Finite Group Databasebeta

← #30637886

Subgroups — #30637886

Order 16256.

188 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 55 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#22550604C211yesmaximal, characteristic
2#22550226C211yesmaximal, characteristic
3#22550168C211yesmaximal, characteristic
4#22549623C211yesmaximal, characteristic
5Q8⋊(C127⋊C8)C211yesmaximal, characteristic
6#22549606C211yesmaximal, characteristic
7#477×C127C211yesmaximal, characteristic
8#16861209C2211yescharacteristic
9#16861207—21no—
10#16861201—21no—
11#16861199—22no—
12C4×Dic254—21no—
13C4×Dic254C2211yescharacteristic
14#16861174—21no—
15#16861142—21no—
16C4⋊(C127⋊C8)C2211yescharacteristic
17#16861133—22no—
18#16861132—21no—
19C4×C127⋊C8C2211yescharacteristic
20C4⋊Q8×C127C2211yescharacteristic
21C4×Q8×C127C2211yescharacteristic
22#107×C127—21no—
23C4⋊C8×C127C2211yescharacteristic
24#103×C127—21no—
25C2×Dic254—21no—
26C2×Dic254D411yescharacteristic
27C2×C127⋊C8—21no—
28C2×C127⋊C8—21no—
29C4⋊Dic127—21no—
30C4⋊Dic127D412yes—
31C4⋊Dic127D411yescharacteristic
32Dic127⋊C4—22no—
33Dic127⋊C4—22no—
34Dic127⋊C4—22no—
35Dic127⋊C4—21no—
36C4×Dic127—22no—
37C4×Dic127—21no—
38C2×Q8×C127—21no—
39C2×Q8×C127D411yescharacteristic
40C2×C8×C127—21no—
41C4⋊C4×C127—21no—
42C4⋊C4×C127—21no—
43C4⋊C4×C127—21no—
44C4⋊C4×C127D411yescharacteristic
45C42×C127—21no—
46C42×C127C2311yescharacteristic
47Dic254—21no—
48Dic254—41no—
49Dic254—41no—
50Dic254Q1612yes—
51C2×Dic127—21no—
52C2×Dic127—21no—
53C2×Dic127—22no—
54C127⋊C8—41no—
55C127⋊C8—41no—
56Q8×C127—21no—
57Q8×C127—21no—
58Q8×C127—42no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—41no—
62C2×C4×C127C2×D411yescharacteristic
63C2×C4×C127C2×D411yescharacteristic
64C2×C4×C127C2×D411yescharacteristic
65C8×C127—41no—
66C22×C127#12011yescharacteristic
67C4×C127—21no—
68C4×C127—41no—
69C4×C127—41no—
70C4×C127—81no—
71C4×C127C2×Q1611yescharacteristic
72C4×C127#13511yescharacteristic
73C4×C127#13711yescharacteristic
74C4×C127#13711yescharacteristic
75Dic127—22no—
76Dic127—42no—
77Dic127—41no—
78C2×C127#45111yescharacteristic
79C2×C127#45211yescharacteristic
80C2×C127#45411yescharacteristic
81#1636—1271nomaximal, Sylow
82C127#163611yescharacteristic, complemented, Sylow
83#557—1271no—
84#487—1271no—
85#477—1271no—
86#477D12711yescharacteristic
87#332—1271no—
88Q8⋊C8—1271no—
89Q8⋊C8—1271no—
90C4⋊Q8—1271no—
91C4⋊Q8—2541no—
92C4⋊Q8C2×D12711yescharacteristic
93#125—2541no—
94#125—2542no—
95C4×Q8—1271no—
96C4×Q8—2541no—
97C4×Q8—2541no—
98C4×Q8C2×D12711yescharacteristic
99#107—21no—
100#107—2541no—
101C4⋊C8—1271no—
102C4⋊C8C2×D12711yescharacteristic
103#103—21no—
104#103—2541no—
105#103—2542no—
106C4×C8—1271no—
107C2×Q8—21no—
108C2×Q8—1271no—
109C2×Q8—2541no—
110C2×Q8C22⋊D12711yescharacteristic
111C2×C8—21no—
112C2×C8—2541no—
113C2×C8—2541no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—1272no—
118C4⋊C4—1271no—
119C4⋊C4—2542no—
120C4⋊C4—2542no—
121C4⋊C4—2542no—
122C4⋊C4—2541no—
123C4⋊C4—2541no—
124C4⋊C4C22⋊D12711yescharacteristic
125C42—21no—
126C42—2542no—
127C42—2541no—
128C42C22×D12711yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—42no—
132Q8—1272no—
133Q8—5081no—
134Q8—5081no—
135Q8—2541no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—2541no—
140C2×C4—2542no—
141C2×C4—2541no—
142C2×C4D4×D12711yescharacteristic
143C2×C4D4×D12711yescharacteristic
144C2×C4C2×C22⋊D12711yescharacteristic
145C8—41no—
146C8—5081no—
147C8—5081no—
148C22#1686117711yescharacteristic
149C4—21no—
150C4—41no—
151C4—41no—
152C4—81no—
153C4—5082no—
154C4—5081no—
155C4—2542no—
156C4Q16×D12711yescharacteristic
157C4#1686122911yescharacteristic
158C4#1686124011yescharacteristic
159C4#1686124111yescharacteristic
160C2#2255003011yescharacteristic
161C2#2255003611yescharacteristic
162C2#2255004711yescharacteristic
subgroupG/H
centerC22#16861177
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#477×C127C2
socle, prime radicalC22×C127#120
hypercenter#477D127
hypocenterC127#1636
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
82. C127#1636semidirect

Maximal subgroups

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

subgroupindex
#225506042
#225502262
#225501682
#225496232
Q8⋊(C127⋊C8)2
#225496062
#477×C1272
#1636127