Finite Group Databasebeta

← #27181065

Subgroups — #27181065

Order 12928.

414 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 133 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#20265688C211yesmaximal, characteristic
2C2×#15692214C211yesmaximal, characteristic, complemented
3#20265519C214yesmaximal, complemented
4#20265502C214yesmaximal, complemented
5#20265219C212yesmaximal, complemented
6#20265179C212yesmaximal, complemented
7#407×C101C211yesmaximal, characteristic, complemented
8C2×#13108074C2211yescharacteristic
9#15692238—21no—
10#15692234C2212yes—
11#15692229C2212yes—
12#15692224—21no—
13C4×C22⋊D101—22no—
14#15692214—22no—
15#15692214C2211yescharacteristic
16#15692214C2214yes—
17C2×C4⋊Dic101C2212yes—
18C2×C22⋊Dic101—21no—
19C2×C4×Dic101—21no—
20#15692189C2214yescomplemented
21#15692187C2214yescomplemented
22#15692180C2214yescomplemented
23#15692177C2214yescomplemented
24C23×C4×C101C2211yescharacteristic
25C2×M16×C101C2212yes—
26C22⋊C8×C101C2214yes—
27#13108074—24no—
28C2×Dic202C2311yescharacteristic
29C2×D404C2311yescharacteristic
30C2×C22⋊D101—21no—
31C2×C22⋊D101—22no—
32C22×Dic101—22no—
33C2×C4×D101—21no—
34C4⋊Dic101—22no—
35C4⋊Dic101C2314yes—
36C4⋊Dic101C2312yes—
37#13108053—22no—
38C22⋊Dic101—24no—
39C22⋊Dic101—21no—
40C22⋊Dic101—22no—
41#13108051—22no—
42C4×Dic101—24no—
43C4×Dic101—21no—
44C24×C101D411yescharacteristic
45C22×C4×C101—24no—
46C22×C4×C101D411yescharacteristic
47C22×C4×C101D412yes—
48C22×C4×C101C2312yes—
49C22×C4×C101C2311yescharacteristic
50M16×C101—24no—
51C2×C8×C101C2314yes—
52C23×C101—22no—
53C23×C101—42no—
54C23×C101C2×D412yes—
55C23×C101C2×D411yescharacteristic
56C22×D101—21no—
57C2×C4×C101—22no—
58C2×C4×C101—24no—
59C2×C4×C101—24no—
60C2×C4×C101C2×D412yes—
61C2×C4×C101C2×D411yescharacteristic
62C2×C4×C101#4114yes—
63C2×C4×C101C2411yescharacteristic
64C22⋊D101—44no—
65C22⋊D101—42no—
66C2×Dic101—24no—
67C2×Dic101—22no—
68C2×Dic101—21no—
69C2×Dic101—44no—
70D404—22no—
71C4×D101—42no—
72Dic202—22no—
73C8×C101—24no—
74C22×C101—22no—
75C22×C101—22no—
76C22×C101—22no—
77C22×C101—22no—
78C22×C101—44no—
79C22×C101#12312yes—
80C22×C101C22×D411yescharacteristic
81C2×D101—41no—
82C2×D101—42no—
83C4×C101—22no—
84C4×C101#12312yes—
85C4×C101C2×#4112yes—
86Dic101—41no—
87Dic101—44no—
88Dic101—42no—
89C2×C101—22no—
90C2×C101—42no—
91C2×C101C2×#12311yescharacteristic
92C2×C101#57512yes—
93D101—81no—
94#3093—1011nomaximal, Sylow
95C101#309311yescharacteristic, complemented, Sylow
96#525—1011no—
97C2×#117—1011no—
98#485—1014no—
99#482—1014no—
100#428—1012no—
101#417—1012no—
102#407D10111yescharacteristic, complemented
103C2×#41—1011no—
104C23×C4C2×D10111yescharacteristic
105C2×M16C2×D10112yes—
106#123—2021no—
107C22⋊Q8—1012no—
108#121—1012no—
109#120—2021no—
110C4×D4—2022no—
111#117—1014no—
112#117—1011no—
113#117—2022no—
114C2×C4⋊C4—1012no—
115C2×C22⋊C4—2021no—
116C2×C42—2021no—
117#107—1014no—
118#106—1014no—
119#103—1014no—
120#102—1014no—
121C22⋊C8C2×D10114yes—
122C24D40411yescharacteristic
123#41—2024no—
124C2×Q8—1011no—
125C2×D4—1011no—
126C2×D4—2022no—
127C2×D4—2021no—
128C22×C4—24no—
129C22×C4—2022no—
130C22×C4—2021no—
131C22×C4D40411yescharacteristic
132C22×C4D40412yes—
133C22×C4C22×D10112yes—
134C22×C4C22×D10111yescharacteristic
135M16—24no—
136C2×C8C22×D10114yes—
137C4⋊C4—1014no—
138C4⋊C4—1012no—
139C4⋊C4—2022no—
140C4⋊C4—2022no—
141C22⋊C4—2024no—
142C22⋊C4—2021no—
143C22⋊C4—2022no—
144C22⋊C4—2022no—
145C42—2024no—
146C42—2021no—
147C23—22no—
148C23—42no—
149C23—2021no—
150C23C2×D40412yes—
151C23C2×D40411yescharacteristic
152Q8—2022no—
153D4—4044no—
154D4—4042no—
155D4—2022no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—4044no—
160C2×C4—4042no—
161C2×C4—2024no—
162C2×C4—2022no—
163C2×C4—2021no—
164C2×C4C2×D40412yes—
165C2×C4C2×D40411yescharacteristic
166C2×C4#1310807314yes—
167C2×C4C23×D10111yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—4041no—
175C22—4042no—
176C22#1569223912yes—
177C22C22×D40411yescharacteristic
178C4—22no—
179C4—4041no—
180C4—4044no—
181C4—4042no—
182C4#1569223912yes—
183C4C2×#1310807312yes—
184C2—22no—
185C2—42no—
186C2—8081no—
187C2C2×#1569223911yescharacteristic
188C2#2026597712yes—
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#407×C101C2
socleC22×C101C22×D4
prime radical#20265688C2
hypercenter#407D101
hypocenterC101#3093
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#15692214C2semidirect
3. #20265519C2semidirect
4. #20265502C2semidirect
5. #20265219C2semidirect
6. #20265179C2semidirect
7. #407×C101C2semidirect
20. #15692189C22semidirect
21. #15692187C22semidirect
22. #15692180C22semidirect
23. #15692177C22semidirect
95. C101#3093semidirect
102. #407D101semidirect

Maximal subgroups

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

subgroupindex
#202656882
C2×#156922142
#202655192
#202655022
#202652192
#202651792
#407×C1012
#3093101