Finite Group Databasebeta

← #30640693

Subgroups — #30640693

Order 16256.

210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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#22550689C211yesmaximal, characteristic, complemented
2#22550312C211yesmaximal, characteristic, complemented
3#22550143C211yesmaximal, characteristic, complemented
4#22549692C211yesmaximal, characteristic, complemented
5#22549684C211yesmaximal, characteristic, complemented
6#22549659C211yesmaximal, characteristic, complemented
7C2×SD32×C127C211yesmaximal, characteristic, complemented
8#16861257—21no—
9#16861241—22no—
10#16861240—21no—
11#16861235—21no—
12#16861232—21no—
13#16861231C2211yescharacteristic
14Q16×D127—21no—
15#16861215C2211yescharacteristic
16#16861153—21no—
17#16861150—21no—
18#16861149C2211yescharacteristic
19#16861145C2211yescharacteristic
20#16861126—21no—
21C2×Q16×C127C2211yescharacteristic
22C2×D8×C127C2211yescharacteristic
23SD32×C127—22no—
24C2×C16×C127C2211yescharacteristic
25#14523249—22no—
26#14523249—41no—
27#14523248—21no—
28#14523248—42no—
29#14523248D411yescharacteristic
30Q8×D127—22no—
31Q8×D127—41no—
32Dic508D411yescharacteristic
33#14523238—22no—
34#14523237—21no—
35#14523236—41no—
36#14523235—22no—
37D1016D411yescharacteristic
38#14523233—41no—
39#14523232—21no—
40#14523232D411yescharacteristic
41#14523231—21no—
42C8×D127—21no—
43C127⋊C16—21no—
44C2×Q8×C127—21no—
45C2×D4×C127—21no—
46Q16×C127—21no—
47Q16×C127D412yes—
48D8×C127—21no—
49D8×C127—21no—
50C2×C8×C127C2311yescharacteristic
51C16×C127—21no—
52Dic254—21no—
53Dic254—42no—
54Dic254D811yescharacteristic
55D508—21no—
56D508—42no—
57D508D811yescharacteristic
58C22⋊D127—21no—
59C22⋊D127—41no—
60C4×D127—21no—
61C4×D127—42no—
62C4×D127—42no—
63C4×D127—41no—
64C127⋊C8—21no—
65C127⋊C8—41no—
66C23×C127—41no—
67Q8×C127—22no—
68Q8×C127—41no—
69D4×C127—41no—
70D4×C127—41no—
71C2×C4×C127—41no—
72C2×C4×C127C2×D411yescharacteristic
73C8×C127C2×D411yescharacteristic
74C8×C127C2×D411yescharacteristic
75C22×C127—81no—
76C22×C127—161no—
77C22×C127AGL(1,ℤ/8)11yescharacteristic
78C2×D127—21no—
79C2×D127—41no—
80C4×C127—42no—
81C4×C127#12011yescharacteristic
82C4×C127C2×D811yescharacteristic
83Dic127—21no—
84Dic127—41no—
85C2×C127—21no—
86C2×C127—161no—
87C2×C127#44711yescharacteristic
88D127—41no—
89D127—81no—
90#2193—1271nomaximal, Sylow
91C127#219311yescharacteristic, complemented, Sylow
92#578—1271no—
93#509—1271no—
94C2×SD32D12711yescharacteristic, complemented
95#472—1271no—
96#362—1271no—
97#359—1271no—
98#350—1271no—
992−1+4—2541no—
100#137—2541no—
101#137—2542no—
102AGL(1,ℤ/8)—2541no—
103#135—1271no—
104#135—2541no—
105C2×Q16—2541no—
106C2×Q16C2×D12711yescharacteristic
107C2×D8C2×D12711yescharacteristic
108#131—1271no—
109SD32—22no—
110SD32—2541no—
111D16—2541no—
112M32—1271no—
113C2×C16C2×D12711yescharacteristic
114#108—1271no—
115#100—2541no—
116#41—1271no—
117#41—5082no—
118#41—5081no—
119#41—2542no—
120#41—2541no—
121C2×Q8—21no—
122C2×Q8—5081no—
123C2×Q8—2542no—
124C2×D4—21no—
125Q16—21no—
126Q16—1271no—
127Q16—2542no—
128Q16C22⋊D12712yes—
129SD16—5081no—
130SD16—2542no—
131SD16—2541no—
132D8—21no—
133D8—21no—
134D8—1271no—
135D8—5081no—
136M16—1271no—
137M16—2541no—
138M16—2541no—
139C2×C8—2541no—
140C2×C8C22×D12711yescharacteristic
141C16—21no—
142C16—2541no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—1271no—
147Q8—5082no—
148Q8—2541no—
149D4—41no—
150D4—41no—
151D4—1271no—
152D4—5082no—
153D4—5081no—
154D4—2541no—
155D4—2541no—
156C2×C4—41no—
157C2×C4—5082no—
158C2×C4—5082no—
159C2×C4—5081no—
160C2×C4—2541no—
161C2×C4D4×D12711yescharacteristic
162C8—5081no—
163C8—2541no—
164C8D4×D12711yescharacteristic
165C8C2×C22⋊D12711yescharacteristic
166C22—81no—
167C22—161no—
168C22—5081no—
169C22—2541no—
170C22#1686123311yescharacteristic
171C4—42no—
172C4—5081no—
173C4—2541no—
174C4#1686117711yescharacteristic
175C4D8×D12711yescharacteristic
176C2—21no—
177C2—161no—
178C2—10161no—
179C2—5081no—
180C2#2255000811yescharacteristic
subgroupG/H
centerC2#22550008
commutator, cosocleC2×C8×C127C23
FrattiniC2×C8C22×D127
FittingC2×SD32×C127C2
socleC2×C127#447
hypercenterC2×SD32D127
hypocenterC127#2193
LCSG ▷ C2×C8×C127 ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #22550689C2semidirect
2. #22550312C2semidirect
3. #22550143C2semidirect
4. #22549692C2semidirect
5. #22549684C2semidirect
6. #22549659C2semidirect
7. C2×SD32×C127C2semidirect
91. C127#2193semidirect
94. C2×SD32D127semidirect

Maximal subgroups

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

subgroupindex
#225506892
#225503122
#225501432
#225496922
#225496842
#225496592
C2×SD32×C1272
#2193127