Finite Group Databasebeta

← #45663329

Subgroups — #45663329

Order 32896.

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#30657366C211yesmaximal, characteristic
2#30657068C211yesmaximal, characteristic
3#30657065C211yesmaximal, characteristic
4#30656669C211yesmaximal, characteristic
5#30656473C211yesmaximal, characteristic
6#30656462C211yesmaximal, characteristic
7#328×C257C211yesmaximal, characteristic
8#22551591—21no—
9#22551590—21no—
10#22551582—21no—
11#22551582—21no—
12#22551571C2211yescharacteristic
13#22551569—21no—
14#22551548—21no—
15C2×C4⋊Dic257—21no—
16C2×C4⋊Dic257C2211yescharacteristic
17C2×#16861597C2211yescharacteristic
18#22551524—21no—
19#22551523—21no—
20#22551517—21no—
21#22551516—21no—
22C22⋊#14523339C2211yescharacteristic
23#22551499—21no—
24C22⋊Q8×C257C2211yescharacteristic
25C22⋊C8×C257C2211yescharacteristic
26#95×C257C2211yescharacteristic
27C2×Dic514—21no—
28C2×Dic514D411yescharacteristic
29C22×Dic257—21no—
30C22×Dic257D411yescharacteristic
31C22×Dic257D411yescharacteristic
32C2×#14523339—21no—
33C4⋊Dic257—21no—
34C4⋊Dic257—21no—
35C4⋊Dic257—21no—
36C4⋊Dic257—42no—
37C4⋊Dic257D411yescharacteristic
38#16861597—21no—
39#16861597—21no—
40#16861597—21no—
41#16861597—21no—
42#16861597—21no—
43#16861597—21no—
44#16861597—21no—
45C22⋊Dic257—21no—
46C4×Dic257—21no—
47C4×Dic257—21no—
48C2×Q8×C257D411yescharacteristic
49C22×C4×C257—21no—
50C22×C4×C257C2311yescharacteristic
51C2×C8×C257—21no—
52C4⋊C4×C257—21no—
53C4⋊C4×C257D411yescharacteristic
54C22⋊C4×C257—21no—
55Dic514—41no—
56Dic514—81no—
57C2×Dic257—21no—
58C2×Dic257—21no—
59C2×Dic257—21no—
60C2×Dic257—21no—
61C2×Dic257—21no—
62C2×Dic257—41no—
63C2×Dic257—41no—
64C2×Dic257—41no—
65C2×Dic257—41no—
66C2×Dic257SD1612yes—
67#14523339—41no—
68C23×C257C2×D411yescharacteristic
69Q8×C257—41no—
70C2×C4×C257—22no—
71C2×C4×C257—21no—
72C2×C4×C257—21no—
73C2×C4×C257—41no—
74C2×C4×C257—41no—
75C2×C4×C257—41no—
76C2×C4×C257C2×D411yescharacteristic
77C2×C4×C257C2×D411yescharacteristic
78C8×C257—41no—
79C22×C257—21no—
80C22×C257—21no—
81C22×C257#12011yescharacteristic
82C22×C257C2×SD1611yescharacteristic
83C22×C257#13711yescharacteristic
84C4×C257—21no—
85C4×C257—21no—
86C4×C257—42no—
87C4×C257—41no—
88C4×C257—41no—
89Dic257—22no—
90Dic257—41no—
91Dic257—41no—
92Dic257—41no—
93Dic257—81no—
94C2×C257—21no—
95C2×C257—21no—
96C2×C257#44811yescharacteristic
97C2×C257#45611yescharacteristic
98C2×C257#45811yescharacteristic
99C257#161111yescharacteristic, complemented, Sylow
100#1611—2571nomaximal, Sylow
101#544—2571no—
102#483—2571no—
103#483—2571no—
104#398—2571no—
105#328—2571no—
106#328D25711yescharacteristic
107#324—2571no—
108C4⋊Q8—5141no—
109C4⋊Q8—5141no—
110#125—5141no—
111#125—5141no—
112C22⋊Q8—2571no—
113C22⋊Q8—5141no—
114C22⋊Q8C2×D25711yescharacteristic
115#117—5141no—
116C2×C4⋊C4—2571no—
117C2×C4⋊C4—2571no—
118C2×C4⋊C4—5141no—
119#106—5141no—
120#106—5141no—
121#103—5141no—
122#103—5141no—
123C22⋊C8—2571no—
124C22⋊C8C2×D25711yescharacteristic
125#95—5141no—
126#95C2×D25711yescharacteristic
127C2×Q8—2571no—
128C2×Q8—5141no—
129C2×Q8D102811yescharacteristic
130C22×C4—2571no—
131C22×C4—2571no—
132C22×C4—21no—
133C22×C4—5141no—
134C22×C4C22×D25711yescharacteristic
135C2×C8—21no—
136C2×C8—5141no—
137C4⋊C4—2571no—
138C4⋊C4—21no—
139C4⋊C4—5141no—
140C4⋊C4—5141no—
141C4⋊C4—5141no—
142C4⋊C4—5141no—
143C4⋊C4—5141no—
144C4⋊C4—5141no—
145C4⋊C4—5141no—
146C4⋊C4—5141no—
147C4⋊C4—5141no—
148C4⋊C4—5141no—
149C4⋊C4—10282no—
150C4⋊C4D102811yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5141no—
153C42—5141no—
154C42—5141no—
155C23D4×D25711yescharacteristic
156Q8—41no—
157Q8—10281no—
158Q8—20561no—
159C2×C4—2572no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—5141no—
164C2×C4—5141no—
165C2×C4—5141no—
166C2×C4—5141no—
167C2×C4—5141no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—10281no—
172C2×C4—10281no—
173C2×C4—10281no—
174C2×C4—10281no—
175C2×C4D4×D25711yescharacteristic
176C2×C4C2×D102811yescharacteristic
177C8—41no—
178C8—10281no—
179C22—21no—
180C22—21no—
181C22#2255156211yescharacteristic
182C22SD16×D25711yescharacteristic
183C22#2255162411yescharacteristic
184C4—21no—
185C4—21no—
186C4—5142no—
187C4—42no—
188C4—41no—
189C4—41no—
190C4—10281no—
191C4—10281no—
192C4—10281no—
193C4—20561no—
194C2—21no—
195C2—21no—
196C2#3065687711yescharacteristic
197C2#3065692111yescharacteristic
198C2#3065692811yescharacteristic
subgroupG/H
centerC22#22551562
commutator, cosocleC22×C4×C257C23
FrattiniC22×C4C22×D257
Fitting#328×C257C2
socleC22×C257#120
prime radicalC23×C257C2×D4
hypercenter#328D257
hypocenterC257#1611
LCSG ▷ C22×C4×C257 ▷ C22×C257 ▷ C257
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C257#1611semidirect

Maximal subgroups

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

subgroupindex
#306573662
#306570682
#306570652
#306566692
#306564732
#306564622
#328×C2572
#1611257