Finite Group Databasebeta

← #44549692

Subgroups — #44549692

Order 32128.

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
1C251⋊#564C211yesmaximal, characteristic
2#30632093C211yesmaximal, characteristic
3#30632055C211yesmaximal, characteristic
4#30631429C211yesmaximal, characteristic
5#30631428C211yesmaximal, characteristic
6#30631428C211yesmaximal, characteristic
7#501×C251C211yesmaximal, characteristic
8#22548707C2211yescharacteristic
9#22548707C2211yescharacteristic
10#22548706—21no—
11#22548706—21no—
12#22548705—21no—
13#22548705—21no—
14#22548705—21no—
15#22548705—21no—
16#22548648—21no—
17#22548646—21no—
18#22548639—21no—
19#22548639—21no—
20#22548626C2211yescharacteristic
21#22548626C2211yescharacteristic
22C4⋊Q8×C251C2211yescharacteristic
23#125×C251C2211yescharacteristic
24#107×C251—21no—
25#106×C251—21no—
26#97×C251C2211yescharacteristic
27C2×C251⋊C8—21no—
28C2×C251⋊C8—21no—
29C4⋊Dic251—21no—
30C4⋊Dic251—21no—
31C4⋊Dic251D411yescharacteristic
32C4⋊Dic251D411yescharacteristic
33C4⋊Dic251D411yescharacteristic
34C4⋊Dic251D411yescharacteristic
35Dic251⋊C4—21no—
36Dic251⋊C4—21no—
37Dic251⋊C4—21no—
38Dic251⋊C4—21no—
39Dic251⋊C4—21no—
40Dic251⋊C4—21no—
41Dic251⋊C4—21no—
42Dic251⋊C4—21no—
43C4×Dic251—21no—
44C4×Dic251—21no—
45C2×Q8×C251—21no—
46C2×C8×C251—21no—
47C4⋊C4×C251—21no—
48C4⋊C4×C251—21no—
49C4⋊C4×C251—21no—
50C4⋊C4×C251—21no—
51C4⋊C4×C251D411yescharacteristic
52C4⋊C4×C251D411yescharacteristic
53C42×C251C2311yescharacteristic
54C2×Dic251—21no—
55C2×Dic251—21no—
56C2×Dic251—21no—
57C2×Dic251—21no—
58C251⋊C8—22no—
59C251⋊C8—41no—
60Q8×C251—42no—
61C2×C4×C251—21no—
62C2×C4×C251—21no—
63C2×C4×C251—41no—
64C2×C4×C251C2×D411yescharacteristic
65C2×C4×C251C2×D411yescharacteristic
66C2×C4×C251C2×D411yescharacteristic
67C8×C251—22no—
68C22×C251#12011yescharacteristic
69C4×C251—21no—
70C4×C251—21no—
71C4×C251—21no—
72C4×C251—41no—
73C4×C251—41no—
74C4×C251—81no—
75Dic251—41no—
76Dic251—41no—
77Dic251—41no—
78Dic251—41no—
79C2×C251#45411yescharacteristic
80C2×C251#45611yescharacteristic
81C2×C251#45611yescharacteristic
82C251#166311yescharacteristic, complemented, Sylow
83#1663—2511nomaximal, Sylow
84#564—2511no—
85#501—2511no—
86#501D25111yescharacteristic
87#491—2511no—
88#330—2511no—
89#330—2511no—
90#330—2511no—
91C4⋊Q8C2×D25111yescharacteristic
92#125—5021no—
93#125—5021no—
94#125—5021no—
95#125—5021no—
96#125—5021no—
97#125—5021no—
98#125—2511no—
99#125—2511no—
100#125C2×D25111yescharacteristic
101#107—21no—
102#107—5021no—
103#106—21no—
104#106—5021no—
105#103—5021no—
106#103—5021no—
107#97—2511no—
108#97—2511no—
109#97C2×D25111yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—5021no—
113C2×C8—5021no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—5021no—
119C4⋊C4—5021no—
120C4⋊C4—5021no—
121C4⋊C4—5021no—
122C4⋊C4—5021no—
123C4⋊C4—5021no—
124C4⋊C4—5021no—
125C4⋊C4—5021no—
126C4⋊C4—5021no—
127C4⋊C4—5021no—
128C4⋊C4—2511no—
129C4⋊C4—2511no—
130C4⋊C4—2511no—
131C4⋊C4—2511no—
132C4⋊C4C22⋊D25111yescharacteristic
133C4⋊C4C22⋊D25111yescharacteristic
134C42—5021no—
135C42—5021no—
136C42C22×D25111yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—5021no—
142C2×C4—5021no—
143C2×C4—5021no—
144C2×C4—5021no—
145C2×C4D4×D25111yescharacteristic
146C2×C4D4×D25111yescharacteristic
147C2×C4C2×C22⋊D25111yescharacteristic
148C8—22no—
149C8—10041no—
150C8—5022no—
151C22#2254868311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—10041no—
159C4—10041no—
160C4—10041no—
161C4—10041no—
162C2#3063185811yescharacteristic
163C2#3063186811yescharacteristic
164C2#3063186911yescharacteristic
subgroupG/H
centerC22#22548683
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
Fitting#501×C251C2
socle, prime radicalC22×C251#120
hypercenter#501D251
hypocenterC251#1663
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
82. C251#1663semidirect

Maximal subgroups

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

subgroupindex
C251⋊#5642
#306320932
#306320552
#306314292
#306314282
#501×C2512
#1663251