Finite Group Databasebeta

← #27170459

Subgroups — #27170459

Order 12928.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C101⋊#564C211yesmaximal, characteristic
2#20265583C211yesmaximal, characteristic
3#20265545C211yesmaximal, characteristic
4#20264919C211yesmaximal, characteristic
5#20264918C211yesmaximal, characteristic
6#20264918C211yesmaximal, characteristic
7#501×C101C211yesmaximal, characteristic
8#15692247C2211yescharacteristic
9#15692247C2211yescharacteristic
10#15692246—21no—
11#15692246—21no—
12#15692245—21no—
13#15692245—21no—
14#15692245—21no—
15#15692245—21no—
16#15692188—21no—
17#15692186—21no—
18#15692179—21no—
19#15692179—21no—
20#15692166C2211yescharacteristic
21#15692166C2211yescharacteristic
22C4⋊Q8×C101C2211yescharacteristic
23#125×C101C2211yescharacteristic
24#107×C101—21no—
25#106×C101—21no—
26#97×C101C2211yescharacteristic
27C2×#11717579—21no—
28C2×#11717579—21no—
29C4⋊Dic101—21no—
30C4⋊Dic101—21no—
31C4⋊Dic101D411yescharacteristic
32C4⋊Dic101D411yescharacteristic
33C4⋊Dic101D411yescharacteristic
34C4⋊Dic101D411yescharacteristic
35#13108053—21no—
36#13108053—21no—
37#13108053—21no—
38#13108053—21no—
39#13108053—21no—
40#13108053—21no—
41#13108053—21no—
42#13108053—21no—
43C4×Dic101—21no—
44C4×Dic101—21no—
45C2×Q8×C101—21no—
46C2×C8×C101—21no—
47C4⋊C4×C101—21no—
48C4⋊C4×C101—21no—
49C4⋊C4×C101—21no—
50C4⋊C4×C101—21no—
51C4⋊C4×C101D411yescharacteristic
52C4⋊C4×C101D411yescharacteristic
53C42×C101C2311yescharacteristic
54Q8×C101—42no—
55C2×C4×C101—21no—
56C2×C4×C101—21no—
57C2×C4×C101—41no—
58C2×C4×C101C2×D411yescharacteristic
59C2×C4×C101C2×D411yescharacteristic
60C2×C4×C101C2×D411yescharacteristic
61C2×Dic101—21no—
62C2×Dic101—21no—
63C2×Dic101—21no—
64C2×Dic101—21no—
65C8×C101—22no—
66#11717579—22no—
67#11717579—41no—
68C22×C101#12011yescharacteristic
69C4×C101—21no—
70C4×C101—21no—
71C4×C101—21no—
72C4×C101—41no—
73C4×C101—41no—
74C4×C101—81no—
75Dic101—41no—
76Dic101—41no—
77Dic101—41no—
78Dic101—41no—
79C2×C101#45411yescharacteristic
80C2×C101#45611yescharacteristic
81C2×C101#45611yescharacteristic
82#1663—1011nomaximal, Sylow
83C101#166311yescharacteristic, complemented, Sylow
84#564—1011no—
85#501—1011no—
86#501D10111yescharacteristic
87#491—1011no—
88#330—1011no—
89#330—1011no—
90#330—1011no—
91C4⋊Q8C2×D10111yescharacteristic
92#125—1011no—
93#125—1011no—
94#125—2021no—
95#125—2021no—
96#125—2021no—
97#125—2021no—
98#125—2021no—
99#125—2021no—
100#125C2×D10111yescharacteristic
101#107—21no—
102#107—2021no—
103#106—21no—
104#106—2021no—
105#103—2021no—
106#103—2021no—
107#97—1011no—
108#97—1011no—
109#97C2×D10111yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—2021no—
113C2×C8—2021no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—1011no—
119C4⋊C4—1011no—
120C4⋊C4—1011no—
121C4⋊C4—1011no—
122C4⋊C4—2021no—
123C4⋊C4—2021no—
124C4⋊C4—2021no—
125C4⋊C4—2021no—
126C4⋊C4—2021no—
127C4⋊C4—2021no—
128C4⋊C4—2021no—
129C4⋊C4—2021no—
130C4⋊C4—2021no—
131C4⋊C4—2021no—
132C4⋊C4C22⋊D10111yescharacteristic
133C4⋊C4C22⋊D10111yescharacteristic
134C42—2021no—
135C42—2021no—
136C42C22×D10111yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—2021no—
142C2×C4—2021no—
143C2×C4—2021no—
144C2×C4—2021no—
145C2×C4D4×D10111yescharacteristic
146C2×C4D4×D10111yescharacteristic
147C2×C4C2×C22⋊D10111yescharacteristic
148C8—22no—
149C8—4041no—
150C8—2022no—
151C22#1569222311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—4041no—
159C4—4041no—
160C4—4041no—
161C4—4041no—
162C2#2026534811yescharacteristic
163C2#2026535811yescharacteristic
164C2#2026535911yescharacteristic
subgroupG/H
centerC22#15692223
commutator, cosocleC42×C101C23
FrattiniC42C22×D101
Fitting#501×C101C2
socle, prime radicalC22×C101#120
hypercenter#501D101
hypocenterC101#1663
LCSG ▷ C42×C101 ▷ C22×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
83. C101#1663semidirect

Maximal subgroups

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

subgroupindex
C101⋊#5642
#202655832
#202655452
#202649192
#202649182
#501×C1012
#1663101