Finite Group Databasebeta

← #22612037

Subgroups — #22612037

Order 9344.

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

normal subgroups only

This group has 150 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×#14556531C211yesmaximal, characteristic
3#17988828C211yesmaximal, characteristic
4#17988414C211yesmaximal, characteristic, complemented
5#17988391C211yesmaximal, characteristic, complemented
6#17988390C211yesmaximal, characteristic, complemented
7#467×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9#14556570—21no—
10#14556537—22no—
11#14556531—22no—
12C2×#11924003C2211yescharacteristic
13C2×#11924003C2211yescharacteristic
14#14556525C2211yescharacteristic
15#14556516—21no—
16C2×Q16×C73C2211yescharacteristic
17C22×C8×C73C2211yescharacteristic
18C22⋊Q8×C73—21no—
19#107×C73C2211yescharacteristic
20#103×C73—21no—
21C2×Dic146—21no—
22Dic292—21no—
23Dic292—21no—
24C4⋊Dic73—21no—
25#11924007—41no—
26C22⋊Dic73—41no—
27#11924003—21no—
28#11924003D412yes—
29C2×Q8×C73—21no—
30C22×C4×C73D411yescharacteristic
31Q16×C73—21no—
32Q16×C73—21no—
33C2×C8×C73—21no—
34C2×C8×C73—21no—
35C2×C8×C73D411yescharacteristic
36C2×C8×C73C2311yescharacteristic
37C4⋊C4×C73—21no—
38C4⋊C4×C73—41no—
39C22⋊C4×C73—41no—
40C23×C73D811yescharacteristic
41Q8×C73—41no—
42Q8×C73—41no—
43C2×C4×C73—21no—
44C2×C4×C73—21no—
45C2×C4×C73—41no—
46C2×C4×C73—41no—
47C2×C4×C73D811yescharacteristic
48C2×C4×C73C2×D411yescharacteristic
49C2×Dic73—41no—
50C2×Dic73—41no—
51Dic146—41no—
52Dic146—41no—
53C8×C73—21no—
54C8×C73C2×D411yescharacteristic
55C8×C73#4111yescharacteristic
56C22×C73—21no—
57C22×C73—21no—
58C22×C73—21no—
59C22×C73C2×D811yescharacteristic
60C4×C73—21no—
61C4×C73—81no—
62C4×C73—81no—
63C4×C73#12111yescharacteristic
64C4×C73#13511yescharacteristic
65Dic73—81no—
66Dic73—81no—
67C2×C73—41no—
68C2×C73#46611yescharacteristic
69C2×C73#51011yescharacteristic
70C2×C73#51011yescharacteristic
71#2219—731nomaximal, Sylow
72C73#221911yescharacteristic, complemented, Sylow
73C2×Q32—731no—
74C2×M32—731no—
75#467—731no—
76#467D7311yescharacteristic
77#367—731no—
78#358—731no—
79#358—731no—
80C2×Q16—731no—
81C2×Q16C2×D7311yescharacteristic
82C22×C8C2×D7311yescharacteristic
83C22⋊Q8—21no—
84C22⋊Q8—1461no—
85Q32—1462no—
86M32—1462no—
87C2×C16—731no—
88C2×C16—731no—
89#107—731no—
90#107C2×D7311yescharacteristic
91#103—21no—
92#103—1461no—
93C2×Q8—21no—
94C2×Q8—1461no—
95C22×C4C22⋊D7311yescharacteristic
96Q16—21no—
97Q16—21no—
98Q16—1461no—
99Q16—1461no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8C22⋊D7311yescharacteristic
103C2×C8C22×D7311yescharacteristic
104C4⋊C4—21no—
105C4⋊C4—41no—
106C4⋊C4—2921no—
107C4⋊C4—1461no—
108C22⋊C4—41no—
109C22⋊C4—2921no—
110C16—732no—
111C16—1461no—
112C23#1192401311yescharacteristic
113Q8—41no—
114Q8—41no—
115Q8—2921no—
116Q8—2921no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—2921no—
122C2×C4—2921no—
123C2×C4#1192401311yescharacteristic
124C2×C4C2×C22⋊D7311yescharacteristic
125C8—21no—
126C8D4×D7311yescharacteristic
127C8#1192402711yescharacteristic
128C22—21no—
129C22—21no—
130C22—21no—
131C22C2×#1192401311yescharacteristic
132C4—21no—
133C4—81no—
134C4—81no—
135C4—5841no—
136C4—5841no—
137C4#1455656311yescharacteristic
138C4#1455661111yescharacteristic
139C2—41no—
140C2#1798882111yescharacteristic
141C2#1798902711yescharacteristic
142C2#1798902811yescharacteristic
subgroupG/H
centerC22C2×#11924013
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#467×C73C2
socleC22×C73C2×D8
hypercenter#467D73
hypocenterC73#2219
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#14556537C2semidirect
4. #17988414C2semidirect
5. #17988391C2semidirect
6. #17988390C2semidirect
72. C73#2219semidirect