Finite Group Databasebeta

← #44549398

Subgroups — #44549398

Order 32128.

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

normal subgroups only

This group has 208 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#30632284C211yesmaximal, characteristic
2#30632023C211yesmaximal, characteristic, complemented
3#30632006C211yesmaximal, characteristic
4#30631626C211yesmaximal, characteristic, complemented
5#30631425C211yesmaximal, characteristic, complemented
6#30631422C211yesmaximal, characteristic
7#324×C251C211yesmaximal, characteristic, complemented
8#22548710—21no—
9#22548705—21no—
10#22548700—21no—
11#22548698—21no—
12#22548694C2211yescharacteristic
13#22548693—21no—
14#22548689C2211yescharacteristic
15C4×C22⋊D251—21no—
16C2×C4⋊Dic251C2211yescharacteristic
17#22548649—21no—
18#22548647—21no—
19#22548640—21no—
20#22548637—21no—
21C251⋊#95—21no—
22C251⋊#95—21no—
23C251⋊#95C2211yescharacteristic
24C2×C4⋊C4×C251C2211yescharacteristic
25C22⋊C8×C251C2211yescharacteristic
26C22⋊C8×C251C2211yescharacteristic
27C2×Dic502D411yescharacteristic
28C2×D1004D411yescharacteristic
29C2×C22⋊D251—21no—
30C22×Dic251—21no—
31C22×Dic251—21no—
32C2×C4×D251—21no—
33C4⋊Dic251—21no—
34C4⋊Dic251—21no—
35C4⋊Dic251D411yescharacteristic
36C4⋊Dic251D411yescharacteristic
37Dic251⋊C4—21no—
38Dic251⋊C4—21no—
39Dic251⋊C4—21no—
40Dic251⋊C4—21no—
41C22⋊Dic251—21no—
42(C2×D251)⋊C4—21no—
43(C2×D251)⋊C4—21no—
44(C2×D251)⋊C4—21no—
45(C2×D251)⋊C4—21no—
46C4×Dic251—21no—
47C22×C4×C251D411yescharacteristic
48C22×C4×C251D411yescharacteristic
49C22×C4×C251C2311yescharacteristic
50C2×C8×C251—21no—
51C2×C8×C251—21no—
52C4⋊C4×C251—21no—
53C4⋊C4×C251—21no—
54C22×D251—21no—
55Dic502—41no—
56D1004—41no—
57C22⋊D251—41no—
58C22⋊D251—41no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—21no—
62C2×Dic251—41no—
63C2×Dic251—41no—
64C2×Dic251—42no—
65C2×Dic251—41no—
66C2×Dic251—41no—
67C4×D251—81no—
68C23×C251C2×D411yescharacteristic
69C2×C4×C251—21no—
70C2×C4×C251—21no—
71C2×C4×C251—21no—
72C2×C4×C251—21no—
73C2×C4×C251—41no—
74C2×C4×C251—41no—
75C2×C4×C251C2×D411yescharacteristic
76C2×C4×C251C2×D411yescharacteristic
77C8×C251—41no—
78C8×C251—41no—
79C22×C251—21no—
80C22×C251—21no—
81C22×C251#12011yescharacteristic
82C22×C251#13511yescharacteristic
83C22×C251#13711yescharacteristic
84C2×D251—41no—
85C2×D251—41no—
86C2×D251—41no—
87C4×C251—21no—
88C4×C251—21no—
89C4×C251—41no—
90C4×C251—41no—
91Dic251—41no—
92Dic251—41no—
93Dic251—41no—
94Dic251—81no—
95Dic251—81no—
96C2×C251—21no—
97C2×C251—21no—
98C2×C251#45211yescharacteristic
99C2×C251#45411yescharacteristic
100C2×C251#45811yescharacteristic
101D251—81no—
102C251#161511yescharacteristic, complemented, Sylow
103#1615—2511nomaximal, Sylow
104#539—2511no—
105#484—2511no—
106#481—2511no—
107#400—2511no—
108#328—2511no—
109#327—2511no—
110#324D25111yescharacteristic, complemented
111#126—5021no—
112#125—5021no—
113#123—5021no—
114#123—5021no—
115C22⋊Q8—5021no—
116C22⋊Q8—2511no—
117#121—2511no—
118C4×D4—5021no—
119C2×C4⋊C4—2511no—
120C2×C4⋊C4C2×D25111yescharacteristic
121#107—5021no—
122#106—5021no—
123#103—5021no—
124#102—5021no—
125C22⋊C8C2×D25111yescharacteristic
126C22⋊C8C2×D25111yescharacteristic
127#95—5021no—
128#95—5021no—
129#95—2511no—
130C2×Q8—2511no—
131C2×D4—5021no—
132C2×D4—2511no—
133C22×C4—5021no—
134C22×C4—5021no—
135C22×C4—5021no—
136C22×C4D100411yescharacteristic
137C22×C4D100411yescharacteristic
138C22×C4C22×D25111yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—5021no—
144C4⋊C4—5021no—
145C4⋊C4—5021no—
146C4⋊C4—5021no—
147C4⋊C4—5021no—
148C4⋊C4—5021no—
149C4⋊C4—2511no—
150C4⋊C4—2511no—
151C22⋊C4—5021no—
152C22⋊C4—5021no—
153C22⋊C4—5021no—
154C22⋊C4—5021no—
155C22⋊C4—5021no—
156C42—5021no—
157C23—5021no—
158C23C2×D100411yescharacteristic
159Q8—10041no—
160D4—10041no—
161D4—10041no—
162D4—10041no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—20081no—
170C2×C4—10041no—
171C2×C4—10041no—
172C2×C4—10042no—
173C2×C4—10041no—
174C2×C4—10041no—
175C2×C4—5021no—
176C2×C4—5021no—
177C2×C4—5021no—
178C2×C4D4×D25111yescharacteristic
179C2×C4D4×D25111yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—10041no—
185C22—10041no—
186C22—10041no—
187C22#2254868511yescharacteristic
188C22#2254873711yescharacteristic
189C22#2254874811yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—20081no—
195C4—20081no—
196C4—10041no—
197C4—10041no—
198C4—10041no—
199C2—21no—
200C2—21no—
201C2—20081no—
202C2#3063185111yescharacteristic
203C2#3063186211yescharacteristic
204C2#3063187811yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC22×C4×C251C23
FrattiniC22×C4C22×D251
Fitting#324×C251C2
socleC22×C251#120
prime radical#22548689C22
hypercenter#324D251
hypocenterC251#1615
LCSG ▷ C22×C4×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #30632023C2semidirect
4. #30631626C2semidirect
5. #30631425C2semidirect
7. #324×C251C2semidirect
102. C251#1615semidirect
110. #324D251semidirect

Maximal subgroups

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

subgroupindex
#306322842
#306320232
#306320062
#306316262
#306314252
#306314222
#324×C2512
#1615251