Finite Group Databasebeta

← #49120408

Subgroups — #49120408

Order 36224.

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

normal subgroups only

This group has 218 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#31827180C211yesmaximal, characteristic
2#31826845C211yesmaximal, characteristic, complemented
3#31826756C211yesmaximal, characteristic, complemented
4#31826755C211yesmaximal, characteristic, complemented
5#31826213C211yesmaximal, characteristic, complemented
6#31826194C211yesmaximal, characteristic, complemented
7D4⋊C8×C283C211yesmaximal, characteristic, complemented
8C2×Dic1132—22no—
9#22583610C2211yescharacteristic
10#22583610C2211yescharacteristic
11#22583596—22no—
12#22583584—21no—
13#22583581—21no—
14C4×D1132C2211yescharacteristic
15#22583569—21no—
16#22583568—21no—
17#22583542—21no—
18#22583541—21no—
19C4⋊(C283⋊C8)C2211yescharacteristic
20#22583532—21no—
21#22583531—21no—
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24C4×C8×C283C2211yescharacteristic
25C2×Dic566—21no—
26C2×Dic566D412yes—
27C2×D1132D411yescharacteristic
28C2×C22⋊D283—22no—
29C2×C4×D283—21no—
30Dic1132—44no—
31C2×C283⋊C8—21no—
32C4⋊Dic283—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283D411yescharacteristic
37C22⋊Dic283—22no—
38(C2×D283)⋊C4—22no—
39(C2×D283)⋊C4—21no—
40C4×Dic283—22no—
41C2×D4×C283D411yescharacteristic
42C22×C4×C283—21no—
43C2×C8×C283—21no—
44C2×C8×C283—21no—
45C4⋊C4×C283D411yescharacteristic
46C22⋊C4×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49Dic566—42no—
50Dic566—42no—
51D1132—21no—
52D1132—21no—
53C22⋊D283—82no—
54C2×Dic283—21no—
55C2×Dic283—22no—
56C2×Dic283—41no—
57C4×D283—41no—
58C4×D283—41no—
59C283⋊C8—41no—
60C23×C283—21no—
61D4×C283—21no—
62D4×C283—21no—
63C2×C4×C283—21no—
64C2×C4×C283—41no—
65C2×C4×C283—41no—
66C2×C4×C283C2×D411yescharacteristic
67C2×C4×C283C2×D411yescharacteristic
68C2×C4×C283C2×D411yescharacteristic
69C8×C283—22no—
70C8×C283—41no—
71C22×C283—41no—
72C22×C283—41no—
73C22×C283—41no—
74C22×C283#12011yescharacteristic
75C2×D283—41no—
76C2×D283—41no—
77C2×D283—41no—
78C4×C283—21no—
79C4×C283—41no—
80C4×C283#13511yescharacteristic
81C4×C283#13511yescharacteristic
82C4×C283#13711yescharacteristic
83C4×C283#13711yescharacteristic
84Dic283—41no—
85Dic283—42no—
86Dic283—81no—
87C2×C283—81no—
88C2×C283#45211yescharacteristic
89C2×C283#45211yescharacteristic
90C2×C283#45311yescharacteristic
91D283—81no—
92C283#163411yescharacteristic, complemented, Sylow
93#1634—2831nomaximal, Sylow
94#555—2831no—
95#494—2831no—
96#476—2831no—
97#476—2831no—
98#333—2831no—
99D4⋊C8—2831no—
100D4⋊C8D28311yescharacteristic, complemented
101C2×Q16—5662no—
102C4⋊Q8—2831no—
103C4⋊Q8—2831no—
104#124—5662no—
105#121—5661no—
106#121—5661no—
107C4×D4—2831no—
108C4×D4C2×D28311yescharacteristic
109#117—5661no—
110#117—5661no—
111#106—5661no—
112#106—5661no—
113C4⋊C8—2831no—
114C4⋊C8C2×D28311yescharacteristic
115#102—5661no—
116#102—5661no—
117C4×C8C2×D28311yescharacteristic
118C2×Q8—2832no—
119C2×Q8—5661no—
120C2×D4—2831no—
121C2×D4—5662no—
122C2×D4D113211yescharacteristic
123C22×C4—21no—
124C22×C4—5661no—
125Q16—11324no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—5661no—
129C4⋊C4—2831no—
130C4⋊C4—5661no—
131C4⋊C4—5661no—
132C4⋊C4—5661no—
133C4⋊C4—5661no—
134C4⋊C4D113211yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—5662no—
137C22⋊C4—5662no—
138C22⋊C4—5661no—
139C42—5662no—
140C42C22×D28311yescharacteristic
141C23—21no—
142C23—5661no—
143Q8—11322no—
144Q8—11322no—
145D4—21no—
146D4—21no—
147D4—5661no—
148D4—5661no—
149D4—22642no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—5661no—
154C2×C4—5662no—
155C2×C4—11321no—
156C2×C4—11321no—
157C2×C4—11321no—
158C2×C4D4×D28311yescharacteristic
159C2×C4D4×D28311yescharacteristic
160C2×C4C2×D113211yescharacteristic
161C8—22no—
162C8—41no—
163C8—11321no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—11321no—
168C22—11321no—
169C22—11321no—
170C22#2258358011yescharacteristic
171C4—21no—
172C4—41no—
173C4—11321no—
174C4—11322no—
175C4—22641no—
176C4#2258362911yescharacteristic
177C4#2258363211yescharacteristic
178C4#2258363911yescharacteristic
179C4#2258364311yescharacteristic
180C2—81no—
181C2—22641no—
182C2#3182662811yescharacteristic
183C2#3182662911yescharacteristic
184C2#3182663411yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
FittingD4⋊C8×C283C2
socleC22×C283#120
prime radical#31827180C2
hypercenterD4⋊C8D283
hypocenterC283#1634
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31826845C2semidirect
3. #31826756C2semidirect
4. #31826755C2semidirect
5. #31826213C2semidirect
6. #31826194C2semidirect
7. D4⋊C8×C283C2semidirect
92. C283#1634semidirect
100. D4⋊C8D283semidirect

Maximal subgroups

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

subgroupindex
#318271802
#318268452
#318267562
#318267552
#318262132
#318261942
D4⋊C8×C2832
#1634283