Finite Group Databasebeta

← #27194180

Subgroups — #27194180

Order 13184.

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

normal subgroups only

This group has 246 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#20268109C212yesmaximal, complemented
3#20267524C212yesmaximal, complemented
4#20267517C211yesmaximal, characteristic, complemented
5#400×C103C211yesmaximal, characteristic, complemented
6C2×#13110105—21no—
7#15693001—22no—
8#15692996—22no—
9#15692995—21no—
10#15692995C2212yes—
11#15692952—22no—
12#15692941—22no—
13C22⋊(C103⋊C8)C2212yes—
14C2×C4⋊C4×C103C2211yescharacteristic
15C2×C4⋊C4×C103C2211yescharacteristic
16#95×C103—21no—
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—
27C2×C103⋊C8—22no—
28C4⋊Dic103—21no—
29C4⋊Dic103D412yes—
30(C2×D103)⋊C4—22no—
31(C2×D103)⋊C4—22no—
32C22×C4×C103—21no—
33C22×C4×C103—21no—
34C22×C4×C103D411yescharacteristic
35C22×C4×C103D411yescharacteristic
36C22×C4×C103C2311yescharacteristic
37C4⋊C4×C103—22no—
38C4⋊C4×C103—22no—
39C23×C103C2×D411yescharacteristic
40C22×D103—22no—
41C2×C4×C103—21no—
42C2×C4×C103—21no—
43C2×C4×C103—21no—
44C2×C4×C103—41no—
45C2×C4×C103—41no—
46C2×C4×C103—41no—
47C2×C4×C103—41no—
48C2×C4×C103—42no—
49C2×C4×C103—41no—
50C2×C4×C103—41no—
51C2×C4×C103SD1612yes—
52C2×C4×C103C2×D412yes—
53C22⋊D103—42no—
54C22⋊D103—42no—
55C2×Dic103—22no—
56D412—42no—
57D412—42no—
58D412—81no—
59C4×D103—44no—
60Dic206—42no—
61C103⋊C8—42no—
62C22×C103—21no—
63C22×C103—21no—
64C22×C103#12011yescharacteristic
65C22×C103C2×SD1611yescharacteristic
66C22×C103AGL(1,ℤ/8)11yescharacteristic
67C2×D103—42no—
68C2×D103—42no—
69C2×D103—42no—
70C4×C103—22no—
71C4×C103—22no—
72C4×C103—41no—
73C4×C103—81no—
74C4×C103—81no—
75Dic103—42no—
76C2×C103—21no—
77C2×C103—21no—
78C2×C103#45011yescharacteristic
79C2×C103#45411yescharacteristic
80C2×C103#45811yescharacteristic
81D103—82no—
82#1616—1031nomaximal, Sylow
83C103#161611yescharacteristic, complemented, Sylow
84#537—1031no—
85#481—1032no—
86#400D10311yescharacteristic, complemented
87#327—1032no—
88#324—1031no—
89C2×#41—2061no—
90C22⋊Q8—2062no—
91#121—1032no—
92#121—2062no—
93#121—2061no—
94C2×C4⋊C4C2×D10311yescharacteristic
95C2×C4⋊C4C2×D10311yescharacteristic
96#106—2062no—
97#102—2062no—
98C22⋊C8—1032no—
99#95—21no—
100#95—21no—
101#95C2×D10311yescharacteristic
102#41—4122no—
103#41—4122no—
104C2×Q8—2061no—
105C2×D4—1032no—
106C2×D4—2061no—
107C2×D4—2061no—
108C2×D4—2062no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—2062no—
112C22×C4C22⋊D10311yescharacteristic
113C22×C4C22⋊D10311yescharacteristic
114C22×C4C22×D10311yescharacteristic
115C2×C8—2062no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—1032no—
119C4⋊C4—2061no—
120C22⋊C4—2062no—
121C22⋊C4—2062no—
122C23—2062no—
123C23C2×C22⋊D10311yescharacteristic
124Q8—4122no—
125D4—8241no—
126D4—4122no—
127D4—4122no—
128D4—4122no—
129D4—4122no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—4124no—
141C2×C4—2062no—
142C2×C4#1311009212yes—
143C2×C4D4×D10312yes—
144C8—4122no—
145C22—21no—
146C22—21no—
147C22—4122no—
148C22—4122no—
149C22—4122no—
150C22#1569298911yescharacteristic
151C22C2×#1311009211yescharacteristic
152C22#1569304611yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—4122no—
159C2—21no—
160C2—21no—
161C2—8242no—
162C2#2026794111yescharacteristic
163C2#2026796311yescharacteristic
164C2#2026798011yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#400×C103C2
socleC22×C103#120
prime radical#20268372C2
hypercenter#400D103
hypocenterC103#1616
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #20268109C2semidirect
3. #20267524C2semidirect
4. #20267517C2semidirect
5. #400×C103C2semidirect
83. C103#1616semidirect
86. #400D103semidirect

Maximal subgroups

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

subgroupindex
#202683722
#202681092
#202675242
#202675172
#400×C1032
#1616103