Finite Group Databasebeta

← #27186110

Subgroups — #27186110

Order 12928.

222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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#20266055C211yesmaximal, characteristic, complemented
2#20266021C211yesmaximal, characteristic, complemented
3#20265085C211yesmaximal, characteristic
4C2×C22⋊#87938—21no—
5C22⋊#11717581—21no—
6C22×C22⋊D101—21no—
7C2×C22⋊Dic101—21no—
8C2×#13108051C2211yescharacteristic
9#15692162C411yescharacteristic, complemented
10C22×D4×C101C411yescharacteristic, complemented
11C22×#87938—41no—
12C2×#11717581—41no—
13C22⋊#87938—22no—
14C22⋊#87938—41no—
15C23×D101D411yescharacteristic
16C2×C22⋊D101—42no—
17C2×C22⋊D101—42no—
18C2×C22⋊D101—41no—
19C2×C22⋊D101—41no—
20C22×Dic101—21no—
21C22×Dic101D411yescharacteristic
22C22⋊Dic101—42no—
23#13108051—41no—
24C24×C101—21no—
25C2×D4×C101—41no—
26C2×D4×C101—42no—
27C22×C4×C101C2×C411yescharacteristic
28C23×C101—22no—
29C23×C101—41no—
30C23×C101—41no—
31C23×C101—41no—
32C23×C101—41no—
33C23×C101—41no—
34C23×C101—41no—
35C23×C101C22⋊C411yescharacteristic
36C22×D101—21no—
37C22×D101—21no—
38C22×D101—41no—
39C22×D101—41no—
40C22×D101D811yescharacteristic
41C22×D101SD1611yescharacteristic
42C2×#87938—42no—
43C2×#87938—81no—
44C2×#87938—81no—
45D4×C101—42no—
46D4×C101—42no—
47C2×C4×C101—21no—
48C2×C4×C101—41no—
49C22⋊D101—44no—
50C22⋊D101—44no—
51C2×Dic101—22no—
52C2×Dic101—21no—
53C2×Dic101—41no—
54C2×Dic101—41no—
55C2×Dic101—41no—
56#11717581—81no—
57C22×C101—21no—
58C22×C101—21no—
59C22×C101—42no—
60C22×C101—42no—
61C22×C101—42no—
62C22×C101—81no—
63C22×C101—81no—
64C22×C101—81no—
65C22×C101—81no—
66C22×C101#9911yescharacteristic
67C22×C101#10211yescharacteristic
68C22×C101#10411yescharacteristic
69C2×D101—21no—
70C2×D101—21no—
71C2×D101—41no—
72C2×D101—41no—
73C2×D101—41no—
74C2×D101—41no—
75C2×D101—81no—
76#87938—82no—
77C4×C101—41no—
78Dic101—42no—
79Dic101—41no—
80C2×C101—21no—
81C2×C101—21no—
82C2×C101—82no—
83C2×C101#32711yescharacteristic
84C2×C101AΣL(1,𝔽16)11yescharacteristic
85C2×C101#35311yescharacteristic
86D101—41no—
87D101—41no—
88#1343—1011nomaximal, Sylow
89C101#134311yescharacteristic, complemented, Sylow
90#392—1011no—
91#342—1011no—
92#323—1011no—
93C22×D4—2021no—
94C22×D4#8793811yescharacteristic, complemented
95C2×C22⋊C4—1011no—
96C2×C22⋊C4—2021no—
97C2×C22⋊C4—2021no—
98C22⋊C8—2021no—
99#95—1011no—
100C24—21no—
101C24—1011no—
102C2×D4—41no—
103C2×D4—42no—
104C2×D4—4042no—
105C2×D4—4041no—
106C2×D4—4041no—
107C2×D4—4042no—
108C22×C4—1011no—
109C22×C4—4041no—
110C22×C4—2021no—
111C22×C4C2×#8793811yescharacteristic
112C2×C8—4041no—
113C22⋊C4—4041no—
114C22⋊C4—4041no—
115C22⋊C4—4042no—
116C22⋊C4—2022no—
117C23—22no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23—41no—
124C23—1011no—
125C23—1011no—
126C23—4041no—
127C23—4041no—
128C23—2021no—
129C23—2021no—
130C23C22⋊#8793811yescharacteristic
131D4—42no—
132D4—42no—
133D4—4044no—
134D4—4044no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—8081no—
138C2×C4—8081no—
139C2×C4—4042no—
140C2×C4—4041no—
141C2×C4—4041no—
142C2×C4—4041no—
143C2×C4—2022no—
144C2×C4—2021no—
145C8—8081no—
146C22—21no—
147C22—21no—
148C22—42no—
149C22—42no—
150C22—42no—
151C22—81no—
152C22—81no—
153C22—81no—
154C22—81no—
155C22—8081no—
156C22—4041no—
157C22—4041no—
158C22—4041no—
159C22—4041no—
160C22—2021no—
161C22—2021no—
162C22#1569231311yescharacteristic
163C22#1569231711yescharacteristic
164C22#1569231911yescharacteristic
165C4—41no—
166C4—8082no—
167C4—4042no—
168C4—4041no—
169C2—21no—
170C2—21no—
171C2—82no—
172C2—4041no—
173C2—4041no—
174C2#2026602811yescharacteristic
175C2#2026607711yescharacteristic
176C2#2026608111yescharacteristic
subgroupG/H
centerC22#15692313
commutatorC22×C4×C101C2×C4
FrattiniC22×C4C2×#87938
FittingC22×D4×C101C4
socleC22×C101#99
prime radical#20265085C2
cosocleC2×#13108051C22
hypercenterC22×D4#87938
hypocenterC101#1343
LCSG ▷ C22×C4×C101 ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #20266055C2semidirect
2. #20266021C2semidirect
9. #15692162C4semidirect
10. C22×D4×C101C4semidirect
89. C101#1343semidirect
94. C22×D4#87938semidirect

Maximal subgroups

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

subgroupindex
#202660552
#202660212
#202650852
#1343101