Finite Group Databasebeta

← #44549349

Subgroups — #44549349

Order 32128.

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

normal subgroups only

This group has 280 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#30632245C211yesmaximal, characteristic
2#30632000C211yesmaximal, characteristic, complemented
3#30631613C211yesmaximal, characteristic, complemented
4#30631422C211yesmaximal, characteristic, complemented
5#30631421C211yesmaximal, characteristic, complemented
6#30631410C211yesmaximal, characteristic, complemented
7#480×C251C211yesmaximal, characteristic, complemented
8C2×D4×D251—21no—
9#22548700—21no—
10#22548697—21no—
11#22548689C2211yescharacteristic
12#22548687—21no—
13#22548685—21no—
14#22548683—21no—
15C2×(C2×D251)⋊C4—21no—
16C2×(C2×D251)⋊C4C2211yescharacteristic
17#22548648—21no—
18#22548635—21no—
19C22⋊(C251⋊C8)C2211yescharacteristic, complemented
20C251⋊#95—21no—
21C251⋊#95C2211yescharacteristic, complemented
22#121×C251C2211yescharacteristic
23C2×C4⋊C4×C251C2211yescharacteristic, complemented
24#107×C251—21no—
25#102×C251—21no—
26C22⋊C8×C251C2211yescharacteristic, complemented
27C23×D251—21no—
28C23×D251D411yescharacteristic
29C2×D1004—21no—
30C2×D1004D411yescharacteristic
31C2×C22⋊D251—21no—
32C2×C22⋊D251—21no—
33C2×C22⋊D251—21no—
34D4×D251—42no—
35D4×D251—42no—
36C22×Dic251—21no—
37C22×Dic251D411yescharacteristic
38C2×C4×D251—21no—
39C2×C251⋊C8—21no—
40C4⋊Dic251D411yescharacteristic
41Dic251⋊C4—21no—
42C22⋊Dic251—21no—
43(C2×D251)⋊C4—21no—
44(C2×D251)⋊C4—21no—
45(C2×D251)⋊C4—21no—
46(C2×D251)⋊C4—21no—
47(C2×D251)⋊C4—42no—
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—
58C22×D251—21no—
59C22×D251—21no—
60C22×D251—42no—
61C22×D251—41no—
62C22×D251—41no—
63C22×D251—81no—
64C22×D251—81no—
65C22×D251D812yes—
66D1004—41no—
67D1004—42no—
68C22⋊D251—42no—
69C22⋊D251—41no—
70C22⋊D251—41no—
71C22⋊D251—81no—
72C2×Dic251—21no—
73C2×Dic251—21no—
74C2×Dic251—41no—
75C2×Dic251—41no—
76C2×Dic251—41no—
77C2×Dic251—41no—
78C4×D251—42no—
79C251⋊C8—41no—
80C23×C251—21no—
81C23×C251C2×D411yescharacteristic
82D4×C251—41no—
83D4×C251—41no—
84D4×C251—41no—
85C2×C4×C251—21no—
86C2×C4×C251—41no—
87C2×C4×C251—41no—
88C2×C4×C251—41no—
89C2×C4×C251—41no—
90C2×C4×C251C2×D411yescharacteristic
91C2×C4×C251C2×D411yescharacteristic
92C8×C251—41no—
93C22×C251—21no—
94C22×C251—21no—
95C22×C251—41no—
96C22×C251—41no—
97C22×C251—41no—
98C22×C251#12011yescharacteristic
99C22×C251C2×D811yescharacteristic
100C22×C251AGL(1,ℤ/8)11yescharacteristic
101C2×D251—22no—
102C2×D251—41no—
103C2×D251—41no—
104C2×D251—42no—
105C2×D251—41no—
106C2×D251—41no—
107C2×D251—41no—
108C2×D251—81no—
109C2×D251—84no—
110C4×C251—21no—
111C4×C251—21no—
112C4×C251—41no—
113C4×C251—81no—
114Dic251—41no—
115Dic251—41no—
116Dic251—81no—
117C2×C251—21no—
118C2×C251—21no—
119C2×C251—81no—
120C2×C251#44711yescharacteristic
121C2×C251#45511yescharacteristic
122C2×C251#45811yescharacteristic
123D251—42no—
124D251—81no—
125C251#160711yescharacteristic, complemented, Sylow
126#1607—2511nomaximal, Sylow
127#534—2511no—
128#480—2511no—
129#480D25111yescharacteristic, complemented
130#397—2511no—
131#327—2511no—
132#327—2511no—
133#323—2511no—
134C22×D4—5021no—
135#123—5021no—
136#123—5021no—
137#121—5021no—
138#121—2511no—
139#121C2×D25111yescharacteristic
140#120—5021no—
141#120—5021no—
142C2×C4⋊C4C2×D25111yescharacteristic, complemented
143C2×C22⋊C4—5021no—
144C2×C22⋊C4—2511no—
145#107—21no—
146#107—5021no—
147#102—21no—
148#102—5021no—
149C22⋊C8—2511no—
150C22⋊C8C2×D25111yescharacteristic, complemented
151#95—5021no—
152#95—2511no—
153C24—5021no—
154C24—2511no—
155C2×D4—21no—
156C2×D4—10042no—
157C2×D4—10042no—
158C2×D4—5021no—
159C2×D4—5021no—
160C2×D4—5021no—
161C2×D4—5021no—
162C2×D4—2511no—
163C2×D4C22⋊D25111yescharacteristic
164C22×C4—21no—
165C22×C4—5021no—
166C22×C4—5021no—
167C22×C4—2511no—
168C22×C4C22×D25111yescharacteristic
169C2×C8—21no—
170C2×C8—5021no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—5021no—
174C4⋊C4—2511no—
175C4⋊C4C22⋊D25111yescharacteristic
176C22⋊C4—21no—
177C22⋊C4—10042no—
178C22⋊C4—5021no—
179C22⋊C4—5021no—
180C22⋊C4—5021no—
181C22⋊C4—5021no—
182C22⋊C4—5021no—
183C23—21no—
184C23—20081no—
185C23—20081no—
186C23—10041no—
187C23—10041no—
188C23—10042no—
189C23—5021no—
190C23—5021no—
191C23—5021no—
192C23—2512no—
193C23D4×D25111yescharacteristic
194D4—41no—
195D4—41no—
196D4—41no—
197D4—20081no—
198D4—10041no—
199D4—10042no—
200D4—10042no—
201D4—10041no—
202D4—10041no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—10042no—
209C2×C4—10041no—
210C2×C4—10041no—
211C2×C4—10041no—
212C2×C4—10041no—
213C2×C4—5021no—
214C2×C4—5021no—
215C2×C4D4×D25111yescharacteristic
216C2×C4C2×C22⋊D25111yescharacteristic
217C8—41no—
218C8—10041no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—20081no—
225C22—20084no—
226C22—10042no—
227C22—10041no—
228C22—10041no—
229C22—10041no—
230C22—10041no—
231C22—10041no—
232C22—5022no—
233C22#2254868311yescharacteristic
234C22D8×D25111yescharacteristic
235C22#2254873911yescharacteristic
236C4—21no—
237C4—21no—
238C4—41no—
239C4—81no—
240C4—20081no—
241C4—10041no—
242C4—10041no—
243C2—21no—
244C2—21no—
245C2—81no—
246C2—20081no—
247C2—10042no—
248C2#3063181911yescharacteristic
249C2#3063186311yescharacteristic
250C2#3063187611yescharacteristic
subgroupG/H
centerC22#22548683
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#480×C251C2
socleC22×C251#120
prime radical#30632245C2
hypercenter#480D251
hypocenterC251#1607
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. #30631613C2semidirect
4. #30631422C2semidirect
5. #30631421C2semidirect
6. #30631410C2semidirect
7. #480×C251C2semidirect
19. C22⋊(C251⋊C8)C22semidirect
21. C251⋊#95C22semidirect
23. C2×C4⋊C4×C251C22semidirect
26. C22⋊C8×C251C22semidirect
125. C251#1607semidirect
129. #480D251semidirect
142. C2×C4⋊C4C2×D251semidirect
150. C22⋊C8C2×D251semidirect

Maximal subgroups

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

subgroupindex
#306322452
#306320002
#306316132
#306314222
#306314212
#306314102
#480×C2512
#1607251