Finite Group Databasebeta

← #27170174

Subgroups — #27170174

Order 12928.

202 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 57 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#20265510C212yesmaximal
2#20265116C211yesmaximal, characteristic
3#20264914C212yesmaximal
4#20264903C211yesmaximal, characteristic
5#544×C101C211yesmaximal, characteristic
6C2×C4⋊Dic101C2211yescharacteristic
7#15692188—22no—
8#15692179—22no—
9C22⋊#11717579C2212yes—
10#15692162—21no—
11#15692162—21no—
12#15692162C2211yescharacteristic
13C4⋊Q8×C101—22no—
14#125×C101—22no—
15C22⋊Q8×C101—21no—
16C22⋊Q8×C101C2212yes—
17#117×C101—21no—
18C2×C4⋊C4×C101C2211yescharacteristic
19C22×Dic101—21no—
20C22×Dic101—21no—
21C2×#11717579—22no—
22C4⋊Dic101—22no—
23C2×Q8×C101—21no—
24C2×Q8×C101D412yes—
25C22×C4×C101D411yescharacteristic
26C22×C4×C101D411yescharacteristic
27C22×C4×C101C2311yescharacteristic
28C4⋊C4×C101—21no—
29C4⋊C4×C101—21no—
30C4⋊C4×C101—21no—
31C4⋊C4×C101—22no—
32C4⋊C4×C101—22no—
33C4⋊C4×C101—22no—
34C4⋊C4×C101D412yes—
35C22⋊C4×C101—22no—
36C42×C101—22no—
37C23×C101C2×D411yescharacteristic
38Q8×C101—42no—
39Q8×C101—81no—
40C2×C4×C101—21no—
41C2×C4×C101—21no—
42C2×C4×C101—22no—
43C2×C4×C101—22no—
44C2×C4×C101—21no—
45C2×C4×C101—41no—
46C2×C4×C101—41no—
47C2×C4×C101Q1612yes—
48C2×C4×C101C2×D412yes—
49C2×Dic101—41no—
50C2×Dic101—41no—
51C2×Dic101—42no—
52C2×Dic101—41no—
53C2×Dic101—41no—
54#11717579—42no—
55C22×C101—21no—
56C22×C101—21no—
57C22×C101#12011yescharacteristic
58C22×C101C2×Q1611yescharacteristic
59C22×C101#13711yescharacteristic
60C4×C101—22no—
61C4×C101—22no—
62C4×C101—42no—
63C4×C101—41no—
64C4×C101—42no—
65Dic101—81no—
66Dic101—81no—
67C2×C101—21no—
68C2×C101—21no—
69C2×C101#45111yescharacteristic
70C2×C101#45411yescharacteristic
71C2×C101#45811yescharacteristic
72#1617—1011nomaximal, Sylow
73C101#161711yescharacteristic, complemented, Sylow
74#544D10111yescharacteristic
75#484—1012no—
76#400—1011no—
77#328—1012no—
78#324—1011no—
79C4⋊Q8—22no—
80#125—22no—
81C22⋊Q8—21no—
82C22⋊Q8C2×D10112yes—
83#117—21no—
84C2×C4⋊C4—1011no—
85C2×C4⋊C4C2×D10111yescharacteristic
86#107—2022no—
87#103—2022no—
88C22⋊C8—1012no—
89#95—1011no—
90#95—2021no—
91#95—2021no—
92C2×Q8—21no—
93C2×Q8C22⋊D10112yes—
94C22×C4—2021no—
95C22×C4—2021no—
96C22×C4C22⋊D10111yescharacteristic
97C22×C4C22⋊D10111yescharacteristic
98C22×C4C22×D10111yescharacteristic
99C2×C8—2022no—
100C4⋊C4—21no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—22no—
106C4⋊C4—2022no—
107C4⋊C4C22⋊D10112yes—
108C22⋊C4—22no—
109C42—22no—
110C23C2×C22⋊D10111yescharacteristic
111Q8—42no—
112Q8—81no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—21no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—4041no—
121C2×C4—4041no—
122C2×C4—4042no—
123C2×C4—4041no—
124C2×C4—4041no—
125C2×C4#1310806412yes—
126C2×C4C2×C22⋊D10112yes—
127C8—4042no—
128C22—21no—
129C22—21no—
130C22#1569222411yescharacteristic
131C22C2×#1310806411yescharacteristic
132C22#1569228611yescharacteristic
133C4—22no—
134C4—22no—
135C4—42no—
136C4—41no—
137C4—42no—
138C4—8081no—
139C4—8081no—
140C2—21no—
141C2—21no—
142C2#2026533311yescharacteristic
143C2#2026535011yescharacteristic
144C2#2026536711yescharacteristic
subgroupG/H
centerC22#15692224
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#544×C101C2
socleC22×C101#120
prime radicalC23×C101C2×D4
hypercenter#544D101
hypocenterC101#1617
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
73. C101#1617semidirect

Maximal subgroups

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

subgroupindex
#202655102
#202651162
#202649142
#202649032
#544×C1012
#1617101