Finite Group Databasebeta

← #49120343

Subgroups — #49120343

Order 36224.

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

normal subgroups only

This group has 240 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, complemented
2#31826837C211yesmaximal, characteristic, complemented
3#31826657C211yesmaximal, characteristic, complemented
4#31826213C211yesmaximal, characteristic, complemented
5D4⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#459×C283C211yesmaximal, characteristic, complemented
8C2×#17985380—22no—
9C2×#17985377—21no—
10#22583610C2211yescharacteristic
11#22583596—22no—
12#22583584—21no—
13#22583581—21no—
14C4×D1132C2211yescharacteristic
15#22583569—21no—
16#22583568—21no—
17C4⋊(C283⋊C8)C2211yescharacteristic
18#22583531—21no—
19C4×C283⋊C8C2211yescharacteristic
20C2×D8×C283—21no—
21#127×C283C2211yescharacteristic
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566D412yes—
26C2×D1132D411yescharacteristic
27C2×C22⋊D283—22no—
28C2×C4×D283—21no—
29#17985380—44no—
30#17985377—42no—
31C2×C283⋊C8—21no—
32C2×C283⋊C8—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283—21no—
35C4⋊Dic283D411yescharacteristic
36C22⋊Dic283—22no—
37(C2×D283)⋊C4—22no—
38(C2×D283)⋊C4—21no—
39C4×Dic283—22no—
40C2×D4×C283—21no—
41C2×D4×C283—21no—
42C2×D4×C283—21no—
43C2×D4×C283D411yescharacteristic
44C22×C4×C283—21no—
45D8×C283—42no—
46C2×C8×C283—21no—
47C4⋊C4×C283D411yescharacteristic
48C22⋊C4×C283—21no—
49C42×C283C2311yescharacteristic
50C22×D283—21no—
51Dic566—42no—
52D1132—21no—
53D1132—21no—
54C22⋊D283—82no—
55C2×Dic283—21no—
56C2×Dic283—22no—
57C4×D283—41no—
58C4×D283—41no—
59C283⋊C8—22no—
60C283⋊C8—41no—
61C23×C283—21no—
62C23×C283—41no—
63D4×C283—21no—
64D4×C283—21no—
65D4×C283—42no—
66D4×C283—41no—
67D4×C283—41no—
68D4×C283—41no—
69D4×C283—41no—
70C2×C4×C283—21no—
71C2×C4×C283—41no—
72C2×C4×C283—41no—
73C2×C4×C283C2×D411yescharacteristic
74C2×C4×C283C2×D411yescharacteristic
75C2×C4×C283C2×D411yescharacteristic
76C8×C283—41no—
77C22×C283—41no—
78C22×C283—41no—
79C22×C283—41no—
80C22×C283—81no—
81C22×C283—81no—
82C22×C283—81no—
83C22×C283#12011yescharacteristic
84C2×D283—41no—
85C2×D283—41no—
86C2×D283—41no—
87C4×C283—21no—
88C4×C283—41no—
89C4×C283#13511yescharacteristic
90C4×C283#13511yescharacteristic
91C4×C283AGL(1,ℤ/8)11yescharacteristic
92C4×C283AGL(1,ℤ/8)11yescharacteristic
93Dic283—41no—
94Dic283—42no—
95C2×C283—81no—
96C2×C283—161no—
97C2×C283#44911yescharacteristic
98C2×C283#44911yescharacteristic
99C2×C283#45311yescharacteristic
100D283—81no—
101C283#162411yescharacteristic, complemented, Sylow
102#1624—2831nomaximal, Sylow
103#555—2831no—
104#492—2831no—
105#459—2831no—
106#459D28311yescharacteristic, complemented
107#333—2831no—
108D4⋊C8—2831no—
109D4⋊C8—2831no—
110C2×SD16—5662no—
111C2×D8—21no—
112C2×D8—5661no—
113C4⋊Q8—2831no—
114#127C2×D28311yescharacteristic
115#124—5662no—
116#121—5661no—
117#121—5661no—
118C4×D4—2831no—
119C4×D4C2×D28311yescharacteristic
120#117—5661no—
121#117—5661no—
122C4⋊C8—2831no—
123C4⋊C8C2×D28311yescharacteristic
124#102—21no—
125#102—5661no—
126C4×C8—2831no—
127C2×Q8—2832no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2831no—
132C2×D4—5662no—
133C2×D4C22⋊D28311yescharacteristic
134C22×C4—21no—
135C22×C4—5661no—
136SD16—11324no—
137D8—42no—
138D8—11322no—
139C2×C8—21no—
140C2×C8—5661no—
141C2×C8—5661no—
142C4⋊C4—2831no—
143C4⋊C4—5661no—
144C4⋊C4—5661no—
145C4⋊C4C22⋊D28311yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—5662no—
148C22⋊C4—5662no—
149C22⋊C4—5661no—
150C42—5662no—
151C42C22×D28311yescharacteristic
152C23—21no—
153C23—41no—
154C23—5661no—
155Q8—11322no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—5661no—
164D4—5661no—
165D4—22642no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5661no—
170C2×C4—5662no—
171C2×C4—11321no—
172C2×C4—11321no—
173C2×C4D4×D28311yescharacteristic
174C2×C4D4×D28311yescharacteristic
175C2×C4C2×C22⋊D28311yescharacteristic
176C8—41no—
177C8—5662no—
178C8—11321no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—11321no—
186C22—11321no—
187C22—11321no—
188C22#2258357811yescharacteristic
189C4—21no—
190C4—41no—
191C4—11321no—
192C4—11322no—
193C4#2258362911yescharacteristic
194C4#2258363011yescharacteristic
195C4#2258363411yescharacteristic
196C4#2258363611yescharacteristic
197C2—81no—
198C2—161no—
199C2—22641no—
200C2#3182660711yescharacteristic
201C2#3182660811yescharacteristic
202C2#3182663111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#459×C283C2
socleC22×C283#120
hypercenter#459D283
hypocenterC283#1624
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #31827180C2semidirect
2. #31826837C2semidirect
3. #31826657C2semidirect
4. #31826213C2semidirect
5. D4⋊(C283⋊C8)C2semidirect
6. #31826192C2semidirect
7. #459×C283C2semidirect
101. C283#1624semidirect
106. #459D283semidirect

Maximal subgroups

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

subgroupindex
#318271802
#318268372
#318266572
#318262132
D4⋊(C283⋊C8)2
#318261922
#459×C2832
#1624283