Finite Group Databasebeta

← #26039005

Subgroups — #26039005

Order 11456.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 103 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×#15668259C211yesmaximal, characteristic, complemented
2C2×D4×D179C211yesmaximal, characteristic, complemented
3#19153109C212yesmaximal, complemented
4#19153099C212yesmaximal, complemented
5#19153088C211yesmaximal, characteristic, complemented
6#19153087C211yesmaximal, characteristic, complemented
7#19153084C211yesmaximal, characteristic, complemented
8#19153083C212yesmaximal, complemented
9#19153081C212yesmaximal, complemented
10#19153071C211yesmaximal, characteristic, complemented
11#121×C179C211yesmaximal, characteristic, complemented
12C23×D179C2212yes—
13#15668259—24no—
14C2×Dic358C2211yescharacteristic, complemented
15C2×D716C2211yescharacteristic
16C2×D716C2211yescharacteristic
17C2×D716C2212yescomplemented
18C2×C22⋊D179C2211yescharacteristic
19C2×C22⋊D179C2212yes—
20C2×C22⋊D179C2211yescharacteristic, complemented
21C2×C22⋊D179C2212yescomplemented
22C2×C22⋊D179C2212yescomplemented
23D4×D179—24no—
24C2×C4×D179C2211yescharacteristic
25C2×C4×D179C2211yescharacteristic, complemented
26C4⋊Dic179C2211yescharacteristic, complemented
27C22⋊Dic179C2212yescomplemented
28(C2×D179)⋊C4C2212yes—
29(C2×D179)⋊C4C2212yescomplemented
30(C2×D179)⋊C4C2212yescomplemented
31C4×Dic179C2212yescomplemented
32C2×D4×C179C2211yescharacteristic
33C2×D4×C179C2212yescomplemented
34C22×C4×C179C2211yescharacteristic, complemented
35C4⋊C4×C179C2211yescharacteristic, complemented
36C22⋊C4×C179C2212yescomplemented
37C22×D179—24no—
38C22×D179—42no—
39C22×D179—42no—
40C22×D179C2312yes—
41C22×D179C2311yescharacteristic
42C22×D179C2311yescharacteristic
43Dic358—22no—
44D716—22no—
45D716—22no—
46D716—42no—
47C22⋊D179—22no—
48C22⋊D179—24no—
49C22⋊D179—22no—
50C22⋊D179—42no—
51C22⋊D179—42no—
52C2×Dic179C2312yes—
53C2×Dic179C2311yescharacteristic
54C2×Dic179C2311yescharacteristic
55C4×D179—22no—
56C4×D179D414yescomplemented
57C23×C179C2311yescharacteristic
58C23×C179C2312yes—
59D4×C179—22no—
60D4×C179—42no—
61C2×C4×C179—22no—
62C2×C4×C179C2311yescharacteristic
63C2×C4×C179C2312yes—
64C2×C4×C179C2311yescharacteristic
65C22×C179—21no—
66C22×C179—22no—
67C22×C179—21no—
68C22×C179—22no—
69C22×C179—21no—
70C22×C179—22no—
71C22×C179C2411yescharacteristic
72C2×D179—21no—
73C2×D179—21no—
74C2×D179—21no—
75C2×D179—22no—
76C2×D179—21no—
77C2×D179—22no—
78C2×D179—21no—
79C2×D179—22no—
80C2×D179—48no—
81C2×D179C2×D412yes—
82C4×C179—21no—
83C4×C179—22no—
84C4×C179C2×D412yes—
85Dic179—21no—
86Dic179—22no—
87Dic179C2×D412yes—
88C2×C179—42no—
89C2×C179—41no—
90C2×C179C22×D411yescharacteristic
91C2×C179H(5,𝔽2)11yescharacteristic
92C2×C179H(5,𝔽2)11yescharacteristic
93D179—22no—
94D179—41no—
95D179—42no—
96C179#53511yescharacteristic, complemented, Sylow
97#535—1791nomaximal, Sylow
98C2×#41—1791no—
99C22×D4—1791no—
100#127—1792no—
101#124—1792no—
102#121—1791no—
103#121—1791no—
104#121—1791no—
105#121D17911yescharacteristic, complemented
106#120—1792no—
107#120—1792no—
108#117—1791no—
109C24—1792no—
110#41—3584no—
111C2×Q8—1791no—
112C2×D4—3584no—
113C2×D4—1791no—
114C2×D4—1792no—
115C2×D4—1791no—
116C2×D4—1792no—
117C2×D4—1792no—
118C2×D4—1791no—
119C2×D4—1791no—
120C2×D4—1792no—
121C2×D4C2×D17911yescharacteristic
122C2×D4C2×D17912yescomplemented
123C22×C4—1791no—
124C22×C4—1791no—
125C22×C4C2×D17911yescharacteristic, complemented
126C4⋊C4—1791no—
127C4⋊C4C2×D17911yescharacteristic, complemented
128C22⋊C4—1792no—
129C22⋊C4—1792no—
130C22⋊C4—1792no—
131C22⋊C4—1792no—
132C22⋊C4C2×D17912yescomplemented
133C42—1792no—
134C23—3584no—
135C23—1792no—
136C23—1791no—
137C23—1791no—
138C23—7162no—
139C23—7162no—
140C23C22×D17912yes—
141C23C22×D17911yescharacteristic
142Q8—3582no—
143D4—22no—
144D4—42no—
145D4—3582no—
146D4—3582no—
147D4—3584no—
148D4—3582no—
149D4—3582no—
150D4—7162no—
151D4—7162no—
152D4—7162no—
153C2×C4—22no—
154C2×C4—3582no—
155C2×C4—1792no—
156C2×C4—1791no—
157C2×C4—1791no—
158C2×C4—1794no—
159C2×C4C22×D17912yes—
160C2×C4C22×D17911yescharacteristic
161C2×C4C22×D17911yescharacteristic
162C22—21no—
163C22—22no—
164C22—21no—
165C22—22no—
166C22—21no—
167C22—22no—
168C22—3581no—
169C22—3581no—
170C22—3581no—
171C22—3582no—
172C22—3581no—
173C22—3582no—
174C22—3581no—
175C22—3582no—
176C22—1792no—
177C22—7168no—
178C22C23×D17911yescharacteristic
179C4—22no—
180C4—21no—
181C4—3582no—
182C4—3581no—
183C4—1792no—
184C4D4×D17912yes—
185C2—42no—
186C2—41no—
187C2—3582no—
188C2—7162no—
189C2—7161no—
190C2C2×D4×D17911yescharacteristic
191C2#1915315811yescharacteristic
192C2#1915315911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D179
commutator, socle, cosocleC22×C179C24
Fitting#121×C179C2
hypercenter#121D179
hypocenterC179#535
LCSG ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#15668259C2semidirect
2. C2×D4×D179C2semidirect
3. #19153109C2semidirect
4. #19153099C2semidirect
5. #19153088C2semidirect
6. #19153087C2semidirect
7. #19153084C2semidirect
8. #19153083C2semidirect
9. #19153081C2semidirect
10. #19153071C2semidirect
11. #121×C179C2semidirect
14. C2×Dic358C22semidirect
17. C2×D716C22semidirect
20. C2×C22⋊D179C22semidirect
21. C2×C22⋊D179C22semidirect
22. C2×C22⋊D179C22semidirect
25. C2×C4×D179C22semidirect
26. C4⋊Dic179C22semidirect
27. C22⋊Dic179C22semidirect
29. (C2×D179)⋊C4C22semidirect
30. (C2×D179)⋊C4C22semidirect
31. C4×Dic179C22semidirect
33. C2×D4×C179C22semidirect
34. C22×C4×C179C22semidirect
35. C4⋊C4×C179C22semidirect
36. C22⋊C4×C179C22semidirect
56. C4×D179D4semidirect
96. C179#535semidirect
105. #121D179semidirect
122. C2×D4C2×D179semidirect
125. C22×C4C2×D179semidirect
127. C4⋊C4C2×D179semidirect
132. C22⋊C4C2×D179semidirect

Maximal subgroups

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

subgroupindex
C2×#156682592
C2×D4×D1792
#191531092
#191530992
#191530882
#191530872
#191530842
#191530832
#191530812
#191530712
#121×C1792
#535179