Finite Group Databasebeta

← #27186396

Subgroups — #27186396

Order 12928.

236 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 64 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#20266197C212yesmaximal
2#20266023C214yesmaximal
3C2×#15692220C211yesmaximal, characteristic
4#15692322—22no—
5C22⋊#11717581C2214yes—
6#15692310—22no—
7C22×Dic202C411yescharacteristic
8#15692220—22no—
9#15692220—22no—
10C2×#13108053C2212yes—
11C2×C4×Dic101C412yes—
12C2×C4×Dic101C2211yescharacteristic
13C2×C4⋊C4×C101C411yescharacteristic
14C2×#11717581—24no—
15C2×Dic202—22no—
16C2×Dic202—24no—
17C22×Dic101C2×C411yescharacteristic
18C22×Dic101C2×C412yes—
19C22×Dic101C2311yescharacteristic
20#13108053—24no—
21C4×Dic101—22no—
22C4×Dic101—22no—
23C4×Dic101D412yes—
24C4×Dic101D412yes—
25C22×C4×C101C2×C412yes—
26C22×C4×C101C2×C411yescharacteristic
27C4⋊C4×C101—22no—
28C23×C101C22×C411yescharacteristic
29C2×C4×C101—22no—
30C2×C4×C101—22no—
31C2×C4×C101—42no—
32C2×C4×C101C22⋊C412yes—
33C2×Dic101—22no—
34C2×Dic101—22no—
35C2×Dic101—22no—
36C2×Dic101—41no—
37C2×Dic101C22⋊C411yescharacteristic
38C2×Dic101C22⋊C411yescharacteristic
39C2×Dic101M1614yes—
40C2×Dic101C2×D412yes—
41Dic202—28no—
42#11717581—44no—
43C22×C101—21no—
44C22×C101—21no—
45C22×C101C2×C22⋊C411yescharacteristic
46C22×C101C2×M1612yes—
47C4×C101—22no—
48C4×C101—42no—
49Dic101—24no—
50Dic101—22no—
51Dic101—21no—
52Dic101#10112yes—
53C2×C101—22no—
54C2×C101#40711yescharacteristic
55C2×C101#41011yescharacteristic
56C2×C101C2×#10111yescharacteristic
57#1467—1011nomaximal, Sylow
58C101#146711yescharacteristic, complemented, Sylow
59C2×C4×Q8—1011no—
60#432—1012no—
61#324—1014no—
62C22×Q8—1011no—
63C4×Q8—2022no—
64C4×Q8—2022no—
65C2×C4⋊C4—1012no—
66C2×C4⋊C4#8793811yescharacteristic
67C2×C42—1011no—
68C2×C42—1012no—
69C4⋊C8—2022no—
70C22⋊C8—1014no—
71#97—2022no—
72C2×Q8—2024no—
73C2×Q8—2022no—
74C22×C4—1011no—
75C22×C4—1011no—
76C22×C4—1012no—
77C22×C4C2×#8793812yes—
78C22×C4C2×#8793811yescharacteristic
79C2×C8—2024no—
80C4⋊C4—22no—
81C4⋊C4—2024no—
82C42—1012no—
83C42—1012no—
84C42—2022no—
85C42—2022no—
86C23C22×#8793811yescharacteristic
87Q8—2028no—
88C2×C4—22no—
89C2×C4—22no—
90C2×C4—42no—
91C2×C4—1011no—
92C2×C4—1011no—
93C2×C4—1012no—
94C2×C4—1014no—
95C2×C4—4041no—
96C2×C4—2022no—
97C2×C4—2022no—
98C2×C4—2022no—
99C2×C4C22⋊#8793812yes—
100C8—4044no—
101C22—21no—
102C22—21no—
103C22C2×C22⋊#8793811yescharacteristic
104C22D101⋊M1612yes—
105C4—22no—
106C4—42no—
107C4—1012no—
108C4—2024no—
109C4—2022no—
110C4—2021no—
111C2—22no—
112C2#2026614911yescharacteristic
113C2#2026615711yescharacteristic
114C2D101⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#87938
commutator, prime radicalC23×C101C22×C4
FrattiniC23C22×#87938
FittingC2×C4⋊C4×C101C4
socleC22×C101C2×C22⋊C4
cosocleC22×Dic101C23
hypercenterC2×C4⋊C4#87938
hypocenterC101#1467
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
58. C101#1467semidirect

Maximal subgroups

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

subgroupindex
#202661972
#202660232
C2×#156922202
#1467101