Finite Group Databasebeta

← #30637758

Subgroups — #30637758

Order 16256.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#22550471C211yesmaximal, characteristic
2#22550211C211yesmaximal, characteristic, complemented
3#22549814C211yesmaximal, characteristic, complemented
4#22549614C211yesmaximal, characteristic, complemented
5#22549610C211yesmaximal, characteristic
6#22549601C211yesmaximal, characteristic, complemented
7#481×C127C211yesmaximal, characteristic
8#16861202—21no—
9#16861199—21no—
10#16861190—21no—
11#16861190—21no—
12#16861188C2211yescharacteristic
13#16861186—21no—
14D4×Dic127—21no—
15C2×Dic127⋊C4C2211yescharacteristic
16#16861142—21no—
17#16861132—21no—
18C22⋊(C127⋊C8)C2211yescharacteristic
19C127⋊#95—21no—
20C127⋊#95—21no—
21C127⋊#95C2211yescharacteristic
22#121×C127C2211yescharacteristic
23C2×C4⋊C4×C127C2211yescharacteristic
24#106×C127—21no—
25#102×C127—21no—
26C22⋊C8×C127C2211yescharacteristic
27C2×Dic254D411yescharacteristic
28C22×Dic127—21no—
29C22×Dic127—21no—
30C22×Dic127D411yescharacteristic
31C22×Dic127D411yescharacteristic
32C2×C127⋊C8—21no—
33C4⋊Dic127—21no—
34C4⋊Dic127D411yescharacteristic
35Dic127⋊C4—21no—
36Dic127⋊C4—21no—
37Dic127⋊C4—21no—
38Dic127⋊C4—21no—
39Dic127⋊C4—21no—
40C22⋊Dic127—21no—
41C22⋊Dic127—21no—
42C22⋊Dic127—21no—
43C22⋊Dic127—21no—
44C4×Dic127—21no—
45C2×D4×C127—21no—
46C2×D4×C127D411yescharacteristic
47C22×C4×C127—21no—
48C22×C4×C127C2311yescharacteristic
49C2×C8×C127—21no—
50C4⋊C4×C127—21no—
51C4⋊C4×C127—21no—
52C4⋊C4×C127D411yescharacteristic
53C22⋊C4×C127—21no—
54Dic254—41no—
55C2×Dic127—21no—
56C2×Dic127—21no—
57C2×Dic127—21no—
58C2×Dic127—21no—
59C2×Dic127—21no—
60C2×Dic127—21no—
61C2×Dic127—41no—
62C2×Dic127—41no—
63C2×Dic127—41no—
64C2×Dic127—41no—
65C2×Dic127—81no—
66C127⋊C8—41no—
67C23×C127—21no—
68C23×C127C2×D411yescharacteristic
69D4×C127—41no—
70D4×C127—41no—
71D4×C127—41no—
72C2×C4×C127—21no—
73C2×C4×C127—41no—
74C2×C4×C127—42no—
75C2×C4×C127—41no—
76C2×C4×C127C2×D411yescharacteristic
77C2×C4×C127C2×D411yescharacteristic
78C8×C127—41no—
79C22×C127—21no—
80C22×C127—21no—
81C22×C127—41no—
82C22×C127—41no—
83C22×C127—41no—
84C22×C127#12011yescharacteristic
85C22×C127#13511yescharacteristic
86C22×C127#13711yescharacteristic
87C4×C127—21no—
88C4×C127—21no—
89C4×C127—41no—
90C4×C127—81no—
91Dic127—41no—
92Dic127—41no—
93Dic127—41no—
94Dic127—41no—
95Dic127—81no—
96C2×C127—21no—
97C2×C127—21no—
98C2×C127—81no—
99C2×C127#45211yescharacteristic
100C2×C127#45411yescharacteristic
101C2×C127#45811yescharacteristic
102#1615—1271nomaximal, Sylow
103C127#161511yescharacteristic, complemented, Sylow
104#539—1271no—
105#484—1271no—
106#481D12711yescharacteristic
107#400—1271no—
108#328—1271no—
109#327—1271no—
110#324—1271no—
111#126—2541no—
112#125—2541no—
113#123—2541no—
114#123—2541no—
115C22⋊Q8—1271no—
116C22⋊Q8—2541no—
117#121C2×D12711yescharacteristic
118C4×D4—2541no—
119C2×C4⋊C4—1271no—
120C2×C4⋊C4C2×D12711yescharacteristic
121#107—2541no—
122#106—21no—
123#103—2541no—
124#102—21no—
125C22⋊C8—1271no—
126C22⋊C8C2×D12711yescharacteristic
127#95—1271no—
128#95—2541no—
129#95—2541no—
130C2×Q8—1271no—
131C2×D4—21no—
132C2×D4C22⋊D12711yescharacteristic
133C22×C4—21no—
134C22×C4—1271no—
135C22×C4—1271no—
136C22×C4—2541no—
137C22×C4—2541no—
138C22×C4C22×D12711yescharacteristic
139C2×C8—21no—
140C2×C8—2541no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—1271no—
144C4⋊C4—2541no—
145C4⋊C4—2541no—
146C4⋊C4—2541no—
147C4⋊C4—2541no—
148C4⋊C4—2541no—
149C4⋊C4—2541no—
150C4⋊C4C22⋊D12711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2541no—
153C22⋊C4—2541no—
154C22⋊C4—2541no—
155C22⋊C4—2541no—
156C42—2541no—
157C23—21no—
158C23D4×D12711yescharacteristic
159Q8—5081no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—10161no—
168C2×C4—5081no—
169C2×C4—5081no—
170C2×C4—5081no—
171C2×C4—5081no—
172C2×C4—2541no—
173C2×C4—2541no—
174C2×C4—2541no—
175C2×C4—2541no—
176C2×C4—2541no—
177C2×C4—2541no—
178C2×C4D4×D12711yescharacteristic
179C2×C4C2×C22⋊D12711yescharacteristic
180C8—41no—
181C8—5081no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#1686117711yescharacteristic
188C22#1686123011yescharacteristic
189C22#1686123811yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—10161no—
195C4—5081no—
196C4—5081no—
197C4—5081no—
198C4—5081no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#2255003511yescharacteristic
203C2#2255004711yescharacteristic
204C2#2255006511yescharacteristic
subgroupG/H
centerC22#16861177
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
Fitting#481×C127C2
socleC22×C127#120
prime radical#121×C127C22
hypercenter#481D127
hypocenterC127#1615
LCSG ▷ C22×C4×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #22550211C2semidirect
3. #22549814C2semidirect
4. #22549614C2semidirect
6. #22549601C2semidirect
103. C127#1615semidirect

Maximal subgroups

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

subgroupindex
#225504712
#225502112
#225498142
#225496142
#225496102
#225496012
#481×C1272
#1615127