Finite Group Databasebeta

← #30637739

Subgroups — #30637739

Order 16256.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#22550505C211yesmaximal, characteristic
2#22550207C211yesmaximal, characteristic
3#22550204C211yesmaximal, characteristic
4#22549808C211yesmaximal, characteristic
5#22549612C211yesmaximal, characteristic
6#22549601C211yesmaximal, characteristic
7#328×C127C211yesmaximal, characteristic
8#16861208—21no—
9#16861207—21no—
10#16861199—21no—
11#16861199—21no—
12#16861188C2211yescharacteristic
13#16861186—21no—
14#16861165—21no—
15C2×C4⋊Dic127—21no—
16C2×C4⋊Dic127C2211yescharacteristic
17C2×Dic127⋊C4C2211yescharacteristic
18#16861141—21no—
19#16861140—21no—
20#16861134—21no—
21#16861133—21no—
22C22⋊(C127⋊C8)C2211yescharacteristic
23C127⋊#95—21no—
24C22⋊Q8×C127C2211yescharacteristic
25C22⋊C8×C127C2211yescharacteristic
26#95×C127C2211yescharacteristic
27C2×Dic254—21no—
28C2×Dic254D411yescharacteristic
29C22×Dic127—21no—
30C22×Dic127D411yescharacteristic
31C22×Dic127D411yescharacteristic
32C2×C127⋊C8—21no—
33C4⋊Dic127—21no—
34C4⋊Dic127—21no—
35C4⋊Dic127—21no—
36C4⋊Dic127—42no—
37C4⋊Dic127D411yescharacteristic
38Dic127⋊C4—21no—
39Dic127⋊C4—21no—
40Dic127⋊C4—21no—
41Dic127⋊C4—21no—
42Dic127⋊C4—21no—
43Dic127⋊C4—21no—
44Dic127⋊C4—21no—
45C22⋊Dic127—21no—
46C4×Dic127—21no—
47C4×Dic127—21no—
48C2×Q8×C127D411yescharacteristic
49C22×C4×C127—21no—
50C22×C4×C127C2311yescharacteristic
51C2×C8×C127—21no—
52C4⋊C4×C127—21no—
53C4⋊C4×C127D411yescharacteristic
54C22⋊C4×C127—21no—
55Dic254—41no—
56Dic254—81no—
57C2×Dic127—21no—
58C2×Dic127—21no—
59C2×Dic127—21no—
60C2×Dic127—21no—
61C2×Dic127—21no—
62C2×Dic127—41no—
63C2×Dic127—41no—
64C2×Dic127—41no—
65C2×Dic127—41no—
66C2×Dic127SD1612yes—
67C127⋊C8—41no—
68C23×C127C2×D411yescharacteristic
69Q8×C127—41no—
70C2×C4×C127—22no—
71C2×C4×C127—21no—
72C2×C4×C127—21no—
73C2×C4×C127—41no—
74C2×C4×C127—41no—
75C2×C4×C127—41no—
76C2×C4×C127C2×D411yescharacteristic
77C2×C4×C127C2×D411yescharacteristic
78C8×C127—41no—
79C22×C127—21no—
80C22×C127—21no—
81C22×C127#12011yescharacteristic
82C22×C127C2×SD1611yescharacteristic
83C22×C127#13711yescharacteristic
84C4×C127—21no—
85C4×C127—21no—
86C4×C127—42no—
87C4×C127—41no—
88C4×C127—41no—
89Dic127—22no—
90Dic127—41no—
91Dic127—41no—
92Dic127—41no—
93Dic127—81no—
94C2×C127—21no—
95C2×C127—21no—
96C2×C127#44811yescharacteristic
97C2×C127#45611yescharacteristic
98C2×C127#45811yescharacteristic
99#1611—1271nomaximal, Sylow
100C127#161111yescharacteristic, complemented, Sylow
101#544—1271no—
102#483—1271no—
103#483—1271no—
104#398—1271no—
105#328—1271no—
106#328D12711yescharacteristic
107#324—1271no—
108C4⋊Q8—2541no—
109C4⋊Q8—2541no—
110#125—2541no—
111#125—2541no—
112C22⋊Q8—1271no—
113C22⋊Q8—2541no—
114C22⋊Q8C2×D12711yescharacteristic
115#117—2541no—
116C2×C4⋊C4—1271no—
117C2×C4⋊C4—1271no—
118C2×C4⋊C4—2541no—
119#106—2541no—
120#106—2541no—
121#103—2541no—
122#103—2541no—
123C22⋊C8—1271no—
124C22⋊C8C2×D12711yescharacteristic
125#95—2541no—
126#95C2×D12711yescharacteristic
127C2×Q8—1271no—
128C2×Q8—2541no—
129C2×Q8D50811yescharacteristic
130C22×C4—21no—
131C22×C4—1271no—
132C22×C4—1271no—
133C22×C4—2541no—
134C22×C4C22×D12711yescharacteristic
135C2×C8—21no—
136C2×C8—2541no—
137C4⋊C4—21no—
138C4⋊C4—1271no—
139C4⋊C4—5082no—
140C4⋊C4—2541no—
141C4⋊C4—2541no—
142C4⋊C4—2541no—
143C4⋊C4—2541no—
144C4⋊C4—2541no—
145C4⋊C4—2541no—
146C4⋊C4—2541no—
147C4⋊C4—2541no—
148C4⋊C4—2541no—
149C4⋊C4—2541no—
150C4⋊C4D50811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2541no—
153C42—2541no—
154C42—2541no—
155C23D4×D12711yescharacteristic
156Q8—41no—
157Q8—10161no—
158Q8—5081no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—1272no—
166C2×C4—5081no—
167C2×C4—5081no—
168C2×C4—5081no—
169C2×C4—5081no—
170C2×C4—2541no—
171C2×C4—2541no—
172C2×C4—2541no—
173C2×C4—2541no—
174C2×C4—2541no—
175C2×C4D4×D12711yescharacteristic
176C2×C4C2×D50811yescharacteristic
177C8—41no—
178C8—5081no—
179C22—21no—
180C22—21no—
181C22#1686117911yescharacteristic
182C22SD16×D12711yescharacteristic
183C22#1686124111yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—10161no—
190C4—5081no—
191C4—5081no—
192C4—5081no—
193C4—2542no—
194C2—21no—
195C2—21no—
196C2#2255001611yescharacteristic
197C2#2255006011yescharacteristic
198C2#2255006711yescharacteristic
subgroupG/H
centerC22#16861179
commutator, cosocleC22×C4×C127C23
FrattiniC22×C4C22×D127
Fitting#328×C127C2
socleC22×C127#120
prime radicalC23×C127C2×D4
hypercenter#328D127
hypocenterC127#1611
LCSG ▷ C22×C4×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
100. C127#1611semidirect

Maximal subgroups

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

subgroupindex
#225505052
#225502072
#225502042
#225498082
#225496122
#225496012
#328×C1272
#1611127