Finite Group Databasebeta

← #22611795

Subgroups — #22611795

Order 9344.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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×#14556535C211yesmaximal, characteristic
2C4×Dic292C211yesmaximal, characteristic, complemented
3#17988412C211yesmaximal, characteristic, complemented
4#17988390C211yesmaximal, characteristic, complemented
5#17988388C211yesmaximal, characteristic
6#17988363C211yesmaximal, characteristic, complemented
7C4×D8×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9C4×Dic146—21no—
10#14556535C414yescomplemented
11C2×#11924003C2211yescharacteristic
12C2×#11924003C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556516—21no—
15C2×D8×C73C2211yescharacteristic
16C4×D4×C73—21no—
17#107×C73C2211yescharacteristic
18#102×C73—21no—
19C4×C8×C73C2211yescharacteristic
20C2×Dic146—21no—
21Dic292—21no—
22Dic292C2×C412yescomplemented
23C4⋊Dic73—21no—
24#11924007—41no—
25C4×Dic73—41no—
26#11924003—21no—
27#11924003C2×C412yescomplemented
28C2×D4×C73—21no—
29C22×C4×C73—41no—
30D8×C73—21no—
31D8×C73C2×C412yes—
32C2×C8×C73D411yescharacteristic
33C2×C8×C73C2311yescharacteristic
34C4⋊C4×C73—21no—
35C22⋊C4×C73—41no—
36C42×C73D411yescharacteristic
37C23×C73—41no—
38D4×C73—22no—
39D4×C73—41no—
40C2×C4×C73—41no—
41C2×C4×C73—82no—
42C2×C4×C73D811yescharacteristic
43C2×C4×C73D811yescharacteristic
44C2×C4×C73C2×D411yescharacteristic
45C2×Dic73—41no—
46C2×Dic73—41no—
47Dic146—22no—
48Dic146—41no—
49C8×C73—21no—
50C8×C73C22×C411yescharacteristic
51C8×C73#4111yescharacteristic
52C22×C73—42no—
53C22×C73—81no—
54C22×C73—81no—
55C22×C73C2×D811yescharacteristic
56C4×C73—21no—
57C4×C73—21no—
58C4×C73—81no—
59C4×C73C4×D411yescharacteristic
60C4×C73#13511yescharacteristic
61Dic73—42no—
62Dic73—81no—
63C2×C73—82no—
64C2×C73C4×D811yescharacteristic
65C2×C73#50911yescharacteristic
66C2×C73#51011yescharacteristic
67#2175—731nomaximal, Sylow
68C73#217511yescharacteristic, complemented, Sylow
69C2×SD32—731no—
70C4×Q16—731no—
71C4×D8D7311yescharacteristic
72#366—731no—
73#358—731no—
74#357—731no—
75#346—731no—
76C2×Q16—731no—
77C2×D8C2×D7311yescharacteristic
78C4×Q8—1461no—
79C4×D4—21no—
80SD32—734no—
81C2×C16—731no—
82C2×C16—731no—
83#107—731no—
84#107C2×D7311yescharacteristic
85#103—1461no—
86#102—21no—
87C4×C8C2×D7311yescharacteristic
88C2×Q8—1461no—
89C2×D4—21no—
90C22×C4—41no—
91Q16—732no—
92Q16—1461no—
93D8—21no—
94D8C4×D7312yes—
95C2×C8C22⋊D7311yescharacteristic
96C2×C8C22×D7311yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—2921no—
99C4⋊C4—1461no—
100C22⋊C4—41no—
101C42—2921no—
102C42C22⋊D7311yescharacteristic
103C16—732no—
104C16—1461no—
105C23—41no—
106Q8—2921no—
107Q8—1462no—
108D4—22no—
109D4—41no—
110C2×C4—41no—
111C2×C4—82no—
112C2×C4—2921no—
113C2×C4—2921no—
114C2×C4#1192401311yescharacteristic
115C2×C4#1192401311yescharacteristic
116C2×C4C2×C22⋊D7311yescharacteristic
117C8—21no—
118C8C2×C4×D7311yescharacteristic
119C8#1192402811yescharacteristic
120C22—42no—
121C22—81no—
122C22—81no—
123C22C2×#1192401311yescharacteristic
124C4—21no—
125C4—21no—
126C4—81no—
127C4—2922no—
128C4—5841no—
129C4C4×C22⋊D7311yescharacteristic
130C4#1455661111yescharacteristic
131C2—82no—
132C2C4×#1192401311yescharacteristic
133C2#1798902311yescharacteristic
134C2#1798902711yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
FittingC4×D8×C73C2
socleC22×C73C2×D8
hypercenterC4×D8D73
hypocenterC73#2175
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×Dic292C2semidirect
3. #17988412C2semidirect
4. #17988390C2semidirect
6. #17988363C2semidirect
10. #14556535C4semidirect
22. Dic292C2×C4semidirect
27. #11924003C2×C4semidirect
68. C73#2175semidirect