Finite Group Databasebeta

← #22611794

Subgroups — #22611794

Order 9344.

160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14556536C211yesmaximal, characteristic
2#17988681C211yesmaximal, characteristic, complemented
3#17988669C211yesmaximal, characteristic
4#17988390C211yesmaximal, characteristic, complemented
5#17988387C211yesmaximal, characteristic
6#17988362C211yesmaximal, characteristic, complemented
7#366×C73C211yesmaximal, characteristic, complemented
8C2×Dic292C2211yescharacteristic
9C2×D584C2211yescharacteristic
10#14556556—21no—
11#14556553—21no—
12#14556536C414yescomplemented
13C2×#11924003C2211yescharacteristic
14#14556514—21no—
15#14556511—21no—
16C8×Dic73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18#107×C73C2211yescharacteristic
19#107×C73C2211yescharacteristic
20C2×Dic146—21no—
21C2×D292—21no—
22C2×C4×D73—41no—
23Dic292—21no—
24Dic292C2×C412yescomplemented
25D584—21no—
26D584C2×C412yes—
27C2×#10596831D411yescharacteristic
28#11924007—41no—
29#11924005—41no—
30C4×Dic73—41no—
31C4×Dic73D411yescharacteristic
32#11924003—21no—
33C2×C8×C73C2311yescharacteristic
34C4⋊C4×C73—21no—
35C4⋊C4×C73—21no—
36C16×C73C2×C412yescomplemented
37C22×D73—41no—
38C2×C4×C73—41no—
39C2×C4×C73—41no—
40C2×C4×C73C2×D411yescharacteristic
41C2×Dic73—41no—
42C2×Dic73D811yescharacteristic
43C2×Dic73D811yescharacteristic
44D292—22no—
45D292—41no—
46C4×D73—82no—
47Dic146—22no—
48Dic146—41no—
49C8×C73C22×C411yescharacteristic
50C8×C73#4111yescharacteristic
51#10596831—21no—
52C22×C73C2×D811yescharacteristic
53C2×D73—42no—
54C2×D73—81no—
55C2×D73—81no—
56C4×C73—81no—
57C4×C73—81no—
58C4×C73C4×D411yescharacteristic
59C4×C73#13511yescharacteristic
60Dic73—21no—
61Dic73—21no—
62Dic73—42no—
63C2×C73C4×D811yescharacteristic
64C2×C73#50911yescharacteristic
65C2×C73#51011yescharacteristic
66D73—82no—
67#2175—731nomaximal, Sylow
68C73#217511yescharacteristic, complemented, Sylow
69C2×SD32—731no—
70C4×Q16—731no—
71C4×D8—731no—
72#366D7311yescharacteristic, complemented
73#358—731no—
74#357—731no—
75#346—731no—
76C2×Q16—731no—
77C2×D8—731no—
78C4×Q8—1461no—
79C4×D4—1461no—
80SD32—734no—
81C2×C16—731no—
82C2×C16C2×D7311yescharacteristic
83#107C2×D7311yescharacteristic
84#107C2×D7311yescharacteristic
85#103—1461no—
86#102—1461no—
87C4×C8—731no—
88C2×Q8—1461no—
89C2×D4—1461no—
90C22×C4—2921no—
91Q16—732no—
92Q16—1461no—
93D8—732no—
94D8—1461no—
95C2×C8—731no—
96C2×C8C22×D7311yescharacteristic
97C4⋊C4—21no—
98C4⋊C4—21no—
99C4⋊C4—2921no—
100C22⋊C4—2921no—
101C42—2921no—
102C42—731no—
103C16—1461no—
104C16C4×D7312yescomplemented
105C23—2921no—
106Q8—2921no—
107Q8—1462no—
108D4—2921no—
109D4—1462no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—2921no—
113C2×C4—5842no—
114C2×C4—731no—
115C2×C4—731no—
116C2×C4D4×D7311yescharacteristic
117C8—1461no—
118C8C2×C4×D7311yescharacteristic
119C8#1192402911yescharacteristic
120C22—2922no—
121C22—5841no—
122C22—5841no—
123C22D8×D7311yescharacteristic
124C4—81no—
125C4—81no—
126C4—2922no—
127C4—1461no—
128C4—1461no—
129C4#1455655311yescharacteristic
130C4#1455661411yescharacteristic
131C2—5842no—
132C2#1798866911yescharacteristic
133C2#1798902111yescharacteristic
134C2#1798902911yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
Fitting#366×C73C2
socleC22×C73C2×D8
hypercenter#366D73
hypocenterC73#2175
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
2. #17988681C2semidirect
4. #17988390C2semidirect
6. #17988362C2semidirect
7. #366×C73C2semidirect
12. #14556536C4semidirect
24. Dic292C2×C4semidirect
36. C16×C73C2×C4semidirect
68. C73#2175semidirect
72. #366D73semidirect
104. C16C4×D73semidirect