Finite Group Databasebeta

← #30637889

Subgroups — #30637889

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#22550601C211yesmaximal, characteristic
2#22550228C211yesmaximal, characteristic
3#22550172C211yesmaximal, characteristic
4#22550172C211yesmaximal, characteristic
5#22549606C211yesmaximal, characteristic
6#22549606C211yesmaximal, characteristic
7#332×C127C211yesmaximal, characteristic
8#16861209C2211yescharacteristic
9#16861207—21no—
10#16861200—21no—
11#16861199—22no—
12Q8×Dic127—21no—
13C4×Dic254C2211yescharacteristic
14C4×Dic254C2211yescharacteristic
15#16861174—21no—
16#16861143—21no—
17#16861143—21no—
18#16861134—21no—
19#16861134—21no—
20#16861132—22no—
21C4×C127⋊C8C2211yescharacteristic
22C4⋊Q8×C127C2211yescharacteristic
23C4⋊C8×C127C2211yescharacteristic
24C4⋊C8×C127C2211yescharacteristic
25C2×Dic254—21no—
26C2×Dic254D411yescharacteristic
27C2×Dic254D411yescharacteristic
28C2×C127⋊C8—21no—
29C4⋊Dic127—22no—
30C4⋊Dic127—21no—
31C4⋊Dic127—21no—
32C4⋊Dic127D411yescharacteristic
33C4⋊Dic127D411yescharacteristic
34Dic127⋊C4—22no—
35Dic127⋊C4—22no—
36Dic127⋊C4—21no—
37Dic127⋊C4—21no—
38C4×Dic127—22no—
39C4×Dic127—21no—
40C4×Dic127—21no—
41C2×Q8×C127—21no—
42C2×C8×C127—21no—
43C2×C8×C127—21no—
44C4⋊C4×C127—21no—
45C4⋊C4×C127D412yes—
46C42×C127C2311yescharacteristic
47Dic254—21no—
48Dic254—21no—
49Dic254—21no—
50Dic254—42no—
51Dic254Q1612yes—
52C2×Dic127—21no—
53C2×Dic127—21no—
54C2×Dic127—21no—
55C2×Dic127—21no—
56C2×Dic127—41no—
57C127⋊C8—41no—
58Q8×C127—41no—
59Q8×C127—41no—
60C2×C4×C127—22no—
61C2×C4×C127C2×D411yescharacteristic
62C2×C4×C127C2×D411yescharacteristic
63C2×C4×C127C2×D411yescharacteristic
64C8×C127—41no—
65C8×C127—41no—
66C22×C127#12011yescharacteristic
67C4×C127—21no—
68C4×C127—42no—
69C4×C127C2×Q1611yescharacteristic
70C4×C127#13511yescharacteristic
71C4×C127#13711yescharacteristic
72C4×C127#13711yescharacteristic
73Dic127—22no—
74Dic127—41no—
75Dic127—41no—
76Dic127—41no—
77Dic127—81no—
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#477—1271no—
87#332D12711yescharacteristic
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—1271no—
97C4×Q8—2541no—
98C4×Q8—2541no—
99#107—2541no—
100#107—2541no—
101C4⋊C8C2×D12711yescharacteristic
102C4⋊C8C2×D12711yescharacteristic
103#103—2541no—
104#103—2541no—
105#103—2542no—
106C4×C8—1271no—
107C2×Q8—21no—
108C2×Q8—1271no—
109C2×Q8—1271no—
110C2×Q8—2541no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—2541no—
114C4⋊C4—21no—
115C4⋊C4—1271no—
116C4⋊C4—1271no—
117C4⋊C4—2542no—
118C4⋊C4—2542no—
119C4⋊C4—2542no—
120C4⋊C4—2541no—
121C4⋊C4—2541no—
122C4⋊C4—2541no—
123C4⋊C4—2541no—
124C4⋊C4D50812yes—
125C42—2542no—
126C42—2541no—
127C42—2541no—
128C42C22×D12711yescharacteristic
129Q8—41no—
130Q8—41no—
131Q8—1272no—
132Q8—5082no—
133Q8—2541no—
134Q8—2541no—
135Q8—2541no—
136C2×C4—22no—
137C2×C4—5081no—
138C2×C4—2541no—
139C2×C4—2541no—
140C2×C4—2541no—
141C2×C4—2541no—
142C2×C4D4×D12711yescharacteristic
143C2×C4D4×D12711yescharacteristic
144C2×C4C2×D50811yescharacteristic
145C8—41no—
146C8—41no—
147C8—5081no—
148C22#1686117911yescharacteristic
149C4—21no—
150C4—42no—
151C4—10161no—
152C4—5081no—
153C4—5081no—
154C4—5081no—
155C4—2542no—
156C4Q16×D12711yescharacteristic
157C4#1686122811yescharacteristic
158C4#1686123811yescharacteristic
159C4#1686123811yescharacteristic
160C2#2255003311yescharacteristic
161C2#2255003911yescharacteristic
162C2#2255005111yescharacteristic
subgroupG/H
centerC22#16861179
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#332×C127C2
socle, prime radicalC22×C127#120
hypercenter#332D127
hypocenterC127#1636
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #332

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
#225506012
#225502282
#225501722
#225496062
#332×C1272
#1636127