Finite Group Databasebeta

← #44549374

Subgroups — #44549374

Order 32128.

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

normal subgroups only

This group has 210 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#30632316C211yesmaximal, characteristic
2#30632018C211yesmaximal, characteristic
3#30632015C211yesmaximal, characteristic
4#30631619C211yesmaximal, characteristic
5#30631423C211yesmaximal, characteristic
6#30631412C211yesmaximal, characteristic
7#328×C251C211yesmaximal, characteristic
8#22548714—21no—
9#22548713—21no—
10#22548705—21no—
11#22548705—21no—
12#22548694C2211yescharacteristic
13#22548692—21no—
14#22548671—21no—
15C2×C4⋊Dic251—21no—
16C2×C4⋊Dic251C2211yescharacteristic
17C2×Dic251⋊C4C2211yescharacteristic
18#22548647—21no—
19#22548646—21no—
20#22548640—21no—
21#22548639—21no—
22C22⋊(C251⋊C8)C2211yescharacteristic
23C251⋊#95—21no—
24C22⋊Q8×C251C2211yescharacteristic
25C22⋊C8×C251C2211yescharacteristic
26#95×C251C2211yescharacteristic
27C2×Dic502—21no—
28C2×Dic502D411yescharacteristic
29C22×Dic251—21no—
30C22×Dic251D411yescharacteristic
31C22×Dic251D411yescharacteristic
32C2×C251⋊C8—21no—
33C4⋊Dic251—21no—
34C4⋊Dic251—21no—
35C4⋊Dic251—21no—
36C4⋊Dic251—42no—
37C4⋊Dic251D411yescharacteristic
38Dic251⋊C4—21no—
39Dic251⋊C4—21no—
40Dic251⋊C4—21no—
41Dic251⋊C4—21no—
42Dic251⋊C4—21no—
43Dic251⋊C4—21no—
44Dic251⋊C4—21no—
45C22⋊Dic251—21no—
46C4×Dic251—21no—
47C4×Dic251—21no—
48C2×Q8×C251D411yescharacteristic
49C22×C4×C251—21no—
50C22×C4×C251C2311yescharacteristic
51C2×C8×C251—21no—
52C4⋊C4×C251—21no—
53C4⋊C4×C251D411yescharacteristic
54C22⋊C4×C251—21no—
55Dic502—41no—
56Dic502—81no—
57C2×Dic251—21no—
58C2×Dic251—21no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—21no—
62C2×Dic251—41no—
63C2×Dic251—41no—
64C2×Dic251—41no—
65C2×Dic251—41no—
66C2×Dic251SD1612yes—
67C251⋊C8—41no—
68C23×C251C2×D411yescharacteristic
69Q8×C251—41no—
70C2×C4×C251—22no—
71C2×C4×C251—21no—
72C2×C4×C251—21no—
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#12011yescharacteristic
82C22×C251C2×SD1611yescharacteristic
83C22×C251#13711yescharacteristic
84C4×C251—21no—
85C4×C251—21no—
86C4×C251—42no—
87C4×C251—41no—
88C4×C251—41no—
89Dic251—22no—
90Dic251—41no—
91Dic251—41no—
92Dic251—41no—
93Dic251—81no—
94C2×C251—21no—
95C2×C251—21no—
96C2×C251#44811yescharacteristic
97C2×C251#45611yescharacteristic
98C2×C251#45811yescharacteristic
99C251#161111yescharacteristic, complemented, Sylow
100#1611—2511nomaximal, Sylow
101#544—2511no—
102#483—2511no—
103#483—2511no—
104#398—2511no—
105#328—2511no—
106#328D25111yescharacteristic
107#324—2511no—
108C4⋊Q8—5021no—
109C4⋊Q8—5021no—
110#125—5021no—
111#125—5021no—
112C22⋊Q8—5021no—
113C22⋊Q8—2511no—
114C22⋊Q8C2×D25111yescharacteristic
115#117—5021no—
116C2×C4⋊C4—5021no—
117C2×C4⋊C4—2511no—
118C2×C4⋊C4—2511no—
119#106—5021no—
120#106—5021no—
121#103—5021no—
122#103—5021no—
123C22⋊C8—2511no—
124C22⋊C8C2×D25111yescharacteristic
125#95—5021no—
126#95C2×D25111yescharacteristic
127C2×Q8—5021no—
128C2×Q8—2511no—
129C2×Q8D100411yescharacteristic
130C22×C4—21no—
131C22×C4—5021no—
132C22×C4—2511no—
133C22×C4—2511no—
134C22×C4C22×D25111yescharacteristic
135C2×C8—21no—
136C2×C8—5021no—
137C4⋊C4—21no—
138C4⋊C4—10042no—
139C4⋊C4—5021no—
140C4⋊C4—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—
153C42—5021no—
154C42—5021no—
155C23D4×D25111yescharacteristic
156Q8—41no—
157Q8—20081no—
158Q8—10041no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—10041no—
166C2×C4—10041no—
167C2×C4—10041no—
168C2×C4—10041no—
169C2×C4—5021no—
170C2×C4—5021no—
171C2×C4—5021no—
172C2×C4—5021no—
173C2×C4—5021no—
174C2×C4—2512no—
175C2×C4D4×D25111yescharacteristic
176C2×C4C2×D100411yescharacteristic
177C8—41no—
178C8—10041no—
179C22—21no—
180C22—21no—
181C22#2254868511yescharacteristic
182C22SD16×D25111yescharacteristic
183C22#2254874711yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—20081no—
190C4—10041no—
191C4—10041no—
192C4—10041no—
193C4—5022no—
194C2—21no—
195C2—21no—
196C2#3063182711yescharacteristic
197C2#3063187111yescharacteristic
198C2#3063187811yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#328×C251C2
socleC22×C251#120
prime radicalC23×C251C2×D4
hypercenter#328D251
hypocenterC251#1611
LCSG ▷ C22×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C251#1611semidirect

Maximal subgroups

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

subgroupindex
#306323162
#306320182
#306320152
#306316192
#306314232
#306314122
#328×C2512
#1611251