Finite Group Databasebeta

← #44549362

Subgroups — #44549362

Order 32128.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#30632015C211yesmaximal, characteristic, complemented
2#30631998C211yesmaximal, characteristic
3#30631617C211yesmaximal, characteristic, complemented
4#30631424C211yesmaximal, characteristic, complemented
5#30631421C211yesmaximal, characteristic
6#30631413C211yesmaximal, characteristic, complemented
7#539×C251C211yesmaximal, characteristic
8C2×C4⋊Dic251C2211yescharacteristic
9C2×Dic251⋊C4—21no—
10#22548648—21no—
11#22548646—21no—
12#22548639—21no—
13#22548636—21no—
14C22⋊(C251⋊C8)C2211yescharacteristic
15C22⋊(C251⋊C8)C2211yescharacteristic
16C251⋊#95—21no—
17C251⋊#95C2211yescharacteristic
18#126×C251—21no—
19#125×C251—21no—
20#123×C251—21no—
21#123×C251—21no—
22C22⋊Q8×C251—21no—
23C22⋊Q8×C251C2211yescharacteristic
24#121×C251C2211yescharacteristic
25C4×D4×C251—21no—
26C2×C4⋊C4×C251C2211yescharacteristic
27C22×Dic251—21no—
28C22×Dic251—21no—
29C2×C251⋊C8—21no—
30C2×C251⋊C8—21no—
31C4⋊Dic251—21no—
32C4⋊Dic251—21no—
33Dic251⋊C4—42no—
34C2×Q8×C251D411yescharacteristic
35C2×D4×C251—21no—
36C2×D4×C251D411yescharacteristic
37C22×C4×C251—21no—
38C22×C4×C251D411yescharacteristic
39C22×C4×C251D411yescharacteristic
40C22×C4×C251C2311yescharacteristic
41C4⋊C4×C251—21no—
42C4⋊C4×C251—21no—
43C4⋊C4×C251—21no—
44C4⋊C4×C251—21no—
45C4⋊C4×C251—21no—
46C4⋊C4×C251—21no—
47C4⋊C4×C251D411yescharacteristic
48C4⋊C4×C251D411yescharacteristic
49C22⋊C4×C251—21no—
50C22⋊C4×C251—21no—
51C22⋊C4×C251—21no—
52C22⋊C4×C251—21no—
53C22⋊C4×C251—21no—
54C42×C251—21no—
55C2×Dic251—22no—
56C2×Dic251—41no—
57C2×Dic251—41no—
58C2×Dic251—41no—
59C2×Dic251—41no—
60C2×Dic251—41no—
61C251⋊C8—41no—
62C251⋊C8—41no—
63C23×C251—21no—
64C23×C251C2×D411yescharacteristic
65Q8×C251—41no—
66D4×C251—41no—
67D4×C251—41no—
68D4×C251—41no—
69C2×C4×C251—21no—
70C2×C4×C251—21no—
71C2×C4×C251—21no—
72C2×C4×C251—21no—
73C2×C4×C251—21no—
74C2×C4×C251—21no—
75C2×C4×C251—21no—
76C2×C4×C251—41no—
77C2×C4×C251—41no—
78C2×C4×C251—81no—
79C2×C4×C251C2×D411yescharacteristic
80C2×C4×C251C2×D411yescharacteristic
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—41no—
93C4×C251—41no—
94C4×C251—41no—
95C4×C251—41no—
96Dic251—42no—
97Dic251—81no—
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#539D25111yescharacteristic
107#483—2511no—
108#480—2511no—
109#398—2511no—
110#328—2511no—
111#327—2511no—
112#324—2511no—
113#126—21no—
114#125—21no—
115#123—21no—
116#123—21no—
117C22⋊Q8—21no—
118C22⋊Q8C2×D25111yescharacteristic
119#121C2×D25111yescharacteristic
120C4×D4—21no—
121C2×C4⋊C4—5021no—
122C2×C4⋊C4—2511no—
123C2×C4⋊C4C2×D25111yescharacteristic
124#107—5021no—
125#106—5021no—
126#103—5021no—
127#102—5021no—
128C22⋊C8—2511no—
129C22⋊C8—2511no—
130#95—5021no—
131#95—2511no—
132C2×Q8C22⋊D25111yescharacteristic
133C2×D4—21no—
134C2×D4C22⋊D25111yescharacteristic
135C22×C4—21no—
136C22×C4—5021no—
137C22×C4—5021no—
138C22×C4C22⋊D25111yescharacteristic
139C22×C4C22⋊D25111yescharacteristic
140C22×C4C22×D25111yescharacteristic
141C2×C8—5021no—
142C2×C8—5021no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—10042no—
150C4⋊C4—5021no—
151C4⋊C4—5021no—
152C4⋊C4C22⋊D25111yescharacteristic
153C4⋊C4C22⋊D25111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—21no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—21no—
159C42—21no—
160C23—21no—
161C23C2×C22⋊D25111yescharacteristic
162Q8—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—81no—
176C2×C4—10041no—
177C2×C4—10041no—
178C2×C4—10041no—
179C2×C4—10041no—
180C2×C4—10041no—
181C2×C4—5022no—
182C2×C4C2×C22⋊D25111yescharacteristic
183C2×C4C2×C22⋊D25111yescharacteristic
184C8—10041no—
185C8—10041no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#2254868411yescharacteristic
192C22#2254873511yescharacteristic
193C22#2254874011yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—20081no—
202C4—10042no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#3063183211yescharacteristic
207C2#3063187011yescharacteristic
208C2#3063187711yescharacteristic
subgroupG/H
centerC22#22548684
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#539×C251C2
socleC22×C251#120
prime radical#121×C251C22
hypercenter#539D251
hypocenterC251#1609
LCSG ▷ C22×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #30632015C2semidirect
3. #30631617C2semidirect
4. #30631424C2semidirect
6. #30631413C2semidirect
104. C251#1609semidirect

Maximal subgroups

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

subgroupindex
#306320152
#306319982
#306316172
#306314242
#306314212
#306314132
#539×C2512
#1609251