Finite Group Databasebeta

← #27170173

Subgroups — #27170173

Order 12928.

202 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 53 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#20265808C211yesmaximal, characteristic
2#20265512C212yesmaximal
3#20264913C212yesmaximal
4#20264903C211yesmaximal, characteristic
5#400×C101C211yesmaximal, characteristic
6#15692254—22no—
7#15692246—22no—
8#15692234—21no—
9#15692234C2212yes—
10#15692214—21no—
11#15692188—22no—
12#15692178—22no—
13C22⋊#11717579C2212yes—
14C2×C4⋊C4×C101C2211yescharacteristic
15C2×C4⋊C4×C101C2211yescharacteristic
16#95×C101—21no—
17#95×C101—21no—
18#95×C101C2211yescharacteristic
19C2×Dic202—21no—
20C2×Dic202D412yes—
21C2×#11717579—22no—
22C4⋊Dic101—21no—
23C4⋊Dic101—21no—
24C4⋊Dic101—21no—
25C4⋊Dic101D412yes—
26#13108053—22no—
27#13108053—22no—
28C22⋊Dic101—22no—
29C4×Dic101—22no—
30C22×C4×C101—21no—
31C22×C4×C101—21no—
32C22×C4×C101D411yescharacteristic
33C22×C4×C101D411yescharacteristic
34C22×C4×C101C2311yescharacteristic
35C4⋊C4×C101—22no—
36C4⋊C4×C101—22no—
37C23×C101C2×D411yescharacteristic
38C2×C4×C101—21no—
39C2×C4×C101—21no—
40C2×C4×C101—21no—
41C2×C4×C101—41no—
42C2×C4×C101—41no—
43C2×C4×C101—41no—
44C2×C4×C101—41no—
45C2×C4×C101—42no—
46C2×C4×C101—41no—
47C2×C4×C101—41no—
48C2×C4×C101Q1612yes—
49C2×C4×C101C2×D412yes—
50C2×Dic101—22no—
51C2×Dic101—22no—
52Dic202—42no—
53Dic202—81no—
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—41no—
63C4×C101—81no—
64C4×C101—81no—
65Dic101—42no—
66Dic101—42no—
67C2×C101—21no—
68C2×C101—21no—
69C2×C101#45111yescharacteristic
70C2×C101#45411yescharacteristic
71C2×C101#45811yescharacteristic
72#1617—1011nomaximal, Sylow
73C101#161711yescharacteristic, complemented, Sylow
74#544—1011no—
75#484—1012no—
76#400D10111yescharacteristic
77#328—1012no—
78#324—1011no—
79C4⋊Q8—2022no—
80#125—2022no—
81C22⋊Q8—1012no—
82C22⋊Q8—2021no—
83#117—2021no—
84C2×C4⋊C4C2×D10111yescharacteristic
85C2×C4⋊C4C2×D10111yescharacteristic
86#107—2022no—
87#103—2022no—
88C22⋊C8—1012no—
89#95—21no—
90#95—21no—
91#95C2×D10111yescharacteristic
92C2×Q8—1012no—
93C2×Q8—2021no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D10111yescharacteristic
97C22×C4C22⋊D10111yescharacteristic
98C22×C4C22×D10111yescharacteristic
99C2×C8—2022no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—1012no—
103C4⋊C4—2022no—
104C4⋊C4—2021no—
105C4⋊C4—2021no—
106C4⋊C4—2021no—
107C4⋊C4—2022no—
108C22⋊C4—2022no—
109C42—2022no—
110C23C2×C22⋊D10111yescharacteristic
111Q8—8081no—
112Q8—4042no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—2022no—
124C2×C4—2022no—
125C2×C4#1310806412yes—
126C2×C4D4×D10112yes—
127C8—4042no—
128C22—21no—
129C22—21no—
130C22#1569222311yescharacteristic
131C22C2×#1310806411yescharacteristic
132C22#1569228511yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—4042no—
139C4—4042no—
140C2—21no—
141C2—21no—
142C2#2026533211yescharacteristic
143C2#2026534911yescharacteristic
144C2#2026536611yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC22×C4×C101C23
FrattiniC22×C4C22×D101
Fitting#400×C101C2
socleC22×C101#120
prime radicalC23×C101C2×D4
hypercenter#400D101
hypocenterC101#1617
LCSG ▷ C22×C4×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

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
#202658082
#202655122
#202649132
#202649032
#400×C1012
#1617101