Finite Group Databasebeta

← #49120369

Subgroups — #49120369

Order 36224.

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#31827185C211yesmaximal, characteristic, complemented
2#31826811C211yesmaximal, characteristic, complemented
3#31826662C211yesmaximal, characteristic, complemented
4#31826212C211yesmaximal, characteristic, complemented
5#31826195C211yesmaximal, characteristic, complemented
6D4⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
7#459×C283C211yesmaximal, characteristic
8C2×#17985380—21no—
9#22583610C2211yescharacteristic
10#22583603—22no—
11#22583597—21no—
12#22583589—21no—
13C4×Dic566C2211yescharacteristic
14#22583575—21no—
15#22583569—21no—
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583531—22no—
18#22583531—21no—
19C4×C283⋊C8C2211yescharacteristic
20C2×D8×C283—21no—
21#127×C283C2211yescharacteristic
22C4×D4×C283C2211yescharacteristic
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566—21no—
26C2×Dic566D411yescharacteristic
27#17985380—42no—
28C2×C283⋊C8—21no—
29C2×C283⋊C8—21no—
30C4⋊Dic283—21no—
31C4⋊Dic283D411yescharacteristic
32C4⋊Dic283D412yes—
33Dic283⋊C4—22no—
34Dic283⋊C4—21no—
35C22⋊Dic283—22no—
36C22⋊Dic283—22no—
37C4×Dic283—22no—
38C4×Dic283—21no—
39C2×D4×C283—21no—
40C2×D4×C283—21no—
41C2×D4×C283—21no—
42C2×D4×C283D411yescharacteristic
43C22×C4×C283—21no—
44D8×C283—42no—
45C2×C8×C283—21no—
46C4⋊C4×C283D411yescharacteristic
47C22⋊C4×C283—21no—
48C42×C283C2311yescharacteristic
49Dic566—21no—
50Dic566—21no—
51Dic566—41no—
52Dic566—41no—
53C2×Dic283—21no—
54C2×Dic283—21no—
55C2×Dic283—22no—
56C283⋊C8—41no—
57C283⋊C8—41no—
58C23×C283—21no—
59C23×C283—41no—
60D4×C283—21no—
61D4×C283—21no—
62D4×C283—42no—
63D4×C283—41no—
64D4×C283—41no—
65D4×C283—41no—
66D4×C283—41no—
67C2×C4×C283—21no—
68C2×C4×C283—41no—
69C2×C4×C283—41no—
70C2×C4×C283C2×D411yescharacteristic
71C2×C4×C283C2×D411yescharacteristic
72C2×C4×C283C2×D411yescharacteristic
73C8×C283—41no—
74C22×C283—41no—
75C22×C283—41no—
76C22×C283—41no—
77C22×C283—81no—
78C22×C283—81no—
79C22×C283—81no—
80C22×C283#12011yescharacteristic
81C4×C283—21no—
82C4×C283—41no—
83C4×C283#13511yescharacteristic
84C4×C283#13511yescharacteristic
85C4×C283AGL(1,ℤ/8)11yescharacteristic
86C4×C283AGL(1,ℤ/8)11yescharacteristic
87Dic283—41no—
88Dic283—42no—
89Dic283—41no—
90C2×C283—81no—
91C2×C283—161no—
92C2×C283#44911yescharacteristic
93C2×C283#44911yescharacteristic
94C2×C283#45411yescharacteristic
95C283#162811yescharacteristic, complemented, Sylow
96#1628—2831nomaximal, Sylow
97#556—2831no—
98#486—2831no—
99#460—2831no—
100#459D28311yescharacteristic
101#332—2831no—
102Q8⋊C8—2831no—
103D4⋊C8—2831no—
104C2×SD16—5661no—
105C2×D8—21no—
106C4⋊Q8—2831no—
107#127C2×D28311yescharacteristic
108#126—5662no—
109#124—5661no—
110C22⋊Q8—5661no—
111C4×Q8—2831no—
112C4×Q8—5661no—
113C4×D4C2×D28311yescharacteristic
114#117—5661no—
115C4⋊C8—2831no—
116C4⋊C8C2×D28311yescharacteristic
117#102—21no—
118#102—5661no—
119#102—5662no—
120C4×C8—2831no—
121C2×Q8—2831no—
122C2×Q8—5661no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4C22⋊D28311yescharacteristic
127C22×C4—21no—
128SD16—11322no—
129D8—42no—
130C2×C8—21no—
131C2×C8—5661no—
132C2×C8—5661no—
133C4⋊C4—2831no—
134C4⋊C4—2832no—
135C4⋊C4—5662no—
136C4⋊C4—5661no—
137C4⋊C4—5661no—
138C4⋊C4C22⋊D28311yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5662no—
141C22⋊C4—5662no—
142C42—5662no—
143C42—5661no—
144C42C22×D28311yescharacteristic
145C23—21no—
146C23—41no—
147Q8—5661no—
148Q8—5661no—
149Q8—11321no—
150Q8—11321no—
151D4—21no—
152D4—21no—
153D4—42no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5661no—
162C2×C4—5662no—
163C2×C4—5661no—
164C2×C4D4×D28311yescharacteristic
165C2×C4D4×D28311yescharacteristic
166C2×C4C2×C22⋊D28311yescharacteristic
167C8—41no—
168C8—11321no—
169C8—11321no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—81no—
174C22—81no—
175C22—81no—
176C22#2258357811yescharacteristic
177C4—21no—
178C4—41no—
179C4—11321no—
180C4—11322no—
181C4—11321no—
182C4#2258362911yescharacteristic
183C4#2258363011yescharacteristic
184C4#2258363411yescharacteristic
185C4#2258363611yescharacteristic
186C2—81no—
187C2—161no—
188C2#3182660711yescharacteristic
189C2#3182660811yescharacteristic
190C2#3182663611yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting, prime radical#459×C283C2
socleC22×C283#120
hypercenter#459D283
hypocenterC283#1628
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. #31827185C2semidirect
2. #31826811C2semidirect
3. #31826662C2semidirect
4. #31826212C2semidirect
5. #31826195C2semidirect
6. D4⋊(C283⋊C8)C2semidirect
95. C283#1628semidirect

Maximal subgroups

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

subgroupindex
#318271852
#318268112
#318266622
#318262122
#318261952
D4⋊(C283⋊C8)2
#459×C2832
#1628283