Finite Group Databasebeta

← #27194317

Subgroups — #27194317

Order 13184.

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

normal subgroups only

This group has 194 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#20268515C211yesmaximal, characteristic
2#20268143C211yesmaximal, characteristic, complemented
3#20268087C211yesmaximal, characteristic, complemented
4#20268082C211yesmaximal, characteristic
5#20267521C211yesmaximal, characteristic, complemented
6#20267518C211yesmaximal, characteristic
7#332×C103C211yesmaximal, characteristic, complemented
8#15693021C2211yescharacteristic
9#15693016—22no—
10#15693010—21no—
11#15693001—21no—
12Q8×Dic103—21no—
13C4×Dic206C2211yescharacteristic
14C4×D412C2211yescharacteristic
15#15692979—21no—
16#15692955—21no—
17#15692953—21no—
18#15692946—21no—
19#15692944—22no—
20#15692943—21no—
21C4×C103⋊C8C2211yescharacteristic
22C4⋊Q8×C103C2211yescharacteristic
23C4⋊C8×C103C2211yescharacteristic
24C4⋊C8×C103C2211yescharacteristic
25C2×Dic206—21no—
26C2×Dic206D411yescharacteristic
27C2×D412D411yescharacteristic
28C2×C4×D103—21no—
29C2×C103⋊C8—21no—
30C4⋊Dic103—22no—
31C4⋊Dic103—21no—
32C4⋊Dic103—21no—
33C4⋊Dic103D411yescharacteristic
34C4⋊Dic103D411yescharacteristic
35Dic103⋊C4—21no—
36(C2×D103)⋊C4—22no—
37(C2×D103)⋊C4—22no—
38(C2×D103)⋊C4—21no—
39C4×Dic103—22no—
40C4×Dic103—21no—
41C2×Q8×C103—21no—
42C2×C8×C103—21no—
43C2×C8×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103D412yes—
46C42×C103C2311yescharacteristic
47C22×D103—21no—
48Q8×C103—41no—
49Q8×C103—41no—
50C2×C4×C103—22no—
51C2×C4×C103C2×D411yescharacteristic
52C2×C4×C103C2×D411yescharacteristic
53C2×C4×C103C2×D411yescharacteristic
54C2×Dic103—21no—
55C2×Dic103—21no—
56C2×Dic103—21no—
57C2×Dic103—41no—
58D412—21no—
59D412—21no—
60C4×D103—41no—
61C4×D103—41no—
62Dic206—21no—
63Dic206—21no—
64Dic206—42no—
65C8×C103—41no—
66C8×C103—41no—
67C103⋊C8—41no—
68C22×C103#12011yescharacteristic
69C2×D103—41no—
70C2×D103—41no—
71C2×D103—41no—
72C4×C103—21no—
73C4×C103—42no—
74C4×C103#13511yescharacteristic
75C4×C103#13511yescharacteristic
76C4×C103#13711yescharacteristic
77C4×C103#13711yescharacteristic
78Dic103—41no—
79Dic103—41no—
80Dic103—41no—
81Dic103—81no—
82C2×C103#45211yescharacteristic
83C2×C103#45211yescharacteristic
84C2×C103#45411yescharacteristic
85D103—81no—
86#1638—1031nomaximal, Sylow
87C103#163811yescharacteristic, complemented, Sylow
88#556—1031no—
89#487—1031no—
90#477—1031no—
91#476—1031no—
92#332D10311yescharacteristic, complemented
93Q8⋊C8—1031no—
94D4⋊C8—1031no—
95C4⋊Q8—1031no—
96C4⋊Q8C2×D10311yescharacteristic
97#126—2062no—
98#124—2061no—
99C22⋊Q8—2061no—
100C4×Q8—1031no—
101C4×Q8—2061no—
102C4×D4—1031no—
103#117—2061no—
104#107—2061no—
105#106—2061no—
106C4⋊C8C2×D10311yescharacteristic
107C4⋊C8C2×D10311yescharacteristic
108#103—2061no—
109#103—2062no—
110#102—2061no—
111C4×C8—1031no—
112C2×Q8—21no—
113C2×Q8—1031no—
114C2×Q8—2061no—
115C2×D4—1031no—
116C22×C4—2061no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2061no—
120C4⋊C4—21no—
121C4⋊C4—1031no—
122C4⋊C4—1031no—
123C4⋊C4—2062no—
124C4⋊C4—2061no—
125C4⋊C4—2061no—
126C4⋊C4—2061no—
127C4⋊C4D41212yes—
128C22⋊C4—2062no—
129C22⋊C4—2062no—
130C22⋊C4—2061no—
131C42—2062no—
132C42—2061no—
133C42C22×D10311yescharacteristic
134C23—2061no—
135Q8—41no—
136Q8—41no—
137Q8—4122no—
138Q8—2061no—
139Q8—2061no—
140D4—2061no—
141D4—2061no—
142C2×C4—22no—
143C2×C4—4121no—
144C2×C4—4121no—
145C2×C4—4121no—
146C2×C4—2061no—
147C2×C4—2061no—
148C2×C4—2061no—
149C2×C4D4×D10311yescharacteristic
150C2×C4D4×D10311yescharacteristic
151C2×C4C2×D41211yescharacteristic
152C8—41no—
153C8—41no—
154C8—4121no—
155C22—4121no—
156C22—4121no—
157C22—4121no—
158C22#1569299111yescharacteristic
159C4—21no—
160C4—42no—
161C4—8241no—
162C4—4121no—
163C4—4121no—
164C4—4121no—
165C4#1569304011yescharacteristic
166C4#1569304211yescharacteristic
167C4#1569305011yescharacteristic
168C4#1569305311yescharacteristic
169C2—8241no—
170C2#2026795411yescharacteristic
171C2#2026795611yescharacteristic
172C2#2026796611yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#332×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#332D103
hypocenterC103#1638
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #20268143C2semidirect
3. #20268087C2semidirect
5. #20267521C2semidirect
7. #332×C103C2semidirect
87. C103#1638semidirect
92. #332D103semidirect

Maximal subgroups

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

subgroupindex
#202685152
#202681432
#202680872
#202680822
#202675212
#202675182
#332×C1032
#1638103