Finite Group Databasebeta

← #22625688

Subgroups — #22625688

Order 9344.

284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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×#14556678C211yesmaximal, characteristic
2#17989567C211yesmaximal, characteristic
3#17989553C212yesmaximal, complemented
4#17989470C212yesmaximal, complemented
5#17988568C211yesmaximal, characteristic
6#14556678—22no—
7#14556678—22no—
8C2×#11924038C2211yescharacteristic
9C2×#11924037C412yescomplemented
10C2×#11924036C2211yescharacteristic
11C22×#10596833C412yescomplemented
12#14556670C2212yes—
13#14556649C414yes—
14#14556645—22no—
15C8×#64408—22no—
16C2×#11924027C2211yescharacteristic
17M16×D73C2212yes—
18#14556509C412yescomplemented
19#14556508C411yescharacteristic, complemented
20#100×C73C411yescharacteristic, complemented
21#11924038—22no—
22#11924037—24no—
23#11924036D412yes—
24#11924036D412yes—
25C2×#10596833—22no—
26C2×#10596833—22no—
27C2×#10596833C2×C412yes—
28C2×#10596833C2×C411yescharacteristic
29C2×#10596833C2×C411yescharacteristic
30C4⋊#64408—22no—
31C22⋊#64408C2×C414yes—
32C4×#64408—22no—
33#11924027—22no—
34#11924027—22no—
35C2×Dic146C2×C411yescharacteristic
36C2×C22⋊D73C2×C412yes—
37C22×Dic73C2×C412yes—
38C2×C4×D73C2311yescharacteristic
39#11924012C2×C412yes—
40#11924011—22no—
41C8×D73—22no—
42C2×D4×C73C2×C411yescharacteristic
43M16×C73C2×C412yes—
44C23×C73C4212yes—
45C22×D73C22×C411yescharacteristic
46C2×#64408—24no—
47D4×C73—22no—
48C2×C4×C73C22×C411yescharacteristic
49C22⋊D73—24no—
50C2×Dic73—22no—
51C2×Dic73—22no—
52C2×Dic73C4212yes—
53C2×Dic73C22×C411yescharacteristic
54C4×D73C2×D412yes—
55C4×D73#4112yes—
56Dic146—22no—
57#10596833—22no—
58#10596833C22⋊C411yescharacteristic
59#10596833C22⋊C411yescharacteristic
60#10596833C22⋊C412yes—
61C8×C73—22no—
62#10596831—22no—
63C22×C73—22no—
64C22×C73—42no—
65C22×C73C2×C4211yescharacteristic
66C2×D73—41no—
67C2×D73C4×D412yes—
68#64408—44no—
69C4×C73C4×D412yes—
70Dic73—22no—
71Dic73C2×C22⋊C411yescharacteristic
72Dic73#11711yescharacteristic
73C2×C73—21no—
74C2×C73—42no—
75C2×C73C4×C22⋊C411yescharacteristic
76D73—22no—
77#1757—731nomaximal, Sylow
78C73#175711yescharacteristic, complemented, Sylow
79C2×#131—731no—
80#413—731no—
81#410—731no—
82#405—732no—
83#344—732no—
84C2×#41—731no—
85#131—1462no—
86#131—1462no—
87C2×M16—732no—
88C2×M16—731no—
89C2×M16—732no—
90C22×C8—731no—
91C22×C8—732no—
92#117—732no—
93#101—732no—
94#100—731no—
95#100#6440811yescharacteristic, complemented
96#99—734no—
97#97—1462no—
98C4×C8—1462no—
99#41—1462no—
100#41—1462no—
101C2×Q8—731no—
102C2×D4—732no—
103C2×D4C2×#6440811yescharacteristic
104C22×C4—731no—
105C22×C4—732no—
106M16—732no—
107M16—1462no—
108M16—1464no—
109M16—1462no—
110M16C2×#6440812yes—
111C2×C8—731no—
112C2×C8—731no—
113C2×C8—732no—
114C2×C8—732no—
115C2×C8—732no—
116C2×C8—1462no—
117C2×C8—1462no—
118C2×C8—1462no—
119C4⋊C4—1462no—
120C22⋊C4—734no—
121C42—1462no—
122C23—731no—
123C23C4×#6440812yes—
124Q8—1462no—
125D4—22no—
126D4—1464no—
127C2×C4—731no—
128C2×C4—732no—
129C2×C4—732no—
130C2×C4—732no—
131C2×C4—1464no—
132C2×C4—1462no—
133C2×C4—1462no—
134C2×C4C22×#6440811yescharacteristic
135C8—22no—
136C8—731no—
137C8—731no—
138C8—732no—
139C8—1462no—
140C8—1462no—
141C22—22no—
142C22—42no—
143C22—2921no—
144C22—732no—
145C22C2×C4×#6440811yescharacteristic
146C4—2924no—
147C4—731no—
148C4—731no—
149C4—1462no—
150C4D4×#6440812yes—
151C2—21no—
152C2—42no—
153C2—1462no—
154C2C22⋊C4×#6440811yescharacteristic
subgroupG/H
centerC2C22⋊C4×#64408
commutatorC22×C73C2×C42
FrattiniC2×C4C22×#64408
Fitting#100×C73C4
socleC2×C73C4×C22⋊C4
hypercenter#100#64408
hypocenterC73#1757
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
3. #17989553C2semidirect
4. #17989470C2semidirect
9. C2×#11924037C4semidirect
11. C22×#10596833C4semidirect
18. #14556509C4semidirect
19. #14556508C4semidirect
20. #100×C73C4semidirect
78. C73#1757semidirect
95. #100#64408semidirect