Finite Group Databasebeta

← #30637888

Subgroups — #30637888

Order 16256.

188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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#22550228C211yesmaximal, characteristic
2#22550171C211yesmaximal, characteristic
3#22550171C211yesmaximal, characteristic
4#22549622C211yesmaximal, characteristic
5Q8⋊(C127⋊C8)C211yesmaximal, characteristic
6Q8⋊(C127⋊C8)C211yesmaximal, characteristic
7#557×C127C211yesmaximal, characteristic
8#16861209C2211yescharacteristic
9#16861142—21no—
10#16861142—21no—
11C4⋊(C127⋊C8)C2211yescharacteristic
12C4⋊(C127⋊C8)C2211yescharacteristic
13#16861133—21no—
14#16861133—21no—
15#16861132—22no—
16C4×C127⋊C8C2211yescharacteristic
17C4⋊Q8×C127—21no—
18C4⋊Q8×C127C2211yescharacteristic
19#125×C127—22no—
20#125×C127—21no—
21C4×Q8×C127—21no—
22C4×Q8×C127—21no—
23C4×Q8×C127C2211yescharacteristic
24C4×Q8×C127C2211yescharacteristic
25C2×Dic254—21no—
26C2×C127⋊C8—21no—
27C2×C127⋊C8—21no—
28C2×C127⋊C8—21no—
29C4⋊Dic127—21no—
30C4⋊Dic127—21no—
31C2×Q8×C127—21no—
32C2×Q8×C127D411yescharacteristic
33C2×Q8×C127D411yescharacteristic
34C4⋊C4×C127—22no—
35C4⋊C4×C127—22no—
36C4⋊C4×C127—22no—
37C4⋊C4×C127—21no—
38C4⋊C4×C127—21no—
39C4⋊C4×C127—21no—
40C4⋊C4×C127D411yescharacteristic
41C4⋊C4×C127D411yescharacteristic
42C4⋊C4×C127D412yes—
43C42×C127—22no—
44C42×C127—21no—
45C42×C127—21no—
46C42×C127C2311yescharacteristic
47Dic254—42no—
48C2×Dic127—41no—
49C127⋊C8—41no—
50C127⋊C8—41no—
51C127⋊C8—41no—
52Q8×C127—21no—
53Q8×C127—21no—
54Q8×C127—21no—
55Q8×C127—41no—
56Q8×C127—41no—
57Q8×C127Q1612yes—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—21no—
61C2×C4×C127—21no—
62C2×C4×C127—22no—
63C2×C4×C127C2×D411yescharacteristic
64C2×C4×C127C2×D411yescharacteristic
65C2×C4×C127C2×D411yescharacteristic
66C22×C127#12011yescharacteristic
67C4×C127—22no—
68C4×C127—21no—
69C4×C127—41no—
70C4×C127—42no—
71C4×C127—41no—
72C4×C127—41no—
73C4×C127C2×Q1611yescharacteristic
74C4×C127#13511yescharacteristic
75C4×C127#13711yescharacteristic
76C4×C127#13711yescharacteristic
77Dic127—81no—
78C2×C127#45111yescharacteristic
79C2×C127#45211yescharacteristic
80C2×C127#45411yescharacteristic
81#1636—1271nomaximal, Sylow
82C127#163611yescharacteristic, complemented, Sylow
83#557D12711yescharacteristic
84#487—1271no—
85#477—1271no—
86#477—1271no—
87#332—1271no—
88Q8⋊C8—1271no—
89Q8⋊C8—1271no—
90C4⋊Q8—21no—
91C4⋊Q8—1271no—
92C4⋊Q8C2×D12711yescharacteristic
93#125—22no—
94#125—21no—
95C4×Q8—21no—
96C4×Q8—21no—
97C4×Q8C2×D12711yescharacteristic
98C4×Q8C2×D12711yescharacteristic
99#107—2541no—
100#107—2541no—
101C4⋊C8—1271no—
102C4⋊C8—1271no—
103#103—2541no—
104#103—2541no—
105#103—2542no—
106C4×C8—1271no—
107C2×Q8—21no—
108C2×Q8—2541no—
109C2×Q8C22⋊D12711yescharacteristic
110C2×Q8C22⋊D12711yescharacteristic
111C2×C8—2541no—
112C2×C8—2541no—
113C2×C8—2541no—
114C4⋊C4—22no—
115C4⋊C4—22no—
116C4⋊C4—22no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—2541no—
121C4⋊C4—2541no—
122C4⋊C4C22⋊D12712yes—
123C4⋊C4C22⋊D12711yescharacteristic
124C4⋊C4C22⋊D12711yescharacteristic
125C42—22no—
126C42—21no—
127C42—21no—
128C42C22×D12711yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—21no—
132Q8—41no—
133Q8—41no—
134Q8—5082no—
135Q8#1452323812yes—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—5081no—
142C2×C4C2×C22⋊D12711yescharacteristic
143C2×C4C2×C22⋊D12711yescharacteristic
144C2×C4C2×C22⋊D12711yescharacteristic
145C8—5081no—
146C8—5081no—
147C8—5081no—
148C22#1686117811yescharacteristic
149C4—22no—
150C4—21no—
151C4—41no—
152C4—42no—
153C4—41no—
154C4—41no—
155C4—10161no—
156C4C2×#1452323811yescharacteristic
157C4#1686122911yescharacteristic
158C4#1686123911yescharacteristic
159C4#1686124011yescharacteristic
160C2#2255003211yescharacteristic
161C2#2255003811yescharacteristic
162C2#2255004911yescharacteristic
subgroupG/H
centerC22#16861178
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#557×C127C2
socle, prime radicalC22×C127#120
hypercenter#557D127
hypocenterC127#1636
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #557

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
#225502282
#225501712
#225496222
Q8⋊(C127⋊C8)2
#557×C1272
#1636127