Finite Group Databasebeta

← #45663363

Subgroups — #45663363

Order 32896.

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#30657366C211yesmaximal, characteristic
2#30657073C211yesmaximal, characteristic
3#30657070C211yesmaximal, characteristic
4#30656677C211yesmaximal, 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⋊Dic257C2211yescharacteristic
16C2×#16861597C2211yescharacteristic
17#22551526—21no—
18#22551525—21no—
19#22551517—21no—
20#22551516—21no—
21C22⋊#14523339C2211yescharacteristic
22#22551499—21no—
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⋊Dic257D411yescharacteristic
37#16861597—21no—
38#16861597—21no—
39#16861597—21no—
40#16861597—21no—
41#16861597—21no—
42#16861597—21no—
43#16861597—21no—
44C22⋊Dic257—21no—
45C4×Dic257—21no—
46C4×Dic257—21no—
47C2×Q8×C257D411yescharacteristic
48C22×C4×C257—21no—
49C22×C4×C257C2311yescharacteristic
50C2×C8×C257—21no—
51C4⋊C4×C257—21no—
52C4⋊C4×C257D411yescharacteristic
53C22⋊C4×C257—21no—
54Dic514—41no—
55Dic514—81no—
56C2×Dic257—21no—
57C2×Dic257—21no—
58C2×Dic257—21no—
59C2×Dic257—21no—
60C2×Dic257—21no—
61C2×Dic257—41no—
62C2×Dic257—42no—
63C2×Dic257—41no—
64C2×Dic257Q1612yes—
65#14523339—41no—
66C23×C257C2×D411yescharacteristic
67Q8×C257—41no—
68C2×C4×C257—21no—
69C2×C4×C257—21no—
70C2×C4×C257—41no—
71C2×C4×C257—41no—
72C2×C4×C257—41no—
73C2×C4×C257—41no—
74C2×C4×C257C2×D411yescharacteristic
75C2×C4×C257C2×D411yescharacteristic
76C8×C257—41no—
77C22×C257—21no—
78C22×C257—21no—
79C22×C257#12011yescharacteristic
80C22×C257C2×Q1611yescharacteristic
81C22×C257#13711yescharacteristic
82C4×C257—21no—
83C4×C257—21no—
84C4×C257—41no—
85C4×C257—41no—
86C4×C257—81no—
87Dic257—22no—
88Dic257—41no—
89Dic257—41no—
90Dic257—41no—
91Dic257—81no—
92C2×C257—21no—
93C2×C257—21no—
94C2×C257#45111yescharacteristic
95C2×C257#45411yescharacteristic
96C2×C257#45811yescharacteristic
97C257#161711yescharacteristic, complemented, Sylow
98#1617—2571nomaximal, Sylow
99#544—2571no—
100#484—2571no—
101#484—2571no—
102#400—2571no—
103#328—2571no—
104#328D25711yescharacteristic
105#324—2571no—
106C4⋊Q8—5141no—
107C4⋊Q8—5141no—
108#125—5141no—
109#125—5141no—
110C22⋊Q8—2571no—
111C22⋊Q8—5141no—
112C22⋊Q8C2×D25711yescharacteristic
113#117—5141no—
114C2×C4⋊C4—2571no—
115C2×C4⋊C4—2571no—
116#107—5141no—
117#107—5141no—
118#103—5141no—
119#103—5141no—
120C22⋊C8—2571no—
121C22⋊C8C2×D25711yescharacteristic
122#95—5141no—
123#95—5141no—
124#95C2×D25711yescharacteristic
125C2×Q8—2571no—
126C2×Q8—5141no—
127C2×Q8D102811yescharacteristic
128C22×C4—2571no—
129C22×C4—2571no—
130C22×C4—21no—
131C22×C4—5141no—
132C22×C4C22×D25711yescharacteristic
133C2×C8—21no—
134C2×C8—5141no—
135C4⋊C4—2571no—
136C4⋊C4—21no—
137C4⋊C4—5141no—
138C4⋊C4—5141no—
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⋊C4D102811yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—5141no—
150C42—5141no—
151C42—5141no—
152C23D4×D25711yescharacteristic
153Q8—41no—
154Q8—10281no—
155Q8—20561no—
156C2×C4—2572no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—5141no—
160C2×C4—5141no—
161C2×C4—5141no—
162C2×C4—5141no—
163C2×C4—5141no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—10281no—
169C2×C4—10282no—
170C2×C4—10281no—
171C2×C4D4×D25711yescharacteristic
172C2×C4C2×D102811yescharacteristic
173C8—41no—
174C8—10281no—
175C22—21no—
176C22—21no—
177C22#2255156211yescharacteristic
178C22Q16×D25711yescharacteristic
179C22#2255162111yescharacteristic
180C4—21no—
181C4—21no—
182C4—5142no—
183C4—41no—
184C4—41no—
185C4—10281no—
186C4—10281no—
187C4—10281no—
188C4—81no—
189C4—20561no—
190C2—21no—
191C2—21no—
192C2#3065689411yescharacteristic
193C2#3065691111yescharacteristic
194C2#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#1617
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
97. C257#1617semidirect

Maximal subgroups

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

subgroupindex
#306573662
#306570732
#306570702
#306566772
#306564732
#306564622
#328×C2572
#1617257