Finite Group Databasebeta

← #30637773

Subgroups — #30637773

Order 16256.

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

normal subgroups only

This group has 202 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#22550212C211yesmaximal, characteristic
3#22550209C211yesmaximal, characteristic
4#22549816C211yesmaximal, 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⋊Dic127C2211yescharacteristic
16C2×Dic127⋊C4C2211yescharacteristic
17#16861143—21no—
18#16861142—21no—
19#16861134—21no—
20#16861133—21no—
21C22⋊(C127⋊C8)C2211yescharacteristic
22C127⋊#95—21no—
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⋊Dic127D411yescharacteristic
37Dic127⋊C4—21no—
38Dic127⋊C4—21no—
39Dic127⋊C4—21no—
40Dic127⋊C4—21no—
41Dic127⋊C4—21no—
42Dic127⋊C4—21no—
43Dic127⋊C4—21no—
44C22⋊Dic127—21no—
45C4×Dic127—21no—
46C4×Dic127—21no—
47C2×Q8×C127D411yescharacteristic
48C22×C4×C127—21no—
49C22×C4×C127C2311yescharacteristic
50C2×C8×C127—21no—
51C4⋊C4×C127—21no—
52C4⋊C4×C127D411yescharacteristic
53C22⋊C4×C127—21no—
54Dic254—41no—
55Dic254—81no—
56C2×Dic127—21no—
57C2×Dic127—21no—
58C2×Dic127—21no—
59C2×Dic127—21no—
60C2×Dic127—21no—
61C2×Dic127—41no—
62C2×Dic127—42no—
63C2×Dic127—41no—
64C2×Dic127Q1612yes—
65C127⋊C8—41no—
66C23×C127C2×D411yescharacteristic
67Q8×C127—41no—
68C2×C4×C127—21no—
69C2×C4×C127—21no—
70C2×C4×C127—41no—
71C2×C4×C127—41no—
72C2×C4×C127—41no—
73C2×C4×C127—41no—
74C2×C4×C127C2×D411yescharacteristic
75C2×C4×C127C2×D411yescharacteristic
76C8×C127—41no—
77C22×C127—21no—
78C22×C127—21no—
79C22×C127#12011yescharacteristic
80C22×C127C2×Q1611yescharacteristic
81C22×C127#13711yescharacteristic
82C4×C127—21no—
83C4×C127—21no—
84C4×C127—41no—
85C4×C127—41no—
86C4×C127—81no—
87Dic127—22no—
88Dic127—41no—
89Dic127—41no—
90Dic127—41no—
91Dic127—81no—
92C2×C127—21no—
93C2×C127—21no—
94C2×C127#45111yescharacteristic
95C2×C127#45411yescharacteristic
96C2×C127#45811yescharacteristic
97#1617—1271nomaximal, Sylow
98C127#161711yescharacteristic, complemented, Sylow
99#544—1271no—
100#484—1271no—
101#484—1271no—
102#400—1271no—
103#328—1271no—
104#328D12711yescharacteristic
105#324—1271no—
106C4⋊Q8—2541no—
107C4⋊Q8—2541no—
108#125—2541no—
109#125—2541no—
110C22⋊Q8—1271no—
111C22⋊Q8—2541no—
112C22⋊Q8C2×D12711yescharacteristic
113#117—2541no—
114C2×C4⋊C4—1271no—
115C2×C4⋊C4—1271no—
116#107—2541no—
117#107—2541no—
118#103—2541no—
119#103—2541no—
120C22⋊C8—1271no—
121C22⋊C8C2×D12711yescharacteristic
122#95—2541no—
123#95—2541no—
124#95C2×D12711yescharacteristic
125C2×Q8—1271no—
126C2×Q8—2541no—
127C2×Q8D50811yescharacteristic
128C22×C4—21no—
129C22×C4—1271no—
130C22×C4—1271no—
131C22×C4—2541no—
132C22×C4C22×D12711yescharacteristic
133C2×C8—21no—
134C2×C8—2541no—
135C4⋊C4—21no—
136C4⋊C4—1271no—
137C4⋊C4—2541no—
138C4⋊C4—2541no—
139C4⋊C4—2541no—
140C4⋊C4—2541no—
141C4⋊C4—2541no—
142C4⋊C4—2541no—
143C4⋊C4—2541no—
144C4⋊C4—2541no—
145C4⋊C4—2541no—
146C4⋊C4—2541no—
147C4⋊C4D50811yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—2541no—
150C42—2541no—
151C42—2541no—
152C23D4×D12711yescharacteristic
153Q8—41no—
154Q8—10161no—
155Q8—5081no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—1272no—
163C2×C4—5082no—
164C2×C4—5081no—
165C2×C4—5081no—
166C2×C4—2541no—
167C2×C4—2541no—
168C2×C4—2541no—
169C2×C4—2541no—
170C2×C4—2541no—
171C2×C4D4×D12711yescharacteristic
172C2×C4C2×D50811yescharacteristic
173C8—41no—
174C8—5081no—
175C22—21no—
176C22—21no—
177C22#1686117911yescharacteristic
178C22Q16×D12711yescharacteristic
179C22#1686123811yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—10161no—
186C4—5081no—
187C4—5081no—
188C4—5081no—
189C4—2542no—
190C2—21no—
191C2—21no—
192C2#2255003311yescharacteristic
193C2#2255005011yescharacteristic
194C2#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#1617
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
98. C127#1617semidirect

Maximal subgroups

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

subgroupindex
#225505052
#225502122
#225502092
#225498162
#225496122
#225496012
#328×C1272
#1617127