Finite Group Databasebeta

← #44549539

Subgroups — #44549539

Order 32128.

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

normal subgroups only

This group has 194 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
2#30632038C211yesmaximal, characteristic, complemented
3#30631983C211yesmaximal, characteristic, complemented
4#30631977C211yesmaximal, characteristic
5#30631432C211yesmaximal, characteristic, complemented
6#30631419C211yesmaximal, characteristic, complemented
7D4⋊C8×C251C211yesmaximal, characteristic
8#22548715C2211yescharacteristic
9#22548715C2211yescharacteristic
10#22548708—22no—
11#22548702—21no—
12#22548694—21no—
13C4×Dic502C2211yescharacteristic
14#22548680—21no—
15#22548674—21no—
16#22548649—21no—
17#22548646—21no—
18C4⋊(C251⋊C8)C2211yescharacteristic
19#22548640—21no—
20#22548640—22no—
21#22548636—21no—
22C4×D4×C251C2211yescharacteristic
23C4⋊C8×C251C2211yescharacteristic
24C4×C8×C251C2211yescharacteristic
25C2×Dic502—21no—
26C2×Dic502—21no—
27C2×Dic502D411yescharacteristic
28C2×C251⋊C8—21no—
29C4⋊Dic251—21no—
30C4⋊Dic251—21no—
31C4⋊Dic251—21no—
32C4⋊Dic251D412yes—
33C4⋊Dic251D411yescharacteristic
34Dic251⋊C4—22no—
35Dic251⋊C4—21no—
36C22⋊Dic251—22no—
37C22⋊Dic251—22no—
38C4×Dic251—22no—
39C4×Dic251—21no—
40C2×D4×C251D411yescharacteristic
41C22×C4×C251—21no—
42C2×C8×C251—21no—
43C2×C8×C251—21no—
44C4⋊C4×C251D411yescharacteristic
45C22⋊C4×C251—21no—
46C42×C251C2311yescharacteristic
47Dic502—21no—
48Dic502—21no—
49Dic502—41no—
50Dic502—41no—
51Dic502—42no—
52C2×Dic251—21no—
53C2×Dic251—21no—
54C2×Dic251—22no—
55C2×Dic251—41no—
56C251⋊C8—41no—
57C23×C251—21no—
58D4×C251—21no—
59D4×C251—21no—
60C2×C4×C251—21no—
61C2×C4×C251—41no—
62C2×C4×C251—41no—
63C2×C4×C251C2×D411yescharacteristic
64C2×C4×C251C2×D411yescharacteristic
65C2×C4×C251C2×D411yescharacteristic
66C8×C251—41no—
67C8×C251—41no—
68C22×C251—41no—
69C22×C251—41no—
70C22×C251—41no—
71C22×C251#12011yescharacteristic
72C4×C251—21no—
73C4×C251—41no—
74C4×C251#13511yescharacteristic
75C4×C251#13511yescharacteristic
76C4×C251#13711yescharacteristic
77C4×C251#13711yescharacteristic
78Dic251—41no—
79Dic251—42no—
80Dic251—41no—
81Dic251—81no—
82C2×C251—81no—
83C2×C251#45211yescharacteristic
84C2×C251#45211yescharacteristic
85C2×C251#45411yescharacteristic
86C251#163811yescharacteristic, complemented, Sylow
87#1638—2511nomaximal, Sylow
88#556—2511no—
89#487—2511no—
90#477—2511no—
91#476—2511no—
92#332—2511no—
93Q8⋊C8—2511no—
94D4⋊C8D25111yescharacteristic
95C4⋊Q8—2511no—
96C4⋊Q8—2511no—
97#126—5022no—
98#124—5021no—
99C22⋊Q8—5021no—
100C4×Q8—5021no—
101C4×Q8—2511no—
102C4×D4C2×D25111yescharacteristic
103#117—5021no—
104#107—5021no—
105#106—5021no—
106C4⋊C8—2511no—
107C4⋊C8C2×D25111yescharacteristic
108#103—5021no—
109#103—5022no—
110#102—5021no—
111C4×C8C2×D25111yescharacteristic
112C2×Q8—5021no—
113C2×Q8—5021no—
114C2×Q8—2511no—
115C2×D4D100411yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—5021no—
120C4⋊C4—5022no—
121C4⋊C4—5021no—
122C4⋊C4—5021no—
123C4⋊C4—5021no—
124C4⋊C4—5021no—
125C4⋊C4—2512no—
126C4⋊C4—2511no—
127C4⋊C4D100411yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—5022no—
130C22⋊C4—5022no—
131C42—5022no—
132C42—5021no—
133C42C22×D25111yescharacteristic
134C23—21no—
135Q8—10042no—
136Q8—10041no—
137Q8—10041no—
138Q8—5021no—
139Q8—5021no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—10041no—
146C2×C4—5021no—
147C2×C4—5021no—
148C2×C4—5022no—
149C2×C4D4×D25111yescharacteristic
150C2×C4D4×D25111yescharacteristic
151C2×C4C2×D100411yescharacteristic
152C8—41no—
153C8—41no—
154C8—10041no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#2254868511yescharacteristic
159C4—21no—
160C4—41no—
161C4—20081no—
162C4—10041no—
163C4—10042no—
164C4—10041no—
165C4#2254873411yescharacteristic
166C4#2254873711yescharacteristic
167C4#2254874411yescharacteristic
168C4#2254874811yescharacteristic
169C2—81no—
170C2#3063185011yescharacteristic
171C2#3063185111yescharacteristic
172C2#3063186111yescharacteristic
subgroupG/H
centerC22#22548685
commutator, cosocleC42×C251C23
FrattiniC42C22×D251
FittingD4⋊C8×C251C2
socleC22×C251#120
prime radicalC2×D4×C251D4
hypercenterD4⋊C8D251
hypocenterC251#1638
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
2. #30632038C2semidirect
3. #30631983C2semidirect
5. #30631432C2semidirect
6. #30631419C2semidirect
86. C251#1638semidirect

Maximal subgroups

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

subgroupindex
#306324072
#306320382
#306319832
#306319772
#306314322
#306314192
D4⋊C8×C2512
#1638251