Finite Group Databasebeta

← #27173109

Subgroups — #27173109

Order 12928.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#20265990C211yesmaximal, characteristic
2#20265618C211yesmaximal, characteristic, complemented
3#20265449C211yesmaximal, characteristic, complemented
4#20264993C211yesmaximal, characteristic, complemented
5#20264985C211yesmaximal, characteristic, complemented
6#20264960C211yesmaximal, characteristic, complemented
7C2×Q32×C101C211yesmaximal, characteristic, complemented
8#15692303—21no—
9#15692287—22no—
10#15692286—21no—
11#15692286—21no—
12#15692278—21no—
13#15692277C2211yescharacteristic
14Q16×D101—21no—
15#15692261C2211yescharacteristic
16#15692201—21no—
17#15692198—21no—
18#15692195C2211yescharacteristic
19#15692191C2211yescharacteristic
20#15692174—21no—
21C2×Q16×C101C2211yescharacteristic
22C2×Q16×C101C2211yescharacteristic
23Q32×C101—22no—
24C2×C16×C101C2211yescharacteristic
25#13108075—22no—
26#13108075—41no—
27#13108074—21no—
28#13108074—42no—
29#13108074D411yescharacteristic
30Q8×D101—22no—
31Q8×D101—41no—
32Dic404D411yescharacteristic
33#13108064—22no—
34#13108064—41no—
35#13108063—21no—
36#13108061—22no—
37#13108061—41no—
38D808D411yescharacteristic
39#13108058—21no—
40#13108058D411yescharacteristic
41#13108057—21no—
42C8×D101—21no—
43#13108049—21no—
44C2×Q8×C101—21no—
45C2×Q8×C101—21no—
46Q16×C101—21no—
47Q16×C101—21no—
48Q16×C101—21no—
49Q16×C101D412yes—
50C2×C8×C101C2311yescharacteristic
51C16×C101—21no—
52Q8×C101—22no—
53Q8×C101—41no—
54Q8×C101—41no—
55Q8×C101—41no—
56C2×C4×C101—41no—
57C2×C4×C101—41no—
58C2×C4×C101C2×D411yescharacteristic
59C22⋊D101—21no—
60C22⋊D101—41no—
61D404—21no—
62D404—42no—
63D404D811yescharacteristic
64C4×D101—21no—
65C4×D101—42no—
66C4×D101—42no—
67C4×D101—41no—
68Dic202—21no—
69Dic202—42no—
70Dic202D811yescharacteristic
71C8×C101C2×D411yescharacteristic
72C8×C101C2×D411yescharacteristic
73#11717579—21no—
74#11717579—41no—
75C22×C101AGL(1,ℤ/8)11yescharacteristic
76C2×D101—21no—
77C2×D101—41no—
78C4×C101—42no—
79C4×C101—81no—
80C4×C101#12011yescharacteristic
81C4×C101C2×D811yescharacteristic
82Dic101—21no—
83Dic101—41no—
84C2×C101—21no—
85C2×C101#44711yescharacteristic
86D101—41no—
87D101—81no—
88#2195—1011nomaximal, Sylow
89C101#219511yescharacteristic, complemented, Sylow
90#578—1011no—
91#510—1011no—
92C2×Q32D10111yescharacteristic, complemented
93#473—1011no—
94#362—1011no—
95#359—1011no—
96#350—1011no—
972−1+4—2021no—
98#137—2021no—
99#137—2021no—
100#137—2022no—
101#135—1011no—
102#135—2021no—
103C2×Q16—2021no—
104C2×Q16C2×D10111yescharacteristic
105C2×Q16C2×D10111yescharacteristic
106#131—1011no—
107Q32—22no—
108Q32—2021no—
109SD32—2021no—
110M32—1011no—
111C2×C16C2×D10111yescharacteristic
112#108—1011no—
113#101—2021no—
114#41—1011no—
115#41—4042no—
116#41—4041no—
117#41—2022no—
118#41—2021no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—4041no—
122C2×Q8—2022no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—1011no—
127Q16—4041no—
128Q16—2022no—
129Q16C22⋊D10112yes—
130SD16—4041no—
131SD16—2022no—
132SD16—2021no—
133D8—1011no—
134M16—1011no—
135M16—2021no—
136M16—2021no—
137C2×C8—2021no—
138C2×C8C22×D10111yescharacteristic
139C16—21no—
140C16—2021no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—1011no—
146Q8—4042no—
147Q8—2021no—
148D4—1011no—
149D4—4042no—
150D4—4041no—
151D4—2021no—
152D4—2021no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—4042no—
156C2×C4—4042no—
157C2×C4—4041no—
158C2×C4—2021no—
159C2×C4D4×D10111yescharacteristic
160C8—4041no—
161C8—2021no—
162C8D4×D10111yescharacteristic
163C8C2×C22⋊D10111yescharacteristic
164C22—4041no—
165C22—2021no—
166C22#1569227911yescharacteristic
167C4—42no—
168C4—81no—
169C4—4041no—
170C4—2021no—
171C4#1569222311yescharacteristic
172C4D8×D10111yescharacteristic
173C2—21no—
174C2—8081no—
175C2—4041no—
176C2#2026530911yescharacteristic
subgroupG/H
centerC2#20265309
commutator, cosocleC2×C8×C101C23
FrattiniC2×C8C22×D101
FittingC2×Q32×C101C2
socleC2×C101#447
prime radical#20265990C2
hypercenterC2×Q32D101
hypocenterC101#2195
LCSG ▷ C2×C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #20265618C2semidirect
3. #20265449C2semidirect
4. #20264993C2semidirect
5. #20264985C2semidirect
6. #20264960C2semidirect
7. C2×Q32×C101C2semidirect
89. C101#2195semidirect
92. C2×Q32D101semidirect

Maximal subgroups

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

subgroupindex
#202659902
#202656182
#202654492
#202649932
#202649852
#202649602
C2×Q32×C1012
#2195101