Finite Group Databasebeta

← #27186234

Subgroups — #27186234

Order 12928.

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#20266158C211yesmaximal, characteristic
2#20266152C211yesmaximal, characteristic
3#20265160C211yesmaximal, characteristic
4C2×#13108084C411yescharacteristic, complemented
5C2×D101⋊C8C411yescharacteristic, complemented
6#15692334—21no—
7#15692314—21no—
8#15692314C412yes—
9#15692312—21no—
10#15692312—21no—
11C2×#13108075C2211yescharacteristic
12M16×D101—21no—
13#15692174C411yescharacteristic, complemented
14#15692171—21no—
15#101×C101C411yescharacteristic, complemented
16#13108084—41no—
17D101⋊C8—41no—
18C2×#11717581—21no—
19C2×#11717581—21no—
20C4⋊#87938—41no—
21C22⋊#87938—22no—
22C4×#87938—41no—
23#13108075—41no—
24#13108075—41no—
25C2×D404C2×C411yescharacteristic
26C2×D404D411yescharacteristic
27C2×D404Q811yescharacteristic
28C2×C4×D101C2×C411yescharacteristic
29C2×C4×D101D411yescharacteristic
30C2×C4×D101D411yescharacteristic
31#13108058—21no—
32#13108057—41no—
33C8×D101—41no—
34C2×Q8×C101C2×C411yescharacteristic
35M16×C101—21no—
36C22×D101C22⋊C411yescharacteristic
37C22×D101C4⋊C411yescharacteristic
38C22×D101C4⋊C411yescharacteristic
39C2×#87938—42no—
40Q8×C101—41no—
41C2×C4×C101C4211yescharacteristic
42C2×C4×C101C22⋊C411yescharacteristic
43C2×C4×C101C4⋊C411yescharacteristic
44C2×Dic101C22⋊C411yescharacteristic
45D404—41no—
46D404—41no—
47D404—41no—
48C4×D101—21no—
49C4×D101—21no—
50C4×D101—21no—
51C4×D101—21no—
52C4×D101—21no—
53C4×D101—21no—
54#11717581—41no—
55#11717581—41no—
56C8×C101—41no—
57#11717579—41no—
58C22×C101#9511yescharacteristic
59C2×D101—21no—
60C2×D101—21no—
61C2×D101—21no—
62C2×D101—41no—
63C2×D101—41no—
64C2×D101—41no—
65#87938—82no—
66C4×C101—21no—
67C4×C101—21no—
68C4×C101—21no—
69Dic101#9911yescharacteristic
70Dic101#9911yescharacteristic
71C2×C101—21no—
72C2×C101#34211yescharacteristic
73D101—41no—
74D101—41no—
75D101—41no—
76#1395—1011nomaximal, Sylow
77C101#139511yescharacteristic, complemented, Sylow
78#413—1011no—
79#410—1011no—
80#408—1011no—
81C2×#41—1011no—
82C2×M16—1011no—
83C2×M16—2021no—
84C22×C8—1011no—
85#117—2021no—
86#101—1011no—
87#101#8793811yescharacteristic, complemented
88#100—2021no—
89#99—1012no—
90#99—2021no—
91C22⋊C8—2021no—
92C22⋊C8—2021no—
93#41—4041no—
94#41—4041no—
95C2×Q8C2×#8793811yescharacteristic
96C2×D4—1011no—
97C2×D4—1011no—
98C2×D4—1011no—
99C22×C4—1011no—
100C22×C4—1011no—
101C22×C4—1011no—
102M16—21no—
103M16—4041no—
104M16—4041no—
105M16—2021no—
106C2×C8—4041no—
107C2×C8—4041no—
108C2×C8—2021no—
109C2×C8—2021no—
110C4⋊C4—4041no—
111C22⋊C4—2022no—
112C42—4041no—
113C23—1011no—
114C23—1011no—
115C23—1011no—
116Q8—41no—
117D4—4041no—
118D4—4041no—
119D4—4041no—
120C2×C4—1011no—
121C2×C4—4042no—
122C2×C4—2021no—
123C2×C4—2021no—
124C2×C4—2021no—
125C2×C4—2021no—
126C2×C4—2021no—
127C2×C4—2021no—
128C2×C4C4×#8793811yescharacteristic
129C2×C4C22⋊#8793811yescharacteristic
130C2×C4C4⋊#8793811yescharacteristic
131C8—41no—
132C8—4041no—
133C8—4041no—
134C8—4041no—
135C22—4041no—
136C22—4041no—
137C22—4041no—
138C22—2021no—
139C22—2021no—
140C22—2021no—
141C22(C2×#87938)⋊C411yescharacteristic
142C4—21no—
143C4—21no—
144C4—21no—
145C4—8082no—
146C4—1011no—
147C4—1011no—
148C2—21no—
149C2—4041no—
150C2—4041no—
151C2—4041no—
152C2#2026605411yescharacteristic
subgroupG/H
centerC2#20266054
commutatorC2×C4×C101C42
FrattiniC2×Q8C2×#87938
Fitting#101×C101C4
socleC2×C101#342
prime radical, cosocleC2×#13108075C22
hypercenter#101#87938
hypocenterC101#1395
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #101

Complements

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

NH ≅ G/Ntype
4. C2×#13108084C4semidirect
5. C2×D101⋊C8C4semidirect
13. #15692174C4semidirect
15. #101×C101C4semidirect
77. C101#1395semidirect
87. #101#87938semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202661582
#202661522
#202651602
#1395101