Finite Group Databasebeta

← #27186032

Subgroups — #27186032

Order 12928.

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 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#20266148C211yesmaximal, characteristic
2#20266119C211yesmaximal, characteristic
3#20265140C211yesmaximal, characteristic
4C2×#13108084—21no—
5C2×C4⋊#87938—21no—
6C2×C22⋊#87938C412yes—
7#15692312—21no—
8C22⋊#11717581C412yescomplemented
9(C2×#87938)⋊C4—21no—
10C22×C4×D101C2211yescharacteristic
11C2×#13108058C411yescharacteristic, complemented
12#15692167—21no—
13#15692167—21no—
14C2×M16×C101C411yescharacteristic, complemented
15C22×#87938—22no—
16#13108084—41no—
17#13108084—41no—
18C2×#11717581—22no—
19C4⋊#87938—41no—
20C4⋊#87938—41no—
21C22⋊#87938—42no—
22C23×D101C2×C411yescharacteristic
23C22×Dic101C2×C411yescharacteristic
24C2×C4×D101—41no—
25C2×C4×D101—41no—
26C2×C4×D101D411yescharacteristic
27C2×C4×D101D411yescharacteristic
28C2×C4×D101D411yescharacteristic
29C2×C4×D101Q811yescharacteristic
30#13108058—41no—
31C2×#11717579—21no—
32C22×C4×C101C2×C411yescharacteristic
33M16×C101—41no—
34C2×C8×C101—21no—
35C23×C101C4211yescharacteristic
36C22×D101—21no—
37C22×D101—21no—
38C22×D101—41no—
39C22×D101—41no—
40C22×D101C22⋊C411yescharacteristic
41C22×D101C4⋊C411yescharacteristic
42C2×#87938—42no—
43C2×#87938—42no—
44C2×#87938—42no—
45C2×C4×C101—21no—
46C2×C4×C101—21no—
47C2×C4×C101C22⋊C411yescharacteristic
48C2×C4×C101C4⋊C411yescharacteristic
49C2×Dic101—41no—
50C2×Dic101C22⋊C411yescharacteristic
51C2×Dic101C4⋊C411yescharacteristic
52C4×D101—21no—
53C4×D101—21no—
54C4×D101—21no—
55C4×D101—21no—
56C4×D101—41no—
57C4×D101—41no—
58#11717581—42no—
59C8×C101—41no—
60#11717579—41no—
61C22×C101—21no—
62C22×C101—21no—
63C22×C101—21no—
64C22×C101#9511yescharacteristic
65C2×D101—21no—
66C2×D101—21no—
67C2×D101—21no—
68C2×D101—21no—
69C2×D101—21no—
70C2×D101—42no—
71C2×D101—42no—
72C2×D101#10011yescharacteristic
73C2×D101#10111yescharacteristic
74#87938—82no—
75C4×C101—21no—
76C4×C101#9911yescharacteristic
77C4×C101#9911yescharacteristic
78Dic101—21no—
79Dic101—21no—
80C2×C101—41no—
81C2×C101#34211yescharacteristic
82C2×C101#34311yescharacteristic
83C2×C101#34411yescharacteristic
84D101—21no—
85D101—21no—
86D101—41no—
87#1305—1011nomaximal, Sylow
88C101#130511yescharacteristic, complemented, Sylow
89#407—1011no—
90#407—1011no—
91#380—1011no—
92C23×C4—1011no—
93C2×M16—1011no—
94C2×M16—2021no—
95C2×M16#8793811yescharacteristic, complemented
96C2×C4⋊C4—2021no—
97C2×C22⋊C4—1012no—
98C22⋊C8—1012no—
99C22⋊C8—2021no—
100C22⋊C8—2021no—
101C22⋊C8—2021no—
102#95—2021no—
103C24—1011no—
104C22×C4—1011no—
105C22×C4—1011no—
106C22×C4—1011no—
107C22×C4—1011no—
108C22×C4—1011no—
109C22×C4—4041no—
110C22×C4—4041no—
111C22×C4—2022no—
112C22×C4C2×#8793811yescharacteristic
113M16—41no—
114M16—4041no—
115M16—4041no—
116M16—4041no—
117C2×C8—21no—
118C2×C8—2022no—
119C2×C8—2021no—
120C4⋊C4—4041no—
121C4⋊C4—4041no—
122C22⋊C4—4042no—
123C23—1011no—
124C23—1011no—
125C23—4041no—
126C23—4041no—
127C23—2021no—
128C23—2021no—
129C23C4×#8793811yescharacteristic
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—1011no—
133C2×C4—1011no—
134C2×C4—4041no—
135C2×C4—4041no—
136C2×C4—4042no—
137C2×C4—4042no—
138C2×C4—4042no—
139C2×C4—4041no—
140C2×C4—2021no—
141C2×C4—2021no—
142C2×C4—2021no—
143C2×C4—2021no—
144C2×C4C22⋊#8793811yescharacteristic
145C2×C4C4⋊#8793811yescharacteristic
146C8—41no—
147C8—4042no—
148C8—4041no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22—1011no—
153C22—1011no—
154C22—4042no—
155C22—4042no—
156C22—2021no—
157C22—2021no—
158C22—2021no—
159C22—2021no—
160C22—2021no—
161C22(C2×#87938)⋊C411yescharacteristic
162C4—21no—
163C4—8082no—
164C4—2021no—
165C4—2021no—
166C4#1569231311yescharacteristic
167C4#1569231411yescharacteristic
168C2—41no—
169C2—4041no—
170C2—2021no—
171C2—2021no—
172C2#2026605511yescharacteristic
173C2#2026605611yescharacteristic
174C2#2026606011yescharacteristic
subgroupG/H
centerC22(C2×#87938)⋊C4
commutatorC23×C101C42
FrattiniC22×C4C2×#87938
FittingC2×M16×C101C4
socleC22×C101#95
prime radicalC23×D101C2×C4
cosocleC22×C4×D101C22
hypercenterC2×M16#87938
hypocenterC101#1305
LCSG ▷ C23×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
8. C22⋊#11717581C4semidirect
11. C2×#13108058C4semidirect
14. C2×M16×C101C4semidirect
88. C101#1305semidirect
95. C2×M16#87938semidirect

Maximal subgroups

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

subgroupindex
#202661482
#202661192
#202651402
#1305101