Finite Group Databasebeta

← #22610876

Subgroups — #22610876

Order 9344.

260 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C4×#11924012C211yesmaximal, characteristic
2C4×C4⋊Dic73C211yesmaximal, characteristic
3#17988346C214yesmaximal
4#533×C73C211yesmaximal, characteristic
5C2×#11924012C2212yes—
6C2×C4⋊Dic73—21no—
7C2×C4×Dic73C2212yes—
8#14556502—21no—
9C4×#10596831—21no—
10#14556498—21no—
11C4⋊Q8×C73C411yescharacteristic, complemented
12C4⋊Q8×C73C411yescharacteristic, complemented
13#125×C73C412yescomplemented
14C22⋊Q8×C73—21no—
15C22⋊Q8×C73—21no—
16C4×Q8×C73—21no—
17C4×Q8×C73—21no—
18#117×C73C2212yes—
19C2×C42×C73C2211yescharacteristic
20C22×Dic73—22no—
21#11924012—22no—
22#11924012Q814yescomplemented
23C2×#10596831—22no—
24C4⋊Dic73—24no—
25C4×Dic73—24no—
26C2×Q8×C73—21no—
27C2×Q8×C73—21no—
28C22×C4×C73D411yescharacteristic
29C22×C4×C73D411yescharacteristic
30C22×C4×C73C2311yescharacteristic
31C4⋊C4×C73—22no—
32C4⋊C4×C73—22no—
33C4⋊C4×C73—21no—
34C4⋊C4×C73—21no—
35C4⋊C4×C73C2×C412yes—
36C4⋊C4×C73C2×C412yes—
37C22⋊C4×C73—22no—
38C42×C73—22no—
39C42×C73C2×C411yescharacteristic
40C42×C73C2×C411yescharacteristic
41C42×C73D411yescharacteristic
42C42×C73D411yescharacteristic
43C23×C73C2×D411yescharacteristic
44Q8×C73—42no—
45Q8×C73—42no—
46C2×C4×C73—22no—
47C2×C4×C73—22no—
48C2×C4×C73—22no—
49C2×C4×C73—41no—
50C2×C4×C73C22⋊C411yescharacteristic
51C2×C4×C73C22⋊C411yescharacteristic
52C2×C4×C73C22⋊C411yescharacteristic
53C2×C4×C73C22⋊C411yescharacteristic
54C2×C4×C73C22×C411yescharacteristic
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×Q812yes—
57C2×C4×C73#4112yes—
58C2×Dic73—24no—
59C2×Dic73—42no—
60C2×Dic73—42no—
61#10596831—24no—
62C22×C73—21no—
63C22×C73—21no—
64C22×C73C2×C22⋊C411yescharacteristic
65C22×C73#12411yescharacteristic
66C22×C73C4⋊Q811yescharacteristic
67C4×C73—21no—
68C4×C73—21no—
69C4×C73—21no—
70C4×C73—42no—
71C4×C73—42no—
72C4×C73#10412yes—
73C4×C73C4×Q812yes—
74C4×C73C22⋊Q812yes—
75Dic73—44no—
76C2×C73—21no—
77C2×C73—21no—
78C2×C73#39111yescharacteristic
79C2×C73C2×#10411yescharacteristic
80C2×C73#42111yescharacteristic
81#1986—731nomaximal, Sylow
82C73#198611yescharacteristic, complemented, Sylow
83#533D7311yescharacteristic
84C4×M16—731no—
85C4×C4⋊C4—731no—
86#339—734no—
87C2×M16—732no—
88C4⋊Q8Dic7311yescharacteristic, complemented
89C4⋊Q8Dic7311yescharacteristic, complemented
90#125Dic7312yescomplemented
91C22⋊Q8—21no—
92C22⋊Q8—21no—
93C4×Q8—21no—
94C4×Q8—21no—
95#117C2×D7312yes—
96C2×C4⋊C4—1461no—
97C2×C42—732no—
98C2×C42C2×D7311yescharacteristic
99#97—1461no—
100C4×C8—1461no—
101#95—1461no—
102C2×Q8—21no—
103C2×Q8—21no—
104C22×C4—1462no—
105C22×C4C22⋊D7311yescharacteristic
106C22×C4C22⋊D7311yescharacteristic
107C22×C4C22×D7311yescharacteristic
108M16—734no—
109M16—1462no—
110C2×C8—1462no—
111C4⋊C4—22no—
112C4⋊C4—22no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—1464no—
116C4⋊C4C2×Dic7312yes—
117C4⋊C4C2×Dic7312yes—
118C22⋊C4—22no—
119C42—22no—
120C42—1464no—
121C42C2×Dic7311yescharacteristic
122C42C2×Dic7311yescharacteristic
123C42C22⋊D7311yescharacteristic
124C42C22⋊D7311yescharacteristic
125C23C2×C22⋊D7311yescharacteristic
126Q8—42no—
127Q8—42no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—2922no—
133C2×C4—2922no—
134C2×C4—1464no—
135C2×C4C22⋊Dic7311yescharacteristic
136C2×C4C22⋊Dic7311yescharacteristic
137C2×C4C22⋊Dic7311yescharacteristic
138C2×C4C22⋊Dic7311yescharacteristic
139C2×C4C22×Dic7311yescharacteristic
140C2×C4C2×C22⋊D7311yescharacteristic
141C2×C4Q8×D7312yes—
142C2×C4#1192402912yes—
143C8—1464no—
144C22—21no—
145C22—21no—
146C22C2×C22⋊Dic7311yescharacteristic
147C22#1455658011yescharacteristic
148C22#1455658911yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—42no—
153C4—42no—
154C4—2924no—
155C4#1455651812yes—
156C4Q8×Dic7312yes—
157C4#1455656712yes—
158C2—21no—
159C2—21no—
160C2#1798849411yescharacteristic
161C2C2×#1455651811yescharacteristic
162C2#1798860411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#533×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#533D73
hypocenterC73#1986
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
11. C4⋊Q8×C73C4semidirect
12. C4⋊Q8×C73C4semidirect
13. #125×C73C4semidirect
22. #11924012Q8semidirect
82. C73#1986semidirect
88. C4⋊Q8Dic73semidirect
89. C4⋊Q8Dic73semidirect
90. #125Dic73semidirect