Finite Group Databasebeta

← C2×#22581790 #31821213

Subgroups — C2×#22581790 #31821213

Order 17792.

5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 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#22581790C2132yesmaximal, direct product factor
2C2×#17984890C215yesmaximal, complemented
3C2×#17984888C2110yesmaximal, complemented
4C22×#14555786C215yesmaximal, complemented
5C2×#41×D139C2110yesmaximal, complemented
6C2×2−1+4×C139C211yesmaximal, characteristic, complemented
7#17984890C22180yescomplemented
8#17984888C221160yescomplemented
9C2×#14555786C22110yescomplemented
10C2×#14555786C22120yescomplemented
11C2×#14555786C22180yescomplemented
12C2×#14555785C22130yescomplemented
13C2×#14555784C22110yescomplemented
14#41×D139C221160yescomplemented
15C2×Q8×D139C22110yescomplemented
16C22×D556C22115yescomplemented
17C2×D4×D139C22130yescomplemented
18C22×C4×D139C22115yescomplemented
192−1+4×C139C22116yescomplemented
20C2×#41×C139C22110yescomplemented
21C22×Q8×C139C2215yescomplemented
22C23×D139C23115yes—
23#14555786C23180yescomplemented
24#14555786C231160yescomplemented
25#14555785C231240yescomplemented
26#14555784C23180yescomplemented
27C2×Dic278C23110yes—
28Q8×D139C23180yescomplemented
29C2×D556C23130yes—
30C2×D556C231120yescomplemented
31C2×C22⋊D139C23120yes—
32D4×D139C231240yescomplemented
33C22×Dic139C2315yes—
34C2×C4×D139C23110yes—
35C2×C4×D139C23130yes—
36C2×C4×D139C231120yescomplemented
37#41×C139C23180yescomplemented
38C2×Q8×C139C23110yes—
39C2×Q8×C139C23140yescomplemented
40C2×D4×C139C23110yes—
41C22×C4×C139C23115yes—
42C22×D139—430no—
43C22×D139C24110yes—
44C22×D139C24160yes—
45Dic278C24140yes—
46D556C241120yes—
47C22⋊D139C24180yes—
48C2×Dic139C2411yescharacteristic
49C2×Dic139C2415yes—
50C2×Dic139C24120yes—
51C4×D139C24140yes—
52C4×D139C241120yes—
53C23×C139C2415yes—
54Q8×C139C24140yes—
55D4×C139C24140yes—
56C2×C4×C139C24110yes—
57C2×C4×C139C24160yes—
58C22×C139—210no—
59C22×C139C25110yes—
60C22×C139C2511yescharacteristic
61C2×D139—220no—
62C2×D139—460no—
63C2×D139C25120yes—
64C4×C139C25120yes—
65Dic139C2512yes—
66Dic139C25110yes—
67C2×C139—210no—
68C2×C139#58512yescomplemented
69C2×C139C2611yescharacteristic
70D139—220no—
71C139C2×#58511yescharacteristic, complemented, Sylow
72C2×#585—1391nomaximal, Sylow
73#585—13932no—
74C2×2−1+4—1395no—
75C2×2−1+4D13911yescharacteristic, complemented
76C2×H(5,𝔽2)—13910no—
77C22×#41—13910no—
78C22×#41—1395no—
792−1+4—13980no—
802−1+4C2×D139116yescomplemented
81H(5,𝔽2)—139160no—
82C2×#41—139160no—
83C2×#41—13910no—
84C2×#41—13920no—
85C2×#41—13980no—
86C2×#41—13910no—
87C2×#41—13930no—
88C2×#41C2×D139110yescomplemented
89C22×Q8—13910no—
90C22×Q8C2×D13915yescomplemented
91C22×D4—13930no—
92C22×D4—13915no—
93C23×C4—13915no—
94C24—13915no—
95#41—13980no—
96#41—139160no—
97#41—13980no—
98#41—139240no—
99#41C22×D139180yescomplemented
100C2×Q8—13980no—
101C2×Q8—13910no—
102C2×Q8C22×D139110yes—
103C2×Q8C22×D139140yescomplemented
104C2×D4—13920no—
105C2×D4—139240no—
106C2×D4—13930no—
107C2×D4—139120no—
108C2×D4C22×D139110yes—
109C22×C4—1395no—
110C22×C4—13910no—
111C22×C4—13930no—
112C22×C4—139120no—
113C22×C4C22×D139115yes—
114C23—55630no—
115C23—13910no—
116C23—13960no—
117C23C23×D13915yes—
118Q8—13940no—
119Q8C23×D139140yes—
120D4—13980no—
121D4—139120no—
122D4C23×D139140yes—
123C2×C4—13920no—
124C2×C4—1391no—
125C2×C4—1395no—
126C2×C4—13940no—
127C2×C4—139120no—
128C2×C4C23×D139160yes—
129C2×C4C23×D139110yes—
130C22—210no—
131C22—27820no—
132C22—55660no—
133C22—13920no—
134C22C24×D139110yes—
135C22C24×D13911yescharacteristic
136C4—1392no—
137C4—13910no—
138C4C24×D139120yes—
139C2—210no—
140C2—27820no—
141C2#2258179012yesdirect product factor
142C2C25×D13911yescharacteristic
subgroupG/H
centerC22C24×D139
commutator, cosocleC2×C139C26
FrattiniC2C25×D139
FittingC2×2−1+4×C139C2
socleC22×C139C25
hypercenterC2×2−1+4D139
hypocenterC139C2×#585
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #22581790C2direct (N × H)
2. C2×#17984890C2semidirect
3. C2×#17984888C2semidirect
4. C22×#14555786C2semidirect
5. C2×#41×D139C2semidirect
6. C2×2−1+4×C139C2semidirect
7. #17984890C22semidirect
8. #17984888C22semidirect
9. C2×#14555786C22semidirect
10. C2×#14555786C22semidirect
11. C2×#14555786C22semidirect
12. C2×#14555785C22semidirect
13. C2×#14555784C22semidirect
14. #41×D139C22semidirect
15. C2×Q8×D139C22semidirect
16. C22×D556C22semidirect
17. C2×D4×D139C22semidirect
18. C22×C4×D139C22semidirect
19. 2−1+4×C139C22semidirect
20. C2×#41×C139C22semidirect
21. C22×Q8×C139C22semidirect
23. #14555786C23semidirect
24. #14555786C23semidirect
25. #14555785C23semidirect
26. #14555784C23semidirect
28. Q8×D139C23semidirect
30. C2×D556C23semidirect
32. D4×D139C23semidirect
36. C2×C4×D139C23semidirect
37. #41×C139C23semidirect
39. C2×Q8×C139C23semidirect
68. C2×C139#585semidirect
71. C139C2×#585semidirect
75. C2×2−1+4D139semidirect
80. 2−1+4C2×D139semidirect
88. C2×#41C2×D139semidirect
90. C22×Q8C2×D139semidirect
99. #41C22×D139semidirect
103. C2×Q8C22×D139semidirect
141. C2#22581790direct (N × H)

Maximal subgroups

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

subgroupindex
#225817902
C2×#179848902
C2×#179848882
C22×#145557862
C2×#41×D1392
C2×2−1+4×C1392
C2×#585139