Finite Group Databasebeta

← #27170100

Subgroups — #27170100

Order 12928.

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

normal subgroups only

This group has 282 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#20265758C211yesmaximal, characteristic
2#20265316C212yesmaximal, complemented
3#20264910C212yesmaximal, complemented
4#20264903C211yesmaximal, characteristic, complemented
5#395×C101C211yesmaximal, characteristic, complemented
6C2×#13108074—21no—
7C2×#13108061—22no—
8#15692235—22no—
9#15692230—22no—
10#15692229—21no—
11#15692229C2212yes—
12#15692179—22no—
13C22⋊#11717579C2212yes—
14C22×Q8×C101C2211yescharacteristic
15C2×C4⋊C4×C101—21no—
16C2×C4⋊C4×C101C2211yescharacteristic
17#95×C101—21no—
18#95×C101C2211yescharacteristic
19#13108074—42no—
20#13108074—42no—
21C2×Dic202—21no—
22C2×D404—21no—
23C2×D404—21no—
24C2×D404D412yes—
25C2×C22⋊D101—22no—
26C2×C4×D101—22no—
27#13108061—44no—
28C2×#11717579—22no—
29C4⋊Dic101—21no—
30C4⋊Dic101D412yes—
31#13108051—22no—
32#13108051—22no—
33C2×Q8×C101—22no—
34C2×Q8×C101—42no—
35C22×C4×C101—21no—
36C22×C4×C101—21no—
37C22×C4×C101D411yescharacteristic
38C22×C4×C101D411yescharacteristic
39C22×C4×C101C2311yescharacteristic
40C4⋊C4×C101—22no—
41C4⋊C4×C101—42no—
42C23×C101C2×D411yescharacteristic
43C22×D101—22no—
44Q8×C101—24no—
45Q8×C101—42no—
46C2×C4×C101—21no—
47C2×C4×C101—21no—
48C2×C4×C101—22no—
49C2×C4×C101—22no—
50C2×C4×C101—21no—
51C2×C4×C101—41no—
52C2×C4×C101—41no—
53C2×C4×C101—41no—
54C2×C4×C101—41no—
55C2×C4×C101—41no—
56C2×C4×C101—41no—
57C2×C4×C101SD1612yescomplemented
58C2×C4×C101C2×D412yes—
59C22⋊D101—42no—
60C22⋊D101—42no—
61C2×Dic101—22no—
62D404—42no—
63D404—42no—
64D404—81no—
65C4×D101—44no—
66Dic202—42no—
67#11717579—42no—
68C22×C101—21no—
69C22×C101—21no—
70C22×C101#12011yescharacteristic
71C22×C101C2×SD1611yescharacteristic
72C22×C101AGL(1,ℤ/8)11yescharacteristic
73C2×D101—42no—
74C2×D101—42no—
75C2×D101—42no—
76C4×C101—22no—
77C4×C101—22no—
78C4×C101—42no—
79C4×C101—41no—
80C4×C101—42no—
81Dic101—42no—
82C2×C101—21no—
83C2×C101—21no—
84C2×C101#45011yescharacteristic
85C2×C101#45611yescharacteristic
86C2×C101B(4,𝔽2)11yescharacteristic
87D101—82no—
88#1604—1011nomaximal, Sylow
89C101#160411yescharacteristic, complemented, Sylow
90#537—1011no—
91#448—1012no—
92#395D10111yescharacteristic, complemented
93#327—1012no—
94#324—1011no—
95C2×#41—2021no—
96C22×Q8C2×D10111yescharacteristic
97C2×SD16—2022no—
98C22⋊Q8—2022no—
99#121—1012no—
100#121—2022no—
101#121—2021no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D10111yescharacteristic
104#103—2022no—
105C22⋊C8—1012no—
106#95—21no—
107#95C2×D10111yescharacteristic
108#41—4042no—
109#41—4042no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—2021no—
113C2×D4—1012no—
114C2×D4—2021no—
115C2×D4—2021no—
116C2×D4—2022no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—2022no—
120C22×C4C22⋊D10111yescharacteristic
121C22×C4C22⋊D10111yescharacteristic
122C22×C4C22×D10111yescharacteristic
123SD16—4044no—
124C2×C8—2022no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—1012no—
128C4⋊C4—2021no—
129C22⋊C4—2022no—
130C22⋊C4—2022no—
131C23—2022no—
132C23C2×C22⋊D10111yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—4042no—
136D4—8081no—
137D4—4042no—
138D4—4042no—
139D4—4042no—
140D4—4042no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—4044no—
153C2×C4—2022no—
154C2×C4#1310806112yescomplemented
155C2×C4D4×D10112yes—
156C8—4042no—
157C22—21no—
158C22—21no—
159C22—4042no—
160C22—4042no—
161C22—4042no—
162C22#1569222311yescharacteristic
163C22C2×#1310806111yescharacteristic
164C22#1569228011yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—4042no—
171C2—21no—
172C2—21no—
173C2—8082no—
174C2#2026532711yescharacteristic
175C2#2026535911yescharacteristic
176C2#2026536311yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#395×C101C2
socleC22×C101#120
prime radical#20265758C2
hypercenter#395D101
hypocenterC101#1604
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #20265316C2semidirect
3. #20264910C2semidirect
4. #20264903C2semidirect
5. #395×C101C2semidirect
57. C2×C4×C101SD16semidirect
89. C101#1604semidirect
92. #395D101semidirect
154. C2×C4#13108061semidirect

Maximal subgroups

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

subgroupindex
#202657582
#202653162
#202649102
#202649032
#395×C1012
#1604101