Finite Group Databasebeta

← #30638030

Subgroups — #30638030

Order 16256.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#22550630C211yesmaximal, characteristic, complemented
2#22550265C211yesmaximal, characteristic
3#22550242C211yesmaximal, characteristic, complemented
4#22550241C211yesmaximal, characteristic, complemented
5#22549617C211yesmaximal, characteristic, complemented
6#22549615C211yesmaximal, characteristic, complemented
7#330×C127C211yesmaximal, characteristic, complemented
8C2×#14523237—21no—
9C2×D1016—21no—
10#16861208—21no—
11#16861206C2211yescharacteristic
12#16861204—21no—
13#16861204—21no—
14#16861201C2211yescharacteristic
15#16861197C2211yescharacteristic
16#16861194—21no—
17#16861189—21no—
18#16861187—21no—
19#16861131—21no—
20#16861131—21no—
21#16861129—21no—
22#16861129—21no—
23#16861120C2211yescharacteristic
24#125×C127C2211yescharacteristic
25#97×C127C2211yescharacteristic
26#97×C127C2211yescharacteristic
27C2×Dic254—21no—
28C2×Dic254D411yescharacteristic
29C2×D508—21no—
30C2×D508—21no—
31C2×D508—21no—
32C2×D508D411yescharacteristic
33C2×C4×D127—21no—
34#14523237—42no—
35D1016—42no—
36C2×C127⋊C8—21no—
37C4⋊Dic127—21no—
38C4⋊Dic127D411yescharacteristic
39C4⋊Dic127D411yescharacteristic
40Dic127⋊C4—21no—
41Dic127⋊C4—21no—
42Dic127⋊C4—21no—
43(C2×D127)⋊C4—21no—
44(C2×D127)⋊C4—21no—
45(C2×D127)⋊C4—21no—
46(C2×D127)⋊C4—21no—
47(C2×D127)⋊C4—21no—
48C4×Dic127—21no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C4⋊C4×C127—21no—
52C4⋊C4×C127—21no—
53C4⋊C4×C127D411yescharacteristic
54C4⋊C4×C127D411yescharacteristic
55C42×C127C2311yescharacteristic
56C22×D127—21no—
57C22×D127—41no—
58Dic254—41no—
59Dic254—81no—
60D508—41no—
61D508—41no—
62D508—41no—
63D508—42no—
64D508—42no—
65C2×Dic127—21no—
66C2×Dic127—21no—
67C2×Dic127—21no—
68C4×D127—81no—
69C127⋊C8—41no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127C2×D411yescharacteristic
73C2×C4×C127C2×D411yescharacteristic
74C2×C4×C127C2×D411yescharacteristic
75C8×C127—22no—
76C8×C127—41no—
77C22×C127#12011yescharacteristic
78C2×D127—41no—
79C2×D127—41no—
80C2×D127—41no—
81C2×D127—81no—
82C2×D127—81no—
83C2×D127—81no—
84C4×C127—21no—
85C4×C127—21no—
86C4×C127—21no—
87C4×C127—41no—
88C4×C127—41no—
89Dic127—41no—
90Dic127—41no—
91Dic127—41no—
92C2×C127#45311yescharacteristic
93C2×C127#45411yescharacteristic
94C2×C127#45411yescharacteristic
95D127—81no—
96D127—161no—
97#1657—1271nomaximal, Sylow
98C127#165711yescharacteristic, complemented, Sylow
99#563—1271no—
100#496—1271no—
101#490—1271no—
102#490—1271no—
103#330—1271no—
104#330D12711yescharacteristic, complemented
105#329—1271no—
106C2×SD16—2541no—
107C2×D8—2541no—
108C4⋊Q8—2541no—
109#127—1271no—
110#126—2541no—
111#126—2541no—
112#125—1271no—
113#125C2×D12711yescharacteristic
114#124—1271no—
115#123—2541no—
116C22⋊Q8—2541no—
117C22⋊Q8—2541no—
118#102—2541no—
119#102—2541no—
120#102—2541no—
121#102—2541no—
122#97—1271no—
123#97C2×D12711yescharacteristic
124#97C2×D12711yescharacteristic
125C2×Q8—1271no—
126C2×Q8—2541no—
127C2×D4—1271no—
128C2×D4—2541no—
129C2×D4—2541no—
130C2×D4—2541no—
131C22×C4—2541no—
132SD16—5082no—
133D8—5082no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—2541no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—1271no—
140C4⋊C4—1271no—
141C4⋊C4—2541no—
142C4⋊C4—2541no—
143C4⋊C4—2541no—
144C4⋊C4—2541no—
145C4⋊C4D50811yescharacteristic
146C4⋊C4D50811yescharacteristic
147C22⋊C4—2541no—
148C22⋊C4—2541no—
149C22⋊C4—2541no—
150C22⋊C4—2541no—
151C22⋊C4—2541no—
152C42—2541no—
153C42C22×D12711yescharacteristic
154C23—5081no—
155C23—2541no—
156Q8—10161no—
157Q8—5081no—
158D4—5081no—
159D4—5081no—
160D4—5082no—
161D4—5082no—
162D4—5081no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—10161no—
166C2×C4—2541no—
167C2×C4—2541no—
168C2×C4—2541no—
169C2×C4D4×D12711yescharacteristic
170C2×C4D4×D12711yescharacteristic
171C2×C4C2×D50811yescharacteristic
172C8—22no—
173C8—41no—
174C8—5081no—
175C22—10161no—
176C22—10161no—
177C22—10161no—
178C22—5081no—
179C22—5081no—
180C22—5081no—
181C22#1686117911yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—5081no—
188C4—5081no—
189C4—5081no—
190C2—20321no—
191C2—10161no—
192C2#2255004511yescharacteristic
193C2#2255005011yescharacteristic
194C2#2255005111yescharacteristic
subgroupG/H
centerC22#16861179
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#330×C127C2
socleC22×C127#120
prime radical#22550265C2
hypercenter#330D127
hypocenterC127#1657
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #22550630C2semidirect
3. #22550242C2semidirect
4. #22550241C2semidirect
5. #22549617C2semidirect
6. #22549615C2semidirect
7. #330×C127C2semidirect
98. C127#1657semidirect
104. #330D127semidirect

Maximal subgroups

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

subgroupindex
#225506302
#225502652
#225502422
#225502412
#225496172
#225496152
#330×C1272
#1657127