Finite Group Databasebeta

← #27170239

Subgroups — #27170239

Order 12928.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#20265901C211yesmaximal, characteristic, complemented
2#20265374C211yesmaximal, characteristic, complemented
3#20265369C211yesmaximal, characteristic
4#20264923C211yesmaximal, characteristic, complemented
5#20264909C211yesmaximal, characteristic, complemented
6#20264906C211yesmaximal, characteristic, complemented
7#486×C101C211yesmaximal, characteristic, complemented
8C2×#13108062—21no—
9C2×#13108059—21no—
10#15692250—22no—
11#15692244—21no—
12#15692235—21no—
13Q8×Dic101—21no—
14C4×Dic202C2211yescharacteristic
15C4×D404C2211yescharacteristic
16#15692213—21no—
17C4⋊#11717579C2211yescharacteristic
18C4⋊#11717579C2211yescharacteristic
19#15692176—21no—
20#15692176—21no—
21C4⋊Q8×C101C2211yescharacteristic
22#127×C101C2211yescharacteristic
23#102×C101—22no—
24C4×C8×C101C2211yescharacteristic
25C2×Dic202D411yescharacteristic
26C2×D404D411yescharacteristic
27C2×C4×D101—21no—
28#13108062—42no—
29#13108059—42no—
30C2×#11717579—21no—
31C2×#11717579—21no—
32C4⋊Dic101—22no—
33C4⋊Dic101D411yescharacteristic
34C4⋊Dic101D411yescharacteristic
35#13108053—21no—
36#13108051—22no—
37#13108051—22no—
38#13108051—21no—
39C4×Dic101—22no—
40C4×Dic101—21no—
41C2×Q8×C101—21no—
42C2×D4×C101—21no—
43C2×D4×C101—21no—
44C2×D4×C101—21no—
45C2×C8×C101—21no—
46C4⋊C4×C101—21no—
47C4⋊C4×C101D412yes—
48C42×C101C2311yescharacteristic
49C23×C101—41no—
50C22×D101—21no—
51Q8×C101—41no—
52Q8×C101—41no—
53D4×C101—42no—
54D4×C101—41no—
55D4×C101—41no—
56D4×C101—41no—
57D4×C101—41no—
58C2×C4×C101—22no—
59C2×C4×C101C2×D411yescharacteristic
60C2×C4×C101C2×D411yescharacteristic
61C2×C4×C101C2×D411yescharacteristic
62C2×Dic101—21no—
63C2×Dic101—21no—
64C2×Dic101—21no—
65D404—21no—
66D404—21no—
67C4×D101—41no—
68C4×D101—41no—
69Dic202—21no—
70Dic202—21no—
71C8×C101—41no—
72#11717579—41no—
73#11717579—41no—
74C22×C101—81no—
75C22×C101—81no—
76C22×C101—81no—
77C22×C101#12011yescharacteristic
78C2×D101—41no—
79C2×D101—41no—
80C2×D101—41no—
81C4×C101—21no—
82C4×C101—42no—
83C4×C101#13511yescharacteristic
84C4×C101#13511yescharacteristic
85C4×C101AGL(1,ℤ/8)11yescharacteristic
86C4×C101AGL(1,ℤ/8)11yescharacteristic
87Dic101—41no—
88Dic101—41no—
89Dic101—41no—
90C2×C101—161no—
91C2×C101#44911yescharacteristic
92C2×C101#44911yescharacteristic
93C2×C101#45411yescharacteristic
94D101—81no—
95#1628—1011nomaximal, Sylow
96C101#162811yescharacteristic, complemented, Sylow
97#556—1011no—
98#486D10111yescharacteristic, complemented
99#460—1011no—
100#459—1011no—
101#332—1011no—
102Q8⋊C8—1011no—
103D4⋊C8—1011no—
104C2×SD16—2021no—
105C2×D8—2021no—
106C4⋊Q8C2×D10111yescharacteristic
107#127C2×D10111yescharacteristic
108#126—2022no—
109#124—2021no—
110C22⋊Q8—2021no—
111C4×Q8—1011no—
112C4×Q8—2021no—
113C4×D4—1011no—
114#117—2021no—
115C4⋊C8—1011no—
116C4⋊C8—1011no—
117#102—22no—
118#102—2021no—
119#102—2021no—
120C4×C8C2×D10111yescharacteristic
121C2×Q8—21no—
122C2×Q8—1011no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—1011no—
127C22×C4—2021no—
128SD16—4042no—
129D8—4042no—
130C2×C8—21no—
131C2×C8—2021no—
132C2×C8—2021no—
133C4⋊C4—21no—
134C4⋊C4—1011no—
135C4⋊C4—1011no—
136C4⋊C4—2022no—
137C4⋊C4—2021no—
138C4⋊C4C22⋊D10112yes—
139C22⋊C4—2022no—
140C22⋊C4—2022no—
141C22⋊C4—2021no—
142C42—2022no—
143C42—2021no—
144C42C22×D10111yescharacteristic
145C23—41no—
146C23—2021no—
147Q8—41no—
148Q8—41no—
149Q8—2021no—
150Q8—2021no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—2021no—
157D4—2021no—
158C2×C4—22no—
159C2×C4—4041no—
160C2×C4—4041no—
161C2×C4—2021no—
162C2×C4—2021no—
163C2×C4—2021no—
164C2×C4D4×D10111yescharacteristic
165C2×C4D4×D10111yescharacteristic
166C2×C4C2×C22⋊D10111yescharacteristic
167C8—41no—
168C8—4041no—
169C8—4041no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—4041no—
174C22—4041no—
175C22—4041no—
176C22#1569222311yescharacteristic
177C4—21no—
178C4—42no—
179C4—4041no—
180C4—4041no—
181C4—4041no—
182C4#1569227411yescharacteristic
183C4#1569227611yescharacteristic
184C4#1569227911yescharacteristic
185C4#1569228211yescharacteristic
186C2—161no—
187C2—8081no—
188C2#2026531911yescharacteristic
189C2#2026532111yescharacteristic
190C2#2026534911yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#486×C101C2
socleC22×C101#120
prime radical#20265369C2
hypercenter#486D101
hypocenterC101#1628
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20265901C2semidirect
2. #20265374C2semidirect
4. #20264923C2semidirect
5. #20264909C2semidirect
6. #20264906C2semidirect
7. #486×C101C2semidirect
96. C101#1628semidirect
98. #486D101semidirect

Maximal subgroups

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

subgroupindex
#202659012
#202653742
#202653692
#202649232
#202649092
#202649062
#486×C1012
#1628101