Finite Group Databasebeta

← #22611990

Subgroups — #22611990

Order 9344.

158 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14556537C211yesmaximal, characteristic, complemented
2C2×#14556535C211yesmaximal, characteristic
3C4×Dic292C211yesmaximal, characteristic, complemented
4C4⋊#11924003C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988388C211yesmaximal, characteristic
7#495×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9C4×Dic146—21no—
10#14556537—22no—
11#14556535—22no—
12C2×#11924003C2211yescharacteristic
13C2×#11924003C2211yescharacteristic
14#14556525C2211yescharacteristic
15#14556516—21no—
16C2×Q16×C73C2211yescharacteristic
17C2×SD16×C73—21no—
18C2×D8×C73C2211yescharacteristic
19#124×C73—21no—
20C4×C8×C73C2211yescharacteristic
21C2×Dic146—21no—
22Dic292—21no—
23Dic292D412yes—
24C4⋊Dic73—21no—
25#11924007—41no—
26C4×Dic73—41no—
27#11924003—21no—
28#11924003—21no—
29C2×Q8×C73—21no—
30C2×D4×C73—21no—
31Q16×C73—21no—
32Q16×C73—21no—
33SD16×C73—42no—
34D8×C73—21no—
35D8×C73—21no—
36C2×C8×C73D411yescharacteristic
37C2×C8×C73C2311yescharacteristic
38C22⋊C4×C73—41no—
39C22⋊C4×C73—41no—
40C42×C73D411yescharacteristic
41C23×C73—41no—
42Q8×C73—41no—
43Q8×C73—41no—
44D4×C73—41no—
45D4×C73—41no—
46C2×C4×C73—41no—
47C2×C4×C73D811yescharacteristic
48C2×C4×C73D811yescharacteristic
49C2×C4×C73C2×D411yescharacteristic
50C2×Dic73—41no—
51C2×Dic73—41no—
52Dic146—22no—
53Dic146—41no—
54C8×C73—21no—
55C8×C73C2×D411yescharacteristic
56C8×C73#4111yescharacteristic
57C22×C73—81no—
58C22×C73—81no—
59C22×C73—81no—
60C22×C73C2×D811yescharacteristic
61C4×C73—21no—
62C4×C73—21no—
63C4×C73—81no—
64C4×C73#12111yescharacteristic
65C4×C73AGL(1,ℤ/8)11yescharacteristic
66Dic73—42no—
67Dic73—81no—
68C2×C73—161no—
69C2×C73#45911yescharacteristic
70C2×C73#50811yescharacteristic
71C2×C73#51011yescharacteristic
72#2211—731nomaximal, Sylow
73C73#221111yescharacteristic, complemented, Sylow
74C2×Q32—731no—
75C2×SD32—731no—
76#495D7311yescharacteristic
77C4×Q16—731no—
78C4⋊C16—731no—
79#358—731no—
80#357—731no—
81C2×Q16—731no—
82C2×Q16C2×D7311yescharacteristic
83C2×SD16—21no—
84C2×D8C2×D7311yescharacteristic
85#124—21no—
86C4×Q8—1461no—
87Q32—1462no—
88SD32—1462no—
89C2×C16—731no—
90C2×C16—731no—
91#107—731no—
92#103—1461no—
93C4×C8C2×D7311yescharacteristic
94C2×Q8—21no—
95C2×Q8—1461no—
96C2×D4—21no—
97Q16—21no—
98Q16—21no—
99Q16—732no—
100Q16—1461no—
101SD16—42no—
102D8—21no—
103D8—21no—
104C2×C8C22⋊D7311yescharacteristic
105C2×C8C22×D7311yescharacteristic
106C4⋊C4—2921no—
107C4⋊C4—1461no—
108C22⋊C4—41no—
109C22⋊C4—41no—
110C42—2921no—
111C42C22⋊D7311yescharacteristic
112C16—1461no—
113C16—1461no—
114C23—41no—
115Q8—41no—
116Q8—41no—
117Q8—2921no—
118Q8—1462no—
119D4—41no—
120D4—41no—
121C2×C4—41no—
122C2×C4—2921no—
123C2×C4—2921no—
124C2×C4#1192401311yescharacteristic
125C2×C4#1192401311yescharacteristic
126C2×C4C2×C22⋊D7311yescharacteristic
127C8—21no—
128C8D4×D7311yescharacteristic
129C8#1192402711yescharacteristic
130C22—81no—
131C22—81no—
132C22—81no—
133C22C2×#1192401311yescharacteristic
134C4—21no—
135C4—21no—
136C4—81no—
137C4—2922no—
138C4—5841no—
139C4#1455656211yescharacteristic
140C4#1455661711yescharacteristic
141C2—161no—
142C2#1798877911yescharacteristic
143C2#1798901711yescharacteristic
144C2#1798902711yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#495×C73C2
socleC22×C73C2×D8
hypercenter#495D73
hypocenterC73#2211
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#14556537C2semidirect
3. C4×Dic292C2semidirect
4. C4⋊#11924003C2semidirect
5. #17988391C2semidirect
73. C73#2211semidirect