Finite Group Databasebeta

← #44549477

Subgroups — #44549477

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#30632407C211yesmaximal, characteristic, complemented
2#30632034C211yesmaximal, characteristic, complemented
3#30631888C211yesmaximal, characteristic, complemented
4#30631882C211yesmaximal, characteristic
5#30631432C211yesmaximal, characteristic, complemented
6#30631419C211yesmaximal, characteristic, complemented
7D4⋊C8×C251C211yesmaximal, characteristic, complemented
8C2×#16860799—21no—
9C2×#16860795—21no—
10#22548715C2211yescharacteristic
11#22548712C2211yescharacteristic
12#22548708—22no—
13#22548702—21no—
14#22548694—21no—
15C4×Dic502C2211yescharacteristic
16#22548680—21no—
17#22548674—21no—
18C4⋊(C251⋊C8)C2211yescharacteristic
19#22548637—22no—
20#22548637—21no—
21#22548635—21no—
22C4×D4×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4×C8×C251C2211yescharacteristic
25C2×Dic502—21no—
26C2×Dic502D411yescharacteristic
27C2×D1004—21no—
28C2×D1004—21no—
29C2×D1004—21no—
30#16860799—42no—
31#16860795—42no—
32C2×C251⋊C8—21no—
33C4⋊Dic251—21no—
34C4⋊Dic251D411yescharacteristic
35C4⋊Dic251D412yes—
36Dic251⋊C4—22no—
37Dic251⋊C4—21no—
38C22⋊Dic251—22no—
39C22⋊Dic251—22no—
40C4×Dic251—22no—
41C4×Dic251—21no—
42C2×D4×C251D411yescharacteristic
43C22×C4×C251—21no—
44C2×C8×C251—21no—
45C2×C8×C251—21no—
46C4⋊C4×C251D411yescharacteristic
47C22⋊C4×C251—21no—
48C42×C251C2311yescharacteristic
49C22×D251—41no—
50Dic502—21no—
51Dic502—21no—
52Dic502—41no—
53Dic502—41no—
54D1004—42no—
55D1004—41no—
56D1004—41no—
57D1004—41no—
58D1004—41no—
59C2×Dic251—21no—
60C2×Dic251—21no—
61C2×Dic251—22no—
62C251⋊C8—41no—
63C23×C251—21no—
64D4×C251—21no—
65D4×C251—21no—
66C2×C4×C251—21no—
67C2×C4×C251—41no—
68C2×C4×C251—41no—
69C2×C4×C251C2×D411yescharacteristic
70C2×C4×C251C2×D411yescharacteristic
71C2×C4×C251C2×D411yescharacteristic
72C8×C251—41no—
73C8×C251—41no—
74C22×C251—41no—
75C22×C251—41no—
76C22×C251—41no—
77C22×C251#12011yescharacteristic
78C2×D251—81no—
79C2×D251—81no—
80C2×D251—81no—
81C4×C251—21no—
82C4×C251—41no—
83C4×C251#13511yescharacteristic
84C4×C251#13511yescharacteristic
85C4×C251AGL(1,ℤ/8)11yescharacteristic
86C4×C251AGL(1,ℤ/8)11yescharacteristic
87Dic251—41no—
88Dic251—42no—
89Dic251—41no—
90C2×C251—81no—
91C2×C251#44911yescharacteristic
92C2×C251#44911yescharacteristic
93C2×C251#45411yescharacteristic
94D251—161no—
95C251#162811yescharacteristic, complemented, Sylow
96#1628—2511nomaximal, Sylow
97#556—2511no—
98#486—2511no—
99#460—2511no—
100#459—2511no—
101#332—2511no—
102Q8⋊C8—2511no—
103D4⋊C8D25111yescharacteristic, complemented
104C2×SD16—5021no—
105C2×D8—5021no—
106C4⋊Q8—2511no—
107#127—2511no—
108#126—5022no—
109#124—5021no—
110C22⋊Q8—5021no—
111C4×Q8—5021no—
112C4×Q8—2511no—
113C4×D4C2×D25111yescharacteristic
114#117—5021no—
115C4⋊C8—2511no—
116C4⋊C8C2×D25111yescharacteristic
117#102—5021no—
118#102—5022no—
119#102—5021no—
120C4×C8C2×D25111yescharacteristic
121C2×Q8—5021no—
122C2×Q8—2511no—
123C2×D4—5021no—
124C2×D4—5021no—
125C2×D4—5021no—
126C2×D4D100411yescharacteristic
127C22×C4—21no—
128SD16—10042no—
129D8—10042no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—5021no—
133C4⋊C4—5022no—
134C4⋊C4—5021no—
135C4⋊C4—5021no—
136C4⋊C4—2511no—
137C4⋊C4—2512no—
138C4⋊C4D100411yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5022no—
141C22⋊C4—5022no—
142C42—5022no—
143C42—5021no—
144C42C22×D25111yescharacteristic
145C23—21no—
146C23—10041no—
147Q8—10041no—
148Q8—10041no—
149Q8—5021no—
150Q8—5021no—
151D4—21no—
152D4—21no—
153D4—10042no—
154D4—10041no—
155D4—10041no—
156D4—10041no—
157D4—10041no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5021no—
162C2×C4—5021no—
163C2×C4—5022no—
164C2×C4D4×D25111yescharacteristic
165C2×C4D4×D25111yescharacteristic
166C2×C4C2×D100411yescharacteristic
167C8—41no—
168C8—41no—
169C8—10041no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—20081no—
174C22—20081no—
175C22—20081no—
176C22#2254868511yescharacteristic
177C4—21no—
178C4—41no—
179C4—10041no—
180C4—10042no—
181C4—10041no—
182C4#2254873611yescharacteristic
183C4#2254873711yescharacteristic
184C4#2254873911yescharacteristic
185C4#2254874311yescharacteristic
186C2—81no—
187C2—40161no—
188C2#3063183311yescharacteristic
189C2#3063183411yescharacteristic
190C2#3063186111yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
FittingD4⋊C8×C251C2
socleC22×C251#120
prime radical#30631882C2
hypercenterD4⋊C8D251
hypocenterC251#1628
LCSG ▷ C42×C251 ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #30632407C2semidirect
2. #30632034C2semidirect
3. #30631888C2semidirect
5. #30631432C2semidirect
6. #30631419C2semidirect
7. D4⋊C8×C251C2semidirect
95. C251#1628semidirect
103. D4⋊C8D251semidirect

Maximal subgroups

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

subgroupindex
#306324072
#306320342
#306318882
#306318822
#306314322
#306314192
D4⋊C8×C2512
#1628251