Finite Group Databasebeta

← #22620312

Subgroups — #22620312

Order 9344.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#17989144C211yesmaximal, characteristic
2C2×#14556591C211yesmaximal, characteristic
3#17988956C214yesmaximal, complemented
4#17988938C214yesmaximal, complemented
5#17988597C214yesmaximal
6C4×M16×C73C211yesmaximal, characteristic
7C22×Dic146C2212yes—
8#14556591—22no—
9#14556591C2212yes—
10#14556591C2212yes—
11#14556591C2212yes—
12#14556583C2212yes—
13#14556570—22no—
14C4×Dic146—22no—
15#14556550C2212yes—
16C2×C4⋊Dic73—22no—
17#14556516C22116yes—
18C2×M16×C73C2212yes—
19C2×C42×C73C2211yescharacteristic
20#97×C73C2212yes—
21C4×C8×C73C2212yes—
22C2×Dic146—28no—
23C2×Dic146—22no—
24C2×Dic146—22no—
25C2×Dic146C2314yes—
26C22×Dic73—22no—
27C4⋊Dic73—24no—
28C4⋊Dic73—24no—
29C4⋊Dic73—22no—
30C4⋊Dic73C2314yes—
31#11924007—24no—
32C22⋊Dic73—22no—
33C4×Dic73—22no—
34C22×C4×C73D412yes—
35C22×C4×C73C2311yescharacteristic
36M16×C73—24no—
37C2×C8×C73C2314yes—
38C42×C73D412yes—
39C42×C73C2311yescharacteristic
40C42×C73C2311yescharacteristic
41C23×C73C2×D411yescharacteristic
42C2×C4×C73—24no—
43C2×C4×C73C2×D412yes—
44C2×C4×C73C2×D411yescharacteristic
45C2×C4×C73C2×D412yes—
46C2×C4×C73#4114yes—
47C2×C4×C73C2411yescharacteristic
48C2×Dic73—24no—
49C2×Dic73—24no—
50C2×Dic73—44no—
51Dic146—28no—
52Dic146—44no—
53Dic146—44no—
54C8×C73—24no—
55C22×C73—22no—
56C22×C73#12412yes—
57C22×C73C22×D411yescharacteristic
58C4×C73—22no—
59C4×C73#12412yes—
60C4×C73#13714yes—
61C4×C73C2×#4112yes—
62Dic73—44no—
63Dic73—44no—
64C2×C73—22no—
65C2×C73C2×#12411yescharacteristic
66C2×C73C2×#13712yes—
67#3139—731nomaximal, Sylow
68C73#313911yescharacteristic, complemented, Sylow
69#533—731no—
70C2×C4⋊Q8—731no—
71#491—734no—
72#487—734no—
73#419—734no—
74C4×M16D7311yescharacteristic
75C22×Q8—732no—
76C2×M16C2×D7312yes—
77C4⋊Q8—732no—
78C4⋊Q8—732no—
79C4⋊Q8—732no—
80C4⋊Q8—1462no—
81#125—732no—
82C22⋊Q8—1462no—
83C4×Q8—1462no—
84#117—732no—
85C2×C4⋊C4—1462no—
86C2×C42C2×D7311yescharacteristic
87#103—7316no—
88#97C2×D7312yes—
89C4×C8C2×D7312yes—
90C2×Q8—734no—
91C2×Q8—1468no—
92C2×Q8—1462no—
93C2×Q8—1462no—
94C22×C4—1462no—
95C22×C4D29212yes—
96C22×C4C22×D7311yescharacteristic
97M16—24no—
98C2×C8C22×D7314yes—
99C4⋊C4—734no—
100C4⋊C4—1464no—
101C4⋊C4—1464no—
102C4⋊C4—1464no—
103C4⋊C4—1462no—
104C22⋊C4—1462no—
105C42—1462no—
106C42D29212yes—
107C42C22×D7311yescharacteristic
108C42C22×D7311yescharacteristic
109C23C2×D29211yescharacteristic
110Q8—2924no—
111Q8—2924no—
112Q8—1468no—
113C2×C4—24no—
114C2×C4—2924no—
115C2×C4—1464no—
116C2×C4—1464no—
117C2×C4C2×D29212yes—
118C2×C4C2×D29211yescharacteristic
119C2×C4C2×D29212yes—
120C2×C4#1192402814yes—
121C2×C4C23×D7311yescharacteristic
122C8—24no—
123C22—22no—
124C22#1455657912yes—
125C22C22×D29211yescharacteristic
126C4—22no—
127C4—2924no—
128C4—2924no—
129C4#1455657912yes—
130C4#1455662414yes—
131C4C2×#1192402812yes—
132C2—22no—
133C2C2×#1455657911yescharacteristic
134C2C2×#1455662412yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×M16×C73C2
socleC22×C73C22×D4
hypercenterC4×M16D73
hypocenterC73#3139
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #17988956C2semidirect
4. #17988938C2semidirect
68. C73#3139semidirect