Finite Group Databasebeta

← #22626051

Subgroups — #22626051

Order 9344.

184 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 66 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#17989602C212yesmaximal
2C2×#14556662C211yesmaximal, characteristic
3#17989550C211yesmaximal, characteristic
4#17989470C212yesmaximal
5#108×D73C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7D73⋊M16C2211yescharacteristic
8#14556670C2211yescharacteristic
9#14556662—22no—
10#14556662—21no—
11#14556662—21no—
12#14556661—22no—
13#14556645—21no—
14C8×#64408—21no—
15M16×D73C2212yes—
16C2×C8×D73C2211yescharacteristic
17#14556527C411yescharacteristic, complemented
18#14556526C412yescomplemented
19#108×C73C411yescharacteristic, complemented
20#11924038—22no—
21#11924038—22no—
22#11924038D411yescharacteristic
23#11924038D411yescharacteristic
24#11924037—21no—
25#11924036—21no—
26C2×#10596833—22no—
27C4⋊#64408—21no—
28C22⋊#64408Q812yes—
29C4×#64408—21no—
30C2×C4×D73C2311yescharacteristic
31#11924012C2×C412yes—
32#11924011—22no—
33C2×#10596831C2×C411yescharacteristic
34C8×D73—22no—
35C8×D73D411yescharacteristic
36C8×D73D411yescharacteristic
37C8×D73Q811yescharacteristic
38C8×D73Q811yescharacteristic
39M16×C73C2×C412yes—
40C2×C8×C73C2×C411yescharacteristic
41C22×D73C2×Q811yescharacteristic
42C2×#64408—22no—
43C2×C4×C73C22×C411yescharacteristic
44C2×Dic73#4111yescharacteristic
45C4×D73C2×D411yescharacteristic
46C4×D73C2×D411yescharacteristic
47C4×D73C2×Q811yescharacteristic
48C4×D73#4111yescharacteristic
49#10596833—21no—
50#10596833—21no—
51#10596833—42no—
52C8×C73—22no—
53C8×C73C4⋊C411yescharacteristic
54C8×C73C4⋊C411yescharacteristic
55#10596831—22no—
56#10596831C4⋊C411yescharacteristic
57#10596831C4⋊C411yescharacteristic
58C22×C73C4×Q811yescharacteristic
59C2×D73—41no—
60C2×D73C22⋊Q811yescharacteristic
61C2×D73C4⋊Q811yescharacteristic
62#64408—42no—
63C4×C73C2×C4⋊C411yescharacteristic
64C4×C73C4×D411yescharacteristic
65Dic73#12111yescharacteristic
66Dic73#12511yescharacteristic
67C2×C73—21no—
68C2×C73#38911yescharacteristic
69D73—21no—
70D73—21no—
71#1953—731nomaximal, Sylow
72C73#195311yescharacteristic, complemented, Sylow
73#430—732no—
74C2×#108—731no—
75C2×#108—731no—
76#405—731no—
77#344—732no—
78C2×M16—731no—
79C2×M16—732no—
80C2×M16—732no—
81C22×C8—731no—
82#117—731no—
83#108—732no—
84#108—731no—
85#108—1461no—
86#108—1461no—
87#108—1462no—
88#108—1462no—
89#108#6440811yescharacteristic, complemented
90#97—1461no—
91C4×C8—1461no—
92C22×C4—731no—
93M16—731no—
94M16—731no—
95M16—732no—
96M16—1462no—
97M16—1462no—
98M16—1462no—
99M16—1461no—
100M16C2×#6440812yes—
101C2×C8—731no—
102C2×C8—731no—
103C2×C8—731no—
104C2×C8—731no—
105C2×C8—731no—
106C2×C8—1462no—
107C2×C8—1462no—
108C2×C8—1461no—
109C2×C8C2×#6440811yescharacteristic
110C4⋊C4—1461no—
111C22⋊C4—732no—
112C42—1461no—
113C23—731no—
114C2×C4—731no—
115C2×C4—731no—
116C2×C4—731no—
117C2×C4—731no—
118C2×C4—731no—
119C2×C4—1462no—
120C2×C4C22×#6440811yescharacteristic
121C8—22no—
122C8—2922no—
123C8—731no—
124C8—731no—
125C8—1461no—
126C8—1461no—
127C8—1462no—
128C8C4⋊#6440811yescharacteristic
129C8C4⋊#6440811yescharacteristic
130C22—2921no—
131C22—731no—
132C22—731no—
133C22Q8×#6440811yescharacteristic
134C4—2922no—
135C4—731no—
136C4—731no—
137C4C2×C4⋊#6440811yescharacteristic
138C4D4×#6440811yescharacteristic
139C2—21no—
140C2—1461no—
141C2—1461no—
142C2#1798953811yescharacteristic
subgroupG/H
centerC2#17989538
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#108×C73C4
socleC2×C73#389
hypercenter#108#64408
hypocenterC73#1953
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
17. #14556527C4semidirect
18. #14556526C4semidirect
19. #108×C73C4semidirect
72. C73#1953semidirect
89. #108#64408semidirect