Finite Group Databasebeta

← #22626931

Subgroups — #22626931

Order 9344.

158 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 41 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(C2×#10596842)⋊C4C211yesmaximal, characteristic
2(C2×#10596842)⋊C4C211yesmaximal, characteristic
3#17989538C211yesmaximal, characteristic
4C22×#10596842—21no—
5C22×#10596842—21no—
6C2×C4⋊#64408—21no—
7C2×C4⋊#64408C411yescharacteristic
8C2×C4×#64408C2211yescharacteristic
9(C2×#64408)⋊C4—21no—
10C4⋊C4×D73C411yescharacteristic
11C2×#10596842—22no—
12C2×#10596842—22no—
13C2×#10596842—41no—
14C2×#10596842—41no—
15C2×#10596842—41no—
16C2×#10596842—41no—
17C22×#64408—21no—
18C22×#64408D411yescharacteristic
19C22×#64408D411yescharacteristic
20C4⋊#64408—41no—
21C4⋊#64408—41no—
22C4⋊#64408—41no—
23C4×#64408—41no—
24C2×C4×D73—21no—
25C2×C4×D73C2×C411yescharacteristic
26C4⋊Dic73C811yescharacteristic, complemented
27#11924007—21no—
28C4⋊C4×C73C811yescharacteristic, complemented
29C22×D73C22⋊C411yescharacteristic
30C2×#64408—21no—
31C2×#64408—21no—
32C2×#64408—21no—
33C2×#64408—21no—
34C2×#64408—41no—
35C2×#64408—41no—
36C2×#64408—41no—
37C2×#64408D811yescharacteristic
38C2×#64408SD1611yescharacteristic
39C2×#64408SD1611yescharacteristic
40C2×#64408Q1611yescharacteristic
41#10596842—42no—
42#10596842—42no—
43C2×C4×C73—21no—
44C2×C4×C73C2×C811yescharacteristic
45C2×Dic73—21no—
46C2×Dic73M1611yescharacteristic
47C4×D73—21no—
48C4×D73—21no—
49C4×D73—41no—
50C4×D73—41no—
51C22×C73C22⋊C811yescharacteristic
52C2×D73#9911yescharacteristic
53C2×D73#10111yescharacteristic
54C2×D73#10211yescharacteristic
55C2×D73#10311yescharacteristic
56C2×D73#10411yescharacteristic
57C2×D73#10411yescharacteristic
58#64408—21no—
59#64408—21no—
60#64408—21no—
61#64408—21no—
62#64408—81no—
63C4×C73—21no—
64C4×C73—41no—
65Dic73—21no—
66Dic73—41no—
67C2×C73#32411yescharacteristic
68C2×C73D4⋊C811yescharacteristic
69C2×C73Q8⋊C811yescharacteristic
70D73#32711yescharacteristic
71D73#32811yescharacteristic
72D73#33011yescharacteristic
73D73#33211yescharacteristic
74#1271—731nomaximal, Sylow
75C73#127111yescharacteristic, complemented, Sylow
76#389—731no—
77#336—731no—
78#336—731no—
79C22×C8—1461no—
80C22×C8—1461no—
81C2×C4⋊C4—731no—
82C2×C4⋊C4—731no—
83C2×C4⋊C4—1461no—
84C2×C42—731no—
85#95—1461no—
86C22×C4—731no—
87C22×C4—731no—
88C22×C4—731no—
89C22×C4—1461no—
90C22×C4—1461no—
91C2×C8—2921no—
92C2×C8—2921no—
93C2×C8—2921no—
94C2×C8—2921no—
95C2×C8—1462no—
96C2×C8—1462no—
97C4⋊C4—2921no—
98C4⋊C4—2921no—
99C4⋊C4—2921no—
100C4⋊C4—731no—
101C4⋊C4—1461no—
102C4⋊C4#1059684211yescharacteristic, complemented
103C42—2921no—
104C23—731no—
105C2×C4—21no—
106C2×C4—2921no—
107C2×C4—2921no—
108C2×C4—2921no—
109C2×C4—2921no—
110C2×C4—2921no—
111C2×C4—731no—
112C2×C4—731no—
113C2×C4—731no—
114C2×C4—731no—
115C2×C4—731no—
116C2×C4—1461no—
117C2×C4—1461no—
118C2×C4—1461no—
119C2×C4—1461no—
120C2×C4—1461no—
121C2×C4—1461no—
122C2×C4—1461no—
123C2×C4C2×#1059684211yescharacteristic
124C8—2922no—
125C8—2922no—
126C22—731no—
127C22—731no—
128C22—731no—
129C22—731no—
130C22—731no—
131C22—731no—
132C22C22⋊#1059684211yescharacteristic
133C4—21no—
134C4—41no—
135C4—2921no—
136C4—5841no—
137C4—1461no—
138C4—1461no—
139C4—1461no—
140C4—1461no—
141C4—1461no—
142C2—731no—
143C2—731no—
144C2—731no—
145C2—731no—
146C2#1798967311yescharacteristic
147C2D4⋊#1059684211yescharacteristic
148C2Q8⋊#1059684211yescharacteristic
subgroupG/H
centerC22C22⋊#10596842
commutatorC2×C4×C73C2×C8
FrattiniC2×C4C2×#10596842
FittingC4⋊C4×C73C8
socleC22×C73C22⋊C8
hypercenterC4⋊C4#10596842
hypocenterC73#1271
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
26. C4⋊Dic73C8semidirect
28. C4⋊C4×C73C8semidirect
75. C73#1271semidirect
102. C4⋊C4#10596842semidirect