Finite Group Databasebeta

← #22625027

Subgroups — #22625027

Order 9344.

172 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D73⋊#101C211yesmaximal, characteristic
2(C2×#64408)⋊Q8C211yesmaximal, characteristic
3#101×D73C211yesmaximal, characteristic
4D73⋊M16—21no—
5C2×C4⋊#64408C411yescharacteristic
6C2×C4×#64408C411yescharacteristic
7#14556652—21no—
8#14556652C412yescomplemented
9(C2×#64408)⋊C4—21no—
10(C2×#64408)⋊C4—21no—
11C2×Q8×D73C2211yescharacteristic
12M16×D73—21no—
13#14556510C411yescharacteristic, complemented
14#14556509—21no—
15#101×C73C411yescharacteristic, complemented
16C22×#64408—21no—
17C22×#64408—21no—
18#11924038—41no—
19#11924037—22no—
20#11924036—41no—
21C4⋊#64408—41no—
22C4×#64408—41no—
23C2×Dic146C2×C411yescharacteristic
24C2×Dic146D411yescharacteristic
25C2×Dic146Q811yescharacteristic
26Q8×D73—41no—
27Q8×D73—41no—
28C2×C4×D73C2×C411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C2×C4×D73D411yescharacteristic
31#11924012—21no—
32#11924011—41no—
33C8×D73—41no—
34C2×Q8×C73C2×C411yescharacteristic
35M16×C73—21no—
36C22×D73C22⋊C411yescharacteristic
37C2×#64408—22no—
38C2×#64408—41no—
39C2×#64408—41no—
40C2×#64408—42no—
41C2×#64408—41no—
42Q8×C73—41no—
43C2×C4×C73C4211yescharacteristic
44C2×C4×C73C22⋊C411yescharacteristic
45C2×C4×C73C4⋊C411yescharacteristic
46C2×Dic73C22⋊C411yescharacteristic
47C2×Dic73C4⋊C411yescharacteristic
48C2×Dic73C4⋊C411yescharacteristic
49C4×D73—21no—
50C4×D73—21no—
51C4×D73—21no—
52C4×D73—21no—
53C4×D73—21no—
54C4×D73—21no—
55Dic146—41no—
56Dic146—41no—
57Dic146—41no—
58#10596833—42no—
59C8×C73—41no—
60#10596831—41no—
61C22×C73#9511yescharacteristic
62C2×D73—21no—
63C2×D73—21no—
64C2×D73#9911yescharacteristic
65C2×D73#9911yescharacteristic
66#64408—42no—
67#64408—81no—
68C4×C73—21no—
69C4×C73—21no—
70C4×C73—21no—
71Dic73—21no—
72Dic73—21no—
73Dic73—21no—
74C2×C73—21no—
75C2×C73#34211yescharacteristic
76D73—21no—
77D73#35511yescharacteristic
78D73#35611yescharacteristic
79#1394—731nomaximal, Sylow
80C73#139411yescharacteristic, complemented, Sylow
81C2×#101—731no—
82C2×#101—731no—
83#391—731no—
84C22×Q8—731no—
85C2×M16—1461no—
86C2×M16—1461no—
87C2×C4⋊C4—731no—
88C2×C42—731no—
89#101—732no—
90#101—731no—
91#101—1461no—
92#101—1461no—
93#101#6440811yescharacteristic, complemented
94#95—1461no—
95#95—1461no—
96C2×Q8—2921no—
97C2×Q8—2921no—
98C2×Q8—731no—
99C2×Q8—731no—
100C2×Q8—731no—
101C2×Q8C2×#6440811yescharacteristic
102C22×C4—731no—
103C22×C4—731no—
104C22×C4—731no—
105C22×C4—1461no—
106C22×C4—1461no—
107M16—21no—
108M16—2921no—
109M16—2921no—
110M16—1462no—
111M16—1461no—
112C2×C8—2921no—
113C2×C8—2921no—
114C4⋊C4—2921no—
115C42—2921no—
116C23—731no—
117Q8—41no—
118Q8—2921no—
119Q8—2921no—
120Q8—2921no—
121C2×C4—2921no—
122C2×C4—2921no—
123C2×C4—2921no—
124C2×C4—2922no—
125C2×C4—731no—
126C2×C4—731no—
127C2×C4—731no—
128C2×C4—1461no—
129C2×C4—1461no—
130C2×C4—1461no—
131C2×C4—1461no—
132C2×C4—1461no—
133C2×C4—1461no—
134C2×C4—1462no—
135C2×C4C4×#6440811yescharacteristic
136C2×C4C22⋊#6440811yescharacteristic
137C2×C4C4⋊#6440811yescharacteristic
138C8—41no—
139C8—2921no—
140C8—2922no—
141C22—731no—
142C22—731no—
143C22—1461no—
144C22—1461no—
145C22(C2×#64408)⋊C411yescharacteristic
146C4—21no—
147C4—21no—
148C4—21no—
149C4—2922no—
150C4—5841no—
151C4—1461no—
152C4—1461no—
153C4—1461no—
154C2—21no—
155C2—731no—
156C2—731no—
157C2—1461no—
158C2#1798946411yescharacteristic
subgroupG/H
centerC2#17989464
commutatorC2×C4×C73C42
FrattiniC2×Q8C2×#64408
Fitting#101×C73C4
socleC2×C73#342
hypercenter#101#64408
hypocenterC73#1394
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
8. #14556652C4semidirect
13. #14556510C4semidirect
15. #101×C73C4semidirect
80. C73#1394semidirect
93. #101#64408semidirect