Finite Group Databasebeta

← #27170764

Subgroups — #27170764

Order 12928.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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#20265573C211yesmaximal, characteristic
2#20265573C211yesmaximal, characteristic
3#20265556C211yesmaximal, characteristic
4#20265528C211yesmaximal, characteristic
5#20265527C211yesmaximal, characteristic
6#20264899C211yesmaximal, characteristic
7#498×C101C211yesmaximal, characteristic
8C2×#13108064—22no—
9#15692255C2211yescharacteristic
10#15692255C2211yescharacteristic
11#15692186—22no—
12#15692186—22no—
13#15692180—22no—
14#15692179—22no—
15C4×#11717579C2211yescharacteristic
16C4×#11717579C2211yescharacteristic
17C4⋊Q8×C101C2211yescharacteristic
18C4⋊Q8×C101C2211yescharacteristic
19#106×C101—22no—
20C4×C8×C101C2211yescharacteristic
21C2×Dic202—21no—
22C2×Dic202—21no—
23#13108064—44no—
24C2×#11717579D412yes—
25C2×#11717579D412yes—
26C4⋊Dic101—21no—
27C4⋊Dic101—21no—
28C4⋊Dic101—21no—
29C4⋊Dic101—21no—
30C2×Q8×C101—21no—
31C2×Q8×C101—21no—
32C2×C8×C101D412yes—
33C4⋊C4×C101—21no—
34C4⋊C4×C101—21no—
35C4⋊C4×C101—21no—
36C4⋊C4×C101—21no—
37C42×C101C2311yescharacteristic
38Q8×C101—42no—
39Q8×C101—42no—
40C2×C4×C101—41no—
41C2×C4×C101—41no—
42C2×C4×C101C2×D411yescharacteristic
43C2×C4×C101C2×D411yescharacteristic
44C2×C4×C101C2×D411yescharacteristic
45C2×Dic101—41no—
46C2×Dic101—41no—
47Dic202—42no—
48Dic202—42no—
49C8×C101—22no—
50#11717579—22no—
51#11717579SD1614yes—
52C22×C101#12711yescharacteristic
53C4×C101—81no—
54C4×C101—81no—
55C4×C101C2×SD1612yes—
56C4×C101#13712yes—
57C4×C101#13712yes—
58Dic101—81no—
59Dic101—81no—
60C2×C101#49211yescharacteristic
61C2×C101#49711yescharacteristic
62C2×C101#49711yescharacteristic
63#1716—1011nomaximal, Sylow
64C101#171611yescharacteristic, complemented, Sylow
65#498—1011no—
66#498—1011no—
67#498D10111yescharacteristic
68#494—1011no—
69#487—1011no—
70#487—1011no—
71#322—1011no—
72C2×Q16—2022no—
73C4⋊Q8—1011no—
74C4⋊Q8—1011no—
75C4⋊Q8C2×D10111yescharacteristic
76C4⋊Q8C2×D10111yescharacteristic
77#106—22no—
78#106—2022no—
79#106—2022no—
80#103—2022no—
81#103—2022no—
82C4×C8—1011no—
83C4×C8—1011no—
84C4×C8C2×D10111yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—2021no—
88C2×Q8—2021no—
89Q16—4044no—
90C2×C8—1012no—
91C2×C8—1012no—
92C2×C8C22⋊D10112yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—2021no—
98C4⋊C4—2021no—
99C4⋊C4—2021no—
100C4⋊C4—2021no—
101C42C22×D10111yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—4042no—
105Q8—4042no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—4041no—
109C2×C4—4041no—
110C2×C4D4×D10111yescharacteristic
111C2×C4D4×D10111yescharacteristic
112C2×C4C2×C22⋊D10111yescharacteristic
113C8—22no—
114C8—1014no—
115C8—2022no—
116C22#1569225111yescharacteristic
117C4—81no—
118C4—81no—
119C4—8081no—
120C4—8081no—
121C4SD16×D10112yes—
122C4#1569228412yes—
123C4#1569228612yes—
124C2#2026554811yescharacteristic
125C2#2026556811yescharacteristic
126C2#2026556911yescharacteristic
subgroupG/H
centerC22#15692251
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#498×C101C2
socle, prime radicalC22×C101#127
hypercenter#498D101
hypocenterC101#1716
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
64. C101#1716semidirect

Maximal subgroups

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

subgroupindex
#202655732
#202655562
#202655282
#202655272
#202648992
#498×C1012
#1716101