Finite Group Databasebeta

← C2×#41×D277 #31800827

Subgroups — C2×#41×D277 #31800827

Order 17728.

890 conjugacy classes of subgroups; only the 455 normal subgroups are shown.

normal subgroups only

This group has 890 conjugacy classes of subgroups — too many to draw. Only its 455 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×#17984564C211yesmaximal, characteristic, complemented
2C2×#17984563C213yesmaximal, complemented
3C2×#17984562C213yesmaximal, complemented
4#41×D277C2116yesmaximal, direct product factor
5C2×Q8×D277C211yesmaximal, characteristic, complemented
6C2×D4×D277C213yesmaximal, complemented
7C22×C4×D277C213yesmaximal, complemented
8C2×#41×C277C211yesmaximal, characteristic, complemented
9C23×D277C2213yes—
10#17984564C2218yescomplemented
11#17984563C22124yescomplemented
12#17984562C22124yescomplemented
13C2×Dic554C2213yescomplemented
14Q8×D277C2218yescomplemented
15C2×D1108C2213yescomplemented
16C2×C22⋊D277C2216yescomplemented
17D4×D277C22124yescomplemented
18C22×Dic277C2213yescomplemented
19C2×C4×D277C2211yescharacteristic
20C2×C4×D277C2213yes—
21C2×C4×D277C2213yescomplemented
22C2×C4×D277C2213yescomplemented
23C2×C4×D277C22124yescomplemented
24#41×C277C2218yescomplemented
25C2×Q8×C277C2211yescharacteristic, complemented
26C2×D4×C277C2213yescomplemented
27C22×C4×C277C2213yescomplemented
28C22×D277—212no—
29C22×D277C23112yes—
30C22×D277C2313yes—
31C22×D277C2311yescharacteristic
32Dic554C23112yescomplemented
33D1108C23112yescomplemented
34C22⋊D277C23124yescomplemented
35C2×Dic277C2311yescharacteristic
36C2×Dic277C2313yes—
37C2×Dic277C23112yescomplemented
38C4×D277C2314yes—
39C4×D277C23112yes—
40C4×D277C23112yescomplemented
41C4×D277C23112yescomplemented
42C23×C277C2313yes—
43Q8×C277C2314yescomplemented
44D4×C277C23112yescomplemented
45C2×C4×C277C2313yes—
46C2×C4×C277C2311yescharacteristic
47C2×C4×C277C23112yescomplemented
48C22×C277—26no—
49C22×C277C2416yes—
50C22×C277C2411yescharacteristic
51C2×D277—26no—
52C2×D277—224no—
53C2×D277#4114yesdirect product factor
54C2×D277C2416yes—
55C2×D277C2412yes—
56C4×C277C2412yes—
57C4×C277C2416yes—
58Dic277C2412yes—
59Dic277C2416yes—
60C2×C277—26no—
61C2×C277C2×#4112yescomplemented
62C2×C277C2511yescharacteristic
63D277—26no—
64D277C2×#4114yesdirect product factor
65C277C22×#4111yescharacteristic, complemented, Sylow
66C22×#41—2771nomaximal, Sylow
67C2×#41—27716no—
68C2×#41—2771no—
69C2×#41—2773no—
70C2×#41—2773no—
71C2×#41D27711yescharacteristic, direct product factor
72C22×Q8—2771no—
73C22×D4—2773no—
74C23×C4—2773no—
75C24—2773no—
76#41—2778no—
77#41—27724no—
78#41—27724no—
79#41C2×D27718yesdirect product factor
80C2×Q8—2778no—
81C2×Q8—2773no—
82C2×Q8C2×D27711yescharacteristic, complemented
83C2×D4—2776no—
84C2×D4—27724no—
85C2×D4—2773no—
86C2×D4C2×D27713yescomplemented
87C22×C4—2773no—
88C22×C4—2773no—
89C22×C4—2773no—
90C22×C4—2771no—
91C22×C4—2773no—
92C22×C4—27724no—
93C22×C4C2×D27713yescomplemented
94C23—2771no—
95C23—27712no—
96C23—2773no—
97C23—55412no—
98C23C22×D27713yes—
99Q8—27712no—
100Q8C22×D27714yescomplemented
101D4—27724no—
102D4—27712no—
103D4C22×D277112yescomplemented
104C2×C4—2771no—
105C2×C4—2773no—
106C2×C4—27712no—
107C2×C4—2774no—
108C2×C4—27712no—
109C2×C4—27712no—
110C2×C4—27712no—
111C2×C4C22×D27713yes—
112C2×C4C22×D27711yescharacteristic
113C2×C4C22×D277112yescomplemented
114C22—26no—
115C22—2774no—
116C22—2772no—
117C22—2776no—
118C22—55424no—
119C22—5546no—
120C22C23×D27716yes—
121C22C23×D27711yescharacteristic
122C4—2772no—
123C4—2776no—
124C4C23×D27712yes—
125C4C23×D27716yes—
126C2—26no—
127C2—2774no—
128C2—5546no—
129C2#41×D27712yesdirect product factor
130C2C24×D27711yescharacteristic
subgroupG/H
centerC2×C4C22×D277
commutator, cosocleC2×C277C25
FrattiniC2C24×D277
FittingC2×#41×C277C2
socleC22×C277C24
hypercenterC2×#41D277
hypocenterC277C22×#41
LCSG ▷ C2×C277 ▷ C277
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#17984564C2semidirect
2. C2×#17984563C2semidirect
3. C2×#17984562C2semidirect
4. #41×D277C2direct (N × H)
5. C2×Q8×D277C2semidirect
6. C2×D4×D277C2semidirect
7. C22×C4×D277C2semidirect
8. C2×#41×C277C2semidirect
10. #17984564C22semidirect
11. #17984563C22semidirect
12. #17984562C22semidirect
13. C2×Dic554C22semidirect
14. Q8×D277C22semidirect
15. C2×D1108C22semidirect
16. C2×C22⋊D277C22semidirect
17. D4×D277C22semidirect
18. C22×Dic277C22semidirect
21. C2×C4×D277C22semidirect
22. C2×C4×D277C22semidirect
23. C2×C4×D277C22semidirect
24. #41×C277C22semidirect
25. C2×Q8×C277C22semidirect
26. C2×D4×C277C22semidirect
27. C22×C4×C277C22semidirect
32. Dic554C23semidirect
33. D1108C23semidirect
34. C22⋊D277C23semidirect
37. C2×Dic277C23semidirect
40. C4×D277C23semidirect
41. C4×D277C23semidirect
43. Q8×C277C23semidirect
44. D4×C277C23semidirect
47. C2×C4×C277C23semidirect
53. C2×D277#41direct (N × H)
61. C2×C277C2×#41semidirect
64. D277C2×#41direct (N × H)
65. C277C22×#41semidirect
71. C2×#41D277direct (N × H)
79. #41C2×D277direct (N × H)
82. C2×Q8C2×D277semidirect
86. C2×D4C2×D277semidirect
93. C22×C4C2×D277semidirect
100. Q8C22×D277semidirect
103. D4C22×D277semidirect
113. C2×C4C22×D277semidirect
129. C2#41×D277direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179845642
C2×#179845632
C2×#179845622
#41×D2772
C2×Q8×D2772
C2×D4×D2772
C22×C4×D2772
C2×#41×C2772
C22×#41277