Finite Group Databasebeta

← #22612140

Subgroups — #22612140

Order 9344.

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

normal subgroups only

This group has 132 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
1#17988828C211yesmaximal, characteristic
2#17988625C211yesmaximal, characteristic
3#17988415C211yesmaximal, characteristic, complemented
4#17988413C211yesmaximal, characteristic, complemented
5#17988392C211yesmaximal, characteristic, complemented
6#17988392C211yesmaximal, characteristic, complemented
7C22⋊C16×C73C211yesmaximal, characteristic
8C2×Dic292C2211yescharacteristic
9#14556570—21no—
10#14556550—21no—
11#14556525C2211yescharacteristic
12#14556525C2211yescharacteristic
13#14556525C2211yescharacteristic
14#14556523—21no—
15#14556516—21no—
16C22×C8×C73C2211yescharacteristic
17C2×C16×C73C2211yescharacteristic
18C2×C16×C73C2211yescharacteristic
19C2×Dic146—21no—
20Dic292—21no—
21Dic292—21no—
22C4⋊Dic73—21no—
23C4⋊Dic73—21no—
24C4⋊Dic73—21no—
25#11924007—41no—
26C22⋊Dic73—41no—
27C22⋊Dic73—41no—
28C4×Dic73—41no—
29C22×C4×C73D411yescharacteristic
30C2×C8×C73—21no—
31C2×C8×C73—21no—
32C2×C8×C73D411yescharacteristic
33C2×C8×C73C2311yescharacteristic
34C16×C73—21no—
35C16×C73—21no—
36C23×C73D811yescharacteristic
37C2×C4×C73—21no—
38C2×C4×C73—21no—
39C2×C4×C73D811yescharacteristic
40C2×C4×C73C2×D411yescharacteristic
41C2×Dic73—41no—
42C2×Dic73—41no—
43C2×Dic73—41no—
44C2×Dic73—41no—
45Dic146—41no—
46Dic146—41no—
47C8×C73—21no—
48C8×C73#4111yescharacteristic
49C8×C73#4111yescharacteristic
50C22×C73—21no—
51C22×C73—21no—
52C22×C73—21no—
53C22×C73C2×D811yescharacteristic
54C4×C73—21no—
55C4×C73#12311yescharacteristic
56C4×C73#13711yescharacteristic
57Dic73—81no—
58Dic73—81no—
59Dic73—81no—
60Dic73—81no—
61C2×C73—41no—
62C2×C73#48011yescharacteristic
63C2×C73#50811yescharacteristic
64C2×C73#51011yescharacteristic
65#2237—731nomaximal, Sylow
66C73#223711yescharacteristic, complemented, Sylow
67#467—731no—
68#427—731no—
69#367—731no—
70#366—731no—
71#358—731no—
72#358—731no—
73C22⋊C16D7311yescharacteristic
74C2×Q16—731no—
75C22×C8C2×D7311yescharacteristic
76C22⋊Q8—1461no—
77#117—1461no—
78C2×C16C2×D7311yescharacteristic
79C2×C16C2×D7311yescharacteristic
80#107—731no—
81#107—731no—
82#107—731no—
83#106—1461no—
84#103—1461no—
85C2×Q8—1461no—
86C22×C4D29211yescharacteristic
87Q16—1461no—
88Q16—1461no—
89C2×C8—21no—
90C2×C8—21no—
91C2×C8D29211yescharacteristic
92C2×C8C22×D7311yescharacteristic
93C4⋊C4—2921no—
94C4⋊C4—1461no—
95C4⋊C4—1461no—
96C4⋊C4—1461no—
97C22⋊C4—2921no—
98C22⋊C4—2921no—
99C42—2921no—
100C16—21no—
101C16—21no—
102C23D58411yescharacteristic
103Q8—2921no—
104Q8—2921no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—2921no—
108C2×C4—2921no—
109C2×C4—2921no—
110C2×C4—2921no—
111C2×C4D58411yescharacteristic
112C2×C4C2×D29211yescharacteristic
113C8—21no—
114C8#1192402711yescharacteristic
115C8#1192402711yescharacteristic
116C22—21no—
117C22—21no—
118C22—21no—
119C22C2×D58411yescharacteristic
120C4—21no—
121C4—5841no—
122C4—5841no—
123C4—5841no—
124C4—5841no—
125C4#1455657511yescharacteristic
126C4#1455662411yescharacteristic
127C2—41no—
128C2#1798890111yescharacteristic
129C2#1798901911yescharacteristic
130C2#1798903011yescharacteristic
subgroupG/H
centerC22C2×D584
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
FittingC22⋊C16×C73C2
socleC22×C73C2×D8
hypercenterC22⋊C16D73
hypocenterC73#2237
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
3. #17988415C2semidirect
4. #17988413C2semidirect
5. #17988392C2semidirect
6. #17988392C2semidirect
66. C73#2237semidirect