Finite Group Databasebeta

← #22626058

Subgroups — #22626058

Order 9344.

332 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 98 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×#14556654C214yesmaximal
2C4×#11924036C211yesmaximal, characteristic
3#17989533C211yesmaximal, characteristic
4C4⋊Q8×D73C211yesmaximal, characteristic
5C2×#11924036C2212yes—
6C2×C4⋊#64408—22no—
7C2×C4⋊#64408C2212yes—
8#14556654—28no—
9C4×#10596833—22no—
10C2×Q8×D73C2212yes—
11#14556591C411yescharacteristic, complemented
12#14556590—22no—
13#14556589C412yescomplemented
14C4⋊C4×D73—22no—
15C42×D73C2211yescharacteristic
16C4⋊Q8×C73C411yescharacteristic, complemented
17C22×#64408—22no—
18#11924036—22no—
19#11924036D414yes—
20C2×#10596833—22no—
21C4⋊#64408—24no—
22C4⋊#64408—44no—
23C2×Dic146—22no—
24C2×Dic146C2×C412yes—
25Q8×D73—24no—
26Q8×D73—24no—
27C2×C4×D73—22no—
28C2×C4×D73D412yes—
29C2×C4×D73C2311yescharacteristic
30C4⋊Dic73—22no—
31#11924007—24no—
32C4×Dic73C2×C411yescharacteristic
33C4×Dic73D412yes—
34C2×Q8×C73C2×C412yes—
35C4⋊C4×C73—22no—
36C42×C73C2×C411yescharacteristic
37C22×D73C2×D411yescharacteristic
38C2×#64408—42no—
39C2×#64408—44no—
40Q8×C73—24no—
41C2×C4×C73—22no—
42C2×C4×C73C22⋊C412yes—
43C2×C4×C73C22×C411yescharacteristic
44C2×Dic73—22no—
45C2×Dic73C22⋊C412yes—
46C2×Dic73C2×D411yescharacteristic
47C4×D73—42no—
48C4×D73—42no—
49C4×D73SD1614yes—
50C4×D73Q1614yes—
51C4×D73C2×D412yes—
52C4×D73#4112yes—
53Dic146—24no—
54Dic146—44no—
55#10596833—24no—
56C22×C73C2×C22⋊C411yescharacteristic
57C2×D73#12411yescharacteristic
58C2×D73#12711yescharacteristic
59C2×D73C2×SD1612yes—
60C2×D73C2×Q1612yes—
61#64408—82no—
62C4×C73—42no—
63C4×C73#10314yescomplemented
64C4×C73C4×D412yes—
65Dic73—42no—
66Dic73#10314yescomplemented
67Dic73#12112yes—
68C2×C73#39011yescharacteristic
69C2×C73C2×#10312yes—
70D73#48712yes—
71D73#49211yescharacteristic
72D73#49411yescharacteristic
73#1956—731nomaximal, Sylow
74C73#195611yescharacteristic, complemented, Sylow
75C2×C4⋊Q8—731no—
76C2×#103—734no—
77C2×C4×C8—731no—
78#384—731no—
79C22×Q8—732no—
80C22×C8—732no—
81C4⋊Q8—732no—
82C4⋊Q8—731no—
83C4⋊Q8—1462no—
84C4⋊Q8#6440811yescharacteristic, complemented
85C2×C4⋊C4—732no—
86C2×C4⋊C4—1462no—
87C2×C4⋊C4—1462no—
88C2×C42—731no—
89#103—1468no—
90C4×C8—1462no—
91C2×Q8—732no—
92C2×Q8—1462no—
93C2×Q8—1464no—
94C2×Q8—1464no—
95C2×Q8C2×#6440812yes—
96C22×C4—732no—
97C22×C4—731no—
98C22×C4—1462no—
99C22×C4—1462no—
100C2×C8—734no—
101C2×C8—1462no—
102C2×C8—1462no—
103C4⋊C4—22no—
104C4⋊C4—2924no—
105C4⋊C4—1464no—
106C4⋊C4—1464no—
107C4⋊C4—1462no—
108C42—732no—
109C42—731no—
110C42C2×#6440811yescharacteristic
111C23—731no—
112Q8—24no—
113Q8—2924no—
114Q8—1464no—
115C2×C4—22no—
116C2×C4—2922no—
117C2×C4—2922no—
118C2×C4—2924no—
119C2×C4—2922no—
120C2×C4—732no—
121C2×C4—731no—
122C2×C4—734no—
123C2×C4—734no—
124C2×C4—732no—
125C2×C4—732no—
126C2×C4—1462no—
127C2×C4C22⋊#6440812yes—
128C2×C4C22×#6440811yescharacteristic
129C8—1464no—
130C22—731no—
131C22—731no—
132C22—732no—
133C22—732no—
134C22C2×C22⋊#6440811yescharacteristic
135C4—42no—
136C4—2922no—
137C4—5842no—
138C4—732no—
139C4—734no—
140C4#1455665414yescomplemented
141C4D4×#6440812yes—
142C2—731no—
143C2—732no—
144C2—731no—
145C2#1798953911yescharacteristic
146C2C2×#1455665412yes—
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4⋊Q8#64408
hypocenterC73#1956
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #14556591C4semidirect
13. #14556589C4semidirect
16. C4⋊Q8×C73C4semidirect
63. C4×C73#103semidirect
66. Dic73#103semidirect
74. C73#1956semidirect
84. C4⋊Q8#64408semidirect
140. C4#14556654semidirect