Finite Group Databasebeta

← C2×#24924106 #36338947

Subgroups — C2×#24924106 #36338947

Order 21376.

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#24924106C2132yesmaximal, direct product factor
2C2×#19128880C215yesmaximal, complemented
3C2×#19128878C2110yesmaximal, complemented
4C22×#14581951C215yesmaximal, complemented
5C2×#41×D167C2110yesmaximal, complemented
6C2×2−1+4×C167C211yesmaximal, characteristic, complemented
7#19128880C22180yescomplemented
8#19128878C221160yescomplemented
9C2×#14581951C22110yescomplemented
10C2×#14581951C22120yescomplemented
11C2×#14581951C22180yescomplemented
12C2×#14581950C22130yescomplemented
13C2×#14581949C22110yescomplemented
14#41×D167C221160yescomplemented
15C2×Q8×D167C22110yescomplemented
16C22×D668C22115yescomplemented
17C2×D4×D167C22130yescomplemented
18C22×C4×D167C22115yescomplemented
192−1+4×C167C22116yescomplemented
20C2×#41×C167C22110yescomplemented
21C22×Q8×C167C2215yescomplemented
22C23×D167C23115yes—
23#14581951C23180yescomplemented
24#14581951C231160yescomplemented
25#14581950C231240yescomplemented
26#14581949C23180yescomplemented
27C2×Dic334C23110yes—
28Q8×D167C23180yescomplemented
29C2×D668C23130yes—
30C2×D668C231120yescomplemented
31C2×C22⋊D167C23120yes—
32D4×D167C231240yescomplemented
33C22×Dic167C2315yes—
34C2×C4×D167C23110yes—
35C2×C4×D167C23130yes—
36C2×C4×D167C231120yescomplemented
37#41×C167C23180yescomplemented
38C2×Q8×C167C23110yes—
39C2×Q8×C167C23140yescomplemented
40C2×D4×C167C23110yes—
41C22×C4×C167C23115yes—
42C22×D167—430no—
43C22×D167C24110yes—
44C22×D167C24160yes—
45Dic334C24140yes—
46D668C241120yes—
47C22⋊D167C24180yes—
48C2×Dic167C2411yescharacteristic
49C2×Dic167C2415yes—
50C2×Dic167C24120yes—
51C4×D167C24140yes—
52C4×D167C241120yes—
53C23×C167C2415yes—
54Q8×C167C24140yes—
55D4×C167C24140yes—
56C2×C4×C167C24110yes—
57C2×C4×C167C24160yes—
58C22×C167—210no—
59C22×C167C25110yes—
60C22×C167C2511yescharacteristic
61C2×D167—220no—
62C2×D167—460no—
63C2×D167C25120yes—
64C4×C167C25120yes—
65Dic167C2512yes—
66Dic167C25110yes—
67C2×C167—210no—
68C2×C167#58512yescomplemented
69C2×C167C2611yescharacteristic
70D167—220no—
71C167C2×#58511yescharacteristic, complemented, Sylow
72C2×#585—1671nomaximal, Sylow
73#585—16732no—
74C2×2−1+4—1675no—
75C2×2−1+4D16711yescharacteristic, complemented
76C2×H(5,𝔽2)—16710no—
77C22×#41—16710no—
78C22×#41—1675no—
792−1+4—16780no—
802−1+4C2×D167116yescomplemented
81H(5,𝔽2)—167160no—
82C2×#41—167160no—
83C2×#41—16710no—
84C2×#41—16720no—
85C2×#41—16780no—
86C2×#41—16710no—
87C2×#41—16730no—
88C2×#41C2×D167110yescomplemented
89C22×Q8—16710no—
90C22×Q8C2×D16715yescomplemented
91C22×D4—16730no—
92C22×D4—16715no—
93C23×C4—16715no—
94C24—16715no—
95#41—16780no—
96#41—167160no—
97#41—16780no—
98#41—167240no—
99#41C22×D167180yescomplemented
100C2×Q8—16780no—
101C2×Q8—16710no—
102C2×Q8C22×D167110yes—
103C2×Q8C22×D167140yescomplemented
104C2×D4—16720no—
105C2×D4—167240no—
106C2×D4—16730no—
107C2×D4—167120no—
108C2×D4C22×D167110yes—
109C22×C4—1675no—
110C22×C4—16710no—
111C22×C4—16730no—
112C22×C4—167120no—
113C22×C4C22×D167115yes—
114C23—66830no—
115C23—16710no—
116C23—16760no—
117C23C23×D16715yes—
118Q8—16740no—
119Q8C23×D167140yes—
120D4—16780no—
121D4—167120no—
122D4C23×D167140yes—
123C2×C4—16720no—
124C2×C4—1671no—
125C2×C4—1675no—
126C2×C4—16740no—
127C2×C4—167120no—
128C2×C4C23×D167160yes—
129C2×C4C23×D167110yes—
130C22—210no—
131C22—33420no—
132C22—66860no—
133C22—16720no—
134C22C24×D167110yes—
135C22C24×D16711yescharacteristic
136C4—1672no—
137C4—16710no—
138C4C24×D167120yes—
139C2—210no—
140C2—33420no—
141C2#2492410612yesdirect product factor
142C2C25×D16711yescharacteristic
subgroupG/H
centerC22C24×D167
commutator, cosocleC2×C167C26
FrattiniC2C25×D167
FittingC2×2−1+4×C167C2
socleC22×C167C25
hypercenterC2×2−1+4D167
hypocenterC167C2×#585
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. #24924106C2direct (N × H)
2. C2×#19128880C2semidirect
3. C2×#19128878C2semidirect
4. C22×#14581951C2semidirect
5. C2×#41×D167C2semidirect
6. C2×2−1+4×C167C2semidirect
7. #19128880C22semidirect
8. #19128878C22semidirect
9. C2×#14581951C22semidirect
10. C2×#14581951C22semidirect
11. C2×#14581951C22semidirect
12. C2×#14581950C22semidirect
13. C2×#14581949C22semidirect
14. #41×D167C22semidirect
15. C2×Q8×D167C22semidirect
16. C22×D668C22semidirect
17. C2×D4×D167C22semidirect
18. C22×C4×D167C22semidirect
19. 2−1+4×C167C22semidirect
20. C2×#41×C167C22semidirect
21. C22×Q8×C167C22semidirect
23. #14581951C23semidirect
24. #14581951C23semidirect
25. #14581950C23semidirect
26. #14581949C23semidirect
28. Q8×D167C23semidirect
30. C2×D668C23semidirect
32. D4×D167C23semidirect
36. C2×C4×D167C23semidirect
37. #41×C167C23semidirect
39. C2×Q8×C167C23semidirect
68. C2×C167#585semidirect
71. C167C2×#585semidirect
75. C2×2−1+4D167semidirect
80. 2−1+4C2×D167semidirect
88. C2×#41C2×D167semidirect
90. C22×Q8C2×D167semidirect
99. #41C22×D167semidirect
103. C2×Q8C22×D167semidirect
141. C2#24924106direct (N × H)

Maximal subgroups

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

subgroupindex
#249241062
C2×#191288802
C2×#191288782
C22×#145819512
C2×#41×D1672
C2×2−1+4×C1672
C2×#585167