Finite Group Databasebeta

← #26012137

Subgroups — #26012137

Order 11072.

334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#14583826C211yesmaximal, characteristic, complemented
2C22×D692C211yesmaximal, characteristic, complemented
3#19149667C211yesmaximal, characteristic, complemented
4#19149664C212yesmaximal, complemented
5#19149658C211yesmaximal, characteristic, complemented
6#19149653C211yesmaximal, characteristic, complemented
7#19149652C212yesmaximal, complemented
8#19149647C212yesmaximal, complemented
9C4×D692C211yesmaximal, characteristic, complemented
10C22⋊C4×D173C212yesmaximal, complemented
11C4×D4×C173C211yesmaximal, characteristic, complemented
12C23×D173C2212yes—
13#14583826—24no—
14C2×Dic346C2211yescharacteristic, complemented
15C2×D692—24no—
16C2×D692C2212yes—
17C2×D692C2211yescharacteristic
18C2×D692C2211yescharacteristic
19C2×C22⋊D173C2212yescomplemented
20C2×C22⋊D173C2212yescomplemented
21C2×C4×D173C2212yescomplemented
22C2×C4×D173C2212yescomplemented
23C4⋊Dic173C2211yescharacteristic, complemented
24#14583805C2212yescomplemented
25C22⋊Dic173C2212yes—
26#14583803C2212yescomplemented
27#14583803C2212yescomplemented
28#14583803C2212yescomplemented
29#14583803C2212yescomplemented
30C2×D4×C173C2211yescharacteristic
31C22×C4×C173C2211yescharacteristic
32C22×C4×C173C2211yescharacteristic, complemented
33C4⋊C4×C173C2211yescharacteristic, complemented
34C22⋊C4×C173C2211yescharacteristic
35C22⋊C4×C173C2211yescharacteristic, complemented
36C42×C173C2211yescharacteristic, complemented
37C22×D173—24no—
38C22×D173—24no—
39C22×D173—42no—
40C22×D173C2312yes—
41C22×D173C2312yes—
42Dic346—22no—
43D692—24no—
44D692—22no—
45D692D414yescomplemented
46C22⋊D173—24no—
47C22⋊D173—42no—
48C2×Dic173C2312yes—
49C2×Dic173C2312yes—
50C4×D173—24no—
51C4×D173—42no—
52C23×C173C2311yescharacteristic
53C23×C173C2311yescharacteristic
54D4×C173—22no—
55C2×C4×C173—22no—
56C2×C4×C173—22no—
57C2×C4×C173C2311yescharacteristic
58C2×C4×C173C2311yescharacteristic
59C2×C4×C173C2311yescharacteristic
60C2×C4×C173C2311yescharacteristic
61C2×C4×C173C2311yescharacteristic
62C22×C173—21no—
63C22×C173—21no—
64C22×C173—21no—
65C22×C173—21no—
66C22×C173—21no—
67C22×C173#4112yescomplemented
68C22×C173C2411yescharacteristic
69C2×D173—22no—
70C2×D173—22no—
71C2×D173—22no—
72C2×D173—22no—
73C2×D173—22no—
74C2×D173—48no—
75C2×D173C2×D414yes—
76C4×C173—21no—
77C4×C173—21no—
78C4×C173—21no—
79C4×C173—21no—
80C4×C173C2×D412yes—
81Dic173—22no—
82Dic173—22no—
83C2×C173—22no—
84C2×C173—41no—
85C2×C173C22×D411yescharacteristic
86C2×C173C2×#4111yescharacteristic
87C2×C173H(5,𝔽2)11yescharacteristic
88D173—24no—
89D173—42no—
90C173#54611yescharacteristic, complemented, Sylow
91#546—1731nomaximal, Sylow
92C2×#41—1731no—
93C22×D4—1731no—
94#124—1731no—
95#123—1732no—
96C22⋊Q8—1731no—
97#121—1731no—
98#121—1732no—
99#120—1732no—
100C4×D4—1731no—
101C4×D4D17311yescharacteristic, complemented
102C2×C22⋊C4—1732no—
103C24—1732no—
104#41—3464no—
105C2×Q8—1731no—
106C2×D4—3464no—
107C2×D4—1732no—
108C2×D4—1732no—
109C2×D4—1732no—
110C2×D4—1731no—
111C2×D4—1731no—
112C2×D4C2×D17311yescharacteristic
113C22×C4—1732no—
114C22×C4—1732no—
115C22×C4C2×D17311yescharacteristic
116C22×C4C2×D17311yescharacteristic, complemented
117C4⋊C4—1731no—
118C4⋊C4—1732no—
119C4⋊C4C2×D17311yescharacteristic, complemented
120C22⋊C4—1732no—
121C22⋊C4—1732no—
122C22⋊C4—1732no—
123C22⋊C4—1732no—
124C22⋊C4—1732no—
125C22⋊C4C2×D17311yescharacteristic
126C22⋊C4C2×D17311yescharacteristic, complemented
127C42C2×D17311yescharacteristic, complemented
128C23—3464no—
129C23—3464no—
130C23—1732no—
131C23—1732no—
132C23—6922no—
133C23C22×D17311yescharacteristic
134C23C22×D17311yescharacteristic
135Q8—3462no—
136D4—22no—
137D4—3464no—
138D4—3464no—
139D4—3462no—
140D4—1734no—
141D4—6922no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—3464no—
145C2×C4—1732no—
146C2×C4—1732no—
147C2×C4—6922no—
148C2×C4C22×D17311yescharacteristic
149C2×C4C22×D17311yescharacteristic
150C2×C4C22×D17311yescharacteristic
151C2×C4C22×D17311yescharacteristic
152C2×C4C22×D17311yescharacteristic
153C22—21no—
154C22—21no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—3462no—
159C22—3462no—
160C22—3462no—
161C22—3462no—
162C22—3462no—
163C22—1734no—
164C22—6928no—
165C22#1458382612yescomplemented
166C22C23×D17311yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—3462no—
172C4—3462no—
173C4D4×D17312yes—
174C2—22no—
175C2—41no—
176C2—3464no—
177C2—6922no—
178C2C2×D4×D17311yescharacteristic
179C2C2×#1458382611yescharacteristic
180C2#1914972511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D173
commutator, socle, cosocleC22×C173C24
FittingC4×D4×C173C2
hypercenterC4×D4D173
hypocenterC173#546
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14583826C2semidirect
2. C22×D692C2semidirect
3. #19149667C2semidirect
4. #19149664C2semidirect
5. #19149658C2semidirect
6. #19149653C2semidirect
7. #19149652C2semidirect
8. #19149647C2semidirect
9. C4×D692C2semidirect
10. C22⋊C4×D173C2semidirect
11. C4×D4×C173C2semidirect
14. C2×Dic346C22semidirect
19. C2×C22⋊D173C22semidirect
20. C2×C22⋊D173C22semidirect
21. C2×C4×D173C22semidirect
22. C2×C4×D173C22semidirect
23. C4⋊Dic173C22semidirect
24. #14583805C22semidirect
26. #14583803C22semidirect
27. #14583803C22semidirect
28. #14583803C22semidirect
29. #14583803C22semidirect
32. C22×C4×C173C22semidirect
33. C4⋊C4×C173C22semidirect
35. C22⋊C4×C173C22semidirect
36. C42×C173C22semidirect
45. D692D4semidirect
67. C22×C173#41semidirect
90. C173#546semidirect
101. C4×D4D173semidirect
116. C22×C4C2×D173semidirect
119. C4⋊C4C2×D173semidirect
126. C22⋊C4C2×D173semidirect
127. C42C2×D173semidirect
165. C22#14583826semidirect

Maximal subgroups

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

subgroupindex
C2×#145838262
C22×D6922
#191496672
#191496642
#191496582
#191496532
#191496522
#191496472
C4×D6922
C22⋊C4×D1732
C4×D4×C1732
#546173