Finite Group Databasebeta

← #22611995

Subgroups — #22611995

Order 9344.

158 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14556534C211yesmaximal, characteristic
2#17988972C211yesmaximal, characteristic
3Q16×Dic73C211yesmaximal, characteristic, complemented
4#17988405C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988389C211yesmaximal, characteristic
7C2×Q32×C73C211yesmaximal, characteristic, complemented
8C2×#11924015—21no—
9C2×D584C2211yescharacteristic
10#14556580—21no—
11Q8×Dic73—21no—
12#14556534—22no—
13C2×#11924003C2211yescharacteristic
14#14556525C2211yescharacteristic
15#14556515—21no—
16C8×Dic73C2211yescharacteristic
17C2×Q16×C73C2211yescharacteristic
18C2×Q16×C73C2211yescharacteristic
19Q32×C73—22no—
20C2×C16×C73C2211yescharacteristic
21C2×D292—21no—
22#11924015—42no—
23D584—21no—
24D584—21no—
25C2×#10596831D411yescharacteristic
26C4⋊Dic73—21no—
27C4⋊Dic73—41no—
28#11924005—41no—
29#11924005—41no—
30C4×Dic73—41no—
31C4×Dic73D411yescharacteristic
32#11924003—21no—
33C2×Q8×C73—21no—
34C2×Q8×C73—21no—
35Q16×C73—21no—
36Q16×C73—21no—
37Q16×C73—21no—
38Q16×C73D412yes—
39C2×C8×C73C2311yescharacteristic
40C16×C73—21no—
41C22×D73—41no—
42Q8×C73—22no—
43Q8×C73—41no—
44Q8×C73—41no—
45Q8×C73—41no—
46C2×C4×C73—41no—
47C2×C4×C73—41no—
48C2×C4×C73C2×D411yescharacteristic
49C2×Dic73—41no—
50C2×Dic73D811yescharacteristic
51C2×Dic73D811yescharacteristic
52D292—41no—
53D292—41no—
54C8×C73C2×D411yescharacteristic
55C8×C73#4111yescharacteristic
56#10596831—21no—
57C22×C73C2×D811yescharacteristic
58C2×D73—81no—
59C2×D73—81no—
60C2×D73—81no—
61C4×C73—42no—
62C4×C73—81no—
63C4×C73#12111yescharacteristic
64C4×C73AGL(1,ℤ/8)11yescharacteristic
65Dic73—21no—
66Dic73—21no—
67Dic73—81no—
68C2×C73#45911yescharacteristic
69C2×C73#50811yescharacteristic
70C2×C73#51011yescharacteristic
71D73—161no—
72#2211—731nomaximal, Sylow
73C73#221111yescharacteristic, complemented, Sylow
74C2×Q32D7311yescharacteristic, complemented
75C2×SD32—731no—
76#495—731no—
77C4×Q16—731no—
78C4⋊C16—731no—
79#358—731no—
80#357—731no—
81C2×Q16C2×D7311yescharacteristic
82C2×Q16C2×D7311yescharacteristic
83C2×SD16—1461no—
84C2×D8—731no—
85#124—1461no—
86C4×Q8—1461no—
87Q32—22no—
88SD32—1462no—
89C2×C16—731no—
90C2×C16C2×D7311yescharacteristic
91#107—731no—
92#103—1461no—
93C4×C8—731no—
94C2×Q8—21no—
95C2×Q8—21no—
96C2×D4—1461no—
97Q16—21no—
98Q16—21no—
99Q16—21no—
100Q16C22⋊D7312yes—
101SD16—2922no—
102D8—1461no—
103D8—1461no—
104C2×C8—731no—
105C2×C8C22×D7311yescharacteristic
106C4⋊C4—2921no—
107C4⋊C4—1461no—
108C22⋊C4—2921no—
109C22⋊C4—2921no—
110C42—2921no—
111C42—731no—
112C16—21no—
113C16—1461no—
114C23—2921no—
115Q8—22no—
116Q8—41no—
117Q8—41no—
118Q8—41no—
119D4—2921no—
120D4—2921no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—2921no—
124C2×C4—731no—
125C2×C4—731no—
126C2×C4D4×D7311yescharacteristic
127C8—1461no—
128C8C2×C22⋊D7311yescharacteristic
129C8#1192402711yescharacteristic
130C22—5841no—
131C22—5841no—
132C22—5841no—
133C22D8×D7311yescharacteristic
134C4—42no—
135C4—81no—
136C4—5841no—
137C4—1461no—
138C4—1461no—
139C4#1455656311yescharacteristic
140C4#1455661511yescharacteristic
141C2—11681no—
142C2#1798878011yescharacteristic
143C2#1798902011yescharacteristic
144C2#1798902911yescharacteristic
subgroupG/H
centerC22D8×D73
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC2×Q32×C73C2
socleC22×C73C2×D8
hypercenterC2×Q32D73
hypocenterC73#2211
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
3. Q16×Dic73C2semidirect
4. #17988405C2semidirect
5. #17988391C2semidirect
7. C2×Q32×C73C2semidirect
73. C73#2211semidirect
74. C2×Q32D73semidirect