Finite Group Databasebeta

← #22608083

Subgroups — #22608083

Order 9344.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#17988759C211yesmaximal, characteristic
2#17988382C211yesmaximal, characteristic, complemented
3#329×C73C211yesmaximal, characteristic, complemented
4#14556639C411yescharacteristic, complemented
5#14556617—21no—
6#14556519—21no—
7#14556510C411yescharacteristic, complemented
8#14556506—21no—
9#124×C73C2211yescharacteristic
10#97×C73—21no—
11#11924029—41no—
12#11924028—21no—
13#11924028—41no—
14Q8×D73—41no—
15#11924016—41no—
16#11924013—41no—
17#11924012—21no—
18C22⋊Dic73—41no—
19C2×Q8×C73C2×C411yescharacteristic
20C2×D4×C73D411yescharacteristic
21C2×C8×C73—41no—
22C22⋊C4×C73—41no—
23C42×C73D411yescharacteristic
24C23×C73—21no—
25Q8×C73—41no—
26D4×C73—41no—
27C2×C4×C73—21no—
28C2×C4×C73—21no—
29C2×C4×C73C22⋊C411yescharacteristic
30C22⋊D73—41no—
31C2×Dic73—81no—
32D292—21no—
33D292—41no—
34C4×D73—41no—
35C4×D73—42no—
36Dic146—21no—
37Dic146—41no—
38C8×C73—42no—
39#10596831—41no—
40C22×C73—41no—
41C22×C73—81no—
42C22×C73#9911yescharacteristic
43C2×D73—41no—
44C4×C73—21no—
45C4×C73—41no—
46C4×C73—41no—
47Dic73—41no—
48Dic73—161no—
49C2×C73—21no—
50C2×C73—81no—
51C2×C73AΣL(1,𝔽16)11yescharacteristic
52D73—81no—
53#1404—731nomaximal, Sylow
54C73#140411yescharacteristic, complemented, Sylow
55#454—731no—
56#354—731no—
57#329D7311yescharacteristic, complemented
582−1+4—731no—
59AGL(1,ℤ/8)—1461no—
60#124C2×D7311yescharacteristic
61#104—1461no—
62#101—731no—
63#99—1461no—
64#97—21no—
65#41—2921no—
66#41—2921no—
67#41—1461no—
68C2×Q8—2921no—
69C2×Q8C4×D7311yescharacteristic
70C2×D4D29211yescharacteristic
71SD16—2921no—
72D8—2921no—
73M16—1461no—
74C2×C8—41no—
75C22⋊C4—41no—
76C22⋊C4—2921no—
77C42C22⋊D7311yescharacteristic
78C23—21no—
79Q8—41no—
80Q8—2921no—
81Q8—1461no—
82D4—41no—
83D4—2921no—
84D4—2921no—
85D4—1461no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—2921no—
89C2×C4—2922no—
90C2×C4—5841no—
91C2×C4#1192400511yescharacteristic
92C8—42no—
93C8—2921no—
94C22—41no—
95C22—81no—
96C22—2921no—
97C22#1455650511yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—2921no—
102C4—11681no—
103C2—21no—
104C2—81no—
105C2—5841no—
106C2#1798837511yescharacteristic
subgroupG/H
centerC2#17988375
commutatorC2×Q8×C73C2×C4
Frattini#124C2×D73
Fitting#329×C73C2
socleC2×C73AΣL(1,𝔽16)
hypercenter#329D73
hypocenterC73#1404
LCSG ▷ C2×Q8×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #17988382C2semidirect
3. #329×C73C2semidirect
4. #14556639C4semidirect
7. #14556510C4semidirect
54. C73#1404semidirect
57. #329D73semidirect