Finite Group Databasebeta

← #27186231

Subgroups — #27186231

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#20266164C211yesmaximal, characteristic
2#20266151C211yesmaximal, characteristic
3#20265149C211yesmaximal, characteristic
4C2×#13108084C411yescharacteristic, complemented
5C2×#13108083—21no—
6C2×D101⋊C8C411yescharacteristic, complemented
7#15692316C412yescomplemented
8#15692315—21no—
9C22⋊#11717581—21no—
10C22⋊#11717581—21no—
11C2×#13108073C2211yescharacteristic
12#15692211—21no—
13#15692170C411yescharacteristic
14#15692169—21no—
15#99×C101C411yescharacteristic
16#13108084—41no—
17#13108083—22no—
18#13108083—41no—
19D101⋊C8—41no—
20C2×#11717581—21no—
21C2×#11717581—21no—
22C2×#11717581—41no—
23#13108073—41no—
24#13108073—41no—
25C2×Dic202C2×C411yescharacteristic
26C2×C22⋊D101D411yescharacteristic
27C2×C22⋊D101Q811yescharacteristic
28C22×Dic101D411yescharacteristic
29C22×Dic101D411yescharacteristic
30C2×C4×D101C2×C411yescharacteristic
31#13108053—41no—
32C22⋊Dic101—21no—
33C4×Dic101—41no—
34C2×D4×C101C2×C411yescharacteristic
35C22⋊C4×C101—21no—
36C23×C101C22⋊C411yescharacteristic
37C23×C101C4⋊C411yescharacteristic
38C22×D101C4⋊C411yescharacteristic
39D4×C101—41no—
40C2×C4×C101—41no—
41C2×C4×C101C4211yescharacteristic
42C22⋊D101—41no—
43C22⋊D101—41no—
44C2×Dic101—21no—
45C2×Dic101—21no—
46C2×Dic101—21no—
47C2×Dic101—21no—
48C2×Dic101—41no—
49C2×Dic101C22⋊C411yescharacteristic
50C2×Dic101C22⋊C411yescharacteristic
51C2×Dic101C4⋊C411yescharacteristic
52C4×D101—21no—
53C4×D101—21no—
54Dic202—41no—
55#11717581—42no—
56#11717581—41no—
57#11717581—41no—
58C22×C101—21no—
59C22×C101—21no—
60C22×C101—41no—
61C22×C101—41no—
62C22×C101#9511yescharacteristic
63C2×D101—21no—
64C2×D101—41no—
65C4×C101—21no—
66C4×C101—81no—
67Dic101—21no—
68Dic101—21no—
69Dic101—81no—
70Dic101#9911yescharacteristic
71Dic101#9911yescharacteristic
72C2×C101—21no—
73C2×C101—41no—
74C2×C101—41no—
75C2×C101#34211yescharacteristic
76D101—41no—
77#1395—1011nomaximal, Sylow
78C101#139511yescharacteristic, complemented, Sylow
79#413—1011no—
80#410—1011no—
81#408—1011no—
82C2×#41—1011no—
83C2×M16—1011no—
84C2×M16—2021no—
85C22×C8—1011no—
86#117—2021no—
87#101—1012no—
88#100—2021no—
89#99—1011no—
90#99—2021no—
91#99#8793811yescharacteristic
92C22⋊C8—2021no—
93C22⋊C8—2021no—
94#41—4041no—
95#41—4041no—
96C2×Q8—1011no—
97C2×D4—1011no—
98C2×D4—1011no—
99C2×D4C2×#8793811yescharacteristic
100C22×C4—1011no—
101C22×C4—1011no—
102C22×C4—1011no—
103M16—4041no—
104M16—4041no—
105M16—2022no—
106C2×C8—4041no—
107C2×C8—4041no—
108C2×C8—2021no—
109C2×C8—2021no—
110C4⋊C4—4041no—
111C22⋊C4—21no—
112C22⋊C4—2021no—
113C42—4041no—
114C23—1011no—
115C23C22⋊#8793811yescharacteristic
116C23C4⋊#8793811yescharacteristic
117Q8—4041no—
118D4—41no—
119D4—4041no—
120D4—4041no—
121C2×C4—41no—
122C2×C4—1011no—
123C2×C4—1011no—
124C2×C4—1011no—
125C2×C4—4041no—
126C2×C4—2021no—
127C2×C4—2021no—
128C2×C4—2021no—
129C2×C4—2021no—
130C2×C4—2021no—
131C2×C4—2021no—
132C2×C4C4×#8793811yescharacteristic
133C8—4041no—
134C8—4041no—
135C8—4042no—
136C22—21no—
137C22—21no—
138C22—41no—
139C22—41no—
140C22—4041no—
141C22—2021no—
142C22(C2×#87938)⋊C411yescharacteristic
143C4—21no—
144C4—81no—
145C4—8081no—
146C4—1011no—
147C4—1011no—
148C4—2021no—
149C4—2021no—
150C2—21no—
151C2—41no—
152C2—41no—
153C2—4041no—
154C2#2026605411yescharacteristic
subgroupG/H
centerC2#20266054
commutatorC2×C4×C101C42
FrattiniC2×D4C2×#87938
Fitting#99×C101C4
socleC2×C101#342
prime radical, cosocleC2×#13108073C22
hypercenter#99#87938
hypocenterC101#1395
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C2×#13108084C4semidirect
6. C2×D101⋊C8C4semidirect
7. #15692316C4semidirect
78. C101#1395semidirect

Maximal subgroups

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

subgroupindex
#202661642
#202661512
#202651492
#1395101