Finite Group Databasebeta

← #44549359

Subgroups — #44549359

Order 32128.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 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#30632017C211yesmaximal, characteristic, complemented
3#30631618C211yesmaximal, characteristic, complemented
4#30631425C211yesmaximal, characteristic, complemented
5#30631421C211yesmaximal, characteristic
6#30631412C211yesmaximal, characteristic, complemented
7#480×C251C211yesmaximal, characteristic
8#22548708—21no—
9#22548705—21no—
10#22548696—21no—
11#22548696—21no—
12#22548694C2211yescharacteristic
13#22548692—21no—
14D4×Dic251—21no—
15C2×Dic251⋊C4—21no—
16C2×Dic251⋊C4C2211yescharacteristic
17#22548646—21no—
18#22548638—21no—
19C22⋊(C251⋊C8)C2211yescharacteristic
20C251⋊#95—21no—
21C251⋊#95C2211yescharacteristic
22#121×C251C2211yescharacteristic
23C2×C4⋊C4×C251C2211yescharacteristic
24#107×C251—21no—
25#102×C251—21no—
26C22⋊C8×C251C2211yescharacteristic
27C2×Dic502D411yescharacteristic
28C22×Dic251—21no—
29C22×Dic251—21no—
30C22×Dic251D411yescharacteristic
31C22×Dic251D411yescharacteristic
32C2×C251⋊C8—21no—
33C4⋊Dic251—21no—
34C4⋊Dic251D411yescharacteristic
35Dic251⋊C4—21no—
36Dic251⋊C4—21no—
37Dic251⋊C4—21no—
38Dic251⋊C4—21no—
39Dic251⋊C4—21no—
40Dic251⋊C4—42no—
41C22⋊Dic251—21no—
42C22⋊Dic251—21no—
43C22⋊Dic251—21no—
44C22⋊Dic251—21no—
45C4×Dic251—21no—
46C2×D4×C251—21no—
47C2×D4×C251D411yescharacteristic
48C22×C4×C251—21no—
49C22×C4×C251C2311yescharacteristic
50C2×C8×C251—21no—
51C4⋊C4×C251—21no—
52C4⋊C4×C251—21no—
53C4⋊C4×C251D411yescharacteristic
54C22⋊C4×C251—21no—
55Dic502—41no—
56C2×Dic251—22no—
57C2×Dic251—21no—
58C2×Dic251—21no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—21no—
62C2×Dic251—21no—
63C2×Dic251—41no—
64C2×Dic251—41no—
65C2×Dic251—41no—
66C2×Dic251—81no—
67C251⋊C8—41no—
68C23×C251—21no—
69C23×C251C2×D411yescharacteristic
70D4×C251—41no—
71D4×C251—41no—
72D4×C251—41no—
73C2×C4×C251—21no—
74C2×C4×C251—41no—
75C2×C4×C251—41no—
76C2×C4×C251—41no—
77C2×C4×C251—41no—
78C2×C4×C251C2×D411yescharacteristic
79C2×C4×C251C2×D411yescharacteristic
80C8×C251—41no—
81C22×C251—21no—
82C22×C251—21no—
83C22×C251—41no—
84C22×C251—41no—
85C22×C251—41no—
86C22×C251#12011yescharacteristic
87C22×C251#13511yescharacteristic
88C22×C251AGL(1,ℤ/8)11yescharacteristic
89C4×C251—21no—
90C4×C251—21no—
91C4×C251—41no—
92C4×C251—81no—
93Dic251—42no—
94Dic251—41no—
95Dic251—41no—
96Dic251—41no—
97Dic251—41no—
98C2×C251—21no—
99C2×C251—21no—
100C2×C251—81no—
101C2×C251#44911yescharacteristic
102C2×C251#45611yescharacteristic
103C2×C251#45811yescharacteristic
104C251#160911yescharacteristic, complemented, Sylow
105#1609—2511nomaximal, Sylow
106#539—2511no—
107#483—2511no—
108#480D25111yescharacteristic
109#398—2511no—
110#328—2511no—
111#327—2511no—
112#324—2511no—
113#126—5021no—
114#125—5021no—
115#123—5021no—
116#123—5021no—
117C22⋊Q8—5021no—
118C22⋊Q8—2511no—
119#121C2×D25111yescharacteristic
120C4×D4—5021no—
121C2×C4⋊C4—5021no—
122C2×C4⋊C4—2511no—
123C2×C4⋊C4C2×D25111yescharacteristic
124#107—21no—
125#106—5021no—
126#103—5021no—
127#102—21no—
128C22⋊C8—2511no—
129C22⋊C8C2×D25111yescharacteristic
130#95—5021no—
131#95—2511no—
132C2×Q8—2511no—
133C2×D4—21no—
134C2×D4C22⋊D25111yescharacteristic
135C22×C4—21no—
136C22×C4—5021no—
137C22×C4—5021no—
138C22×C4—2511no—
139C22×C4—2511no—
140C22×C4C22×D25111yescharacteristic
141C2×C8—21no—
142C2×C8—5021no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—10042no—
146C4⋊C4—5021no—
147C4⋊C4—5021no—
148C4⋊C4—5021no—
149C4⋊C4—5021no—
150C4⋊C4—5021no—
151C4⋊C4—5021no—
152C4⋊C4—2511no—
153C4⋊C4C22⋊D25111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—5021no—
156C22⋊C4—5021no—
157C22⋊C4—5021no—
158C22⋊C4—5021no—
159C42—5021no—
160C23—21no—
161C23D4×D25111yescharacteristic
162Q8—10041no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—20081no—
172C2×C4—10041no—
173C2×C4—10041no—
174C2×C4—10041no—
175C2×C4—5022no—
176C2×C4—5021no—
177C2×C4—5021no—
178C2×C4—5021no—
179C2×C4—5021no—
180C2×C4—5021no—
181C2×C4—5021no—
182C2×C4D4×D25111yescharacteristic
183C2×C4C2×C22⋊D25111yescharacteristic
184C8—41no—
185C8—10041no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#2254868311yescharacteristic
192C22#2254873411yescharacteristic
193C22#2254873911yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—81no—
198C4—10042no—
199C4—10041no—
200C4—10041no—
201C4—10041no—
202C4—10041no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#3063182911yescharacteristic
207C2#3063186811yescharacteristic
208C2#3063187611yescharacteristic
subgroupG/H
centerC22#22548683
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#480×C251C2
socleC22×C251#120
prime radical#121×C251C22
hypercenter#480D251
hypocenterC251#1609
LCSG ▷ C22×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #30632017C2semidirect
3. #30631618C2semidirect
4. #30631425C2semidirect
6. #30631412C2semidirect
104. C251#1609semidirect

Maximal subgroups

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

subgroupindex
#306322822
#306320172
#306316182
#306314252
#306314212
#306314122
#480×C2512
#1609251