Finite Group Databasebeta

← C2×#20295863 #28377841

Subgroups — C2×#20295863 #28377841

Order 13952.

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#20295863C2132yesmaximal, direct product factor
2C2×#16812747C215yesmaximal, complemented
3C2×#16812745C2110yesmaximal, complemented
4C22×#13182030C215yesmaximal, complemented
5C2×#41×D109C2110yesmaximal, complemented
6C2×2−1+4×C109C211yesmaximal, characteristic, complemented
7#16812747C22180yescomplemented
8#16812745C221160yescomplemented
9C2×#13182030C22110yescomplemented
10C2×#13182030C22120yescomplemented
11C2×#13182030C22180yescomplemented
12C2×#13182029C22130yescomplemented
13C2×#13182028C22110yescomplemented
14#41×D109C221160yescomplemented
15C2×Q8×D109C22110yescomplemented
16C22×D436C22115yescomplemented
17C2×D4×D109C22130yescomplemented
18C22×C4×D109C22115yescomplemented
192−1+4×C109C22116yescomplemented
20C2×#41×C109C22110yescomplemented
21C22×Q8×C109C2215yescomplemented
22C23×D109C23115yes—
23#13182030C23180yescomplemented
24#13182030C231160yescomplemented
25#13182029C231240yescomplemented
26#13182028C23180yescomplemented
27C2×Dic218C23110yes—
28Q8×D109C23180yescomplemented
29C2×D436C23130yes—
30C2×D436C231120yescomplemented
31C2×C22⋊D109C23120yes—
32D4×D109C231240yescomplemented
33C22×Dic109C2315yes—
34C2×C4×D109C23110yes—
35C2×C4×D109C23130yes—
36C2×C4×D109C231120yescomplemented
37#41×C109C23180yescomplemented
38C2×Q8×C109C23110yes—
39C2×Q8×C109C23140yescomplemented
40C2×D4×C109C23110yes—
41C22×C4×C109C23115yes—
42C23×C109C2415yes—
43C22×D109—430no—
44C22×D109C24110yes—
45C22×D109C24160yes—
46Q8×C109C24140yes—
47D4×C109C24140yes—
48C2×C4×C109C24110yes—
49C2×C4×C109C24160yes—
50C22⋊D109C24180yes—
51C2×Dic109C2411yescharacteristic
52C2×Dic109C2415yes—
53C2×Dic109C24120yes—
54D436C241120yes—
55C4×D109C24140yes—
56C4×D109C241120yes—
57Dic218C24140yes—
58C22×C109—210no—
59C22×C109C25110yes—
60C22×C109C2511yescharacteristic
61C2×D109—220no—
62C2×D109—460no—
63C2×D109C25120yes—
64C4×C109C25120yes—
65Dic109C25110yes—
66Dic109C2512yes—
67C2×C109—210no—
68C2×C109#58512yescomplemented
69C2×C109C2611yescharacteristic
70D109—220no—
71C2×#585—1091nomaximal, Sylow
72C109C2×#58511yescharacteristic, complemented, Sylow
73#585—10932no—
74C2×2−1+4—1095no—
75C2×2−1+4D10911yescharacteristic, complemented
76C2×H(5,𝔽2)—10910no—
77C22×#41—10910no—
78C22×#41—1095no—
792−1+4—10980no—
802−1+4C2×D109116yescomplemented
81H(5,𝔽2)—109160no—
82C2×#41—109160no—
83C2×#41—10910no—
84C2×#41—10920no—
85C2×#41—10980no—
86C2×#41—10910no—
87C2×#41—10930no—
88C2×#41C2×D109110yescomplemented
89C22×Q8—10910no—
90C22×Q8C2×D10915yescomplemented
91C22×D4—10930no—
92C22×D4—10915no—
93C23×C4—10915no—
94C24—10915no—
95#41—10980no—
96#41—109160no—
97#41—10980no—
98#41—109240no—
99#41C22×D109180yescomplemented
100C2×Q8—10980no—
101C2×Q8—10910no—
102C2×Q8C22×D109110yes—
103C2×Q8C22×D109140yescomplemented
104C2×D4—10920no—
105C2×D4—109240no—
106C2×D4—10930no—
107C2×D4—109120no—
108C2×D4C22×D109110yes—
109C22×C4—1095no—
110C22×C4—10910no—
111C22×C4—10930no—
112C22×C4—109120no—
113C22×C4C22×D109115yes—
114C23—10960no—
115C23—10910no—
116C23—43630no—
117C23C23×D10915yes—
118Q8—10940no—
119Q8C23×D109140yes—
120D4—10980no—
121D4—109120no—
122D4C23×D109140yes—
123C2×C4—10920no—
124C2×C4—1091no—
125C2×C4—1095no—
126C2×C4—10940no—
127C2×C4—109120no—
128C2×C4C23×D109160yes—
129C2×C4C23×D109110yes—
130C22—210no—
131C22—10920no—
132C22—43660no—
133C22—21820no—
134C22C24×D109110yes—
135C22C24×D10911yescharacteristic
136C4—1092no—
137C4—10910no—
138C4C24×D109120yes—
139C2—210no—
140C2—21820no—
141C2#2029586312yesdirect product factor
142C2C25×D10911yescharacteristic
subgroupG/H
centerC22C24×D109
commutator, cosocleC2×C109C26
FrattiniC2C25×D109
FittingC2×2−1+4×C109C2
socleC22×C109C25
hypercenterC2×2−1+4D109
hypocenterC109C2×#585
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20295863C2direct (N × H)
2. C2×#16812747C2semidirect
3. C2×#16812745C2semidirect
4. C22×#13182030C2semidirect
5. C2×#41×D109C2semidirect
6. C2×2−1+4×C109C2semidirect
7. #16812747C22semidirect
8. #16812745C22semidirect
9. C2×#13182030C22semidirect
10. C2×#13182030C22semidirect
11. C2×#13182030C22semidirect
12. C2×#13182029C22semidirect
13. C2×#13182028C22semidirect
14. #41×D109C22semidirect
15. C2×Q8×D109C22semidirect
16. C22×D436C22semidirect
17. C2×D4×D109C22semidirect
18. C22×C4×D109C22semidirect
19. 2−1+4×C109C22semidirect
20. C2×#41×C109C22semidirect
21. C22×Q8×C109C22semidirect
23. #13182030C23semidirect
24. #13182030C23semidirect
25. #13182029C23semidirect
26. #13182028C23semidirect
28. Q8×D109C23semidirect
30. C2×D436C23semidirect
32. D4×D109C23semidirect
36. C2×C4×D109C23semidirect
37. #41×C109C23semidirect
39. C2×Q8×C109C23semidirect
68. C2×C109#585semidirect
72. C109C2×#585semidirect
75. C2×2−1+4D109semidirect
80. 2−1+4C2×D109semidirect
88. C2×#41C2×D109semidirect
90. C22×Q8C2×D109semidirect
99. #41C22×D109semidirect
103. C2×Q8C22×D109semidirect
141. C2#20295863direct (N × H)

Maximal subgroups

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

subgroupindex
#202958632
C2×#168127472
C2×#168127452
C22×#131820302
C2×#41×D1092
C2×2−1+4×C1092
C2×#585109