Finite Group Databasebeta

← #30638049

Subgroups — #30638049

Order 16256.

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

normal subgroups only

This group has 208 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#22550624C211yesmaximal, characteristic
2#22550286C211yesmaximal, characteristic, complemented
3#22550270C211yesmaximal, characteristic, complemented
4#22550236C211yesmaximal, characteristic, complemented
5#22549615C211yesmaximal, characteristic, complemented
6#22549615C211yesmaximal, characteristic, complemented
7#330×C127C211yesmaximal, characteristic, complemented
8C2×Dic508—21no—
9C2×#14523237—21no—
10#16861209C2211yescharacteristic
11#16861197C2211yescharacteristic
12#16861197C2211yescharacteristic
13#16861194—21no—
14#16861194—21no—
15#16861187—21no—
16#16861187—21no—
17#16861184—21no—
18#16861184—21no—
19#16861142—21no—
20#16861140—21no—
21#16861134—21no—
22#16861131—21no—
23#16861120C2211yescharacteristic
24#125×C127C2211yescharacteristic
25#97×C127C2211yescharacteristic
26#97×C127C2211yescharacteristic
27C2×Dic254—21no—
28C2×Dic254D411yescharacteristic
29C2×Dic254D411yescharacteristic
30C2×D508—21no—
31C2×D508—21no—
32C2×D508D411yescharacteristic
33C2×D508D411yescharacteristic
34C2×C4×D127—21no—
35C2×C4×D127—21no—
36Dic508—42no—
37#14523237—42no—
38C2×C127⋊C8—21no—
39C4⋊Dic127—21no—
40C4⋊Dic127—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—
48(C2×D127)⋊C4—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—21no—
58Dic254—41no—
59Dic254—41no—
60Dic254—41no—
61Dic254—41no—
62D508—41no—
63D508—41no—
64D508—81no—
65D508—81no—
66C2×Dic127—21no—
67C2×Dic127—21no—
68C2×Dic127—41no—
69C4×D127—81no—
70C4×D127—81no—
71C127⋊C8—22no—
72C2×C4×C127—21no—
73C2×C4×C127—21no—
74C2×C4×C127C2×D411yescharacteristic
75C2×C4×C127C2×D411yescharacteristic
76C2×C4×C127C2×D411yescharacteristic
77C8×C127—22no—
78C8×C127—41no—
79C22×C127#12011yescharacteristic
80C2×D127—41no—
81C2×D127—41no—
82C2×D127—41no—
83C2×D127—41no—
84C2×D127—41no—
85C2×D127—41no—
86C4×C127—21no—
87C4×C127—21no—
88C4×C127—21no—
89C4×C127—41no—
90C4×C127—41no—
91Dic127—41no—
92Dic127—41no—
93Dic127—81no—
94C2×C127#45311yescharacteristic
95C2×C127#45511yescharacteristic
96C2×C127#45611yescharacteristic
97D127—81no—
98D127—81no—
99#1661—1271nomaximal, Sylow
100C127#166111yescharacteristic, complemented, Sylow
101#562—1271no—
102#501—1271no—
103#497—1271no—
104#489—1271no—
105#330D12711yescharacteristic, complemented
106#329—1271no—
107#329—1271no—
108C2×Q16—2541no—
109C2×SD16—2541no—
110C4⋊Q8—1271no—
111#125C2×D12711yescharacteristic
112#124—1271no—
113#124—1271no—
114#123—2541no—
115#123—2541no—
116C22⋊Q8—2541no—
117C22⋊Q8—2541no—
118#121—2541no—
119#121—2541no—
120#107—2541no—
121#106—2541no—
122#103—2541no—
123#102—2541no—
124#97—1271no—
125#97C2×D12711yescharacteristic
126#97C2×D12711yescharacteristic
127C2×Q8—1271no—
128C2×Q8—1271no—
129C2×Q8—2541no—
130C2×D4—1271no—
131C2×D4—1271no—
132C2×D4—2541no—
133C2×D4—2541no—
134C22×C4—2541no—
135C22×C4—2541no—
136Q16—5082no—
137SD16—5082no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—2541no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2541no—
144C4⋊C4—2541no—
145C4⋊C4—2541no—
146C4⋊C4—2541no—
147C4⋊C4D50811yescharacteristic
148C4⋊C4D50811yescharacteristic
149C22⋊C4—2541no—
150C22⋊C4—2541no—
151C22⋊C4—2541no—
152C22⋊C4—2541no—
153C22⋊C4—2541no—
154C22⋊C4—2541no—
155C42C22×D12711yescharacteristic
156C23—2541no—
157C23—2541no—
158Q8—5081no—
159Q8—5081no—
160Q8—5081no—
161Q8—5081no—
162D4—10161no—
163D4—10161no—
164D4—5081no—
165D4—5081no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—10161no—
169C2×C4—10161no—
170C2×C4—5081no—
171C2×C4—2541no—
172C2×C4—2541no—
173C2×C4D4×D12711yescharacteristic
174C2×C4D4×D12711yescharacteristic
175C2×C4C2×D50811yescharacteristic
176C8—22no—
177C8—41no—
178C8—2542no—
179C22—5081no—
180C22—5081no—
181C22—5081no—
182C22—5081no—
183C22—5081no—
184C22—5081no—
185C22#1686117911yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—10161no—
192C4—5081no—
193C4—5081no—
194C2—10161no—
195C2—10161no—
196C2#2255004511yescharacteristic
197C2#2255005511yescharacteristic
198C2#2255006111yescharacteristic
subgroupG/H
centerC22#16861179
commutator, cosocleC42×C127C23
FrattiniC42C22×D127
Fitting#330×C127C2
socleC22×C127#120
prime radical#22550624C2
hypercenter#330D127
hypocenterC127#1661
LCSG ▷ C42×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #22550286C2semidirect
3. #22550270C2semidirect
4. #22550236C2semidirect
5. #22549615C2semidirect
6. #22549615C2semidirect
7. #330×C127C2semidirect
100. C127#1661semidirect
105. #330D127semidirect

Maximal subgroups

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

subgroupindex
#225506242
#225502862
#225502702
#225502362
#225496152
#330×C1272
#1661127