Finite Group Databasebeta

← #22586466

Subgroups — #22586466

Order 9088.

172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14556047C211yesmaximal, characteristic
2#17985906C211yesmaximal, characteristic
3C2×#101×C71C211yesmaximal, characteristic
4C2×#11765849—21no—
5C2×C4⋊Dic71C411yescharacteristic
6C2×C4×Dic71C411yescharacteristic
7#14556047—21no—
8#14556047C412yescomplemented
9C71⋊#95—21no—
10C71⋊#95—21no—
11C22×Q8×C71C2211yescharacteristic
12C2×M16×C71—21no—
13#101×C71—21no—
14#101×C71C412yescomplemented
15C22×Dic71—21no—
16C22×Dic71—21no—
17#11765849—22no—
18#11765849—41no—
19C2×C71⋊C8—41no—
20C4⋊Dic71—41no—
21C4×Dic71—41no—
22C2×Q8×C71—41no—
23C2×Q8×C71—41no—
24C2×Q8×C71C2×C411yescharacteristic
25C2×Q8×C71C2×C411yescharacteristic
26C2×Q8×C71D411yescharacteristic
27C2×Q8×C71Q811yescharacteristic
28C22×C4×C71C2×C411yescharacteristic
29C22×C4×C71D411yescharacteristic
30C22×C4×C71D411yescharacteristic
31M16×C71—22no—
32M16×C71—41no—
33C2×C8×C71—41no—
34C23×C71C22⋊C411yescharacteristic
35Q8×C71—41no—
36Q8×C71—41no—
37Q8×C71—41no—
38Q8×C71—41no—
39C2×C4×C71—21no—
40C2×C4×C71—21no—
41C2×C4×C71—21no—
42C2×C4×C71—21no—
43C2×C4×C71—21no—
44C2×C4×C71—21no—
45C2×C4×C71C4211yescharacteristic
46C2×C4×C71C22⋊C411yescharacteristic
47C2×C4×C71C22⋊C411yescharacteristic
48C2×C4×C71C4⋊C411yescharacteristic
49C2×C4×C71C4⋊C411yescharacteristic
50C2×C4×C71C4⋊C411yescharacteristic
51C2×Dic71—22no—
52C2×Dic71—41no—
53C2×Dic71—41no—
54C2×Dic71—42no—
55C2×Dic71—41no—
56C8×C71—42no—
57C71⋊C8—42no—
58C22×C71—21no—
59C22×C71—21no—
60C22×C71#9511yescharacteristic
61C22×C71#9911yescharacteristic
62C22×C71#9911yescharacteristic
63C4×C71—21no—
64C4×C71—21no—
65C4×C71—21no—
66C4×C71—21no—
67C4×C71—21no—
68C4×C71—21no—
69Dic71—42no—
70Dic71—81no—
71C2×C71—21no—
72C2×C71—21no—
73C2×C71#34211yescharacteristic
74C2×C71#35511yescharacteristic
75C2×C71#35611yescharacteristic
76#1394—711nomaximal, Sylow
77C71#139411yescharacteristic, complemented, Sylow
78C2×#101—711no—
79C2×#101D7111yescharacteristic
80#391—711no—
81C22×Q8C2×D7111yescharacteristic
82C2×M16—21no—
83C2×M16—1421no—
84C2×C4⋊C4—711no—
85C2×C42—711no—
86#101—21no—
87#101—712no—
88#101—1421no—
89#101Dic7112yescomplemented
90#95—1421no—
91#95—1421no—
92C2×Q8—41no—
93C2×Q8—41no—
94C2×Q8Dic14211yescharacteristic
95C2×Q8C4×D7111yescharacteristic
96C2×Q8C2×Dic7111yescharacteristic
97C2×Q8C22⋊D7111yescharacteristic
98C22×C4—1421no—
99C22×C4—1421no—
100C22×C4C4×D7111yescharacteristic
101C22×C4D28411yescharacteristic
102C22×C4C22⋊D7111yescharacteristic
103M16—22no—
104M16—41no—
105M16—2841no—
106M16—1422no—
107C2×C8—41no—
108C2×C8—2841no—
109C4⋊C4—2841no—
110C42—2841no—
111C23(C2×D71)⋊C411yescharacteristic
112Q8—41no—
113Q8—41no—
114Q8—41no—
115Q8—41no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—2841no—
123C2×C4—2841no—
124C2×C4—2842no—
125C2×C4—2841no—
126C2×C4—1422no—
127C2×C4C4×Dic7111yescharacteristic
128C2×C4(C2×D71)⋊C411yescharacteristic
129C2×C4C22⋊Dic7111yescharacteristic
130C2×C4Dic71⋊C411yescharacteristic
131C2×C4Dic71⋊C411yescharacteristic
132C2×C4C4⋊Dic7111yescharacteristic
133C8—42no—
134C8—2842no—
135C22—21no—
136C22—21no—
137C22C71⋊#9511yescharacteristic
138C22#1455604211yescharacteristic
139C22#1455604211yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—2842no—
147C4—5681no—
148C2—21no—
149C2—21no—
150C2#1798576511yescharacteristic
151C2#1798579511yescharacteristic
152C2#1798579711yescharacteristic
subgroupG/H
centerC22#14556042
commutatorC2×C4×C71C42
FrattiniC22×Q8C2×D71
FittingC2×#101×C71C2
socleC22×C71#99
hypercenterC2×#101D71
hypocenterC71#1394
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
8. #14556047C4semidirect
14. #101×C71C4semidirect
77. C71#1394semidirect
89. #101Dic71semidirect