Finite Group Databasebeta

← #27173095

Subgroups — #27173095

Order 12928.

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

normal subgroups only

This group has 210 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, complemented
2#20265613C211yesmaximal, characteristic, complemented
3#20265444C211yesmaximal, characteristic, complemented
4#20264993C211yesmaximal, characteristic, complemented
5#20264985C211yesmaximal, characteristic, complemented
6#20264960C211yesmaximal, characteristic, complemented
7C2×SD32×C101C211yesmaximal, characteristic, complemented
8#15692303—21no—
9#15692287—22no—
10#15692286—21no—
11#15692281—21no—
12#15692278—21no—
13#15692277C2211yescharacteristic
14Q16×D101—21no—
15#15692261C2211yescharacteristic
16#15692199—21no—
17#15692196—21no—
18#15692195C2211yescharacteristic
19#15692191C2211yescharacteristic
20#15692172—21no—
21C2×Q16×C101C2211yescharacteristic
22C2×D8×C101C2211yescharacteristic
23SD32×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#13108063—21no—
35#13108062—41no—
36#13108061—22no—
37D808D411yescharacteristic
38#13108059—41no—
39#13108058—21no—
40#13108058D411yescharacteristic
41#13108057—21no—
42C8×D101—21no—
43#13108049—21no—
44C2×Q8×C101—21no—
45C2×D4×C101—21no—
46Q16×C101—21no—
47Q16×C101D412yes—
48D8×C101—21no—
49D8×C101—21no—
50C2×C8×C101C2311yescharacteristic
51C16×C101—21no—
52C23×C101—41no—
53Q8×C101—22no—
54Q8×C101—41no—
55D4×C101—41no—
56D4×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×C101—81no—
76C22×C101—161no—
77C22×C101AGL(1,ℤ/8)11yescharacteristic
78C2×D101—21no—
79C2×D101—41no—
80C4×C101—42no—
81C4×C101#12011yescharacteristic
82C4×C101C2×D811yescharacteristic
83Dic101—21no—
84Dic101—41no—
85C2×C101—21no—
86C2×C101—161no—
87C2×C101#44711yescharacteristic
88D101—41no—
89D101—81no—
90#2193—1011nomaximal, Sylow
91C101#219311yescharacteristic, complemented, Sylow
92#578—1011no—
93#509—1011no—
94C2×SD32D10111yescharacteristic, complemented
95#472—1011no—
96#362—1011no—
97#359—1011no—
98#350—1011no—
992−1+4—2021no—
100#137—2021no—
101#137—2022no—
102AGL(1,ℤ/8)—2021no—
103#135—1011no—
104#135—2021no—
105C2×Q16—2021no—
106C2×Q16C2×D10111yescharacteristic
107C2×D8C2×D10111yescharacteristic
108#131—1011no—
109SD32—22no—
110SD32—2021no—
111D16—2021no—
112M32—1011no—
113C2×C16C2×D10111yescharacteristic
114#108—1011no—
115#100—2021no—
116#41—1011no—
117#41—4042no—
118#41—4041no—
119#41—2022no—
120#41—2021no—
121C2×Q8—21no—
122C2×Q8—4041no—
123C2×Q8—2022no—
124C2×D4—21no—
125Q16—21no—
126Q16—1011no—
127Q16—2022no—
128Q16C22⋊D10112yes—
129SD16—4041no—
130SD16—2022no—
131SD16—2021no—
132D8—21no—
133D8—21no—
134D8—1011no—
135D8—4041no—
136M16—1011no—
137M16—2021no—
138M16—2021no—
139C2×C8—2021no—
140C2×C8C22×D10111yescharacteristic
141C16—21no—
142C16—2021no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—1011no—
147Q8—4042no—
148Q8—2021no—
149D4—41no—
150D4—41no—
151D4—1011no—
152D4—4042no—
153D4—4041no—
154D4—2021no—
155D4—2021no—
156C2×C4—41no—
157C2×C4—4042no—
158C2×C4—4042no—
159C2×C4—4041no—
160C2×C4—2021no—
161C2×C4D4×D10111yescharacteristic
162C8—4041no—
163C8—2021no—
164C8D4×D10111yescharacteristic
165C8C2×C22⋊D10111yescharacteristic
166C22—81no—
167C22—161no—
168C22—4041no—
169C22—2021no—
170C22#1569227911yescharacteristic
171C4—42no—
172C4—4041no—
173C4—2021no—
174C4#1569222311yescharacteristic
175C4D8×D10111yescharacteristic
176C2—21no—
177C2—161no—
178C2—8081no—
179C2—4041no—
180C2#2026530911yescharacteristic
subgroupG/H
centerC2#20265309
commutator, cosocleC2×C8×C101C23
FrattiniC2×C8C22×D101
FittingC2×SD32×C101C2
socleC2×C101#447
hypercenterC2×SD32D101
hypocenterC101#2193
LCSG ▷ C2×C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #20265990C2semidirect
2. #20265613C2semidirect
3. #20265444C2semidirect
4. #20264993C2semidirect
5. #20264985C2semidirect
6. #20264960C2semidirect
7. C2×SD32×C101C2semidirect
91. C101#2193semidirect
94. C2×SD32D101semidirect

Maximal subgroups

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

subgroupindex
#202659902
#202656132
#202654442
#202649932
#202649852
#202649602
C2×SD32×C1012
#2193101