Finite Group Databasebeta

← #44549366

Subgroups — #44549366

Order 32128.

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

normal subgroups only

This group has 254 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#30632264C211yesmaximal, characteristic
2#30632000C211yesmaximal, characteristic, complemented
3#30631618C211yesmaximal, characteristic, complemented
4#30631422C211yesmaximal, characteristic, complemented
5#30631421C211yesmaximal, characteristic, complemented
6#30631412C211yesmaximal, characteristic, complemented
7#480×C251C211yesmaximal, characteristic, complemented
8C2×#16860809—21no—
9#22548693—21no—
10#22548692—21no—
11#22548689C2211yescharacteristic
12#22548688—21no—
13#22548687—21no—
14#22548687—21no—
15C2×Dic251⋊C4—21no—
16C2×Dic251⋊C4C2211yescharacteristic
17#22548648—21no—
18#22548635—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
27#16860809—42no—
28#16860809—42no—
29C2×Dic502—21no—
30C2×D1004D411yescharacteristic
31C2×C22⋊D251—21no—
32C2×C22⋊D251—21no—
33C2×C22⋊D251—21no—
34C22×Dic251—21no—
35C22×Dic251—21no—
36C22×Dic251D411yescharacteristic
37C22×Dic251D411yescharacteristic
38C2×C4×D251—21no—
39C2×C251⋊C8—21no—
40C4⋊Dic251D411yescharacteristic
41Dic251⋊C4—21no—
42Dic251⋊C4—21no—
43Dic251⋊C4—21no—
44Dic251⋊C4—42no—
45C22⋊Dic251—21no—
46(C2×D251)⋊C4—21no—
47(C2×D251)⋊C4—21no—
48C2×D4×C251—21no—
49C2×D4×C251D411yescharacteristic
50C22×C4×C251—21no—
51C22×C4×C251C2311yescharacteristic
52C2×C8×C251—21no—
53C4⋊C4×C251—21no—
54C4⋊C4×C251—21no—
55C4⋊C4×C251D411yescharacteristic
56C22⋊C4×C251—21no—
57C22×D251—21no—
58Dic502—42no—
59D1004—41no—
60C22⋊D251—42no—
61C22⋊D251—41no—
62C22⋊D251—41no—
63C22⋊D251—81no—
64C2×Dic251—21no—
65C2×Dic251—21no—
66C2×Dic251—22no—
67C2×Dic251—21no—
68C2×Dic251—21no—
69C2×Dic251—42no—
70C2×Dic251—41no—
71C2×Dic251—41no—
72C2×Dic251—41no—
73C2×Dic251D812yes—
74C4×D251—42no—
75C251⋊C8—41no—
76C23×C251—21no—
77C23×C251C2×D411yescharacteristic
78D4×C251—41no—
79D4×C251—41no—
80D4×C251—41no—
81C2×C4×C251—21no—
82C2×C4×C251—41no—
83C2×C4×C251—41no—
84C2×C4×C251—41no—
85C2×C4×C251—41no—
86C2×C4×C251C2×D411yescharacteristic
87C2×C4×C251C2×D411yescharacteristic
88C8×C251—41no—
89C22×C251—21no—
90C22×C251—21no—
91C22×C251—41no—
92C22×C251—41no—
93C22×C251—41no—
94C22×C251#12011yescharacteristic
95C22×C251C2×D811yescharacteristic
96C22×C251AGL(1,ℤ/8)11yescharacteristic
97C2×D251—41no—
98C2×D251—41no—
99C2×D251—41no—
100C4×C251—21no—
101C4×C251—21no—
102C4×C251—41no—
103C4×C251—81no—
104Dic251—22no—
105Dic251—42no—
106Dic251—41no—
107Dic251—41no—
108C2×C251—21no—
109C2×C251—21no—
110C2×C251—81no—
111C2×C251#44711yescharacteristic
112C2×C251#45611yescharacteristic
113C2×C251#45811yescharacteristic
114D251—81no—
115C251#161011yescharacteristic, complemented, Sylow
116#1610—2511nomaximal, Sylow
117#537—2511no—
118#480—2511no—
119#480D25111yescharacteristic, complemented
120#398—2511no—
121#327—2511no—
122#327—2511no—
123#324—2511no—
124C2×#41—5021no—
125C22⋊Q8—5021no—
126C22⋊Q8—5021no—
127#121—5021no—
128#121—5021no—
129#121—5021no—
130#121—2511no—
131#121C2×D25111yescharacteristic
132C2×C4⋊C4—5021no—
133C2×C4⋊C4—2511no—
134C2×C4⋊C4C2×D25111yescharacteristic
135#107—21no—
136#107—5021no—
137#102—21no—
138#102—5021no—
139C22⋊C8—2511no—
140C22⋊C8C2×D25111yescharacteristic
141#95—5021no—
142#95—2511no—
143#41—10042no—
144#41—10042no—
145C2×Q8—5021no—
146C2×D4—21no—
147C2×D4—5021no—
148C2×D4—5021no—
149C2×D4—5021no—
150C2×D4—2511no—
151C2×D4C22⋊D25111yescharacteristic
152C22×C4—21no—
153C22×C4—5021no—
154C22×C4—5021no—
155C22×C4—5021no—
156C22×C4—2511no—
157C22×C4—2511no—
158C22×C4C22×D25111yescharacteristic
159C2×C8—21no—
160C2×C8—5021no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—10042no—
164C4⋊C4—5021no—
165C4⋊C4—5021no—
166C4⋊C4—5021no—
167C4⋊C4—2511no—
168C4⋊C4C22⋊D25111yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—5021no—
171C22⋊C4—5021no—
172C22⋊C4—5021no—
173C23—21no—
174C23—5021no—
175C23D4×D25111yescharacteristic
176Q8—10042no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—20081no—
181D4—10041no—
182D4—10041no—
183D4—10041no—
184D4—10042no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—10042no—
191C2×C4—10041no—
192C2×C4—10041no—
193C2×C4—10042no—
194C2×C4—10041no—
195C2×C4—5022no—
196C2×C4—5021no—
197C2×C4—5021no—
198C2×C4—5021no—
199C2×C4—5021no—
200C2×C4—2512no—
201C2×C4D4×D25111yescharacteristic
202C2×C4C2×C22⋊D25111yescharacteristic
203C8—41no—
204C8—10041no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—10041no—
211C22—10041no—
212C22—10041no—
213C22#2254868311yescharacteristic
214C22D8×D25111yescharacteristic
215C22#2254873911yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—81no—
220C4—10042no—
221C4—10041no—
222C4—10041no—
223C4—5022no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—20081no—
228C2#3063181911yescharacteristic
229C2#3063186811yescharacteristic
230C2#3063187611yescharacteristic
subgroupG/H
centerC22#22548683
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#480×C251C2
socleC22×C251#120
prime radical#30632264C2
hypercenter#480D251
hypocenterC251#1610
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. #30632000C2semidirect
3. #30631618C2semidirect
4. #30631422C2semidirect
5. #30631421C2semidirect
6. #30631412C2semidirect
7. #480×C251C2semidirect
115. C251#1610semidirect
119. #480D251semidirect

Maximal subgroups

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

subgroupindex
#306322642
#306320002
#306316182
#306314222
#306314212
#306314122
#480×C2512
#1610251