Finite Group Databasebeta

← #27169725

Subgroups — #27169725

Order 12928.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#20265733C211yesmaximal, characteristic
2#20265129C212yesmaximal
3#20264919C211yesmaximal, characteristic, complemented
4#20264918C212yesmaximal, complemented
5#330×C101C211yesmaximal, characteristic, complemented
6C2×#13108057—22no—
7#15692254C412yes—
8#15692247C2211yescharacteristic
9#15692233—22no—
10#15692220—22no—
11#15692213C412yes—
12C42×D101C2211yescharacteristic
13#15692166C2212yes—
14C8×Dic101—22no—
15#125×C101C2211yescharacteristic
16#97×C101C2212yes—
17C2×Dic202—22no—
18C2×C4×D101C2×C411yescharacteristic
19C2×C4×D101D412yes—
20#13108057—28no—
21C2×#11717579—22no—
22C4⋊Dic101C2×C412yes—
23#13108053—22no—
24#13108053—22no—
25#13108051—22no—
26C4×Dic101—22no—
27C4×Dic101C2×C411yescharacteristic
28C4×Dic101D412yes—
29C2×C8×C101—22no—
30C4⋊C4×C101—22no—
31C4⋊C4×C101C2×C412yes—
32C42×C101C2311yescharacteristic
33C22×D101C22⋊C411yescharacteristic
34C2×C4×C101—22no—
35C2×C4×C101C22×C411yescharacteristic
36C2×C4×C101C2×D412yes—
37C2×Dic101—22no—
38C2×Dic101C22⋊C411yescharacteristic
39C2×Dic101C22⋊C412yes—
40C4×D101—22no—
41C4×D101—24no—
42Dic202—44no—
43C8×C101—24no—
44#11717579—24no—
45C22×C101C2×C22⋊C411yescharacteristic
46C2×D101—21no—
47C2×D101—22no—
48C4×C101—21no—
49C4×C101—22no—
50C4×C101—42no—
51Dic101—42no—
52Dic101#10112yes—
53Dic101#10414yes—
54C2×C101C2×#10111yescharacteristic
55C2×C101C2×#10412yes—
56D101—41no—
57#1526—1011nomaximal, Sylow
58C101#152611yescharacteristic, complemented, Sylow
59#533—1011no—
60C4×M16—1012no—
61#330—1011no—
62#330—1012no—
63#330D10111yescharacteristic, complemented
64C2×M16—2022no—
65C4⋊Q8—1012no—
66#125—1011no—
67#125C2×D10111yescharacteristic
68C22⋊Q8—2022no—
69C4×Q8—2022no—
70#117—1012no—
71C2×C42—1011no—
72#97—1012no—
73#97C2×D10112yes—
74C4×C8—2022no—
75C2×Q8—2022no—
76C22×C4—1011no—
77C22×C4—1012no—
78M16—2028no—
79C2×C8—22no—
80C2×C8—2022no—
81C4⋊C4—22no—
82C4⋊C4—1012no—
83C4⋊C4—2022no—
84C4⋊C4—2022no—
85C4⋊C4C4×D10112yes—
86C22⋊C4—2022no—
87C42—1011no—
88C42—1012no—
89C42—2022no—
90C42C22×D10111yescharacteristic
91C23—1011no—
92Q8—4044no—
93C2×C4—22no—
94C2×C4—1011no—
95C2×C4—1012no—
96C2×C4—2024no—
97C2×C4—2022no—
98C2×C4—2022no—
99C2×C4C2×C4×D10111yescharacteristic
100C2×C4D4×D10112yes—
101C8—24no—
102C8—2024no—
103C22—2021no—
104C22—2022no—
105C22C22⋊C4×D10111yescharacteristic
106C4—21no—
107C4—22no—
108C4—42no—
109C4—1012no—
110C4—1014no—
111C4—4042no—
112C2—4041no—
113C2#101×D10111yescharacteristic
114C2#104×D10112yes—
subgroupG/H
centerC22C22⋊C4×D101
commutatorC2×C4×C101C22×C4
FrattiniC42C22×D101
Fitting#330×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC22×D101C22⋊C4
cosocleC42×C101C23
hypercenter#330D101
hypocenterC101#1526
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20264919C2semidirect
4. #20264918C2semidirect
5. #330×C101C2semidirect
58. C101#1526semidirect
63. #330D101semidirect

Maximal subgroups

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

subgroupindex
#202657332
#202651292
#202649192
#202649182
#330×C1012
#1526101