Finite Group Databasebeta

← #27194112

Subgroups — #27194112

Order 13184.

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#20268372C211yesmaximal, characteristic
2#20267930C212yesmaximal, complemented
3#20267524C212yesmaximal, complemented
4#20267517C211yesmaximal, characteristic, complemented
5#395×C103C211yesmaximal, characteristic, complemented
6C2×#13110105—21no—
7C2×#13110092—22no—
8#15693001—22no—
9#15692996—22no—
10#15692995—21no—
11#15692995C2212yes—
12#15692945—22no—
13C22⋊(C103⋊C8)C2212yes—
14C22×Q8×C103C2211yescharacteristic
15C2×C4⋊C4×C103—21no—
16C2×C4⋊C4×C103C2211yescharacteristic
17#95×C103—21no—
18#95×C103C2211yescharacteristic
19#13110105—42no—
20#13110105—42no—
21C2×Dic206—21no—
22C2×D412—21no—
23C2×D412—21no—
24C2×D412D412yes—
25C2×C22⋊D103—22no—
26C2×C4×D103—22no—
27#13110092—44no—
28C2×C103⋊C8—22no—
29C4⋊Dic103—21no—
30C4⋊Dic103D412yes—
31(C2×D103)⋊C4—22no—
32(C2×D103)⋊C4—22no—
33C2×Q8×C103—22no—
34C2×Q8×C103—42no—
35C22×C4×C103—21no—
36C22×C4×C103—21no—
37C22×C4×C103D411yescharacteristic
38C22×C4×C103D411yescharacteristic
39C22×C4×C103C2311yescharacteristic
40C4⋊C4×C103—22no—
41C4⋊C4×C103—42no—
42C23×C103C2×D411yescharacteristic
43C22×D103—22no—
44Q8×C103—24no—
45Q8×C103—42no—
46C2×C4×C103—21no—
47C2×C4×C103—21no—
48C2×C4×C103—22no—
49C2×C4×C103—22no—
50C2×C4×C103—21no—
51C2×C4×C103—41no—
52C2×C4×C103—41no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103SD1612yescomplemented
58C2×C4×C103C2×D412yes—
59C22⋊D103—42no—
60C22⋊D103—42no—
61C2×Dic103—22no—
62D412—42no—
63D412—42no—
64D412—81no—
65C4×D103—44no—
66Dic206—42no—
67C103⋊C8—42no—
68C22×C103—21no—
69C22×C103—21no—
70C22×C103#12011yescharacteristic
71C22×C103C2×SD1611yescharacteristic
72C22×C103AGL(1,ℤ/8)11yescharacteristic
73C2×D103—42no—
74C2×D103—42no—
75C2×D103—42no—
76C4×C103—22no—
77C4×C103—22no—
78C4×C103—42no—
79C4×C103—41no—
80C4×C103—42no—
81Dic103—42no—
82C2×C103—21no—
83C2×C103—21no—
84C2×C103#45011yescharacteristic
85C2×C103#45611yescharacteristic
86C2×C103B(4,𝔽2)11yescharacteristic
87D103—82no—
88#1604—1031nomaximal, Sylow
89C103#160411yescharacteristic, complemented, Sylow
90#537—1031no—
91#448—1032no—
92#395D10311yescharacteristic, complemented
93#327—1032no—
94#324—1031no—
95C2×#41—2061no—
96C22×Q8C2×D10311yescharacteristic
97C2×SD16—2062no—
98C22⋊Q8—2062no—
99#121—1032no—
100#121—2062no—
101#121—2061no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D10311yescharacteristic
104#103—2062no—
105C22⋊C8—1032no—
106#95—21no—
107#95C2×D10311yescharacteristic
108#41—4122no—
109#41—4122no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—2061no—
113C2×D4—1032no—
114C2×D4—2061no—
115C2×D4—2061no—
116C2×D4—2062no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—2062no—
120C22×C4C22⋊D10311yescharacteristic
121C22×C4C22⋊D10311yescharacteristic
122C22×C4C22×D10311yescharacteristic
123SD16—4124no—
124C2×C8—2062no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—1032no—
128C4⋊C4—2061no—
129C22⋊C4—2062no—
130C22⋊C4—2062no—
131C23—2062no—
132C23C2×C22⋊D10311yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—4122no—
136D4—8241no—
137D4—4122no—
138D4—4122no—
139D4—4122no—
140D4—4122no—
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—4124no—
153C2×C4—2062no—
154C2×C4#1311009212yescomplemented
155C2×C4D4×D10312yes—
156C8—4122no—
157C22—21no—
158C22—21no—
159C22—4122no—
160C22—4122no—
161C22—4122no—
162C22#1569298911yescharacteristic
163C22C2×#1311009211yescharacteristic
164C22#1569304611yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—4122no—
171C2—21no—
172C2—21no—
173C2—8242no—
174C2#2026794111yescharacteristic
175C2#2026797311yescharacteristic
176C2#2026797711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#395×C103C2
socleC22×C103#120
prime radical#20268372C2
hypercenter#395D103
hypocenterC103#1604
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #20267930C2semidirect
3. #20267524C2semidirect
4. #20267517C2semidirect
5. #395×C103C2semidirect
57. C2×C4×C103SD16semidirect
89. C103#1604semidirect
92. #395D103semidirect
154. C2×C4#13110092semidirect

Maximal subgroups

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

subgroupindex
#202683722
#202679302
#202675242
#202675172
#395×C1032
#1604103