Finite Group Databasebeta

← #27173144

Subgroups — #27173144

Order 12928.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#20265927C211yesmaximal, characteristic, complemented
2#20265367C212yesmaximal
3#20264972C211yesmaximal, characteristic, complemented
4#20264968C212yesmaximal, complemented
5#455×C101C211yesmaximal, characteristic
6#15692253—21no—
7#15692248—22no—
8#15692247—21no—
9#15692236—22no—
10#15692236C2212yes—
11#15692232—22no—
12#15692170—22no—
13#15692170C2212yes—
14H(5,𝔽2)×C101C2211yescharacteristic
15#137×C101—21no—
16#124×C101C2211yescharacteristic
17#104×C101—21no—
18#100×C101C2211yescharacteristic
19C2×Dic202—21no—
20C22×Dic101D412yes—
21C4⋊Dic101—21no—
22C4⋊Dic101—21no—
23#13108053—22no—
24#13108053—22no—
25#13108053—22no—
26#13108053—42no—
27C22⋊Dic101—22no—
28C22⋊Dic101—22no—
29C22⋊Dic101—42no—
30C22⋊Dic101D412yes—
31C4×Dic101—21no—
32#41×C101—21no—
33#41×C101—41no—
34C2×Q8×C101D411yescharacteristic
35C2×D4×C101—22no—
36C2×D4×C101—41no—
37C2×D4×C101C2311yescharacteristic
38Q16×C101—41no—
39SD16×C101—41no—
40M16×C101—21no—
41C22⋊C4×C101—22no—
42C42×C101D411yescharacteristic
43C23×C101—22no—
44C23×C101C2×D412yes—
45Q8×C101—21no—
46Q8×C101—41no—
47D4×C101—21no—
48D4×C101—41no—
49D4×C101—42no—
50D4×C101—41no—
51C2×C4×C101—22no—
52C2×C4×C101—21no—
53C2×C4×C101—21no—
54C2×C4×C101—41no—
55C2×C4×C101C2×D411yescharacteristic
56C2×Dic101—22no—
57C2×Dic101—22no—
58C2×Dic101—42no—
59C2×Dic101—42no—
60Dic202—81no—
61C8×C101—41no—
62C22×C101—22no—
63C22×C101—42no—
64C22×C101—41no—
65C22×C101—82no—
66C22×C101#12011yescharacteristic
67C4×C101—21no—
68C4×C101—41no—
69C4×C101—41no—
70C4×C101—41no—
71Dic101—42no—
72Dic101—42no—
73Dic101—82no—
74C2×C101—21no—
75C2×C101—42no—
76C2×C101—81no—
77C2×C101B(4,𝔽2)11yescharacteristic
78#2201—1011nomaximal, Sylow
79C101#220111yescharacteristic, complemented, Sylow
80#563—1011no—
81#458—1012no—
82#455D10111yescharacteristic
83#354—1011no—
84#352—1012no—
85H(5,𝔽2)C2×D10111yescharacteristic
86#137—21no—
87C4⋊Q8—2021no—
88#126—2022no—
89#125—2021no—
90#124C2×D10111yescharacteristic
91#123—1012no—
92#123—2022no—
93C22⋊Q8—2022no—
94#104—21no—
95#100C2×D10111yescharacteristic
96#99—1012no—
97#99—2022no—
98#41—21no—
99#41—41no—
100C2×Q8—2021no—
101C2×Q8C22⋊D10111yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D10111yescharacteristic
105C22×C4—1012no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—4042no—
110C4⋊C4—2022no—
111C4⋊C4—2022no—
112C4⋊C4—2021no—
113C4⋊C4—2021no—
114C4⋊C4—2022no—
115C22⋊C4—22no—
116C22⋊C4—1012no—
117C22⋊C4—4042no—
118C22⋊C4—2022no—
119C22⋊C4—2022no—
120C42—2021no—
121C42C22⋊D10111yescharacteristic
122C23—22no—
123C23D4×D10112yes—
124Q8—21no—
125Q8—41no—
126Q8—8081no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—4042no—
136C2×C4—4042no—
137C2×C4—2022no—
138C2×C4—2022no—
139C2×C4C2×C22⋊D10111yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#1569222311yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—8082no—
151C4—4042no—
152C4—4042no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#2026536311yescharacteristic
subgroupG/H
centerC2#20265363
commutator, cosocleC2×D4×C101C23
FrattiniC2×D4C22×D101
Fitting#455×C101C2
socleC2×C101B(4,𝔽2)
prime radicalH(5,𝔽2)×C101C22
hypercenter#455D101
hypocenterC101#2201
LCSG ▷ C2×D4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #20265927C2semidirect
3. #20264972C2semidirect
4. #20264968C2semidirect
79. C101#2201semidirect

Maximal subgroups

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

subgroupindex
#202659272
#202653672
#202649722
#202649682
#455×C1012
#2201101