Finite Group Databasebeta

← #27169757

Subgroups — #27169757

Order 12928.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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#125×D101C211yesmaximal, characteristic
2#20265232C212yesmaximal
3#20264919C211yesmaximal, characteristic, complemented
4#20264918C212yesmaximal, complemented
5#330×C101C211yesmaximal, characteristic, complemented
6#15692247C2211yescharacteristic
7#15692246C412yes—
8#15692245—22no—
9C4⋊C4×D101—22no—
10C4⋊C4×D101C412yes—
11C42×D101C2211yescharacteristic
12#15692184—22no—
13#15692167—22no—
14#15692166C2212yes—
15#125×C101C2211yescharacteristic
16#97×C101C2212yes—
17C2×C4×D101—22no—
18C2×C4×D101C2×C411yescharacteristic
19C2×C4×D101D412yes—
20C2×#11717579—22no—
21C4⋊Dic101—22no—
22C4⋊Dic101C2×C412yes—
23#13108053—22no—
24#13108053—22no—
25#13108053—22no—
26C4×Dic101C2×C411yescharacteristic
27C4×Dic101D412yes—
28C2×C8×C101—22no—
29C4⋊C4×C101—22no—
30C4⋊C4×C101C2×C412yes—
31C42×C101C2311yescharacteristic
32C22×D101C22⋊C411yescharacteristic
33C2×C4×C101—22no—
34C2×C4×C101C22×C411yescharacteristic
35C2×C4×C101C2×D412yes—
36C2×Dic101—22no—
37C2×Dic101C22⋊C412yes—
38C2×Dic101C22⋊C411yescharacteristic
39C4×D101—22no—
40C4×D101—42no—
41C4×D101—44no—
42C8×C101—42no—
43#11717579—42no—
44C22×C101C2×C22⋊C411yescharacteristic
45C2×D101—22no—
46C2×D101#10112yes—
47C4×C101—21no—
48C4×C101—22no—
49C4×C101—42no—
50Dic101—21no—
51Dic101—22no—
52Dic101—42no—
53C2×C101C2×#10111yescharacteristic
54C2×C101#42112yes—
55D101—22no—
56#1534—1011nomaximal, Sylow
57C101#153411yescharacteristic, complemented, Sylow
58C2×#125—1011no—
59#432—1012no—
60#330—1011no—
61#330—1012no—
62#330D10111yescharacteristic, complemented
63#125—1012no—
64#125—1011no—
65#125—2022no—
66#125C2×D10111yescharacteristic
67C2×C4⋊C4—1012no—
68C2×C4⋊C4—2022no—
69C2×C42—1011no—
70C4⋊C8—2022no—
71C22⋊C8—2022no—
72#97—1012no—
73#97C2×D10112yes—
74C22×C4—1012no—
75C22×C4—1011no—
76C22×C4—2022no—
77C2×C8—22no—
78C2×C8—2022no—
79C4⋊C4—22no—
80C4⋊C4—1012no—
81C4⋊C4—2022no—
82C4⋊C4—2022no—
83C4⋊C4—2022no—
84C4⋊C4—2022no—
85C4⋊C4C4×D10112yes—
86C42—1011no—
87C42—1012no—
88C42C22×D10111yescharacteristic
89C23—1011no—
90C2×C4—22no—
91C2×C4—1011no—
92C2×C4—1012no—
93C2×C4—4042no—
94C2×C4—4044no—
95C2×C4—2022no—
96C2×C4—2022no—
97C2×C4C2×C4×D10111yescharacteristic
98C2×C4D4×D10112yes—
99C8—42no—
100C8—4042no—
101C22—1012no—
102C22—2022no—
103C22C22⋊C4×D10111yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—4042no—
108C4—2021no—
109C4—2022no—
110C2—2022no—
111C2#101×D10111yescharacteristic
112C2#2026519212yes—
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#1534
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
57. C101#1534semidirect
62. #330D101semidirect

Maximal subgroups

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

subgroupindex
#125×D1012
#202652322
#202649192
#202649182
#330×C1012
#1534101