Finite Group Databasebeta

← #14580849

Subgroups — #14580849

Order 2624.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10620310C211yesmaximal, characteristic, complemented
2C22×C4×D41C211yesmaximal, characteristic, complemented
3#13050149C212yesmaximal, complemented
4#13050140C211yesmaximal, characteristic, complemented
5#13050139C211yesmaximal, characteristic, complemented
6#13050138C211yesmaximal, characteristic, complemented
7#13050134C212yesmaximal, complemented
8#13050126C212yesmaximal, complemented
9#13050124C212yesmaximal, complemented
10#13050122C211yesmaximal, characteristic, complemented
11C22⋊Q8×C41C211yesmaximal, characteristic, complemented
12C23×D41C2211yescharacteristic
13C2×Q8×C41C2211yescharacteristic, complemented
14C22×C4×C41C2211yescharacteristic
15C2×C22⋊D41C2212yes—
16C22×Dic41C2211yescharacteristic
17#10620310—24no—
18C2×D164C2212yes—
19C2×D164C2212yes—
20C2×D164C2211yescharacteristic, complemented
21C2×C4×D41—24no—
22C2×C4×D41C2211yescharacteristic
23C2×C4×D41C2211yescharacteristic
24C2×C4×D41C2211yescharacteristic
25C2×C4×D41C2211yescharacteristic
26C2×C4×D41C2212yescomplemented
27C4⋊C4×C41C2211yescharacteristic, complemented
28C4⋊C4×C41C2212yescomplemented
29C22⋊C4×C41C2212yes—
30#10620281C2212yes—
31#10620281C2212yes—
32#10620281C2212yescomplemented
33#10620281C2212yescomplemented
34C4⋊Dic41C2211yescharacteristic, complemented
35#10620279C2212yescomplemented
36C4×Dic41C2212yescomplemented
37C23×C41C2311yescharacteristic
38C22×D41—22no—
39C22×D41—22no—
40C22×D41—22no—
41C22×D41C2312yes—
42C22×D41C2311yescharacteristic
43C22×D41C2311yescharacteristic
44Q8×C41—22no—
45C2×C4×C41—22no—
46C2×C4×C41C2312yes—
47C2×C4×C41C2312yes—
48C2×C4×C41C2311yescharacteristic
49C2×C4×C41C2311yescharacteristic
50C22⋊D41—24no—
51C2×Dic41—22no—
52C2×Dic41C2312yes—
53C2×Dic41C2311yescharacteristic
54C2×Dic41C2311yescharacteristic
55D164—24no—
56D164—24no—
57D164—22no—
58C4×D41—22no—
59C4×D41—22no—
60C4×D41—22no—
61C4×D41—24no—
62C4×D41D414yescomplemented
63C22×C41—21no—
64C22×C41—21no—
65C22×C41#4112yescomplemented
66C22×C41C2411yescharacteristic
67C2×D41—28no—
68C2×D41—21no—
69C2×D41—21no—
70C2×D41—21no—
71C2×D41—21no—
72C2×D41—22no—
73C2×D41—22no—
74C2×D41—22no—
75C2×D41C2×D412yes—
76C2×D41#4112yescomplemented
77C4×C41—21no—
78C4×C41—22no—
79C4×C41—22no—
80C4×C41C2×D412yes—
81Dic41—21no—
82Dic41—22no—
83Dic41C2×D412yes—
84C2×C41—22no—
85C2×C41C22×D411yescharacteristic
86C2×C41C2×#4111yescharacteristic
87C2×C41C2×#4111yescharacteristic
88D41—22no—
89D41—22no—
90D41—42no—
91#525—411nomaximal, Sylow
92C41#52511yescharacteristic, complemented, Sylow
93C2×#41—411no—
94C23×C4—411no—
95#123—412no—
96C22⋊Q8—411no—
97C22⋊Q8D4111yescharacteristic, complemented
98#121—411no—
99#121—411no—
100#120—412no—
101C4×D4—412no—
102C4×D4—412no—
103#117—411no—
104C24—411no—
105#41—824no—
106C2×Q8C2×D4111yescharacteristic, complemented
107C2×D4—412no—
108C2×D4—412no—
109C2×D4—412no—
110C2×D4—411no—
111C22×C4—411no—
112C22×C4—411no—
113C22×C4—411no—
114C22×C4—412no—
115C22×C4—411no—
116C22×C4—411no—
117C22×C4—824no—
118C22×C4C2×D4111yescharacteristic
119C4⋊C4—411no—
120C4⋊C4—412no—
121C4⋊C4C2×D4111yescharacteristic, complemented
122C4⋊C4C2×D4112yescomplemented
123C22⋊C4—412no—
124C22⋊C4—412no—
125C22⋊C4—412no—
126C22⋊C4—412no—
127C22⋊C4C2×D4112yes—
128C42—412no—
129C23—411no—
130C23—411no—
131C23—412no—
132C23—822no—
133C23—822no—
134C23—822no—
135C23C22×D4111yescharacteristic
136Q8—22no—
137D4—824no—
138D4—824no—
139D4—824no—
140D4—822no—
141C2×C4—22no—
142C2×C4—411no—
143C2×C4—414no—
144C2×C4—412no—
145C2×C4—411no—
146C2×C4—822no—
147C2×C4—824no—
148C2×C4—822no—
149C2×C4—822no—
150C2×C4—822no—
151C2×C4C22×D4112yes—
152C2×C4C22×D4111yescharacteristic
153C2×C4C22×D4112yes—
154C2×C4C22×D4111yescharacteristic
155C22—21no—
156C22—21no—
157C22—412no—
158C22—412no—
159C22—828no—
160C22—821no—
161C22—821no—
162C22—821no—
163C22—821no—
164C22—822no—
165C22—822no—
166C22—822no—
167C22#1062031012yescomplemented
168C22C23×D4111yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—412no—
173C4—821no—
174C4—822no—
175C4D4×D4112yes—
176C2—22no—
177C2—822no—
178C2—822no—
179C2—1642no—
180C2C2×D4×D4111yescharacteristic
181C2#41×D4111yescharacteristic
182C2C2×#1062031011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D41
commutator, socle, cosocleC22×C41C24
FittingC22⋊Q8×C41C2
hypercenterC22⋊Q8D41
hypocenterC41#525
LCSG ▷ C22×C41 ▷ C41
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10620310C2semidirect
2. C22×C4×D41C2semidirect
3. #13050149C2semidirect
4. #13050140C2semidirect
5. #13050139C2semidirect
6. #13050138C2semidirect
7. #13050134C2semidirect
8. #13050126C2semidirect
9. #13050124C2semidirect
10. #13050122C2semidirect
11. C22⋊Q8×C41C2semidirect
13. C2×Q8×C41C22semidirect
20. C2×D164C22semidirect
26. C2×C4×D41C22semidirect
27. C4⋊C4×C41C22semidirect
28. C4⋊C4×C41C22semidirect
32. #10620281C22semidirect
33. #10620281C22semidirect
34. C4⋊Dic41C22semidirect
35. #10620279C22semidirect
36. C4×Dic41C22semidirect
62. C4×D41D4semidirect
65. C22×C41#41semidirect
76. C2×D41#41semidirect
92. C41#525semidirect
97. C22⋊Q8D41semidirect
106. C2×Q8C2×D41semidirect
121. C4⋊C4C2×D41semidirect
122. C4⋊C4C2×D41semidirect
167. C22#10620310semidirect

Maximal subgroups

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

subgroupindex
C2×#106203102
C22×C4×D412
#130501492
#130501402
#130501392
#130501382
#130501342
#130501262
#130501242
#130501222
C22⋊Q8×C412
#52541