Finite Group Databasebeta

← #22625869

Subgroups — #22625869

Order 9344.

256 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 94 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×#14556660C212yesmaximal
2C2×#14556659C212yesmaximal
3#17989533C211yesmaximal, characteristic
4#17989531C211yesmaximal, characteristic
5#97×D73C211yesmaximal, characteristic
6C2×C4⋊#64408—22no—
7C2×C4⋊#64408C2211yescharacteristic
8C2×C4⋊#64408C2211yescharacteristic
9C2×C4⋊#64408C2212yes—
10#14556660—24no—
11#14556659—24no—
12(C2×#64408)⋊C4—22no—
13C2×C8×D73C2212yes—
14C42×D73C2211yescharacteristic
15#14556502C411yescharacteristic, complemented
16#14556501C412yescomplemented
17#97×C73C411yescharacteristic, complemented
18C22×#64408—21no—
19C22×#64408—21no—
20C22×#64408—22no—
21C4⋊#64408—22no—
22C4⋊#64408—22no—
23C4⋊#64408—22no—
24C4⋊#64408—22no—
25C4⋊#64408—44no—
26C2×C4×D73D412yes—
27C2×C4×D73C2311yescharacteristic
28C2×#10596831C2×C412yes—
29C8×D73D414yes—
30C8×D73Q814yes—
31C4×Dic73C2×C411yescharacteristic
32C4×Dic73Q812yes—
33C2×C8×C73C2×C412yes—
34C42×C73C2×C411yescharacteristic
35C22×D73C2×D411yescharacteristic
36C2×#64408—42no—
37C2×#64408—41no—
38C2×#64408—41no—
39C2×#64408—44no—
40C2×#64408—42no—
41C2×#64408—42no—
42C2×C4×C73C4⋊C412yes—
43C2×C4×C73C22×C411yescharacteristic
44C2×Dic73C4⋊C412yes—
45C2×Dic73C2×Q811yescharacteristic
46C4×D73—22no—
47C4×D73—22no—
48C4×D73C2×D412yes—
49C4×D73C2×Q812yes—
50C8×C73C4⋊C414yescomplemented
51#10596831C4⋊C414yescomplemented
52C22×C73C2×C4⋊C411yescharacteristic
53C2×D73#12711yescharacteristic
54C2×D73C4⋊Q811yescharacteristic
55C2×D73AGL(1,ℤ/8)12yes—
56C2×D73#13712yes—
57#64408—82no—
58#64408—81no—
59#64408—81no—
60C4×C73—22no—
61C4×C73C2×C4⋊C412yes—
62Dic73—22no—
63Dic73C4⋊Q812yes—
64C2×C73#38411yescharacteristic
65C2×C73#42812yes—
66D73#49611yescharacteristic
67D73#49711yescharacteristic
68D73#50112yes—
69#1847—731nomaximal, Sylow
70C73#184711yescharacteristic, complemented, Sylow
71C2×#107—732no—
72C2×#106—732no—
73C2×#97—731no—
74#384—731no—
75#382—731no—
76C22×C8—732no—
77C2×C4⋊C4—731no—
78C2×C4⋊C4—731no—
79C2×C4⋊C4—732no—
80C2×C4⋊C4—1462no—
81C2×C42—731no—
82#107—1464no—
83#106—1464no—
84#97—732no—
85#97—731no—
86#97#6440811yescharacteristic, complemented
87#95—1462no—
88C22×C4—731no—
89C22×C4—732no—
90C22×C4—1461no—
91C22×C4—1461no—
92C22×C4—1462no—
93C2×C8—732no—
94C2×C8—734no—
95C2×C8—734no—
96C2×C8C2×#6440812yes—
97C4⋊C4—2924no—
98C4⋊C4—1462no—
99C4⋊C4—1462no—
100C4⋊C4—1462no—
101C4⋊C4—1462no—
102C42—732no—
103C42—731no—
104C42C2×#6440811yescharacteristic
105C23—731no—
106C2×C4—2924no—
107C2×C4—2921no—
108C2×C4—2922no—
109C2×C4—2921no—
110C2×C4—2922no—
111C2×C4—2922no—
112C2×C4—731no—
113C2×C4—732no—
114C2×C4—732no—
115C2×C4—732no—
116C2×C4—1462no—
117C2×C4—1462no—
118C2×C4C4⋊#6440812yes—
119C2×C4C22×#6440811yescharacteristic
120C8—734no—
121C8C4⋊#6440814yescomplemented
122C22—731no—
123C22—731no—
124C22—732no—
125C22—732no—
126C22C2×C4⋊#6440811yescharacteristic
127C4—22no—
128C4—5842no—
129C4—5841no—
130C4—5841no—
131C4—732no—
132C4—1462no—
133C4C2×C4⋊#6440812yes—
134C2—731no—
135C2—731no—
136C2—732no—
137C2#1798953311yescharacteristic
138C2#1798959812yes—
subgroupG/H
centerC22C2×C4⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#97×C73C4
socleC22×C73C2×C4⋊C4
hypercenter#97#64408
hypocenterC73#1847
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
15. #14556502C4semidirect
16. #14556501C4semidirect
17. #97×C73C4semidirect
50. C8×C73C4⋊C4semidirect
51. #10596831C4⋊C4semidirect
70. C73#1847semidirect
86. #97#64408semidirect
121. C8C4⋊#64408semidirect