Finite Group Databasebeta

← #27194330

Subgroups — #27194330

Order 13184.

212 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 57 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#20268137C211yesmaximal, characteristic
2#20268076C211yesmaximal, characteristic, complemented
3#20268001C211yesmaximal, characteristic, complemented
4#20267535C211yesmaximal, characteristic
5Q8⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
6Q8⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
7#559×C103C211yesmaximal, characteristic
8C2×#13110095—21no—
9#15693021C2211yescharacteristic
10#15692952—21no—
11C4⋊(C103⋊C8)C2211yescharacteristic
12C4⋊(C103⋊C8)C2211yescharacteristic
13#15692945—21no—
14#15692944—21no—
15#15692942—22no—
16C4×C103⋊C8C2211yescharacteristic
17#127×C103C2211yescharacteristic
18#124×C103—21no—
19#124×C103—21no—
20#123×C103—22no—
21C4×Q8×C103C2211yescharacteristic
22C4×Q8×C103C2211yescharacteristic
23C4×D4×C103—21no—
24C4×D4×C103—21no—
25C2×Dic206—21no—
26#13110095—42no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103—21no—
32C2×Q8×C103D411yescharacteristic
33C2×Q8×C103D411yescharacteristic
34C2×D4×C103—21no—
35C2×D4×C103—21no—
36C2×D4×C103D412yes—
37C22×C4×C103—22no—
38C4⋊C4×C103—21no—
39C4⋊C4×C103—21no—
40C4⋊C4×C103D411yescharacteristic
41C4⋊C4×C103D411yescharacteristic
42C22⋊C4×C103—22no—
43C22⋊C4×C103—22no—
44C22⋊C4×C103—22no—
45C42×C103—21no—
46C42×C103—21no—
47C42×C103C2311yescharacteristic
48C23×C103—22no—
49Q8×C103—21no—
50Q8×C103—21no—
51Q8×C103—21no—
52Q8×C103—21no—
53D4×C103—42no—
54D4×C103—41no—
55D4×C103—41no—
56D4×C103—41no—
57D4×C103—41no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—82no—
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×Dic103—41no—
67Dic206—41no—
68Dic206—41no—
69C103⋊C8—41no—
70C103⋊C8—41no—
71C103⋊C8—41no—
72C22×C103—42no—
73C22×C103—42no—
74C22×C103—42no—
75C22×C103#12011yescharacteristic
76C4×C103—21no—
77C4×C103—41no—
78C4×C103—41no—
79C4×C103—41no—
80C4×C103—41no—
81C4×C103#13511yescharacteristic
82C4×C103#13511yescharacteristic
83C4×C103AGL(1,ℤ/8)11yescharacteristic
84C4×C103#13711yescharacteristic
85Dic103—81no—
86C2×C103—82no—
87C2×C103#44911yescharacteristic
88C2×C103#45211yescharacteristic
89C2×C103#45511yescharacteristic
90#1640—1031nomaximal, Sylow
91C103#164011yescharacteristic, complemented, Sylow
92#559D10311yescharacteristic
93#486—1031no—
94#475—1031no—
95#462—1031no—
96#331—1031no—
97Q8⋊C8—1031no—
98Q8⋊C8—1031no—
99C2×Q16—2061no—
100C4⋊Q8—1031no—
101#127C2×D10311yescharacteristic
102#124—21no—
103#124—21no—
104#123—22no—
105C4×Q8C2×D10311yescharacteristic
106C4×Q8C2×D10311yescharacteristic
107C4×D4—21no—
108C4×D4—21no—
109#106—2061no—
110C4⋊C8—1031no—
111C4⋊C8—1031no—
112#103—2061no—
113#103—2061no—
114#102—2062no—
115C4×C8—1031no—
116C2×Q8—2061no—
117C2×Q8C22⋊D10311yescharacteristic
118C2×Q8C22⋊D10311yescharacteristic
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D10312yes—
122C22×C4—22no—
123Q16—4122no—
124C2×C8—2061no—
125C2×C8—2061no—
126C2×C8—2061no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2061no—
130C4⋊C4—2061no—
131C4⋊C4C22⋊D10311yescharacteristic
132C4⋊C4C22⋊D10311yescharacteristic
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C42—21no—
137C42—21no—
138C42C22×D10311yescharacteristic
139C23—22no—
140Q8—21no—
141Q8—21no—
142Q8—21no—
143Q8—21no—
144Q8—4121no—
145Q8—4121no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—82no—
156C2×C4—4121no—
157C2×C4C2×C22⋊D10311yescharacteristic
158C2×C4C2×C22⋊D10311yescharacteristic
159C2×C4C2×C22⋊D10311yescharacteristic
160C8—4121no—
161C8—4121no—
162C8—4121no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1569299011yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—8241no—
173C4#1569304111yescharacteristic
174C4#1569304111yescharacteristic
175C4#1569304611yescharacteristic
176C4#1569305111yescharacteristic
177C2—82no—
178C2#2026793611yescharacteristic
179C2#2026795311yescharacteristic
180C2#2026796911yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#559×C103C2
socleC22×C103#120
prime radical#127×C103C22
hypercenter#559D103
hypocenterC103#1640
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #559

Complements

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

NH ≅ G/Ntype
2. #20268076C2semidirect
3. #20268001C2semidirect
5. Q8⋊(C103⋊C8)C2semidirect
6. Q8⋊(C103⋊C8)C2semidirect
91. C103#1640semidirect

Maximal subgroups

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

subgroupindex
#202681372
#202680762
#202680012
#202675352
Q8⋊(C103⋊C8)2
#559×C1032
#1640103