Finite Group Databasebeta

← #27187436

Subgroups — #27187436

Order 12928.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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#20266163C212yesmaximal
2#20266088C214yesmaximal, complemented
3#20265753C211yesmaximal, characteristic
4D101⋊M16—22no—
5#15692316C2214yes—
6#15692315—22no—
7C2×#13108074C2211yescharacteristic
8C22×Dic202C411yescharacteristic
9#15692255C2212yes—
10#15692243C412yes—
11#15692239—22no—
12#15692235—22no—
13#117×C101C411yescharacteristic
14#13108084—42no—
15#13108083—24no—
16D101⋊C8—42no—
17#13108074—42no—
18C2×Dic202—21no—
19C2×Dic202—42no—
20C2×Dic202C2×C412yes—
21C2×Dic202C2311yescharacteristic
22C2×D404C2×C411yescharacteristic
23C2×C22⋊D101D412yes—
24C22×Dic101—21no—
25C2×C4×D101D412yes—
26C4⋊Dic101—24no—
27#13108051—24no—
28C22×C4×C101C2×C411yescharacteristic
29C4⋊C4×C101—21no—
30C22⋊C4×C101—21no—
31C42×C101C2×C412yes—
32C23×C101C22⋊C411yescharacteristic
33C22×D101C22⋊C412yes—
34C2×C4×C101—22no—
35C2×C4×C101—22no—
36C2×C4×C101C22⋊C411yescharacteristic
37C2×C4×C101C22×C411yescharacteristic
38C22⋊D101—42no—
39C2×Dic101—22no—
40C2×Dic101—42no—
41C2×Dic101C2×D412yes—
42D404—41no—
43C4×D101—22no—
44C4×D101—22no—
45Dic202—41no—
46Dic202—42no—
47Dic202—42no—
48#11717581—44no—
49C22×C101—21no—
50C22×C101—41no—
51C22×C101C2×C22⋊C411yescharacteristic
52C2×D101—22no—
53C2×D101—42no—
54C4×C101—21no—
55C4×C101—42no—
56C4×C101#9912yes—
57Dic101—22no—
58Dic101—42no—
59C2×C101—21no—
60C2×C101—41no—
61C2×C101C2×#9911yescharacteristic
62D101—42no—
63#2135—1011nomaximal, Sylow
64C101#213511yescharacteristic, complemented, Sylow
65#536—1011no—
66#413—1012no—
67#356—1014no—
68C2×#41—1011no—
69C22×Q8—1011no—
70C2×M16—2022no—
71C4⋊Q8—1012no—
72#124—1012no—
73#123—2022no—
74C22⋊Q8—2022no—
75#117#8793811yescharacteristic
76#101—1014no—
77#100—2022no—
78#41—4042no—
79C2×Q8—1011no—
80C2×Q8—1012no—
81C2×Q8—4042no—
82C2×Q8—2021no—
83C2×D4—1012no—
84C2×D4—1011no—
85C22×C4—1012no—
86C22×C4—2021no—
87C22×C4C2×#8793811yescharacteristic
88M16—4042no—
89M16—2024no—
90C2×C8—4042no—
91C4⋊C4—21no—
92C4⋊C4—2024no—
93C22⋊C4—21no—
94C22⋊C4—2024no—
95C42C2×#8793812yes—
96C23—1012no—
97C23C22⋊#8793811yescharacteristic
98Q8—4042no—
99Q8—4041no—
100Q8—4042no—
101D4—4041no—
102D4—4042no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—1012no—
106C2×C4—4042no—
107C2×C4—2022no—
108C2×C4—2022no—
109C2×C4—2022no—
110C2×C4C22⋊#8793811yescharacteristic
111C2×C4C22×#8793811yescharacteristic
112C8—4044no—
113C22—21no—
114C22—41no—
115C22—4042no—
116C22—2022no—
117C22C2×C22⋊#8793811yescharacteristic
118C4—21no—
119C4—42no—
120C4—4042no—
121C4—2022no—
122C4#1569231412yes—
123C2—21no—
124C2—41no—
125C2—4042no—
126C2C2×#1569231411yescharacteristic
subgroupG/H
centerC2C2×#15692314
commutatorC2×C4×C101C22×C4
FrattiniC2×C4C22×#87938
Fitting#117×C101C4
socleC2×C101C2×#99
prime radicalC2×#13108074C22
cosocleC2×Dic202C23
hypercenter#117#87938
hypocenterC101#2135
LCSG ▷ C2×C4×C101 ▷ C22×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #20266088C2semidirect
64. C101#2135semidirect

Maximal subgroups

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

subgroupindex
#202661632
#202660882
#202657532
#2135101