Finite Group Databasebeta

← #27170165

Subgroups — #27170165

Order 12928.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#20265774C211yesmaximal, characteristic
2#20265513C211yesmaximal, characteristic, complemented
3#20265496C211yesmaximal, characteristic
4#20265116C211yesmaximal, characteristic, complemented
5#20264915C211yesmaximal, characteristic, complemented
6#20264912C211yesmaximal, characteristic
7#324×C101C211yesmaximal, characteristic, complemented
8#15692250—21no—
9#15692245—21no—
10#15692240—21no—
11#15692238—21no—
12#15692234C2211yescharacteristic
13#15692233—21no—
14#15692229C2211yescharacteristic
15C4×C22⋊D101—21no—
16C2×C4⋊Dic101C2211yescharacteristic
17#15692189—21no—
18#15692187—21no—
19#15692180—21no—
20#15692177—21no—
21#15692162—21no—
22#15692162—21no—
23#15692162C2211yescharacteristic
24C2×C4⋊C4×C101C2211yescharacteristic
25C22⋊C8×C101C2211yescharacteristic
26C22⋊C8×C101C2211yescharacteristic
27C2×Dic202D411yescharacteristic
28C2×D404D411yescharacteristic
29C2×C22⋊D101—21no—
30C22×Dic101—21no—
31C22×Dic101—21no—
32C2×C4×D101—21no—
33C4⋊Dic101—21no—
34C4⋊Dic101—21no—
35C4⋊Dic101D411yescharacteristic
36C4⋊Dic101D411yescharacteristic
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41C22⋊Dic101—21no—
42#13108051—21no—
43#13108051—21no—
44#13108051—21no—
45#13108051—21no—
46C4×Dic101—21no—
47C22×C4×C101D411yescharacteristic
48C22×C4×C101D411yescharacteristic
49C22×C4×C101C2311yescharacteristic
50C2×C8×C101—21no—
51C2×C8×C101—21no—
52C4⋊C4×C101—21no—
53C4⋊C4×C101—21no—
54C23×C101C2×D411yescharacteristic
55C22×D101—21no—
56C2×C4×C101—21no—
57C2×C4×C101—21no—
58C2×C4×C101—21no—
59C2×C4×C101—21no—
60C2×C4×C101—41no—
61C2×C4×C101—41no—
62C2×C4×C101C2×D411yescharacteristic
63C2×C4×C101C2×D411yescharacteristic
64C22⋊D101—41no—
65C22⋊D101—41no—
66C2×Dic101—21no—
67C2×Dic101—21no—
68C2×Dic101—21no—
69C2×Dic101—41no—
70C2×Dic101—41no—
71C2×Dic101—42no—
72C2×Dic101—41no—
73C2×Dic101—41no—
74D404—41no—
75C4×D101—81no—
76Dic202—41no—
77C8×C101—41no—
78C8×C101—41no—
79C22×C101—21no—
80C22×C101—21no—
81C22×C101#12011yescharacteristic
82C22×C101#13511yescharacteristic
83C22×C101#13711yescharacteristic
84C2×D101—41no—
85C2×D101—41no—
86C2×D101—41no—
87C4×C101—21no—
88C4×C101—21no—
89C4×C101—41no—
90C4×C101—41no—
91Dic101—41no—
92Dic101—41no—
93Dic101—41no—
94Dic101—81no—
95Dic101—81no—
96C2×C101—21no—
97C2×C101—21no—
98C2×C101#45211yescharacteristic
99C2×C101#45411yescharacteristic
100C2×C101#45811yescharacteristic
101D101—81no—
102#1615—1011nomaximal, Sylow
103C101#161511yescharacteristic, complemented, Sylow
104#539—1011no—
105#484—1011no—
106#481—1011no—
107#400—1011no—
108#328—1011no—
109#327—1011no—
110#324D10111yescharacteristic, complemented
111#126—2021no—
112#125—2021no—
113#123—2021no—
114#123—2021no—
115C22⋊Q8—1011no—
116C22⋊Q8—2021no—
117#121—1011no—
118C4×D4—2021no—
119C2×C4⋊C4—1011no—
120C2×C4⋊C4C2×D10111yescharacteristic
121#107—2021no—
122#106—2021no—
123#103—2021no—
124#102—2021no—
125C22⋊C8C2×D10111yescharacteristic
126C22⋊C8C2×D10111yescharacteristic
127#95—1011no—
128#95—2021no—
129#95—2021no—
130C2×Q8—1011no—
131C2×D4—1011no—
132C2×D4—2021no—
133C22×C4—2021no—
134C22×C4—2021no—
135C22×C4—2021no—
136C22×C4D40411yescharacteristic
137C22×C4D40411yescharacteristic
138C22×C4C22×D10111yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—1011no—
144C4⋊C4—1011no—
145C4⋊C4—2021no—
146C4⋊C4—2021no—
147C4⋊C4—2021no—
148C4⋊C4—2021no—
149C4⋊C4—2021no—
150C4⋊C4—2021no—
151C22⋊C4—2021no—
152C22⋊C4—2021no—
153C22⋊C4—2021no—
154C22⋊C4—2021no—
155C22⋊C4—2021no—
156C42—2021no—
157C23—2021no—
158C23C2×D40411yescharacteristic
159Q8—4041no—
160D4—4041no—
161D4—4041no—
162D4—4041no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—8081no—
170C2×C4—4041no—
171C2×C4—4041no—
172C2×C4—4042no—
173C2×C4—4041no—
174C2×C4—4041no—
175C2×C4—2021no—
176C2×C4—2021no—
177C2×C4—2021no—
178C2×C4D4×D10111yescharacteristic
179C2×C4D4×D10111yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—4041no—
185C22—4041no—
186C22—4041no—
187C22#1569222511yescharacteristic
188C22#1569227711yescharacteristic
189C22#1569228811yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—8081no—
195C4—8081no—
196C4—4041no—
197C4—4041no—
198C4—4041no—
199C2—21no—
200C2—21no—
201C2—8081no—
202C2#2026534111yescharacteristic
203C2#2026535211yescharacteristic
204C2#2026536811yescharacteristic
subgroupG/H
centerC22#15692225
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#324×C101C2
socleC22×C101#120
prime radical#15692229C22
hypercenter#324D101
hypocenterC101#1615
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #20265513C2semidirect
4. #20265116C2semidirect
5. #20264915C2semidirect
7. #324×C101C2semidirect
103. C101#1615semidirect
110. #324D101semidirect

Maximal subgroups

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

subgroupindex
#202657742
#202655132
#202654962
#202651162
#202649152
#202649122
#324×C1012
#1615101