Finite Group Databasebeta

← #27186233

Subgroups — #27186233

Order 12928.

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

normal subgroups only

This group has 162 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
1#20266163C211yesmaximal, characteristic
2#20266156C211yesmaximal, characteristic
3#20265145C211yesmaximal, characteristic
4D101⋊M16—21no—
5#15692334—21no—
6#15692316C412yescomplemented
7#15692315—21no—
8#15692314C412yes—
9#15692313—21no—
10C2×#13108074C2211yescharacteristic
11C22×#11717579C411yescharacteristic, complemented
12#15692167—21no—
13#15692167—21no—
14C2×M16×C101C411yescharacteristic, complemented
15#13108084—41no—
16#13108083—22no—
17D101⋊C8—41no—
18C4⋊#87938—41no—
19C22⋊#87938—22no—
20C4×#87938—41no—
21#13108074—41no—
22#13108074—41no—
23C2×Dic202C2×C411yescharacteristic
24C2×D404C2×C411yescharacteristic
25C2×C22⋊D101D411yescharacteristic
26C2×C22⋊D101Q811yescharacteristic
27C2×C4×D101D411yescharacteristic
28C2×C4×D101D411yescharacteristic
29C2×#11717579—21no—
30C2×#11717579—41no—
31C22×C4×C101C2×C411yescharacteristic
32M16×C101—41no—
33C2×C8×C101—21no—
34C23×C101C4⋊C411yescharacteristic
35C22×D101C22⋊C411yescharacteristic
36C22×D101C4⋊C411yescharacteristic
37C2×#87938—42no—
38C2×C4×C101—21no—
39C2×C4×C101—21no—
40C2×C4×C101C4211yescharacteristic
41C2×C4×C101C22⋊C411yescharacteristic
42C22⋊D101—41no—
43C22⋊D101—41no—
44C2×Dic101C22⋊C411yescharacteristic
45C2×Dic101C4⋊C411yescharacteristic
46D404—41no—
47C4×D101—21no—
48C4×D101—21no—
49C4×D101—21no—
50C4×D101—21no—
51Dic202—41no—
52#11717581—42no—
53C8×C101—41no—
54#11717579—41no—
55C22×C101—21no—
56C22×C101—41no—
57C22×C101#9511yescharacteristic
58C2×D101—21no—
59C2×D101—21no—
60C2×D101—41no—
61C2×D101—41no—
62#87938—82no—
63C4×C101—21no—
64C4×C101#9911yescharacteristic
65C4×C101#9911yescharacteristic
66Dic101—21no—
67Dic101—21no—
68C2×C101—21no—
69C2×C101—41no—
70C2×C101#34211yescharacteristic
71D101—41no—
72D101—41no—
73#1395—1011nomaximal, Sylow
74C101#139511yescharacteristic, complemented, Sylow
75#413—1011no—
76#410—1011no—
77#408—1011no—
78C2×#41—1011no—
79C2×M16—2021no—
80C2×M16#8793811yescharacteristic, complemented
81C22×C8—1011no—
82#117—2021no—
83#101—1012no—
84#100—2021no—
85#99—1012no—
86#99—2021no—
87C22⋊C8—2021no—
88C22⋊C8—2021no—
89#41—4041no—
90#41—4041no—
91C2×Q8—1011no—
92C2×D4—1011no—
93C2×D4—1011no—
94C2×D4—1011no—
95C22×C4—1011no—
96C22×C4—1011no—
97C22×C4C2×#8793811yescharacteristic
98M16—41no—
99M16—4041no—
100M16—2022no—
101C2×C8—21no—
102C2×C8—4041no—
103C2×C8—4041no—
104C2×C8—2021no—
105C4⋊C4—4041no—
106C22⋊C4—2022no—
107C42—4041no—
108C23—1011no—
109C23—1011no—
110C23C4⋊#8793811yescharacteristic
111Q8—4041no—
112D4—4041no—
113D4—4041no—
114D4—4041no—
115C2×C4—21no—
116C2×C4—21no—
117C2×C4—1011no—
118C2×C4—1011no—
119C2×C4—4042no—
120C2×C4—2021no—
121C2×C4—2021no—
122C2×C4—2021no—
123C2×C4—2021no—
124C2×C4C4×#8793811yescharacteristic
125C2×C4C22⋊#8793811yescharacteristic
126C8—41no—
127C8—4042no—
128C8—4041no—
129C22—21no—
130C22—41no—
131C22—4041no—
132C22—4041no—
133C22—2021no—
134C22—2021no—
135C22(C2×#87938)⋊C411yescharacteristic
136C4—21no—
137C4—8082no—
138C4—2021no—
139C4—2021no—
140C4#1569231311yescharacteristic
141C4#1569231411yescharacteristic
142C2—21no—
143C2—41no—
144C2—4041no—
145C2—4041no—
146C2#2026605511yescharacteristic
subgroupG/H
centerC4#15692313
commutatorC2×C4×C101C42
FrattiniC22×C4C2×#87938
FittingC2×M16×C101C4
socleC2×C101#342
prime radical, cosocleC2×#13108074C22
hypercenterC2×M16#87938
hypocenterC101#1395
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
6. #15692316C4semidirect
11. C22×#11717579C4semidirect
14. C2×M16×C101C4semidirect
74. C101#1395semidirect
80. C2×M16#87938semidirect

Maximal subgroups

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

subgroupindex
#202661632
#202661562
#202651452
#1395101