Finite Group Databasebeta

← C103×#1517 #27190883

Subgroups — C103×#1517 #27190883

Order 13184.

264 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 104 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#532×C103C211yesmaximal, characteristic
2#431×C103C211yesmaximal, characteristic, complemented
3#382×C103C211yesmaximal, characteristic, complemented
4#327×C103C214yesmaximal, complemented
5C2×#41×C103—21no—
6C4⋊Q8×C103C411yescharacteristic, complemented
7#127×C103C411yescharacteristic, complemented
8#124×C103—21no—
9#121×C103—21no—
10#121×C103C2212yes—
11C4×D4×C103—21no—
12C4×D4×C103C412yescomplemented
13C2×C4⋊C4×C103—21no—
14C2×C42×C103C2211yescharacteristic
15C4⋊C8×C103—21no—
16C22⋊C8×C103C2212yes—
17C4×C8×C103—21no—
18#95×C103—21no—
19#95×C103C2212yes—
20#41×C103—42no—
21#41×C103—42no—
22C2×Q8×C103—21no—
23C2×D4×C103—22no—
24C2×D4×C103—21no—
25C2×D4×C103—21no—
26C2×D4×C103C2×C412yes—
27C22×C4×C103—22no—
28C22×C4×C103—22no—
29C22×C4×C103D411yescharacteristic
30C22×C4×C103D411yescharacteristic
31C22×C4×C103C2311yescharacteristic
32C2×C8×C103—22no—
33C4⋊C4×C103—21no—
34C4⋊C4×C103—42no—
35C4⋊C4×C103C2×C412yes—
36C22⋊C4×C103—22no—
37C22⋊C4×C103—22no—
38C42×C103C2×C411yescharacteristic
39C42×C103C2×C411yescharacteristic
40C42×C103D411yescharacteristic
41C42×C103D411yescharacteristic
42C23×C103—22no—
43C23×C103C2×D411yescharacteristic
44Q8×C103—42no—
45D4×C103—42no—
46D4×C103—42no—
47D4×C103—42no—
48D4×C103—42no—
49D4×C103—42no—
50C2×C4×C103—22no—
51C2×C4×C103—41no—
52C2×C4×C103—41no—
53C2×C4×C103—44no—
54C2×C4×C103—42no—
55C2×C4×C103—42no—
56C2×C4×C103—42no—
57C2×C4×C103C22⋊C411yescharacteristic
58C2×C4×C103C22⋊C411yescharacteristic
59C2×C4×C103C22⋊C411yescharacteristic
60C2×C4×C103C22⋊C411yescharacteristic
61C2×C4×C103D812yes—
62C2×C4×C103SD1612yes—
63C2×C4×C103C22×C411yescharacteristic
64C2×C4×C103C2×D411yescharacteristic
65C8×C103—42no—
66C22×C103—21no—
67C22×C103—21no—
68C22×C103—42no—
69C22×C103—42no—
70C22×C103—42no—
71C22×C103C2×C22⋊C411yescharacteristic
72C22×C103C2×D811yescharacteristic
73C22×C103C2×SD1611yescharacteristic
74C4×C103—21no—
75C4×C103—21no—
76C4×C103—21no—
77C4×C103—21no—
78C4×C103—42no—
79C4×C103—82no—
80C4×C103#10212yes—
81C4×C103#10212yes—
82C2×C103—21no—
83C2×C103—21no—
84C2×C103—82no—
85C2×C103#41011yescharacteristic
86C2×C103C2×#10211yescharacteristic
87C2×C103#42111yescharacteristic
88#1517C10311yesmaximal, characteristic, direct product factor, Sylow
89C103#151711yescharacteristic, direct product factor, Sylow
90#532C2×C10311yescharacteristic
91#431C2×C10311yescharacteristic, complemented
92#382C2×C10311yescharacteristic, complemented
93#327C2×C10314yescomplemented
94C2×#41—21no—
95C4⋊Q8C4×C10311yescharacteristic, complemented
96#127C4×C10311yescharacteristic, complemented
97#124—21no—
98#121—21no—
99#121C22×C10312yes—
100C4×D4—21no—
101C4×D4C4×C10312yescomplemented
102C2×C4⋊C4—21no—
103C2×C42C22×C10311yescharacteristic
104C4⋊C8—21no—
105C22⋊C8C22×C10312yes—
106C4×C8—21no—
107#95—21no—
108#95C22×C10312yes—
109#41—42no—
110#41—42no—
111C2×Q8—21no—
112C2×D4—22no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4C2×C4×C10312yes—
116C22×C4—22no—
117C22×C4—22no—
118C22×C4D4×C10311yescharacteristic
119C22×C4D4×C10311yescharacteristic
120C22×C4C23×C10311yescharacteristic
121C2×C8—22no—
122C4⋊C4—21no—
123C4⋊C4—42no—
124C4⋊C4C2×C4×C10312yes—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C42C2×C4×C10311yescharacteristic
128C42C2×C4×C10311yescharacteristic
129C42D4×C10311yescharacteristic
130C42D4×C10311yescharacteristic
131C23—22no—
132C23C2×D4×C10311yescharacteristic
133Q8—42no—
134D4—42no—
135D4—42no—
136D4—42no—
137D4—42no—
138D4—42no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—44no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4C22⋊C4×C10311yescharacteristic
147C2×C4C22⋊C4×C10311yescharacteristic
148C2×C4C22⋊C4×C10311yescharacteristic
149C2×C4C22⋊C4×C10311yescharacteristic
150C2×C4D8×C10312yes—
151C2×C4SD16×C10312yes—
152C2×C4C22×C4×C10311yescharacteristic
153C2×C4C2×D4×C10311yescharacteristic
154C8—42no—
155C22—21no—
156C22—21no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22C2×C22⋊C4×C10311yescharacteristic
161C22C2×D8×C10311yescharacteristic
162C22C2×SD16×C10311yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—82no—
169C4#102×C10312yes—
170C4#102×C10312yes—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#410×C10311yescharacteristic
175C2C2×#102×C10311yescharacteristic
176C2#421×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×C22⋊C4
commutatorC2×C4C22×C4×C103
Frattini, cosocleC22×C4C23×C103
prime radical#532×C103C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. #431×C103C2semidirect
3. #382×C103C2semidirect
4. #327×C103C2semidirect
6. C4⋊Q8×C103C4semidirect
7. #127×C103C4semidirect
12. C4×D4×C103C4semidirect
88. #1517C103direct (N × H)
89. C103#1517direct (N × H)
91. #431C2×C103semidirect
92. #382C2×C103semidirect
93. #327C2×C103semidirect
95. C4⋊Q8C4×C103semidirect
96. #127C4×C103semidirect
101. C4×D4C4×C103semidirect

Maximal subgroups

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

subgroupindex
#532×C1032
#431×C1032
#382×C1032
#327×C1032
#1517103