Finite Group Databasebeta

← #30638057

Subgroups — #30638057

Order 16256.

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
1C127⋊#564C211yesmaximal, characteristic
2#22550282C211yesmaximal, characteristic
3#22550244C211yesmaximal, characteristic
4#22549618C211yesmaximal, characteristic
5#22549617C211yesmaximal, characteristic
6#22549617C211yesmaximal, characteristic
7#501×C127C211yesmaximal, characteristic
8#16861201C2211yescharacteristic
9#16861201C2211yescharacteristic
10#16861200—21no—
11#16861200—21no—
12#16861199—21no—
13#16861199—21no—
14#16861199—21no—
15#16861199—21no—
16#16861142—21no—
17#16861140—21no—
18#16861133—21no—
19#16861133—21no—
20#16861120C2211yescharacteristic
21#16861120C2211yescharacteristic
22C4⋊Q8×C127C2211yescharacteristic
23#125×C127C2211yescharacteristic
24#107×C127—21no—
25#106×C127—21no—
26#97×C127C2211yescharacteristic
27C2×C127⋊C8—21no—
28C2×C127⋊C8—21no—
29C4⋊Dic127—21no—
30C4⋊Dic127—21no—
31C4⋊Dic127D411yescharacteristic
32C4⋊Dic127D411yescharacteristic
33C4⋊Dic127D411yescharacteristic
34C4⋊Dic127D411yescharacteristic
35Dic127⋊C4—21no—
36Dic127⋊C4—21no—
37Dic127⋊C4—21no—
38Dic127⋊C4—21no—
39Dic127⋊C4—21no—
40Dic127⋊C4—21no—
41Dic127⋊C4—21no—
42Dic127⋊C4—21no—
43C4×Dic127—21no—
44C4×Dic127—21no—
45C2×Q8×C127—21no—
46C2×C8×C127—21no—
47C4⋊C4×C127—21no—
48C4⋊C4×C127—21no—
49C4⋊C4×C127—21no—
50C4⋊C4×C127—21no—
51C4⋊C4×C127D411yescharacteristic
52C4⋊C4×C127D411yescharacteristic
53C42×C127C2311yescharacteristic
54C2×Dic127—21no—
55C2×Dic127—21no—
56C2×Dic127—21no—
57C2×Dic127—21no—
58C127⋊C8—22no—
59C127⋊C8—41no—
60Q8×C127—42no—
61C2×C4×C127—21no—
62C2×C4×C127—21no—
63C2×C4×C127—41no—
64C2×C4×C127C2×D411yescharacteristic
65C2×C4×C127C2×D411yescharacteristic
66C2×C4×C127C2×D411yescharacteristic
67C8×C127—22no—
68C22×C127#12011yescharacteristic
69C4×C127—21no—
70C4×C127—21no—
71C4×C127—21no—
72C4×C127—41no—
73C4×C127—41no—
74C4×C127—81no—
75Dic127—41no—
76Dic127—41no—
77Dic127—41no—
78Dic127—41no—
79C2×C127#45411yescharacteristic
80C2×C127#45611yescharacteristic
81C2×C127#45611yescharacteristic
82#1663—1271nomaximal, Sylow
83C127#166311yescharacteristic, complemented, Sylow
84#564—1271no—
85#501—1271no—
86#501D12711yescharacteristic
87#491—1271no—
88#330—1271no—
89#330—1271no—
90#330—1271no—
91C4⋊Q8C2×D12711yescharacteristic
92#125—1271no—
93#125—1271no—
94#125—2541no—
95#125—2541no—
96#125—2541no—
97#125—2541no—
98#125—2541no—
99#125—2541no—
100#125C2×D12711yescharacteristic
101#107—21no—
102#107—2541no—
103#106—21no—
104#106—2541no—
105#103—2541no—
106#103—2541no—
107#97—1271no—
108#97—1271no—
109#97C2×D12711yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—2541no—
113C2×C8—2541no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—1271no—
119C4⋊C4—1271no—
120C4⋊C4—1271no—
121C4⋊C4—1271no—
122C4⋊C4—2541no—
123C4⋊C4—2541no—
124C4⋊C4—2541no—
125C4⋊C4—2541no—
126C4⋊C4—2541no—
127C4⋊C4—2541no—
128C4⋊C4—2541no—
129C4⋊C4—2541no—
130C4⋊C4—2541no—
131C4⋊C4—2541no—
132C4⋊C4C22⋊D12711yescharacteristic
133C4⋊C4C22⋊D12711yescharacteristic
134C42—2541no—
135C42—2541no—
136C42C22×D12711yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—2541no—
142C2×C4—2541no—
143C2×C4—2541no—
144C2×C4—2541no—
145C2×C4D4×D12711yescharacteristic
146C2×C4D4×D12711yescharacteristic
147C2×C4C2×C22⋊D12711yescharacteristic
148C8—22no—
149C8—5081no—
150C8—2542no—
151C22#1686117711yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—5081no—
159C4—5081no—
160C4—5081no—
161C4—5081no—
162C2#2255004711yescharacteristic
163C2#2255005711yescharacteristic
164C2#2255005811yescharacteristic
subgroupG/H
centerC22#16861177
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#501×C127C2
socle, prime radicalC22×C127#120
hypercenter#501D127
hypocenterC127#1663
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
83. C127#1663semidirect

Maximal subgroups

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

subgroupindex
C127⋊#5642
#225502822
#225502442
#225496182
#225496172
#501×C1272
#1663127