Finite Group Databasebeta

← #27194329

Subgroups — #27194329

Order 13184.

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

normal subgroups only

This group has 212 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#20268526C211yesmaximal, characteristic
2#20268139C211yesmaximal, characteristic
3#20267998C211yesmaximal, characteristic, complemented
4#20267534C211yesmaximal, characteristic
5Q8⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6#20267521C211yesmaximal, characteristic, complemented
7#475×C103C211yesmaximal, characteristic, complemented
8C2×#13110095—21no—
9#15693018C2211yescharacteristic
10#15693010—21no—
11#15693009—21no—
12#15693006—22no—
13C4×Dic206C2211yescharacteristic
14C4×D412—21no—
15#15692983—21no—
16C4⋊(C103⋊C8)C2211yescharacteristic
17#15692945—21no—
18#15692941—22no—
19C4×C103⋊C8C2211yescharacteristic
20C4⋊Q8×C103C2211yescharacteristic
21C4×Q8×C103C2211yescharacteristic
22#106×C103—21no—
23C4⋊C8×C103C2211yescharacteristic
24#103×C103—21no—
25C2×Dic206D411yescharacteristic
26C2×D412—21no—
27C2×D412—21no—
28C2×D412D412yes—
29C2×C4×D103—22no—
30#13110095—42no—
31C2×C103⋊C8—21no—
32C2×C103⋊C8—21no—
33C4⋊Dic103D411yescharacteristic
34Dic103⋊C4—21no—
35(C2×D103)⋊C4—22no—
36(C2×D103)⋊C4—22no—
37(C2×D103)⋊C4—22no—
38C4×Dic103—21no—
39C2×Q8×C103—21no—
40C2×Q8×C103D411yescharacteristic
41C2×C8×C103—21no—
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103D411yescharacteristic
46C42×C103—21no—
47C42×C103C2311yescharacteristic
48C22×D103—22no—
49Q8×C103—21no—
50Q8×C103—21no—
51Q8×C103—41no—
52Q8×C103—41no—
53C2×C4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—41no—
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×Dic103—21no—
60C2×Dic103—21no—
61D412—42no—
62D412—41no—
63D412—41no—
64D412—41no—
65D412—41no—
66C4×D103—82no—
67Dic206—21no—
68Dic206—21no—
69C8×C103—41no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103#12011yescharacteristic
73C2×D103—42no—
74C2×D103—42no—
75C2×D103—42no—
76C4×C103—21no—
77C4×C103—41no—
78C4×C103—41no—
79C4×C103—81no—
80C4×C103#13511yescharacteristic
81C4×C103#13511yescharacteristic
82C4×C103AGL(1,ℤ/8)11yescharacteristic
83C4×C103#13711yescharacteristic
84Dic103—41no—
85Dic103—41no—
86C2×C103#44911yescharacteristic
87C2×C103#45211yescharacteristic
88C2×C103#45511yescharacteristic
89D103—82no—
90#1640—1031nomaximal, Sylow
91C103#164011yescharacteristic, complemented, Sylow
92#559—1031no—
93#486—1031no—
94#475D10311yescharacteristic, complemented
95#462—1031no—
96#331—1031no—
97Q8⋊C8—1031no—
98Q8⋊C8—1031no—
99C2×Q16—2061no—
100C4⋊Q8C2×D10311yescharacteristic
101#127—1031no—
102#124—2061no—
103#124—2061no—
104#123—2062no—
105C4×Q8—1031no—
106C4×Q8C2×D10311yescharacteristic
107C4×D4—2061no—
108C4×D4—2061no—
109#106—21no—
110C4⋊C8—1031no—
111C4⋊C8C2×D10311yescharacteristic
112#103—21no—
113#103—2061no—
114#102—2062no—
115C4×C8—1031no—
116C2×Q8—21no—
117C2×Q8—1031no—
118C2×Q8C22⋊D10311yescharacteristic
119C2×D4—1032no—
120C2×D4—2061no—
121C2×D4—2061no—
122C22×C4—2062no—
123Q16—4122no—
124C2×C8—21no—
125C2×C8—2061no—
126C2×C8—2061no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—1031no—
131C4⋊C4—2061no—
132C4⋊C4C22⋊D10311yescharacteristic
133C22⋊C4—2062no—
134C22⋊C4—2062no—
135C22⋊C4—2062no—
136C42—21no—
137C42—2061no—
138C42C22×D10311yescharacteristic
139C23—2062no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—2061no—
145Q8—2061no—
146D4—4122no—
147D4—4121no—
148D4—4121no—
149D4—4121no—
150D4—4121no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—8242no—
155C2×C4—2061no—
156C2×C4—2061no—
157C2×C4D4×D10311yescharacteristic
158C2×C4D4×D10311yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C8—41no—
161C8—4121no—
162C8—4121no—
163C22—4122no—
164C22—4122no—
165C22—4122no—
166C22#1569298911yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—4121no—
172C4—4121no—
173C4#1569304111yescharacteristic
174C4#1569304211yescharacteristic
175C4#1569304811yescharacteristic
176C4#1569305211yescharacteristic
177C2—8242no—
178C2#2026793511yescharacteristic
179C2#2026795111yescharacteristic
180C2#2026796711yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#475×C103C2
socleC22×C103#120
prime radical#15693018C22
hypercenter#475D103
hypocenterC103#1640
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #20267998C2semidirect
5. Q8⋊(C103⋊C8)C2semidirect
6. #20267521C2semidirect
7. #475×C103C2semidirect
91. C103#1640semidirect
94. #475D103semidirect

Maximal subgroups

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

subgroupindex
#202685262
#202681392
#202679982
#202675342
Q8⋊(C103⋊C8)2
#202675212
#475×C1032
#1640103