Finite Group Databasebeta

← #49120488

Subgroups — #49120488

Order 36224.

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

normal subgroups only

This group has 212 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#31826817C211yesmaximal, characteristic, complemented
3#31826667C211yesmaximal, characteristic, complemented
4#31826213C211yesmaximal, characteristic, complemented
5D4⋊(C283⋊C8)C211yesmaximal, characteristic, complemented
6#31826192C211yesmaximal, characteristic, complemented
7#474×C283C211yesmaximal, characteristic, complemented
8C2×#17985379—21no—
9#22583610C2211yescharacteristic
10#22583596—22no—
11#22583584—21no—
12#22583581—21no—
13C4×D1132C2211yescharacteristic
14#22583569—21no—
15#22583568—21no—
16C4⋊(C283⋊C8)C2211yescharacteristic
17#22583534—21no—
18#22583533—22no—
19C4×C283⋊C8C2211yescharacteristic
20C4⋊Q8×C283C2211yescharacteristic
21C4×D4×C283C2211yescharacteristic
22#107×C283—21no—
23C4⋊C8×C283C2211yescharacteristic
24#102×C283—21no—
25C2×Dic566D412yes—
26C2×D1132D411yescharacteristic
27C2×C22⋊D283—22no—
28C2×C4×D283—21no—
29#17985379—42no—
30C2×C283⋊C8—21no—
31C2×C283⋊C8—21no—
32C4⋊Dic283—21no—
33C4⋊Dic283—21no—
34C4⋊Dic283D411yescharacteristic
35C22⋊Dic283—22no—
36(C2×D283)⋊C4—22no—
37(C2×D283)⋊C4—21no—
38C4×Dic283—22no—
39C2×Q8×C283—21no—
40C2×D4×C283D411yescharacteristic
41C22×C4×C283—21no—
42C2×C8×C283—21no—
43C4⋊C4×C283—21no—
44C4⋊C4×C283—21no—
45C4⋊C4×C283D411yescharacteristic
46C22⋊C4×C283—21no—
47C42×C283C2311yescharacteristic
48C22×D283—21no—
49Dic566—42no—
50D1132—21no—
51D1132—21no—
52C22⋊D283—82no—
53C2×Dic283—21no—
54C2×Dic283—22no—
55C4×D283—41no—
56C4×D283—41no—
57C283⋊C8—41no—
58C283⋊C8—41no—
59C23×C283—21no—
60Q8×C283—41no—
61Q8×C283—41no—
62D4×C283—21no—
63D4×C283—21no—
64C2×C4×C283—21no—
65C2×C4×C283—41no—
66C2×C4×C283—41no—
67C2×C4×C283—41no—
68C2×C4×C283C2×D411yescharacteristic
69C2×C4×C283C2×D411yescharacteristic
70C2×C4×C283C2×D411yescharacteristic
71C8×C283—41no—
72C22×C283—41no—
73C22×C283—41no—
74C22×C283—41no—
75C22×C283#12011yescharacteristic
76C2×D283—41no—
77C2×D283—41no—
78C2×D283—41no—
79C4×C283—21no—
80C4×C283—41no—
81C4×C283—81no—
82C4×C283#13511yescharacteristic
83C4×C283#13511yescharacteristic
84C4×C283AGL(1,ℤ/8)11yescharacteristic
85C4×C283#13711yescharacteristic
86Dic283—41no—
87Dic283—42no—
88C2×C283—81no—
89C2×C283#44911yescharacteristic
90C2×C283#45211yescharacteristic
91C2×C283#45511yescharacteristic
92D283—81no—
93C283#164611yescharacteristic, complemented, Sylow
94#1646—2831nomaximal, Sylow
95#555—2831no—
96#487—2831no—
97#474D28311yescharacteristic, complemented
98#461—2831no—
99#333—2831no—
100D4⋊C8—2831no—
101D4⋊C8—2831no—
102C2×SD16—5661no—
103C4⋊Q8—2831no—
104C4⋊Q8C2×D28311yescharacteristic
105#124—5662no—
106#121—5661no—
107#121—5661no—
108C4×D4—2831no—
109C4×D4C2×D28311yescharacteristic
110#117—5661no—
111#117—5661no—
112#107—21no—
113C4⋊C8—2831no—
114C4⋊C8C2×D28311yescharacteristic
115#103—5662no—
116#103—5661no—
117#102—21no—
118C4×C8—2831no—
119C2×Q8—21no—
120C2×Q8—2832no—
121C2×D4—2831no—
122C2×D4—5662no—
123C2×D4C22⋊D28311yescharacteristic
124C22×C4—21no—
125C22×C4—5661no—
126SD16—11322no—
127C2×C8—21no—
128C2×C8—5661no—
129C2×C8—5661no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2831no—
133C4⋊C4—5661no—
134C4⋊C4—5661no—
135C4⋊C4C22⋊D28311yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5662no—
138C22⋊C4—5662no—
139C22⋊C4—5661no—
140C42—5662no—
141C42C22×D28311yescharacteristic
142C23—21no—
143C23—5661no—
144Q8—41no—
145Q8—41no—
146Q8—11322no—
147D4—21no—
148D4—21no—
149D4—5661no—
150D4—5661no—
151D4—22642no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5661no—
157C2×C4—5662no—
158C2×C4—11321no—
159C2×C4—11321no—
160C2×C4D4×D28311yescharacteristic
161C2×C4D4×D28311yescharacteristic
162C2×C4C2×C22⋊D28311yescharacteristic
163C8—41no—
164C8—11321no—
165C8—11321no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—11321no—
170C22—11321no—
171C22—11321no—
172C22#2258357811yescharacteristic
173C4—21no—
174C4—41no—
175C4—81no—
176C4—11321no—
177C4—11322no—
178C4#2258362911yescharacteristic
179C4#2258363011yescharacteristic
180C4#2258363411yescharacteristic
181C4#2258364111yescharacteristic
182C2—81no—
183C2—22641no—
184C2#3182660711yescharacteristic
185C2#3182662511yescharacteristic
186C2#3182664111yescharacteristic
subgroupG/H
centerC22#22583578
commutator, cosocleC42×C283C23
FrattiniC42C22×D283
Fitting#474×C283C2
socleC22×C283#120
prime radical#31827180C2
hypercenter#474D283
hypocenterC283#1646
LCSG ▷ C42×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #31826817C2semidirect
3. #31826667C2semidirect
4. #31826213C2semidirect
5. D4⋊(C283⋊C8)C2semidirect
6. #31826192C2semidirect
7. #474×C283C2semidirect
93. C283#1646semidirect
97. #474D283semidirect

Maximal subgroups

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

subgroupindex
#318271802
#318268172
#318266672
#318262132
D4⋊(C283⋊C8)2
#318261922
#474×C2832
#1646283