Finite Group Databasebeta

← C101×#1517 #27166871

Subgroups — C101×#1517 #27166871

Order 12928.

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×C101C211yesmaximal, characteristic
2#431×C101C211yesmaximal, characteristic, complemented
3#382×C101C211yesmaximal, characteristic, complemented
4#327×C101C214yesmaximal, complemented
5C2×#41×C101—21no—
6C4⋊Q8×C101C411yescharacteristic, complemented
7#127×C101C411yescharacteristic, complemented
8#124×C101—21no—
9#121×C101—21no—
10#121×C101C2212yes—
11C4×D4×C101—21no—
12C4×D4×C101C412yescomplemented
13C2×C4⋊C4×C101—21no—
14C2×C42×C101C2211yescharacteristic
15C4⋊C8×C101—21no—
16C22⋊C8×C101C2212yes—
17C4×C8×C101—21no—
18#95×C101—21no—
19#95×C101C2212yes—
20#41×C101—42no—
21#41×C101—42no—
22C2×Q8×C101—21no—
23C2×D4×C101—22no—
24C2×D4×C101—21no—
25C2×D4×C101—21no—
26C2×D4×C101C2×C412yes—
27C22×C4×C101—22no—
28C22×C4×C101—22no—
29C22×C4×C101D411yescharacteristic
30C22×C4×C101D411yescharacteristic
31C22×C4×C101C2311yescharacteristic
32C2×C8×C101—22no—
33C4⋊C4×C101—21no—
34C4⋊C4×C101—42no—
35C4⋊C4×C101C2×C412yes—
36C22⋊C4×C101—22no—
37C22⋊C4×C101—22no—
38C42×C101C2×C411yescharacteristic
39C42×C101C2×C411yescharacteristic
40C42×C101D411yescharacteristic
41C42×C101D411yescharacteristic
42C23×C101—22no—
43C23×C101C2×D411yescharacteristic
44Q8×C101—42no—
45D4×C101—42no—
46D4×C101—42no—
47D4×C101—42no—
48D4×C101—42no—
49D4×C101—42no—
50C2×C4×C101—22no—
51C2×C4×C101—41no—
52C2×C4×C101—41no—
53C2×C4×C101—44no—
54C2×C4×C101—42no—
55C2×C4×C101—42no—
56C2×C4×C101—42no—
57C2×C4×C101C22⋊C411yescharacteristic
58C2×C4×C101C22⋊C411yescharacteristic
59C2×C4×C101C22⋊C411yescharacteristic
60C2×C4×C101C22⋊C411yescharacteristic
61C2×C4×C101D812yes—
62C2×C4×C101SD1612yes—
63C2×C4×C101C22×C411yescharacteristic
64C2×C4×C101C2×D411yescharacteristic
65C8×C101—42no—
66C22×C101—21no—
67C22×C101—21no—
68C22×C101—42no—
69C22×C101—42no—
70C22×C101—42no—
71C22×C101C2×C22⋊C411yescharacteristic
72C22×C101C2×D811yescharacteristic
73C22×C101C2×SD1611yescharacteristic
74C4×C101—21no—
75C4×C101—21no—
76C4×C101—21no—
77C4×C101—21no—
78C4×C101—42no—
79C4×C101—82no—
80C4×C101#10212yes—
81C4×C101#10212yes—
82C2×C101—21no—
83C2×C101—21no—
84C2×C101—82no—
85C2×C101#41011yescharacteristic
86C2×C101C2×#10211yescharacteristic
87C2×C101#42111yescharacteristic
88#1517C10111yesmaximal, characteristic, direct product factor, Sylow
89C101#151711yescharacteristic, direct product factor, Sylow
90#532C2×C10111yescharacteristic
91#431C2×C10111yescharacteristic, complemented
92#382C2×C10111yescharacteristic, complemented
93#327C2×C10114yescomplemented
94C2×#41—21no—
95C4⋊Q8C4×C10111yescharacteristic, complemented
96#127C4×C10111yescharacteristic, complemented
97#124—21no—
98#121—21no—
99#121C22×C10112yes—
100C4×D4—21no—
101C4×D4C4×C10112yescomplemented
102C2×C4⋊C4—21no—
103C2×C42C22×C10111yescharacteristic
104C4⋊C8—21no—
105C22⋊C8C22×C10112yes—
106C4×C8—21no—
107#95—21no—
108#95C22×C10112yes—
109#41—42no—
110#41—42no—
111C2×Q8—21no—
112C2×D4—22no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4C2×C4×C10112yes—
116C22×C4—22no—
117C22×C4—22no—
118C22×C4D4×C10111yescharacteristic
119C22×C4D4×C10111yescharacteristic
120C22×C4C23×C10111yescharacteristic
121C2×C8—22no—
122C4⋊C4—21no—
123C4⋊C4—42no—
124C4⋊C4C2×C4×C10112yes—
125C22⋊C4—22no—
126C22⋊C4—22no—
127C42C2×C4×C10111yescharacteristic
128C42C2×C4×C10111yescharacteristic
129C42D4×C10111yescharacteristic
130C42D4×C10111yescharacteristic
131C23—22no—
132C23C2×D4×C10111yescharacteristic
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×C10111yescharacteristic
147C2×C4C22⋊C4×C10111yescharacteristic
148C2×C4C22⋊C4×C10111yescharacteristic
149C2×C4C22⋊C4×C10111yescharacteristic
150C2×C4D8×C10112yes—
151C2×C4SD16×C10112yes—
152C2×C4C22×C4×C10111yescharacteristic
153C2×C4C2×D4×C10111yescharacteristic
154C8—42no—
155C22—21no—
156C22—21no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22C2×C22⋊C4×C10111yescharacteristic
161C22C2×D8×C10111yescharacteristic
162C22C2×SD16×C10111yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—21no—
167C4—42no—
168C4—82no—
169C4#102×C10112yes—
170C4#102×C10112yes—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#410×C10111yescharacteristic
175C2C2×#102×C10111yescharacteristic
176C2#421×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×C22⋊C4
commutatorC2×C4C22×C4×C101
Frattini, cosocleC22×C4C23×C101
prime radical#532×C101C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. #431×C101C2semidirect
3. #382×C101C2semidirect
4. #327×C101C2semidirect
6. C4⋊Q8×C101C4semidirect
7. #127×C101C4semidirect
12. C4×D4×C101C4semidirect
88. #1517C101direct (N × H)
89. C101#1517direct (N × H)
91. #431C2×C101semidirect
92. #382C2×C101semidirect
93. #327C2×C101semidirect
95. C4⋊Q8C4×C101semidirect
96. #127C4×C101semidirect
101. C4×D4C4×C101semidirect

Maximal subgroups

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

subgroupindex
#532×C1012
#431×C1012
#382×C1012
#327×C1012
#1517101