Finite Group Databasebeta

← #22625033

Subgroups — #22625033

Order 9344.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#17989568C211yesmaximal, characteristic
2#17989562C211yesmaximal, characteristic
3#17988570C211yesmaximal, characteristic
4C2×#11924038C411yescharacteristic, complemented
5C2×#11924036C411yescharacteristic, complemented
6#14556670—21no—
7#14556650—21no—
8#14556650C412yes—
9#14556648—21no—
10#14556648—21no—
11C2×#11924029C2211yescharacteristic
12M16×D73—21no—
13#14556510C411yescharacteristic, complemented
14#14556507—21no—
15#101×C73C411yescharacteristic, complemented
16#11924038—41no—
17#11924036—41no—
18C2×#10596833—21no—
19C2×#10596833—21no—
20C4⋊#64408—41no—
21C22⋊#64408—22no—
22C4×#64408—41no—
23#11924029—41no—
24#11924029—41no—
25C2×D292C2×C411yescharacteristic
26C2×D292D411yescharacteristic
27C2×D292Q811yescharacteristic
28C2×C4×D73C2×C411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C2×C4×D73D411yescharacteristic
31#11924012—21no—
32#11924011—41no—
33C8×D73—41no—
34C2×Q8×C73C2×C411yescharacteristic
35M16×C73—21no—
36C22×D73C22⋊C411yescharacteristic
37C22×D73C4⋊C411yescharacteristic
38C22×D73C4⋊C411yescharacteristic
39C2×#64408—42no—
40Q8×C73—41no—
41C2×C4×C73C4211yescharacteristic
42C2×C4×C73C22⋊C411yescharacteristic
43C2×C4×C73C4⋊C411yescharacteristic
44C2×Dic73C22⋊C411yescharacteristic
45D292—41no—
46D292—41no—
47D292—41no—
48C4×D73—21no—
49C4×D73—21no—
50C4×D73—21no—
51C4×D73—21no—
52C4×D73—21no—
53C4×D73—21no—
54#10596833—41no—
55#10596833—41no—
56C8×C73—41no—
57#10596831—41no—
58C22×C73#9511yescharacteristic
59C2×D73—21no—
60C2×D73—21no—
61C2×D73—21no—
62C2×D73—41no—
63C2×D73—41no—
64C2×D73—41no—
65#64408—82no—
66C4×C73—21no—
67C4×C73—21no—
68C4×C73—21no—
69Dic73#9911yescharacteristic
70Dic73#9911yescharacteristic
71C2×C73—21no—
72C2×C73#34211yescharacteristic
73D73—41no—
74D73—41no—
75D73—41no—
76#1395—731nomaximal, Sylow
77C73#139511yescharacteristic, complemented, Sylow
78#413—731no—
79#410—731no—
80#408—731no—
81C2×#41—731no—
82C2×M16—731no—
83C2×M16—1461no—
84C22×C8—731no—
85#117—1461no—
86#101—731no—
87#101#6440811yescharacteristic, complemented
88#100—1461no—
89#99—732no—
90#99—1461no—
91C22⋊C8—1461no—
92C22⋊C8—1461no—
93#41—2921no—
94#41—2921no—
95C2×Q8C2×#6440811yescharacteristic
96C2×D4—731no—
97C2×D4—731no—
98C2×D4—731no—
99C22×C4—731no—
100C22×C4—731no—
101C22×C4—731no—
102M16—21no—
103M16—2921no—
104M16—2921no—
105M16—1461no—
106C2×C8—2921no—
107C2×C8—2921no—
108C2×C8—1461no—
109C2×C8—1461no—
110C4⋊C4—2921no—
111C22⋊C4—1462no—
112C42—2921no—
113C23—731no—
114C23—731no—
115C23—731no—
116Q8—41no—
117D4—2921no—
118D4—2921no—
119D4—2921no—
120C2×C4—2922no—
121C2×C4—731no—
122C2×C4—1461no—
123C2×C4—1461no—
124C2×C4—1461no—
125C2×C4—1461no—
126C2×C4—1461no—
127C2×C4—1461no—
128C2×C4C4×#6440811yescharacteristic
129C2×C4C22⋊#6440811yescharacteristic
130C2×C4C4⋊#6440811yescharacteristic
131C8—41no—
132C8—2921no—
133C8—2921no—
134C8—2921no—
135C22—2921no—
136C22—2921no—
137C22—2921no—
138C22—1461no—
139C22—1461no—
140C22—1461no—
141C22(C2×#64408)⋊C411yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—5842no—
146C4—731no—
147C4—731no—
148C2—21no—
149C2—2921no—
150C2—2921no—
151C2—2921no—
152C2#1798946411yescharacteristic
subgroupG/H
centerC2#17989464
commutatorC2×C4×C73C42
FrattiniC2×Q8C2×#64408
Fitting#101×C73C4
socleC2×C73#342
hypercenter#101#64408
hypocenterC73#1395
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
4. C2×#11924038C4semidirect
5. C2×#11924036C4semidirect
13. #14556510C4semidirect
15. #101×C73C4semidirect
77. C73#1395semidirect
87. #101#64408semidirect