Finite Group Databasebeta

← #27170163

Subgroups — #27170163

Order 12928.

208 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 53 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#20265510C211yesmaximal, characteristic, complemented
2#20265493C211yesmaximal, characteristic
3#20265116C211yesmaximal, characteristic, complemented
4#20264914C211yesmaximal, characteristic, complemented
5#20264911C211yesmaximal, characteristic
6#20264903C211yesmaximal, characteristic, complemented
7#539×C101C211yesmaximal, characteristic
8C2×C4⋊Dic101C2211yescharacteristic
9#15692188—21no—
10#15692186—21no—
11#15692179—21no—
12#15692176—21no—
13C22⋊#11717579C2211yescharacteristic
14C22⋊#11717579C2211yescharacteristic
15#15692162—21no—
16#15692162—21no—
17#15692162C2211yescharacteristic
18#126×C101—21no—
19#125×C101—21no—
20#123×C101—21no—
21#123×C101—21no—
22C22⋊Q8×C101—21no—
23C22⋊Q8×C101C2211yescharacteristic
24#121×C101C2211yescharacteristic
25C4×D4×C101—21no—
26C2×C4⋊C4×C101C2211yescharacteristic
27C22×Dic101—21no—
28C22×Dic101—21no—
29C2×#11717579—21no—
30C2×#11717579—21no—
31C4⋊Dic101—21no—
32C4⋊Dic101—21no—
33C2×Q8×C101D411yescharacteristic
34C2×D4×C101—21no—
35C2×D4×C101D411yescharacteristic
36C22×C4×C101—21no—
37C22×C4×C101D411yescharacteristic
38C22×C4×C101D411yescharacteristic
39C22×C4×C101C2311yescharacteristic
40C4⋊C4×C101—21no—
41C4⋊C4×C101—21no—
42C4⋊C4×C101—21no—
43C4⋊C4×C101—21no—
44C4⋊C4×C101—21no—
45C4⋊C4×C101—21no—
46C4⋊C4×C101D411yescharacteristic
47C4⋊C4×C101D411yescharacteristic
48C22⋊C4×C101—21no—
49C22⋊C4×C101—21no—
50C22⋊C4×C101—21no—
51C22⋊C4×C101—21no—
52C22⋊C4×C101—21no—
53C42×C101—21no—
54C23×C101—21no—
55C23×C101C2×D411yescharacteristic
56Q8×C101—41no—
57D4×C101—41no—
58D4×C101—41no—
59D4×C101—41no—
60C2×C4×C101—21no—
61C2×C4×C101—21no—
62C2×C4×C101—21no—
63C2×C4×C101—21no—
64C2×C4×C101—21no—
65C2×C4×C101—21no—
66C2×C4×C101—21no—
67C2×C4×C101—41no—
68C2×C4×C101—41no—
69C2×C4×C101—81no—
70C2×C4×C101C2×D411yescharacteristic
71C2×C4×C101C2×D411yescharacteristic
72C2×Dic101—41no—
73C2×Dic101—41no—
74C2×Dic101—42no—
75C2×Dic101—41no—
76C2×Dic101—41no—
77#11717579—41no—
78#11717579—41no—
79C22×C101—21no—
80C22×C101—21no—
81C22×C101—41no—
82C22×C101—41no—
83C22×C101—41no—
84C22×C101#12011yescharacteristic
85C22×C101#13511yescharacteristic
86C22×C101#13711yescharacteristic
87C4×C101—21no—
88C4×C101—21no—
89C4×C101—41no—
90C4×C101—41no—
91C4×C101—41no—
92C4×C101—41no—
93C4×C101—41no—
94Dic101—81no—
95Dic101—81no—
96C2×C101—21no—
97C2×C101—21no—
98C2×C101—81no—
99C2×C101#45211yescharacteristic
100C2×C101#45411yescharacteristic
101C2×C101#45811yescharacteristic
102#1615—1011nomaximal, Sylow
103C101#161511yescharacteristic, complemented, Sylow
104#539D10111yescharacteristic
105#484—1011no—
106#481—1011no—
107#400—1011no—
108#328—1011no—
109#327—1011no—
110#324—1011no—
111#126—21no—
112#125—21no—
113#123—21no—
114#123—21no—
115C22⋊Q8—21no—
116C22⋊Q8C2×D10111yescharacteristic
117#121C2×D10111yescharacteristic
118C4×D4—21no—
119C2×C4⋊C4—1011no—
120C2×C4⋊C4C2×D10111yescharacteristic
121#107—2021no—
122#106—2021no—
123#103—2021no—
124#102—2021no—
125C22⋊C8—1011no—
126C22⋊C8—1011no—
127#95—1011no—
128#95—2021no—
129#95—2021no—
130C2×Q8C22⋊D10111yescharacteristic
131C2×D4—21no—
132C2×D4C22⋊D10111yescharacteristic
133C22×C4—21no—
134C22×C4—2021no—
135C22×C4—2021no—
136C22×C4C22⋊D10111yescharacteristic
137C22×C4C22⋊D10111yescharacteristic
138C22×C4C22×D10111yescharacteristic
139C2×C8—2021no—
140C2×C8—2021no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—2021no—
148C4⋊C4—2021no—
149C4⋊C4C22⋊D10111yescharacteristic
150C4⋊C4C22⋊D10111yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—21no—
156C42—21no—
157C23—21no—
158C23C2×C22⋊D10111yescharacteristic
159Q8—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—81no—
173C2×C4—4041no—
174C2×C4—4041no—
175C2×C4—4042no—
176C2×C4—4041no—
177C2×C4—4041no—
178C2×C4C2×C22⋊D10111yescharacteristic
179C2×C4C2×C22⋊D10111yescharacteristic
180C8—4041no—
181C8—4041no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1569222411yescharacteristic
188C22#1569227511yescharacteristic
189C22#1569228511yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—41no—
195C4—41no—
196C4—41no—
197C4—8081no—
198C4—8081no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2026533911yescharacteristic
203C2#2026535011yescharacteristic
204C2#2026536711yescharacteristic
subgroupG/H
centerC22#15692224
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#539×C101C2
socleC22×C101#120
prime radical#121×C101C22
hypercenter#539D101
hypocenterC101#1615
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #20265510C2semidirect
3. #20265116C2semidirect
4. #20264914C2semidirect
6. #20264903C2semidirect
103. C101#1615semidirect

Maximal subgroups

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

subgroupindex
#202655102
#202654932
#202651162
#202649142
#202649112
#202649032
#539×C1012
#1615101