Finite Group Databasebeta

← #36368967

Subgroups — #36368967

Order 22144.

242 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 60 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#26012513C211yesmaximal, characteristic, complemented
2C4×C4⋊#10621924C211yesmaximal, characteristic, complemented
3#26012345C212yesmaximal, complemented
4#26012343C212yesmaximal
5#26012028C211yesmaximal, characteristic
6C2×C4⋊#10621924—21no—
7C2×C4×#10621924—21no—
8C4⋊#13063443—21no—
9#19149736C2212yes—
10#19149734—21no—
11(C2×#10621924)⋊C4C2212yes—
12#19149674—21no—
13#19149670C411yescharacteristic, complemented
14#19149668C411yescharacteristic, complemented
15#19149664—21no—
16#19149655C2211yescharacteristic
17#19149654C2211yescharacteristic
18C4×D692—21no—
19C4×D692C411yescharacteristic, complemented
20#19149636—21no—
21C42×D173C2211yescharacteristic
22C4×Q8×C173C411yescharacteristic, complemented
23C22×#10621924—22no—
24C2×#13063443—22no—
25C4⋊#10621924—24no—
26C4×#10621924—42no—
27C2×D692—21no—
28C2×D692C2×C411yescharacteristic
29C2×C4×D173—21no—
30C2×C4×D173D411yescharacteristic
31C2×C4×D173D411yescharacteristic
32C2×C4×D173C2311yescharacteristic
33C4⋊Dic173—21no—
34C4⋊Dic173C2×C411yescharacteristic
35#14583805—21no—
36#14583805—21no—
37#14583803—21no—
38#14583803—21no—
39#14583803—21no—
40#14583803—21no—
41#14583803—21no—
42C4×Dic173C2×C411yescharacteristic
43C4×Dic173D411yescharacteristic
44C4×Dic173D411yescharacteristic
45C2×Q8×C173C2×C411yescharacteristic
46C4⋊C4×C173—21no—
47C4⋊C4×C173C2×C411yescharacteristic
48C42×C173—21no—
49C42×C173C2×C411yescharacteristic
50C2×#10621924—24no—
51C2×#10621924—42no—
52C2×#10621924—42no—
53#13063443—42no—
54C22×D173—21no—
55C22×D173C2×D411yescharacteristic
56D692—41no—
57D692—41no—
58D692—41no—
59C2×Dic173—21no—
60C2×Dic173C22⋊C411yescharacteristic
61C2×Dic173C22⋊C411yescharacteristic
62C2×Dic173C2×D411yescharacteristic
63C4×D173—21no—
64C4×D173—21no—
65C4×D173—22no—
66C4×D173—41no—
67C4×D173—42no—
68Q8×C173—41no—
69C2×C4×C173—21no—
70C2×C4×C173—21no—
71C2×C4×C173C22⋊C411yescharacteristic
72C2×C4×C173C22⋊C411yescharacteristic
73C2×C4×C173C22×C411yescharacteristic
74C22×C173C2×C22⋊C411yescharacteristic
75C2×D173—21no—
76C2×D173—21no—
77C2×D173—41no—
78C2×D173—41no—
79C2×D173—41no—
80C2×D173AGL(1,ℤ/8)11yescharacteristic
81C2×D173#13711yescharacteristic
82#10621924—44no—
83C4×C173—21no—
84C4×C173—21no—
85C4×C173—41no—
86C4×C173—41no—
87C4×C173#10412yes—
88Dic173—21no—
89Dic173—21no—
90Dic173—21no—
91Dic173—41no—
92C2×C173#41011yescharacteristic
93C2×C173#41711yescharacteristic
94C2×C173C2×#10411yescharacteristic
95D173—21no—
96D173—21no—
97D173—81no—
98C173#150911yescharacteristic, complemented, Sylow
99#1509—1731nomaximal, Sylow
100#529—1731no—
101#432—1731no—
102C4×C4⋊C4—1731no—
103#328—1732no—
104#327—1732no—
105#126—3461no—
106#125—1731no—
107#124—1731no—
108#123—3461no—
109C22⋊Q8—1731no—
110#121—1731no—
111C4×Q8#1062192411yescharacteristic, complemented
112C4×D4—3461no—
113C4×D4—1731no—
114#117—3461no—
115C2×C4⋊C4—3461no—
116C2×C42—3461no—
117C2×C42—1731no—
118C4⋊C8—3461no—
119C22⋊C8—1732no—
120#97—3461no—
121#95—1732no—
122C2×Q8C2×#1062192411yescharacteristic
123C2×D4—3461no—
124C2×D4—1731no—
125C22×C4—3462no—
126C22×C4—3461no—
127C22×C4—1731no—
128C22×C4—1731no—
129C22×C4—1731no—
130C2×C8—3462no—
131C4⋊C4—21no—
132C4⋊C4—3461no—
133C4⋊C4—3461no—
134C4⋊C4—3461no—
135C4⋊C4—3464no—
136C4⋊C4—1731no—
137C4⋊C4C2×#1062192411yescharacteristic
138C22⋊C4—3461no—
139C22⋊C4—3461no—
140C22⋊C4—3461no—
141C22⋊C4—3461no—
142C22⋊C4—3461no—
143C42—21no—
144C42—1731no—
145C42—1731no—
146C42—1731no—
147C42—6922no—
148C42C2×#1062192411yescharacteristic
149C23—3461no—
150C23—1731no—
151Q8—41no—
152D4—6921no—
153D4—6921no—
154D4—6921no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—3461no—
158C2×C4—3461no—
159C2×C4—3462no—
160C2×C4—3464no—
161C2×C4—3461no—
162C2×C4—1731no—
163C2×C4—1731no—
164C2×C4—1731no—
165C2×C4—6921no—
166C2×C4—6922no—
167C2×C4—6922no—
168C2×C4—6922no—
169C2×C4C22⋊#1062192411yescharacteristic
170C2×C4C22⋊#1062192411yescharacteristic
171C2×C4C22×#1062192411yescharacteristic
172C8—6922no—
173C22—3461no—
174C22—3461no—
175C22—1731no—
176C22—1731no—
177C22—6921no—
178C22—6921no—
179C22—6921no—
180C22C2×C22⋊#1062192411yescharacteristic
181C4—21no—
182C4—21no—
183C4—41no—
184C4—41no—
185C4—3461no—
186C4—3461no—
187C4—3461no—
188C4—6924no—
189C4—6921no—
190C4#1914974412yes—
191C2—3461no—
192C2—3461no—
193C2—13841no—
194C2#2601247011yescharacteristic
195C2#2601248211yescharacteristic
196C2C2×#1914974411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
FittingC4×Q8×C173C4
socleC22×C173C2×C22⋊C4
prime radical#19149654C22
cosocleC2×C4×D173C23
hypercenterC4×Q8#10621924
hypocenterC173#1509
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #26012513C2semidirect
2. C4×C4⋊#10621924C2semidirect
3. #26012345C2semidirect
13. #19149670C4semidirect
14. #19149668C4semidirect
19. C4×D692C4semidirect
22. C4×Q8×C173C4semidirect
98. C173#1509semidirect
111. C4×Q8#10621924semidirect

Maximal subgroups

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

subgroupindex
#260125132
C4×C4⋊#106219242
#260123452
#260123432
#260120282
#1509173