Finite Group Databasebeta

← #30649016

Subgroups — #30649016

Order 16256.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#22550353C211yesmaximal, characteristic, complemented
2#22550197C212yesmaximal, complemented
3#22550180C212yesmaximal, complemented
4#22550073C212yesmaximal, complemented
5#22550014C212yesmaximal, complemented
6#22549976C212yesmaximal, complemented
7C4×#14523236C212yesmaximal, complemented
8#22549937C211yesmaximal, characteristic, complemented
9#540×C127C211yesmaximal, characteristic
10C22×Dic254C2211yescharacteristic
11C2×#14523236C2212yes—
12C2×#14523236C2212yes—
13C4×Dic254C2212yes—
14C4×Dic254C2212yes—
15#16861174—22no—
16#16861168C2211yescharacteristic
17#16861165—22no—
18#16861142C2212yes—
19#16861140C2212yes—
20C4⋊(C127⋊C8)C2212yes—
21#16861132C2212yes—
22#16861132C2212yes—
23#16861130C2212yes—
24#16861130C2212yes—
25C22⋊(C127⋊C8)C2212yes—
26#16861120C2211yescharacteristic
27C4×C127⋊C8C2211yescharacteristic
28#127×C127C2211yescharacteristic
29#125×C127C2211yescharacteristic
30#123×C127—22no—
31#121×C127—22no—
32#121×C127C2212yes—
33C4×D4×C127C2212yes—
34#117×C127C2211yescharacteristic
35C2×Dic254—24no—
36C2×Dic254—21no—
37C2×Dic254C2312yes—
38C22×Dic127—21no—
39#14523236—24no—
40#14523236—24no—
41C2×C127⋊C8C2312yes—
42C2×C127⋊C8C2312yes—
43C4⋊Dic127C2312yes—
44Dic127⋊C4—22no—
45Dic127⋊C4—22no—
46C22⋊Dic127—21no—
47C4×Dic127—22no—
48C4×Dic127—22no—
49C4×Dic127—21no—
50C2×D4×C127—22no—
51C2×D4×C127—22no—
52C2×D4×C127C2312yes—
53C22×C4×C127—22no—
54C22×C4×C127C2311yescharacteristic
55C4⋊C4×C127—22no—
56C4⋊C4×C127D412yes—
57C4⋊C4×C127C2312yes—
58C22⋊C4×C127—22no—
59C22⋊C4×C127—22no—
60C22⋊C4×C127D412yes—
61C42×C127C2311yescharacteristic
62C42×C127C2311yescharacteristic
63Dic254—24no—
64Dic254—22no—
65Dic254#4114yes—
66C2×Dic127—24no—
67C2×Dic127—22no—
68C2×Dic127—22no—
69C127⋊C8—22no—
70C127⋊C8—22no—
71C23×C127—22no—
72C23×C127C2×D411yescharacteristic
73D4×C127—22no—
74D4×C127—22no—
75D4×C127—82no—
76D4×C127—82no—
77C2×C4×C127—22no—
78C2×C4×C127—22no—
79C2×C4×C127—82no—
80C2×C4×C127C2×D412yes—
81C2×C4×C127C2×D412yes—
82C2×C4×C127C2×D411yescharacteristic
83C2×C4×C127C2411yescharacteristic
84C22×C127—21no—
85C22×C127—22no—
86C22×C127—42no—
87C22×C127—42no—
88C22×C127—42no—
89C22×C127C22×D411yescharacteristic
90C4×C127—21no—
91C4×C127—22no—
92C4×C127—22no—
93C4×C127—42no—
94C4×C127C2×#4112yes—
95Dic127—24no—
96Dic127—42no—
97C2×C127—41no—
98C2×C127—82no—
99C2×C127#52511yescharacteristic
100C2×C127#57712yes—
101#3126—1271nomaximal, Sylow
102C127#312611yescharacteristic, complemented, Sylow
103#540D12711yescharacteristic
104#519—1271no—
105#482—1272no—
106#479—1272no—
107#460—1272no—
108#448—1272no—
109#440—1272no—
110C4×SD16—1272no—
111#433—1271no—
112C22×Q8—1271no—
113C2×SD16—1272no—
114C2×SD16—1272no—
115#127C2×D12711yescharacteristic
116#125C2×D12711yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D12712yes—
120C4×Q8—1272no—
121C4×Q8—1272no—
122C4×Q8—2542no—
123C4×D4C2×D12712yes—
124#117—1271no—
125#117—2542no—
126#117C2×D12711yescharacteristic
127#107—1272no—
128#106—1272no—
129C4⋊C8—1272no—
130#103—1272no—
131#103—1272no—
132#102—1272no—
133#102—1272no—
134C22⋊C8—1272no—
135#97—1271no—
136C4×C8—1271no—
137C2×Q8—1272no—
138C2×Q8—2544no—
139C2×Q8—2541no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D12712yes—
143C22×C4—22no—
144C22×C4—2541no—
145C22×C4C22×D12711yescharacteristic
146SD16—2544no—
147SD16—2544no—
148C2×C8—1272no—
149C2×C8—1272no—
150C4⋊C4—22no—
151C4⋊C4—1272no—
152C4⋊C4—2542no—
153C4⋊C4—2542no—
154C4⋊C4C22⋊D12712yes—
155C4⋊C4C22×D12712yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—2541no—
159C22⋊C4C22⋊D12712yes—
160C42—2541no—
161C42—2542no—
162C42—2542no—
163C42C22×D12711yescharacteristic
164C42C22×D12711yescharacteristic
165C23—22no—
166C23C2×C22⋊D12711yescharacteristic
167Q8—1274no—
168Q8—2544no—
169Q8—2542no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—2542no—
178C2×C4—2544no—
179C2×C4—2542no—
180C2×C4C2×C22⋊D12712yes—
181C2×C4C2×C22⋊D12712yes—
182C2×C4C2×C22⋊D12711yescharacteristic
183C2×C4C23×D12711yescharacteristic
184C8—2542no—
185C8—2542no—
186C22—21no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D12711yescharacteristic
192C4—21no—
193C4—22no—
194C4—22no—
195C4—42no—
196C4—5082no—
197C4—2544no—
198C4#41×D12712yes—
199C2—41no—
200C2—82no—
201C2#2255038311yescharacteristic
202C2#2255068712yes—
subgroupG/H
centerC22C22×C22⋊D127
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
Fitting, prime radical#540×C127C2
socleC22×C127C22×D4
hypercenter#540D127
hypocenterC127#3126
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #22550353C2semidirect
2. #22550197C2semidirect
3. #22550180C2semidirect
4. #22550073C2semidirect
5. #22550014C2semidirect
6. #22549976C2semidirect
7. C4×#14523236C2semidirect
8. #22549937C2semidirect
102. C127#3126semidirect

Maximal subgroups

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

subgroupindex
#225503532
#225501972
#225501802
#225500732
#225500142
#225499762
C4×#145232362
#225499372
#540×C1272
#3126127