Finite Group Databasebeta

← #44549397

Subgroups — #44549397

Order 32128.

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#30632282C211yesmaximal, characteristic
2#30632023C211yesmaximal, characteristic, complemented
3#30632003C211yesmaximal, characteristic
4#30631627C211yesmaximal, characteristic, complemented
5#30631423C211yesmaximal, characteristic, complemented
6#30631412C211yesmaximal, characteristic, complemented
7#327×C251C211yesmaximal, characteristic
8#22548708—21no—
9#22548705—21no—
10#22548696—21no—
11#22548696—21no—
12#22548694C2211yescharacteristic
13#22548692—21no—
14D4×Dic251—21no—
15C2×C4⋊Dic251C2211yescharacteristic
16C2×Dic251⋊C4C2211yescharacteristic
17#22548649—21no—
18#22548646—21no—
19#22548640—21no—
20#22548636—21no—
21C22⋊(C251⋊C8)C2211yescharacteristic
22C251⋊#95—21no—
23C251⋊#95—21no—
24#121×C251C2211yescharacteristic
25C22⋊C8×C251C2211yescharacteristic
26#95×C251C2211yescharacteristic
27C2×Dic502D411yescharacteristic
28C22×Dic251—21no—
29C22×Dic251—21no—
30C22×Dic251D411yescharacteristic
31C22×Dic251D411yescharacteristic
32C2×C251⋊C8—21no—
33C4⋊Dic251—21no—
34C4⋊Dic251—21no—
35C4⋊Dic251—21no—
36C4⋊Dic251D411yescharacteristic
37Dic251⋊C4—21no—
38Dic251⋊C4—21no—
39Dic251⋊C4—21no—
40Dic251⋊C4—21no—
41Dic251⋊C4—21no—
42C22⋊Dic251—21no—
43C22⋊Dic251—21no—
44C22⋊Dic251—21no—
45C22⋊Dic251—21no—
46C4×Dic251—21no—
47C2×D4×C251—21no—
48C2×D4×C251D411yescharacteristic
49C22×C4×C251—21no—
50C22×C4×C251C2311yescharacteristic
51C2×C8×C251—21no—
52C4⋊C4×C251D411yescharacteristic
53C22⋊C4×C251—21no—
54Dic502—41no—
55C2×Dic251—21no—
56C2×Dic251—21no—
57C2×Dic251—21no—
58C2×Dic251—21no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—41no—
62C2×Dic251—42no—
63C2×Dic251—41no—
64C2×Dic251—81no—
65C251⋊C8—41no—
66C23×C251—21no—
67C23×C251C2×D411yescharacteristic
68D4×C251—41no—
69D4×C251—41no—
70D4×C251—41no—
71C2×C4×C251—21no—
72C2×C4×C251—41no—
73C2×C4×C251—41no—
74C2×C4×C251—41no—
75C2×C4×C251—41no—
76C2×C4×C251C2×D411yescharacteristic
77C2×C4×C251C2×D411yescharacteristic
78C8×C251—41no—
79C22×C251—21no—
80C22×C251—21no—
81C22×C251—41no—
82C22×C251—41no—
83C22×C251—41no—
84C22×C251#12011yescharacteristic
85C22×C251#13511yescharacteristic
86C22×C251#13711yescharacteristic
87C4×C251—21no—
88C4×C251—21no—
89C4×C251—41no—
90C4×C251—81no—
91Dic251—41no—
92Dic251—41no—
93Dic251—41no—
94Dic251—41no—
95Dic251—81no—
96C2×C251—21no—
97C2×C251—21no—
98C2×C251—81no—
99C2×C251#45211yescharacteristic
100C2×C251#45411yescharacteristic
101C2×C251#45811yescharacteristic
102C251#161511yescharacteristic, complemented, Sylow
103#1615—2511nomaximal, Sylow
104#539—2511no—
105#484—2511no—
106#481—2511no—
107#400—2511no—
108#328—2511no—
109#327D25111yescharacteristic
110#324—2511no—
111#126—5021no—
112#125—5021no—
113#123—5021no—
114#123—5021no—
115C22⋊Q8—5021no—
116C22⋊Q8—2511no—
117#121C2×D25111yescharacteristic
118C4×D4—5021no—
119C2×C4⋊C4—2511no—
120C2×C4⋊C4—2511no—
121#107—5021no—
122#106—5021no—
123#103—5021no—
124#102—5021no—
125C22⋊C8—2511no—
126C22⋊C8C2×D25111yescharacteristic
127#95—5021no—
128#95—5021no—
129#95C2×D25111yescharacteristic
130C2×Q8—2511no—
131C2×D4—21no—
132C2×D4D100411yescharacteristic
133C22×C4—21no—
134C22×C4—5021no—
135C22×C4—5021no—
136C22×C4—2511no—
137C22×C4—2511no—
138C22×C4C22×D25111yescharacteristic
139C2×C8—21no—
140C2×C8—5021no—
141C4⋊C4—5021no—
142C4⋊C4—5021no—
143C4⋊C4—5021no—
144C4⋊C4—5021no—
145C4⋊C4—5021no—
146C4⋊C4—5021no—
147C4⋊C4—5021no—
148C4⋊C4—5021no—
149C4⋊C4—2511no—
150C4⋊C4D100411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—5021no—
153C22⋊C4—5021no—
154C22⋊C4—5021no—
155C22⋊C4—5021no—
156C42—5021no—
157C23—21no—
158C23D4×D25111yescharacteristic
159Q8—10041no—
160D4—41no—
161D4—41no—
162D4—41no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—20081no—
169C2×C4—10042no—
170C2×C4—10041no—
171C2×C4—10041no—
172C2×C4—5021no—
173C2×C4—5021no—
174C2×C4—5021no—
175C2×C4—5021no—
176C2×C4—5021no—
177C2×C4—5021no—
178C2×C4D4×D25111yescharacteristic
179C2×C4C2×D100411yescharacteristic
180C8—41no—
181C8—10041no—
182C22—21no—
183C22—21no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22#2254868511yescharacteristic
188C22#2254873411yescharacteristic
189C22#2254874411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—81no—
194C4—20081no—
195C4—10041no—
196C4—10041no—
197C4—10041no—
198C4—10041no—
199C2—21no—
200C2—21no—
201C2—81no—
202C2#3063185011yescharacteristic
203C2#3063186111yescharacteristic
204C2#3063187811yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#327×C251C2
socleC22×C251#120
prime radical#121×C251C22
hypercenter#327D251
hypocenterC251#1615
LCSG ▷ C22×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #30632023C2semidirect
4. #30631627C2semidirect
5. #30631423C2semidirect
6. #30631412C2semidirect
102. C251#1615semidirect

Maximal subgroups

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

subgroupindex
#306322822
#306320232
#306320032
#306316272
#306314232
#306314122
#327×C2512
#1615251