C181#42111yescharacteristic
92D181—21no—
93D181—21no—
94C181#198611yescharacteristic, complemented, Sylow
95#1986—1811nomaximal, Sylow
96#533—1811no—
97C4×M16—1811no—
98C4×C4⋊C4—1811no—
99#339—1812no—
100#339—1812no—
101C2×M16—1812no—
102C4⋊Q8—1811no—
103C4⋊Q8—1811no—
104#125—1811no—
105#125#1062438211yescharacteristic, complemented
106C22⋊Q8—3621no—
107C22⋊Q8—3621no—
108C4×Q8—3621no—
109C4×Q8—3621no—
110#117—1811no—
111#117—1811no—
112C2×C4⋊C4—3621no—
113C2×C42—1812no—
114C2×C42—1811no—
115#97—3621no—
116C4×C8—3621no—
117#95—3621no—
118C2×Q8—3621no—
119C2×Q8—3621no—
120C22×C4—3622no—
121C22×C4—1811no—
122C22×C4—1811no—
123C22×C4—1811no—
124M16—3622no—
125M16—1814no—
126C2×C8—3622no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—3621no—
130C4⋊C4—3621no—
131C4⋊C4—3624no—
132C4⋊C4—3621no—
133C4⋊C4—3621no—
134C4⋊C4—1811no—
135C4⋊C4—1811no—
136C4⋊C4C2×#1062438211yescharacteristic
137C4⋊C4C2×#1062438211yescharacteristic
138C22⋊C4—3621no—
139C22⋊C4—3621no—
140C42—3621no—
141C42—3621no—
142C42—3624no—
143C42—1811no—
144C42—1811no—
145C42—1811no—
146C42C2×#1062438211yescharacteristic
147C23—1811no—
148Q8—7242no—
149Q8—7242no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—3622no—
153C2×C4—3624no—
154C2×C4—3621no—
155C2×C4—3621no—
156C2×C4—1811no—
157C2×C4—1811no—
158C2×C4—1811no—
159C2×C4—1812no—
160C2×C4—1812no—
161C2×C4—7241no—
162C2×C4—7242no—
163C2×C4—7242no—
164C2×C4C22⋊#1062438211yescharacteristic
165C2×C4C22⋊#1062438211yescharacteristic
166C2×C4C22×#1062438211yescharacteristic
167C8—3624no—
168C22—3621no—
169C22—3621no—
170C22—1811no—
171C22—1811no—
172C22C2×C22⋊#1062438211yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—3621no—
178C4—1812no—
179C4—1812no—
180C4—7244no—
181C4—7241no—
182C4—7241no—
183C4Q8×#1062438212yes—
184C2—3621no—
185C2—3621no—
186C2(C2×#10624382)⋊Q811yescharacteristic
187C2D181⋊#10411yescharacteristic
188C2#2604227611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
Fitting#125×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D181C2×D4
cosocleC2×C4×D181C23
hypercenter#125#10624382
hypocenterC181#1986
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #19153815C4semidirect
13. #19153815C4semidirect
14. #19153808C4semidirect
22. #125×C181C4semidirect
25. #15668459Q8semidirect
94. C181#1986semidirect
105. #125#10624382semidirect

Maximal subgroups

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

subgroupindex
C4×#156684592
C4×C4⋊#106243822
#260421492
#260418352
#1986181