Finite Group Databasebeta

← #22625030

Subgroups — #22625030

Order 9344.

162 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 38 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#17989574C211yesmaximal, characteristic
2#17989561C211yesmaximal, characteristic
3#17988559C211yesmaximal, characteristic
4C2×#11924038C411yescharacteristic, complemented
5C2×#11924037—21no—
6C2×#11924036C411yescharacteristic, complemented
7#14556652C412yescomplemented
8#14556651—21no—
9C22⋊#10596833—21no—
10C22⋊#10596833—21no—
11C2×#11924027C2211yescharacteristic
12#14556547—21no—
13#14556506C411yescharacteristic
14#14556505—21no—
15#99×C73C411yescharacteristic
16#11924038—41no—
17#11924037—22no—
18#11924037—41no—
19#11924036—41no—
20C2×#10596833—21no—
21C2×#10596833—21no—
22C2×#10596833—41no—
23#11924027—41no—
24#11924027—41no—
25C2×Dic146C2×C411yescharacteristic
26C2×C22⋊D73D411yescharacteristic
27C2×C22⋊D73Q811yescharacteristic
28C22×Dic73D411yescharacteristic
29C22×Dic73D411yescharacteristic
30C2×C4×D73C2×C411yescharacteristic
31#11924007—41no—
32C22⋊Dic73—21no—
33C4×Dic73—41no—
34C2×D4×C73C2×C411yescharacteristic
35C22⋊C4×C73—21no—
36C23×C73C22⋊C411yescharacteristic
37C23×C73C4⋊C411yescharacteristic
38C22×D73C4⋊C411yescharacteristic
39D4×C73—41no—
40C2×C4×C73—41no—
41C2×C4×C73C4211yescharacteristic
42C22⋊D73—41no—
43C22⋊D73—41no—
44C2×Dic73—21no—
45C2×Dic73—21no—
46C2×Dic73—21no—
47C2×Dic73—21no—
48C2×Dic73—41no—
49C2×Dic73C22⋊C411yescharacteristic
50C2×Dic73C22⋊C411yescharacteristic
51C2×Dic73C4⋊C411yescharacteristic
52C4×D73—21no—
53C4×D73—21no—
54Dic146—41no—
55#10596833—42no—
56#10596833—41no—
57#10596833—41no—
58C22×C73—21no—
59C22×C73—21no—
60C22×C73—41no—
61C22×C73—41no—
62C22×C73#9511yescharacteristic
63C2×D73—21no—
64C2×D73—41no—
65C4×C73—21no—
66C4×C73—81no—
67Dic73—21no—
68Dic73—21no—
69Dic73—81no—
70Dic73#9911yescharacteristic
71Dic73#9911yescharacteristic
72C2×C73—21no—
73C2×C73—41no—
74C2×C73—41no—
75C2×C73#34211yescharacteristic
76D73—41no—
77#1395—731nomaximal, Sylow
78C73#139511yescharacteristic, complemented, Sylow
79#413—731no—
80#410—731no—
81#408—731no—
82C2×#41—731no—
83C2×M16—731no—
84C2×M16—1461no—
85C22×C8—731no—
86#117—1461no—
87#101—732no—
88#100—1461no—
89#99—731no—
90#99—1461no—
91#99#6440811yescharacteristic
92C22⋊C8—1461no—
93C22⋊C8—1461no—
94#41—2921no—
95#41—2921no—
96C2×Q8—731no—
97C2×D4—731no—
98C2×D4—731no—
99C2×D4C2×#6440811yescharacteristic
100C22×C4—731no—
101C22×C4—731no—
102C22×C4—731no—
103M16—2921no—
104M16—2921no—
105M16—1462no—
106C2×C8—2921no—
107C2×C8—2921no—
108C2×C8—1461no—
109C2×C8—1461no—
110C4⋊C4—2921no—
111C22⋊C4—21no—
112C22⋊C4—1461no—
113C42—2921no—
114C23—731no—
115C23C22⋊#6440811yescharacteristic
116C23C4⋊#6440811yescharacteristic
117Q8—2921no—
118D4—41no—
119D4—2921no—
120D4—2921no—
121C2×C4—41no—
122C2×C4—2921no—
123C2×C4—731no—
124C2×C4—731no—
125C2×C4—731no—
126C2×C4—1461no—
127C2×C4—1461no—
128C2×C4—1461no—
129C2×C4—1461no—
130C2×C4—1461no—
131C2×C4—1461no—
132C2×C4C4×#6440811yescharacteristic
133C8—2921no—
134C8—2921no—
135C8—2922no—
136C22—21no—
137C22—21no—
138C22—41no—
139C22—41no—
140C22—2921no—
141C22—1461no—
142C22(C2×#64408)⋊C411yescharacteristic
143C4—21no—
144C4—81no—
145C4—5841no—
146C4—731no—
147C4—731no—
148C4—1461no—
149C4—1461no—
150C2—21no—
151C2—41no—
152C2—41no—
153C2—2921no—
154C2#1798946411yescharacteristic
subgroupG/H
centerC2#17989464
commutatorC2×C4×C73C42
FrattiniC2×D4C2×#64408
Fitting#99×C73C4
socleC2×C73#342
hypercenter#99#64408
hypocenterC73#1395
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×#11924038C4semidirect
6. C2×#11924036C4semidirect
7. #14556652C4semidirect
78. C73#1395semidirect