Finite Group Databasebeta

← #27194411

Subgroups — #27194411

Order 13184.

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

normal subgroups only

This group has 200 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#20268068C211yesmaximal, characteristic
3#20267998C211yesmaximal, characteristic, complemented
4#20267537C211yesmaximal, characteristic, complemented
5#20267523C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic
7#498×C103C211yesmaximal, characteristic, complemented
8C2×#13110095—21no—
9#15693016—22no—
10#15693010—21no—
11#15693001—21no—
12Q8×Dic103—21no—
13C4×Dic206C2211yescharacteristic
14C4×D412C2211yescharacteristic
15#15692979—21no—
16#15692954—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692945—21no—
20#15692941—21no—
21C4⋊Q8×C103C2211yescharacteristic
22C4⋊Q8×C103C2211yescharacteristic
23#106×C103—22no—
24C4×C8×C103C2211yescharacteristic
25C2×Dic206D411yescharacteristic
26C2×D412D411yescharacteristic
27C2×C4×D103—21no—
28#13110095—42no—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C4⋊Dic103—22no—
32C4⋊Dic103D411yescharacteristic
33C4⋊Dic103D411yescharacteristic
34Dic103⋊C4—21no—
35(C2×D103)⋊C4—22no—
36(C2×D103)⋊C4—22no—
37(C2×D103)⋊C4—21no—
38C4×Dic103—22no—
39C4×Dic103—21no—
40C2×Q8×C103—21no—
41C2×Q8×C103—21no—
42C2×C8×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103D412yes—
47C42×C103C2311yescharacteristic
48C22×D103—21no—
49Q8×C103—41no—
50Q8×C103—41no—
51Q8×C103—41no—
52Q8×C103—41no—
53C2×C4×C103—22no—
54C2×C4×C103—41no—
55C2×C4×C103C2×D411yescharacteristic
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×Dic103—21no—
59C2×Dic103—21no—
60C2×Dic103—21no—
61D412—21no—
62D412—21no—
63C4×D103—41no—
64C4×D103—41no—
65Dic206—21no—
66Dic206—21no—
67C8×C103—22no—
68C103⋊C8—41no—
69C103⋊C8—41no—
70C22×C103#12011yescharacteristic
71C2×D103—41no—
72C2×D103—41no—
73C2×D103—41no—
74C4×C103—21no—
75C4×C103—42no—
76C4×C103—81no—
77C4×C103#13511yescharacteristic
78C4×C103#13511yescharacteristic
79C4×C103AGL(1,ℤ/8)11yescharacteristic
80C4×C103#13711yescharacteristic
81Dic103—41no—
82Dic103—41no—
83Dic103—41no—
84C2×C103#44911yescharacteristic
85C2×C103#45211yescharacteristic
86C2×C103#45611yescharacteristic
87D103—81no—
88#1652—1031nomaximal, Sylow
89C103#165211yescharacteristic, complemented, Sylow
90#556—1031no—
91#498D10311yescharacteristic, complemented
92#474—1031no—
93#462—1031no—
94#332—1031no—
95Q8⋊C8—1031no—
96D4⋊C8—1031no—
97C2×Q16—2061no—
98C4⋊Q8C2×D10311yescharacteristic
99C4⋊Q8C2×D10311yescharacteristic
100#126—2062no—
101#124—2061no—
102C22⋊Q8—2061no—
103C4×Q8—1031no—
104C4×Q8—2061no—
105C4×D4—1031no—
106#117—2061no—
107#107—2061no—
108#106—22no—
109C4⋊C8—1031no—
110C4⋊C8—1031no—
111#103—2061no—
112#102—2061no—
113C4×C8C2×D10311yescharacteristic
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—1031no—
117C2×D4—1031no—
118C22×C4—2061no—
119Q16—4122no—
120C2×C8—21no—
121C2×C8—2061no—
122C2×C8—2061no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—1031no—
127C4⋊C4—1031no—
128C4⋊C4—2062no—
129C4⋊C4—2061no—
130C4⋊C4C22⋊D10312yes—
131C22⋊C4—2062no—
132C22⋊C4—2062no—
133C22⋊C4—2061no—
134C42—2062no—
135C42—2061no—
136C42C22×D10311yescharacteristic
137C23—2061no—
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—2061no—
143Q8—2061no—
144D4—2061no—
145D4—2061no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—4121no—
149C2×C4—4121no—
150C2×C4—2061no—
151C2×C4—2061no—
152C2×C4—2061no—
153C2×C4D4×D10311yescharacteristic
154C2×C4D4×D10311yescharacteristic
155C2×C4C2×C22⋊D10311yescharacteristic
156C8—22no—
157C8—4121no—
158C8—4121no—
159C22—4121no—
160C22—4121no—
161C22—4121no—
162C22#1569298911yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—4121no—
167C4—4121no—
168C4—4121no—
169C4#1569304211yescharacteristic
170C4#1569304211yescharacteristic
171C4#1569304811yescharacteristic
172C4#1569305011yescharacteristic
173C2—8241no—
174C2#2026793511yescharacteristic
175C2#2026795011yescharacteristic
176C2#2026797311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#498×C103C2
socleC22×C103#120
prime radicalC2×D412D4
hypercenter#498D103
hypocenterC103#1652
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
3. #20267998C2semidirect
4. #20267537C2semidirect
5. #20267523C2semidirect
7. #498×C103C2semidirect
89. C103#1652semidirect
91. #498D103semidirect

Maximal subgroups

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

subgroupindex
#202685152
#202680682
#202679982
#202675372
#202675232
#202675202
#498×C1032
#1652103