Finite Group Databasebeta

← #38786920

Subgroups — #38786920

Order 25664.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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#27165785C211yesmaximal, characteristic, complemented
2#27165782C211yesmaximal, characteristic, complemented
3#27165768C211yesmaximal, characteristic, complemented
4#27165766C212yesmaximal, complemented
5#27165764C212yesmaximal, complemented
6#27165763C211yesmaximal, characteristic, complemented
7#27165759C211yesmaximal, characteristic, complemented
8#27165758C212yesmaximal, complemented
9SD16×D401C212yesmaximal, complemented
10#27165743C211yesmaximal, characteristic, complemented
11C2×SD16×C401C211yesmaximal, characteristic, complemented
12#20264367—21no—
13#20264367C2212yescomplemented
14#20264366—22no—
15#20264366C2211yescharacteristic
16#20264366C2211yescharacteristic
17#20264366C2211yescharacteristic, complemented
18#20264365—21no—
19#20264365C2212yes—
20Q8×D401—21no—
21Q8×D401C2212yescomplemented
22C2×C22⋊D401—22no—
23D4×D401—21no—
24D4×D401C2212yes—
25Dic1604C2211yescharacteristic, complemented
26#20264356C2212yescomplemented
27#20264355C2211yescharacteristic, complemented
28#20264355C2211yescharacteristic, complemented
29#20264354C2212yescomplemented
30#20264353C2212yescomplemented
31D3208C2211yescharacteristic, complemented
32#20264351C2212yescomplemented
33#20264350C2211yescharacteristic, complemented
34#20264349C2212yescomplemented
35C8×D401C2212yescomplemented
36C2×Q8×C401C2211yescharacteristic, complemented
37C2×D4×C401C2211yescharacteristic
38SD16×C401C2212yescomplemented
39SD16×C401C2212yescomplemented
40C2×C8×C401C2211yescharacteristic, complemented
41C22×D401—22no—
42Dic802—22no—
43Dic802D411yescharacteristic
44Dic802C2311yescharacteristic
45Dic802C2311yescharacteristic
46D1604—22no—
47D1604D411yescharacteristic
48D1604C2311yescharacteristic
49D1604C2311yescharacteristic
50C22⋊D401—21no—
51C22⋊D401—21no—
52C22⋊D401—22no—
53C22⋊D401—22no—
54C22⋊D401D412yes—
55C2×Dic401—22no—
56C4×D401—22no—
57C4×D401—21no—
58C4×D401—21no—
59C4×D401—22no—
60C4×D401C2312yes—
61#15691999C2312yes—
62C23×C401—21no—
63Q8×C401—21no—
64Q8×C401C2312yes—
65D4×C401—21no—
66D4×C401C2312yes—
67C2×C4×C401—21no—
68C2×C4×C401C2311yescharacteristic
69C8×C401C2311yescharacteristic
70C8×C401C2311yescharacteristic
71C22×C401—22no—
72C22×C401—81no—
73C22×C401C2×D411yescharacteristic
74C2×D401—21no—
75C2×D401—21no—
76C2×D401—82no—
77C2×D401C2×D412yes—
78C4×C401—22no—
79C4×C401C2×D411yescharacteristic
80C4×C401C2411yescharacteristic
81Dic401—21no—
82Dic401—21no—
83Dic401C2×D412yes—
84C2×C401—21no—
85C2×C401—42no—
86C2×C401C22×D411yescharacteristic
87D401—22no—
88D401—41no—
89D401—41no—
90C401#57711yescharacteristic, complemented, Sylow
91#577—4011nomaximal, Sylow
922−1+4—4011no—
93H(5,𝔽2)—4011no—
94#137—4011no—
95#137—4012no—
96AGL(1,ℤ/8)—4011no—
97AGL(1,ℤ/8)—4012no—
98#135—4012no—
99#135—4011no—
100C2×SD16—4012no—
101C2×SD16D40111yescharacteristic, complemented
102#131—4011no—
103#41—8022no—
104#41—8021no—
105#41—8021no—
106#41—4012no—
107#41—4012no—
108#41—4011no—
109#41—4011no—
110#41—4011no—
111C2×Q8—8021no—
112C2×Q8—4012no—
113C2×Q8C2×D40111yescharacteristic, complemented
114C2×D4—8021no—
115C2×D4—8022no—
116C2×D4—4012no—
117C2×D4C2×D40111yescharacteristic
118Q16—4012no—
119Q16—4011no—
120SD16—4012no—
121SD16—4012no—
122SD16—4011no—
123SD16—4011no—
124SD16C2×D40112yescomplemented
125SD16C2×D40112yescomplemented
126D8—4012no—
127D8—4011no—
128M16—4011no—
129M16—4012no—
130C2×C8—4012no—
131C2×C8C2×D40111yescharacteristic, complemented
132C23—21no—
133C23—8022no—
134Q8—21no—
135Q8—8022no—
136Q8—4011no—
137Q8—4011no—
138Q8—4011no—
139Q8C22×D40112yes—
140D4—21no—
141D4—8022no—
142D4—8022no—
143D4—8021no—
144D4—8021no—
145D4—8022no—
146D4—4012no—
147D4—4011no—
148D4—4011no—
149D4—4011no—
150D4C22×D40112yes—
151C2×C4—21no—
152C2×C4—8022no—
153C2×C4—8022no—
154C2×C4—8022no—
155C2×C4—8021no—
156C2×C4—8021no—
157C2×C4—4012no—
158C2×C4C22×D40111yescharacteristic
159C8—4012no—
160C8C22×D40111yescharacteristic
161C8C22×D40111yescharacteristic
162C22—22no—
163C22—81no—
164C22—8021no—
165C22—8021no—
166C22—32082no—
167C22—4012no—
168C22D4×D40111yescharacteristic
169C4—22no—
170C4—8021no—
171C4—8021no—
172C4—4012no—
173C4D4×D40111yescharacteristic
174C4C23×D40111yescharacteristic
175C2—21no—
176C2—42no—
177C2—8022no—
178C2—16041no—
179C2—16041no—
180C2C2×D4×D40111yescharacteristic
subgroupG/H
centerC2C2×D4×D401
commutator, cosocleC4×C401C24
FrattiniC4C23×D401
FittingC2×SD16×C401C2
socleC2×C401C22×D4
hypercenterC2×SD16D401
hypocenterC401#577
LCSG ▷ C4×C401 ▷ C2×C401 ▷ C401
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #27165785C2semidirect
2. #27165782C2semidirect
3. #27165768C2semidirect
4. #27165766C2semidirect
5. #27165764C2semidirect
6. #27165763C2semidirect
7. #27165759C2semidirect
8. #27165758C2semidirect
9. SD16×D401C2semidirect
10. #27165743C2semidirect
11. C2×SD16×C401C2semidirect
13. #20264367C22semidirect
17. #20264366C22semidirect
21. Q8×D401C22semidirect
25. Dic1604C22semidirect
26. #20264356C22semidirect
27. #20264355C22semidirect
28. #20264355C22semidirect
29. #20264354C22semidirect
30. #20264353C22semidirect
31. D3208C22semidirect
32. #20264351C22semidirect
33. #20264350C22semidirect
34. #20264349C22semidirect
35. C8×D401C22semidirect
36. C2×Q8×C401C22semidirect
38. SD16×C401C22semidirect
39. SD16×C401C22semidirect
40. C2×C8×C401C22semidirect
90. C401#577semidirect
101. C2×SD16D401semidirect
113. C2×Q8C2×D401semidirect
124. SD16C2×D401semidirect
125. SD16C2×D401semidirect
131. C2×C8C2×D401semidirect

Maximal subgroups

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

subgroupindex
#271657852
#271657822
#271657682
#271657662
#271657642
#271657632
#271657592
#271657582
SD16×D4012
#271657432
C2×SD16×C4012
#577401