Finite Group Databasebeta

← #27186637

Subgroups — #27186637

Order 12928.

202 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 62 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#20266194C212yesmaximal
2#20266036C214yesmaximal, complemented
3#20265730C211yesmaximal, characteristic
4#15692322C2214yes—
5C22⋊#11717581—22no—
6C4×#11717581—22no—
7#15692254C2212yes—
8#15692246C412yes—
9#15692232—22no—
10C4×Dic202—22no—
11#15692214C411yescharacteristic
12C2×C4×Dic101C2211yescharacteristic
13#117×C101C411yescharacteristic
14C2×#11717581—24no—
15C2×Dic202—22no—
16C22×Dic101D412yes—
17C4⋊Dic101—22no—
18C4⋊Dic101C2×C412yes—
19#13108053—22no—
20#13108053—22no—
21C22⋊Dic101—21no—
22C4×Dic101—21no—
23C4×Dic101C2×C411yescharacteristic
24C4×Dic101D412yes—
25C4×Dic101C2311yescharacteristic
26C22×C4×C101C2×C411yescharacteristic
27C4⋊C4×C101C2×C412yes—
28C22⋊C4×C101—21no—
29C42×C101—21no—
30C23×C101C22⋊C411yescharacteristic
31C2×C4×C101—22no—
32C2×C4×C101—22no—
33C2×C4×C101C22⋊C411yescharacteristic
34C2×C4×C101C22×C411yescharacteristic
35C2×Dic101—24no—
36C2×Dic101—22no—
37C2×Dic101C22⋊C412yes—
38C2×Dic101C2×D412yes—
39Dic202—44no—
40#11717581—44no—
41C22×C101—21no—
42C22×C101—22no—
43C22×C101C2×C22⋊C411yescharacteristic
44C4×C101—21no—
45C4×C101—42no—
46C4×C101#10112yes—
47Dic101—22no—
48Dic101—42no—
49Dic101#13514yes—
50C2×C101—41no—
51C2×C101C2×#10111yescharacteristic
52C2×C101#41612yes—
53#1544—1011nomaximal, Sylow
54C101#154411yescharacteristic, complemented, Sylow
55#533—1011no—
56#431—1012no—
57#332—1014no—
58C4⋊Q8—1012no—
59#125—1012no—
60C22⋊Q8—2022no—
61C4×Q8—2022no—
62#117—1011no—
63#117#8793811yescharacteristic
64C2×C42—1011no—
65C4⋊C8—1014no—
66C22⋊C8—2022no—
67C4×C8—2022no—
68C2×Q8—2022no—
69C22×C4—1012no—
70C22×C4C2×#8793811yescharacteristic
71C2×C8—2024no—
72C4⋊C4—1012no—
73C4⋊C4—2022no—
74C4⋊C4—2022no—
75C4⋊C4—2022no—
76C4⋊C4C2×#8793812yes—
77C22⋊C4—21no—
78C22⋊C4—2021no—
79C42—21no—
80C42—1012no—
81C42—1011no—
82C42—1011no—
83C42—2021no—
84C23C22⋊#8793811yescharacteristic
85Q8—4044no—
86C2×C4—22no—
87C2×C4—22no—
88C2×C4—1012no—
89C2×C4—1012no—
90C2×C4—2024no—
91C2×C4—2022no—
92C2×C4C22⋊#8793811yescharacteristic
93C2×C4C22×#8793811yescharacteristic
94C8—4044no—
95C22—21no—
96C22—22no—
97C22C2×C22⋊#8793811yescharacteristic
98C4—21no—
99C4—42no—
100C4—1014no—
101C4—4042no—
102C4—2022no—
103C4#1569231612yes—
104C2—41no—
105C2C2×#1569231611yescharacteristic
106C2#2026616712yes—
subgroupG/H
centerC2×C4C22⋊#87938
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#117×C101C4
socleC22×C101C2×C22⋊C4
prime radicalC23×C101C22⋊C4
cosocleC4×Dic101C23
hypercenter#117#87938
hypocenterC101#1544
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #20266036C2semidirect
54. C101#1544semidirect

Maximal subgroups

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

subgroupindex
#202661942
#202660362
#202657302
#1544101